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Telecommunications
Transmission
Engineering
Volume 1 - Principles

Second Edition

Technical Personnel
American Telephone and Telegraph Company,
Bell Telephone Companies,
and
Bell Telephone Laboratories

Bell System Center for Technical Education

Copyright © 1977
American Telephone and Telegraph Co.
Chapter 6, Copyright © 1964
'Chapters 7 and 8 Copyright © 1959, 1964, 1970 by
Bell Telephone Laboratories, Inc.

Prepared for Publication by
Western Elect'ric Company, Inc.
Technical Publications
Winston-Salem, North Carolina

FIRST J!JDITION
SECOND EDITION

1974
1977

Printed in the United States of America

Telecomm unications
Transmission
Engineering

Introduction
Communication Engineering is concerned with the planning, design,
implementation, and operation of the network of channels, switching
machines, and user terminals required to provide communication
between distant points. Transmission Engineering is the part of
Communication Engineering which deals with the channels, the transmission systems which carry the channels, and the combinations of
the many types of channels and systems which form the network of
facilities. It is a discipline which combines many skills from science
and technology with an understanding of economics, human factors,
and system operations.
This three-volume book is written for the practicing Transmission
and for the student of transmission engineering in an undergraduate curriculum. The material was planned and organized to
make it useful to anyone concerned with the many facets of Communication Engineering. Of necessity, it represents a view of the status
of communications technology at a specific time. The reader should be
constantly aware of the dynamic nature of the subject.
En~ineer

Volume 1, Principles, covers the transmission engineering principles that apply to communication systems. It defines the characteristics of various types of signals, describes signal impairments
arising in practical channels, provides the basis for understanding the
relationships between a communication network and its components,
and provides an appreciation of how transmission objectives and
aohievable performance are interrelated.
Volume 2, Facilities, emphasizes the application of the principles
of Volume 1 to the design, implementation, and operation of transmission systems and facilities which form the telecommunications
iii

iv

Introduction

network. The descriptions are illustrated by examples taken from
modern types of facilities most of which represent equipment of
Bell Laboratories design and Western Electric manufacture; these
examples are used because they are familiar to the authors.
Volume 3, Networks and Services, shows how the principles of
Volume 1 are applied to the facilities described in Volume 2 to provide a variety of public and private telecommunication services. This
volume reflects a strong Bell System operations viewpoint in its consideration of the problems of providing suitable facilities to meet
customer needs and expectations at reasonable cost.
The material has been prepared and reviewed by a. large number
of technical personnel of the American Telephone and Telegraph
Company, Bell Telephone Companies, and Bell Telephone Laboratories. Editorial support has been provided by the Technical Publications Organization of the Western Electric Company. Thus, the book
represents the cooperative efforts of many people in every major
organization of the Bell System and it is difficult to recognize individual contributions. One exception must be made, however. The
material in Volume 1 and most of Volume 2 has been prepared by
Mr. Robert H. Klie of the Bell Telephone Laboratories, who was
associated in this endeavor with the Ben System Center for Technical
Education. Mr. Klie also coordinated the preparation of Volume 3.
C. H. Elmendorf, III
Assistant Vice President Transmission Division.
American Telephone and Telegraph Company

Volume 1 - Principles

Preface

This volume, comprised of five sections, covers the basic principles
involved in transmitting communication signals over Bell System
facilities. Section 1 provides a broad description of the transmission
environment and an overview of how transmission parameters affect
the performance of the network. The second section consists of a
review of most of the mathematical relationships involved in transmission engineering. A wide range of subj ects is discussed, from an
explanation of and justification for the use of logarithmic units
(decibels) to a summary of information theory concepts.
The third· section is devoted to the characterization of the principal types of signals transmitted over Bell System facilities. Speech,
television, PICTUREPHONE®, digital and analog data, address, and
supervisory signals are described. Multiplexed combinations of signal
types are also characterized. The fourth section describes a variety
of impairments suffered by signals transmitted over practical channels, which have imperfections and distortions. Also discussed are
the units in which impairments are expressed and the methods by
which they are measured. The fifth section discusses the derivation
of transmission objectives, gives many established values of these
objectives, and relates them to requirements applied to system design
and operation. The section concludes with a chapter on international
communications and internationally applied transmission objectives.
v

Contents
iii

Introduction

v

Preface
SECTION 1
Chapter 1.

1-1

1

BACKGROUND
The Transmission Environment ........................ .

3
3

Transmission Paths
The Station Set
Customer Loops ........... .
Switching Machines
Trunks ...... ~ •. ' ............ .

4:
4:
5

Switching Arrangements ........... .
The Local Switching Hierarchy
The Toll Switching Hierarchy

8

10

1-3

Impact of System Multiplicity on Network Performance

14:

1-4

Maintenance and Maintenance Support ...

16

1-2

Chapter 2.
2-1

Introduction To Transmission

7
8

18

Message Signals ...............
........
........
Speech. ... . ... ........ . ..... .... ... . . . .. .... ......... . .........
Program .......................................................
Video. . .... ... ... . .... . ... ... .. .... ..... . ... .. . . .. . . .. . . .. ...
Data and Facsimile .............................................
Control Signals ..................
. . . . . . . . . . . . . . . . . . . . . ..

18
19
20
20

2-2

Channels ..........................

23

2-3

Voice-Frequency (VF) Transmission .......... .
Modes of Voice-Frequency Transmission .. .
Voice-Frequency Repeaters ................ .

25
25

Carrier Systems ................................ .
High-Frequency Line Equipment
Modulating Equipment ... .
Multiplex Equipment ....... .

28

Ancillary Equipment and Functions

83

2-4

2-5

vii

21
22

27

81
82
82

Contents

viii
SECTION 2
Chapter 3.
3-1

3-2

3-3

3-4

ELEMENTS OF TRANSMISSION ANALySIS.............
Fundamentals of Transmission Theory

35
37

Power and Voltage Relations in Linear Circuits ................. .
The Decibel ............................................... .
Loss, Delay, and Gain ....................................... .

37
39

Transmission Level Point ..................................... .
Commonly Used TLPs ................................... .
Illustrative Applications of TLP ................................. .

48

Signal and Noise Measurement ............ .
Volume ............................... .
Noise ................................ .
Display Techniques ......... .

53

Addition of Power in DB .......... .

59

Chapter 4.

Four-Terminal Linear Networks

45
49
51

54
56
58

63

4-1

The Basic Laws .......... .
Ohm's Law ............................................. .
Kirchoff's Laws .......................... .

64
64
65

4-2

Application and Theorems ..............................
Equivalent Networks .....
....................
Thevenin's, or Pollard's, Theorem
... ............
Superposition Theorem ...................................
Compensation Theorem ..........................................

67
67
69
70
72

4-3

Network Impedance Relationships ....
. . . . . . . . . . . . . . . . . . . . . . ..
Image Impedance ...............................................
T-Network Equivalent .........
................
Transfer Effects .........................................
Sending-End Impedance .........
............ .........
Alignment Charts ....... . . . . . . . . . . . . . . . . . . . . . . . . .
Insertion Loss and Phase Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Return Loss ....................................................
Echo - Magnitude and Delay ...
.....................
Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73
73
75
76
78
85
90
90
92
94
98

4-4

Network Analysis ...................................
Mesh Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nodal Analysis ..........................................
Determinants ....................................................
Matrix and Linear Vector Space Analyses ........................

100
100
102
103
103

4-5

Transformers
...............................................
104
Impedance Matching ............................................ 104
Separating and Combining ........................ , . . . . . . . . . . . . .. 106

4-6

Resonant Circuits

109

4-7

Filters

110

ix

Contents
Chapter 5.

Transmission Line Theory ................................. . 115

5-1

Discrete Component Line Simulation . .
.............
Characteristic Impedance ....................................
Attenuation Factor .............................................
Propagation Constant ...........................................

115
117
119
120

5-2

Line With Distributed Parameters
Characteristic Impedance .......................................
Propagation Constant ..........................................
Attenuation Factor ............................................
Velocity of Propagation ........................................
Reflections .............................................. .

121
122
123
124
125
125

.
.
.
.

5-3

134
Loaded Lines ................................................ .
Analysis ...................................................... . 134
Inductive Loading .................. . ......................... . 136

5-4

Coaxial Cable ..................................................... 139

Chapter 6.

Wave Analysis ........... .

142

6-1

Instrumentation ................. .

143

6-2

Periodic Signals .................................................. 146
Fourier Series Representation ................................... 146
The (sin x) Ix Function .......................................... 156

6-3

~onperiodic

Signals ........................
. . . . . . . . . . . . . . . . . . .. 157
The Fourier Transform Pair
........
. . . . . . . . . . . . . . .. 157
Transmission Response .......................................... 160

Chapter 7.

Negative Feedback Amplifiers ............................. . 168

7-1

The Principle of Negative Feedback

7-2

Applications of Feedback .......................................... 169

7 -3

Benefits of Feedback .............................................. 170

7-4

Circuit Configurations ............................................. 172
Series and Shunt Feedback ...................................... 173
Bridge-Type Feedback .......................................... 174

7 -5

Design Considerations .............................................
Gain and Feedback .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Nonlinear Distortion and Overload ...............................
Noise and Terminations .........................................
Summary ................... .............................

168

177
177
180
184
186

Contents

x
Chapter 8

Modulation

188

8-1

Properties of Amplitude-Modulated (AM) Signals
..........
Double Sideband with Transmitted Carrier ....
..........
Double Sideband Suppressed Carrier .........................
Single Sideband ............................................
Vestigial Sideband ...................................

189
193
197
197
201

8-2

Properties of Angle-Modulated Signals .............
Phase Modulation and Frequency Modulation. . . . . . . .
Phasor Representation ........................................
Average Power of an Angle-Modulated Wave. . . . .
Bandwidth Required for Angle-Modulated Waves

203
203
207
208
209

8-3

Properties of Pulse Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pulse Amplitude Modulation ..............................
Pulse Duration Modulation ..................................
Pulse Position Modulation .......................................
Pulse Code Modulation ......................................

210
211
212
214
215
215

Chapter 9

Probability and Statistics ..

219

9-1

Elements of Probability Theory .,
Axioms ....................... .
Set Operations ......................... .

221
221
222

9-2

Discrete and Continuous Functions ........
.........
Mapping ...................................................
Cumulative Distribution Function ..............................
Probability Density Function ....................................

228
228
230
231

9-3

The Principal Parameters ..........................................
Expected Value .................................................
Variance .......................................................
Standard Deviation .............................................

233
233
234
235

9-4

Sums of Random Variables ........................................ 237

9-5

Distribution Functions ....................................
Gaussian or Normal Distribution ......................
Poisson Distribution ..................................
Binomial Distribution ...........................................
Binomial-Poisson-Normal Relationships ...........................
Log-Normal Distribution ........................................
Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Rayleigh Distribution ...........................................

239
239
243
244
246
246
247
249

9-6

Statistics .........................................................
Central Values and Dispersions ................. .............
Histogram .....................................................
Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

249
249
251
252

Contents
Chapter 10.

Information Theory ............... .

xi
256
257

10-1

The Historical Basis of Information Theory

10-2

The Unit of Information .......................................... 259

10-3

Entropy ........................................................ . 260

10-4

The Communication System ....................................... 264
Coding ........................................................ 265
Noise ......................................................... 265

10-5

The Fundamental Theorems .......................................
The Noiseless Channel ...........................
The Discrete Channel with Noise ..............
Channel Capacity with an Average Power Limitation

266
267
268
268

10-6

Channel Symmetry ........... .

269

Chapter 11.

Engineering Economy .

273

11-1

Time Value of Money ....... .
The Earning Power of Money
Equivalent Time-Value Expressions

275
275
276

11-2

Economy Study Parameters ........ .
Capital Costs ................. .
Plant Operations Costs
Dynamic Effects on Analysis .....

277
280
285
287

11-3

Economy Study Techniques ..........
. . . . . . . . . . . . . . . ..
Analytic Alternatives .............
. . . . . . . . . . . . . . . . . . ..
Study Assumptions ........
.........
........
Summary of the Comparison Study Process. . . . . . . . . . . . . . . .

291
292
294
296

SECTION 3

SIGNAL CHARACTERIZATION

Chapter 12. Speech Signals ......................................

299
301

12-1

The Single-Channel Speech Signal ...........................
Speech Signal Energy Distribution and Channel Response .........
Single Constant-Volume Talker ...........................
Sources of Volume Variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Single Variable-Volume Talker ..........
. ................

302
302
305
305
308

12-2

Multichannel Speech ..................... .

311

12-3

Load Capacity of Systems ........................................ 314
Multichannel Speech and Overload ....
. ...................... 315
Effect of Shaped TLP Characteristics ........................... 316

12-4

Program Signals ............... .

318

Contents

xii
Chapter 13.

Signalling ............................................... . 321

13-1

Signalling on Loops ............
.....................
Common Battery Operation. . . . .
......................
Supervision on Loops and PBX-CO Trunks ....
Address Signalling on Loops .. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . ..
Alerting Signals on Loops
. . . . . . ..

323
323
325
328
332

13-2

Signalling on Trunks ........... .
DC Loop Signalling on Trunks
Panel Call Indicator (PCI) System
Revertive Pulsing ....... .
Derived DC Signalling on Trunks
AC Signalling on Trunks ....

335
336
339
339
342
346

13-3

Out-of-Band ~ignalling
Out-of-Band SF Signalling .... .
Out-of-Band Digital Systems ............... .

348
349
349

13-4

Special Services Signalling
Tandem Signalling Links
Service Demands and Plant Complexities

349
350
350

Chapter 14.

Data Signals .......... .

351

14-1

Digital Signal Transmission Considerations
Signal Amplitudes ................... .
Error Rate and Signal-to-Noise Ratio
Channel Characteristics ........ ................ . ............ .

352
352
354
355

14-2

Digital Signal Characteristics ....
Amplitude Shift Keyed Signals
Phase Shift Keyed Signals '"
Frequency Shift Keyed Signals

358
359
372
373

14-3

Analog Data Signals .............................................
Medium-Speed Voiceband Data ..................................
Low-Speed Medical Data .......................................
Low-Speed Analog Data .............. . . . . . . . . . . . . . . . . . . . . . . . . ..

375
376
376
377

Chapter 15.

Video Signals ............................................. 379

15-1

Television Signals ................................................
Standard Monochrome Baseband Signals .........................
Baseband Color Signals ........................................
Broadcast Signals ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Closed Circuit Signals ..........................................

379
380
388
390
392

15-2

Picturephone Signals ............... .
Scanning .. , ........................ .
Modulation ................. .
Amplitude ................................................... .

393
394
394
396

Contents
15-3

Telephotograph Signals
Scanning ..... .
Bandwidth ........ .

Chapter 16.

Mixed Signal Loading

xiii
397
397
398

399

16-1

Mixed Signals and Overload

400

16-2

Mastergroup Speech Signal Load

401

16-3

Mastergroup Mixed Signal Load
Speech and Idle Channel Signals
Speech and Address Signals
Speech and Data Signals
Speech and Video Signals

402
402
405
406
407

16-4

System-Signal Interactions
System Misalignment
Carrier and Pilot Signals
Compandors ........................ .
TASI ..
Microwave Radio Systems

407
407
407
408
408
409

SECTION 4
Cha pter 17

IMPAIRMENTS AND THEIR MEASUREMENT
Noise and Crosstalk

410
413

17-1

Coupling
.............. .
Currents and Circuit Relationships
Coupling Paths and Their Control

413
414
416

17-2

Induced Noise and Crosstalk .....
Power System Noise ........... .
Impulse Noise ....................... .
Single-Frequency Interference .. .
Crosstalk ..................... .

421
421
423
424
425

17-3

System-Generated Noise and Cro.sstalk
Random Noise ....... .
Intermodulation Noise and Crosstalk
Digital Signal Noise Impairments

427
427
431
435

17-4

Noise and Crosstalk Measurements
436
Parameters and Units - Noise Measurements
437
Speech Crosstalk Measurements
438
Digital Measurements ................... .
447
Random Noise Measurements .................................. . 449

xiv

Contents

Chapter 18. Amplitude/Frequency Response

455

18-1

Telephone Channels - Speech Signal Transmission
Channel Bandwidth
Circuit Loss and Loss Variations
Amplitude/Frequency Distortion
Measurements ............ .

455
456
457
458
459

18-2

Telephone Channels - Data Transmission
Available Bandwidth .......... .
Loss and Loss Changes
....... .
Inband Distortion
Measurements ........... .

459
460
461
461
462

18-3

Wideband Digital Channels
Available Bandwidths
Measurements

463
464
465

18-4

Video Channels ............ .
Bandwidth ....... .
Cutoff Characteristics ....
Loss and Loss Changes
Differential Gain ...
Inband Distortion ..
Measurements ..

465
465
466
466
467
467
468

18-5

........

Transmission Systems ............. .
Bandwidth ................. .
Inband Distortion ....... .
Loss-Time Variations ............... .

470
471
471
472

Chapter 19. Timing and Synchronization Errors

474

19-1

Frequency Offset ................................ .
Speech and Program Signal Impairment
Digital Data Signal Impairment
AnalO'g System Impairments
Digital System Impairment ......... .

474
477
477
477
478

19-2

Other Incidental Modulation .... .
Gain and Phase Hits ......................... .
Jitter ................................... .
Dropouts ................... .

479
479
479
480

19-3

The Synchronizing Network ............................... .

481

Chapter 20.

Echo in Telephone Channels ........... .

482

20-1

EchO' SO'urces ........................ .

482

20-2

Nature of Echo Impairments
Speech Signals .................... .
Digital Data Signals ......... .
Telephotograph Signals ..... .

486
486
491
491

Contents
20-3

Echo Measurement and Control .. .
Echo Return Loss ........... .
Singing Return Loss ............... .
Echo. Suppresso.rs .... .

Chapter 21.

Phase Distortion

xv
492
492
494
494
496

Phase /Frequency Mathematical Characterization .,
Departure From Linear Phase
........ .
Phase Delay ............. .
Delay Disto.rtion ............ .
Envelo.pe Delay ......... .
Envelope Delay Distortion
Illustrative Characteristics ....... .
Intercept Distortion
.......... .
Quadrature Disto.rtion ....... .
Differential Phase ..................... .

496
496
498
499

21-2

Phase Distortio.n in Telephone Channels
Phase/Frequency Impairments
Quadrature Disto.rtion

511
511
512

21-3

Phase Distortion in Broadband Channels
Phase/Frequency Disto.rtion ..
Quadrature Disto.rtion
Differential Phase .......... .

513
513
513
514

21-4

Measurement, Evaluation, and Control of Phase Distortion ....
514
Phase/Frequency Measurement and Evaluation
........ 514
Pha.se Distortion Control .
...........
516

21-1

Chapter 22.
22-1

22-2

Maintenance and Reliability ....

500
5~1

501
501
505
509

520

Maintenance ......................... .
Sources of Deterioration and Failure
Maintenance Systems and Equipment

521

Reliability· .................... .
Sources of Failure ..............
. ...... .
Designs for Reliability .........
. ..................... .
Network Operating Methods and Procedures ................ .

526

522
523

527
529

531

SECTION 5

OBJECTIVES AND CRITERIA ..

533

Chapter 23.

Subjective Testing

536

23-1

Subjective Test Methods .. .
Threshold Testing ....... .
Pair-Comparison Testing
Comment Scale Testing - Category Judgments

537
537

538
539

xvi

Contents

23-2

Test Plan and Procedures ........................................
Setting Goals .................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Test Locale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Te·st Conditions ................................................
Test Procedures ...............................................

23-3

Data Analysis ................................................... 546

Chapter 24.

541
541
542
543
545

Grade of Service ......................................... . 551

24-1

A Graphic Derivation of Grade of Service .......................... 551
Customer Opinion Distributions ................................. 552
Relation of Connection Losses to Subjective Test Results
........ 553

24-2

Mathematical Derivation of Grade of Service ....................... 556

24-3

Uses of the Grade-of-Service Concept ............................. ,
Engineering Compromises ......................................
Performance Evaluation ....................... . . . . . . . . . . . . . . . ..
Time Effects on Grade of Service .........
. . . . . . . . . ..

566
566
568
569

24-4

Loss-N oise-Echo Grade of Service ...
Connection Loudness Loss and Noise Model
Talker Echo Model ....... .
Loss-Noise-Echo Model .. .
Subjective Opinion Models

570
571
573
573
574

Chapter 25.

Determination and Application of Objectives

577

25-1

Determination ................................................... 577

25-2

Interpretation ...................................................
Static Impairment Characteristics .... ..........................
Probabilistic Characteristics ....................................
Multiple Impairments ..........................................
Objectives, Requirements, and Limits ............... . . . . . . . . . . . ..

578
579
580
581
581

25-3

Allocation .......................................................
Allocation Assuming Power Addition ............................
Cost Effects ...................................................
Allocation for Digital Transmission

583
583
584
586

25-4

Translation ......................................................
Objectives to Requirements .....................................
Transmission Level Point Translations ..........................
Indices ........................................................
System Parameter Effects ......................................

588
588
589
589
590

Chapter 26.
26-1

Transmission Objectives .................................. . 593

Voice-Frequency Channel Objectives ............................... 593
Bandwidth .................................................... 594
Frequency Resonse Characteristic Distortion
........
594

Contents

xvii

Network Loss Design Plans
Echo Objectives ..
Loss Objectives .......... .
Loss Maintenance Limits
Message Circuit Noise .... .
Impulse Noise ........... .
Intelligible Crosstalk ... .
Single-Frequency Interference
Frequency Offset. . . . . . . . . . . . . . . . . . .. . .................. .
Overload ............................ .
Miscellaneous Impairments
...............
. ...... .
Telephone Station Sets ..................................... .

595

601
603
606
607
608
609
610
611
611
611
612

612
613
615

26-2

Wideband Digital Signal Transmission Objectives ............ .
Performance Evaluation .................................. .
Design Applications ..................... .

26-3

617
Video Transmission Objectives ...........
. ......... .
617
Random Noise ......................... . .......... .
619
Low-Frequency Noise ...................................... .
619
Impulse Noise ....
. . . . . . . . . .. . .......... .
620
Single-Frequency Interference .............................. .
620
Echo ..................................................... .
623
Crosstalk ....................................... .
624
Differential Gain and Phase ..
Audio/Video Delay ............................................ . 624
625
Luminance / Chrominance Delay

Chapter 27.

Economic Factors

627

27-1

Objectives .............................................. .
Determination of Objectives
Allocation of Objectives
Economic Objectives

627
627
629
630

27-2

Design Compromises
Circuit Devices ... .
Circuits ............ .
Physical Design .... .
Systems ......... '" .. .

631
631
632
632
634

27-3

Application Compromises
Components
........ .
Systems ............... .

636
636
637

International Telecommunications ..

638

The International Telecommunication Union
Organizational Structure of the ITU

639
641

Chapter 28.
28-1

xviii

Contents
Study Groups and Working Parties ........ .
Characteristics of International Operations

642
644

28-2

The Evolving International Network ...............................
World Numbering Plan .........................................
Signalling .................................................
Traffic and Operating
...............................
Routing Plan ..............................................
Transmission and Maintenance
..................

644
644
646
646
647
649

28-3

Transmission Parameters and Objectives .......................
Noise .............
....................................
Channel Loading ...
................................

650
650
652

Index

654

Telecommunications
Transmission
Engineering

Section 1
Background
The Bell System should be regarded as a single, huge, and far-flung
telecommunications system made up of station sets, cables, switching
systems, transmission systems, wires, and a conglomeration of other
hardware of all sorts and sizes. This telecommunications system has
grown rapidly and is still growing at a rapid rate. It has within it a
large number of interconnected and interrelated systems and subsystems, each of which was designed with an approach that provided
for successful development and overall Bell System evolution. This
relationship between the parts and the total has permitted the orderly
growth of a giant and the rendering of telecommunications services
throughout the United States, Canada, and indeed the world.
Historically, the first telephone systems consisted of two remote
station sets interconnected by wires normally used for telegraph
communications. As interest in telephone communication built up,
the transmission capabilities of the station sets and the interconnecting wires were gradually improved. Soon, manually operated switching systems were introduced in local communities to provide flexible
interconnections among people living close together and sharing a
high community of interest. These switching systems and the
surrounding station sets and interconnecting wires have become
known as the local plant.
The expanding local areas, the increasing demands for a wider
range of services, and improvements in technology soon permitted
the interconnection of one central office with another. As these
interconnections increased in numbers and distances over which
service had to be provided grew larger, the evolving long distance
network became a separate entity known as the toll plant. Larger
and more complex switching and transmission systems were designed
to meet the unique needs of this part of the overall system.

2

Background

Vol. 1

Chapter 1 provides an overview of the operating Bell System plant
with emphasis on the transmission and switching facilities that provide nationwide telephone service. Equipment used for other services
that share the message network facilities is also briefly discussed.
An introduction to transmission concepts is given in Chapter 2.
Brief descriptions of telephone, program, television, and data signals
are presented, transmission terminology is defined, and basic techniques and modes of transmission are explained. Some specialized
equipment, used to improve plant performance, is described to
illustrate the interactions of various parts of the network.

Background

Chapter 1

The Transmission Environment
The Bell System provides a variety of communications services to
large numbers of people over a very wide geographical area. To
accomplish this task, a vast and complex physical plant has evolved.
This plant is by no means static; it is highly dynamic in terms of
growth, change, and the manner in which it is used for providing
customer services.
The services provided by the Bell System are not readily categorized .
. The basic service of voice communications is handled by what is known
as the switched message network; however, some services such as
telegraph, facsimile, and voiceband data also utilize this network.
In addition, a growing list of other services (e.g., point-to-point
private line, television network service, wideband data, etc.) are
provided, some of which require special switching arrangements
and some of which require no switching at all.
The provision of transmission paths, or channels, and the flexible
interconnection of these paths by switching are the two principal
functions performed by the switched message network, the largest
of the service categories that use the plant. The facilities involved
are shared by many other services provided by the Bell System. The
network transmission paths, highly variable in length, are of two
major types, customer loops and interoffice trunks. The switching
arrangements are also of two maj or types, local and toll. The design,
operation, and maintenance of this huge network is further complicated by the multiplicity of its parts.
1-1

TRANSMISSION PATHS

Transmission paths are designed to provide economic and reliable
transmission of signals between terminals. The designs must accom-

3

4

Background

Vol. 1

modate a wide range of applied signal amplitudes and must guarantee
that impairments are held to acceptably low values so that received
signals can be recovered to satisfy the needs of the recipient, whether
a person or a machine.
Many transmission paths are designed as two-wire circuits; that
is, transmission may occur simultaneously in both directions over a
single pair of wires. Other paths, voice-frequency or carrier, are designed as four-wire; each of the two directions of transmission is
carried on a separate wire pair.
The four maj or elements in transmission paths are station equipment (telephones, data sets, etc.), customer loops (cables and wires
that connect station equipment to central offices), local and toll
trunks (interconnections between central offices, consisting of cables
or transmission systems and the transmission media they use), and
the switching equipment (found primarily in the central offices). In
its simplest form, a transmission path might consist of two station
sets interconnected by a pair of wires.

The Station Set
The station set accepts a signal from a source and converts it to
an electrical form suitable for transmission to a receiver which
reverses the process at a distant point. In most cases the station
set is a telephone; however, many other types of station sets are used.
Examples include facsimile sets, which operate to convert modulated
light beams to modulated electrical analog signals and back to light
at the receiving station, and voiceband data sets, which translate
the signal format used by a computer to an electrical representation
suitable for transmission over the telephone network and then back
to the appropriate computer signal format. Many of these types of
sets must meet transmission requirements for voice communications.

Customer loops
The station set is connected to the central office by the customer
loop. This connection is most commonly made through a pair of
insulated wires bundled together with many other wire pairs into

Chap. 1

The Transmission Environment

5

a cable which may be carried overhead on poles, underground in
ducts, or buried directly in the ground. For urban mobile service,
however, the loop consists of a radio connection. between the station
set and the central office. The design of the customer loop must satisfy
transmission requirements for all types of signals to be carried, e.g.,
speech, data, dial pulsing, TOUCH-TONE®, ringing, or supervision.
Loops are busy (Le., connected to trunks or other loops) only a
small percentage of the time - in some cases, less than 1 percent
of the time. Where suitable calling patterns exist, this has led to
the consideration of line concentrators for introduction between the
station sets and the central office. A concentrator is"a small switching
machine which allows a number of loops to be connected to the
central office over a smaller number of shared lines which are, in
effect, trunks.
For some services, the loop plant is frequently reconfigured. In
providing private branch exchange (PBX) services, for example,
the loop plant provides PBX trunks connecting the customer's
switching arrangement to the local or serving central office. In
other services, loop plant may be used to form a part of a loop
to be intermixed with trunks to provide an extended loop, or it may
be used as a part of a channel between various customer locations
for the transmission of wideband signals.

Switching Machines

For switched message telephone service, the loop connects the
station set to a switching machine in the local central office, which
enables connections to be established directly to other local station
sets or, through trunks and other switching offices, to any other
station set on the switched network. The various types of switching
offices which house this equipment are illustrated in Figure 1-1.
The principal switching machines in use today are electromechanical, e.g., the step-by-step and the crossbar types. Coming into
increasing use, however, are electronic switching systems, which
provide improvements in flexibility, versatility, and ease of maintenance, along with a considerable reduction of space requirements.

Background

6

e

End office
(class 5)

Toll center
(class 4)

aQ
~

~

Primary center
(class3)

-x••••

Vol. 1
Tandem office
T1 Sector tandem
T2 High-volume or
directional tandem

Station set and loop
Interoffice trunk
Tandem trunk
Intertandem trunk
Toll connecting trunk
Intertoll trunk

Sectional center
(class 2)

(Some nonstandard symbols are used on this sketch.)

SECT

Figure 1-1. A simplified telephone system.

Chap. 1

The Transmission Environment

7

Transmission paths are provided through switching machines in
a variety of ways and by a number of different mechanisms, including
step-by-step switches, crossbar switches, and ferreed switching networks. These all have one thing in common, the ability to connect
anyone of a set of several thousand terminals to any other in the
set. By design, this is accomplished with only a minimum of blocking
during the busiest hour; i.e., only a very small percentage of calls is
not completed as a result of all paths being busy. Each of the many
paths is designed to provide satisfactory transmission quality through
the central office.
As mentioned earlier, many transmission circuits are operated on
a two-wire basis and, as a result, are also switched on a two-wire
basis. Thus, especially in the local area, most switching machines
provide two-wire paths. In the toll network, most of the transmission
paths are four-wire; as a result, many toll switching machines must
provide four-wire switching and transmission paths.

Trunks

The transmission paths which interconnect switching machines are
called trunks. One essential difference between a loop and a trunk
is that a loop is permanently associated with a station set, whereas
a trunk is a common connection shared by many users. There are
several classes and types of trunks depending on signalling features,
operating functions, classes of switching offices interconnected, transmission bandwidth, etc.
There are three principal types of interoffice trunks: local (interoffice, tandem, and intertandem), toll connecting, and intertoll. These
trunk types and the switching offices that they interconnect are
illustrated in Figure 1-1 which shows a representative metropolitan
area and typical connections to the toll portion of the network.
All trunks must provide transmission and supervision in both
directions simultaneously. However, trunks are designated one-way
or two-way according to whether signalling is provided in both directions or only one. Two-way signalling is usually provided on intertoll
trunks; calls can be originated on the trunk from the switching
machine at either end. One-way signalling is the usual method of

8

Background

Vol. 1

operating local and toll connecting trunks; therefore, separate trunk
groups are provided for the two directions of originating traffic
between the two offices involved.
Any trunk may use carrier transmission systems. However, local
and toll connecting trunks rely heavily on voice-frequency cable
media, although short-haul analog and digital carrier systems are
becoming more widely used, especially in large metropolitan areas.
The intertoll trunks, for the most part, utilize long-haul analog carrier
systems and microwave radio relay systems.

1-2

SWITCHING ARRANGEMENTS

The service offered by the Bell System consists fundamentally of
providing transmission capability upon demand between two or more
points. Implied by "upon demand" is a switching arrangement capable
of finding the distant end or ends of a desired connection and completing the connection between the originating and distant ends
promptly and accurately. This is accomplished by a large number of
switching machines connected together and organized around considerations of geography, concentrations of population, communities
of interest, and diversity of facilities. These switching arrangements
are illustrated in Figure 1-1 and may be broadly classified as either
the local switching hierarchy (utilized for local transmission) or the
toll switching hierarchy (utilized for transmission outside the local
area). The switching equipment of either arrangement, however, is
not totally divorced from that of the other. For example, tandem
offices, operated by an associated company, are frequently used to
switch toll traffic. Two methods are used. One is to segregate trunks
between interlocal and toll use by maintaining separate groups. The
second is to use a common tandem trunk group for both toll and
interlocal. When trunks are so shared, the more severe transmission
requirements for either use musfbe applied to the common group.

The Local Switching Hierarchy

Figure 1-2 illustrates the various degrees of complexity that may
be involved in switching within a local area. The simplest connection

Chap. 1

9

The Transmission Environment

EO

o----------------+-~t_j~~~---------------o

(a) Station-to-station connection; same end office

EO

EO

A

)(

•

I

I

)

~ ~

, " - - - _....

I

/

,/
",.

B ,/,/

c /

,/

I

./
",.

,/

/

(
/

I

I

\

\

" .....

G
"

I

"

....
0

~

E

(b) Station-to-station connections using local trunks

Note:
Symbols are same as in Figure 1-1.

Figure 1-2. Illustrative telephone connections.

"l

10

Background

Vol. 1

in the switched network is from one station set to another through
a single local central office. Transmission over such a connection
involves only the two station sets, their loops, and the transmission
path through the switching machine as shown in Figure 1-2 (a).
A connection in a multioffice area might be set up between two
local, or class 5, offices in a number of ways as shown in Figure 1-2 (b) .
Within the metropolitan area, it can be seen that trunks might interconnect two offices directly, using trunk A. Alternately, one, two,
or three tandem switching machines might be used; with one machine,
trunks Band C are used; with two machines, trunks B, D, and G
are used. Finally, if three machines are involved, trunks B, E, F,
and G are all used. These tandem machines, used in large metropolitan areas, provide economies through switching versus trunk
facility costs and also provide alternate routing of traffic.
The complexity of the transmission network is obviously increased by this multitrunk local area switching arrangement, which
is quite separate from the toll switching hierarchy discussed below.
Since a connection might use just one interoffice trunk between the
two end offices or as many as four tandem and intertandem trunks
interconnecting the end offices and the tandem offices, the network
arrangement must be designed and built according to objectives that
take into account the number of trunks that might be connected together in tandem to complete a connection from one station to
another. While local trunks are usually short, their numbers comprise
the largest segment of trunks in the Bell System.

The Toll Switching Hierarchy

The hierarchy of toll switching offices, developed to facilitate the
transmission of signals beyond a local area, is illustrated in
Figure 1-3. Working from the top down, it can be seen that the
hierarchy consists of regional centers, sectional centers, primary
centers, toll centers, and end offices. These centers and offices are also
classified by a numbering system as shown in Figure 1-4. The figure
also shows the quantity of each type of office operating in the Bell
System in early 1970.

Chap. 1

11

The Transmission Environment

Regional center

Regional center
(1)

".,..
".,..

(1)

/'

/'

/

/

I

I

/

/

/

".,..

/

".,..

/

/

".,..

/

/
/

/

/

\

(

/

/
/

.............

/

".,.."""

\ (1)

/(2)

\

\

/

---

\
\

\

-- - -- -

\

- - -.....(1)

--

/

>

Class 5
E01

E02

Notes:
1. Numbers in () indicate order of choice of route at each center
for calls originating at EOl.

2. Arrows from a center indicate trunk groups to other lower rank
centers that home on it. (Omitted in right chain.)
3. Dashed lines indicate high-usage groups.

Figure 1-3. Choice of routes on assumed call.

Background

12

Vol. 1
APPROXIMATE NO.
IN SERVICE, 1970

CLASS

DESIGNATION

1

Regional center

10*

2

Sectional center

50

3

Primary center

200

4

Toll center

1000

5

End office

10,000-15,000

*In addition to the ten regional centers in the U.S.A., there are two in Canada.

Figure 1-4. The toll switching hierarchy (Bell System only).

Access to the toll network is made through toll connecting trunks.
In general, they are classified with local trunks since they are
relatively short and intermixed on facilities with interoffice, tandem,
and intertandem trunks. Generally, toll connecting trunks provide
connections between class 5 and class 4 offices (end offices and toll
centers). However, since class 5 offices may connect into the toll network at any level of the hierarchy, toll connecting trunks may also
connect to class 3, class 2, or class 1 offices as well as to class 4 offices.
In these cases, the higher offices also perform the functions of class 4
offices. The facilities used by toll connecting trunks may be voicefrequency or carrier. The termination at the class 5 office is two-wire;
at the higher class offices it may be two-wire or four-wire, depending
on the switching machine.
The toll switching network is provided with intertoll trunks
between various combinations of office classes. One such combination
is shown in Figure 1-3. Note that final trunk groups (Le., those carrying traffic for which they are the only route and overflow traffic for
which they are the "last choice" route) are provided between each
lower ranking office and the higher ranking office on which it homes.
All regional centers are interconnected by final trunk groups. Highusage trunk groups, which provide for alternate routing, are installed
between any two offices that have sufficient community of interest.
Automatic switching of toll circuits facilitates the use of alternate
routing, so that a number of small loads may be concentrated into
large trunk groups, resulting in higher efficiencies and attendant
economies.

Chap. 1

The Transmission Environmeht

13

The order of choice of trunks for a call originating in end office 1
and terminating in end office 2 is indicated in Figure 1-3 by the
numbers in parentheses. In the example there are ten possible routes
for the call. Note that the first choice route involves two intermediate
links. In many cases a single direct link, which would be first choice,
exists between the two toll centers. Only one route requires seven
intermediate links (intertoll trunks in tandem), the maximum permitted in the design of the network.
The probability that a call will require more than n links in tandem
to reach its destination decreases rapidly as n increases from 2 to 7.
First, a large majority of toll calls are between end offices associated
with the same regional center. The maximum number of toll trunks
in these connections is therefore less than seven. Second, even a call
between telephones associated with different regional centers is
routed over the maximum of seven intermediate toll links only when
all of the normally available high-usage trunk groups are busy. The
probability of this happening in the case illustrated in Figure 1-3 is
only p5, where p is the probability that all trunks in anyone highusage group are busy. Finally, many calls originate above the base
of the hierarchy since each higher class of office incorporates the
functions of lower class toll offices and usually has some class 5
offices homing on it. Figure 1-5 makes these points more specific.
The middle column of this table shows, for the hypothetical system
NUMBER OF INTERMEDIATE
LINKS, n

PROBABILITY
FIGURE 1-3

1961 STUDY

Exactly 1

0.0

0.50

2 or more

1.0

0.50

Exactly 2

0.9

0.30

3 or more

0.1

0.20

4 or more

0.1

0.06

5 or more

0.0109

0.01

6 or more

0.00109

0

Exactly 7

0.00001

0

Figure 1-5. Probability that n or more links will be required to complete a toll calt.

14

Background

Vol. 1

of Figure 1-3, the probability that the completion of a toll call will
require n or more links between toll centers, for values of n from
1 to 7. In computing probabilities for this illustration, the assumptions are: (1) the chance that all trunks in anyone high-usage group
are simultaneously busy is 0.1; (2) the solid line routes are always
available; and (3) of the available routes the one with the fewest
links will always be selected. The values in Figure 1-5 illustrate
that connections requiring more and more links become increasingly
unlikely. These numbers are, of course, highly idealized and simplified.
Actual figures from a Bell System study made in 1961 al c shown
in the last column of the table of Figure 1-5. These numbers represent
the probability of encountering n links in a completed toll call between
an office near White Plains, New York, and an office in the Sacramento, California, region. The assumption was made that all traffic
had alternate routing available and that blocking due to final groups
was negligible. Note that at that time 50 percent of the calls were
completed over only one intermediate link. This is not possible in the
layout shown in Figure 1-3, where it may be assumed that traffic
volume does not yet justify a direct trunk between toll centers. The
maximum number of links involved in the 1961 study was five; this
number was required on only 1 percent of the calls.

More recent studies, reported informally, indicate that the trend
continues in the direction of involving fewer trunk links in toll calls.
In 1970, approximately 75 percent of all toll calls were completed
over only one intertoll trunk; 20 percent required two intertoll trunks
in tandem; about 4 percent required three trunks; the remaining
1 percent required four or more intertoll trunks in tandem. This trend
is a result of increasing connectivity between offices by providing
increased numbers of high-usage trunk groups (direct connections)
between lower classes of offices in the hierarchy.

1-3

IMPACT OF SYSTEM MULTIPLICITY ON
NETWORK PERFORMANCE

The provision of customer-to-customer communications channels
can involve a multiplicity of instrumentalities, facilities, and systems
interconnected in many ways. Station sets, loops, and end offices are

Chap. 1

The Transmission Environment

15

particularly important, especially in the switched message network,
since they are used in every connection. Toll connecting and intertoll
trunks, toll transmission systems, and toll switching machines are
also important when communications beyond the local area are
considered. The overall comprises a complex configuration of plant
items whose interactions give rise to several broad problems in the
total network design and operation.
The first problem is that the accumulation of performance imperfections (such as loss, noise, and impedance irregularities) from a
large number of systems leads to severe requirements on individual
units and to great concern with the mechanisms causing imperfections
and with the ways in which imperfections accumulate.
The second problem is that the variable complement of systems
forming overall connections makes quite complex the problem of
economically allocating tolerable imperfections among these systems.
Deriving objectives for a connection of fixed length and composition
is a problem involving customer reactions and economics. However,
when these objectives must be met for connections of widely varying
length and composition, the problem of deriving objectives for a
particular system requires an even more complex statistical study
involving considerable knowledge of plant layout, operating procedures, and the performance of other systems.
A third problem involves the satisfactory operation of each part
with nearly all other parts. Compatibility is particularly important
when new equipment and new systems are being developed, because
the existing plant and the new interact importantly in many ways
and also because plant growth must take place by gradual additions
rather than by massive junking and replacement.
A fourth problem is that of reliability. Only small percentages
of outage time are acceptable for the communications services provided by the Bell System, and these must account for all causes
of failure-equipment failure, natural or man-made disaster, operating errors, etc.
Finally, to be complete, any discussion of the environment must
recognize that telephone plant and power transmission and distribution systems share the same geography, either aerially or under-

16

Background

Vol. 1

ground. This fact is important from a safety standpoint and from
the standpoint of quality of transmission on telephone facilities.
Power systems may come in contact with telephone plant as a result
of storms, plant failures, or induction, endangering customers,
employees, and property unless protective measures are applied. The
presence of power systems in proximity to the telephone plant can
also be damaging from the standpoint of quality of telephone transmission since noise induction is a distinct possibility.

1-4

MAINTENANCE AND MAINTENANCE SUPPORT

The switching patterns that have been described impose strict
requirements on all transmission circuits. For example, up to seven
intertoll trunks may be connected in tandem, and successive calls
between the same two telephones may take different routes which
involve different numbers and kinds of circuits. The losses encountered
on calls routed over different numbers of links must not vary excessively, nor may the transmission quality vary significantly. If
unsatisfactory transmission occurs, it cannot be observed by an
operator as in the past, and the customer's attempt to report the
trouble disconnects the impaired circuit, making difficult the identification of the source of trouble.
To cope with this situation, many central offices have extensive
test facilities associated with them. Some of these facilities are test
switchboards which have access to the lines and trunks in the office
by manual patch or cross-connecting means. New automatic test
facilities are also now available and are used extensively to test
interoffice trunks by way of special trunk circuits and access arrangements provided in the switching machines. In addition, many central
offices are equipped with voiceband data test centers for both
DATA-PHONE® and private line service.
A great variety of portable, special purpose, and general purpose
test equipment is also usually available in most central offices. This
equipment, fixed and portable, manual and automatic, is described in
greater detail later.
Extensive test equipment is also available for special services. For
example, test equipment for television and wideband data services is

Chap. 1

The Transmission Environment

17

located at the Television Operating Centers and the Wideband Data
Test and Service Bays.
In addition to equipment that is directly involved in maintenance,
there is an extensive list of equipment and transmission system
features that may be classified as maintenance support. These equipment and service features are designed to facilitate trouble identification, isolation, and repair, to prevent extensive proliferation of
trouble conditions, to provide for emergency restoration of broadband
facilities on a temporary basis, to provide for remote telemetering
and remote control of maintenance equipment and alarms, and to
provide special communications channels (order wires) for maintenance personnel. These also are described in greater detail in a later
chapter.
REFERENCES

Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N. C.: Western Electric
Company, Inc., 1970).

1. Technical Staff of Bell Telephone Laboratories.

2. Bell System Technical Reference PUB41005, Data Communications Using
the Switched Telecommunications Network (American Telephone and Telegraph Company, August 1970).

3. Switching Systems (American Telephone and Telegraph Company, 1961).

Background

Chapter 2

Introduction To Transmission
The movement of intelligence from one point to another is the
basic task of the Bell System. The intelligence to be moved can be
called a message, regardless of the form it takes or its purpose. The
most common form, of course, is speech, and the telephone system
was initially developed around the need for voice communications.
Over the years, however, many other types of messages (such as
facsimile, program, video, and data) have evolved.
In general, transmission technology has advanced in parallel with
this evolution, providing a means of translating these messages into
electrical signals and developing the communications channels that
make it possible to transmit the messages in reversible form via
existing transmission media. Extension of the capabilities of the
existing multiple-link plant and the development of new plant
compatible with the old and capable of fulfilling transmission requirements are among the problems confronting the transmission engineer.
The variety of message signals and types of channels interact in
many ways. Different types of message signals require channels of
various bandwidths and operating characteristics. These channels
utilize voice-frequency and carrier facilities which must meet stringent requirements if they are to provide satisfactory service economically. To meet these requirements, it is sometimes necessary to
use specially designed ancillary equipment on the channels or systems.

2-1

MESSAGE SIGNALS

The characterization of transmitted message signals is essential
to an understanding of how such signals interact. with the channels
over which they are transmitted. The message signal is defined as

18

Chap. 2

Introduction To Transmission

19

an electrical representation of a message, which can be transmitted
in its electrical form from source to destination. Qualitative descriptions of the more common signals found in the Bell System are given
here. The signals described in this chapter include voice, program,
video, data and facsimile, and control signals. The latter, usually
classified as signalling and supervision, are transmitted in order to
activate switching operations and to perform other subsidiary functions. Variations of these signal types are used to transmit all
messages presently offered as Bell System communication services.
Any of the signals may be transmitted in either digital or analog
form; the choice is dependent in some cases on the transmission
facilities available. More detailed quantitative characterizations of
all these signal types are given in Chapters 12 through 16.

Speech
The most common signal transmitted over Bell System facilities
is the speech signal, an electrical signal generated in the telephone
station set as an analog of the acoustical speech wave generated
in the voice box, or larynx, of the speaking telephone user. This
signal carries most of its information in a band of frequencies
between 200 Hz and 3500 Hz. Most of the energy is peaked near
800 Hz; most of the articulation is above 800 Hz. It has higher
frequency and lower frequency components, but these are not normally transmitted. It is an extremely complex signal, not only because
of the large number of frequency components it contains, but also
because of the wide range of amplitudes that any component may
have and because of the rapidity with which the frequency and
amplitude of its components may change.
Another complexity is the time relationships inherent in the speech
signal. By one definition or criterion, the signal duration might be
measured from the time the connection is established until it is broken.
By another criterion, the signal duration might be defined as the
speaking interval-during a typical telephone connection, each party
speaks about half the time and listens the other half. But the
situation is even more complex. There are short intervals, sometimes
only milliseconds in length, during which a speaker pauses for breath
or for other reasons. Signal duration could be defined as covering
the time between those pauses. So, it is a matter of definition; care

20

Background

Vol. 1

must be taken to define the signal precisely when circumstances
demand it, for example, when considering system loading or crosstalk
effects.

Program
Program signals are those associated with the distribution of
radio program material, the audio portion of television program
material, or "wire music" systems. These signals are usually transmitted over one-way channels having a somewhat wider bandwidth
than the standard voice-frequency message channel. The signals may
include speech and a wide range of musical material. The signal
energy is usually maintained at a higher average level than that of
switched telephone voice-frequency signals and may be transmitted
continuously for hours; however, since there is such a small percentage of circuits assigned to this type of service, little effect is felt
in system loading.
Video

There are three types of video signals commonly transmitted
over Bell System facilities-television, PICTUREPHONE®, and
multilevel facsimile. Multilevel facsimile represents a very small
percentage of transmitted signals and is described as a data signal.
Brief descriptions of television and PICTUREPHONE signals are
given here.
A television signal contains information in electrical form from
which a picture cail be re-created with fidelity. A still monochrome
picture may be expressed as a variation in luminance over a
two-dimensional field. In a moving picture, however, the luminance
function also varies with time. The moving picture, therefore, is
a function of three independent variables: luminance, position, and
time.
The electrical signal (characterized in Chapter 15) consists of
a current or voltage amplitude which is a function of time. At any
instant, the signal can represent the value of luminance at only one
point in the picture. It is necessary, therefore, in the translation
of a complete picture into an electrical signal, that the picture be
scanned in a systematic manner. If the scanning pattern is sufficiently

Chap. 2

21

Introduction To Transmission

detailed and conducted rapidly, a satisfactory reproduction of picture
detail and motion is obtained. The basic system consists of a series
of scans in nearly horizontal lines from left to right, starting at the
top of the image field. When the bottom of the field is reached, the
process is started again from the top with alternate fields interlaced
to form a frame.
For the successful decoding of the signal into a picture at the
receiver, it is necessary to transmit a key to the scanning pattern.
In the standard signal, this consists of frequent short-duration
synchronizing pulses indicating characteristic points in the course
of the scanning pattern, such as the beginning of scanning lines and
fields. This is coupled with the condition that the motion of the
scanning spot between pulses is uniform with time in the field of
view. The picture signal is interrupted during retrace time and
replaced by a black signal known as a blanking pulse. Because of
this, the return trace is not visible in the picture.
The PICTUREPHONE signal is conceptually similar to the television signal. Both signals use a frame rate of 30 per second and
a field rate of 60 per second. Lines from alternate fields are interlaced. The following tabulation compares the two signals in other
important respects:

TELEVISION
PICTUREPHONE

SCAN RATE

LlNES/ FIELD

BANDWIDTH

15.75 kHz

525

4.3 MHz

8.0 kHz

250

1.0 MHz

The signal duration in television operation is long, an hour or more,
with only short breaks for commercial and station-break announcements. These hardly qualify as signal terminations for most situations. For PICTUREPHONE signal transmission, the signal duration
is the full period of the call since picture information is transmitted
in both directions during this entire period.

Data and facsimile
The basic data signal usually consists of a train of pulses which
represent, in coded form, the information to be transmitted. Such
signals are processed in many ways to make them suitable for
transmission over Bell System facilities. To represent coded values

22

Background

Vol. 1

of the signal, the amplitude may be shifted, the frequency may be
shifted, or the phase of a carrier may be shifted. In addition, the
relative positions of pulses or the duration of pulses may be changed.
The speed with which changes are made, no matter which parameter
is changed, determines to a large extent the bandwidth required to
transmit data signals. Transmission speeds used in the Bell System
vary from a few bits (binary digits) per second for supervisory
control channels, to a few hundred bits per second for teletype or
telegraph signals, to over one megabit per second for use on digital
carrier systems.
Some two-valued facsimile signals (black and white facsimile)
closely resemble binary data signals and may be compared with them
in many ways. Multivalued facsimile signals are more like video
signals, as mentioned earlier; they produce pictures at slow speeds
with gradations of grey between black and white. Such facsimile
signals are often regarded as special forms of data because channel
requirements for facsimile transmission are quite similar to those
for data transmission. The latter signals, together with other forms
of data (such as the electrocardiogram signal), may be regarded as
analog data signals.
Data signal durations are highly variable. Some data messages
tend to be very short while others can last for hours. Facsimile
messages last several minutes typically.
Control Signals

In order to implement the functions of any switched network, it
is necessary to transmit three types of control, or signalling, information. These are (1) alerting signals, (2) address signals, and (3)
supervisory signals. These signals are usually transmitted over the
loops or trunks directly involved in an overall connection. However,
they may also be transmitted over a separate, dedicated signalling
channel used as a common signalling facility for many message channels. Such a common channel system is under study and development.
Alerting signals include the ringing signal, which is supplied to
a loop to alert the customer to an incoming call on his line, and a
variety of signals that are used to alert operators to a need for

Chap. 2

Introduction To Transmission

23

assistance on a call. Addressing signals provide information, transmitted over loops and trunks, concerning the desired destination of
the call (the called number) and, sometimes, the identification of the
calling number. Supervisory signals are used to indicate a demand
for service, the termination of a call, and the busy jidle status of each
loop or trunk.
Many forms of addressing and supervisory signals are employed.
These include pulsing of the direct current supplied on loops for
talking purposes or on voice-frequency trunks for supervision, changes
in state of direct current supplied on voice-frequency trunks, and
single-frequency or multiple-frequency alternating current signals
which may be transmitted within or outside the voiceband of a carrier
or voice-frequency circuit. The most important of these signals are
described and characterized in Chapter 13.
Many other types of signalling information are transmitted for
subsidiary functions. These include dial tone, audible ringing tone,
coin signals ( deposi t, return, and collect), busy and reorder tones,
and recorded announcements such as time and weather information.
N one of these relates importantly to transmission work, however,
and so they are not described in detail.
The duration of information signals varies widely. Addressing
signals last for only a short time, one to several seconds. Supervisory
signals, on the other hand, may be present for minutes, hours, or even
days when a trunk, for example, is not called into use. It is
interesting to note that address signals may be regarded as transient
by nature, and supervisory signals are steady state.

2-2

CHANNELS

A channel is defined as a frequency band, or its equivalent in the
time domain, established in order to provide a communications path
between a message source and its destination. The characteristics
of the signal derived from the message source determine the requirements imposed upon the channel in respect to bandwidth, signal-tonoise performance, etc.
In the switched telephone message network, a variety of channels
are provided on a full-time, dedicated basis in the form of loops,

24

Background

Vol. 1

local trunks, toll connecting trunks, and intertoll trunks. Each
such channel is a well defined entity between its terminals for long
periods of time. Changes in the channel makeup or configuration can
be made only by changing soldered connections or by patching within
a jack field.
The end-to-end frequency band established between station sets
in a built-up telephone call is also a channel. This frequency band
is dedicated and maintained only for the duration of the call. In
this case, the channel is made up of other tandem-connected channelsthe interconnected loops and trunks used to establish the connection.
With the advent of time division switching and its integration
with time division transmission systems, the end-to-end concept of
a channel in a built-up telephone connection may have to be modified.
Present systems maintain the integrity of the channel in the time
domain equivalent of the analog channel, but it is theoretically
possible to change channel assignments during a call. Analog channel
assignments are changed during a call in the TASI system, described
later in this chapter.
Thus, channels in the switched telephone message network may be
regarded as fixed, changeable, or switchable. In any case, each type
of channel must be designed to have a transmission response that
will satisfy the objectives set for the type of service to be provided.
That is, they must be of sufficient bandwidth, must have gain/
frequency and phase/frequency characteristics that are well controlled, and must not be contaminated by excessive noise or other
interference. These parameters will be discussed more quantitatively
in later chapters.
Channels may also be regarded as one-way or two-way. Carrier
systems are usually operated on a four-wire basis, a separate path
for each direction of transmission. On one such path the dedicated
band of frequencies (Le., the channel) carries signal energy in one
direction only, and so each path represents a one-way channel. Voicefrequency circuits (loops and trunks), on the other hand, are frequently operated so that both directions of transmission are carried
on the same wire pair-a two-way channel. In any case, in the
switched message network, loops and trunks must be capable of full
duplex, i.e., two-way simultaneous usage.

Chap. 2

Introduction To Transmission

25

In this discussion, definitions involving channels in the switched
telephone message network have been stressed. It must be recognized
that many other types of channels are provided in the Bell System.
These include very wideband channels for high-speed data or video
signal transmission, channels somewhat wider than speech channels
for radio and television program or sound signals, voiceband channels
that are specially treated to meet data or facsimile transmission
objectives, and very narrowband channels for telegraph and low-speed
data signal transmssion.

2-3

VOICE-FREQUENCY (VF) TRANSMISSION

To a large extent, the line facilities and apparatus that are applied
in practice to the local telephone plant operate at voice frequency. The
loop plant employs a two-wire mode of operation almost exclusively,
and the local network trunk plant is operated in both the two-wire
and the four-wire modes. In either mode, the transmission medium
introduces signal loss which must be controlled within established
limits in order to provide satisfactory service. When the losses exceed
the established limits, compensation must be made by means of voicefrequency repeaters (amplifiers and associated circuit features)
whose gains are designed to restore signal amplitudes. For economical
circuit design, then, proper choice must be made of the minimum
wire size compatible with circuit length, as well as the appropriate
repeater type relative to mode of operation, wire size, and circuit
length.

Modes of Voice-Frequency Transmission

The telephone station set is basically a four-wire instrument, one
that requires two wires for the transmitter and two wires for the
receiver. If the four-wire nature of the set were extended into the
entire local plant including both loops and trunks, four wires would
have to be provided for every connection including the transmission
paths through the switching machines. Such an arrangement, illustrated in Figure 2-1 (a), would offer some transmission advantages,
but it would be inordinately expensive since it would nearly double the
amount of copper required for cables and other types of conductors
needed to provide transmission paths and would impose a burden on

26

Background

Vol. 1

Switches

(0) Four-wire connection

Switches

(b) Two-wire connection

Figure 2-1. Voice-frequency modes of transmission.

local switching machines, nearly all of which provide two-wire
transmission paths only. To avoid this expense, the station set is
provided with circuitry that combines the transmitter and receiver
conductors so that only one pair of wires is needed for transmission
in both directions. This arrangement, called two-wire transmission,
is illustrated in Figure 2-1 (b) .

Chap. 2

Introduction To Transmission

27

Two-wire transmission is used almost exclusively in loops and
commonly in short trunks between local central offices. However,
when trunks are long or when the bandwidth is significantly greater
than the 4 kHz used for speech transmission, the technical problems
are such that four-wire transmission is necessary. Net losses can be
held at lower values, and there are fewer echo and singing paths.
Therefore, there are applications for four-wire voice-frequency circuits even before carrier applications become economical.
Voice-Frequency Repeaters
The selection of repeater type in solving voice-frequency application problems depends on the required gain and on the mode of
transmission, two-wire or four-wire. The E-type repeater, shown
schematically in Figure 2-2, is used in many two-wire trunks and
some loops to provide the necessary gain and equalization. Its unique
shunt and series negative impedance characteristics provide gain in
both directions of transmission in a two-wire circuit.

Series converter

Line

Shunt converter

Figure 2-2. Negative impedance repeater for a two-wire repeatered line.

Background

28

Vol. 1

The repeaters used in four-wire lines use separate amplifiers for
each direction of transmission. Figure 2-3 shows how four-wire repeaters are used in a four-wire trunk. Notice that repeaters used
along the line connect four-wire to four-wire, while at the ends of the
trunk the arrangement provides interconnection between four-wire
and two-wire facilities.
New designs, designated facility terminals, are now available to
provide either two-wire or four-wire gain. In addition, this equipment
provides flexibility in interconnecting equipment needed for other
circuit functions such as signalling and equalization as required.

2-4

CARRIER SYSTEMS

Since the per-channel copper costs for VF transmission are often
prohibitive, carrier systems have been developed to reduce overall
costs by the substitution of electronics for copper. Carrier systems
(which for the purpose of this discussion include microwave radio
systems) are broadband, multichannel, four-wire facilities. The carrier principle proves to be economical because its broadband, multichannel features allow one carrier channel to be used for a multiplicity
of narrower band channels (for speech, data, or other signal transmission). These individual channels operate, of course, in the fourwire mode also, since there is a separate path for each direction of
transmission.
Systems designed for submarine cable operation and some shorthaul carrier systems use a mode of transmission called equivalent
four-wire. In this mode, the two directions of transmission are
separated in frequency on a single pair of wires, rather than in space
on separate wire pairs. Two circuit arrangements that are commonly
used are illustrated in the block diagrams of Figure 2-4 (a) and
(b). The advantage of this mode, of course, is that only one pair is
required for both directions of transmission.
A carrier system may be regarded as consisting functionally of
three major parts: (1) high-frequency line or radio relay equipment
which, with the transmission medium, provides a broadband channel
of specified characteristics to permit simultaneous bidirectional transmission of a wide range of communications signals; (2) modulating
equipment to process signals from one form to another more suitable
for transmission in each direction of transmission from the terminal;

()
:T

o
l'

t\)

--.

4-wire facility

I~

Repeater with 4.wire
terminating set

I Repeater

I

I
I

I

I

I

I
I
I

I

I

I

Repeater with 4-wire
terminating set

Repeater

I

I

I

I

~=~=lC3=~~~r2= ~=~
Network

c
n
C)"

....
;:,

-I
0

I

I

I

I

I

I
I
1

I

I
I

I

1

::l

Network

I
..

-I
-.:
0
CI'

-'1

l-;:<~~lu!

Figure 2-3. Four-wire repeatered line.

t\)

"0

Vol. 1

Background

30

--+

HF

J

1

l
HF

-+

HP

LF

+--

LP

L

COMB.

LF

+-

J
HF and LF

\/
t

LP

+-

LF

HP

~

HF

t

HF
and
LF

I

SPLIT.

1

HF
and
LF

I

J

(a) Single amplifier connection

----+

HF

~

V
HF

---+

HP

HP

----.

HF

LF

+--

LP

LP

+-

LF

/

~

LF

4--

(b) Dual amplifier connectio,:,

Figu.re 2-4. Equivalent four-wire repeater configurations.

Chap. 2

Introduction To Transmission

31

and (3) multiplexing equipment which combines, at the system input,
and separates, at the system output, the various signals sent through
the system. To achieve efficient equipment packaging, the modulating
and multiplexing equipment are usually combined. Together these
three major parts provide transmission channels having fixed gain,
acceptably low noise and distortion, and high velocity of propagation.

High-Frequency line Equipment

To provide a broadband channel, high-frequency line equipment
must perform a number of functions which differ depending on the
type of system. The basic function found in all systems is that of
amplification to compensate for losses in the medium between repeater
points. Such compensation may require the gain to be a nonflat
function of frequency and, as such, it is often considered as the first
step in equalization.
In analog coaxial cable systems, amplification is the only primary
function of the high-frequency line equipment. Other functions, such
as regulation to maintain constant the overall system gain in the
presence of temperature changes, and equalization to compensate
for small deviations in the transmission response, are also provided,
but for present purposes they may be regarded as secondary. Another
secondary function is that of protection line switching; in the event
of failure or for line maintenance, service may be switched automatically or manually to a spare line.
Another important function of the line equipment of some shorthaul cable systems is frequency frogging, whereby the signal is
modulated alternately between two frequency bands at each repeater.
This process is required to control systematic impairments (equalization) that arise due to the transmission response of the medium
and to liniit unwanted crosstalk paths.
The repeaters in the high-frequency line equipment in microwave
radio systems also provide gain as their primary function. Secondary
functions include modulation to translate the signal from high radio
frequencies to intermediate or baseband frequencies (where designs
of amplifiers are more tractable), frequency frogging between radio

32

Background

Vol. 1

frequency bands, and high-speed switching to provide alternate paths
for the signals in order to overcome the effects of fading in the
medium (the atmosphere) or to overcome the effects of equipment
failure.
In the high-frequency line equipment of digital systems there are
two primary functions. In addition to providing gain, a digital
repeater regenerates the transmitted pulses and reshapes them for
transmission to the next repeater. The regeneration process must
also include a timing function so that the pulses are transmitted
in correct time relationship to one another.

Modulating Equipment

Input signals to a carrier system must be processed to make them
suitable for transmission over the line equipment. The processing is
usually referred to as modulation. There are several forms of modulation, and they may be used singly or in combination according to
the needs of the system.
The process involves modifying the signal in some reversible
manner to prepare it for combining with other signals or for transmission over the high-frequency line or both. This may be accomplished by varying (modulating) a carrier in amplitude or frequency
in accordance with the amplitude and frequency variations of the
input signal (sometimes called the baseband signal); or the input
signal, regarded as a continuous wave, may be sampled in time and
then coded into a stream of pulses as is done in digital transmission
systems.

Multiplex Equipment

Multiplexing means the combining of multiple signals for simultaneous transmission over a common medium. The simplest form
of multiplexing might be called space division multiplexing. It occurs
when many signals are transmitted over separate pairs of wires all
in the same cable. The term is usually applied, however, to the
two categories called frequency division multiplex and time division
mUltiplex.

Chap. 2

Introduction to Transmission

33

If in a frequency division multiplex (FDM) system a number of
signals modulate carriers at some high frequencies, they may be
transmitted simultaneously over a common medium pr~>vided (1)
the band of each signal covers a part of the broadband spectrum of
the high-frequency line equipment different from -all other modulated signals and (2) the total bandwidth does not exceed that of the
high-frequency line equipment. Such signals are combined in electrical
networks in the transmitting terminal of the system and are separated
by frequency-selective networks at the receiving terminal.
In a time division multiplex (TDM) system, the pulses, which are
formed for different signals in the modulating equipment, are interspersed in a regular time relationship at the transmitting terminal.
Timing pulses, transmitted with the signal information, permit the
operation and control of gate circuits at the receiving terminal. These
circuits separate the signals from one another so that they may be
processed, or demodulated, individually at the receiving terminal of
the system.
2-5

ANCILLARY EQUIPMENT AND FUNCTIONS

Included in the transmission plant are a large number of equipment items and operating techniques that have been developed so
that transmission and operating requirements may be met more
economically. Among these are circuits such as compandors and echo
suppressors, operating techniques such as frogging, and complete
switching/transmission systems that employ time assignment speech
interpolation techniques.
The word compandor is made up of syllables taken from the words
COMpressor and exPANDOR. The performance of some carrier systems is improved, especially for speech signals, by the- use of these
devices. At the transmitting terminals of a telephone circuit, speech
signal amplitudes are compressed into a narrower than normal range
and then restored by the expandor at the receiving terminal. The result is a significant reduction of noise during periods of small signal
transmission and during quiet intervals. These are the periods when
noise is most objectionable to the telephone user.
In addition to compensating for losses incurred in the medium, the
design of telephone trunks involves dealing with and overcoming

34

Background

Vol. 1

various other impairments suffered in the course of transmission. One
such impairment is echo. If a trunk is so designed that the likelihood
of a disturbing echo is high, it is often equipped with an echo suppressor. This device acts as a pair of voice-operated switches; while
one subscriber is talking, the echo suppressor inserts high loss in the
opposite direction of transmission to attenuate the echo before it is
returned to the speaker.
Two types are used, full and split. In the full echo suppressor, the
voice-operated switches and echo attenuation circuits for both directions of transmission are located at one end of the trunk. In the split
echo suppressor, the circuitry is split between the two ends of the
four-wire trunk.
The performance of transmission systems is often improved by
some kind of frogging, a term adopted from the railroad industry
where a frog is a special section of rail used to cross one track over
another. In transmission, some impairments may accumulate due to
channels being in close relationship to one another. These relationships and the impairments can be altered significantly by frogging
in space (by changing the medium or by reversing or transposing
wire positions) or by frequency frogging (changing the relative positions of channels in a common spectrum). Both space and frequency
frogging techniques are used in telephone practice.
A Time Assignment Speech Interpolation (TASI) system is used
to increase the efficiency of bandwidth utilization on some transmission systems. It operates as a high-speed switching system to allow
a number of talkers to share a smaller number of trunks on the highfrequency line. The switches are voice-operated and allow a channel
in the transmission system to be taken from a speaker during breaks
in his conversation. These breaks occur during periods that a user is
listening, rather than talking, and during other pauses in normal
conversation.

REFERENCES

1. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N. C.: Western Electric
Company, Inc., 1970), Chapter 29.

Telecommunications
Transmission
Engineering

Section 2
Elements oj Transmission Analysis
In this section of the book a number of technical subjects are
treated in a manner designed to acquaint the reader with fundamental
principles of transmission analysis, which have application to transmission system design, operation, and planning. The subjects are
covered in a series of nine chapters.
While the book has been written for persons with an electrical
engineering background, it must be appreciated that each of the
subjects covered in this section has been worthy of entire textbooks
at both the undergraduate and graduate levels of study. It has been
impossible, therefore, to discuss most of these subj ects without using
a higher level of mathematics than can normally be assumed for
second or third year undergraduate students. For the most part,
the mathematics used are presented without apology, without proof,
and without thorough mathematical development that might satisfy
a mathematician. For additional background information, the inquisitive reader is referred to the literature listed at the end of
each cha pter.
Chapter 3 provides a transition from the "Background" section
of the book to the more theoretical subjects to follow. Some terminology is defined, and justification for the use of logarithmic units in
transmission work is presented. The concept of transmission level
points is discussed, and measurements of certain types of signals
and interferences are described.
Chapters 4 and 5 cover the related subjects of "Four-Terminal
Linear Networks" and "Transmission Line Theory." The material
in these chapters includes discussions of the basic Ohm's and Kirchoff's laws and their application; the analysis of networks and their
interactions, impedance relationships, return loss and reflections; and
transformer and hybrid coil theory and applications. Transmission
lines are treated in terms of equivalent circuits, characteristic impedance, primary electrical constants, velocity of propagation, and
loading.
35

36

Elements of Transmission Analysis

Vol. 1

Chapter 6, on wave analysis, is presented in order to increase the
reader's understanding of the Fourier series and Fourier transform.
This permits a more general understanding of time-domain and
frequency-domain relationships between signals and transmission
channels.
Chapter 7 covers negative feedback amplifiers from the points-ofview of how design limitations and compromises are made to
accomplish design objectives and how these objectives are related to
the performance of transmission systems in the field. The principal
benefits of feedback are discussed and means for providing feedback,
as well as the manner in which feedback mechanisms interact with
each other, are described.
In Chapter 8, a number of methods of signal processing are described in order to show how signals are modified for more efficient
transmission over existing media and then restored to their original
form for final transmission to the receiver. Various forms of amplitude, angle, and pulse modulation processes are covered.
"Probability and Statistics" is the subject of Chapter 9. The
application of this branch of science to transmission system design
and operation is among the most important aspects of transmssion
work. Without the application of probability and statistics, the Bell
System could not operate economically and perhaps could not operate
at all. The terminology and symbology of this branch of mathematics
are first described. Examples of statistical and probabilistic analyses
are given to illustrate how such techniques may be used to solve
transmission problems.
Chapter 10 covers a brief history and description of information
theory and its application in transmission engineering. Mathematical
expressions are presented to show the theoretically maximum channel
capacity for both ideal (distortion-free) channels and for typical
noisy channels. While the subj ect is of most concern to development
and research workers, an understanding of the principles should
enhance the work of the transmission engineer in the field.
Chapter 11, the last chapter of this section, consists of a presentation of the more important aspects of conducting engineering economy
studies. Transmission problems usually have more than one technically sound solution; the selection of one of several alternative lines
of action can often be best made on the basis of economic comparisons
of the alternatives.

Elements of Transmission Analysis

Chapter 3

Fundamentals of Transmission Theory
Transmission systems for communications are made up of a large
number of tandem-connected two-port (four-terminal) discrete networks and distributed networks such as transmission lines. In the
analysis of transmission systems, the properties of these networks
must be defined mathematically. Logarithmic units are commonly used
because the ratios of currents, voltages, and powers found in these
networks are large and awkard to manipulate. If the input-output
relations, or transfer characteristics, of the individual two-port networks are determined, the transfer characteristics of the tandem connection of several such networks can be found by taking a product of
the appropriate network transfer characteristics.
Transmission parameters of communication systems are measured
in a manner consistent with mathematical analysis techniques. Thus,
many types of test equipment are designed to measure signal and
interference amplitudes in logarithmic units (decibels). Other test
equipment types measure more conventional parameters, such as volts,
amperes, or milliwatts. Some test instruments are arranged to display
signals or interferences as functions of either time or frequency.
3-1

POWER AND VOLTAGE RELATIONS IN LINEAR CIRCUITS

Some of the mathematical relations necessary for the evaluation of
system performance can be explained in terms of the simple circuit
diagram of Figure 3-1. The transducer in this circuit is assumed to
be linear; i.e., the relation of the output signal to the input signal can
be described by a set of linear djiferential equations with constant
coefficients.
37

38

Elements of Transmission Analysis

Vol. 1

Energy is transferred from generator to load via the linear twoport transducer. The transducer
may
take on a wide variety of
Linear
two-port
forms, ranging from a simple pair
transducer
of wires to a complex assortment
of cables and amplifiers, modulators, filters, and other circuits. The
Generator ' - - - - - - - - - '
Load
four terminals are associated in
pairs; the pair connected to the
Figure 3-1. Terminated two-port circuit. generator is commonly called the
input port and the pair connected
to the load as the output port. If the energy at the output is greater
than at the input, the transducer is said to have gain. If the energy
is less at the output than at the input, the transducer is said to have
loss.
As illustrated in Figure 3-1, a generator may be characterized by
its open-circuit voltage, E', and its internal impedance, Ze, and a
load by its impedance, Z L. If the signal produced by the generator is
periodic, it may be represented by a Fourier series, V == VI + V 2 • • • •
Vk + ... V n , each term of which has the form

+

(3-1)

or, more conveniently,
(3-2)
In Equations (3-1) and (3-2), the subscript k represents the lcth
term of the Fourier series, V k represents its instantaneous voltage,
and Ek represents its peak voltage. The input-output relations of the
transducer are not dependent on the presence or absence of other
similar terms in the series nor of their magnitudes. The F'Ourier series
signal representation is thus convenient for this type of analysis.
For example, if the generator voltage of Figure 3-1 is a singlefrequency signal represented by
(3-3)

Fundamentals of Transmission Theory

Chap. 3

39

the ratio of V 1 to V 2 is given by

(3-4a)
Where the radian frequency, w, is the same for E1 and E2 (generally
true except for modulators), this equation may be written
(3-4b)
As mentioned above, the ratios encountered in telephone transmission
are often very large, and the numerical values involved are awkward.
Moreover, it is frequently necessary to form the products of several
ratios in order to express the gain or loss of a network or a tandem
connection of networks. The expression and manipulation of voltage
or power ratios are simplified by the use of logarithmic units. The
natural logarithm (In) of the ratio of Equation (3-4b) is a complex
number.

The real and imaginary parts of Equation (3-5) are uniquely
identifiable, which is to say
a

== In

f3

== 4>1 - 4>2, the phase constant.

(E 1/E 2 ) , the attenuation constant, }
(3-6)

and

When this measure of voltage (or current) ratio is used, a is said
to be expressed in nepers and f3 in radians. The term neper is an
adaptation of Napier, the name of the Scottish mathematician credited
with the invention of natural logarithms.

The Decibel

The logarithmic unit of signal ratio which now finds wide
acceptance is the decibel (dB). The decibel is equal to 0.1 bel, a unit
named for Alexander Graham Bell whose investigations of the

40

Vol. 1

Elements of Transmission Analysis

human ear revealed its logarithmic response. Strictly speaking, the
decibel is defined only for power ratios; however, as a matter of
common usage, voltage or current ratios also are expressed in
decibels. The precautions required to avoid misunderstanding of
such usage are developed in the following.
If two powers, PI and P2, are expressed in the same units (watts,
microwatts, etc.), then their ratio is a dimensionless quantity, and
as a matter of definition
D

== 10 log

(P1/P2)

dB

(3-7)

where log denotes logarithm to the base 10, and D expresses the
relative magnitude of the two powers in decibels. If an arbitrary
power is represented by po, then

D == 10 log (PI/PO) - 10 log (Pz/Po)

dB.

(3-8)

Each of the terms on the right of Equation (3-8) represents a power
ratio expressed in dB, and their difference is a measure of the relative
magnitudes of P1 and P2. Thus, the value of this difference is independent of the value assigned to po. However, it is often convenient
to use a value of one milliwatt for po. The terms 10 log (p';po) and
10 log (Pz/Po) are then expressions of power (PI or pz) relative to
one milliwatt, abbreviated dBm. Note, however, that their difference
is in dB, not dBm. In short, Equation (3-7) is a measure of the
difference in dB between P1 and P2. Note that nepers and decibels
may be related by the expression nepers/dB == 20 log 2.718 == 8.686.
This relationship is derived from the definitions of N aperian and
common logarithms.
As mentioned above, voltage and current ratios are also often
expressed in decibels as a matter of common usage. Such relationships are simple and direct when the impedances are equal at the
points where the voltages or currents are measured. If the impedances
are not equal, errors may be introduced unless care is taken to use
appropriate correction factors as explained below.
If there is an rms drop of e volts across a complex impedance
(Z
R
jX ohms) as a result of an rms current of i amperes

==

+

Chap. 3

Fundamentals of Transmission Theory

41

flowing through the impedance, the power dissipated in the impedance
may be written
watts.

(3-9)

The rms voltage and rms current are related by Ohm's law, discussed
in Chapter 4, in such a way that i = ell Z I. By substituting this
value in Equation (3-9) and expanding 1 Z 12 , it can be shown that
the power dissipated may also be written
watts.

(3-10)

Using appropriate subscripts to indicate two different measurements, the value of p from Equation (3-9) may be substituted in
Equation (3-7) to yield

dB.

(3-11)

Similarly, the value of p from Equation (3-10) may be substituted
in Equation (3-7). This gives

(3-12)

The terms beyond 20 log (i 1/i2) and 20 log (el/e2) in Equations
(3-11) and (3-12) give rise to serious error unless they are included
when expressing voltage and current ratios in decibels except when
the impedances Z 1 and Z2 are equal. The extent of these errors may
best be illustrated by some simple examples.

42

Elements of Transmission Analysis

Vol. 1

Example 3-1:
Let
PI == 2 m W == 0.002 watt,
'P2 == 1 mW == 0.001 watt.

Then, from Equation (3-7)

D == 10 log (Pljp2) == 10 log 2 == 3 dB.
Let
Rl == 10 ohms, R2 == 10 ohms, Xl == 10 ohms, X 2 == 10 ohms.

Then, from Equation (3-9)

il

(pl/Rd

1/2

== (0.002/10) 1/2 == 0.014 Amp

~

(P2/R2 )

1/2

== (0.001/10) 1/2 == 0.01 Amp

and from Ohm's law
el ==

il

I Zl I == 0.014 V 102 + 102 == 0.2 volt

~

i2

I Z2 I == 0.01 V 102 + 102 == 0.14 volt.

==

From Equation (3-11)

+ 10 log (R jR2)
== 20 log (0.014/0.01) + 10 log 1

D == 20 log

(i1/~)

1

== 3 dB.
From Equation (3-12)

D == 20 log (et!e2) - 10 log (R 1 jR2 )

(1

-

10 log (1

+ XX 2jR
jR
+
2
12

12)
2)

2

== 20 log (0.2/0.14) - 10 log 1 - 10 log 1
== 3 dB.
Thus, no error results from computing the current or voltage
differences in dB simply by taking 20 log of the current or voltage
ratios. This is because the impedances Zl and Z2 are equal and all
terms after the first in Equations (3-11) and (3-12) reduce to zero.

Chap. 3

43

Fundamentals of Transmission Theory

Example 3-2:
In this example, the assumption is again
P1
P2

==
==

2 mW

== 0.002 watt
1 m W == 0.001 watt.

==

10 log (P1/P2)

Then
D

Now, assume R1

== 10 log 2 == 3 dB.

== 10 ohms, Rz == 20 ohms, and Xl == X 2 == o.

From Equation (3-9)
i1

iz

==
==

==
(pz/R 2) 1/2 ==

== 0.014 Amp
(0.001/20) 1/2 == 0.007 Amp.
(0.002/10) 1/2

(p1/Rd 1/2

From Ohm's law
e1
e2

== i1 IZ1 I == 0.014 X 10 == 0.14 volt
== i2 I Zz I == 0.007 X 20 == 0.14 volt.

From Equation (3-11)
D

==

20 log (i 1/i2 )

~

20 log 2

==

6- 3

+ 10 log (Rt/R z)

+ 10 log (1/2)

== 3 dB.

From Equation (3-12)
D

== 20 log (e1/e2) - 10 log
== 20 log 1 - 10 log (1/2)
== 0 + 3 + 0 == 3 dB.

(Rt/R 2 )

(1

-

10 log (1

+ XX12/R12)
+
2/R 2)
z
2

- 10 log 1

Once again the three expressions for D give the same answer, 3 dB.
Note, however, that in this example significant errors would occur
if D were computed for current or voltage ratios without concern

Elements of Transmission Analysis

Vol. 1

for the impedance of the circuits. In the case of the current ratio,
the answer would have been 6 dB; in the case of the voltage ratio,
the answer would have been 0 dB.

Example 3-3:
Once again, assume

Pl == 2 mW

== 0.002 watt

P2 == 1 m W == 0.001 watt.

Then

D == 10 log (Pt/P2) == 10 log 2 == 3 dB.
Now, assume RI == 10 ohms, R2 == 20 ohms, Xl == 20 ohms, and
X 2 == 10 ohms.
From Equation (3-9)

== 0.014 Amp

it

(P1/R 1) 1/2 == (0.002/10) 1/2

~.

(P2/R 2)1/2 == (0.001/20) 1/2 == 0.007 Amp.

From Ohm's law
el

==

e2 ==

I Zl I == 0.014 V 102 + 202 == 0.31 volt
2
2
i2 I Z2 I == 0.007 V 20 + 10 == 0.16 volt.
i1

Then, from Equation (3:"'11)

D == 20 log (i1/iz)
== 20 log 2
~ 6-

+ 10 log (R1/R2)

+ 10 log

(1/2)

3== 3 dB.

From Equation (3-12)
(1
D' == 20 log (e1/ e2) - 10 log (R 1/R2) -10 log (1

== 20 log 2 - 10 log (1/2)
== 6 + 3 - 6 == 3 dB.,

- 10 log (5/1.25)

+ X12/R12)
+ X22/R22),

Chap. 3

Fundamentals of Transmission Theory

45

Again, as in Example 3-2, the value of D is 3 dB no. matter ho.W
co.mputed. Ho.wever, the importance o.f including the impedance
facto.rs in the computatioli is demonstrated.

loss, Delay, and Gain
There are several different methods of describing the transfer
characteristics of a two.-Po.rt netwo.rk. Such characteristics require
specificatio.n o.f fo.ur co.mplex quantities representing input and o.utput
relationships. However, in many cases where the network enviro.nment (such as so.urce and load impedances) is contro.lled, the transfer
can often be characterized more readily by one frequency-dependent
co.mplex num.ber describing the loss (or gain) and phase shift through
the netwo.rk. Several different means o.f expressing the transfer
characteristic have co.me into. use, each having merit fo.r a particular
set o.f circumstances and each depending in part o.n the definitio.n of
the network parameters invo.lved.
Insertion Loss, and Phase Shift. In the circuit of Figure 3-1, assume
that it has been determined that power, P2, is delivered to. the Io.ad,
Z L,' when the open-circuit voltageE', is applied. Next assume that
the two.-port network is remo.ved, the generato.r is' co.nnected directly
to. the load, and the power delivered to ZL is po. The difference in dB
between po andp2 is called the insertio.n 10.sS' o.f the two.-Po.rt netwo.rk;
i.e.,

Insertio.n loss

== 10 log

(PO/P2)

(3-13)

-dB.

If the impedances are matched thro.ughout, there is no. ambiguity

in expressing, insertion loss, as a vo.ltage o.r current ratio. The instantaneo.us vo.ltages, Vo and V 2" corresPo.nding respectively to po and
be expressed in terms of peak values,. Eo and E 2 • By pro.ceed-ingas in the development of Equatio.n (3-6), the insertio.n loss and
a definition of the insertion phaseshijt may be written:
P2~' may

InsertiQu·losg.= 20 log (Eo/E2) == 20 log (10/12 )
Insertion phase shift

= 57.3 (4;>0 -

where 2 are gi veIl in radians.

cp2)

dB;

degrees

(3-14.)
(3-15)

46

Elements of Transmission Analysis

Vol. 1

If the transducer of Figure 3-1 furnishes gain, then E2 > Eo, and
the insertion loss values are negative. In order to avoid talking about
negative loss, it is customary to write
Insertion gain

== 20 log

(E 2 /E o)

dB.

(3-16)

If complex gain is expressed in the form of Equation (3-5), the
phase shift will be the negative of the value found in Equation (3-15).
Unfortunately, there is no standard name which clearly distinguishes
between the phase shift calculated from a loss ratio and that calculated from a gain ratio. The ambiguity is entirely a matter of
algebraic sign and can always be resolved by observing the effect of
substituting a shunt capacitor for the transducer. This gives a negative sign to the value of CP2 and a positive change in the phase of
Equation (3-15).
Phase and Envelope Delay. The phase delay and envelope delay of a
circuit are defined as
~""'-'''''''''''"

;,

Phase delay

== f3 /(1)

~~J:l~~!91?~_~~1;)._~ . " ~!!!~ .~
where f3 is in radians, (1) is in radians per second, and delay is therefore expressed in seconds. In accordance with the sign convention
adopted previously, both the phase and the envelope delay of an
"all-pass" network are positive at all finite frequencies. The above
expressions show that the .enyelQp.~.~~Jay.jsth~ rate. Qf .ch~.n.J~~~, SlJ.'
slope! o:f th~pp~~~. (~~I~ycuJ·ye. If the phase del~y is linear .oyer t.be
~f~e~~ncy band of interest, the enveIop'e'delay is a constant ov.,er
that band .
......................

,., ".~I

For cables or similar transmission media, the phase shift is usually
quoted ,lnx~q.!~n~h.,I!~:r, . mile. In this case, IJhas_~,~l~~y,~ ..~!!~,~!l.y.e~o:Qe
delays are expressed in ~,~~QpdS,.Jl~r.rni1e. Their reci procal~ are called
VllJJ&.e.. . J.l.cJ2.Q!ty and G;;;1!P velocity,,'" ~~spectivelY;-ancf"the' units are
miles ~er second. ,~. ".".,--~ ..,,- . ,~ .. ',.,," , "..
."
.- - , .
Available Gain. The maximum power available from a source of
internal impedance, ZG, is obtained when the load connected to its
terminals is equal to its conjugate, ZG~ i.e., if

== RG + jXG }
Z: == RG - jXG.
ZG

and

(3-17)

Chap. 3

Fundamentals of Transmission Theory

47

It should be noted that maximizing available power is not necessarily the optimum relationship because, when conjugate impedances
are interconnected, large reflections occur. As a result, other impedance relationships are preferable. For an open-circuit generator
voltage having an rms value, e, the maximum available power is
PaC

== e 2 / 4R G•

(3-18)

The power actually delivered to Z L in Figure 3-1 is also maximized
if the output impedance of the transducer is conjugate to ZI,.
Designating this power as Pa2 leads to a definition of available gain,
ga, as
ga

== 10 log (Pa2/Pac).

(3-19)

Transducer Gain. Ordinarily the impedances do not meet the conjugacy requirements, and it is necessary to define the transducer
gain, gt, of the two-port circuit as
gt

== 10 log (PLjPaG)

(3-20)

where PL is the power actually delivered to the load. Transducer
gain is dependent on load impedance and can never exceed available
gain. Transducer gain is equal to available gain only when the load
impedance is equal to the conjugate of the network output impedance.
Power Gain. Finally, power gain, gp, is defined as
(3-21)

where Pl is the power actually delivered to the input port of the
transducer. The power gain is equal to the transducer gain of a
network when the input impedance of the network is equal to the
conjugate of the source impedance. The power gain is equal to the
insertion gain of the network when the input impedance of the network is equal to the load impedance connected to the output of the
network.

48

3-2

Elements of Transmission Analysis

Vol. 1

TRANSMISSION LEVEL POINT

In designing transmission circuits and laying them out for operation and maintenance, it is necessary to know the signal amplitude
at various points in the system. These values can be determined
conveniently by use of the transmission level point concept.

The transmission level at any point in a transmission circuit
or s'ystem is the ratio, expressed in decibels, of the power of
a signal at that point to the power of the same signal at
a reference point called the zero transmission level point
(0 TLP).
Thus, any point in a transmission circuit or system may be referred
to as a transmission level point. Such a point is usually designated
as a -x dB TLP, where x is the designed loss from the 0 TLP to
that point. Since the losses of transmission facilities and circuits tend
to vary with frequency, the TLP is specified for designated frequencies. For voiceband circuits, this frequency is usually 1000 Hz.
For analog carrier systems, the frequency in the carrier band must
be specified.
The TLP concept is convenient because it enables circuit losses
or gains to be quickly and accurately determined by finding the difference between the transmission level point values at the points of interest. This principle may be exten~ed from relatively simple circuits,
such as message trunks, to very complex broadband transmission
systems where the TLP values often vary with frequency across the
carrier band.
The transmission level point concept is also a convenience in that
signals and various forms of interference can easily be expressed in
values referred to the same transmission level point. This facilitates
the addition of interference amplitudes, the expression of signal-tonoise ratios, and the relation of performance to objectives in system
evaluation. These important advantages are apparent where various
types of signals and interferences are involved.
Transmission level points are applied within the switched message
network and special services networks. Similar concepts are applied
to wideband services such as PICTUREPHONE, television, and wideband data signal transmission. The channels used for these services
are g,iven specially-defined transmission reference points.

Chap. 3

Fundamentals of Transmission Theory

49

Confusion often arises because the word level is used (properly
and improperly) in so many ways. Frequent references may be found
to such things as power level, voltage level, signal level, or speech
level. To add to the confusion, the word level is often used interchangeably with the word power. Here, level is generally used only
as a part of the· phrase transmission level point. Signal power and
voltage are referred to in appropriate units such as watts, milliwatts,
dBm, volts, or dBV.
A troublesome correlation exists between transmission level point
and power. When a test signal of the correct frequency is applied to
a properly adjusted circuit at a power in dBm that corresponds
numerically with the TLP at which it is applied, the test signal power
measured at any other TLP in the circuit corresponds numerically
with the designated TLP value. Careless use of terminology often
leads to referring to a TLP as the x dBm level point. It cannot be
stressed too strongly that this is improper terminology even if it
happens that a test signal of x dBm is measured at the x dB
TLP. This correlation is unfortunate in that it has led to some confusion. On the other hand, when properly used, TLPs simplify loss
computations.
While 0 T LP is used in this book as the abbreviation for the reference transmission level point, it should be pointed out that severa]
other forms of terminology are sometimes used elsewhere. These include zero level, zero-level point, O-dB point, O-dB TL, and 0 SL (SL
for system level) .

Comr:non1y Used TLPs
Application of the transmission level point concept must begin
with the choice of a common datum or reference point and the
arbitrary assignment of O-dB transmission level to that point. Other
transmiss,ion level points in the trunk or system are then related
to the reference point by the number of dB of gain from the reference point to the point of interest. If (in a properly adjusted circuit)
a signal of x dBm is applied or measured at the reference point and
if that signal is measured as y dBm at the point of interest, the
point of interest is designated as the (y-x) dB transmission level
point.

50

Elements of Transmission Analysis

Vol. 1

The O-dB transmission level point ( 0 TLP) is so defined as a
matter of convenience and uniformity. It would be convenient also
to have the 0 TLP available as an access point for connecting probes
and measuring equipment. However, there is no requirement that
such an access point be available and, in fact, as a result of changes
in circuit arrangements resulting from changing objectives, the
o TLP is seldom available physically in the toll plant.
()r!gjn.,alJy, the 0 TLP was conveniently defined at the transmitting
of a tolJ switchbo~rd. Intertoll trunks were equipped at each
end with 4-dB pads which could be switched in or out of the circuit
to suit best the needs of a particular application. As technology improved and the need for better performance increased, these pads
were reduced to 2 dB; later, under the via net loss (VNL) design
plan, they were eliminated entirely from the intertoll trunks. The loss
corresponding to that of the pads is now assigned to the toll connecting trunks, two of which must be used in each toll connection.
j~~k

With these changes in intertoll trunk designs, it would have been
possible to redefine the reference transmission level point. However,
this would have resulted in changing all transmission level point
values. It was instead deemed desirable to maintain the original
o TLP concept as well as other important transmission level points.
As a result, the o-!!tgoing side of the switch to which an intertoll
trunk is cOIlIlect~d is, designated a -2 q.13 TLP. aJl~l Ule outgoing.side
J)'( .the switch at which a local area trunk is terminated is defined ~s
OTLP.
In the layout of four-wire trunks, a patch bay, called the four-wire
patch bay, is usually provided to facilitate test, maintenance, and circuit rearrangements between the trunks and the switching machine
terminations. Transmission level points at these four-wire patch bays
have been standardized for all four-wire trunks. On the transmitting
side the TLP is -16 dB, and on the receiving side the TLP is +7 dB.
Thus, a four-wire trunk, whether derived from voice-frequency or
carrier facilities, must be designed to have 23-dB gain between
four-wire patch bays. These standard transmission level points are
necessary to permit flexible telephone plant administration.
In four-wire circuits, the TLP concept is easily understood and
applied because each transmission path has only one direction of

Chap. 3

Fundamentals of Transmission Theory

51

transmission. In two-wire circuits, however, confusion or ambiguity
may be introduced by the fact that a single point may be properly
designated as two different TLPs, each depending on the assumed
direction of transmission.
Illustrative Applications of TlP

The transmission level point concept is applied to an individual
trunk as illustrated in Figure 3-2. The circuit elements within each
trunk are interconnected by design to produce predetermined gains
and losses so that each point in the trunk may be assigned a transmission level value. Some of the important transmission level points
discussed earlier and the assignment of transmission level point values
within a toll trunk are illustrated in the figure.
Starting in the upper left corner of the diagram, the outgoing side
of the switch is designated as the -2 dB TLP. As the circuit is
followed from left to right, the office equipment transforms the circuit
from two-wire to four-wire. The diagram shows an office loss of
14 dB so that, at the input to the four-wire trunk (MOD IN), the
TLP value is -16 dB; i.e., the input to the four-wire trunk is a
-16 dB TLP. As the connection is traced toward the right, the trunk
between office A and office B provides +23 dB of gain so that the
output of the trunk (DEMOn OUT) is a +7 dB TLP. The office
equipment has 11 dB of loss to effect a -4 dB TLP at the office side
of the first switch encountered in office B.
If the circuit is followed from right to left, similar losses are
observed and appropriate transmission level points are shown along
the circuit. Note that at closely related points (four-wire trunk input
and output), the transmission level points are quite different for
the two directions of transmission. In the two-wire circuits, the same
point (electrically), e.g., the switch at the end of the trunk, has two
values of TLP, -2 dB for one direction and -4 dB for the other.
Figure 3-3 shows a built-up connection of three toll trunks and
illustrates the fact that the transmission level point concept is applied
to an individual trunk and not to the built-up connection. If the
circuit is traced from left to right, the TLP is shown as -2 dB at
office A and -4 dB at office B. Each of the interconnected trunks
from A to n is shown with specific TLPs, -2 dB at the left and

I

TlP(dB>-2 -

I

L... (dB)

I
II
I

r--I

I

-

-

-

14

I

-OffkeA I

-=16- -

"I

...

I
Office

.

equipment

Termmal

I.. _____ I..

~

I
I

11

--t7_ _
.
__

-I

I - rnre'ctio;- I transmiSSIon
of, .

I
-.J

-

I

-23

I
I

1 ..- - - - -

Switch

L

Ioffi;8 -

-=4--,

+7 - - -, - -

"I

11

I

---+j

I

1

.

I
I

1

Office

Termmal

equipment

1

I

Switch

I.

I

23

-

'

14

L _____-~ ____'

01

"l

I

Loss (dB)

m
Ci"
3

I g

~2 .!!!(dB)-.J

Cit

a.
Figure 3-2. TlPs in four-wire toll 'trunk terminated in two-wire switching offices.

'"""""

Q

:l

en

3

TlP (dB) -2

.~.

-6 -2

Loss (dB) ,..

~t..

4

-5
5

.1..

3

_I

o·o

»
:l

rI

Q

~
Cit·

I

I

1

I

L_~e~

_-1

L __

1

Office8

L __

Office"':"' _ _

J

Figure 3-3. TlPs in a tandem connection of toll trunks-one direction of trcmsmission.

L _

~ce~_.J

<

~

-

Chap. 3

Fundamentals of Transmission Theory

53

- (2 + L) dB at the right, where L is the trunk loss in dB. That is,
transmission level points are redefined for each trunk in the built-up
connection. Thus, there is no one unique 0 TLP for the Bell System.
Each trunk has a defined 0 TLP which often is a reference that does
not exist in fact.
By common consent and usage, transmission level point values are
found by determining the gain or loss between TLPs at 1000 Hz in
the circuit of interest. The use of modulators in the terminal equipment of frequency division multiplex carrier systems produces a shift
of frequency from 1000 Hz in the original circuit to some higher
frequency in the carrier system. The TLP value can be determined
at the higher frequency and related to the 1000-Hz value in the
original circuit to obtain the TLP in the carrier system.
If the value of a transmission level point is not known, it can be
determined by measurement. The process depends on the direction
of transmission and on having proper values of pad losses and amplifier gains in the circuit between a known TLP, A, and the TLP to
be determined, X. If the unknown is to be established by transmitting
from A to X, a 1000-Hz signal (or equivalent in a carrier channel)
may be applied at A and measured at A and X. The TLP at X is
determined by subtracting from the TLP value at A the loss (in dB)
from A to X. If the TLP at X is to be determined by transmitting
from X to A, the value at X is the value of the TLP at A plus the
loss (in dB) from X to A.
In order to avoid overloading transmission systems, the applied
test signal power (in dBm) should be at least 10 dB below the TLP
value at any point. Since signal power is often expressed in terms
of its value at 0 TLP, the unit dBmO is used as an abbreviation for
"dBm at 0 TLP."
3-3

SIGNAL AND NOISE MEASUREMENT

The TLP concept is valuable in system design, op'eration, and
maintenance in that it provides a means of calculating signal and
interference amplitudes at given points in a system asweU as
the gains or losses between TLPs; nevertheless, operating syste~s
must be checked at times by actual measurement to see that signal
or interference amplitudes are being maintained at the expected, or

54

Elements of Transmission Analysis

Vol. 1

calculated, values. When there is excessive gain or loss in a system,
measurement is also a means of locating trouble.
In the telephone system there are complex signals and noises to be
measured. Simple instruments are inadequate, particularly since they
do not take into account any of the subjective factors which determine
the final evaluation of a telephone circuit. Both the instruments and
units of measure used in telephony for signal and noise measurements
must be adapted to the special needs involved.
Since telephone circuits operate with signal and interference powers
which rarely are as large as 0.1 watt and which may be lower than
10- 12 watt, the use of the watt as a unit of measurement is awkward.
A more convenient unit is the milliwatt, or 10- 3 watt. An exception
is in rad,io transmitter work, where output power is frequently measured in watts.
Many other types of equipment are used for evaluating transmission quality and facilitating maintenance procedures. These include
oscillators, ammeters, voltmeters, and transmission measuring sets.
The parameters measured, the units of measurement, and the techniques involved are all important aspects of transmission engineering.
The cathode ray oscilloscope is one of the most powerful of these
specialized instruments in that the parameters of interest can be
displayed for study and analysis.

Volume
The amplitude of a periodic signal can be characterized by any of
four related values: the rms, the peak, the peak-to-peak, or the average. The choice depends upon the particular. purpose for which the
information is required. It is more difficult to deal with non-periodic
signals such as the speech signals transmitted over telephone circuits
where the rms, peak, peak-to-peak, and average values and the ratio
of one to another are all irregular functions of time, so that one
number cannot easily specify any of them.
Regardless of the difficulty of the problem, the amplitude of the
telephone signal must be measured and characterized in some fashion
that will be useful in designing and operating systems involving
electronic equipment and transmission media of various kinds. Signal
amplitudes must be adjusted to avoid overload and distortion, and

Chap. 3

Fundamentals of Transmission Theory

55

gain and loss must be measured. If none of the simple characterizations is adequate, a new one must be invented. The unit used for expressing speech signal amplitude is called the volume unit (vu). It
is an empirical kind of measure evolved initially to meet the needs
of AM radio broadcasting and is not definable by any precise mathematical formula. The volume is determined by reading a volume
indicator, called the vu meter, in a carefully specified fashion. *
The development of the vu meter was a joint project of the Bell
System and two large broadcasting networks. Its principal functions
are measuring signal amplitude to enable the user to avoid overload
and distortion, checking transmission gain and loss for the complex
signal, and indicating the relative loudness of the signal when
converted to sound.
The vu meter can be used equally well for all speech, whether male
or female. There is some difference between music and speech in this
respect, and so a different reading technique is used for each.
The meter scale is logarithmic, and the readings bear the same relationship to each other as do decibels; however, the scale units are
in vu, not in dB. The transient response (damping characteristic) of
the meter movement prevents the meter needle from registering very
short high-amplitude impulses such as those created by percussive
sounds in speech. A correlation between talker volume and long-term
average power and peak power can be established. Also, a vu meter
reading for a sinusodial signal delivered to a 600-ohm resistive
termination is numerically equal to the power in dBm delivered to
the termination. Such correlations are valuable, but the fact that they
exist should not be allowed to confuse the real definition of volume
and VUe Putting it as simply as possible, a -10 vu talker is one whose
signal is read on a calibrated volume indicator (by someone who
knows how) as -10 VUe It should be noted that the vu meter has a
flat frequency response over the audible range, and it is not frequency
weighted in any fashion. Some, but not all, meters calibrated in dB
can be used to read vu; however, the transient response of the meter
movement must meet certain carefully defined specifications as in
the vu meter.

*Objective measurements of speech signals are now possible [3, 4].

Elements of Transmission Analysis

56

Vol. 1

Noise

The measurement of telephone channel noise, like the measurement
of volume, is an effort to characterize a complex signal. The measurement is further complicated by an interest in how much it annoys the
telephone user rather than in the absolute power. Consider the requirements of a meter which can measure the subjective effects of
noise:
(1) The readings should take into consideration the fact that the
interfering effect of noise is a function of frequency as well
as of amplitude.
(2) When dissimilar noise components are present simultaneously,
the meter should combine them in the same manner as do the
ear and brain to measure the overall interfering effect.
(3) When different types of noise cause equal interference as
determined in subjective tests, use of the meter should give
equal readings.
The 3-type noise measuring set is essentially an electronic voltmeter
which meets these requirements, respectively, by incorporating (1)
frequency weighting, (2) a detector approximating an rms detectort
and (3) a transient response similar to that of the human ear.
The first of the requirements for noise measurement involves annoyance and the effect of noise on intelligibility. Since both are functions
of frequency, frequency weighting is included in the set. To determine
the weighting characteristic, annoyance was measured in the absence
of speech by adjusting the amplitude of a tone until it was as annoying as a reference 1000-Hz tone. This was done for many tones and
many observers, and the results are averaged and plotted. A similar
experiment was performed in the presence of speech at average received volume to determine the effect of noise on articulation. The
results of the two experiments were combined and smoothed, resulting
in the C-message weighting curve shown in Figure 3-4. The experiments were made with a 500-type telephone; therefore, the weighting
curve includes the frequency characteristic of this telephone as well
as the hearing of the average subscriber. The remainder of the telephone plant is assumed to provide transmission which is essentially
flat across the band of a voice channel. Therefore, the C-message

57

Fundamentals of Transmission Theory

Chap. 3
0

-10
Ii)
~

~

0

~

-20

Q)

IX

-30

-40
100

200

500

1000

2000

5000

Frequency (Hz)

Figure 3-4. C-message frequency weighting.

weighting is applicable to measurements made almost anywhere
except across the telephone receiver.
To illustrate the significance of the weighting curve of Figure 3-4,
a 200-Hz tone of given power is found to be 25 dB less disturbing to
a listener using a 500-type telephone than a 1000-Hz tone of the same
power. Hence, the weighting network incorporated in the noise meter
has 25 dB more loss at 200 Hz than at 1000 Hz.
Other weighting networks can be substituted in 3-type noise
measuring sets. For example, the 3 KC FLAT network may be used
to measure the power density of Gaussian noise. This network has
a nominal low-pass response down 3 dB at 3 kHz and rolls off at
12 dB per octave. The response to Gaussian noise is almost identical
to that of an ideal (sharp cutoff) 3-kHz low-pass filter.
The second factor affecting the measurement of the interfering
effect of noise involves the evaluation of simultaneous occurrences of
noise components at different frequencies and of different characteristics. Experimentally, narrow bands of noise were used in various
combinations. It was found that the closest agreement between the
judgment of the listener and the reading of the noise measuring set
was obtained when the noises were added on an rms, or power, basis.
Thus, for example, if two tones hav,ing equal interfering effect when

58

Elements of Transmission Analysis

Vol. 1

applied individually are applied simultaneously, the effect when both
are present is 3 dB worse than for each separately.
The third factor which affects the manner in which noise must be
measured is the transient response of the human ear. It has been
found that, for sounds shorter than 200 milliseconds, the human ear
does not fully appreciate the true power in the sound. For this reason
the meter on the noise measuring set (as well as the vu meter) is
designed to give a full indication on bursts of noise longer than
200 milliseconds. For shorter bursts, the meter indication decreases.
These three characteristics of the 3-type noise measuring setfrequency weighting, power addition, and transient response-essentially prescribe the way message circuit noise is measured for speech
signal transmission. This is not yet enough; a noise reference datum
and a scale of measurement must also be provided.
The chosen reference is 10- 12 watt, or -90 dBm. The scale marking is in decibels, and measurements are expressed in decibels above
reference noise (dBrn). A 1000-Hz tone at a power of -90 dBm gives
a O-dBrn reading regardless of which weighting network is used. For
all other measurements, the weighting must be specified. The unit
dBrnc is commonly used when readings are made using the C-message
weighting network.
As with dBm power readings, vu and dBrn readings may be taken
at any transmission level point and referred to O-dB TLP by subtracting the TLP value from the meter reading. Thus a typical noise
reading might be 25 dBrn at O-dB TLP, abbreviated 25 dBrnO.
Similarly, values of dBrnc referred to 0 TLP are identified as dBrncO.
Other noise measuring instruments have been designed to evaluate
the effects of noise on other types of signals or in other types of
channels.

Display Techniques
Among the many specialized measurements that are needed in the
evaluation of transmission circuits and signals are those taken from
displays of signal or interference amplitudes on the tube face of a
cathode ray oscilloscope. Two types of displays are commonly used.
One type shows ampHtude as a function of time and the other shows
amplitude as a function of frequency. These are referred to as timedomain and frequency-domain displays.

Fundamentals of Transmission Theory

Chap. 3

3-4

59

ADDITION OF POWER IN D8

The merits of expressing power and power ratios in dBm and dB,
respectively, have been demonstrated by the preceding discussions.
A difficulty arises, principally in noise and interference studies, when
it is necessary to find the sum of two or more powers that are given
in dBm. Although the necessary steps are straightforward (the values
must be converted to milliwatts, added, and then reconverted to dBm),
they are time consuming. Specifically, suppose powers PI dBm and
P 2 dBm are being dissipated in a circuit and it is desired to determine
the sum, also in dBm.
The expression for the sum of the two powers is
P

== PI + P2 milliwatts.

This may also be written
P

== PI

(1

+ P2/PI).

(3-22)

The sum and each of the individual powers may be expressed as P,.
PI, and P 2 dBm and the summing expression may be represented by
the shorthand notation

"+"

where P

==

P2
P == PI
10 log p, PI l~Og PI, and P 2 == 10 log P2.

Equation (3-22) may be written in logarithmic form as
10 log P == 10 log PI

+ 10 log (1 + P2/PI)

or
where Sp

==

10 log P == 10 log PI
1 + P2/Pl. Then,
P

where Sp

== 10 log Sp

== PI + Sp

+ 10 log Sp
dBm

(3-23)

dB.

It is convenient to assign the symbol PI to the larger of the two
powers to be added (to either, if they are equal) so that Sp lies in
the range of 1 < Sp < 2 and Sp is in the range of 0 < Sp < 3 dB. The
value of Sp is shown in Figure 3-5 as a function of the difference
between PI and P 2 in dB. Thus, the sum of two powers can be determined by first finding the value of PI - P2 , next estimating the
value of Sp from the figure, and then adding Sp to PI as in
Equation (3-23). It should be noted that this method may be applied

Vol. 1

Elements of Transmission Analysis

60
3.0

2.5

2.0

~
\

\

iii'

~

~

1.5

1.0

~'"~~
~

0.5

...............

0

o

2

6

8

r--- r---- ....

10

12

14

16

18

20

Figure 3-5. Power sum of two signals both expressed in dBm.

to any two powers, such as dBW or dBrnc, expressed in dB relative
to an absolute value.
In the foregoing, it is assumed that the two powers to be added
act independently and that the resultant is the linear sum of the two
components. Such an assumption is valid, for example, when two
sine waves of different frequencies or a sine wave and a band of
random noise are to be added. It is not true when two sine waves of
the same frequency are to be added. In this case, the two are said
to be coherent, the resultant power depends on the phase relationship between them, and the summing process must be treated
somewhat differently.
For two sine waves of the same frequency, the power sum may be
written as
P

==

(VPl

+ VP2 cos ,8) + (VP2 sin 8)
2'

2

milliwatts

where (J is the phase angle between the two sine waves. The above
equation may also be written
P

or

== PI + P2 + 2 VPIP2 cos 8
(3-24)

Chap. 3

Fundamentals of Transmission Theory

61

This expression may be converted to a logarithmic form similar to
Equation (3-23) and is then written
dBm
where Sv

(3-25)

== 10 log 8 v
== 10 log (1 + P2/Pl + 2 VP2/PI cos 6)

dB.

Of primary interest in noise and interference studies is the case
in which 6 == 0, i.e., the case representing in-phase addition of interferences. As in the earlier analysis, it is convenient to assign the
symbol PI to the larger of the two interference signals to be added
so that 8 v lies in the range 1 < 8 v < 4 and Sv is in the range
o < Sv < 6 dB. With this choice (6 == 0), the value of Sv is shown in
Figure 3-6 as a function of the difference between PI and P 2 in dB.
The sum for such in-phase addition may thus be found by determining PI - P 2, estimating the value of Sv from the figure, and then
adding Sv to PI as in Equation (3-25).
The subscripts P and v applied to Sp and Sv are used to denote
"power" and "voltage" addition as these processes are commonly
called. The shorthand notation used to represent in-phase addition is
usually written
a form analogous to that used earlier to represent "power" addition.
6

5

4

"" ""
~

~

~

~

~

~~
I

o

o

2

4

6

8

10

12

14

16

r-18

20

Pl-P2(dB)

Figure 3-6. Power sum of two in-phase signals both expressed in dBm.

62

Elements of Transmission Analysis

Vol. 1

REFERENCES

1. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N. C.: Western Electric
Company, Inc., 1970).

2. Cochran, W. T. and D. A. Lewinski. "A New Measuring Set for Message
Circuit Noise," Bell System Tech. J., Vol. 39 (July 1960).
3. Brady, P. T. "Statistical Basis for Objective Measurement of Speech Levels,"
Bell System Tech. J., Vol. 44 (Sept. 1965).
4. Brady, P. T. "Equivalent Peak Level: A Threshold-Independent SpeechLevel Measure," Journal of the Acoustical Society of America, Vol. 44 (Sept.
1968) .

Elements of Transmission Analysis

Chapter 4

Four-Terminal Linear Networks
The transmission of an electrical signal from transmitting to receiving terminal is accomplished by transferring energy from one
electrical network to the next until the receiving terminal is reached.
An understanding of the complete transmission process requires an
understanding of the general principles of linear alternating-current
networks and of how they interact when they are tandem-connected
to form a complete signal path from transmitter to receiver. Linear
networks are those whose output voltages or currents are directly
proportional to the -input voltages or currents. The networks may
or may not be bilateral.
An understanding of the mathematical properties of network impedances and their interactions is made easier by several basic
theorems. The analysis of transformers, series and parallel resonant
circuits, and electric wave filters are of special interest.
Network computations are approached differently depending on
whether the problem is one of analysis or synthesis. In analysis the
stimulus and the network are given, and the problem is to determine
the response of the network to the stimulus; i.e., the problem is to
determine the output given the input and the network configuration.
In synthesis the stimulus and response (input and output) are given,
and the problem is to determine the network configuration and component values that satisfy the given input-output relationships. Since
the synthesis process is of interest only to the network designer and
developer, the primary concern here is only with analysis; however,
there are references at the end of the chapter which describe some

63

Elements of Transmission Analysis

64

Vol. 1

of the increasingly sophisticated methods of both analysis and
synthesis that are now available.
In considering the layout and application of transmission circuits,
it is essential that basic limitations be recognized. It is also important
to recognize circumstances in which these limitations do or do not
apply and the corrective measures that may be appropriate to overcome the limitations in specific situations. These situations may be
as simple as connecting a telephone station set to its ,loop or as complex as changing the mode of operation of the message network so
that a trunk is added to a built-up connection covering thousands of
miles. In either case, judgements must be exercised as to the effects.
Lengthy and clumsy calculations, previously avoided by the use of
charts and nomographs, are now made simple and tractable by the use
of high-speed digital computers.
For many purposes in telephone transmission analysis, the performance of a circuit, a piece of equipment, or even a complete system
may be approximated over the voice range of frequencies by its
performance at one frequency. Such approximations are often made
by measuring performance at 1000 Hz. The procedure has the merit
of simplicity, especially in measuring transmission line loss, but it
neglects certain elements of the transmission process which must be
measured over the whole band of frequencies. No single frequency
can be fully representative of a complex electrical wave, nor can
transmission through a complex network be fully represented by
transmission at a single frequency.
4-1

THE BASIC LAWS

In the analysis of the usual electrical networks making up communications circuits. Ohm's and Kirchoff's laws are of fundamental importance. Certain other theorems which are of considerable assistance
in analyzing and characterizing networks and their performance have
been derived from these laws.
Ohm's Law

The current, I, which !lows through an impedance, Z ohms, is
equal to the voltage developed across the impedance divided by the
value of the impedance, or

I=E/Z

amperes.

(4-1)

Four-Terminal Linear Networks

Chap. 4

This law is illustrated in Figure 4-1
where E and I may be direct or
alternating voltages and currents
and where Z may be a simple resistor or a complex impedance involving resistance, inductance, and
ca paci tance.

65
I
---+

Z

Kirchoff's Laws

Law 1: At any point in a circuit, Figure 4-1. Simple series circuit conthere is as much current
taining an impedance, Z.
flowing to the point as
there is flowing away from it. For example, at point x in
Figure 4-2,
(4-2)

Law 2: In any closed electrical circuit, the algebraic (or vector)
sum of the electromotive forces (emf's) and the potential
drops is equal to zero. In Figure 4-2,

== 0,
E - ItZ A - I 2ZB == 0,
I~B - I3Zc == O.
E - ItZ A

and

-

The arrows in Figure 4-2 indicate
the assumed direction of current
flow. A battery is assumed to produce a voltage rise from the negative to the positive terminal. A
voltage due to current flowing
through an impedance is assumed
to be in the direction of positive to
negative corresponding to the assumed direction of current flow.
This accounts for the signs of the
terms in Equations (4-3).

I3Zc

I
x

ZB

+
13

Zc

Figure 4-2. Simple series-parallel
circuit.

66

Vol. 1

Elements of Transmission Analysis

r--------,
I

ZA

I

ZB

I

I
I

I

I

I
I
I
I
I
I
L ______ --1
(0) T network

r---- ----,

I

I

ZE

I
I

I
ZD

ZF

I
I
I
I

I
I
I

I

L ______ ---1
(b) 11' network

Figure 4-3. Equivalent networks.

ZL

Chap. 4
4-2

67

Four-Terminal Linear Networks

APPLICATION AND THEOREMS

The application of Ohm's and Kirchoff's laws to more complicated
circuits involves setting up simultaneous linear equ2.tions for solution.
This can be very laborious, and several network theorems have been
developed to expedite the process.

Equivalent Networks

From their configurations, two important types of networks are
called the T and 1T electrical networks. A three-element T structure
and a three-element 1T structure can be interchanged provided certain
relations exist between the elements of the two structures and
provided the impedances can be realized.
Figure 4-3 represents two forms of a circuit connecting a generator
of voltage E and impedance ZG to a receiver having impedance ZL.
If the impedances enclosed in the boxes are related by the relationships shown in Figure 4-4, one box may be substituted for the other
without affecting the voltages or currents in the circuit outside the
boxes.
This property of networks permits any three-terminal structure,
no matter how complex, to be reduced to a simple T. For example,
a 1T to T transformation permits converting the circuit in
Figure ~-5 (a) to that shown in Figure 4-5 (b). By combining Zc
T TO 1T

1T TO T

ZA

=

ZB =

Zc

=

ZDZE
ZD+ZE+ZF
ZEZF
ZD

+ ZE + ZF
ZFZD

ZD+ZE+ZF

ZD

=

ZE

=

ZF =

ZAZB+ZBZC+ZCZA
ZB
ZAZB+ZBZC+ZCZA
Zc
ZAZB+ZBZC+ZCZA

Figure 4-4. Equivalent network relationships.

ZA

68

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Elements of Transmission Analysis

with Zs and ZB with Z6 and making a second 1T to T transformation,
Figure 4-5 (b) can be reduced to the simple T shown in Figure 4-5 (c).
These relationships apply only to networks having three terminals.
Similar relations can be developed for four-terminal networks.
Figure 4-6 is a typical four-terminal network. If only the voltages
measured across terminals 2-2 are significant, the five impedances
in Figure 4-6 (a) can be replaced by the T structure in Figure 4-6 (b) .

ZA

Zs

ZE

ZB

Za
I

Z'E
Z'F

ZD

Zc

Z'F
Z'D

Zs
Zs

Z4

(0)

(b)
Z4

ZA

Z'A

Z'B

(c)

Figure 4-5. Successive simplification of networks by 1T to T transformations.

Chap. 4

Four-Terminal linear Networks

69
2

Zc

2

2

(b)

(0)

Figure 4-6. Equivalent four-terminal networks.

Thevenin's, or Pollard's, Theorem
For the purpose of simplifying calculations, an arrangement such
as that in Figure 4-7(a) may be considered as two networks with
one supplying energy to the other. The first of these networks is
then replaced by an equivalent simplified circuit consisting of an
emf and an impedance in series, as shown in Figure 4-7 (b) .
Thevenin's theorem gives the rules required for this simplification
as follows: The current in any impedance, ZL, connected to two
terminals of a network is the same as that resulting from connecting
ZL to a simple generator whose generated voltage is the open-circuit
voltage at the original terminals to which ZL was connected and
whose internal impedance is the impedance of the network looking

Z9

Zs

Z3

Z7

ZIO

]z,
ZL

Z4

Zs

Zll

(0)

Figure 4-7. Application of Thevenin's theorem.

(b)

70

Elements of Transmission Analysis

Vol. 1

back from those terminals with all generators in the original network
replaced by their internal impedances.
. For example, if the equivalent emf, E' in Figure 4-7 (b), is the opencircuit voltage at the terminals of Figure 4-7 (a) and if the equivalent
impedance, Z' of Figure 4-7 (b), is the impedance presented at the
terminals of Figure 4-7 (a) when E is made zero, the two circuits are
equivalent. Another way to compute Z' is to set it equal to the opencircuit voltage at the network terminals divided by the short-circuit
current at the terminals. Under these conditions the load draws the
same current as in the original connection.
Superposition Theorem

If a network has two or more generators, the current through any
component impedance is the sum of the currents obtained by considering the generators one at a time, each of the generators other
than the one under consideration being replaced by its internal
impedance.
Multigenerator networks can be solved by Kirchoff's laws, but their
solution by superposition requires less complicated mathematics. Perhaps of even greater importance is the fact that this theorem is a
useful tool for visualizing the currents in a circuit.
Before an example of the superposition theorem is given, it may
be beneficial to review the concepts of the internal impedance of a
generator. The open-circuit voltage of a battery is greater than the
voltage across its terminals when supplying current to a load. The
open-circuit voltage is a fixed value determined by the electrochemical
properties of the materials from which the battery is made. Under
load, the decrease in terminal voltage is due to the voltage drop
across the internal resistance of the battery. If it were possible to
construct a battery from materials that had no resistance, the battery
would have no internal resistance and no internal voltage drop. Since
there are no materials with infinite conductivity, every practical voltage source can be resolved into a voltage in series with an internal
resistance or impedance.
Perhaps the superposition theorem can be most easily explained
by working out a simple problem. In Figure 4-8 (a), which way
does the current flow in the lO-ohm resistor?

Chap. 4

Four-Terminal Linear Networks

71

r----,

r----'
8 ohms

6 ohms

+
RA = 2 ohms

RB =.4 ohms

EA = 30 volts

EB = 60 volts

+

I
I

I
L ___ .J

I

L ___

(0)

Bat A

Bat B

r----,

r---,

I

I
I

+--+

I
I

I
I

---.

2 amps

1 amp

I

1,

•I
I

I

RB

RA

amp

+

I
I
I

L ___

L ___ .J
Bat A

-

(c)

(b)

r---,

r---,
+
.4 amps

+
L ___ ...J

L ___ ..J
Bat A

(d)

Figure 4-8. Superposition theorem.

Bat B

Bat B

72

Vol. 1

Elements of Transmission Analysis

According to the theorem the currents caused by each battery
should be determined, in turn, with all other batteries replaced by
their internal resistances. The currents indicated in Figures 4-8 (b)
and 4-8(c) are computed by Ohm's law. The currents flowing in
the circuit with two batteries are the sum of these component
currents; of course, sum means algebraic sum (or vector sum if the
problem is ac). Currents flowing in opposite directions subtract.
The resultant currents are shown in Figure 4-8 (d), which shows
that the IO-ohm resistor carries one ampere in the upward direction.
The direction of the current in the IO-ohm resistor could have been
estimated by inspection, since the resistances are symmetrical and
the 60-volt battery produces the larger component of current. However, going through the arithmetic illustrates the application of the
theorem.
Compensation Theorem

Any linear impedance in a network
generator, one having zero internal
voltage at every instant is equal in
instantaneous voltage drop caused by
the replaced impedance.

may be replaced by an ideal
impedance, whose generated
amplitude and phase to the
the current flowing through

In Figure 4-9 (a), the impedance has been separated from the rest
of the network for consideration. The equations of Kirchoff's laws
determine the currents and voltages in all parts of the network.
According to the compensation theorem, these equations would not
be altered if the network is changed to that of Figure 4-9 (b) where
the generator voltage is the product of current I and impedance Z
from Figure 4-9 (a) .
I
--.

I

-----+

'"

>
~z

Network

~

Network
Same as in (a)

..,
(0)

(b)

Figure 4-9. Illustration of compensation theorem.

Chap. 4

4-3

Four-Terminal Linear Networks

73

NETWORK IMPEDANCE RELATIONSHIPS

The analysis of a four-terminal network and its interactions in
tandem connections is primarily related to the impedances of the
network itself and of its terminations. Relationships among these
impedances permit calculation of transmission effects (attenuation
and phase shift), return loss, echo (magnitude and delay), power
transfer, and stability. The networks may be relatively simple discrete
components, such as transformers or attenuators, or they may be
transmission lines, radio circuits, or carrier circuits, any of which
may have gain or loss.
Image Impedance

In a four-terminal network, such as that in Figure 4-10, impedances
Z 1 and Z2 may be found such that if a generator of impedance Z 1 is
connected between terminals 1-1 and impedance Z2 is connected as

a load between terminals 2-2, the impedances looking in both directions at 1-1 are equal and the impedances looking in both directions
at 2-2 are also equal. Impedances Zl and Z2 are called the image
impedances of the network.
The values of Zl and Z2 may be determined from Ohm's law and
the solution of two simultaneous equations. From inspection of
Figure 4-10, the two equations may be written as

Zl

== ZA +

+

(ZB
Z2)ZC
ZB+ZC+Z2

and

where ZA, ZB, and Zc are the impedances of the T-network equivalent
to the four-terminal network.
Solving for Z 1 and Z2 yields

and

Z2=~(

ZB+ZC ) (ZB+

Z~:~J.

74

Elements of Transmission Analysis

Vol. 1

r------------,
2

Zc

2

L ___________ .J

Figure 4- 10. Image termination of a four-terminal network.

Examination of the latter equations and Figure 4-10 reveals some
interesting relationships. The parenthetical expressions (ZA+ Zc)
and (ZB + Zc) are seen to be the impedances of the T network if
the impedances are computed, respectively, from terminals 1-1 with
terminals 2-2 open and from terminals 2-2 with terminals 1-1 open.
Zc) and ZB
(.ZAZC)/(ZA
Zc)
Similarly, ZA + (ZBZC)/(ZB
are the impedances at terminals 1-1 and 2-2 if the opposite pair of
terminals is short-circuited.

+

+

+

Thus, the image impedances of a four-terminal network are most
easily determined by measuring the open-circuit and short-circuit
impedances as above. Then,
Zl

== yZocZse

Z2

== yZ' ocZ'se

and

(4-4)
,

where

== impedance at 1-1 with 2-2 open
Z se == impedance at 1-1 with 2-2 short-circuited
Z'De == impedance at 2-2 with 1-1 open
Z'se == impedance at 2-2 with 1-1 short-circuited.
Zoe

(4-5)

Chap. 4

Four-Terminal Linear Networks

75

As shown previously, the conversion of any complex network to an
equivalent T network can be accomplished for any given frequency.
Thus, the processes described above permit the determination of the
image impedances of a network at any frequency.
Note that if the network is symmetrical, i.e., ZA == ZB, the image
impedances are equal, Zl == Z2.

T-Network Equivalent

In the above determination of network image impedances as functions of open-circuit and short-circuit impedances measured (or
computed) from the input and output terminals of the network, the
assumed impedances of the T network were mathematically eliminated. Sometimes, however, it is also necessary to determine values
of ZA, ZB, and Zc of Figure 4-10 in terms of the open-circuit and
short-circuit measurements. For a four-terminal network containing
only passive components or one in which the gains in the two
directions of transmission are equal, this may again be accomplished
by solving simultaneous equations.
In the discussion of image impedance, the following relationships
among the impedances of Figure 4-10 are shown:
(4-6a)
Z'oe == ZB

+ Zc,

or ZB ==Z'oe - Zc

( 4-6b)
(4-7a)

and
Z'se == Z B

+ Z ZAZc
+ Z'c

(4-7b)

A

Into Equations (4-7a and b), substitute the value of ZA and ZB
from Equations (4-6a and b) and solve for Zc:
Zc ==

V

(Z' oe

Zc ==

V

(Zoe - Zse) Z' oe

-

Z'se) Zoe

(4-8)

and also
(4-9)

76

Vol. 1

Elements of Transmission Analysis

The values of Zc from Equations ( 4-8) and (4-9) may now be
substituted directly in Equations (4-6a and b) to give expressions
for ZA and ZB in terms of input and output open-circuit and shortcircuit impedances. Thus, all legs of the equivalent T network
may be determined from these measurements provided the network
is bilateral, i.e., contains only passive components or has equal gain'
in the two' directions of transmission.
If the network contains sources of amplification such that the·
gains in the two directions of transmission are not equal, the circuit
cannot be reduced to a simple equivalent T network. Transfer effects,
which account for the difference in gain in the two dire~tions,must
be taken into account.

Transfer Effects

The determination of image impedances of a four-terminal network
and the conversion of such a network to an equivalent T configuration
permit input and output current and voltage relationships to be
established directly from the application of Ohm's and Kirchoff's laws.
However, these relationships may be applied directly 'Only when the
four-terminal network is bilateral. When it is not bilateral, these
I,

12
~

1

I'

r--- -• - --1
I

ZI

I

I

>
<~

:

I

I

..

Zl

~

I

I

t

I

E

I

1L __

'V.
_ __

~_.~

I

Z2
<--

I

I

I
I

I

If

2

VI

V2

1

~

I

I
I
__ J

Figure 4~ rl~ Il11dge~terminoted.network.

>

Chap. 4

Four-Terminal Linear Networks

77

relatively simple relationships do not apply directly because of
transfer effects that occur as current flows through the network.
Consider the circuit of Figure 4-11. This circuit is similar to
Figure 4-10 except that impedance Z1 is replaced by a voltage
generator having an internal impedance equal to Z1. The circuit
arrangements result in voltage Vl across terminals 1-1 and voltage
V 2 across terminals 2-2 when the network is terminated in its image
impedances, Z1 and Zz. The input current is 11, and the output
current is I z.
If the voltage source is connected at the 2-2 terminals, analogous
voltage and current expressions may be written with the symbols
V and I changed to V' and I'.

, The following

relationships may then be written as definitions:

( 4-10)
1'1 V' 1
I'z V'z'

( 4-11)

== V G1- Z GZ- 1

( 4-12)

GZ- 1

==

and
G1

where G1 is sometimes called the image transfer efficiency.
In these equations, the currents and voltages are complex quantities. The current-voltage products in Equations (4-10) and (4-11)
are quantities usually called volt-amperes, or apparent power. Thus,
Equations (4-10) and (4-11) may be regarded as the gain, in the 1-2
or 2-1 direction, in apparent power resulting from transmission
through the network. Equation (4-12) expresses the geometric mean
of the apparent power gain in the two directions. In all cases, these
definitions apply only when the network is image-terminated.

78

Elements of Transmission Analysis

Vol. 1

It is convenient to express the quantity G1 in terms of open-circuit
and short-circuit impedances. It can be shown that G1 may take any
of the following forms:

J
1
1+J
1

1_

G1

== yZ;;;- yZ::
y

Zoe

+y

Zse

Z'se
Z'oe
Z:se ;
Zoe

y-W:::- yZ;;; .
y Z' oc + y Z' se '

( 4-13)

( 4-14)

and
( 4-15)
These equations for G1 will be found useful in subsequent discussions of sending-end impedance, echo, and stability.
Sending-End Impedance

The sending-end impedance of a four-terminal network is the
impedance seen at the input of the network when the output is terminated in any impedance, bZ2 ; b is a factor used as a mathematical
convenience to modify the terminating image impedance, Z2. When
bZ2 is equal to the image impedance, Z2 (i.e., b == 1), the sending-end
impedance, Zs, is equal to the image impedance, Zl. It is important
to consider the effects on the value of Zs of different impedance values
for bZ2 , because these effects are related to phenomena such as
return loss, singing, and talker echo, any or all of which may be
important when a network is terminated in other than its image
impedance, as in Figure 4-12.
The development of useful expressions for the analysis of the
performance of a four-terminal network terminated in other than
its image impedance can be demonstrated conveniently by starting
with the image-terminated case as illustrated in Figure 4-13. The
voltage V 1 is equal to E /2, as shown, because of the assumption of
image terminations at both ends of the network. At the receiving
terminals 2-2, the network is again assumed to be terminated in its

Chap. 4

79

Four-Terminal Linear Networks

12
1

2

..

~

Zs

~

<>
VI

VZ

1

2

~

. If b is written in polar form as X L (), the values
of X and () may be written as X == I a
jf3 I or X == ya2
132 and
() == tan -,-1 13/01..

+

+

+

Four alignment charts, Figures 4-15, 4-16, 4-17, and 4-18 may be
used to solve expressions in the form

~+

i 2: ==

Q L cf>. Figures 4-15

and 4-16 give values for Q for various combinations of X and 8,
while Figures 4-17 and 4-18 give values for 1> for various combinations of X and (). The following examples illustrates the use of the
charts.

Example 4-1: Use of Alignment Charts

Given: b

== 4

To evaluate:

L 70°

== X

L ()

1-b

---;--=-

l+b

First, refer to Figure 4-15. Mark X == 4 on the left-hand
vertical scale and () == 70° on the right-hand vertical scale.
Use a straight edge to connect these points and read Q == 0.848
on the left side of the Q scale. Next refer to Figure 4-17. Again
mark the points X == 4 and () == 70°. With the straight edge,
read 1> == - 153.5° on the right-hand side of the 1> scale. Thus,
b) == 0.848 L -153.5°.
(1 - b) / (1

+

Note that the charts in Figures 4-15 through 4-18 can be used for a
quick evaluation of changes in either the magnitude or phase angle, or
both, of a termination on a network. These evaluations, useful in determining the performance of circuits and in judging what may be done
to improve performance, may be made by using alignment charts or
may be even more conveniently made by use of a digital computer.

86

Vol. 1

Elements of Transmission Analysis

0.10

'.0

10.0

1-X L()
=Q Lcf>
1 +X L()

9.5

X = 0.10 to 10.0
() = 0° to ± 180°

90°

95°

0.11
9.0

Notes:
1. For () from 0° to ±90°, read left-hand Q scale.

8.5

2. For () from ±90° to ± 180°, read right-hand Q scale.

8.0

4. As X L () approaches 1 L 0° (or 1 L 180°),
Q becomes approximately I 1 - X I (
1+ X )
~
orTT-=X\'

0.12

3. For ()

0.13

>

80°

100°

75°

105°

70°

110°

65°

115°

60°

120°

55°

125°

50°

130°

45°

135°

40°

140°

35°

145°

30°

150°

25°

155°

2O·

160·

180°, use 360° - ().

7.5
0.14
7.0
0.15
6.5
0.16
0.17

X

0.18

6.0

Q
5.5

0.19
0.20

±()

5.0

4.5

0.25

4.0

3.5
0.30

I.~

3.0
0.40
0.5

1."'0
I.",S
I..so
'.SS

2.5

I.0
,'>S
,·80
.90
<'0

2.0

IS·
12.05.----.
10_
o5. 7 . 5 ·
0·

0.6
0.7
1.0°·8-

Figure 4-15. Alignment chart Q 1.

165·
17O·
180·

Chap. 4

Four-Terminal Linear Networks

87

',00
0.050

20.0
1
19.5

-x L8

1+XL8 =QLcf>
{0.05 to 0.10

19.0
18.5

90°

95°

X=
10.0 to 20.0
8=

0° to ±180°
100°

0.055
18.0
17.5

Notes:
1. For 8 from 0° to ±90°, read left-hand Q scale.
2. For 8 from ±90° to ± 180°, read right-hand Q scale.
3. For 8> 180°, use 360° - 8.

105°

17.0
0.060
16.5

70°

110°

65°

115°

60°

120°

55°

125°

50°

130°

45°

135°

40°

140 0

35°

145°

30 0

1500

16.0

0.065

X

15.5

Q

15.0

±8

14.5
0.070
14.0
13.5
0.075
13.0
0.080

12.5
12.0

0.085
11.5
0.090
11.0
0.095

10.5
O.8182~

0.100

Figure 4-16. Alignment chart Q2.

155°

20°

160°

15°
12.5°--1-0
5°7.5°_
0-

0°

10.0

25 0

165°
170°
180°

88

Elements of Transmission Analysis

Vol. 1

00

0.10

10.0
1 - X L(J

1

9.5
0.11

+X L(J
X= 0.10 to 10.0
(J

9.0

= Q LI/>

= 0° to ±180°

180°
10900

175°

8.5
0.12
8.0

1. If (J is

0.13
7.5
0.14
7.0

170°

15°

165°

20°

160°

25°

155°

30°

150°

35°

145°

40°

140°

45°

135°

SOO

130°

55°

125°

60°

120°

65°

115°

{ positive, I/> is negative.
negative, I/> is positive.

:>

I/> scale.
3. For X < 1, read left-hand I/> scale.
2. For X

4. For (J
0.15

10°
Notes:

1, read right-hand

>+

180°, use (J - 360°.

6.5
0.16
0.17
0.18

6.0
1><0
'>'0

5.5

1>00
Icr'po

0.19

X

0.20

5.0

'.:Jo

=+1/>

4.5
0.25

±(J

Icreo
Icr>
I.
°
I. OCto
crSo

4.0
3.5

0.30
3.0
0.35
0.40

2.5

0.50

2.0

5. For (J

>-

6. For (J

= 0° or 180° and

0.60
0.70
0.80
0.90
1.0

7. ForX

180°, use (J

= 1 and

{(J
(J

+ 360°.
{X
X

>

1, I/>

= 1~Oo.

< 1,cp = 0

.

from 0° to ± 180°, I/> =+ 90°.
from ± 180° to ± 360°, I/>
± 90°.

=

85·

Figure 4- 17. Alignment chart cf> 1.

70·

110·

75·

lOS·

82.5. 80·'!!'£':::=

100·
90·

Chap. 4

0.050

Four-Terminal Linear Networks

89

20.0
19.5

1 - X L8
l+XL8=QLCP

19.0

X= {0.05toO.10
10 to 20

lB.S

8 = 0° to ±180°

0.055

lB.O
17.5

Notes:

17.0

positive, cp is negative.
1. If 8 is { negative, cp is positive.

16.5

3. For X

2. For

0.060

X > 1, read right-hand cp scale.
< 1, read left-hand cp scale.

4. For8>

0.065

+ 1BOO, use 8-360°.

16.0

S. For 8> - 1BO°, use 8

15.5

6. For 8

= 0° or 1BOo and

+ 360°.
X> 1,cp= 1BO°.
{ X < 1, cp = 00.

15.0

x

14.5

0.070

14.0
13.5
0.075

±9
13.0

O.OBO

12.5

12.0
0.OB5
11.5
0.090

11.0

0.095

10.5

0.100

10.0 - - -_ _ _ _ _ _...:.:.:!'::J..~~---_-..ll.:.=======:::..z: 90'

',0
".4 0

Figure 4-18. Alignment chart cf>2.

75'

85. 82 .5 ' 80' 77.5'

lOS'
100'

90.

Elements of Transmission Analysis

Vol. 1

Insertion Loss and Phase Shift

The insertion loss and insertion phase shift of a four-terminal
network placed between two impedances may be determined by
Equations (3-13), (3-14), and (3-15) and by using relationships
similar to those of Equations (4-26) and (4-27) for impedance values.
However, the general case, when the terminating impedances and the
input and output image impedances are all different, contains many
interaction terms which may be difficult to evaluate. Furthermore,
this most general situation is usually of only academic interest; since
all terminals are accessible, it is sometimes easier to measure the
insertion loss than to compute it. Often, the subject network is either
symmetrical and has only one value of image impedance, or it is a
transmission line of characteristic impedance, Zo~

Return Loss

The return loss is a measure of the loss in the return path due to
an impedance mismatch. In the analysis of speech transmission, it is
a convenient measure of the echo caused by a mismatch. The return
loss is related to the reciprocal of the absolute value of the reflection
coefficient, a term which relates impedances at a point of connection
in such a way as to give a measure of the voltage or current reflected
from the mismatch point towards the transmitting end of a circuit.
From Figure 4-19, the reflection coefficient, p, at the terminals of
Z L may be written for voltage,

ZL-Za
pv == ZL
Za'

(4-28)

Za-ZL
Pi == Za +ZL·

(4-29)

+

or for current,

The return loss at these terminals is given by 20 log (1/1 pi) dB; i.e.,

+

1 == 20 log I Za
Return loss ==,20 log TPT
Za _ ZL!
ZL

.

(4-30)

Chap. 4

Four-Terminal Linear Networks

91

The expression for return loss, Equation (4-30), may also be
written in the form
1

The bracketed expression in this equation may be written in polar
form as (1 - X L 8) / (1
X L 8). Thus, the alignment charts of
Figures 4-15 to 4-18 may be used
to determine the return loss at a
junction between two impedances
such as that shown in Figure 4-19.

+

The actual voltage across the
load, Z L, is equal to the voltage
which would be present across an
impedance matched to Ze plus the
reflected voltage. As Z L approaches
Figure 4-19. Junction between two
zero, the reflection coefficient apimpedances.
proaches -1, the measured voltage
across ZL approaches zero, the return loss approaches 0 dB, and all the energy is reflected back to Z I,.
As ZL approaches infinity, the reflection coefficient approaches +1,
the voltage across ZL approaches its open-circuit value (twice the
value across ZL under matched conditions), and the return loss again
approaches 0 dB. When ZL equals Ze, the reflection coefficient is zero
in magnitude and angle, the voltage across Z L is one-half the opencircuit value, and the return loss is infinite.
The effects of impedance mismatch on return loss are illustrated
in Figure 4-20 which shows that the return loss increases as the angle,
8, decreases and as the ratio of I ZL/Ze I or I Ze/ZL I approaches
unity. The angle 8 is that between the load and generator impedances.
The values of the parameters of Figure 4-20 may be written
ZL == I ZL I L 8L, Ze == I Ze I L 8G, and 8 == 18L - 8G I·

Vol. 1

Elements of Transmission Analysis

92

40

35

30

25
aD

~

j
E

20

i
'"

8
15

10

- - - - - - - - - - 50

0

_ _ _- - - - - - - - - - - 70

0

5

o

o

0.2

0.4

0.6

0.8

1.2

1.0

Impedance ratio, I ZL/Za I or I Za/ZL

1.4

I

Figure 4-20. Return loss variations.

Echo -

Magnitude and Delay

Return now to Figure 4-14. The condition at terminals 2-2 is one
of mismatch; the effect of the mismatch could be evaluated in terms
of return loss, as above, sImply by using values in Equation (4-30)
such that ZG = Z2, and ZL = bZ2. However, it is often desirable to
evaluate the magnitude of the reflected voltage or current wave and

Chap. 4

Four-Terminal Linear Networks

93

to determine the delay encountered by the reflected wave in transmission through the network.
Consider first the magnitude of the reflected wave. From Equation
(4-22), b = (Z2
Zr)/Z2, or Zr = Z2(b - 1). The total current at
the output is

+

Z2(b

+ 1)

,

( 4-31)

The voltage across Zr may be regarded as the reflected voltage due
to the mismatch, It is written

Substitution of Equation (4-31) yields

Er = E2

(I-b)
( b-l)
b + 1 = -E2 1 + b .

The output current, from Figure (4-14), may be written also as

From Ohm's law,

and

A useful expression for the ratio of reflected to incident current is
obtained by dividing Ir by 12 :
Ir

-y;:-

1- b

l+b'

( 4-32)

94

Elements of Transmission Analysis

Vol. 1

It can be shown that a similar relationship exists for a mismatch
at the input; i.e.,

(4-33)
Equations similar to (4-32) and (4-33) can also be developed to
show the ratio of reflected to incident voltages.
Echo evaluations must, of course, take into account the loss encountered in transmission through the network an appropriate number of times. Successive reflections become increasingly attenuated
and at some point may be ignored.
The time delay or transit time for a wave to propagate through
a four-terminal network may be shown to be
()

T

==

2 X 360 0 X f

(4-34)

where () is the angle of G r in degrees and f is the frequency in
hertz. Then, the round-trip delay for an echo to be transmitted
through a network and back again is
(4-35)
Power Transfer

In Figure 4-19, E and Ze represent a source of power. This source
may be a telephone instrument, a repeater amplifier, or the sending
side of any point in a telephone connection. The impedance Z L is the
load which receives the power transmitted. It may be another telephone instrument or a radio antenna-the receiving side of any
point in a connection. The amount of power transferred from the
source to the load may be determined by the relative values of ZG
and Z L. The power transferred can be shown to be a maximum under
three different assumptions as follows:
(1) If ZG is a fixed impedance and there is no restriction on the
selection of Z L, the power transferred is· a maximum value
when ZL is the conjugate of ZG, that is, when ZL and ZG have
equal components of resistance and their reacti~ components
are equal and opposite. This may be written ZG == R
jX,
and Z L == Z; == R - jX.

+

Chap. 4

95

Four-Terminal Linear Networks

(2) If Za is a fixed impedance and the magnitude of ZL can be
selected but not its angle, the power transferred is a
maximum when the absolute values of ZL and Za are equal
( I ZL I == I Za I ). That is, the impedances are equal disregarding phase.
(3) If both Za and ZL are pure resistances, the power transferred
is a maximum when the source and load resistances are equal
(Ra

== Rd.

Figure 4-21 shows power and efficiency relationships for case (3)
over a range of load resistance values from 0 to 2R a• Curve (A)
shows that the power delivered to the load, R L, is zero when RL == 0,
increases to 25 percent of the maximum possible when RL == Ra, and
then gradually decreases as RL is further increased. The total power
that can be developed, designated as 100 percent, is that delivered to
the internal resistance of the generator when RL == 0, i.e., a short
100

90

~,

~1

80

+ P2 = total power

'\ ~)

70

,

" "V"'-

60
1:

~ 50

CII

c...

(y

40

30

/

20

10

0

f

o

/

~

./

0.4

,.,."....--

/

'"'-...
P2

(A)

~

~V
0.2

r

% efficiency

...........

----

r----.. ~

= power in external circuit

~

0.6

0.8

1.0

l.2

1.4

1.6

RdRc;

Figure 4-21. Maximum power transfer.

1.8

2.0

Elements of Transmission Analysis

96

Vol. 1

circuit. As the value of RL is increased the total power developed
decreases as shown by curve (B). When RL == R G , the total power is
50 percent of the maximum, half delivered to the generator resistance
and half to the load resistance. The total power decreases to zero
when RL == 00, an open circuit. Curve (C) shows the efficiency of
the circuit, Le., the percentage of the total generated power that is
delivered to the load as a function of the ratio of the load resistance
to the generator resistance. The condition of maximum power delivered to the load, RL == R G , approximates the most desirable condition in telephony since, in most applications, the primary interest
is in delivering maximum power to the load regardless of the
efficiency.
However, in telephony another transmission parameter must be
considered, the generation of reflections or echoes. The necessity
for compromise between delivering maximum power to a load and
maintaining reasonable performance in respect to reflections can
best be illustrated by an example.
Example 4-2: Power Transfer and Return Loss
In Figure 4-19, let ZG == 900 -;200 ohms and let E == 1 volt

rms at 1000 Hz.
(a) What is the return loss at 1000 Hz at the junction between
ZG and ZL and what is the power delivered to ZL when
ZL == 900 + j200?
(b) What is the return loss at 1000 Hz at the junction between
ZG and Z L and what is the power delivered to Z L when
ZL == 922 + jO?

Case a:
Return loss == 20 log

1

TPT ==

ZG

== 900 - j200 == 922 L -12.5°

ZL

== 900 + j200 == 922 L +12.5°

ZL _
ZG -

922 L -12.5° _ 1 L -250
922 L +12.5° -

1

Chap. 4

Four-Terminal Linear

I (1-1 L -25°)~(1 +

Return loss = 20 log

= 20 log

Ne'tworks

97
1 L -25,0)

I

I 0.22 ~ +900 I

= 13.2 dB,
where the value of (1 - 1 L -25°) / (1 + 1 L -25°) is found
from Figures 4-15 and 4-17. Alternatively, the return loss may
be determined by interpolation in Figure 4-20.
To determine the power delivered to the load, the current may
first be determined:
E
1 LO
1= Ze + ZL = 1800 = 0.000554 ampere, rms.

Then,

PL

= J2R = 0.000554
L

2

X 900

= 0.000276 watt.

Case b:
Ze = 900 - j200
ZL = 922 +jO
Ze
ZL

922 L -12.5° _ 1 L -12 50
922 LO
.

Return loss '- 20 log

I (1 _
1

:=

20 log 0.11

= 19.2 dB.

1 L -12.5°)

~(1 + 1 L -12.5°) I

98

Vol.

Elements of Transmission Analysis

The power delivered to the load is computed as follows:
1=

E

_

1 LO

_

1 LO
j200

+ ZL - 900 - j200 + 922 - 1822 1822 + j200
0.000542 + jO.000060

ZG

3,360,000

== 0.000545 ampere.
PL

== J2R == 0.0005452 X 922
L

== 0.000274 watt.
Thus, an increase of 19.2 - 13.2 == 6 dB in return loss (resulting in a 6-dB reduction in echo amplitude) is achieved by providing a resistive termination of a value equal to the absolute
value of the source, 922 ohms. For this improvement, the delivered power of 0.000276 watt is reduced to 0.000274 watt, a
negligible penalty of 10 log 0.000276/0.000274 == 0.03 dB.

Stability

When a circuit is unstable, it is said to be singing; that is, unwanted signal currents and voltages flow in the circuit without an
external source of applied signal energy. In Figure 4-22, such con-

1
,..

~

I
aZ,

I

I
Zs

~

....
1

ZR
4

,..
2

Figure 4-22. Four-terminal network; mismatched at input and output.

bZ2

1

Chap. .4

Four-Terminal Linear Networks

99

ditions of instability would result in signal current flow in aZ 1, bZ2 ,
and in the network.
The complete development of mathematical criteria for absolute
stability or absolute instability is not undertaken here. However,
stability criteria are presented with some background to indicate how
they are derived.
If currents are circulating in the input circuit of Figure 4-22 without an external source of energy, there must be zero impedance at
the frequency at which current is observed. That is, if such a current
is circulating through the input, then, at that frequency

aZl

+ Zs == o.

It can be shown that when such a condition exists a similar condition
exists at the output; that is,

For such a condition to exist, the sending-end impedance, Zs, must
have a negative resistance component equal to the positive resistance
component of aZ1, and the reactive component of impedance Zs
must be equal in magnitude but opposite in sign to the reactive
component of aZl. Thus, stability is guaranteed if neither aZl nor
Zs has a negative resistance component and at least one has a positive
resistance component.
A stability index can be derived in terms used earlier in this
chapter . It may be written
Stability index == 1 _ G1

(

a) ( 11+b
- b ).

11+a

(4-36)

The two parenthetical expressions are of a form which can be
evaluated by the alignment charts of Figures 4-15 through 4-18.
Note that if the network is terminated at either end in its image
impedance, it cannot be made to sing. Under these conditions
a == 1 or b == 1, and the stability index _ 1, a criterion for absolute
stability.

100

Elements of Transmission Analysis

The condition for singing is that the stability index

Vol. 1

==

0, i.e., that

1

(4-37)
The circuit will not sing provided the magnitude of G1 is slightly less
than that given by Equation (4-37). A sample calculation of this
type circuit- is given in Figure 4-23.
Usually, a network is terminated in impedances such that the
stability index falls between the extremes of 0 and 1. The/ margin
against singing may be found by
Singing margin

4-4

= 20 log IG, (! + :)

(! + ~) I.

(4-38)

NETWORK ANALYSIS

The preceding material on the basic network laws and their applications provides the tools for network analysis. Some extensions
of these tools and some added sophistication in mathematical manipulations make the analysis job applicable to very complex network
configurations.

Mesh Analysis

A circuit of any complexity may be analyzed by considering each
mesh of the circuit independently and writing an equation for the
voltage relations in each. To do this, of course, it is first necessary
to define a mesh.
In Figure 4-2, for example, nodes are defined as those points at
which individual series combinations of components are interconnected. The series combinations are called branches (each Z in
Figure 4-2 may be made up of series-connected elements in any combination). A mesh may then be regarded as openings in the network
schematic such as those that might be observed in a fish net. The
boundary of a mesh, called the mesh contour, is made up of network

Chap. 4

Oaz

°1

l-a
-l+a

°a

1

l-b

°bZ 2

°2

~

°b

"Q"

+50

0

0

0

+10

0

+20

0

+30

0

+40

0

+50

0

+60

0

+70

0

101

Four-Terminal Linear Networks

-90

0

-90

0

-90

0

-90

0

-90

0

-90

0

-90

0

-90

0

-90

0

-140

0

-90

0

-100

0

-110

0

-120

0

-130

0

-140

0

-150

0

-160

0

+80

0

-90

0

-170

0

+90

0

-90

0

-180

0

(,-a)
l+a

"Q"

(~)=IGII
l+b

_90

0

-120

0

1.73 (0.370) (0.578)

0

0

-90

0

_90

0

1.00

1.19 +10

0

_90

0

-100

0

1.19 (0.841) (0.841)

1.43 +20

0

_90

0

_110

0

1.43 (0.700) (0.700)

1.73 +30

0

_90

0

-120

0

1.73 (0.578) (0.578)

2.15 +40

0

_90

0

-130

0

2.15 (0.465) (0.465)

2.70 +50

0

_90

0

-140

0

2.70 (0.370) (0.370)

3.70 +60

0

_90

0

-150

0

3.70 (0.270) (0.270)

5.50 +70

0

_90

0

-160

0

5.50 (0.182) (0.182)

12.0 +80

0

_90

0

-170

0

12.0 (0.083) (0.083)

+90

0

_90

0

2.70 +30

0

1.00

00

-180'

(1.0)

00

(0)

(1.0)

(0)

(Jaz

1

=

=
=
=
=
=
=
=
=
=
=
=

angle of Zb the input image impedance.

= angle of aZb assumed to be -90

0a =

worst angle of a in

0
•

(~).
l+a

I a 1=
02 =

angle of Z2, the output image impedance.

0bZ =

angle of bZ2 , assumed to be _90

2

0b =

I b 1=

1.

worst angle of b in

TOTAL
LOSS
(DB)

Notes:
01

MIN

__
l'_X _ _
l_

0
•

l-b) .
(l+b

1.

Figure 4-23. Computations for guaranteed stability.

0.214

6.7

1.0

0.0

0.708

1.5

0.490

3.1

0.334

4.8

0.216

6.7

0.137

8.7

0.073

11.4

0.033

14.8

0.0069 21.5
0

00

102

Elements of Transmission Analysis

Vol. 1

branches. The least number of independent loops, or closed meshes,
is one greater than the difference between the number of branches
and the number of nodes. The number of independent loops determines the number of independent mesh equations needed to solve
the network problem. Examination of Figure 4-2 shows that there
are three branches and two nodes. Application of the rule indicates
there are two independent meshes.
In mesh analysis, the parameters of the branches are expressed
as impedances, the independent variables are the voltages and the
voltage drops in each of the branches of a mesh, and the dependent
variables are the currents in each branch of a mesh. A simple
example of mesh analysis of the circuit of Figure 4-2 may be performed by using the rule above regarding the number of independent
meshes in the circuit and by applying Kirchoff's laws.
Thus, the equations

and

provide the two independent equations for the two independent
meshes. If the values of E, ZA, ZB, and Zc are known, the two mesh
currents can be determined from these equations.

Noda I Ana lysis

In nodal analysis, the branch parameters are most conveniently
expressed as admittances (recall that admittance is the reciprocal
of impedance; i.e., Y == ljZ) , the dependent variables are the voltages at the individual nodes, and the independent variables are the
currents entering and leaving each node. Simultaneous equations are
written for node currents, and their solution is the nodal analysis
of the network. The number of independent nodal equations that
may be written is one less than the number of nodes.
There is, of course, a direct correspondence between mesh and
nodal equations. One approach is often found superior to the other,

Chap. 4

Four-Terminal Linear Networks

103

and the choice, while theoretically a matter of indifference, is often
important from the points of view of convenience and flexibility in
treating such things as parasitic circuit elements or active device
parameters. The more complex circuits are usually more easily
analyzed by the nodal approach.
Finding solutions to mesh or nodal circuit equations can become
quite complex when all circuit elements are considered. Such equations, except in the simplest cases, are now usually solved by the use
of an electronic computer.

Determinants

In simple networks, brute-force solution of simultaneous equations
by successive substitution of one equation in another is generally
simple and straightforward. Only modest amounts of network complexity, however, make this approach to finding solutions prohibitive
in the amount of time consumed. Further, the processes become so
involved that the accuracy of the work must always be carefully
checked to guard against error.
The coefficients of the dependent variables of the simultaneous
equations may be arranged in rows and columns corresponding to the
terms of the equations. If the resulting array is square (i.e., if it has
the same number of rows and columns), solutions to the simultaneous
equations can be found by the methods of determinants [2].

Matrix and Linear Vector Space Analyses

While it is often possible to determine significant but not complete
characteristics of a network by means of voltage, current, and
impedance measurements made at the terminals, such expressions
may not completely define the network. These expressions, however,
are often useful in relating the network performance to its interaction
with other interconnected networks and in defining certain properties
of the subject network. The coefficients of terms in the mathematical
expressions derived from such measurements and observations may
be arranged in matrix form; the matrix mayor may not be square.
Mathematical manipulation of the matrix expressions provides a

104

Elements of Transmission Analysis

Vol. 1

convenient method of network analysis. This may be regarded as a
"black box" approach to analysis, which ignores the internal structure
of the network but permits specification of its external behavior. The
application of the concepts of linear vector spaces to matrix analysis
adds a significantly greater amount of power to network analysis [3].

4-5

TRANSFORMERS

Many types of transformers, sometimes called repeat coils, are used
in telecommunications circuits. In most cases, the applications differ
significantly from those applying to alternating current power distribution systems where the principal use is to step alternating voltages up or down. In communications circuits, in addition to voltage
transformation, transformers are used to match impedances, to split
and combine transmission paths, to separate alternating and direct
ourrents, and to provide dc isolation between circuits. Impedance
matching and the splitting and combining of transmission paths are
discussed in some detail because of their importance in transmission.

Impedance Matching
Unequal ratio transformers are used to match unequal impedances
to permit maximum energy transfer. The currents through any two
windings of such a transformer are inversely proportional to the
number of turns in the two windings. The voltages across the two
windings are directly proportional to the number of turns in the
two windings. Thus,
(4-39)
where N1 and N2 are the number of turns on the primary and secondary windings, respectively.
No power is dissipated in an ideal transformer, illustrated in
Figure 4-24, and in addition the phase relation between the voltage
and current on the two sides of the transformer is exactly the same.
Therefore, the product of voltage Vs across the primary winding and
currentls through the primary winding is equal to the corresponding

Chap. 4

Four-Terminal Linear Networks

105

Is

---+

----.

Zs

Figure 4-24. Transformer circuit.

product for the secondary winding; that is,

Then, substituting this value of V s/VL in Equation (4-39),

(4-40)

From Ohm's law, V L

==

IL ZL. Substituting the values of V L and

I L from Equations (4-39) and (4-40),

(4-41)
Then,

Vs

(Nl)2

-y; == Zs == N2 ZL

(4-42)

and
(4-43)

106

Elements of Transmission Analysis

Vol. 1

The relationship shown in Equation (4-43) is used when a transformer is being designed for the purpose of providing an impedance
match, i.e., to provide a design in which Zs == Za.
Commercial transformers approach the efficiency of ideal transformers very closely. Small losses are occasioned by currents induced
in the core (eddy current losses), by flux in the core (hysteresis
losses), and by current flowing in the copper windings.

Separating and Combining

A common means of separating and combining transmission
paths is by the use of a transformer called a hybrid coil, a complex
circuit component. Although the operation of a hybrid coil is somewhat difficult to analyze, a simplified and idealized coil structure
may suffice to illustrate how it is used in some common circuit
applications.
In the circuit configuration of Figure 4-25 (a), the hybrid coil
characteristics are such that, if Zd and/or Zc are signal sources, the
energy is divided equally between the two loads Za and Zb provided
certain impedance relationships are satisfied. If Za and/or Zb are
signal sources, the energy is similarly divided equally between Zd
and Zc. These hybrid coil characteristics are exploited in combining
and separating analog signals (including pilots and test signals), in
providing parallel transmission paths in protection switching systems,
and in providing the interface between two-wire and four-wire voicegrade facilities (four-wire terminating sets).

In the circuit of Figure 4-25 (b), assume that Za == Zb, Zc == Zd,
and the number of turns on each of the three windings of the hybrid
transformer are the same. With these assumptions, assume a signal
source in the branch containing Z d as shown in Figure 4-25 (c). The
currents in the right-hand branches of the circuit divide equally between Za and Zb and are cancelled in Zc. Thus, there is no transmission from Zd to Zc. If the signal source were in series with Zc,
the currents would again divide equally between Za and Zb. Their

Chap. 4

Four-Terminal Linear Networks

r-------<
Zc

107

•

Za

= BAL NET.

(a) Application

(b) Circuit
Note:
.indi~ates

same polarity.

•
Za

b

>-<:~...J\j""'--~

,

I

I
I

e

(c) Circuit balance

J

(d) Circuit balance

Figure 4-25. Hybrid circuit relationships.

effects would cancel, however, due to the polarity of the magnetic
fields in the center-tapped winding of the transformer. Hence, there
would be no transmission from Zc to Zd.
Now assume the signal source to be in series with Za as shown in
Figure 4-25 (d). It is convenient to imagine the circuit to be opened
between points band e. Under these conditions and with Zc == Z(l,
the voltage induced between points a and d is exactly equal to the
voltage drop in Zc so that the voltage at b equals that at e. Then,
since points band e are at the same potential, they may be connected
without causing current to flow in Z b. Thus, there is no transmission
from Za to Zb.

108

Vol. 1

Elements of Transmission Analysis

In each of the above examples, transmission from one impedance
to another involves an equal division of energy to two other impedances; each load impedance dissipates half the power from the
source, a loss of 3 dB. In addition, core and copper losses are typically
about 0.5 dB. Thus, in designing or analyzing transmission circuits
in which equal ratio hybrids* are used, 3.5-dB loss is usually assumed
for the hybrid.
A common application of hybrid circuits is at the interface between two-wire and four-wire facilities. Such a circuit, illustrated in
Figure 4-26, is known as a four-wire terminating set. Transmission
... - -

Two-wire facility -~~--

Four-wire facility -

Terminating set

-

~

HYB

.. -

-

Trunk A

Trunk B

- - - ------.

Figure 4-26. Hybrid application-four-wire terminating set.

is from the amplifier with output impedance Za to the two-wire trunk
with impedance Zd, and from the two-wire trunk Zd to the amplifier
with impedance Zb. When transmitting from Zd to Zb, half the energy
is dissipated in Za, but the signal is not transmitted through the
amplifier because of its one-way transmission characteristics. When
transmitting from Za to Zd, half the power is lost in Zc. The important
thing, however, is that no energy reaches Zb. If this were not so,
the signal would circulate through the two sides of the four-wire
*In some applications, unequal ratio hybrids are used. The design of such
hybrids involves careful selection of impedances and turns ratios, a process
too complex to be covered here.

Chap. 4

Four-Terminal Linear Networks

109

trunk and the hybrid circuits at each end, being amplified by the
amplifier circuits each time. This could result in circuit instability, or
singing, as previously discussed.
The loss between Z a and Z b or between Z c and Z d is known as
hybrid balance. In carefully controlled laboratory circuits, a balance
of 50 dB is easily achievable. However, in the application described,
impedance Zd represents any of a large number of two-wire trunks
which may be switched into the connection. The impedances of these
trunks vary widely, and so only a compromise value may be used
for Zc to provide control of echoes that are returned to the speaker
at four-wire terminating sets.
When supposedly matched impedances are in reality unequal in
either their resistive or reactive components, or both, the hybrid
balance deteriorates so that the achievable balance may be much less
than 50 dB. When this occurs, echo is produced in the transmission
circuit. The echo may be evaluated in terms of the return loss at
the junction between the two-wire facility and the hybrid which may
be calculated as described previously.

4-6

RESONANT CIRCUITS

By an appropriate combination of resistors, inductors, and capacitors, circuits may be designed to resonate, i.e., to have extremely
high or low loss at a selected frequency. Such circuits, which may
be either series or parallel, are often designed as two-terminal networks which then are used as components of a larger, more complicated four-terminal network. Resonance occurs when the inductive
and capacitive components of reactance are equal. That is, when
(4-44)
The resonant frequency may be found by solving Equation (4-44)
for IT:

IT ==

1
------:=

211

V LC

(4-45)

110

Elements of Transmission Analysis

Vol. 1

Selectivity, i.e., the difference in transmission between the resonant
frequency and other frequencies, is determined by the amount of
resistance in the circuit. Since the resistance is usually concentrated
in the inductor, the objective is to have the ratio of the reactance of
the inductor to its resistance as high as possible. This ratio is known
as the quality factor, or Q, of the inductor and is expressed by
(4-46)
Series Resonance. In a resonant circuit having the inductance and
capacitance in series, the circuit reactance is zero at the resonant
frequency, where the inductive and capacitive reactances are equal
as in Equation (4-44) ; the impedance has a minimum value at this
frequency and is equal to the resistance of the circuit. If this resistance
is small, the resonant frequency current is large compared to that
at other frequencies, as shown in Figure 4-27. One application of
series resonance is in the use of a capacitor of proper value in series
with a telephone receiver winding, repeating coil winding, or other
inductance, where it is desired to increase the current at specific
frequencies.
Parallel Resonance. In a parallel (often called anti-resonant) circuit,
one having the inductance and capacitance in parallel, the impedance
of the combination is a maximum at the resonant frequency, where
the inductance and capacitive reactances are equal. Since the impedance is a maximum, the current is a minimum at the resonant frequency. The selectivity of the circuit is decreased as the resistance
is increased, reaching a point where the circuit essentially loses its
resonant characteristics. This is shown in Figure 4-28. A parallel
resonant circuit is often called a tank circuit since it acts as a storage
reservoir for electric energy.

4-7

FILTERS

An electrical network of inductors and capacitors designed to
permit the flow of current at certain frequencies with little or no
attenuation and to present high attenuation at other frequencies
is called an electric wave filter. Simple filter configurations and characteristics are illustrated in Figures 4-29 and 4-30. Low-pass and
high-pass filters can be combined to give the characteristics of band-

Chap. 4

Four-Terminal Linear Networks

111

L

R
\

0.01

..AAA

"" ..

C

--1E-

r--... r.

R=(On

R =1 2.5n

tw)=0.4

'\..,

~~

L=O.l H

C = 0.254p.f

R = as indicated

I

~

\,
~
~~
~

l

~
J

0.005

III

Q,

E



L

~

0.003

Vol. 1

R =lOon

I~

0.001

R=2.sn

~

~

~

rt

VJ I(
/ /
j

I{

I

J'f

\,- /'/
\l

o
o

l/

Vi

,
/i

J

400

800

1200

1600

2000

2400

Frequency

Figure 4-28. Curves of current values in parallel resonant circuit.

a high ratio of reactance to resistance is to use mechanical vibrating
systems, such as the piezo-electric crystal. In an electric circuit
such as a filter, a crystal acts as an impedance exhibiting both
resonant and anti-resonant properties. Crystal filters find wide
application in broadband carrier systems.
Older and well known filter structures such as the m-derived and
constant-k image parameter designs are still used. They can provide

Chap. 4

L

113

Four-Terminal Linear Networks

L
c::

.2
c::

'0

::;)

II)

~

::;)

c::

~

u

(a) Circuit

Frequency

Frequency

(b) Current

(c) Attenuation

Figure 4-29. Low-pass filter.

c

----1~----t

C

c::

~

::;)

u

(a) Circuit

Frequency

Frequency

(b) Current

(c) Attenuation

Figure 4-30. High-pass filter.

characteristics that satisfy many needs, and they have the further
attributes of being relatively easy to design, synthesize, and realize;
however, more sophisticated approaches have become necessary as
requirements have become more stringent, bandwidths have become
wider, and useful frequencies have been pushed higher in the spectrum. Some of the distinguished scientists who have made significant
contributions in this field are Bode, Butterworth, Campbell, Darlington, Foster, Guillemin, Johnson, Shea, and Zobel.

114

Elements of Transmission Analysis

Vol. 1

REFERENCES

1. Guillemin, E. A. Communicq,tion Networks, Vol. 1 (New York: John Wiley
and Sons, Inc., 1931).

2. Bode, H. W. Network Analysis and Feedback Amplifier Design (Princeton,
N. J.: D. Van Nostrand Company, Inc., 1945).
3. Huelsman, L. P. Circuits, Matrices, and Linear Vector Spaces (New York:
McGraw-Hill Book Company, Inc., 1963).
4. Kuo, F. F. Network Analysis and Synthesis (New York: John Wiley and
Sons, Inc., 1962).
5. Johnson, W. C. Transmission Lines and Networks (New York: McGraw-Hill
Book Company, Inc., 1950).

6. Reference Data for Radio Engineers (Indianapolis: Howard W. Sams and
Company, Inc., Oct. 1968).

Elements of Transmission Analysis

Chapter 5

Transmission Line Theory
Electromagnetic wave theory provides the basis for transmission
line analysis. Involved are such factors as impedance, impedance
matching, loss, velocity of propagation, reflection, and transmission.
Knowledge of all these parameters is necessary to an understanding
of electrical signal transmission over metallic wire media.
Transmission networks are made up of resistors, capacitors, and
inductors. The characteristics of such components are called lumped
constants. A transmission line is an electrical circuit whose constants
are not lumped but are uniformly distributed over its length. With
care, the theory of lumped constant networks can be applied to transmission lines, but lines exhibit additional characteristics which
deserve consideration.
The detailed characterization of a given type of cable is dependent
on the physical design of the cable. Wire gauge, type of insulation,
twisting of the wire pairs, etc., have important effects on attenuation,
phase shift, impedance, and other parameters. For the most part, the
treatment here pertains to two-wire parallel conductors. However,
the analysis is also extended and applied to a coaxial conductor
configuration.
5-1

DISCRETE COMPONENT LINE SIMULATION

It is convenient to analyze transmission line characteristics in
terms of equivalent discrete-component, four-terminal networks. The
conductors of an ideal simple transmission line, evenly spaced and
extending over a considerable distance, have self-inductance, L, and
resistance, R, which are series-connected elements that must be included in the discrete component equivalent network. Since the line
115

116

Elements of Transmission Analysis

Vol. 1

appears electrically the same when viewed from either end, the
equivalent circuit must be symmetrical. Thus, the components of
the equivalent network are split and connected as shown in Figure 5-l.
The insulation between the wires is never perfect; there is some
leakage between them. The leakage resistance may be very large, as
in a dry cable, or it may be fairly small, as in the case of a wet openwire pair. Hence, the equivalent circuit must contain a conductance,
G, in shunt between the line conductors. Also, any two conductors in
close proximity to one another have the properties of a capacitor;
therefore, the circuit must have shunt capacitance, C.
These line parameters (resistance, inductance, conductance, and
capacitance) are the primary constants and are usually expressed in
per-mile values of ohms, millihenries, micromhos, and microfarads.
Derived from these are the characteristic impedance and propagation
constant; they are the secondary constants, both of which are functions of frequency. Although all primary and secondary constants
vary with changes in temperature, they are usually expressed as
constants at 68 F with correction factors for small changes in
temperature. Both primary and secondary constants are often used
to characterize transmission lines or equivalent circuits.
0

In the discussion of networks in Chapter 4, it was suggested that
any circuit could be simulated by a T structure. It is not surprising
then to find that a useful equivalent circuit for a transmission line is
the T network shown in Figure 5-1. For convenience, series constants
Rand L can be combined as impedance ZA, and shunt constants C
and G as impedance Zc as shown in Figure 5-2. For the present, the
relationship to line length is ignored.
R/2

c

L/2

L/2

R/2

G

Figure 5-1. Primary constants of a section of uniform line.

117

Transmission Line Theory

Chap. 5

Figure 5-2. Equivalent network of a section of uniform line.

The equivalent circuits in Figure 5-1 or 5-2 are poor approximations of a real transmission line because all of the distributed constants have been concentrated at one point. The approximation is
improved by having two T sections in tandem and, in the ultimate,
the best representation is an infinite number of tandem-connected
T sections, each having the constants of an infinitely short section
of the real line.
Characteristic Impedance

An example of the simulation of a very long uniform transmission
line by an infinite number of identical, recurrent, and symmetrical
T networks is shown in Figure 5-3. The input impedance at point

a

b

d

I
I
I To infinity

I

----+

I
Figure 5-3. Uniform line simulated by an infinite number of identical networks.

118

Elements of Transmission Analysis

Vol. 1

a is Zoo Now open the line at b and again measure the impedance of
the line towards the right. Removing one section from an infinite
number of sections produces no effect, so the impedance still
measures Zoo
The impedance at point a was Zo when the first section was connected to an infinite line presenting impedance Zo at b. If the first
section is terminated at b by a discrete-component network of impedance Zo, the impedance would still measure Zo at point a. In a
transmission line, Zo is called the characteristic impedance. It is related to the equivalent T structure in Figure 5-2 by the expression
ohms.

(5-1)

Impedances ZA and Zc contain inductance and capacitance. Since
the reactances of inductors and capacitors are functions of frequency,
the characteristic impedance of a real or simulated transmission line
is also a function of frequency. This property must be recognized
when selecting a network which is to terminate a line in its characteristic impedance over a band of frequencies.

It is often more convenient to determine Zo by test than by computation. This can be done by measuring the impedance presented by
the line when the far end is open-circuited (Zoe) and when it is
short-circuited (Zse). Then, it can be shown that
Zo = yZoeZse

ohms,

(5-2)

an equation similar to those given for network image impedances,
Equations (4-4) and (4-5).
To summarize, every transmission line has a characteristic impedance, Zoo It is determined by the materials and physical arrangement used in constructing the line. For any given type of line, Zo is
by definition independent of the line length but is a function of frequency. The input impedance to a line is dependent on line length
and on the termination at the far end. As the length increases, the
value of the input impedance approaches the characteristic impedance
irrespective of the far-end termination.
The term characteristic impedance is properly applied only to uniform transmission lines. The corresponding property of a discrete

Chap. 5

Transmission Line Theory

119

component network is called image impedance as previously discussed.
However, if the network is symmetrical, it has a single image impedance which is analogous to the characteristic impedance of a uniform
line and, as the number of network sections is increased, the impedance approaches the characteristic impedance of the line being
simulated.
Attenuation Factor

If a symmetrical T section is terminated in its image impedance
(Zo) and voltage EI is applied to the input terminals, current II flows

at the input. In general, the output voltage and current, E2 and 12 is
less than El and II. Let Idl2 be designated by a; this is the attenuation factor for the T section. Also, let lnl Idl21 == a; this is known
as the attenuation constant for the T network. Then,
(5-3)

If a number of symmetrical T sections of image impedance Zo are
connected in tandem and terminated in Z 0 as shown in Figure 5-4,
each T section is terminated in Zo, and the ratio of its input current
to its output current is a. Thus, from the figure

I ~~ I == I ~: I == I ~: I == I ~: I == a.

(5-4)

To find the ratio of the input current to the output current for the
series, the terms of Equation (5-4) may be multiplied to give

I ~: I = 1 ~: I . I ~: I . I ~: I

·1

~: I= a'

or, for n sections of identical series-connected T networks terminated
in Z 0 at both ends,
_II
_ - a n - ena

In+l -

-

,

(5-5)

where an == ena is the attenuation factor for the n series-connected
Tnetworks.

Elements of Transmission Analysis

120

Vol. 1

Figure 5-4. Line composed of identical T sections.

Propagation Constant

The ratio of input to output current, 1./12, in a symmetrical
T section terminated in its image impedance, Zo, is generally a
complex number which may be expressed in a number of forms to
indicate a change of both magnitude and phase. For the network of
Figure 5-2 when it is terminated in Zo at both input and output, the
current ratio is

~ == 1 +
12

ZA
2Zc

+

Z0
Zc

== 1 +

ZA
2Zc

+ JZ + ( Z
A

" Zc

A ) 2

2Zc

(5-6a)

or, in more general terms,
~12 -

e'Y -

-

e(lX+j(3)

(5-6b)

where 'Y is a complex number called the propagation constant, or
complex attenuation constant. Its real and imaginary parts are
defined by
'Y

== a+i{3,

(5-7)

where a is the attenuation constant, which represents a change in
magnitude, and f3 is the wavelength constant, or phase constant,

Chap. 5

Transmission Line Theory

121

which represents a change in phase. When applied to actual transmission lines with distributed parameters, both constants are usually
expressed in terms of units of distance; a is usually expressed as
nepers per mile or dB per mile, and (3 is usually expressed as radians
per mile or degrees per mile.
For the network of Figure 5-2, the value of 'Y may be computed
from Equations (5-6a) and (5-6b) as
(5-8)
If the bracketed expression in Equation (5-8) is written in polar
form as A L {3, where A is the absolute value and {3 the angle, then
'Y

== In Ae

j

{3==

In A

+ j{3.

(5-9)

Since the real and imaginary parts of this equation must equal the
corresponding parts of Equation (5-7),
Ii
a

III == In
== In A == In IJ;

+ + Zol

IZA/2 ZcZc

.
nepers/T sectIon
(5-10a)

and
~

J-I

== arg

+ + Zo

ZA/2 ZcZc

ra d·lans/T sect·Ion

(5-10b)

where arg stands for argument or angle of.
Since the attenuation constant can also be expressed in decibels
per T section, Equation (5-10a) may be written
a

== In A nepers/section == 8.686 InA dB/section == 20 log A dB/section.

This relationship must not be used indiscriminately; it applies only to
an infinite line and a line or discrete-component simulation terminated
inZo.
5-2

LINE WITH DISTRIBUTED PARAMETERS

Characterization of transmission lines involves the same electrical
parameters (primary and secondary constants) as those used in
characterizing discrete component networks. In lines, however, these

Vol. 1

Elements of Transmission Analysis

122

parameters are not discrete and concentrated. They are distributed
uniformly along the line. Relationships between primary and secondary constants and between these parameters and other transmission
line characteristics (including velocity of propagation, reflections and
reflection loss, standing wave ratios, impedance matching, insertion
loss, and return loss) must therefore be established in terms of
distributed parameters.

Characteristic Impedance

A single T section may represent a line having distributed elements
but at one frequency only. In order to construct an artificial line in
simple T -section configurations of discrete elements to simulate a real
line, it is necessary to construct many tandem-connected T-sections
to simulate even very short sections of line. As the number of sections
is increased and the elemental length of line is reduced, the artificial
line approaches the actual line in its characteristics over a wide band
of frequencies.
Consider an elemental length of line, ale Let Z be the impedance
per unit length along the line and Y be the admittance per unit
length across the line. The T section of Figure 5-5 represents the

ZA

2

R+jwL

ZIlZ

ZA

2

2

2

R/2

I

I

L/2

Zlll

2

R/2

2

I

L/2

IL _ _ _ _ _ ...JI

IL _____ -.JI

j-. ------,1
I
I
I

+ jwL

,------"

\'-----1
I

R

1

1

1

Zc=y;:-= YIlZ

G

C

I

I
L ______ --.J

Yc

.

= G + JWC = Ylll

Figure 5-5. T-sedion equivalent of a short length of line.

Chap. 5

Transmission line Theory

123

equivalent network of a line having length ilZ. The value of ZA and
Zc of Figure 5-5 may be written

and
Zc

==

1

YilZ.

Substituting these values in Equation (5-1) gives the characteristic
impedance for a lumped constant network as
.../ (ZilZ)2
Z 0_- ~
4

+~

ohms.

Y

For a line with distributed parameters, let ilZ approach zero; then,
the characteristic impedance is
Zo

lim
ill~O

==

~ ZY

ohms

(5-11a)

or, in terms of primary constants,

Z _ .../R+iwL
0 - ~ G +jwC

ohms.

(5-11b)

Propagation Constant

From the previous derivation of the expression for the propagation
constant of an equivalent network, Equation (5-8) may be rewritten

By expanding the terms under the radical sign by the binominal
theorem and rearranging terms, this expression may be written
(5-12)

124

Elements of Transmission Analysis

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Also, expanding e'Y as a power series yields
e'Y = 1

+ 'Y + ;~ + ...

(5-13)

As shown in Figure 5-5, the terms Z A, ZC, and 'Y all place ~l in the
numerators of Equations (5-12) and (5-13). As ~l approaches zero,
the higher terms of these expansions become insignificant. Combining
the two equations and truncating the series yields

This equation may be solved algebraically to give

for the conditions of Figure 5-5 and for length
made up of l/~l sections,

~l.

For any length, l,

'Y = yZY l,

and for a unit length, l

= 1, the propagation constant is
(5-14)

where a is in nepers or dB per unit length and f3 is in radians or
degrees per unit length. The values of Z and Yare found from the
primary constants of the line.

Attenuation Factor

Previously, the attenuation factor for a number of identical,
symmetrical T sections having lumped constants was defined for
tandem connections of such sections. Here, where the transmission
line is made up of distributed parameters, as the length of an elemental section ~l approaches zero, the attenuation constant becomes
a nepers per unit length. Then the expression for the attenuation
factor analogous to that of Equation (5-5) is given as
Attenuation factor =

eal.

(5-15)

Chap. 5

Transmission line Theory

125

Velocity of Propagation
The phase shifts represented by the f3 term in Equation (5-6b)
express the angular difference in radians between the input and
output signals; they imply a time delay between the input signal
current (or voltage) and the output signal current (or voltage).
This can be used to compute the velocity of propagation through the
network or transmission line. The velocity is given by
ltJ

V

== fi'

(5-16)

typically expressed as miles per second.
Equation (5-16) shows that the velocity of propagation is a
function of frequency, since .w == 2'1T/. However, f3 is also frequencydependent since it is made up of reactances derived from ZA and Zc
of Equation (5-8). Thus, while a transmission line having either
discrete or distributed elements tends to introduce delay distortion
(a non-linear phase/frequency characteristic) because the velocity of
propagation is different at different frequencies, it is theoretically
possible to design a line having no delay distortion by designing f3
to be directly proportional to cu.

Reflections
Only lines which are uniform and which are terminated in their
characteristic impedance have so far been considered. As long as
the signal is presented with the same impedance at all points in a
connection, the only loss is attenuation.
However, if one line with characteristic impedance ZG is joined
to a second line with characteristic impedance Z L, an additional
transmission loss is observed. While the signal is traveling in the first
line, it has a voltage-to-current ratio EG/IG == ZG. Before the signal
can enter the second line, it must adjust to a new voltage-to-current
ratio EL/IL == ZL. In making this adjustment, a portion of the signal
is reflected back towards the sending end of the connection.

It is not surprising that there should be a reflection at an abrupt
change in the electrical characteristics of a line. There is a disturbance in any form of wave energy' at a discontinuity in the

126

Elements of Transmission Analysis

Vol. 1

transmission medium. For example, sound is reflected from a cliff;
light is reflected by a mirror. These conditions are equivalent to a
line terminated in either an open circuit or a short circuit; all of the
energy in the incident wave is reflected. A less abrupt change in
impedance would cause a partial reflection. For example, a landscape
is mirrored in the surface of a pool of water because part of the light
falling on the water is reflected. The bottom of the pool is also visible
if the pool is not too deep, since part of the light falling on the water
passes through the discoNtinuity of the air-water junction and illuminates the bottom. Such a partial reflection occurs when two circuits
with different impedances are joined, as in Figure 5-6. The power,

x

I

I
I

I
Zc= I ZG I LOG

I
I

P ----~------~~~ P L

Pr ....4.....- - " , , )

Z G ' - ---+ ZL

Figure 5-6. Reflection at an impedance discontinuity.

P, in the signal arriving at junction x is divided. A portion of the
signal, P L , is transmitted through the junction to the load ZL. The
remainder of the signal, P r, is reflected and travels back towards the
source. If ZG and ZL were equal, the power, P, would all be delivered
to Z L ; there would be no reflection.

Reflection Loss. A concept frequently used to describe the effect of
reflections is that of reflection loss, which is defined as the difference
in dB between the power that is actually transferred from one circuit
to the next and the power that would be transferred if the impedance
of the second circuit were identical to that of the· first.

Chap. 5

127

Transmission line Theory

Consider the circuit of Figure 5-6 where the impedances do not
match. The current in the circuit is I == E/(Ze + Zd. The power
deli vered to Z L, the load, is

where RL is the resistive component of the load impedance. If
impedance ZL matched Ze, that is, ZL == Ze, the current in the circuit
would be 1m == E/2Ze, and the power delivered to the load would be

The ratio of the two values of power is

Thus, the reflection loss may be written
Reflection loss

== 10 log ~: == 20 log ~ ~:

== 20 log

Ze

1

+ ZL + 20 log"J cos
()G
cos ()L
1

2 yZGZL

dB.

(5-17)

Thus, the reflection loss has two components. The first is related
to the inverse of the reflection factor, defined as K, where
K _12 yZ;;Z;:1
ZG
ZL .

+

(5-18)

The second is dependent on the angular relationships between the
two mismatched circuits.

128

Elements of Transmission Analysis

Vol. 1

It is possible to have negative reflection loss, or reflection gain.
This does not mean that power can be generated at an impedance
discontinuity. It results from the choice of identical impedances as
the reference condition for zero reflection loss which is not the condition for maximum power transfer, as pointed out in Chapter 4.
Standing Wave Ratio. A second concept that is useful in describing
the effect of reflections is that of. a standing wave ratio. This concept
may be approached from the point of view of a theoretically lossless
transmission line.

Equation (5-11) gives the expression for the characteristic impedance of a line as

0-"

Z _JR+jwL
G + jwC

ohms.

In this equation, the components that produce loss are the resistance
and conductance, Rand G. When these are negligible relative to jwL
and jwC, they may be ignored. This is often true at very high frequencies because of the ,w terms in the expression for Zoo Under these
conditions, the characteristic impedance reduces to
Zo == yLIC

ohms.

(5-19 )

When the Rand G terms are negligible, the propagation constant
for the lossless line is determined from Equation (5-14) to be
'Y

== jw YLC.

(5-20)

Thus, Equations (5-19) and (5-20) show that for a lossless line
the characteristic impedance is a pure real number and the propagation constant is a pure imaginary number. When the propagation
constant is expressed as 'Y == a
j/3, the value of attenuation then
becomes a == 0, and the value of the phase shift constant becomes
/3 == w YLC.

+

The voltage at any point, x, on a lossless transmission line may be
shown to be
Vx

== Vi e /3x + V 2 e- /3x volts,
j

j

(5-21)

Transmission Line Theory

Chap. 5

129

where V1 and V 2 represent the incident and reflected voltages,
respectively, when the line is not terminated in its characteristic
impedance, Z 0, and where x is the distance from the load to the point
of measurement [5].
The velocity of propagation may be found for the lossless line by
substituting the value f3 =w y'LC in Equation (5-16). Thus,

For some structures (such as a coaxial transmission line), the velocity
of propagation approaches 186,300 miles per second, the velocity of
light propagation.
It can be seen from Equation (5-21) that voltage Vx is represented
as the sum of two traveling waves, the incident and reflected voltage
waves. The voltage may also be expressed in terms of trigonometric
functions [5]:

Vx

= V (COS fJx +
L

j::

sin fJX)

= V L cos f3x + jlL Zo sin fiX,

(5-22)

where i L, V L, and ZL are, respectively, the current and voltage at
the load and the impedance of the load.
For a given frequency and value of x (distance from the load),
Equation (5-22) can show Vx == 0, e.g., when V L == 0 or when
coos fix
j (ZO/ZL) sin fix == O. This can occur when fix == n1T (n,
an odd integer) and when ZL is simultaneously infinite, an opencircuit termination. It can also occur when ZL == 0 (short circuit)
and fix == n71' (n, an even integer) simultaneously. These are two
cases of special interest which produce standing waves, i.e., waves
which do not propagate along the line but which pulsate between
minimum and maximum values at all points except those at which

+

Vx

== o.

In the more general case of a line having loss and not terminating
in Zo, standing waves are also produced but not necessarily with null

130

Elements of Transmission Analysis

Vol. 1

points at which Vx == 0. The ratio of maximum to minimum voltages
in the envelope along the line is known as the voltage standing wave
ratio (VSWR). The VSWR may vary from one to infinity. When a
line is terminated in its characteristic impedance, there is no reflected
wave and, as a result, the maximum and minimum are the same value
to give the ratio of unity. For the boundary conditions of ZL ==
or 00 or for ex == 0, the minima of the envelope are nulls, the value
of Vx == 0, and the VSWR is infinite.

°

For cases not involving the boundary conditions of Z L == 0, ZL == 00,
and ex == 0, the transmission phenomenon can often be analyzed to
advantage in terms of a combination of traveling and standing waves;
then, the VSWR is used as a measure of the required degree of impedance match. If it is sometimes convenient to perform analyses
in terms of currents instead of voltages, analogous expressions are
used.
Impedance Makhing. An impedance discontinuity can sometimes be
eliminated by introducing a transformer as an impedance matching
device at the junction. In Figure 5-7, the impedance to the left of
x, Zl, does not match the impedance to the right of y, Z2. By connecting a transformer of turns ratio, Nx/N y == yZ t/Z2 , into the
circuit between x and y, the line to the left of x is made to look into
an impedance Zl, while the line to the right of y looks back into Z2. In

Figure 5-7. Unequal impedances matched

by a transformer.

Chap. 5

Transmission ,Line Theory

131

practice, such a transformer would have a loss of a fraction of a
dB, but the reflection loss is reduced to near zero. Typical examples
of this technique are the transformer in a telephone station set and
the input and output transformers in a repeater amplifier.
A network (or pad) with image impedances of Zl and Z2 would
give the same result as the transformer in Figure 5-7. Impedance
matching pads find limited application because they have a minimum
loss determined by their image impedance ratio. For example, a pad
with image impedances of 600 and 500 ohms (a ratio of 1.2) would
have a loss of at least 3.75 dB; one with a ratio of 2 would have a
minimum loss of about 8 dB.
Advantage is often taken of the standing wave phenomenon in highfrequency transmission lines. A proper connection of a short-circuited
stub of line onto a transmission line at the proper pojnt, one-quarter
or one-half wavelength from the load, often provides a means for
good impedance matching. *
At very high frequencies, in addition to the short-circuited stub
technique it is sometimes practical to match impedances by introducing a section of transmission line with gradually changing dimensions. The most common application of this technique is the tapered
open-wire line between a TV antenna and the twin lead running to
the receiver.
Insertion loss. Insertion loss, discussed in Chapters 3 and 4, may be
defined as the loss resulting from the insertion of a network between
a source and a load. Further consideration of this factor is desirable
because important contributions to insertion loss occur as a result
of reflections due to impedance mismatches.

Consider the circuits of Figure 5-8. If the four-terminal network
or transmission line is not present, as in Figure 5-8 (a), the current
supplied to Z L is
II

== E/(ZG + Zd.

*Standing wave ratios, reflection coefficients, wavelengths, complex impedances,
and other transmission relationships are conveniently computed by Smith charts,
nomographic diagrams that display these relationships in a convenient form
[4, 5, and 7]. Accurate and extensive calculations of these values and relationships are today carried out on an electronic computer.

132

Elements of Transmission Analysis

Vol. 1

Symmetrical
four-terminal
network or
transmission
line with
characteristic
impedance

Zo

(a)

(b)

Figure 5-8. Circuits for insertion loss analysis.

When the network is inserted in the circuit, Figure 5-8 (b), the current
in Z L may be shown to be

12

==

2E Zo e-1'
- (Zo - ZG) (Zo - Zd e- 21"

(Zo

+ ZG)

(Zo

+ Zd

(Zo

+ ZG)

(Zo

+ Zd

Then,
11

7;

==

-

(Zo - ZG) (Zo - ZL)
2(ZG + Zd Zo e- Y

2

e - 1'

which, when factored, gives

~ ==[(Zo + ZG) (Zo + ZdJ [1 _ (Zo -ZG) (Zo - Zd e- 21'
12

2 (ZG

+ Zd

Zo

e-1'

(Zo

+ ZG)

(Zo

+ Zd

J.

(5-23)

The second bracketed term is usually neglected. It results from
interactions due to network termination impedances not being the
proper image impedances for the network. If the network is a
transmission line of any significant length, the term e- 21' makes the
interaction effect negligible. If either ZG or ZL is equal to Zo or, in
the case of a network, is the true image impedance, the interaction
effect vanishes completely.

Chap. 5

Transmission Line Theo.ry

133

Thus, the insertion loss is usually written,

.

InsertIon loss ~ 20 log

I (Zo
+ ZG) (Zo + Zd I
2 (ZG + Zd Zo e-Y

dB.

The right side of this equation may be rearranged to give

.

InsertIOn loss ~ 20 log

- 20 log
where

a

I (Zo
+ ZG) I
I (Zo + Zd I
2 yZoZG + 20 log 2 yZOZL
I

ZG + ZL
2 yZGZL

I + 8.686 a

dB.
(5-24)

is the real component of the propagation constant 'Y.

The approximation to the insertion loss given in Equation (5-24)
contains three reflection terms and the attenuation constant, a. The
three reflection terms are seen to be related to the reflection factor
defined in Equation (5-18). The first two of these increase the
insertion loss as a result of the mismatch between either Zo and ZG
or Zo and ZL. The third is a negative term representing the reflection
loss due to the mismatch between ZG and ZL when the intermediate
networ k is not present.
Terms corresponding to the term 20 log ycos (JG/cos (JL of Equation
(5-17) do not appear in the equation for insertion loss because, in
the insertion loss definition, the ratio of currents (or, more precisely,
powers) is taken with respect to the same impedance, ZL. Thus, the
power factor term reduces to unity.
If the transmission line is short or for any other reason has very
low loss, the insertion loss expression of Equation (5-24) must be
modified by the interaction (second bracketed) term in Equation
(5-23). The evaluation of this equation is usually quite laborious but
computer programs, tables, and nomographs are available to simplify
computations.
Return Loss. In the design of two-wire circuits, the amount of signal
reflected at a junction is of interest because the reflected energy
represents an echo of which the amplitude must be controlled. As

Elements of Transmission Analysis

134

Vol. 1

discussed in Chapter 4, the difference in dB between the incident
current or voltage and the reflected current or voltage at an impedance
discontinuity is called return loss. If the two impedances at a junction are matched, the return loss is infinite, since there is no energy
reflected. The greater the difference between impedances on each
side of a junction, the lower the return loss. At the junction of two
lines of impedance Z 1 and Z 2,
Return loss

1 == 20 log
== 20 log IPT

+

\ Zl
Zl _ Z21
Z2

dB,

(5-25)

where p is the reflection coefficient.
In the telephone plant, a serious source of low return loss is the
interface between two-wire and four-wire facilities; four-wire terminating sets contain a compromise balancing network that may not
match the impedance of the office wiring or other connected two-wire
circuits. The most serious problem occurs at class 5 switching offices
where toll connecting trunks are switched to a variety of loops with
a wide range of impedances.
In the Bell System, the term structural return loss is commonly used
as a measure of the departure of the characteristic impedance of a
transmission medium from its design or nominal value. The term is
descriptive of the fact that such impedance departures are primarily
due to systematic and repetitive deformations of the physical structure of the medium. The values of Z used in Equation (5-25) may
be regarded as the nominal and measured values of the characteristic
impedance of the medium to determine the structural return loss.
5-3

LOADED LINES

In the previous discussion of velocity of propagation, it was pointed
out that transmission lines normally introduce delay distortion. It
was further suggested that delay distortion can be theoretically
eliminated by design. An understanding of the theoretical basis for
such a design is of some interest. Of far great practical importance
is the application of the relationships involved to the reduction of
attenuation over most of the voice-frequency band.
Analysis

To achieve the theoretical design of a distortionless line, it is
necessary that the series impedance, Z, and the shunt admittance, Y,

Tra nsm ission Li ne Theory

Chap. 5

135

have the same angle. This requirement may be expressed
wL

wC

R==G'
or
(5-26)

LG ==RC.
The impedance and admittance may be written Z == R
Y == G
jwC, respectively. Thus,

+

+ jwL

and

(5-27)
When this expression is substituted in Equation (5-14),
'Y

== yZY == Z

'Y

== a + jf3 == yGjR

yGjR

== Z yCjL

(5-28)

Then,

(R

+ jwL)

and
a

== yRG == RyCjL

(5-29)

f3

== wL yGjR == w yLC

(5-30)

v

== wjf3 == Ij y'LC

(5-31)

With Equations (5-26) and (5-27) substituted in Equation (5-11a),

Zo

==

yZjY

== yRjG == yLjC

ohms.

( 5-32)

Thus, when wLjR == wCjG, the attenuation (a), the velocity (v),and
the characteristic impedance (Zo) are independent of frequency, and
Zo is a pure resistance. Such a line, terminated in its characteristic
impedance, has no loss distortion or delay distortion. Note, however,
that the attenuation and velocity both decrease, and the characteristic
impedance increases.

136

Elements of Transmission Analysis

Vol. 1

Unfortunately, a transmission line having such optimum characteristics is not readily attainable in practice. In transmission lines
made up of pairs in well maintained cables, the value of the conductance, G, is very small. It is not desirable to increase it artificially
because that would increase the attenuation correspondingly as indicated in Equation (5-29). The value of capacitance cannot be changed
appreciably because of practical considerations of spacing between
conductors. To approach the optimum condition where LG == RC as
indicated by Equation (5-26), it would be necessary either to increase
the inductance, L, or to reduce the resistance R. The latter is not
economical (it may be accomplished by increasing the size of the
wire), and so the only remaining alternative is to increase the inductance. This practice, known as inductive loading, is used to approach
the conditions sought, especially to reduce the line attenuation.
Inductive Loading

In considering the effect of inductive loading, note that the configuration of the T section of Figure 5-5 is basically that of a lowpass filter as illustrated in Figure 4-29. The critical frequency of
such a structure is the frequency below which there is very little
attenuation (ideally none) and above which the attenuation increases
very rapidly. For the structure of Figure 5-5 in which G == 0, this
frequency is

1

Hz.
Ie 1TyLC

(5-33)

When applied to lines loaded with discrete elements, the value of L
is the load coil inductance. Although the inductive component of the
line impedance of the load section should be added, it is usually
negligible. Similarly, the value of C to be used is the primary constant
value of capacitance for the medium multiplied by the length of
the load section. In theory, this value should be increased by the
capacitance of the load coil, but this also is usually negligible.
As previously mentioned, series inductance may be added to reduce
the attenuation in a cable pair. Below the critical frequency, Ie, the
attenuation is reduced as indicated by Equation (5'-29). Unfortunately, line inductance cannot be increased by loading without

Chap. 5

137

Transmission Line Theory

increasing resistance by virtue of the wire used in the load coils.
Because of the resistance increase and other frequency-dependent
limitations in the application of inductive loading, the attenuation
is, in practice, more nearly ,a == (Ry'C/L) /2 than the value of
Equation (5-29). Above the critical frequency, the attenuation increases rapidly. The effect of increasing L by installing load coils in
a line is illustrated by Figure 5-9.
Loading Methods. Loading may be accomplished by either of two
practical methods. The first, called continuous loading, involves
placing magnetic material (e.g., permalloy tape) around the copper
conductors. This method is expensive and has been employed in only
a few cases on submarine cable installations. The second method
uses discrete inductances introduced along the line at regular intervals.
16

14

I.
/i

12

6

4

/

--

N°7

/

~ .... _-- ~/

I
I

I
I

I.

/4

H88 loading

500

2000

1000

3000

5000

Frequency (Hz)

Figure 5-9. Insertion loss of 12,000 feet of 26-gauge cable measured
between terminations of 900 ohms in series with 2 JLf.

138

Elements of Transmission Analysis

Vol. 1

Below the critical frequency, the transmission line analysis for such
an arrangement is reasonably accurate on the assumption that such
components are uniformly distributed along the line but this
assumption does not hold above the critical frequency.
Load Coil Spacing. Load coils introduce impedance discontinuities
into an otherwise smooth or uniform line. This effect is minimized
by making the spacing between load coils short compared to the
wavelength of the transmitted signal and by spacing the coils precisely along the line. Imprecise coil spacing and coil resistance both
introduce transmission irregularities in the passband primarily as a
result of the deterioration of the structural return loss of the medium.
General rules for the precision of spacing of load coils have been
worked out, and manufacturing limits on the allowable variation in
coil parameters are imposed. Corrective measures to overcome
situations that, due to geographical or other considerations, cannot
be adj usted to meet requirements on the uniformity of coil spacing
are given in the form of building-out network specifications. General
rules on allowable spacing deviations as applied to interlocal trunks
are as follows:

(1) The deviation of the average spacing from the nominal or
standard value should not exceed ±2 percent.
(2) The deviations of the length of individual sections from the
average section length should not exceed ±3 percent.
(3) The percentage of deviation of each section length from the
average section length should be determined and the
numerical average of these percentages, disregarding signs,
should be 1.2 percent or less, where practicable.
End sections, nominally designed as one-half the standard length, are
frequently built out by the use of additional discrete components to
correct the electrical length of the section (overcoming natural length
discrepancies) or to correct the impedance of the structure to conform with impedance matching requirements at the central office.
A number of loading arrangements have been standardized in the
Bell System. The spacing between coils, or loading-section length, is

Chap. 5

139

Transmission Line Theory

designated by a series of code letters. The codes for the more common
spacings are as follows:
B

C
D

E
H

3000
929
4500
5575
6000

feet
feet
feet
feet
feet

M
X
y
Z

9000
680
2130
5280

feet
feet
feet
feet

This spacing code is combined with numerals to designate wire gauge
and load inductance values. For example, the cable of Figure 5-9
is designated as 26H88 loading, indicating 26-gauge wire, 6000-foot
spacing, and load coils of 88 millihenries inductance. This inductance
is equally divided between two coils wound on a toroidal core. Each
coil is connected in one side of the line' in such a manner that the
two inductances add (series aiding) to give the required value. These
loading arrangements have been designed to achieve the greatest
practicable reduction in attenuation and not to achieve a minimum of
delay distortion. Thus, the criterion for minimum delay distortion
given in Equation (5-26) is not met.
5-4

COAXIAL CABLE

Consideration of transmission lines thus far has been confined to
lines made up of two parallel wire conductors. However, a coaxial
configuration of conductors may be used to advantage where high
and very high frequencies are involved. The conducting pair consists
of a cylindrical tube in which is centered a wire as shown in

Figure 5-10. Coaxial cable.

140

Elements of Transmission Analysis

Vol. 1

Figure 5-10. In practice, the central wire is held in place quite
accurately by insulating material which may take the form of a solid
or plastic foam core, discs or beads strung along the center conductor.
or a spirally wrapped plastic string. In such a conducting pair, equal
and opposite currents flow in the central wire and the outer tube, just
as equal and opposite currents flow in the more ordinary parallel wires.
At high frequencies, a unit length of coaxial in which the dielectric
loss in the insulation is negligible (effectively gaseous) would have an
inductance which is about one-half the inductance of two parallel
wires separated by a distance equal to the radius of the coaxial tube.
The capacitance of the same coaxial is approximately twice that of
two parallel wires separated by the same distance and having the
same diameter as that of the central coaxial conductor. If the outside
radius of the central conductor is designated a and the internal
radius of the tube is b, the characteristic impedance at high frequencies neglecting leakage is approximately

Zo ==

.6rr
"C

b

== 138 log a

ohms.

(5-34)

The attenuation constant per mile, where both conductors are of
the same material, varies 'as the square root of frequency and is
approximately

_
a -

R _
-6
2Zo - 24.4 X 10

vi-(a1+b bl)jnepers/mlle.

[

(5-35)

loga

where a and b are in centimeters. From Equation (5-35) it may be
determined that minimum attenuation is obtained when the coaxial
is so designed that b /a == 3.6. With this configuration, Zo is about
77 ohms. The attenuation varies with temperature by approximately
0.11 percent per degree Fahrenheit.
The present standard coaxial used for transmission in the Bell
System employs a copper tube 0.369 inches in inside diameter and
a copper center wire 0.1003 inches in diameter. This, it will be noted,
approximates the optimum ratio specified above for minimum attenuation. The nominal impedance is 75 ohms, somewhat lower than

Chap. 5

Transmission Line Theory

141

would be computed by use of Equation (5-34). This is because the
insulation, which is a composite of air and polyethylene discs, has
a dielectric constant of about 1.1. Velocity of propagation in the
coaxial approaches closely the speed of light. A study of the basic
characteristics of the coaxial shows that at the high frequencies
assumed, the attenuation is substantially less than that of a parallel
wire line of comparable dimensions. The attenuation is approximately
3.95 dB/mile at 1 MHz and at 20°C. More important is the fact that
at frequencies of interest the shielding effect of the outer cylindrical
conductor prevents interference from external sources of electric
energy. The shielding effect also prevents radiation losses of the
energy being transmitted over the coaxial. Thus, crosstalk between
coaxials is minimum.

REFERENCES

1. Anner, G. E. and W. L. Everitt. Communication Engineering (New York:

McGraw-Hill Book Company, Inc., 1956).
2. Schelkunoff, S. A. Electromagnetic Waves (Princeton, N. J.: D. Van Nostrand
Company, Inc., 1943).
3. Johnson, W. C. Transmission Lines and Networks (New York: McGraw-Hill
Book Company, Inc., 1950).
4. Ware, L. A. and H. R. Reed. Communication Circuits (New York: John Wiley
and Sons, Inc., 1955).
5. Skilling, H. H. Electric Transmission Lines ( New York: McGraw-Hill Book
Company, Inc., 1951).
6. Creamer, W. J. Communication Networks and Lines (New York: Harper and
Brothers, 1951).
7. Smith, P. H. "Transmission Line Calculator," Electronics (Jan. 1939 and
Jan. 1944).

Elements of Transmission Analysis

Chapter 6

Wave Analysis
A signal may often be represented by a function whose value is
specified at every instant of time. In transmission work, however,
this type of characterization is not always the most convenient to
use because information about transmission lines and networks is
usually presented as functions of frequency rather than of time.
Therefore, a method is needed for translating between time-domain
and frequency-domain expressions of signal and network characteristics. It is pos1stible to pass from one domain to the other by using
mathematical transformations. This ability is useful in providing
answers to questions which arise when a pulse signal expressed as
a time-domain function is applied to a transmission line whose
characteristics are known in terms of frequency-domain functions.
These questions might be: How does the pulse look at the output of
the line? What are the frequency spectra of pulse signals as functions
of pulse repetition rates and duty cycles? What is· the resultant
energy distribution? What are the bandwidth considerations?
The duality between frequency and time domains in describing
signals and linear networks is a concept that can become so familiar
that a person may often unconsciously transfer from one domain
to the other without effort. For instance, a sine wave of frequency
10 might be pictured in the time domain as a curve which crosses the
time axis 2/0 times per second or in the frequency domain as a narrow
spike located at a point 1 == 10 on the frequency axis and characterized
by two numbers giving its amplitude and phase. In this simple case,
a method of passing from one of these representations to the other
is simple to visualize and to formulate. The frequency, amplitude,
and phase can be obtained from a time-domain representation of a
sinusoidal wave by merely counting and measuring appropriate dimensions; on the other hand, if the frequency, amplitude, and phase
are given, the time-domain waveform can be constructed. However,
for more complicated waveforms, this transformation is not so simple,
142

Chap. 6

Wave Analysis

143

and a well defined mathematical procedure must be employed to pass
from one domain to the other.
The Fourier transform pair is the mathematical formulation of
this useful concept; as such, it is indispensable for dealing with
signals and linear networks. A review of some of the important properties of the Fourier transform and illustrations of its uses can give
a qualitative understanding of its meaning and application. The
reader is referred to standard mathematics texts for more rigorous
treatments of the subject.

6-1

INSTRUMENTATION

To complement the mathematical procedures of defining signals,
interferences, or networks by means of the Fourier transform pair,
field or laboratory observations are often needed to study engineering
problems of maintenance, design, or performance evaluations. Two
types of instrumentation are commonly used to display signals and
interferences in the time or frequency domain for visual study.
These are the cathode ray oscilloscope, which displays a signal or an
interference in the time domain, and the spectrum analyzer, which
displays signal or interference components in a frequency band.

Figure 6-1 illustrates, in a simple block diagram, the operation
of a cathode ray oscilloscope. The position of the cathode ray spot
on the tube face is a function of the voltages impressed on the horizontal and vertical deflection plates. The output signal of the sawtooth generator is impressed on the horizontal deflection plates and
causes the spot to move repetitively from left to right. The signal
under study, usually a periodic time function, is applied to the vertical
deflection plates. This causes the spot to move vertically in accordance
with the voltage applied and, when the two signals are properly
synchronized, a time-domain representation of the test signal waveform is traced on the tube face.
The operation of a spectrum analyzer is somewhat more complicated. A sawtooth signal is used to deflect the spot from left to right

Elements of Transmission Analysis

144

Vol. 1

t ----.

~

Signal
under
test

I
Defled;o, plote.

~

ri
Sawtooth
generator

1
i l C o t h o d e ray
tube

~--------------------

t---+

Figure 6-1. Cathode ray oscilloscope operation (time domain).

on the tube face as in the cathode ray oscilloscope. However, the
signal applied to the vertical plates must be subj ected to a number
of transformations before it can be so used. The signal consists of a
broad band of frequencies illustrated by the band from IB to IT in
Figure 6-2. This signal is impressed at the input to the analyzer and
mixed with the output of the tunable oscillator. This oscillator is
driven by the sawtooth generator. Its output signal varies in frequency to sweep across the band from fB to IT in a repetitive fashion
as the output voltage of the sawtooth generator increases from its
minimum to its maximum value. This process converts the signal,
in effect, from a voltage-frequency function to a voltage-time function.
The output of the mixer, however, has many unwanted components.
A bandpass filter is used to select the desired component, which is
then impressed on the vertical deflection plates of the cathode ray

Chap. 6

Wave Ana lysis

145

Signal
under

Bandpass
filter

Mixer

Tunable
oscillator

t
t--+

Figure 6-2. Spectrum analyzer operation (frequency domain).

tube. The filtering is usually accomplished through several stages of
intermediate frequencies where the bandlimiting is more easily
effected.

146
6-2

Elements of Transmission Analysis

Vol. 1

PERIODIC SIGNALS

The alternative descriptions of periodic s'ignals in the time and
frequency domains are based upon the fact that when sine waves
of appropriate frequencies, phases, and amplitudes are combined,
their sum can be made to approximate any periodic signal. Similarly,
anyone of these signals can be decomposed into its component sine
waves.

Fourier Series Representation

A good starting point for discussing wave analysis is the familiar
Fourier series representation of periodic functions given by
00

f (t) =

~o +

2:

(An cos nWot

+ Bn sin 1U1Jot) ,

(6-1)

n=l

where Ao, An, and Btl are constants that may be computed by the
following equations [1] :
21T

AD =

!f

f(tjdt,

(6-2)

o

21T

An =

-.l (

f (t) cos nt dt,

(6-3)

7T "

o

and

B.

=!

21T

f

f(tj sin nt dt.

(6-4)

o

The interval over which the integration is performed, 0 to 27T, is
the fundamental period of the function f ( t) .
The validity of the Fourier series may be demonstrated by displaying a square wave simultaneously on an oscilloscope and on a

Chap. 6

Wave Analysis

147

spectrum analyzer. The spectral components of such a signal may be
filtered and displayed on the two instruments in various combinations.
To illustrate such a demonstration, Equation (6-1) may be rewritten
00

f (t) =

~o - +

2:

Cn cos (nwot

+ 

FL

Polar signal nonreturn to zero

Polar signal return to zero,
50% duty cycle

Bipolar signal return to zero,
50% duty cycle

Figure 6-8. Some signal formats for a random signal.

the familiar (sin x) Ix form. Note
that the expression has a continuous distribution of energy at all
frequencies, rather than at discrete
frequencies as indicated for the
o +7/2
-7/2
components of the Fourier series
t ---.
for the periodic function represented by Equation (6-10). The
function of Equation (6-13) is a
Figure 6-9. A single pulse.
pure real and, therefore, the components of the signal in the time domain are all cosine functions, in
phase at t == O. Values for g (.w) in Equation (6-13) may be found by
using appropriate values for A and T and, substituting x == WT /2, by
use of the plotted values of (sin x) /x in Figure 6-7.
The Impulse. An impulse is approximated when a rectangular pulse
is narrowed without limit while keeping its area (AT in Figure 6-9)

160

Elements of Transmission Analysis

Vol. 1

unchanged. To simplify the treatment, the area may be assumed
to be equal to unity. Thus, in the time domain an impulse is a signal
having energy but infinitesimal duration.
The corresponding frequency spectrum may be found from Equation (6-13) by noting the assumption that AT == 1 and that
(sin wTj2) / (wT/2) == 1 when w'T/2 == 0 (see Figure 6-7). Thus,
the resulting spectrum contains all frequencies from - 00 to
00
of equal phase at t == 0 and each having an amplitude of unity. This
description of an impuse is useful in discussing the impulse response
of a network.

+

Transmission Response

Transmission of nonperiodic signals through a network or transmission line may be studied by Fourier transform methods in either
the frequency or time domain.
Frequency Response. The complex frequency spectrum can often be
utilized to simplify rather complicated problems. The advantages
to be had by operating in the frequency domain arise from the
relatively simple relationship between input and output signals
transmitted through linear networks or transmission lines when
the relationship is specified in that dimension. In a typical problem,
the input signal has a spectrum gi(.W) and the output go(w). The
transmission path can be described by a frequency function which is
its transfer impedance (transfer voltage or current ratio), or what is
commonly called its frequency response. This function, H (w), can
be established by computation from the known circuit constants of
the system or network. It can also be found experimentally by applying a sine-wave test signal of known characteristics at the input and
measuring amplitude and relative phase at the output.

The relationship between the input and output spectra of a signal
applied to a network is particularly simple;
(6-14)
where go, gi, and H are, in general, complex functions of the radian
frequency, (tl. In polar form, the amplitude and phase relationships
are, respectively,

I go(w) I == I H(w) II gi(W) I
Oo(w) == Oh('W) + Oi(W)

(6-15)
(6-16)

Chap. 6

Wave Analysis

161

The validity of these relations rests upon the superposition principle since go «(u) is computed by assuming that it is a linear combination of the responses of the network to each frequency component
(taken individually) in the input wave. This observation implies
that if the response of a linear system to the gamut of sine-wave
excitations is known, then its response to any other waveform can be
found uniquely by decomposing that wave into its Fourier components
and computing the response to each individual component. The output
waveform, f 0 (t), can be found by evaluating the Fourier integral of
go (w) . The principle outlined here is the basis for all sine-wave
testing techniques used in practice. It should be noted, however,
that it is useful only for linear systems since it is only in such systems
that superposition is generally valid. In the case of a nonlinear
device, such as a rectifier, the response to each input waveform must
be computed separately; the complex frequency response of the network does not allow generalization to include other functions.
Impulse Response. Transmission through a network can also be completely described in terms of its impulse response, which is defined
as the function h (t) that would be found at the output as a result of
applying an impulse (previously defined) to the input terminals.
Since the time function applied to the input has a flat frequency
spectrum, it would be expected that h (t) will have a spectrum which
differs from flatness by the frequency characteristic of the network.
In other words, H (w) gives the frequency and phase spectra of h (t) .
Expressed analytically, a unit impulse input to a network H (w)
produces an output h (t) given by
(6-17)

F [h(t)] ==H(w)

from which it follows that
H fw)

==

f
-

«I

h (t) e - j(fJtdt

(6-18)

00

and also
h ( t)

= 2~

i ~~

H ( 6J)

e'o' Ik.!.

(6-19)

162

Elements of Transmission Analysis

Vol. 1

The impulse response is, of course, a real function of time. Certain
relationships between H (,w), H (-,w) , and the conjugate of H (ell),
written H*(w), can be shown [4]. These lead to the following:
H (-ell)

== H* (w)
(6-20)

I H(w) I == I H(-w) I
where HR and HI are the real and imaginary parts, respectively,
of H (ell).
These are extremely important mathematical properties of any
physical transmission path - network or transmission line. The first
expression in the series of equations numbered (6-20) shows that
the transfer impedance of the network, H (w), expressed for negative
frequencies, H (-,w), is equal to its conjugate expressed for positive
frequencies, H* (,w). From this fact, the second expression is derived
directly to show that the real part of the impedance function, HR (ell),
has even symmetry about zero frequency. The third expression shows
that the imaginary (phase) component of H (w), HI, has odd symmetry
about zero frequency. The last expression, showing the relation between absolute values of H, follows from the first.
Bandwidth. It was previously shown, in the discussion of the single
rectangular pulse, that the ability to establish limits of integration led
to a useful expression for a frequency domain description of the pulse.
In a similar manner, the recognition of the finite bandwidth of a
channel makes practical the impulse response analysis of transmission
through a network.

An examination of the Fourier integral of Equation (6-19) indicates that in order to determine the function of time corresponding to
a particular frequency spectrum, it is necessary to know that spectrum
from - 00 to
00. However, in the application of Fourier synthesis
to any real situation, the signal under study is always generated by
a source capable of producing only a finite range of frequencies.

+

Chap. 6

Wave Ana lysis

163

Similarly, the signal is carried on a channel capable of transmitting
only a finite bandwidth. Hence, it is necessary to examine the spectrum only in this region, and the signal can be assumed to be zero
outside this region. Such a finite bandwidth would restrict the number
of time functions which can be synthesized to those whose fastest
time rate of change is of the same order as the rate of the highest
frequency component that may be present.
In practice, limits are used which depend upon the characteristics
of the physical system or circuit being dealt with, rather than using
the infinite limits given in Equation (6-19). This equation may be
modified to account for the finite bandwidth of any real system, and
the Fourier integral can be written
(6-21)

Example 6-2: Impulse Response of an Ideal Low-Pass Filter
As an example of the usefulness of the Fourier transform pair,
consider a problem in pulse transmission, where information is
being transmitted in digital form. At the transmitting terminal,
a pulse is either sent or not sent at times t 1 , ~, etc. The problem
is to tell, after the signal has been transmitted through the transmission medium (represented here by a low-pass filter), whether
or not a pulse is present for each signal element or time slot at
the receiver.
For this example, assume that the difference between two
successive coded signals, illustrated by S1 and S2 in Figure 6-10,

2

345

6

7

8

2345678

t---...

Figure 6-10. Successive code signals.

164

Elements of Transmission Analysis

Vol. 1

lies in the fact that 8 1 has a
pulse in position 5, whereas 8 2
does not. Further assume
that these signals are passed
through a low-pass filter which
has an idealized transmission characteristic shown in
Figure 6-11. This idealized
transmission
characteristic
o ~----------~----o
has a constant finite value of
f~
attenuation (assumed to be
o dB for this problem) from
Figure 6-11. Idealized low-pass trans- zero frequency to /1 and has
mission characteristic.
infinite attenuation above /1.
lt has no delay distortion for
frequencies from zero to /1; delay distortion above It is of no consequence since there is no signal transmission above /1. (This is
an easy case to analyze; such characteristics are impossible to
achieve but can be approximated. More achievable characteristics
are more complicated to analyze.) The example, then, illustrates
how bandwidth limitation alone can cause energy in the fourth
position of 8 2 to spill over into pulse position 5.
If the transmission characteristic of the network is known, it
is next necessary to assume a spectrum for the input pulse at
position 4 and, in turn, determine its effect on the pulse or lack
of pulse in position 5. Although the first inclination would
probably be to assume a rectangular pulse like that of Figure 6-9
(even though real pulses are never exactly rectangular), the
problem can be simplified by assuming an impulse. Compare
the spectrum of an impulse (flat versus frequency, with no
phase reversals) with the spectrum of a rectangular pulse in
the region of (() == 0 (almost flat for very low frequencies). It
is seen that, if the transmitted bandwidth is small enough compared to the first frequency at which (sin x) Ix becomes zero, the
output will be the same whether the input is taken to be a narrow
rectangular pulse or an impulse. Since the spectrum of an impulse
is easier to handle analytically, the input is assumed to be an
impulse. If it is desired to refine the results later, the input
spectrum may be modified to have the (sin x) Ix shape, or the
frequency response, H (cu), may be modified.

Wave Analysis

Chap. 6

Moreover, if the input
signal is assumed to be an impulse, the task is to determine
the signal (as a function of
time) at the output of a path
having the 'transmission characteristic shown in Figure
6-11.
First
notice
that
I H (w) I can be plotted for
negative as well as positive
frequencies. By the relations
of Equations (6-20), the plot
would look like Figure 6-12,
where (tJ1 = 2Tr/1 has been
substituted for 11.

165

I II
H(ru)

t

I

I'

Figure 6- 12. Idealized low-pass characteristic (positive and
negative frequencies).

If Equation (6-19) is applied to Figure 6-12 and constant
delay is ignored, the output pulse may be represented as

The term H(w) in Equation (6-19) is shown in Figure 6-12 to
be equal to unity in the interval from -WI to +'W1 and so does not
appear in the above expression for h (t).
This equation may be integrated to yield
h(t)

=

(tJ1

X sin 'WIt

'1T

(tJ1t

This is a (sin x) Ix function
of time plotted in Figure 6-13.
On this plot, t
0 is arbitrary; for a physical network
which approximates the characteristic of Figures 6-11 and
6-12, the zero time point represents the absolute delay of
the transmission path. The
optimum time for the next

t

h(t)

=

t---+

Figure 6-13. h(t) at output of lowpass transmission path.

166

Elements of Transmission Analysis

Vol. 1

pulse is at t = 1/ (2fd because h (t) goes through zero at that
point, and interpulse (or intersymbol) interference is minimized.
If the cutoff of the transmission path is at 500 kHz, then the
interval between impulses should be 1 microsecond (repetition
rate, 1 MHz). A shorter interval would tend to make the receiver
think a pulse is present when in fact it is not; a longer interval
would result in some cancellation when the following pulse is
present. The spacing of pulses to avoid intersymbol interference
is one of the fundamental requirements in pulse transmission.
The necessity for distinguishing between the presence or
absence of a pulse in position 5 of 8 1 and 8 2 in Figure 6-10 is
importantly dependent on a design that minimizes the effect of
the presence of an unwanted signal in position 5 due to the pulse
in position 4. This is accomplished by relating, in the design,
the system transmission characteristic and pulse repetition rate
so that the next pulse position (position 5) corresponds to the
crossover of pulse number 4 at time 1/ (2fd as illustrated in
Figure 6-13.
This example illustrates the way in which the Fourier transform
pair can be used. If an input signal which is a given function of
time is assumed, the signal (as a function of time) at the output
of a network can be found if the transmission characteristic of the
network is known. The results may be expressed in very general
functional terms in order to display the nature of a problem, or
specific formulas may be used to obtain specific numerical results.
In any particular case, finding the solution may be easy (as in
Example 6-2) or may involve laborious or sophisticated mathematical
manipulation of the specific functions involved in the problem. The
basic idea remains the same.
Another class of transmission problems involves circuits having
bandpass characteristics. Such problems are often difficult to solve
directly but are amenable to solution by the methods of Fourier
analysis using an equivalent low-pass circuit arrangement such as
that in Example 6-2 [5, 6].
REFERENCES

1. Scott, R. E. Linear Circuits (Reading, Mass. : Addison-Wesley Publishing
Company, Inc., 1960).

2. Re ference Data for Radio Engineers (Indianapolis: Howard W. Sams and
Company, Inc., Sixth Edition, 1975), p. 44-12.

Chap. 6

Wave Analysis

167

3. Franks, L. E. Signal Theory (Englewood Cliffs, N. J.: Prentice-Hall, Inc.,
1969) .
4. Bogert, B. P. et al. (Special issue on the fast Fourier transform) IEEE
Transactions on Audio and Electroacoustics, Vol. A U-15 (June 1967).
5. Technical Staff of Ben Telephone Laboratories. Transmission Systems for
Communications, Revised Third Edition (Winston-Salem, N. C.: Western
Electric Company, Inc., 1964), Appendix A.
6. Sunde, E. D. "Theoretical Fundamentals of Pulse Transmission," I and II,
Bell System Tech. J., Vol. 33 (May 1954) pp. 721-788 and (July 1954) pp.
987-1010.
7. Watson, G. N. and E. T. Whittaker. A Course of Modern Analysis (Cambridge: University Press, 1940).
8. Wylie, C. R., Jr. Advanced Engineering Mathematics (New York: McGrawHill Book Company, Inc., 1951).
9. Van Valkenburg, M. E. Network Analysis (Englewood Cliffs, N. J.: PrenticeHall, Inc., 1964).
10. Everitt, W. L. and G. E. Anner. Communication Engineering (New York:
McGraw-Hill Book Company, Inc., 1956).

Elements of Transmission Analysis

Chapter 7

Negative Feedback Amplifiers
Detailed knowledge of feedback principles is needed only by those
involved in the design and development of active transmission circuits.
However, the high performance of modern transmission equipment
is so dependent on the use of negative feedback that it appears desirable to provide some appreciation of why feedback is used, what it
accomplishes, how it operates in electronic circuits, what some of the
design limitations are, and what limitations exist in its application.
With the design of feedback amplifiers used as the basis for discussion, feedback mechanisms and the interactions among them may be
covered as background for an understanding of the interdependence
of system and amplifier, or repeater, performance.
Negative feedback is commonly used in transmission systems for
communications because it acts to suppress unwanted changes in
amplifier gain and sUbstantially reduces harmonic distortion and interchannel modulation noise. It also facilitates the design of amplifiers
having much better broadband return loss characteristics than can
be achieved without feedback.
7-1

THE PRINCIPLE OF NEGATIVE FEEDBACK

In its simplest form, a negative feedback amplifier can be regarded
as a combination of an ordinary amplifier (the fL circuit) and a
passive network (the f3 circuit) ; by means of the latter, a portion of
the output signal of the amplifier is combined out of phase with its
input signal as illustrated in Figure 7-1. Ideally, this phase difference
is 180 degrees and hence the term negative feedback.
The gain of a feedback amplifier may be written
1 - fLf3
168

(7-1)

Chap. 7

Negative Fe'edback Amplifiers

169

Figure 7-1. Feedback amplifier configuration.

Without feedback (f3 == 0), the gain would be simply e2/ el == IL. Thus,
one effect of feedback is the reduction of gain by the term 1/ (1 - .ILf3).
In general, the IL gain is very much larger than unity. As a result,
an approximation may be derived from Equation (7-1) as follows:
1

1 -1Lf3

(1/1L) - f3 ~

1

-7f;

(7-2)

that is, the gain of a feedback amplifier is approximately proportional to f3-circuit loss and is independent of J.L-circuit gain.
These characteristics result in feedback amplifiers having attributes
that far outweigh the disadvantage of reduced amplifier gain; consequently, in modern design, negative feedback is used in nearly all
electronic amplifiers. It is especially valuable in amplifiers used in
transmission systems where many amplifiers are connected in tandem.
Here, without feedback the cumulative effect of small imperfections
in individual amplifiers would be intolerable.
7 -2

APPLICATIONS OF FEEDBACK

The design of transmission systems involves finding simultaneous
solutions to problems of bandwidth, repeater spacing, and signal-tonoise performance. These in turn are related to channel capacity,
transmission loss in the medium and the achievabiIity of compensating

170

Elements of Transmission Analysis

Vol. 1

gain, the cumulation of interferences such as thermal and intermodulation noise, and the provision of adequate signal load carrying
capacity. The design of amplifiers to meet such requirements is made
possible by feedback. It is incorporated in amplifiers of line repeaters
used in analog and digital cable systems as well as in the amplifiers
that are found in all types of terminal and station equipment.
One other important transmission system application is the use
of feedback in dynamic backward-acting regulator and equalizer
circuits. Such circuits utilize one or more single-frequency signals,
called pilots, which are applied to a transmission system at the
transmitting terminal at precise and carefully controlled frequencies
and amplitudes. Immediately following a point of regulation, the
pilot signal is picked off the line, rectified, and compared with a
reference voltage. The error signal, i.e., the difference between the
rectified pilot and the reference, is fed back to the input of a regulating amplifier through a network. The response of this network
to the error signal changes the transmission gain in a direction and
by an amount to correct the pilot amplitude at the output of the
regulator. By the use of several pilots appropriately positioned in the
signal spectrum, complex gain/frequency corrections are made across
the entire signal band, resulting in dynamic equalization of the highfrequency line.
7-3

BENEFITS OF FEEDBACK

Once a system design is chosen, any departure from the ideal
represents a penalty in performance. Departures in system gain result
in increases in thermal noise if the gain is less than the design value
or in intermodulation noise if the gain is greater than desired.
Furthermore, in the latter situation the system may become overloaded. In addition to the performance penalties, such gain departures
carry a cost penalty because they must be compensated by some form
of equalization to correct the gain/frequency or delay /frequency
characteristic, or both, to within tolerable limits over the transmission
band.
Equation (7 -2) shows that the gain of a feedback amplifier is
nearly independent of the JL circuit. Thus, departures from the ideal
gain/frequency characteristic (i.e., departures from design values)
that are caused by changes in the J.L circuit are effectively reduced

Chap. 7

Negative Feedback Amplifiers

171

by feedback. These changes may be caused by manufacturing, aging,
and temperature-induced variations in ,u-circuit components, which
include the active devices. Gain variations caused by power supply
fluctuations are also reduced.
The nonlinear input/output characteristics of all active devices are
another source of impairment in broadband electronic circuits. This
type of impairment, often referred to as harmonic distortion or intermodulation noise, is also reduced by the use of negative feedback. If
no other benefits accrued from using feedback, this alone would justify
application in analog cable transmission systems and in FM terminal
equipment of microwave radio systems.
Additional feedback benefits accrue in the resolution of problems
involving amplifier input and output impedances. Usually it is required that these impedances, or at least their absolute values, match
the impedances of the circuits to which they connect. In nonfeedback
amplifiers it is nearly always difficult to meet this requirement because the desired impedances are incompatible with the impedances
of the devices used in the amplifiers. Circuit compromises often must
be made to achieve an acceptable impedance match. In feedback amplifiers, however, the provision of feedback increases the flexibility of
the design choices that can be made, and it is usually possible to
achieve a better impedance match over a wide bandwidth by using a
feedback amplifier than by using a nonfeedback amplifier.
Example 7-1: Feedback Effects

This simple example illustrates how a p,-gain change of about
0.8 dB may be suppressed by feedback to an amplifier gain change
of approximately 0.1 dB.
Let the overall gain of an amplifier be 10 dB; that is,
e2
el

e2
el

20 log -== 10; -

=<

3.16.

From Equation (7-2),
1

.!: p,f3

=<

3.16.

Elements of Transmission Analysis

172

Assume the IL gain (without feedback) is 20 log pIL

Vol. 1

== 30 dB; then

== 31.6

and, by substitution,

f3

= 0.284.

Now, let the JL gain increase from 30 dB to 30.8 dB; that is, IL
increases by about 10 percent from 31.6 to 34.8.
Then the overall amplifier gain is
e2

el

34.8
32
1 - 34.8 (-0.284) - .

and
20 log ~ = 20 log 3.2 == 10.09 dB.
el
Thus a 10 percent change in JL-circuit gain is held to about a 1.3
percent change in overall gain (0.09 dB).
The fact that the amplifier gain increased as the JL gain increased is due to the phase relationships implied by the simple
substitutions made. In complex feedback structures, the amplifier
gain might increase or decrease over limited portions of the band
and within a limited range of the ft-gain change.

7-4

CIRCUIT CONFIGURATIONS

The principal circuit configurations useful in feedback circuits can
be classified most easily in terms of the way in which the J.L and f3
circuits are connected to each other and to the external interconnections at amplifier input and output. The variety of connections that
can be made cannot be clearly demonstrated by a simple drawing
such as that of Figure 7-1. The actual situation is that shown
broadly by Figure 7-2 in which the J.L, /3, input, and output circuits
are interconnected by means of six-terminal networks. The classification of feedback circuits then depends on the forms which these
six-terminal networks assume.

Negative Feedback Amplifiers

Chap. 7

a;

ao

b,

bo

Input

Output
coupling
network

coupling
network

Input

173

Co

C,

Ii

Output

fo

dt

f3
do

Figure 7-2. Feedback amplifier representation.

IllustratiO'ns O'f sO'me O'f the more cO'mmO'n feedback amplifier
structures are given in Figures 7-3 thrO'ugh 7-6. Where apprO'priate,
the netwO'rk terminals are identified in accO'rdance with the nO'tation
used in Figure 7-2. The /1- circuits cO'mmO'nly have O'ne, twO', O'r three
stages of gain; an unlimited number O'f netwO'rk cO'nfiguratiO'ns may
be fO'und in the passive netwO'rks shO'wn in the figures. TO' avO'id
cO'mplexity here, the internal netwO'rk cO'nfiguratiO'ns are generally
O'mitted in the figures.

Series and Shunt Feedback
The cO'nfiguratiO'n O'f Figure 7-3 is called series feedback because,
as seen frO'm the input and O'utput terminals, the JL and f3 circuits
are in series. The f3 circuit, shown here as a 1T arrangement O'f three
impedances (A, B, and C) may be much simpler O'r much mO're cO'mplex than that illustrated. The effective line terminals (ei, Ii, eo, and lo)
are shown at the high sides O'f the transfO'rmers since the transfO'rmer
characteristics in this case may be added directly to' thO'se of the
cO'nnecting circuits.
Figure 7-4 shO'WS hO'W feedback may be prO'vided by means of
shunt cO'nnectiO'ns. The _f3 circuit, here represented as a T netwO'rk
O'f the three impedances, may again take O'n any O'f an unlimited

174

Vol. 1

Elements of Transmission Analysis

r--------,

bi

I
I
I
I

Ci

I
I

Ii

I

I

I

Co

I

I

I
I
I

d;

10
do

I

I

I

L ______ -.J

Figure 7-3. Series feedback amp.lifier.

number of configurations. Note that the connecting terminals (input
and output), f3 network, and JL network are all in parallel.
Series and shunt feedback designs are simple and they are convenient for many applications. The feedback phenomenon tends to
change the effective input and output impedances of the amplifier to
very high or very low values. As a result, it is possible to build out
these impedances conveniently by the use of discrete components to
achieve a good impedance match to the connecting network or transmission line. A disadvantage is that the line or connecting impedances
form a part of the JLf3 loop. As a result, variations in the line impedance, sometimes large and impossible to control, affect the JLf3
characteristic; in some cases, the effect may be great enough to
cause amplifier instability.
Bridge-Type Feedback

These difficulties may be mitigated by using bridge-type feedback
circuits. Many variations of these circuits exist, but the configuration

Chap. 7

Negative Feedback Amplifiers

175

r------,
I
I

'Op{J

a;

I
I

II

I

I

I
I

I

I

IL __
ei

{3

I

I

__--.J

ao

Ci

fi

d;

eo
Co

bi

bo

do

[}~~

fo

Figure 7-4. Shunt feedback amplifier.

that is most commonly used, especially for broadband repeaters in
analog cable systems, is the high-side hybrid feedback arrangement
illustrated in Figure 7-5. Several network branches must be added in
this configuration to provide hybrid balance and input and output
impedance control. These branches are designated Zn and Zl in
Figure 7-5. The advantages of this circuit include the achievement of
minimum noise and improved intermodulation performance while
controlling both the input and output impedances.
Figures 7-3 through 7-5 show symmetrical arrangements at each
end of the amplifier. This has been done only to simplify the illustrations. The number of configurations is increased greatly by combining different types of connections at input and output. Furthermore, circuit advantages can sometimes be realized by providing
multiple loop configurations. An example of such a configuration is
given in Figure 7-6. Here, a feedback amplifier with a series feedback network Zf31, similar to that of Figure 7-3, is shown with local
shunt feedback Zf32 around the last stage of a three-stage configuration in the JL path. The impedances Zil and Zi2 are interstage networks
in the JL path.

176

Elements of Transmission Analysis

Vol. 1

Input[J
Ij

--,

rI

I

I

I
I
I
I

I
I
I
B

IL

_________ ...JI

Figure 7-5. Amplifier with high-side hybrid feedback.

I"P",~

Figure 7-6. Three-stage series feedback amplifier with local shunt feedback on
last stage.

Chap. 7
7-5

Negative Feedback Amplifiers

177

DESIGN CONSIDERATIONS

It is not possible to review here the entire procedure followed in
designing a feedback amplifier nor is it desirable to do so. However,
some important relationships and design limitations are discussed
in order to provide an improved understanding of how transmission
systems operate and how system performance is related to the design
of the individual amplifier.

Gain and Feedback

The shape and magnitude of the gain/frequency characteristic are
basic design considerations. The closeness of the gain/frequency
characteristic to the desired characteristic may be determined by
the degree of circuit complexity that can be tolerated; however, the
better the match, the better will be the ultimate transmission charact~ristic of the system. Equipment size and power dissipation may
also be important considerations in making this first set of compromises in amplifier design.
Characteristic Shaping. The characteristics of feedback amplifiers are
all complex functions of frequency which are importantly related to
the transmission characteristics of all of the networks making up
the complete amplifier and its external terminations.

In many applications, it is desirable to design the amplifier to a
flat gain, one that is equal over the entire transmitted band. In the
case of line repeaters for analog cable systems, it is usually desirable
to have the gain of the amplifier sections of the repeaters match the
loss of the cable section over the band of interest. In either case,
the desired flat or shaped gain/frequency characteristic is produced
primarily by proper design of the .$-circuit network since the gain
is approximately equal to -1/.$ as shown in Equation (7-2). Some
gain shaping may also be provided in those networks that are outside the IL.$ loop, such as the coupling networks shown in many of
the figures as simple transformers.
To achieve optimum signal-to-noise performance, it is also desirable in many cases to shape the feedback/frequency characteristic
of an amplifier. For example, it is possible to increase low-frequency
feedback at the expense of high-frequency feedback. This can be ac-

178

Elements of Transmission Analysis

Vol. 1

complished by careful designs of all networks in the JLf3 loop, using
frequency-dependent reactive components, since the feedback is, by
definition, proportional to 1/ (1-J-Lf3).
Gain and Phase Margins. The selection of a circuit configuration and
the amount of feedback to be provided depend on the magnitudes of
the gain and bandwidth required and on the characteristics of available active devices. These considerations include the linearity of the
device input/output characteristics, the noise figure of the input
device, and the need for minimizing variations in circuit parameters
due to device aging and ambient temperature changes.

As shown in Equation (7-2), the insertion gain of a feedback
amplifier is
J-L
1-1-tf3 ~ -

e2
el

1

If·

The total gain around the feedback loop is defined as J-tf3, where J-L is
the total gain provided by the active devices (and their related
J-L-circuit networks) and f3 is the loss of the network that connects the
output back to the input. From these relationships, the loop gain
in dB is
20 log JLf3 = 20 log J-t

+ 20 log f3 ~ 20 log JL -gR

(7-3)

where gR is the insertion gain of the complete closed-loop amplifier
in dB. It is approximately equal to -20 log f3. Thus,
20 log J.L

~

20 log J.Lf3

+ gR

dB.

(7-4)

That is, the sum of the loop gain and insertion gain cannot exceed
the total gain available in the J-L circuit. It is therefore impossible to
get loop gain in excess of the difference between the JL gain and the
desired insertion gain. When the desired loop gain is greater, the
design is said to be gain limited.
Most broadband amplifier designs, however, are not gain limited;
the need for adequate stability margins is usually controlling. In the
gain expression 11-/ (1-J-tf3) , the denominator may become zero, depending on phase relationships, when J-tf3 = 1. If J-tf3 is equal to unity
at any frequency, in-band or out-of-band, the amplifier may become
unstable and break into spontaneous oscillation at that frequency if
the phase of J-tf3 is unfavorable. If it were possible to hold 1J-tf31 > > 1

Chap. 7

Negative Feedback Amplifiers

179

for all frequencies, this would not be a problem, but every active
device has some frequency above which its gain decreases monotonically. The rate of decrease may be enhanced by circuit stray inductance or capacitance. Thus, there is always a frequency at which

1/L131

= 1.

Two criteria must be satisfied to guarantee a stable amplifier;
the phase must be greater than 0 degrees where 11L131 passes through
o dB, and 1/L131 must represent several dB of loss where the phase
passes through 0 degrees. These criteria are known as the phase
and gain margins in an amplifier design. If an amplifier has such
margins, it is said to meet the Nyquist stability criteria. Such margins
are illustrated in Figure 7-7 where the characteristics are plotted
on an arbitrary, normalized frequency scale. A phase margin of about
30 degrees and gain margin of about 10 dB, as illustrated, allow for
variations in device characteristics which result from manufacturing
processes, aging, and temperature effects.
The achievement of adequate phase and gain margins sets an upper
limit on the achievable in-band feedback. When this limit is lower
than that set solely by gain considerations, the design is said to be
stability limited.
Ideally, maximum stability margins would result if the phase of
the /Lf3 characteristic could be held at 180 degrees. Then, the gain
60

- ...... '-...
..

40

Ift~l,
20

o

V

-20
0.001

/

V

.......

-- 1\,

'7 /

0.01 0.02

J

0

I --.

~ ~Passband-

--.

120

" "r\"l.

,

ft~ phase / '

Q)
Q)

m

~

~-- "'- "'-

0.05 0.1 0.2

'Cii'

0.5

1

...

2

GI

240

Sl
0

~

Q.

10dB

~

,,-+

10

360

""" l-

"I;

5

~

20

50

Normalized frequency

Figure 7-7. Typical feedback amplifier characteristics.

120
100

180

Elements of Transmission Analysis

Vol. 1

+

expressiQn eQuId be written as 1/ (1 IJLf31 ). Within the transmissiQn
band the phase is Qften cQntrQlled to' apprQach this cQnditiQn. HQwever, Qut-of-band phase changes due to' phase shifts inherently assQciated with any gain/frequency characteristic, such as the gain
cutQff mentiQned earlier. FurthermQre, fQr very high frequencies the
prQpagatiQn time around the feedback IQop cQntributes additional
phase shift which can be minimized, but not eliminated, by careful
design.

Nonlinear Distortion and Overload

In addition to' the related consideratiQns Qf gain and achievable
feedback, the related cQmbinatiQn of overload, gain, and nQnlinear
distortion must be considered in feedback amplifier design. These
can be studied by first examining the phenomenon Qf nQnlinear distortiQn and its reduction by feedback and then re1ating these to. the
problems Qf gain and Qverload.
Nonlinear Distortion. The generation of intermodulatiQn prQducts
caused by nonlinear input/output characteristics of transistQrs is a
very cQmplex phenomenQn. The analysis here is Qversimplified in Qrder
to illustrate hQW products are generated, how feedback tends to.
suppress them, and how gain and Qverload are affected.

The nQnlinear input/output vQltage relatiQnships Qf an amplifier
may be represented by the expressiQn
(7-5)
where eo and ei are the output and input signal voltages, and the a
coefficients provide magnitude values of various wanted and unwanted components in the output signal. If the input signal has
many frequency components, Equation (7-5) may be used to study
the intermodulation phenomenQn by assuming

ei == A cos at

+ B cos {3t + C CQS )It.

When this value Qf ei is substituted in EquatiQn (7-5), the expressiQn
can be expanded by trigonometric identities. The Qutput vQltage
then cQntains an infinite number Qf terms consisting Qf variQus combinatiQns of input signal compQnents; the magnitudes are repre-

Chap. 7

Negative Feedback Amplifiers

181

sented by the coefficients A, B, and C of the input signal and ao, aI,
etc., of the input/output expression. Fortunately, in most applications,
the magnitudes of terms in Equation (7-5) having exponents of the
fourth power and higher are so small they usually may be ignored.
To demonstrate the nonlinear phenomenon and the effects of feedback, a few specific terms of the output voltage, extracted from expansion of Equation (7-5) after substituting the expression for ei,
may be examined. The terms of interest are
(7-6)
e2

== a2 AB cos

es

== ~ as ABC cos
2

(a+f3) t
(a+,B-y) t.

(7-7)
(7-8)

The first term, Equation (7-6), is a component of the output which
corresponds exactly with the first term of the input signal (A cos at)
except for the coefficient al. This coefficient may be regarded as a
measure of the gain of the amplifier, gR. As shown in Equation (7-4),
the value of gR, and therefore the value of aI, is a function of the
feedback, P-f3.
Equation (7-7) represents an intermodulation distortion component
derived from the second-order term of Equation (7-5). The coefficient of this term involves magnitudes A and B of the two intermodulating input signal components and the coefficient az of Equation
(7 -5). The value of az is a function of the feedback, ./1-13; to a first
approximation, the value of a2 is reduced in direct proportion to the
amount of feedback provided.
Equation (7-8) represents an intermodulation distortion component
derived from the expansion of the third-order term of Equation
(7-5). The coefficient involves the magnitudes A, B, and C of the
three intermodulating input signal components and the coefficient as
of Equation (7-5). The value of aa is also reduced by feedback but
not by as simple a relationship as al and az. Second-order modulation
components, fed back to the input, mix with fundamental signal
components to produce products that appear at the output as thirdorder products. The result is that the reduction of third-order intermodulation is not quite as effective as the reduction of second-order
intermodulation.

182

Elements of Transmission Analysis

Vol. 1

There are many more terms in the three-frequency expansion of
Equation (7-5) [2]. The distribution of the intermodulation products
across the band, the frequency characteristics of the transmitted
signal and the amplifier gain, the modulation coefficients, the feedback, and other phenomena make the calculation of intermodulation
noise in system design a problem that is most tractable when solved
by a digital computer. In contrast with computation, amplifier and
system performance is more easily determined by measurements involving a noise loading technique.
The above discussion of nonlinear distortion is predominantly
qualitative. For design purpose, the factors above are often manipulated in such a way as to define 20 log M2 and 20 log M3 as the
ratios, expressed in decibels, of the second harmonic (M 2 ) or the
third harmonic (M3) to a O-dBm fundamental at the output of a
repeater. These modulation coefficients prove useful in analog cable
system design. They are, of course, related to the a coefficients of
Equation (7-5).
Overload. The coefficients 20 log M2 and 20 log M3 are essentially
constant over most of the signal amplitude range of interest (though
they may be functions of frequency). However, as overload is approached, departures from constant values of 20 log M2 and 20 log M3
are observed as are departures from normally constant gain. These
observations lead to a number of definitions of overload in a feedback amplifier. Typical characteristics are plotted in Figure 7-8 for
departures of 20 log M3 and gain from their nominal values as
functions of the signal power at the output of a repeater. Three
definitions of overload are discussed briefly below; two are related
to departure of 20 log M3 from a constant value, and one is related
to the departure of gain from constant value.
Definition 1: By this definition, the overload point is that value of
output signal power at which 20 log M 3 , the third-order modulation
coefficient, increases by 0.5 dB relative to its nominal constant value.
This is identified as point P R1 at 20 dBm in Figure 7-8. This definition, appropriate for use in systems limited by intermodulation, is
conservative in the sense that only a slight performance impairment
results from exceeding the limit by a small amount. A relatively
small amount of overload margin would be allowed in a design
based on this definition.

Chap. 7

Negative Feedback Amplifiers

183

20

15

~

m

...2
o
C'4

10

c:
Q)

m

c:
..c:
U
C

5

ai'

~
c:

'0

2

m

-=
Q)

m

c:
C
..c:
U

16

18
Signal power (dBm)

Figure, 7-8. Overload point definitions as applied to a typical amplifier.

Definition 2: In this case the overload point is defined as that
value of output signal power at which the third-harmonic power
increases by 20 dB for a 1-dB increase in signal power; this corresponds to a 17-dB increase in 20 log M 3 • Since under these conditions
very serious transmission impairment may result, a more generous
overload margin must be provided. This definition of overload is
recommended by the CCITT. * Its use is justified by the statistics of
system performance interactions in long analog cable systems and
by the amplitude/frequency statistics of a broadband signal; together, these statistics are used to show a very low probability of
overload. The overload point is illustrated by point PR2 in Figure 7-8
at a signal power of about 25.5 dBm.
Definition 3: The overload phenomenon may be related to changes
in amplifier gain, whereby the overload point is defined as the signal

* Commite Consultatif International Telegraphique et Telephonique, Recommendation G.222, IId Plenary Assembly, (New Delhi: December 8-16, 1960).

184

Elements of Transmission Analysis

Vol. 1

power at the output at which the amplifier gain departs from its
nominal value by 0.5 dB, as illustrated by point P R3 on the lower
portion of Figure 7-8. For this illustration, the overload point is
about 26.5 dBm. The use of this definition may be appropriate when
intermodulation distortion is not a maj or consideration.
The range of values of defined amplifier overload points is fairly
wide, for example, 6.5 dB in Figure 7-8. However, in the event that
the overload point is exceeded under definition 2 or 3, perfo.rmance
degradation is so severe that wider system margins must be provided in most cases. Thus, the actual operating value of load might
well be approximately the same no matter which definition is used.
Noise and Terminations

It is desirable to introduce the subj ect of thermal noise generation
in networks and systems here in order to relate the phenomenon to
amplifier design and, thus, to overall system performance [3].
It can be shown that the available noise power of a thermal noise
source is directly proportional to the product of the bandwidth of
the system or detector and the absolute temperature of the source.
This relation can be expresed as
Pa == kT B watts,

(7-9)

where k is Boltzmann's constant (1.3805 X 10- 23 joule per Kelvin),
T is the absolute temperature in Kelvins (290 K is taken as room
temperature), and B is the bandwidth in hertz. Available noise power
may also be expressed as

Pa == -174 + 10 log B

dBm.

(7-10)

The noise figure for a two-port network is defined as follows:
"The noise figure at a specified input frequency is the ratio of (1)
the total noise power per unit bandwidth at a co.rresponding output
frequency available at the output when the noise temperature of the
input source is standard (290 K) to. (2) that portion of this output
power engendered at the input frequency by the input source" [4].
The noise figure, when applied according to this definition to a narrow
band, dB, is called a spot noise figure. The spot noise figure may vary
as a function of frequency.

Chap. 7

Negative Feedback Amplifiers

185

Alternately, the spot noise figure, nF, can be expressed in terms
of signal-to-noise ratios. Such an expression may be written
Psi/Pni
Pso/Pno

nF = --"'--'---

(7-11)

where P represents power and the subscripts are 8 for signal, n for
noise, i for input, and 0 for output. Here, the noise figure is defined
as the ratio (Psi/Pni) of the available signal-to-noise power ratio at
the input of the two-port network to the available signal-to-noise
power ratio (Pso/Pno) at the output of the two-port when the temperature of the noise source is standard (T = 290 K).
The value of pni can be determined, by substitution in Equation (7 -9), as pni = kTilB. The ratio Psi/Pso is the gain, ga (/), of the
network. The substitution of these values in Equation. (7-11) yields
nF =

Pno
ga (/) kTilB

(7-12)

Examination of Equation (7-12) shows that the noise figure of an
amplifier is importantly related to the thermal noise generated at
the input (where the signal is at its lowest amplitude), to the gain
of the amplifier, and to any sources of noise picked up within the
amplifier that make the output noise greater than the input noise
amplified by ga (/). These internal noise sources are to some extent
subject to control by circuit design techniques. The dominant source,
however, is usually at the amplifier input. Here, the noise source is
outside the /Lf3 loop and, as a result, the noise figure is not improved
by feedback.
The selection of components and the design of the input circuits
of amplifiers for minimum noise figure is important in transmission
system design. The cumulation of noise in tandem-connected amplifiers is directly related to the nominal noise figure of each and to
ten times the logarithm of the number of amplifiers in tandem.
Thus, when the number of amplifiers has been set by repeater spacing,
gain, and bandwidth considerations, the noise performance is controlled by the individual noise figures of the amplifiers.
As mentioned, the design of feedback amplifiers and their classification into a variety of types depend on the forms which the six-

186

Elements of Transmission Analysis

Vol. 1

terminal coupling networks take and the manner in which f3 and fL
circuits and external circuit connections are made. At the input, the
design must simultaneously (1) satisfy return loss requirements by
providing a termination to properly match the amplifier input impedance to the line impedance, (2) minimize the noise figure of the
first-stage device by suitably matching its input impedance to the
driving point impedance, and (3) meet feedback and gain-shaping
requirements. At the output, the design must again satisfy impedance
matching and feedback requirements and, in addition, must minimize
penalties in nonlinear and overload performance that might result
from improper last-stage terminations. In general, these combinations
of requirements can best be met by the use of hybrid feedback connections, described previously and illustrated in Figure 7-5.

Summary

The design and application of negative feedback amplifiers in
transmission systems has been described in terms of three sets of
interrelated parameters: (1) gain and feedback, (2) nonlinear distortion and overload, and (3) noise and terminations. These relationships are neither unique nor independent of one another. All
must be considered simultaneously in the design process.
Design criteria that are involved when a new design is to be undertaken include the bandwidth, the gain, the lowest amplitude the signal
may be allowed to reach without picking up excessive noise, the
highest permissible signal amplitude that will not exceed overload or
intermodulation limits, gain and feedback shaping, device bias conditions, and many others. Only the most important have been touched
on in this chapter.
REFERENCES

1. Bode, H. W. Network Analysis and Feedback Amplifier Design (Princeton,
N.J.: D. Van Nostrand and Company, Inc., 1945).
2. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N.C.: Western Electric
Company, Inc., 1970), p. 241.
3. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N.C.: Western Electric
Company, Inc., 1970), Chapters 8 and 16.

Chap. 7

Negative Feedback Amplifiers

187

4. American Standards Association. Definition of Electrical Terms, ASA-C42.65,
1957.
5. Thomas, D. E. "High Frequency Transistor Amplifiers," Bell System Tech. J.,
Vol. 38 (Nov. 1959).
6. Hakim, S. S. Junction Transistor Circuit Analysis (New York: John Wiley
and Sons, Inc., 1962).
7. Blecher, F. H. "Design Principles for Single Loop Feedback Amplifiers,"
Trans. IRE, Vol. CT-4 (Sept. 1957).

Elements of Transmission Analysis

Chapter 8

Modulation
Communication signals must usually be transmitted via some
medium separating the transmitter from the receiver. Since the
information to be sent is rarely in the best form for direct transmission, efficiency of transmission requires that it be processed in
some manner before being transmitted. Modulation may be defined
as that process whereby a signal is converted from its original form
into one more suitable for transmission over the medium between
the transmitter and receiver [1]. The process may shift the signal
frequencies to facilitate transmission or to change the bandwidth
occupancy, or it may materially alter the form of the signal to
optimize noise or distortion performance. At the receiver this process
is reversed by methods called demodulation.
Satisfactory transmission and demodulation of modulated signals
depend on the introduction by the medium of no more than a specified
amount of distortion. The effects of distortion in the medium may
be quite different for different modulation modes. If maximum distortion values are exceeded, signal impairments at the receiver are
excessive. Distortions that must be considered are of many types.
They include amplitude distortion, which results from the variation
of transmission loss with frequency, and phase distortion (often
expressed as delay distortion), which results from the departure from
linear of the phase/frequency characteristic of the channel. Other
forms of signal impairment which may result in imperfect signal
demodulation include nonlinear channel input/output characteristics,
frequency offset, amplitude and phase jump, echoes, and noise. These
impairments are treated in later chapters. They are treated in this
chapter only where they result directly from the modulation or
demodulation process.
The modulation process can be represented mathematically by an
equation which, in its most general form, can be used to express any
188

Chap. 8

189

Modulation

of several forms of modulation. The several forms include amplitude
modulation, angle modulation (frequency or phase), and pulse modulation. While other expressions are more representative of the various
forms of pulse modulation, there is one form of the equation that
lends itself particularly to studies of amplitude and angle modulation,
M (t)

== a (t)

cos [Wet

+ 
 fc/2, the baseband and lower sideband signals overlap. Ambiguity
or distortion, which can occur in the recovered signal, may be avoided
in design by choosing frequencies to make fb < fc/2.
*Note that while the mathematical analysis for product modulation is linear,
the physical rea liz a tion of the process often involves the use of nonlinear devices.
The mode of operation in these cases still results in a quasi-linear process output.

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CD

"'0

.~

Q.

E
 1 in Equation (8-3). This ensures that there are no phase
reversals in the carrier component.
For a single-frequency modulating wave, an equals zero in Equation (8-5) and, letting ao == 1 and C4n == 1, the modulated wave is
M (t)

== cos cvet + 2m

cos (cv c -'CVm) t

+ 2m

cos (CVc +Wm) t.

(8-8)

In many instances the use of exponential notation for periodic
functions has advantages over the trigonometric notation which has
been used thus far in this chapter. A particularly useful application
is in the phasor representation of modulated waves as an aid in
understanding the various modulation processes. A sinusoidal carrier,
cos wct, can be written

where Re represents the real part of the complex quantity and

ejCl)ct

== cos CV ct+·J·SIn CVct •

The exponential ejCl)c t is a counterclockwise rotating phasor of unit
length in the complex plane, and its real part is its projection on
the real axis. This phasor is shown for three values of time in
Figure 8-3.

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Imaginary axis

/

+

--- --I

Complex plane

"

t-~
- 4 (t)]

1

2 cos

[2 w et

+ 24>(t)] t5

(8-20)

The second term can be assumed to consist of a large number of
sinusoidal sideband components about a carrier frequency of 2fe Hz;
therefore, the average value of the second term of Equation ,(8-20)
is zero. Thus, the average power is given by the zero frequency term
Ae2

(8-21)

Pavg ="2R'

This, of course, is the same as the average power in the absence of
modulation.

Bandwidth Required for Angle-Modulated Waves

For the low-index case, where the peak phase deviation is less
than 1 radian, most of the signal information of an angle-modulated
wave is carried by the first-order sidebands. It follows that the
bandwidth required is at least twice the frequency of the highest
frequency component of interest in the modulating signal. This
would permit the transmission of the entire first-order sideband.
For the high-index signal a different method called the quasistationary approach must be used [4]. In this approach, the assumption is made that the modulating waveform is changing very slowly
so that static response can be used. For example, assume that a
I-volt baseband signal causes a I-MHz frequency deviation of the
carrier. This corresponds to kl
21T X 106 radians per volt-sec.
Then, if the modulating signal has a I-volt peak, the peak frequency
deviation is 1 MHz. Thus, it is obvious that if the rate of change of
frequency is very small the bandwidth is determined by the peakto-peak frequency deviation. It was mathematically proven by J. R.
Carson in 1922 that frequency modulation could not be accommodated

=

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in a narrower band than amplitude modulation, but might actually
require a wider band [5]. The quasi-stationary approach for large
index indicates that the minimum bandwidth required is equal to
the peak-to-peak (or twice the peak) frequency deviation.
Thus, for. low-index systems (X < 1) the minimum bandwidth is
given by 2fT, where fT is the highest frequency in the modulating
signal. For high-index systems (X > 10), the minimum bandwidth
is given by 21lF, where AF is the peak frequency deviation. It would
be desirable to have an estimate of the bandwidth for all anglemodulated systems regardless of index. A general rule (first stated
by J. R. Carson in an unpublished memorandum dated August 28,
1939) is that the minimum bandwidth required for the transmission
of an angle-modulated signal is equal to two times the sum of the
peak frequency deviation and the highest modulating frequency to be
transmitted. Thus,
Bw

== 2 (fT + tlF)

Hz.

(8-22)

This rule (called Carson's rule) gives results which agree quite well
with the bandwidths actually used in the Bell System. It should be
realized, however, that this is only an approximate rule and that the
actual bandwidth required is to some extent a function of the waveform of the modulating signal and the quality of transmission desired.
8-3

PROPERTIES OF PULSE MODULATION

In pulse-modulation systems the unmodulated carrier is usually
a series of regularly recurrent pulses. Modulation results from
varying some parameter of the transmitted pulses, such as the amplitude, duration, or timing. If the baseband signal is a continuous
waveform, it is broken up by the discrete nature of the pulses. In
considering the feasibility of pulse modulation, it must be recognized
that the continuous transmission of information describing the
modulating function is unnecessary, provided the modulating function
is bandlimited and the pulses occur often enough. The necessary
conditions are expressed by the sampling principle, as subsequently
discussed.
It is usually convenient to specify the signalling speed or pulse
rate in bauds. A baud is defined as the unit of modulation rate

Chap. 8

Modulation

211

corresponding to a rate of one unit interval per second; i.e.,
baud == liT where T is the minimum signalling interval in seconds.
When the duration of signalling elements in a pulse stream is constant, the baud rate is equal to the number of signalling elements
or symbols per second. Thus, the baud denotes pulses per second
in a manner analogous to hertz denoting cycles per second. Note
that all possible pulses are counted whether or not a pulse is sent,
since no pulse is usually also a valid symbol. Since there is no restriction on the allowed amplitudes of the pulses, a baud can contain
any arbitrary information rate in bits per second. Unfortunately,
bits per second is often used incorrectly to specify a digital transmission rate in bauds. For binary symbols of equal time duration,
the information rate in bits per second is equal to the signalling
speed in bauds if there is no redundancy. In general, the relation
between information rate and signalling rate depends upon the coding
scheme employed.

Sampling
In any physically realizable transmission system, the message or
modulating function is limited to a finite frequency band. Such a
band limited function is continuous with time and limited in its
possible range of excursions in a small time interval. Thus, it is only
necessary to specify the amplitude of the function at discrete time
intervals in order to specify it exactly. The basic principle discussed
here is called the sampling theorem, which in a restricted form
states [6] :
If a message that is a magnitude-time function is sampled instantaneously at regular intervals and at a rate at least twice the
highest significant message frequency, then the samples contain
all of the information of the original message.
The application of the sampling theorem reduces the problem of
transmitting a continuously varying message to one of transmitting information representing a discrete number of amplitude
samples per given time interval. For example, a message bandlimited
to fT hertz is completely specified by the amplitudes at any set of points
in time spaced T seconds apart, where T == 112fT [7]. Hence, to transmit a bandlimited message, it is only necessary to transmit 2fT
independent values per second. The time interval, T, is often referred
to as the Nyquist interval.

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The process of sampling can be thought of as the product modulation of a message function and a set of impulses, as shown in
Figure 8-15. The message function of time, v (t), is multiplied by a
train of impulses, c (t), to produce a series of amplitude-modulated
pulses, 8 (t). If the spectrum (i.e., the Fourier transform) of v (t)
is given by F (f) as shown in Figure 8-15, the spectrum of the
sampled wave, 8 (t), is then shown by S (f) in the figure. The output
spectrum, S  2fT, so that the sidebands do not overlap. Note also that all
sidebands around all harmonics of the sampling frequency have the
same amplitude. This is a result of the fact that the frequency
spectrum of an impulse is flat with frequency. In a practical case,
of course, finite width pulses would have to be used for the sampling
function, and the spectrum of the sampled signal would fall off with
frequency as the spectrum of the sampling function does.
The amplitude-modulated pulse signal that results from sampling
the input message may be transmitted to the receiver in any form
that is convenient or desirable from a transmission standpoint. At
the receiver the incoming signal, which may no longer resemble the
impulse train, must be operated on to re-create the original pulse
amplitude-modulated sample values in their original time sequence
at a rate of 2fT samples per second. To reconstruct the message, it
is necessary to generate from each sample a proportional impulse and
to pass this regularly spaced series of impulses through an ideal
low-pass filter having a cutoff frequency fT. Examination of the
spectrum of S (I) in Figure 8-15 makes the feasibility of this obvious.
Except for an overall time delay and possibly a constant of proportionality, the output of this filter would then be identical to the original
message. Ideally, then, it is possible to transmit information exactly,
given the instantaneous amplitude of the message at intervals spaced
not further than 112fT seconds apart.
Pulse Amplitude Modulation

In pulse amplitude modulation (PAM), the amplitude of a pulse
carrier is varied in accordance with the value of the modulating
wave as shown in Figure 8-16(c). It is convenient to look upon

Chap. 8

Modulation

213

I

T

o

2T
T

4T
3T

= 1/1.

sec

6T
sT

7T

~~I-L--l-----II~I
o

18

21.

I. =

31. I

---+

1fT Hz

Figure 8-15. Sampling with an impulse· modulator.

PAM as modulation in which the value of each instantaneous sample
of the modulating wave is caused to modulate the amplitude of a
pulse. Signal processing in time division multiplex terminals often
begins with PAM, although further processing usually takes place
before the signal is launched onto a transmission system.

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Elements of Transmission Analysis

(a)
Time

Pulse carrier

(b)

(c)

PDM

(d)

PPM

(e)

Figure 8-16. Examples of pulse-modulation systems.

Pulse Duration Modulation

Pulse duration modulation (PDM), sometimes referred to as pulse
length modulation or pulse width modulation, is a particular form of
pulse time modulation. It is modulation of a pulse carrier in which
the value of each instantaneous sample of a continuously varying

Chap. 8

Modulation

215

modulating wave is caused to produce a pulse of proportional duration,
as shown in Figure 8-16 (d). The modulating wave may vary the
time of occurrence of the leading edge, the trailing edge, or both
edges of the pulse. In any case, the message to be transmitted is
composed of sample values at discrete times, and each value must
be uniquely defined by the duration of a modulated pulse.
In PDM, long pulses expend considerable power during the pulse
while bearing no additional information. If this unused power is
subtracted from PDM so that only transitions are preserved, another
type of pulse modulation, called pulse position modulation, results.
The power saved represents the fundamental advantage of pulse
position modulation over PDM.
Pulse Position Modulation

A particular form of pulse time modulation, in which the value
of each instantaneous sample of a modulating wave varies the position
of a pulse relative to its unmodulated time of occurrence, is pulse
position modulation (PPM). This is illustrated in Figure 8-16 (e).
The variation in relative position may be related to the modulating
wave in any predetermined unique manner. Practical applications
of PPM systems have been on a modest scale, even though their instrumentation can be extremely simple.
If either PDM or PPM is used to time division multiplex several
channels, the maximum modulating signal must not cause a pulse to
enter adj acent allotted time intervals. In telephone systems with high
peak-to-rms ratios, this requirement leads to a very wasteful use of
time space. In fact, almost all of the time available for modulation
is wasted because many of the busy channels may be expected to be
inactive and most of the rest will be carrying small signal power.
Consequently, although PPM is more efficient than PDM, both fall
short of the theoretical ideal when used for multiplexing ordinary
telephone channels.
Pulse Code Modulation

A favored form of pulse modulation is that known as pulse code
modulation (PCM). This mode of signal processing may take any of
several forms; each requires the successive steps of sampling, quan-

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tizing, and coding. If the input signal is analog in nature, the sampling
is usually a sampling of the signal amplitude; if the signal is digital,
the sampling process may take the form of time sampling to determine
the time of occurrence of transitions from one signal state to another.
The process of sampling, common to pulse modulation generally,
was described previously. Following is a discussion of quantizing
and several forms of coding.
Quantizing. Instead of attempting the impossible task of transmitting the exact amplitude of a sampled signal, suppose only certain
discrete amplitudes of sample size are allowed. Then, when the
message is sampled in a PAM system, the discrete amplitude nearest
the true amplitude is sent. When received and amplified, this signal
sample has an amplitude slightly different from any of the specified
discrete steps because of the disturbances encountered in transmission. But if the noise and distortion are not too great, it is possible
to tell accurately which discrete amplitude of the signal was transmitted. Then the signal can be reformed, or a new signal created
which has the amplitude originally sent.

Representing the message by a discrete and therefore limited
number of signal amplitudes is called quantizing. It inherently introduces an initial error in the amplitude of the samples, giving rise to
quantization noise. But once the message information is in a quantized
state, it can be relayed for any distance without further loss in
quality, provided only that the added noise in the signal received at
each repeater is not too great to prevent correct recognition of the
particular amplitude each given signal is intended to represent. If
the received signal lies between a and b and is closer to b, it is surmised that b was sent. If the noise is small enough, there are no
errors. Note, therefore, that in quantized signal transmission the
maximum noise is determined by the number of bits in the code;
while in analog signal transmission, it is controlled by the repeater
spacing, the characteristics of the medium, and the amplitude of the
transmitted signal.
Coding. A quantized sample can be sent as a single pulse having
certain possible discrete amplitudes or certain discrete positions with
respect to a reference position. If, however, many discrete sample
amplitudes are required (100 for example), it is difficult to design
circuits that can distinguish between amplitudes. It is much less

Chap. 8

Modulation

217

difficult to design a circuit that can determine whether or not a pulse
is present. If several pulses are used as a code group to describe the
amplitude of a single sample, each pulse can be present (1) or
absent (0). For instance, if three pulse positions are used, then a
code can be devised to represent the eight different amplitudes shown
in Figure 8-17. These codes are, in fact, just the numbers (amplitudes) at the left written in binary notation. In general, a code group
of n on-off pulses can be used to represent 2 n amplitudes. For example, 7 binary pulses yield 128 sample levels.
AMPLITUDE
REPRESENTED

0
1
2

3
4

5

6
7

CODE

000
001
010
011
100
101
110
111

Figure 8-17. Binary code representation of sample amplitudes.

It is possible, of course, to code the amplitude in terms of a number
of pulses which have discrete amplitudes of 0, 1, and 2 (ternary, or
base 3) or 0, 1, 2, and 3 (quaternary, or base 4), etc., instead of the
pulses with amplitudes 0 and 1 (binary, or base 2). If ten levels are
allowed for each pulse, then each pulse in a code group is simply a
digit or an ordinary decimal number expressing the amplitude of the
sample. If n is the number of pulses and b is the base, the number of
quantizing levels the code can express is bn • To decode this code group,
it is necessary to generate a pulse which is the linear sum of all
pulses in the group, each pulse of which is multiplied by its place
value (1, b, b2 , b3 ••• ) in the code.
Differential Pulse Code Modulation. This form of pulse modulation has
two major potential advantages that can sometimes be used advantageously in particular design situations. First, it can sometimes
result in a lower digital rate than straight PCM coding and yet give

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equivalent transmission performance. Second, the sampling, quantizing, and coding of a signal can be accomplished without the use of
large amounts of common equipment. Thus, in situations where large
numbers of signals need not be processed simultaneously, it may be
more economical than conventional PCM.
Many forms of differential PCM exist [8]. One, known as delta
modulation, samples the analog signal at a high rate and codes the
samples in terms of the change of signal amplitude from sample to
sample. The digital rate must be higher than the sampling rate
given previously (sampling at a rate at least twice the highest
message frequency) because of distortion that might be introduced
when the rate of change of signal amplitude is high. The combined
sampling and coding process, however, may still result in a lower
net digital rate.
REFERENCES

1. Panter, P. F. Modulation, Noise, and Spectral Analysis (New York: McGrawHill Book Company, Inc., 1965), p. 1.
2. Rieke, J. W. and R. S. Graham. "The L3 Coaxial System - Television Terminals," Bell System Tech. J., Vol. 32 (July 1953), pp. 915-942.
3. Blecher, F. H. and F. J. Hallenbeck. "The Transistorized A5 Channel Bank
for Broadband Systems," Bell System Tech. J., Vol. 41 (Jan. 1952), pp. 321-359.
4. Rowe, H. E. Signals and Noise in Communication Systems (Princeton: D. Van
Nostrand Company, 1965), pp. 103 and 119-124.
5. Carson, J. R. "Notes on the Theory of Modulation," Proc. IRE (Feb. 1922).
6. Black, H. S. Modulation Theory (Princeton: D. Van Nostrand Company, 1953),
p.37.
7. Oliver, B. M., J. R. Pierce, and C. E. Shannon. "The Philosophy of PCM,"
Proc. IRE, Vol. 36 (Nov. 1948), pp. 1324-1331.
8. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N. C.: Western Electric
Company, Inc., 1970), pp. 592-597 and Chapter 5.

Elements of Transmission Analysis

Chapter 9

Probability and Statistics
The parameters in most engineering problems are not unique or
deterministic; that is, they can assume a range of values. If extreme
or worst case values of the important parameters are used, solutions
to such problems are seldom economical, frequently inaccurate, and
sometimes not even realizable. Probabilistic solutions must be sought;
that is, the nature of the distribution of parameters must be studied
and understood, appropriate values must be found to represent the
parameters in question, and answers must be found that adequately
represent the range of values that the solutions can take 'on as a
result of the range of values of the important parameters. The tools
for finding economic solutions to such problems are provided by the
related subjects, probability and statistics.
While the use of extreme values of parameters often leads to
impractical solutions to problems, the use of other parameter values
(nominal, mean, or average) may also lead to equally impractical
solutions. It is important to consider overall distributions of values;
in some cases only the average is important, but in other cases extreme
values (the tails of the distributions) may have to be taken into
account. Sometimes, the extreme cases are solved by legislating
against them. For example, telephone loops may be laid out by assuming the use of a single gauge of wire in the cables used in the loop
plant. If this were done, the losses of loops longer than some specific
value would exceed the loss that can give satisfactory service. Loops
having such excess loss are avoided by applying loop design rules that
require the addition of gain devices, the use of loading coils, or the use
of heavier gauge wire when the loop length exceeds the limit. Losses,
however, are still functions of all the parameters mentioned (wire
gauge, distance, loading, and gain). If the rules are written so that
no possible connection could have excessive loss, the solution would
be uneconomical; if too many connections have excess loss, grade
219

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of service suffers. Thus, the problem is to find an economical compromise which can provide an overall satisfactory grade of service.
Since the Bell System is so large and complex, it is impractical
to measure the values of all similar parameters (noise and loss on
all trunks, for example) in order to determine the performance of
any part of the plant or to describe the characteristics of any part
of the plant. Instead, the plant is described on the basis of statistical
parameters using only a few key numbers, such as one to represent
some central or average value and one to represent the dispersion
or spread of the data. Estimates of such numbers can be determined
by measuring only a properly chosen sample of the total universe
of values.
Probability theory provides a mathematical basis for the evaluation
and manipulation of statistical data. The theory treats events that
may occur singly or in combination as a result of interacting phenomena which themselves may be occurring sequentially or simultaneously.
Following a classical process of deductive reasoning, the theory
of probability [1] evolved from a number of postulates which were
based on experimental observations. The postulates were tested and,
where necessary, modified to fit observed data. Finally, clearly defined
axioms evolved, and the entire theory was built upon these axioms.
Probability theory provides the means for expressing or describing
a set of observations more efficiently than by enumerating all numbers
in the set. The unknowns are expressed as functions of a random
variable; these functions, which describe the domain and range of the
unknown, are derived by a mapping process. This process, together
with some of the terminology and symbology that are unique to
probability theory, must be described.
The mean (or expected value) , the standard deviation, and the variance are the principal parameters used in expressions for discrete and
continuous functions of a random variable. Methods of summing random variables are available and a number of different types of distributions may be used to represent communications phenomena of
various characteristics. Each is represented by a different distribution
function. Where functional relationships are not known, statisical
analyses are often used.

Chap. 9
9-1

Probability and Statistics

221

ELEMENTS OF PROBABILITY THEORY

Probability theory is applied to the study of and relationships
among sets of observations or data. The largest set, consisting of
all the observations or all the data, is known as the universe, the
domain, or the sample space. Subsets, which are made up of certain
interrelated elements defined according to some specified criteria, are
all contained in the sample space. The interrelations among subsets,
often referred to simply as sets, are conveniently displayed for study
in a sketch called a Venn diagram
in which the sample space is displayed as a square. Subsets are
depicted as geometrical figures
within the square; within each
S
figure are located all the elements
of that subset.
Figure 9-1 is an example of a
Venn diagram illustrating the relationships among sets A, B, and C
and the sample space, S, of which Figure 9-1. Venn diagram of three
they are parts. Examination of
subsets.
Figure 9-1 shows that C is a subset
of B, B is a subset of A, and A is a subset of S. It follows that C is
a subset of A and that Band C are subsets of S. The above statements regarding subsets may be written as follows:

C C B, B C A, A C S, C C A, B C S, C

c S,

where the symbol C is used to indicate that every element of the
subset shown at the closed end of the symbol is also an element of
the larger set shown at the open end of the symbol. Thus, C c B
(C is contained in B) may also be written B :> C (B contains C).

Axioms
A number of axioms form the basis of probability theory. These
are

(1) The probability of an event, A, is the ratio of the outcomes
favorable to A to the total number of outcomes, n, where it is
assumed that all n outcomes are equally likely. H,ere the

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total number of events represents the sample space, and the
event A represents the subset of the sample space which
satisfies some specific criterion. The axiom may be expressed
P(A) == nA/ n.
(2) Probability is a positive real number between 0 and 1 inclusive;

i.e.,
O; that is,
P (A n B) disjoint

== P (cp) == O.

If this conclusion is combined with Axiom 5, it may be stated that
if two events are mutually exclusive, the probability of at least one of
them is the sum of their individual probabilities; that is,
P (A U B) disjoint

== P (A) + P (B) .

If the occurrence of an event in no way depends on the occurrence
of a second event, the two are independent. Mathematically, A and B
are independent if
P(A I B)

== P(A)

I A)

== P(B).

or if
P(B

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Then from Equation (9-4) or (9-5), it is seen that p(AnB) =
P(A) P(B). Note that this does not mean that P(A n B) = O. The
fact that two events are independent means that there is no
functional relationship between their probabilities of occurrence.
The expression p(An B) = 0 says that A can never occur when B
does, a functional relationship of mutual exclusion.
If events A and B can occur simultaneously, then a certain fraction
of events B have event A associated with them. If this fraction is
the same as the fraction of all possible events that have event A
associated with them, then the events A and B are independent.
Symbolically, independence implies that

This can be demonstrated by combining the definition of independence with Axiom 6. If A and B are statistically independent, the
probability of their simultaneous occurrence is the product of their
individual probabilities, that is,
P (A n B) independent

= P (A) P (B) .

(9-10)

Note that Equation (9-10) is symmetric in A and B. This implies
that if A is independent of B, then B is independent of A. This need
be true only in the statistical sense. It is important to recognize the
difference between statistical dependence and causal dependence.
From the causal viewpoint, subscriber complaints are dependent on
noisy trunks, but noisy trunks are not dependent on subscriber complaints. Statistical analysis would merely show a dependence or
correlation between the two without any indication as to which is
the cause and which is the effect.
Much statistical work is simplified if it can be assumed that events
are either mutually exclusive or independent. -Where events are
mutually exclusive, the probability of at least one of the events is the
simple sum of the probabilities of the mutually exclusive events. The
probability of the simultaneous occurrence of independent events
may be found as the product of the probabilities of the independent
events.

Chap. 9

227

Probability and Statistics

Example 9-1:

This example concerns a group of 1000 trunks between two
cities. All these trunks are measured for loss and noise. It is
found that 925 trunks meet the noise objective, 875 trunks meet
the loss objective, and 850 trunks meet both objectives. If a
connection is established between the two cities and if there is
an equal probability that any trunk may be used, what relationships can be evaluated from the foregoing set operations in
regard to calls between the two cities?
Various events and their probabilities may now be tabulated,
as in Figure 9-4; symbolic and numerical values are both given
in the table below. A Venn diagram of the relationships among
the subsets of trunks is given in Figure 9-6.
EVENT

NOTE

NO. OF OCCURRENCES

PROBABILITY OR
RELATIVE FREQUENCY

=

=

S

1

n

=

1000

A

2

nl =

925

nl/n =

925/1000 =

0.925

B

2

~ =

875

~/n =

875/1000 =

0.875

A'

3

na =

75

B'

3

n4 =

125

n4/n

A()B

4

n5 =

850

n5/n =

A()B'

4

n6

=

75

n6/n =

75/1000

A'nB

4

n7 =

25

n7/n =

25/1000

A'nB'

4

ns =

50

ns/n =

50/1000 =

0.05

AlB

5

ng =

850

n5/ (n7+n5) =

850/875 =

0.971

BI

6

850

n5/ (n6+n5) =

850/925

0.919

A

nlO

=

n/n

1000/1000

na/n =

75/1000

=

125/1000

1

= 0.075

=

850/1000 =

=
=

=

0.125
0.85
0.075
0.025

Notes:
1. S is the sample space, 1000 trunks.
2. A and B are two subsets, the trunks which meet the noise
objective and the loss objective, respectively.

3. A' and B' are the complements of A and B.
4. These are the four mutually exclusive events which make
up the sample space, S.

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5. A I B, the event A given B, consists of those trunks meeting
the noise objective among the trunks which meet the loss
objective.
6. B I A, the event B given A, contains the trunks meeting
the loss objective among those that meet the noise
objective.

7. AU B represents all the trunks that meet the noise objective, the loss objective, or both.

S

= 925 trunks
= 1000 trunks

B

= 875 trunks

A

A'

nB=

25 trunks

Figure 9-6. Venn diagram for a set of trunks.

9-2

DISCRETE AND CONTINUOUS FUNCTIONS

An important objective in working with statistics and with probability theory is a more efficient way of describing a set of observations than by enumerating all of the numbers in the set. A common
problem is that of characterizing a set of measurements which are
supposed to be similar or identical but which are not. The random
variable is a function which may be discrete, as the trunks in
Example 9-1, where the trunks either met objectives or they did not.
The random variable may also be continuous. In Example 9-1, the
data may have related to actual measurements of loss and noise, and
the random variable might have represented the distribution of these
measurements, i.e., the number of trunks showing noise or loss values
in some recognizable measurement system such as dB of loss or
dBrncO of noise.
Mapping

Consider a sample space made up of elements designated as Pi.
By a process called mapping, the elements of the space (or domain)

Probability and Statistics

Chap. 9

229

can be expressed in terms of a random variable, X, which is plotted
along an axis. The mapping process is illustrated in Figure 9-7 where
X (Pi) == Xi. By virtue of the rule of correspondence, each element,
Pi, maps into one and only one value, Xi, although it is possible for
more than one Pi to map into the same Xi. While every element Pi
must map into some value, Xi, it is not necessary that every Xi be 'an
image of an element, Pi.
Theoretically, the variable X (Pi) may take any value from
00 to
00 as indicated in Figure 9-7. It is generally true, however,
that the mapping process establishes a restricted range of X between
minimum and maximum values. This is also illustrated in Figure 9-7.
-

+

s

Range~
-co+-

I

---+ + co

I

Xmin

Figure 9-7. Mapping.

If the elements of a sample space exhibit characteristics that
involve two parameters, the mapping becomes a two-dimensional
process as illustrated by Figure 9-8 where the trunks of Example 9-1
are mapped onto the x-x and y-y axes. The various events then map
into areas in the x-y plane of Figure 9-8.
As mentioned previously, the random variable, X or Y, may be continuous or discrete. In either case, the treatment and manipulation
of data depend on the ability to express these variables by suitable
functional relationships, such as the cumulative distribution function
or the probability density function.

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Figure 9-8. Mapping in two dimensions.

Cumulative Distribution Function

A real random variable (r.v.) is a real function whose domain is
the sample space, S, and whose range is the real line (the x axis). The
r.v. also satisfies the conditions (1) that the set {pi:X (Pi) < Xa}* is
an event for any real number, Xi, and (2) that the probability
P {Pi :X (pi) = ± oo} is equal to zero. The function describing the
probability distribution of the random variable is called the cumulative
distribution function (c.d.f.) and may be written [2]
(9-11)
*In expressions such as this, the braces define the 8et and the colon is read

8uch that.

Chap. 9

Probability and Statistics

231

This equation states that the c.d.f. is a function equal to the probability that the variable, X (representing the elements, pi, of the
sample space), is equal to or less than the value Xi. For present purposes, this equation must meet the following conditions:
(1) It is a real function of a real number.
(2) It is right-continuous; that is, the value of the function

Fx (x) at any point is equal to or less than the given value
[X (Pi) < Xi in Equation (9-11)].
(3) It is single-valued, monotonic, non decreasing.
(4) lim

Fx(x)

== 0;

X~-oo

lim

Fx(x)

== 1.

x~oo

The random variable, X, may be continuous or discrete or mixed.
When X is continuous, the c.d.f. is continuous. When X is discrete,
the c.d.f. is not continuous and, when plotted, appears as a set of
steps. These relationships show that X (Pi) may take on values from
- 00 to + 00 ; the c.d.f. correspondingly takes on values from 0 to 1
for X(Pi) == -00 to X(Pi) == +00.
If an estimation of a continuous c.d.f. is plotted as in Figure 9-9,
the curve looks like an uneven staircase having flat treads and discontinuities in place of vertical risers. As the number of observations
increases and the granularity of readings becomes finer, the treads
and risers become smaller. A continuous c.d.f. is a smooth curve as
illustrated in Figure 9-10.
It should be noted that the plot of a discrete c.d.f. would also look
like Figure 9-9.
Probability Density Function

The derivative of the c.d.f. is defined as the probability density
function (p.d.f.). It may be written

Ix (x) == dF x(x) /dx.
The function is illustrated in Figure 9-11.

(9-12)

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Elements of Transmission Analysis

100
90

~

~

c:

GI
::I

IT

l

60

GI

.~

'6

f

GI

>

":S

~::I
U

20
10
0
0

40

50

60

70

80

90

Measurement values
:x; ----.

Figure 9-9. Approximation to a continuous c.d.f.

1.0

H

0.75

VII
~
Q"

~

0.50

~

a

..Q

~

0.25

Il..

0
0

100

50
Measurement values

x---+

Figure 9-10. A continuous c.d.f.

100

Chap. 9

Probability and Statistics

233

Ix(x)

50

100

x---+

Figure 9-11. Probability density function.

9-3

THE PRINCIPAL PARAMETERS

Expected value, variance, and standard deviation are terms that
define the important and useful characteristics of random variables.
The definitions of other parameters, sometimes useful in statistical
studies but seldom used in probability theory, are given later. When
available data permit the use of approximations or estimates of the
random variable, estimates of expected value, variance, and standard
deviation may also be used for statistical analysis.
Expected Value

The expected, or mean, value of a random variable, X, may be
estimated from repeated trials of an appropriate experiment by

(9-13 )
n

where

2:

Xi

is the sum of the values

Xi.

and n is the total number

i=l

of values of x. H,ere, Xi is the numerical value that the random
variable, X, takes for the ith trial.

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If the random variable is discrete, the expected value may be
found by
n

E[X]

= X = 2: xiP{X = Xi},
X

i

(9-14)

=l

where Xi represents the discrete values assumed by the variable, X.
If the random variable is continuous, the expected value is found by
+00

E [X]

= X = .r

X

Ix (x) dx.

(9-15)

The term expectation has been extended to include the expectation
of any function of X, provided X has a probability function. The
expectation of g (X) is
+00

E[g(X)]

=

!

g(x) Ix(x) dx,

where Ix (x) is the probability density function. Of particular interest
is g (X) = X2, the mean squared value, or
+00

E[X2]

=.r

x 2 /x(x) dx = X2.

(9-16)

Variance

The expected value of a random variable gives no information regarding the variation or range of values that may be assumed by a
random variable. The most useful measure of this parameter is the
variance, defined as the expectation of the square of the deviations
of observations from their mean, or expected, value. The expression
for the variance, which may be derived from the function of the
random variable, is
+00

 O.

The corresponding probability density function is a sequence of
impulses expressed
00

Ix(x)

==

~
AX
e-A. ~ - , - .

X=o

x.

(9-27)

In these equations, A is a constant. The derivation of the Poisson
distribution is based on the assumptions that the number of observations, n, is large (usually greater than 50), that the probability of
success, p, is small (less than 0.075n), and that the product of the
two, np, is a constant. Among the properties of the Poisson distribu-

244

Elements of Transmission Analysis

tion are the facts that A is equal to
the mean value and that the variance, a-2, is also equal to A. The
Poisson distribution is illustrated
in Figure 9-16 for A = 3.

tx(X)

0.2

0.1

o

o

1

2

3

4

5
x

6

7

8

9

10

9

10

---+

(0) Density function

Fx(x)

~

I

I

o

r
o

1

Vol. 1

:2

3

4

5

6

7

8

This distribution is useful in
studying the control of defects in
a manufacturing process, the occurrence of accidents or rare disease, and the congestion of traffic,
including telephone traffic. It has
also been used to represent the
statistics of discontinuities in a
transmission medium due to certain manufacturing processes and
to damage caused by rocks falling
upon the cable during installation.

X---+
(b) Distribution function

Binomial Distribution
Figure 9-16. Poisson distribution.

A combination of n different obj ects taken x at a time is called

a selection of x out of n with no attention given to the order of
arrangement. The number of combinations of such a selection is

denoted by. (

~).

It is defined as

n!
x! (n-x)

If p is the probability of sucess in any single trial and q == 1-p is
the probability of failure, then the probability of success for x times
out of n trials is given by

(9-28)

Chap. 9

Probability and Statistics

245

This is known as the binomial distribll;tion. Its density function may
be written

/x(X)

n

0.2

tx(x)

=

0.1

.Z (~)

p"

qn-%.

(9-29)

x=O

This function is a sequence of impulses as illustrated by Figure 9-17,
where n = 9 and p = q = 1/2.

o
X-+

Figure 9-17. Density function for
binomial distribution.

The mean value of the binomial
distribution is equal to np and the
variance
, is (T2 = npq.

Example 9-5:
Consider the 1000 trunks of Example 9-1. Recall that 850
of these trunks meet both noise and loss objectives. Thus,
150 trunks fail to meet the loss or the noise objective or both. In
five consecutive connections using these trunks, where equal
probability of using any trunk is assumed, (1) what is the
probability that all five connections will be satisfactory with
respect to both noise and loss and (2) what is the probability
that two out of five calls will be unsatisfactory?
850

== 1000 == 0.85
q == 1 - p == 0.15
n == 5 trials
x == 5 successful trials.

(1) p

Using Equation (9-28),
p (x)

== 5! (55~5) ! (0.855)

Since it can be shown that O!

(0.155-5).

== 1 and XO == 1, P (x) == 0.855 == 0.44.

246

Elements of Transmission Analysis

Vol. 1

== 0.15
q == 0.85

(2) p

n==5

x

== 2.

Again using Equation (9-28),
P(x)

5!

== 2!(5-2)!
== 0.14.

(0.15 2 ) (0.85 5- 2 )

Bi nom ia I-Poisson-Norma I Relationsh ips

The three distributions described so far are related to one
another. If np and nq are both greater than 5, the binomial distribution can be closely approximated by a normal distribution with
standardized variable,
z==

x-np
ynpq .

The unit nornlal density function, Equation (9-24), may then be
written

f z ()
Z

==

__1__ e- z2/ 2 •
y2'1T

If, in the binomial distribution, n is large and the probability, p,
of an event is close to zero (q == I-p is nearly 1), the event is
called a rare event. In practice, an event can be considered rare
if n > 50 and if np < 5. In such a case, the binomial distribution is
very closely approximated by the Poisson distribution with A == np.
For this case the Poisson density function, Equation (9-27), may
be written
co

fx(x)

== e-np

~

Li

x=o

(np) x

x!

log-Normal Distribution

Here the random variable is normally distributed when expressed
in logarithmic units, for example, decibels. Commercially available

Chap. 9

Probability and Statistics

247

graph paper is designed so that a log-normal distribution plots as
a straight line.
The log-normal distribution is often encountered in transmission
work. In some cases, where the phenomena to be analyzed are
multiplicative, the treatment of log-normal distributions is straightforward because in logarithmic form the phenomena are additive
and so may be treated as any other random variable in which additive
combinations are under consideration. An example is the evaluation
of the overall gain or loss of a circuit containing many tandemconnected components, each of which may be represented by a random
variable whose distribution is log-normal. A transmission system
having a number of transmission line sections and a number of
amplifiers in tandem can be so analyzed.
In some cases, the phenomena are individually log-normal but
are combined in such, a way that the antilogarithms must be considered as the random variables. An example is found in the analysis
of signal voltages of combinations of talker signals in multichannel
telephone transmission systems. Here, the individual talker distributions are log-normal. The distributions, however, combine by
voltage (not log-voltage) to produce a total signal which must be
characterized with sufficient accuracy to evaluate the probability of
system overload. The analysis, which must be made by graphical or
mathematical approximations, has been applied to load-rating theory
for transmission systems [3].
Uniform Distribution

This distribution, sometimes called a rectangular distribution
from the shape of the density function, is represented by the density
function
fx(x)

1
== ----"
Xb - Xa

Xa

<

X 
'

=

0

(9-31)

== 0,
This density function, illustrated by Figure 9-19, is often used to
approximate microwave fading phenomena.
9-6

STATISTICS

The subject of statistics covers
the treatment and analysis of data
and the relationships between the
data and samples taken from the
data. Statistics also includes methods of evaluating the confidence
in the accuracy of the relationships
inferred from data samples.
o

Central Values and Dispersions

1

202

For many purposes, statements
of the central value, X, and the
dispersion, U", provide an adequate Figure 9-19. Rayleigh density function.
summary of a set of observations.
Estimates of central values and dispersions, based on experimental
outcomes, are frequently used instead of functional relationships
which are often not known.

250

Eleme·nts of Transmission Analysis

Vol. 1

There are a number of ways of expressing both the central value
and the dispersion of a random variable. Since the mean and variance
are most easily treated, it is frequently convenient to transform other
measures of central values or dispersions to the mean and variance.
A specific reason for this convenience is that the relationships of the
mean and variance of a subset of samples to the mean and variance
of the sample are simple and essentially independent of the nature of
the density and distribution functions representing the sample space.
Central Values. A central value may be regarded as an average,
where the word average is used in its broadest sense. Following
is a list of expressions for the central value of a set of observations
that might be used in various circumstances:

(1) The median is a central value of the random variable defined
such that, in a set of observations, half the observations have
values greater than the median and half less than the median.
If a number of discrete observations are arranged in order of
magnitude, the median is the middle one if there is an odd
number of observations. If there is an even number of observations, the median is the arithmetic average of the two middle
observations.
(2) The midrange is one-half the sum of the largest and smallest
of the observations.
(3) The mode is the most common value of the variable. It is an
estimate of the value of x at the maximum of the density
function, Equation (9-12). If the density function has two
or more maxima, the distribution is described as bimodal or
multimodal.
(4) The geometric mean is the nth root of the magnitude of the
product of all n observations.
(5) The root mean square (rms) is the square root of the arithmetic mean of the squares of the observations.
(6) The arithmetic mean is the measure having the greatest utility
in probability theory. It is sometimes simply called the mean

Chap. 9

Probability and Statistics

251

value or the average, where here average has a narrower connotation than used earlier. Arithmetic mean is an estimate of
mathematical expectation. As shown previously in Equation
(9-13), the estimate of the mean may be written

n

where

2:

Xi

is the sum of the values of the observations,

Xi,

i=l

and n is the total number of observations.
Dispersions. A complete description of the dispersion might consist
of a tabulation of all deviations. The deviation of any observation, in
turn, is the magnitude of the difference between that observation and
some stated central value of the observations. Some central value
of deviations may be defined as a measure of dispersion. Several
commonly used expressions and definitions for dispersions are given
in the following:

(1) The range is simply the difference between the smallest and
largest observations in the sample.
(2) The mean deviation is the arithmetic mean of absolute deviations about the mean central value. It is seldom used.
(3) The standard deviation is the measure of dispersion which
is used as the basis for most of the mathematical treatment
of dispersion values in probability theory and in statistical
analysis. It is sometimes called the rms deviation. It is given
the Greek letter u as its symbol. The square of the standard
deviation is the variance.

Histogram
Sometimes it is desirable to display graphically the number of
observations that fall in certain small ranges or intervals. The entire
range of observations is divided into cells, and the number of obser-

252

Eleme'nts of Transmission Analysis

Vol. 1

vations falling in each cell is listed. The upper bound of each cell is
included in the cell. A graphical representation, shown in Figure 9-20,
may be prepared by showing values of x as the abscissa and constructing at each cell a rectangle having an area proportional to the
number of observations in the cell. The resulting diagram is called
a histogram. If the ordinate is expressed in terms of the fraction
or percentage of total observations, the histogram is also called a
relative frequency diagram. This is illustrated by the right-hand
ordinate scale in Figure 9-20. The illustration is a plot of the data
of Example 9-2 and of the c.d.f. illustrated by Figure 9-9.

'"

30

30

25

25

20

20

c:

.Q

C
i::

S1
..0
0

ci
Z

~
t'
c:
CD

:)

0CD

15

15

.::
CD

>

.~

10

10

5

5

Gi
a.::

10
Measurement values, quantized
x~

Figure 9-20. Histogram.

Sampling

Sampling involves the measurement of some elements of a universe
or sample space. By proper choice of sampling procedure, parameters
describing the samples can be used to establish relationships between
the parameters of the samples and the parameters of the universe
from which they were drawn. Thus, sampling is useful in the estimation of the parameters of the sample space.
Sampling theory is also useful in the determination of the significance of differences between two samples. Tests of significance and
decision theory depend on sampling theory [4].

Chap. 9

Probability and Statistics

253

To assure the validity of the results of a sampling procedure,
samples must be chosen so that they are representative of the universe.
One such process is called random sampling. This may be accomplished physically, for example, by drawing the samples from a bowl
in which the universe is represented by properly identified slips of
paper or other representative elements. The bowl is agitated before
each drawing of a sample to guarantee random selection. Tables of
random numbers are also available and can sometimes be used to
advantage.
If a sample is drawn from the universe, recorded, and then placed
back into the universe before the next is drawn, the process is called
sampling with replacement. If it is not returned, the process is called
sampling without replacement. Both processes are used, the choice
depending on circumstances. The process of determining the method
of sampling is involved in the design of the experiment.
As previously discussed, the sum of random variables may be
expressed in terms of probability theory as the addition of two or
more functions of the random variable. Summing may also be a
statistical process. A sample may be drawn from one sample space
and another sample from the same sample space or from a second
one. The two values are added and recorded, and the samples are
returned and mixed. The process is repeated many times, and from
the recorded data the mean and variance may be computed for the
summed data by Equations (9-21) and (9-22). Such a process is
often necessary when the parameters of the two original sample
spaces are not known.
If one value is drawn from each of several similar universes or
if several values are drawn from a single universe, independence
among the members of the sample is maintained by sampling with
replacement. The relationships among the samples can then be used
to estimate the parameters of the original universe (s). Such a
sample is called a random sample. The size of the sample is designated
by the number of members or values, n.
The mean of the sample is the sum of the sample values divided by

n. Thus, the mean of the sample means is equal to the mean of the
universe. The variance of the sample means is equal to the variance
of the universe divided by the sample size.

254

Elements of Transmission Analysis

Vol. 1

Estimation. Estimation involves the drawing of inferences about a
universe or sample space from measurements of a sample drawn from
the sample space. Estimation is sometimes broken down into point
estimation and interval estimation. In point estimation a particular
parameter, such as the mean of the unknown universe, is sought.
In interval estimation two values are sought between which some
fraction (such as 99 percent) of the unknown universe is believed
to lie. In some respects, interval estimation is simply two problems
in point estimation.

In choosing the methods of estimation, the sample and the set of
observations based on it may contain extraneous material which does
not belong but which may have a serious effect on the estimate.
Estimation may have as one of its objectives the identification and
elimination of such invalid data.
In experimentation and production, measurements are made to be
used as samples from the potential universe of measurements that
might be made. The universe as a whole is nonexistent; its parameters
are not and cannot be known, and there is no way to determine what
they really are. However, it is expected that, if many measurements
are made and the results expressed statistically, the computed values
will very nearly represent "true values" for the universe. Since the
universe is in fact nonexistent and since the "true values" cannot
really be defined, there is no way to define a best estimation. I t is
necessary to rely on statistical analyses to determine that results
are consistent and unbiased.
This discussion of estimation has been presented to give realization
that, while there are similarities between the methods of estimation
and prediction, there are significant differences, too. Space does not
permit a more thorough discussion of estimation but one more point
must be stressed, that of confidence limits.
Confidence Limits. In addition to making estimates of sample space
parameters, it is often desirable to express a measure of the limits
of confidence in the values. If there is a sample of n observations
having a mean value of Xn taken from a sample space having a standard deviation of cr, the mean of the sample space may be said to have a
value x lying between limits of acr/yn and -an/yn about x. This
interval is called a confidence interval and its two end values,

Chap. 9

Probability and Statistics

255

X -t- aU"/yn, .are the confidence limits. If by using this estimation
procedure to set the interval it is expected that the right answer is
obtained 99.7 percent of the time (the area under the normal density
curve between ± 3U" points, i.e., a = 3), the limits are called 99.7
percent confidence limits. Methods are available for determining limits
for various levels of confidence for different types of distributions [4].
REFERENCES

1. Papoulis, A. Probability, Random Variables, and Stochastic Processes (New
York: McGraw-Hill Book Company, Inc., 1965).

2. Thomas, J. B. An Introduction to Statistical Communication Theory (New
York: John Wiley and Sons, Inc., 1969).
3. Holbrook, B. D. and J. T. Dixon. "Load Rating Theory for Multi-Channel
Amplifiers," Bell System Tech. J., Vol. 18 (Oct. 1939), pp. 624-644.
4. Spiegel, M. R. "Theory and Problems of Statistics," Schaum's Outline Series
(New York: McGraw-Hill Book Company, Inc., 1961).
5. Fry, T. C. Probability and Its Engineering Uses (Princeton, N. J.: D. Van
N ostrand Company, Inc., 1928).
6. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. I
(New York: John Wiley and Sons, Inc., 1957).
7. Wortham, A. W. and T. E. Smith. Practical Statistics in Experimental Design
(Columbus, Ohio: Charles E. Merrill Books, Inc., 1959).

Elements of Transmission Analysis

Chapter 10

Information Theory
The significance and impact of information theory on the conception, design, and understanding of communication systems have
been very large in the years since the publication in 1948 of
Shannon's first paper on the subject, later published in book form [1].
While the subject has its roots and genesis in abstract mathematical
thinking, its importance is so great that it cannot be bypassed or
overlooked here on the excuse that its thorough understanding
requires a full knowledge of underlying mathematical principles
which are beyond the scope of this book and assumed level of
academic background of its readers.
The transmission and storage of information-by human speech,
letters, newspapers, machine data, television, and countless other
means-are among the most commonplace and most important aspects
of modern life. The processes have at least three major facets:
syntactic, semantic, and pragmatic.
The syntactic aspects of information involve the number of possible
symbols, words, or other elements of information, together with the
constraints imposed by the rules of the language or coding system
being used. Syntactics also involves the study of the informationcarrying capabilities of communications channels and the design
of coding systems for efficient information transmission with high
reliability.
In communications engineering, the technical problems of the syntactic aspects of information are of primary concern. While this may
appear to restrict the engineering role to one that is relatively superficial, it must be recognized that the semantic and pragmatic aspects
of information transmission may be seriously degraded if excessive
syntactic errors are introduced. Therefore, the importance of these
256

Chap. 10

Information Theory

257

other aspects of information transmission must be appreciated while
the technical problems of transmitting and storing information are
being solved.
The semantic aspects of information often involve the ultimate
recipient of the information. The understanding of a message depends
on whether the person receiving it has the deciphering key or understands the language. The problems of semantics generally have little
to do with the properties of the communication channel per see
The pragmatic aspects of information involve the value or utility
of information. This is even more a function of the ultimate recipient
than semantics. The pragmatic content of information depends
strongly on time. For example, in a production management system,
the information on production, sales, inventories, distribution, etc.,
is made available at regular intervals. If the information is late, its
value may be significantly decreased; indeed it may be worthless
to the recipient.
Ultimately, the value of any information system is dependent on
all three aspects of storage and transmission of information. The
user's willingness to pay for a system is a function of its practical
utility, and a more complex and expensive system can be justified
only by the increased utility of faster response times or greater
accuracy.
The purposes here are (1) to present a brief historical sketch of
the mathematical background to Shannon's work, (2) to provide
some appreciation for the subject in terms of what is meant by
information and its important relationships to probability theory,
(3) to present enough mathematical ~ackground to illustrate the
importance and power of information theory, and (4) to present
the fundamental theorems of information theory and discuss their
relationship to transmission system design and operating problems.
10-1

THE HISTORICAL BASIS OF INFORMATION THEORY

The basis upon which most modern communication theory is built
has an extensive, implicit background in the work of Fourier. Early
in the nineteenth century he demonstrated the great utility of sinusoidal oscillations as building blocks for representing complex
phenomena and, by his studies on heat flow, he revealed the nature

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of factors governing response time in physical systems. This led to
the modern description of communications systems in terms of available bandwidth, which, in turn, is related to the impulse response of
the system when signals more complicated than sine waves are impressed. The signal itself is regarded as having a spectrum defining
the relative importance of different frequencies in its composition
and a bandwidth determined by the frequency range. If the bandwidth
of the system is less than that of the signal, imperfect transmission
occurs.
During the late 1920s, Nyquist and Hartley \made significant contributions [2, 3, 4]. Hartley's work quantified the relationship between signalling speed, channel bandwidth, and channel time of
availability. Nyquist's analyses led to conclusions that are now
well-known throughout the communications industry as Nyquist's
criteria for pulse transmission [3]. They apply to the suppr2ssion
of intersymbol interference in a bandlimited medium. The criteria
may be stated as follows:
(1) Theoretically error-free transmission of information may be
achieved if the signalling rate of the transmitted signal is
properly related to the impulse response of the channel as
discussed in Chapter 6. These conditions are met if the time
of occurrence of any pulse corresponds to the zero amplitude
crossings of pulses received during any other time interval.
When the proper conditions are met, the maximum signalling
rate is 211 bauds, where 11 is the cutoff frequency of the
channel expressed in terms of a low-pass filter characteristic.
(2) Equally valid error-free transmission of information may be
accomplished if the channel characteristic produces zero
amplitude crossings of the received pulses at intervals corresponding to those halfway between adj acent signal impulses.
In this case, the receiving circuits are adjusted to detect
transitions in the signal at intervals corresponding to those
times halfway between adjacent signal impulses. (At the cost
of doubling the band, criteria 1 and 2 can be met simultaneously by providing a certain channel characteristic, namely
the so-called raised cosine characteristic. This channel characteristic is often used because it provides margin for departures
from ideal in filter design, in the timing circuits needed to
perform the detection function, and in protection against
external sources of interference.)

Chap. 10

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259

(3) The third criterion for error-free transmission is that the
area under a received signal pulse should be proportional to
the corresponding impressed signal pulse value. The response
to each impulse, therefore, has zero area for every signalling
interval except its own.
Nyquist and Hartley were concerned with maximum efficiency
(highest speed) of transmission of telegraph signals in a bandlimited
system; the rate of transmission must take into account performance
limitations due to intersymbol interference and interrelated channel
and signal characteristics. Insofar as external sources of interference
were concerned, they assumed an ideal, noise-free transmission
medium. As a result of his work, Nyquist's name has found a place
in the technical vocabulary in such terms as Nyquist bandwidth,
Nyquist rate, and Nyquist interval.
Applying their research efforts to a generalized channel and to
considerations of performance in the presence of noise and interference from external sources, Wiener and Shannon made significant
contributions to communications theory during the 1940s and 1950s
[1, 5, 6]. Shannon, particularly, is credited with initiating the
science of information theory.
10-2

THE UNIT OF INFORMATION

To be useful, information must be expressed in some form of
symbology that is known and understandable to both the originator
and the recipient of a message. The symbology may be spoken or
written English, French, or German; it may be the dots and dashes
of Morse code; it may be the varying waveforms of a television video
signal; it may be the Os and 1 s of a binary code, etc. Although information is popularly associated with the idea of knowledge, in information theory it is associated with the uncertainty in the content of a
message and the resolution of that uncertainty upon receipt of the
message.
If a message source forms messages as a set of distinct entities,
such as Morse code symbols, the source is called a discrete source.
If the messages form a set whose members can differ minutely, such
as the acoustic waves at a telephone set or the light variation picked
up by a television camera, the message source is said to be a continuous source. In either case, it is possible to express the information

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in terms of equivalent discrete symbols. If the message produces a
continuous signal, the translation from a continuous to a discrete
format is accomplished by the use of the sampling theorem and a
process of quantization (see Chapter 8).
The simplest discrete format is binary; that is, the information is
expressed in symbols that can attain one of two equally likely values.
The unit used to express the binary format is the bit (binary digit).
In binary terms, the number of information symbols generated may
be expressed as

m

== log2 n bits,

(10-1)

where m, the amount of information, is a function of the logarithm of
the number of outcomes, n, that may be attained by the message
source. In Equation (10-1), the logarithm is taken to the base 2;
this has been found to be the most convenient in solving theoretical
communication problems because most practical system applications
are binary. * Therefore, the unit most generally used in information
theory is the bit.
Although bit was derived from binary digit, the two are really
different and care should be exercised in their use. The bit is a measure of information, while a binary digit is a symbol used to convey
that information. To illustrate the difference, consider a channel
capable of transmitting 2400 arbitrarily chosen off-or-on pulses per
second. Such a channel has an information capacity of 2400 bits per
second but, if the channel is used to transmit a completely repetitive
series of off-on pulses at 2400 per second, the actual rate of information transmission is 0 bits per second despite the fact that the channel
is then transmitting 2400 binary digits per second. To say the channel
is transmitting 2400 bits per second under these conditions is to
misuse the word bit.
10-3

ENTROPY

It should be recognized now that the information contained in a
message is a matter of probability. The message is a set of symbols
taken from a larger set. If there is no uncertainty about what the
*Information can, of course, be measured in logarithmic units other than those
to the base 2. If base 10 is used, the information is measured in decimal digits,
or hartleys; if the base e is used, information is in natural units, or nats.

Chap. 10

Information Theory

261

m~ssage

is (what set of symbols is expected by the recipient), the
message contains no information. If there is uncertainty and by
successful receipt and decoding of the message the uncertainty is
resolved, an amount of information has been transmitted equal to
that defined by Equation (10-1). Something more is needed, however,
some measure of the uncertainty in a message before it is decoded.
This measure is called entropy.
Since a coded message is chosen from among a set of code symbols,
there are more choices and, therefore, more uncertainty in long
messages than in short messages. For example, there are just two
possible messages consisting of one binary digit (0 or 1), four messages consisting of two binary digits (00,01,10, or 11),16 consisting
of four binary digits, and so on. The entropy in the message increases
for each of these cases as the number of choices increases. If the
freedom of choice and the uncertainty decrease, the entropy decreases.
If a message source is not synchronous, that is, not producing
information symbols at a constant rate, it is said to have an entropy,
H, of so many bits per symbol (letter, word, or message). However,
if the source does produce symbols at a constant rate, its entropy, H',
is expressed as so many bits per second.
The simple expression in Equation (10-1) may be expanded as an
expression for entropy by including a factor for the expectation of
each possible outcome:

n

== -

L:

Pi log2 Pi bits per symbol.

(10-2)

i=I

In this equation, there are n independent symbols, or outcomes,
whose probabilities of occurrence are PI, P2 ••• pn.
Equation (10-2) may be used to illustrate the effect on the entropy
of a source when probability PI is changed. For the simple case in
which there are just two choices (X with probability PI and Y
with probability P2 == 1 - PI), the value of H is plotted in Figure 10-l.
Examination of the figure makes it clear that for this case the entropy,

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1.0 ,...----r--~_~-___r-----,

0.8 ~--+--',*,--I----+-~~--t

Probability, PI

Figure 10-1. Entropy of a simple source.

H, is a maximum of one bit per symbol when Pl == P2 == 1/2 and that
the entropy is zero when Pl == 0 or 1 (no uncertainty in the message).

It may be shown that this situation is typical even when the
number of choices is large. The entropy is a maximum when the
probabilities of the various choices are about equal and is a small
value when one of the choices has a probability near unity.
Example 10·1:

Given an honest coin. If it is tossed once, there are two
equally probable outcomes, namely, head or tail. The entropy
is computed by Equation (10-2) as
H == -[0.5(-1.0)

+ 0.5(-1.0)]

== 1.0 bit.
If the coin has two heads, the probability of a head is unity. Then

H == - (1.0 log2 1.0)

== 0 bit.
Thus, the tossing of a two-headed coin gives no information. The
outcome has no uncertainty; it is always heads.

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Example 10-2:

Given an honest die. One roll of such a die can result in any
one of six equally probable outcomes. Thus, using Equation
(10-2) again, it is seen that the entropy of the source (the die) is
H ==- -log2 (1/6)

==- 2.58 bits.
Now, assume the die is loaded; in this case the outcomes are not
equally probable. Assume the following probabilities for the
various possible outcomes:
DIE FACE

PROBABILITY

1
2
3

0.4
0.2
0.1
0.1
0.1
0.1

4
5

6
H ==- - (0.4log2 0.4

+ 0.21og

2

0.2

+ 0.4log2 0.1)

==- 2.32 bits.
An example of a more complex relationship between probability
of occurrence and entropy is illustrated by an evaluation of the
information content of the written English language. As a first
approximation, the occurrence of the 27 symbols representing the
26 letters of the alphabet and a space may be assumed to be equally
probable. Such an approximation sets the upper bound at
H ==- log2 27 ==- 4.75 bits per symbol.

This approximation, however, is inaccurate since the probabilities of
occurrence are quite different for different letters. For example, in
typical English text the l'etter E occurs with a probability of about
0.13, while Z occurs with a probability of only about 0.0008. By considering such probabilities and other refinements, the information
content of English text is estimated to be about one bit per symbol.

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10-4

THE COMMUNICATION SYSTEM
The term information has been defined in terms of logarithmic

units (bits), and the measure of information has been defined as
entropy in bits. The concept of information transfer from a source
to a destination has been described as a probabilistic phenomenon
involving the probabilities of message generation by the source and
the resolution of the uncertainties at the destination. These concepts
may now be more specifically related to the communication system.
The general communication system is commonly represented in
one simplified form by a sketch such as the block diagram of
Figure 10-2. The system is made up of a source of information and
a destination for the information. Between the source and destination
are a transmitter, a channel to carry the information, and a receiver.
The function of the transmitter is to process the message from the
source into a form suitable for transmission over the channel, a
process frequently referred to as channel coding. The receiver reverses
this process to restore the signal to 'us original form so that the message can be delivered to the destination in suitable form. This process
is called decoding. The channel in such a system interconnects the
physically separated transmitter and receiver. It is often assumed
to be ideal, introducing no noise or distortion. This is, in fact, never
achievable; every channel introduces some noise and distortion. It
should also be recognized that there are noise sources that enter the
system at places other than the channel; however, it is convenient
to assume that all the perturbations on ideal signal transmission are

Information
source

Receiver

TransmItter

Signal

Noise
source

Destination

Received
signal

Figure 10-2. Block schematic of a general communication system.

Chap. 10

Information Theory

265

introduced into the channel by a source external to the channel, as
shown in Figure 10-2.
Coding

The coding (and decoding) of messages in the transmitter (and
receiver) of the communication system of Figure 10-2 may take any
of a large number of forms and may be done for a number of different
reasons. At the source the signal is often encoded for the purpose
of increasing the entropy of the source. Morse's dot-dash coding of
alphabetical symbols is an example; he assigned short dot-dash
symbols to those letters most frequently found in English text and
longer symbols to those less frequently encountered. Encoding is
found in the transmitter where the purpose may be to increase
the efficiency of transmission over the channel, i.e., to increase the
rate of transmission of information. Encoding may also provide error
detection, error correction, or both. A thorough review of coding
principles and techniques is beyond the scope of this chapter; however,
practical applications of coding techniques appear in Chapter 8
(Modulation) and in several chapters of Volume 2 in which terminals
for specific systems are described.
Noise

Noise contains components whose characteristics generally can be
defined in probability terms and thus theoretically in terms of
information. The presence of noise in a communication system adds
bits of information and increases the uncertainty of the received
signal; therefore, one might erroneously conclude that noise is beneficial. However, since the added noise perturbs the original set of
choices, it introduces an undesirable uncertainty.
Figure 10-3 illustrates a simple case of how noise may introduce
errors in transmission. The transmitted message, shown in Figure
10-3 (a) as a series of Os and 1s, is transformed into a series of plus
(for 1) and minus (for 0) voltages in Figure 10-3 (b). This signal
is perturbed by an interfering noise depicted in Figure 10-3 (c). The
signal and noise voltages add as in Figure 10-3 (d), and the receiver
translates the received composite signal into the received message of
Figure 10-3 (e) which contains three errors.
The noise introduced in a communication system, such as that
illustrated in Figure 10-2, may consist of any of a large number of
kinds of interference introduced in the transmission path. Its

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(a) Transmitted
message
(b) Transmitted
signal

(c) Added noise

(d) Received signal
and noise
(e) Received message
(Errors are underlined)

I

111110100010

Figure 10-3. Effect of noise on transmission.

characteristic may be well-defined by some probabilistic expression;
Gaussian or Poisson distributions are examples. Intersymbol interference, resulting from gain or envelope delay distortion (or both),
may be regarded as noise. Signal-dependent distortion of the signal
itself, due to nonlinear devices, may also be considered as noise.
Other possible types of interference (noise) include frequency offset
or frequency shift, sudden amplitude or phase hits due to external
influences, echoes (perhaps due to impedance mismatches), or crosstalk due to some other signal being superimposed on the wanted signal
by way of an unwanted path. Any or all of these interferences can
produce transmission errors.

10-5

THE FUNDAMENTAL THEOREMS

The value and broad scope of information theory are expressed
succinctly by Pierce: "To me the indubitably valuable content of
information theory seems clear and simple. It embraces the ideas
of the information rate or entropy of an ergodic message source, the
information capacity of noiseless and noisy channels, and the efficient
encoding of messages produced by the source, so as to approach

Information Theory

Chap. 10

267

errorless transmission at a rate approaching the channel capacity.
The world of which information theory gives us an understanding
of clear and present value is that of electrical communication systems
and, especially, that of intelligently designing such systems" [7].
Shannon presents a large number of theorems, all of which pertain
to the comments quoted above. There are three, however, that are
basic and of sufficient importance to discuss here. These are (1) the
fundamental theorem for the noiseless channel, (2) the fundamental
theorem for the discrete channel with noise, and (3) the theorem for
the channel capacity with an average power limitation.
The Noiseless Channel

Let a source have an entropy of H bits per symbol and a channel
have a capacity of C bits per second. Then it is possible to encode the
output, m', of the source in such a way as to transmit at the average
rate of C/H - E symbols per second over the channel, where E is
arbitrarily small. This may be written

m'

==

C
H -

E

symbols per second.

(10-3)

It is not possible to transmit at an average rate greater than C/H.
It is necessary to distinguish carefully between the m of Equation (10-1) expressed in bits and the m' of Equation (10-3) expressed
in symbols per second. The quantity m as used in Equation (10-1)
is a measure of information produced by a source (in the simple
binary case, the number of 1s and Os). Then,
H'

== m'H

bits per second,

(10-4)

where m' is the average number of symbols produced per second, H is
the entropy produced by the source in bits per symbol, and H' is the
entropy in bits per second.
For cases of interest, H' < C and the number of symbols per
second is
H' <
Isecon
d.
m ' -- -U= ~
H sym b
0 s per

(10-5)

268

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Vol. 1

Equations (10-3) and (10-5) are equivalent since E in Equation (10-3)
is the amount by which CjH exceeds m' in Equation (10-5). Thus,
a source may produce symbols at a rate of m' symbols per second.
The entropy may be such that the information produced is only H
bits per symbol or H' bits per second. The theorem shows that as
long as H' < C, the source may be coded so that a rate of C /H - E
symbols per second may be transmitted over the channel of capacity
C. A rate greater than C /H cannot be achieved by any coding without
error in transmission.
The Discrete Channel with Noise

Consider a discrete channel with a capacity, C, and a discrete
source with an entropy, H'. If H' < C, there exists a coding system
such that the output of the source can be transmitted over the channel
with an arbitrarily small frequency of errors (or an arbitrarily small
equivocation). If H' > C, it is possible to encode the source so that
the equivocation is less than H' -C+e where e is arbitrarily small.
There is no method of encoding which gives an equivocation less
than H'-C.
It seems strange to find a theorem relating to a "discrete channel
with noise" that has no explicit mention of noise in its statement.
However, this situation arises from the manner in which Shannon
leads up to the theorem. Shannon defines the capacity, C, of the
discrete channel with noise as
C

== Max [H' (x)

bits per second.

- H'y(x)]

(10-6)

In this equation, C is given as the maximum value of source x with
entropy H'(x) minus the conditional entropy H'y(x). The latter, in
turn, is defined as the equivocation, which measures the average
ambiguity of the received signal due to the presence of noise in the
system. Thus, noise is included by implication.
Channel Capacity with an Average Power Limitation

The capacity of a channel of band W perturbed by white noise*
of power P noise when the average transmitter power is limited to P max
is given by
C

== W I Og2

Pmax

+

p.

P noise

notse

•

bIts per second.

*White noise has a flat or constant power spectral density.

(10-7)

Chap. 10

Information Theory

269

Shannon explains, "This means that by sufficiently involved coding
max + Pnoise
syst ems we can t ransml·t b·lnary d··t
19l s a t th e rat e W I Og2 P p.
nO'lse

bits per second, with arbitrarily small frequency of errors. It is
not possible to transmit at a higher rate by any encoding system
without definite positive frequency of errors" [1]. In Equation (10-7),
W is the bandwidth in hertz; P max and P noise are signal and noise
powers that may be expressed in any consistent set of units (as a
ratio, the units cancel out in the equation). As a final restriction,
Shannon points out that to approximate this limiting rate of transmission the transmitted signals must approximate white noise in
statistical properties. Coding, used to improve the transmission rate,
is accomplished only at the expense of introducing delay and complexity. To achieve or approach the limiting rate may introduce
sufficient delay in practice as to make the process impractical.
Other theorems of Shannon give the rate of information transmission for other sets of conditions. For example, the condition of peak
power rather than average power limitation is covered. For noise
other than white noise the transmission rate cannot be stated explicitly but can be bounded. The bounds are usually near enough to
being equal that most practical problems can be solved satisfactorily.
10-6

CHANNEL SYMMETRY

It may be shown that the maximum rate of transmission of information (the capacity) can be determined for a symmetical channel
by straightforward means but that the computation for an unsymmetical channel becomes complicated [7]. A symmetrical channel is
one in which the probability, p, of a 0 from the source being received
as a 0 is equal to the probability that a 1 from the source is received
as a 1. Thus, the probability that a transmitted 0 would be received as
a 1 and the the probability that a 1 would be received as a 0 are
both equal to (1-p). Most practical problems involve symmetrical
channels.
Example 10-3:

Given the symmetrical channel of Figure 10-4(a) having a
transmitter, x, a receiver, y, and additive noise; given channel
performance such that p = 0.9 [as shown in Figures 10-4 (b) and
10-4 (c) ] ; and given the statistics of the transmitter such that
the probability of a 1 is 0.6 and of a 0 is 0.4. What is the entropy
of the signal received at y?

270

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Elements of Transmission Analysis

From Equation (10-2), the entropy of the transmitter is
H (x) == - (0.6Iog2 0.6

+ 0.4log2 0.4)

== 0.97 bit per symbol.

The rate of transmission, R, may be shown by an expression
similar to Equation (10-6),
R == H'(x) - H'y(x) bits per second.

The equivocation, H'y(x), may be found by
H'y(x) == -p log2 P -

(1-p) log2 (1-p)

== -0.9 log2 0.9 - 0.11og2 0.1 == 0.469 bit per second.
Thus,

R == 0.97 - 0.469

== 0.501 bit per second.

This is the entropy of the signal at y for the situation in
Figure 10-4 (b).

I

Transmitter

I
I

[:]

(0)

Symmetrical
channel

Receiver

~No;e

I
I
I

0
I

I~P=0.97.'
(b)

PI

(x)

Po (x)

io~o~I

= 0.6
= 0.4
0

I
I

(c)

p. (")
Po (x)

= 0.5

........ p

i)-;::::'

h....-1>
\.

p=0.9

~
•.
1""- 1>
i)-;::::'

l..'

0

.,

Po (y)

= 0.6 X
= 0.4 X

0.9
0.9

+ 0.4 X 0.1 = 0.58
+ 0.6 X 0.1 = 0.42

= PoY
= 0.5 X

0.9

+ 0.5 X 0.1 = 0.5

0

I

p=0.9

1~

= 0.5

PI (y)

~-'::::-0l

\{J

::::::r1
I

........ p

p=0.9

I

~ -'::::- 0

"1

PI (y)

0

Figure 10-4. Transmission over a discrete symmetrical channel with noise.

271

Information Theory

Chap. 10

Next, assume that the transmitter may be encoded differently
so that pdx) == Po(x) == 0.5 as illustrated in Figure 10-4(c).
What is now the entropy of the signal received at y?
For this condition,
H' (x)

== -0.5 log2 0.5 -

0.5 log2 0.5

==

1.0 bit per second.

The channel is the same as in Figure 10-4 (b) . Therefore, the
new rate is

R

== 1 -

0.469

== 0.531 bit per second.

Thus, the entropy of the signal received at y has been increased
by increasing the entropy of the transmitter.
For the channel assumed, one having p == 0.9, this can be shown
to be the maximum rate and thus the channel capacity, C, of
Equation (10-6).
It may be shown that if the symmetrical channel has performance such that p == 0.99, the maximum rate improves to
0.92 bit per second when the source entropy is unity.

REFERENCES

1. Shannon, C. E. and W. Weaver. The Mathematical Theory of Communication
(Urbana, Ill.: The University of Illinois Press, 1963).

2. Nyquist, H. "Certain Factors Affecting Telegraph Speed," Bell System
Tech. J., Vol. 3 (April 1924).
3. Nyquist, H. "Certain Topics in Telegraph Transmission Theory," A.I.E.E.
Transactions, Vol. 47 (April 1928) .
4. Hartley, R. V. L. "Transmission of Information," Bell System Tech. J.,
Vol. 7 (July 1928).
5. Wiener, N. Cybernetics (Cambridge, Mass.: Technology Press, 1948).
6. Wiener, N. Extrapolation, Interpolation, and Smoothing of Stationary Time
Series (New York: John Wiley and Sons, Inc., 1949).
7. Pierce, J. R. Symbols, Signals and Noise: The Nature and Process of Communication (New York: Harper and Brothers, 1961).

272

Elements of Transmission Analysis

Vol. 1

8. Hyvarinen, L. P. Information Theory for Systems Engineers (New York:
Springer-Verlag, 1968).
9. Raisbeck, G. Information Theory-An Introduction for Scientists and
Engineers (Cambridge, Mass.: M.LT. Press, 1963).
10. Bennett, W. R. and J. R. Davey. Data Transmission (New York: McGrawHill Book Company, Inc., 1965).

Elements of Transmission Analysis

Chapter 11

Engineering Economy
Solutions to. engineering problems are usually cDnsidered complete
Dnly after economic analyses have been made of several alternative
solutiDns and the results cDmpared. This is true in the field Df transmission as it is in any Dther field. SDmetimes, a chDice must be made
Dn the basis Df incomplete infDrmation and it becDmes necessary to.
exercise engineering judgement in respect to the impact of intangible
aspects Df the problem. Bell System Dbjectives are to. prDvide economically the best possible service. To. meet these Dbjectives, engineering
eCDnomy studies must be made to demDnstrate the value Df new systems, new services, and specific prDpDsals fDr netwDrk expansiDn;
service and perfDrmance improvements must also be evaluated.
Financial accDunting and engineering are fields that appear to be
quite remote frDm each Dther; hDwever, there are numerous pDints
Df contact in the paths fDIIDwed by the two. prDfessiDns. BDth are CDncerned with the use of capital and expense funds. The major difference
is that in financial accDunting these funds are dealt with in retrospect
by examining the results Df expenditures while in engineering one Df
several alternate future CDurses Df action must be selected to. use
available funds mDst effectively.
There are two broad categories of expenditure which CDnsume most
Df the funds available to. the Bell System. One is the CDSt Df operating

the business and maintaining the plant in service. These expenses are
charged in the periDd in which they are accrued; they are planned,
budgeted, cDntrolled, and paid DUt Df current revenues. The second
is the capital required to. construct the new plant needed to. satisfy

273

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growing service demands. Capital expenditures are paid out of funds
accumulated as retained earnings from current revenues, the sale of
stocks and bonds, depreciation, deferred taxes, and investment tax
credits. Funds are planned, budgeted, controlled, and spent in accordance with procedures generally categorized as the construction
program.
Planning and implementing the construction program involve many
factors that affect the choice of a course of action. Relative service
and performance capability, operating conditions, maintenance complexities, revenues, and costs must all be considered. Costs are given
considerable weight because they provide a tangible and quantitative
measure of relative worth in terms that most people understand.
Many types of cost studies are made to determine the effects of
some action on pricing policy, financial position, or accounting results.
Such studies must often be made within the constraints of the Uniform System of Accounts prescribed by the Federal Communications
Commission. Many are made after a course of action has been determined. Engineering economy studies are intended to show which
of several plans is economically most attractive in fulfilling service
requirements. Therefore, they are important aids in making decisions
which cumulatively result in the formulation of the construction program. In the field of transmission engineering, as in many other areas,
there are often several possible courses of action which may be
feasible. Therefore, familiarity with the principles of engineering
economy studies is necessary in fulfilling transmission engineering
functions.
An engineering economy study may be made (1) to determine
which of several plans or methods of doing a job will be the most
economical over a given time interval; (2) to prepare cost estimates
for studies of new and existing service offerings or special service
arrangements; (3) to establish priorities for discretionary plant investment opportunities; and (4) to establish revenue and capital requirements over long periods of time as major projects are programmed and initiated [1]. Objectives such as these are often satisfied
by studies in which engineering data are used as input information.
The provision of the necessary data for such studies requires an understanding of basic engineering economy principles and often contributes
valuable perspective on the total engineering problem.

Chap. 11
11-1

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275

TIME VALUE OF MONEY

Engineering economy studies deal wtih money to be spent or received in various amounts and at different times. The objective of such
studies is to evaluate the money involved in the plans under consideration; therefQre, it is essential to understand the basic rules that govern
the comparison of money spent or received at different times. An
understanding of the time value of money is implicit in the basic rules
of economy studies and in the application of sound principles to the
conduct of such studies. Simply, it must be understood that a dollar
today is not equal to a dollar a year from now or a year ago. However, there are means of expressing such dollars in equivalent terms,
i.e., means of expressing the time value of money.
The Earning Power of Money

There are costs involved in the use of money that are derived from
the potential earning power that money has as a commodity. These
costs must be measured in terms of this earning power which is a
continuous function of time that increases with the period of use.
The term interest is often used to represent the earning power of
money. However, the term is most applicable to designate the return
on borrowed money, Le., debt. In engineering economy studies of the
type to be considered here, it is common practice to use a composite
of debt interest and equity return. The composite return, equivalent
to the cost of all capital, is determined according to the percentage
of each type in the capital structure.
The effect of return on the time value of money may be evaluated
for a particular time relative to another (usually taken as a reference,
T == 0) by the expression
DT=o
D T =l

1

== 1 + i

(11-1 )

where D is the value of money at times denoted by the subscripts
and i is the rate of return for the period. Thus, if one dollar is needed
one year from now (T == 1) and if the rate of return, i, is 0.10, only
91 cents are required now (T == 0).
The rate of return may be compounded at intervals of typically
(though not necessarily) one year. Compounding involves the computation of the value of money on the bas:is of the return on the

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original ·amount plus the accrued return during the compounding
interval. Thus, to determine the value of money where the return has
been compounded over n intervals
1

DT=o
DT=n

==

DT=n

== DT=o (1 + i) n

(1

+ i)n

or
(11-2)

The interpretation of Equations (11-1) and (11-2) are that if an
amount D is to be made available at a future time, T == n, a smaller
amount of money may be made available now, T == 0, when it is
invested with a rate of return, i.
Equivalent Time-Value Expressions

In the conduct of engineering economy studies, several time-value
equivalencies are used; the choice depends on the nature of the study.
Sometimes it is desirable to express all costs in terms of equivalent
amounts at a time arbitrarily chosen and defined as "the present." In
other studies, it is desirable to express costs in terms of some selected
time in the past or the future. In some cases, it is desirable to express
the costs as an annuity, an amount of money that must be provided, in
equal amounts and at equal intervals, to be equivalent to a single
lump-sum amount at a specified time.
The expressions used are all equivalent to one another and may be
converted from one form to another, as desired. The following are
such commonly-used expressions.
Future worth of a present amount, a form similar to Equation
(11-2) ,
F/P

==

(1

+ i)n

.

(11-3)

Present worth of a future amount,
(11-4)
Future worth of an annuity,
(11-5)

Chap. 11

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277

Annuity for a future amount,
(11-6)

Present worth of an annuity,
(11-7)

Annuity from a present amount,

+

i(1 i)n
A/P= (l+i)n-l

(11-8)

The symbols used in Equations (11-3) through (11-8) are i for
return rate, n for the number of time periods (compounding intervals) , F for the future worth of an amount, P for the present worth,
and A for an annuity. Future worth and present worth are methods
of expressing money values as a single amount at some particular time.
Application of Equations (11-3) through (11-8) is greatly facilitated by the use of tabulations found in many standard texts [1]. In
addition, such· equations may now easily be solved by the use of
modern engineering calculators. An illustration of how these equations may be applied is given in Figure 11-1. Here, the value of $1,000
in year 8, point A, may be traced through various processes to the
future and past and finally back to the same value, $1,000 in year 8.
11-2

ECONOMY STUDY PARAMETERS

The plant is a dynamic conglomeration of telecommunications gear
which grows each year in size and complexity. Additions to the plant
must be chosen with care to insure that continually increasing service
requirements are met, that they are met economically, and that performance objectives are satisfied. The processes of anticipating needs,
recommending new plant, and implementing a construction program
are, in most telephone companies, engineering functions that begin
long before the year of implementation.
To aid in the implementation of construction programs, engineering
economy studies are made to determine which course of action is
most attractive economically. Although initial and recurrent costs are
the most important factors affecting engineering economy studies,

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Year - - .

CONVERSION

DESCRIPTION

A-+B

Single amount in year 8 to
single amount in year 20

B-+C

C-+D

D-+E

E-+F

F-+A

Single amount in year 20
to equal amount in years
14 to 20
Equal amounts in years
14 to 20 to single amount
in year 13
Single amount in year 13
to single amount in year 0
Slingle amount in year 0
to equal amounts in years
1 to 8
Equal amounts in years 1
to 8 to single amount in
year 8

FACTOR

FIP
(i = 0.1,
n =12)

AIF
(i = 0.1,

EQUIVALENCE

EQUATION

B = 3.1384A
= $3138.40

11-3

C = 0.1054B
= $330.79/yr

11-6

D = 4.8684C
= $1610.42

11-7

E = 0.2897D
= $466.54

11-4

n = 7)

PIA
(i = 0.1,
n = 7)

PIF
(i = 0.1,
n = 13)

AlP
(i

n

=
=

FIA
(i

n

=
=

F

=
=

A

== 11.4359 F

0.1,
8)
0.1,
8)

~

0.1874E
$87.43/yr.

11-8

11-5

$1000

Figure 11-1. Time-value equivalence.

there are other vital parameters, such as life of plant, service requirements, inflation, the debt-to-equity ratio of the company, composite
cost of capital, and tax laws which must be taken into consideration.
An engineering economy study must take into account the interval
over which the problem is to be studied and its relation to the life of
the plant involved. If these time intervals are not the same, adj ust-

Chap. 11

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279

ments must be made in the study program. The choice of interval is
a matter of judgment; it may be relatively short, such as two or
three years, or it may continue, at least in theory, indefinitely into
the future. Since most telephone plant has long life, the study period
is often taken as 10 to 20 years.
Long-range planning is undertaken in order to provide guidance
for gross changes in plant makeup. Studies of traffic and private line
growth patterns, shifts in population densities, emerging new services,
and expected new system des-igns must be made and continually refined. The basis for long-term planning is a simplified 30- to 40-year
customer services forecast with incremental five-year study periods.
Adequate time must be allowed for the complex processes of evaluation, compromise, and final decision. Long-range studies must include
some evaluation of the effects of the planning results in the period immediately following the selected study period. Planning decisions
finally come into focus in the form of current planning processes
about three years before implementation is scheduled. Construction
programs are reviewed and adjusted during these three years and at
least three times during the final year.
Provision must be made in the planning process for flexibility and
changes. For example, traffic and priyate line forecasts might show
a need five years in the future for a substantial number of new trunks
between two cities 50 miles apart. Since cable pairs between the two
cities are limited in number, a T1 Carrier System or systems, a new
radio system, and a new multipair cable installation must all be considered. The results of long-range studies might show the new
multipair cable to be most economical. Two years later, during the
preparation of the first construction program for the proposed project,
it might become evident that these two cities are along a major route
that has developed a need for a large number of circuits and for which
a new microwave radio system must be installed. The circuits needed
for the original project may be provided much more economically by
the new radio system. Such adjustments and changes are frequently
made to achieve a more economical program.
Other unforeseen events may cause construction program changes.
As plans are reviewed, changes in the economic climate may require
upward or downward adjustments in the budget, which must be reflected in corresponding changes in the construction program. For
example, emergency needs may have developed from massive plant
damage caused by a hurricane or the unanticipated rapid growth of

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a new industrial park may impose a sudden and unexpected demand
for new facilities. Such events are reviewed frequently by committees
which are empowered to approve certain changes in the construction
program in order to meet the unexpected need.
The economic analysis of engineering problems primarily involves
consideration of a number of aspects of costs. Included are a variety
of capital costs that are incurred because investors provide funds
needed to acquire plant and operations costs that are incurred by the
existence of the plant. Such things as the changing technology and
inflation must also be considered for their effects on costs.
Capital Costs

The costs associated with the acquisition of property are called
capital costs; accounting procedures are used to monitor, control, and
recover such costs. The property is an asset assigned for accounting
purposes to a specific plant account. Capital costs related to engineering economy studies include the concept of the composite cost of
money, the first-cost investment, and the sources of capital used to
recover the cost of the investment. The process of capitalization of
money invested in plant involves recurring annual costs having three
elements: return, capital repayment, and income taxes.
The Composite Cost of Money. Money needed to pay the initial costs
of plant investments is obtained from a number of sources each of
which involves cost factors that must be evaluated for engineering
economy studies. The two basic sources of money are called debt
capital and equity capital. The ratio of the debt capital (obtained by
borrowing) to the total capital (debt plus equity) carried on the books
of a company is called the debt ratio. A discussion of a desirable or
optimum debt ratio for a regulated industry, a subject of continuing
scrutiny and study on the part of industry management and regulatory
agencies, is beyond the scope of this text. However, an understanding
of the relation of the debt ratio to the composite cost of money is
necessary in making engineering economy analyses.

The composite cost of money, or return rate, may be expressed by
an equation that relates the composHe cost of money, i, to the debt
ratio, r, the interest paid on the debt, i d , and the return on equity
(stock dividends and retained earnings), i e • These are expressed
(11-9)

Chap. 11

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281

Thus, if the debt ratio is 45 percent, the composite cost of money is
i

== 0.45i + O.55ie
d

.

It must be recognized that the debt ratio, debt interest, and equity
return may all change with time. However, such variations are usually
not accounted for in engineering economy studies because they are not
predictable and they generally tend to affect alternative study plans
proportionately. Long-term forecasts of debt and equity costs must
sometimes be changed to reflect changes in the corporate debt ratio.
First Costs. The amount of money required to build a new plant is
called the first cost. The first cost of a project is the invested capital
upon which the rate of return is initially calculated. (Later, the return rate is based on unrecovered investment.) Included are the costs
of materials, transportation, labor and incidentals related to installation, supervision, tools, engineering, and a number of other miscellaneous items. These costs are accumulated during the construction
interval and do not recur during the life of that plant item; however,
they must be recovered during the life of the plant if the company
operation is to be based on sound economic principles.
Capital Recovery. Physical plant may wear out, be made obsolete by
new technology, or fail to meet changing requirements. Whatever the
reason, it must ultimately be replaced. The capital invested is dissipated by the end of plant life unless it is repayed by some method.
Capital recovery is generally accomplished by means of depreciation
accounting, a method by which the capital is repaid annually out of
current revenues over the life of the plant. Capital expenditures are
thus converted to annual costs which repay the initia.J cost. In a continuing business, the repayment is not actually made to the investor; the
money is reinvested in other new plant or assets. The investment is
protected by the transfer of capital from old to new plant in installments as the old plant is used up in service.

Depreciation accounting practices must be based upon the service
life of the plant to which they are applied and must also be carried
out in a manner that satisfies legal requirements. They must also
reflect adequately a number of related factors that enter into the
costs of the business such as salvage.
Life of Plant. In conducting an engineering economy study, it is
imperative that the life of the particular plant involved in the study
be used rather than some broad average that is applied for the purpose

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of determining depreciation rates for accounting purposes. Sometimes,
plant life may be established by the conditions of the problem. For
example, a study may be made of alternate plans for installing additional equipment in a building that is scheduled for retirement in a
short period of time, say five years. In such a case, the plans under
study must provide for the repayment in five years of all capital expenses involved with suitable adjustments for salvage at the termination of the study period. In other cases, the life of a plant item may
depend on the life of other items. Such might be the case if the life
of aerial wire or cable were limited by the life of the pole line on
which it is placed. The pole line may be near the end of its useful life
or it might be terminated by action of public authorities.
If the conditions of the problem do not give an indication of the life
of plant, life must be estimated and engineering judgment must be
exercised. Even in such cases, estimated life only rarely coincides with
the average life used for depreciation accounting purposes.

Salvage. A significant capital cost in an engineering economy
study is the net salvage value of the p.Jant upon remova1. The value
may depend on whether salvage is for scrap, trade-in value, or resale.
Removal costs (to be subtracted from the gross salvage value) may
be quite different depending on whether the salvage is for scrap or
reuse. Conservative assumptions should be made as accurately as
possible in respect to the possible reuse of plant and removal costs.
Straight-Line Depreciation. The accounting method under the Uniform System of Accounts prescribed by the Federal Communications
Commission for the Bell System and other common carriers requires
the application of straight-line depreciation for financial statements.
Because it is used for the book records of the firm, it is also called
book depreciation. With this procedure, a capital investment is written
off by an equal amount each year during the expected life of the plant;
that is, for each year, an amount of revenue (equal to the depreciation
rate multiplied by the original first cost amount) is accounted for in
the company books as having paid for the depreciation of that item
of plant. The rate is determined by the following:
. .
Annual depreCIatIon rate

==

100 - percent net salvage
I t rf
(
)
pan
1 e years

%.

Recall that life may terminate for a number of reasons (deterioration, obsolescence, rearrangements, etc.) and that for engineering

Chap. 11

283

Engineering Economy

economy studies life must be carefully defined. "Average life" is often
unsatisfactory in these studies.
Figure 11-2 illustrates the 100-dollar-per-year, straight-line depreciation of a $1000 investment and also shows a tabulation of annual
composite return payments that must be made on the balance (book
value) of the investment. Note that the charge is reduced each year
since the return on the unrecovered capital is r'educed from year to
year.

YEAR
END

COMPOSITE
RETURN
@ 8.5%

UNDEPRECIATED
BALANCE BEFORE
YEAR-END PAYMENT

YEAR-END
PAYMENT

BALANCE
AFTER
PAYMENT

TOTAL
PAID

$1000.00

0

1

$ 85.00

$1085.00

$ 185.00

900.00

2

76.50

976.50

176.50

800.00

3

68.00

868.00

168.00

700.00

4

59.50

759.50

159.50

600.00

5

51.00

651.00

151.00

500.00

6

42.50

542.50

142.50

400.00

7

34.00

434.00

134.00

300.00

8

25.50

325.50

125.50

200.00

9

17.00

217.00

117.00

100.00

10

8.50

108.50

108.50

0.00

$1467.50

Figure 11-2. Straight-line depreciation and return accounting.

Book depreciation of a capital investment is related to the term,
book value. After a plant item has been installed and the depreciation
of the investment has been started in the accounting procedures, the
item is said to have a certain book value. It is computed as the gross
plant investment minus the accumulated depreciation. Sometimes the
gross plant investment value is called book cost and undepreciated
plant is called net plant.

Accelerated Depreciation. In accounting, depreciation is recognized
as an expense that may be deducted from revenues before income tax
is computed. Tax laws now permit specific forms of accelerated depreciation to be used by public utilities for tax depreciation. Higher

Elements of Transmission Analysis

284

Vol. 1

rates are applied during the early years of the life of a plant item and
lower rates during later years. The rate of depreciation varies somewhat but, in principle, it follows a curve like that of Figure 11-3.
The figure compares straight-line and accelerated depreciation of a
1000-dollar plant item having an expected life of 10 years.

400

]

300

"0

:Be:

.2
0
·u
l!!
a.
QI

0

200

Straight-line

100

Year-end

Figure 11-3. Depreciation of a 1OOO-dollar plant item over a 10-year period.

A number of specific methods of accelerated depreciation accounting
may be used [1, 2, 3]. These include the double declining balance
(DDB) method, the one-and-one-half declining balance (1.5-DB)
method, and the sum-of-years-digits (SOYD) method. In the DDB
method, the investment is depreciated at a constant annual rate, 2/n,
of the undepreciated balance where n is the life of the plant item in
years. The accrued depreciation cannot exceed the depreciable value
of the item, Le., the initial investment less net salvage. The 1.5-DB
method is similar but the depreciation rate is 1.5/n.
In the SOYD method, the life of plant in years is used to determine
the rate of depreciation. For example, suppose a plant item is to be
depreciated over a five year period. The sum of years digits is determined by Sd == 5
4
3
2
1 == 15. The depreciation rate used
at the end of each year is remaining life/ Sd. Thus, in the first year,
the depreciation rate is (5) /15 == 0.333 and, in the last year, the rate
is (1) /15 == 0.067.

+ + + +

Investment Tax Credits. The investment tax credit is a significant
source of capital funds that must be included in many economy studies.

Chap. 11

Engineering Economy

285

This credit is provided under tax laws to encourage business investment and expansion. It is a direct tax reduction allowed for certain
qualifying items of property; buildings and land are usually not included. The tax credit has no effect on the value of the initial investment used to establish the depreciation base.
In many situations, fluctuations in income and other variables are
recognized by law and provisions are made to carry gains or losses
forward or backward from the year in which they occur. Investment
tax credit laws change from time to time. It is essential, when they
are to be considered in an economy study, that the law, definitions,
and rules current at the time of the analysis be clearly understood.
Income Tax. Annual costs associated with any investment must include income tax, a tax on earnings after payment of all expenses.
These earnings include dividends paid to stockholders and the amount
added to retained earnings. Specific values of income tax to be used
in economy studies are not furnished and, as a result, the tax obligation must be determined for each alternative plan. Capital cost tabulations, which reflect accelerated tax depreciation and investment tax
credit, are available for operating company use. Thus, annual cost
percentages for taxes can be determined on the basis of estimates of
life and net salvage for use in economy studies. The burden of income
tax, as well as return on the investment, must be borne throughout the
life of the investment. Therefore, money invested in new plant costs
more than money spent on current expenses such as operations,
repairs, and rearrangements.

Plant Operations Costs

N early all costs are either recurring costs associated with the operation of the plant or are capital costs that are dealt with by methods,
such as depreciation accounting, that make them equivalent to recurring costs. Plant operations costs are paid out of revenues. They
can be regarded as being depreciated immediately, at the time they
are incurred. In making engineering economy studies that involve the
comparison of alternative plans, many of these costs ean be and should
be ignored because they are common to the alternative plans. In
making such analyses, it is important to choose only those items for
extended treatment that differ from plan to plan.

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The following list of recurring costs is made up of a number of
typical items that should be considered for analysis in any study. This
list is not all-inclusive.
(1) Maintenance Costs: These are frequently important ingredients
of engineering economy analyses. They include the costs of
labor and material associated with plant upkeep, the related
costs of training, testing of facilities, test equipment, plant
rearrangements, and miscellaneous items such as shop repairs,
tool expenses, and building maintenance and engineering work.

(2) Operating Costs: These include a wide range of costs primarily
related to traffic, commercial, marketing, accounting, and administrative work. These costs are usually common to alternate
plans; thus, they are seldom involved in engineering economy
studies of the type being considered here. They are, of course,
important components in overall company economy studies and
may enter a detailed engineering study where, for example,
network traffic management or the location of operator assignments might be involved in comparing alternative means of
providing facilities for traffic management or operator services.
(3) Rent: This is a cost that is only occasionally an important
element in engineering economy studies.
(4) Lease: The leasing of buildings, equipment, and motor vehicles
is an increasingly important form of obtaining capital goods.
Studies involving leases can be complex since leasing is considered to be an alternate form of debt financing.

(5) Energy: The cost of energy must be considered in these
analyses where it is not common to alternate plans. Primary
power increases with the size and complexity of the plant. The
cost of convers~on equipment and standby equipment needed to
ensure reliability must be included in cost comparisons.
(6) Miscellaneous Taxes: Sales, occupation and use, and ad valorem
taxes must all be considered where appropriate. These taxes
are especially important in considering tax depreciation.
Specifically excluded are social security and unemployment
taxes, usually treated as loading factors on labor costs.
In general, capital expenditures made in the past cannot be undone
or affected by engineering decisions made today. They must be recovered over the anticipated life of the plant through depreciation.

Chap. 11

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287

Ho.wever, when plant is retired, pro.perty tax, maintenance, rent,
energy, and many o.perating expenses are no. Io.nger incurred.
Dynamic Effects on Analysis

Since it is necessary to. deal with the future, engineering eco.nomy
studies are bo.und to. be subject to. all the uncertainties o.f predictio.n.
Amo.ng these uncertainties are changes in technology, unanticipated
demands for new services, and unpredictable variatio.ns in the economic climate such as changes o.f inflatio.nary trends.
New Technology. Advances in technology result in improved electronic components, design techniques, and operating efficiencies. Thus,
equipment that is less expensive, takes less space, uses less power,
and pro.vides mo.re channels o.r higher speeds of o.peratio.n beco.mes
available and must be co.nsidered as a possible replacement for existing
equipment. The partial obso.lescence and early retirement o.f older
equipment become subjects of serious engineering economy studies.
Services and Service Features. New services, such as DATA-PHONE®
digital service, and new service features, such as the custom calling
features of stored program electro.nic switching systems, also have
an impact on engineering economy studies and on pro.blems of early
equipment retirement due to functional obso.lescence. If the, new
services are to. be intro.duced in an area where existing equipment is
incapable o.f pro.viding them, replacement is mandatory and the eco.no.mic problems are tho.se o.f determining the extent, the mo.st efficient
means, and the o.ptimum time to. carry out the replacement program.
Inflation. In recent years, higher returns have been required to. protect investments against inflatio.n. As a result, it has been necessary
to. use higher return rates in cost studies. As inflationary trends have
co.ntinued, it has become evident that these effects must also be applied
to o.ther costs. One straightforward method of accomplishing this end
is to. estimate future Co.sts explicitly as of the time o.f occurrence and
to use such estimates in the study. For example, if an item currently
costing $1,000 is needed now and another is needed one year from
no.w, $1,070 should be used in the study for the second item if a
7 percent change in cost due to. inflatio.n is anticipated.

This method of acco.unting fo.r inflationary effects is effective but
tedious to use where many future costs must be considered. In some
Co.st comparison studies, a "co.nvenience" rate may sometimes be used

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to represent the net impact of inflation on future cost estimates and
on their present worth as expressed in Equation (11-4) and (11-7).
This convenience rate should· be regarded only as an arithmetic
short-cut to simplify the analysis. Detailed treatment of inflation and
its effects are beyond the scope of this chapter.

Convenience Rate. If the cost in each year is greater than that in
the previous year by an inflation rate, h, and if the cost at the beginning of the first year is A o, the cost at the end of any succeeding year,
n, may be determined by
(11-10)

The present worth of this amount is found by Equation (11-4) as

1

+ h)n

== Ao ( 1 +T

(11-11)

.

The convenience rate, c, may be defined as a rate such that the
present worth of the initial amount, Ao (uninflated), over n years is
equal to the value in Equation (11-11); that is

(1 + h)n
c == Ao 1 + i
( +l)D

Ao 1

.

This equation may be manipulated to derive
i - h
.
c==l+h ~'t-h

.

(11-12)

The convenience rate, c, may be used in analyses involving cost items
inflating at rate h. Since several different convenience rates would
be required in a study involving items that are subject to different
rates of inflation, this procedure is sometimes difficult to apply. Also,
it should be stressed that the present worth of taxes, book depreciation, and the tax factor must be determined by the composite cost of
money rate and not by the convenience rate. The convenience rate, c,
may be substituted for i (the composite cost of money) only in
Equations (11-4) and (11-7).

Economy Study Applications. While care must be used in apply,ing the convenience rate, it is a valuable concept when properly used.

Chap. 11

Engineering Economy

289

For example, there are many computer programs, such as the exchange feeder route analysis program (EFRAP), that have wide
application in several types of engineering economy studies suitable
for computer analysis. Many such programs were written before inflation effects were recognized as important. The convenience rate
can be conveniently adapted to these programs which would otherwise have to be completely rewritten to include the effects of inflation.

Example 11-1:
In this example, only maintenance expenses associated with
two alternate plans are computed by two methods to show how
results may be distorted if inflation effects are ignored. Plan A
involves $500 per year maintenance expense for a single capital
expenditure for a plant item having a IO-year life. Plan B involves
$600 per year maintenance expense for one capital expenditure
(BI) having a IO-year life and $600 per year maintenance expense for a second capital expenditure (B2) having an 8-year
life and installed at the beginning of the third year of the plan.
The composite cost of money, i, is taken as 12 percent and the
inflation rate for maintenance expenses is 8 percent per annum.
The maintenance expenses of the two plans are to be compared
on the basis of present worth of expenditures (PWE), first by
ignoring the effect of inflation and second by considering these
expenses inflated and by applying the convenience rate. The PWE
analysis recognizes cash flows for capital expenditures, net salvage, income taxes, and operations costs when they occur and
sums the present worths of these amounts.
For the first analysis, the present worth of maintenance expenses for Plan A may be computed by Equation (11-7) as the
present worth of an annuity with i == 0.12 and n == 10 years. For
Plan B, expense Bl is similarly computed but for expense B2,
the expense must first be computed as the present worth of an
annuity for 8 years (i == 0.12) and then by Equation (11-4) to
determine the present worth of a future amount for 2 years, the
interval between the beginning of the plan and the expenditure
of B2. Then, under Plan A, the PWE for maintenance expenses is

PWE A -

(1.1210 - 1) 500 - $2825
0.12 X 1.1210 -

290

Elements of Transmission Analysis

Vol. 1

For expense B1,

==

PWE B1

(1.12 10 - 1) 600
0.12 X 1.12 10

== $3390

.

For expense B2,
8
(1.12 - 1) X 600 - $2980
0.12 X 1.128
-

PWE B2 --

at the end of the second year of the study plan. This amount is
converted to the beginning of the plan, year 0, by

PWE B2

==

(1

2980

+ 0.12)2 == $2376

.

Thus, for Plan B, the total present worth of expenditures for
maintenance is

PWE B

== PWE + PWE == 3390 + 2376 == $5766
B1

B2

.

From this analysis, it would be concluded that the present worth
of maintenance expenses for Plan B is

PWEB

-

PWEA

== 5766 -

2825

== $2941

more than for Plan A.
For the second analysis, the effects of inflation are included in
computing the PWE for both plans. Equations (11-7) and
(11-4) are used as in the earlier analysis but the convenience
rate, c, is used in place of the composite cost of money, i. The
convenience rate is determined by Equation (11-12) as
_ 1.12 - 1.08 _ 0 037
c1.08
-.
or 3.7 percent. With this substitution, the present worth of
expenditure, A, is calculated as

PWE

A

==

(1.037 10 - 1) 500
0.037 X 1.03710

$4117

.

291

Engineering Economy

Chap. 11

Expenditure B1 is computed as

==

PWEB1

(1.037 10 - 1) 600
0.037 X 1.03710

== $4940

.

Expenditure B2 is computed in terms of the end of the second
year as

==

PWE B2

8

(1.037 - 1) 600 - $4090
0.037 X 1.0378 -

and brought to year 0, the beginning of the plan, by

PWE B2

==

(1

4090

+ 0.037)2 == $3803

.

Thus, for Plan B, the present worth of expenditures is

PWEB

== 4940 + 3803 == $8743

Now, Plan B costs exceed Plan A costs by 8743 - 4117
considerably more than the $2941 previously computed.

== $4626,

This example shows the effect of inflation on only one element
of a plan comparison economy study. The conclusions illustrate
the importance of evaluating the effects of inflation and the
manner in which the convenience rate may be used.
11-3

ECONOMY STUDY TECHNIQUES

Many approaches and different techniques may be used to achieve
the objectives of an engineering economy study, i.e., selecting one
alternative course of action in preference to others by comparing their
costs. Three of these methods have been found to give equivalent
results in that the same alternative is selected. The method used depends on the nature of the available data, the ease of application, and
the purposes for which the study is being made. The three methods
are called the internal rate of return (IROR) , present worth of annual
costs (PWAC), and present worth of expenditures (PWE).
In conducting economy studies, certain assumptions must be made
and clearly understood in order to be sure that comparisons are based
on equivalent conditions. The assumptions must make all alternatives
under study equivalent in terms of provision of service, life of plant,

292

Elements of Transmission Analysis

Vol. 1

and effects of plant retirement. The studies are usually carried out by
using only incremental costs, those that are different for the various
plans. Common costs are eliminated from consideration.
In transmission engineering studies, it is now found that the PWE
method is most easily applied and leads to the most useful results. This
method is illustrated by an outline of the entire study process.
Analytic Alternatives

While most engineering economy studies of the types being considered are based on PWE analyses, some knowledge of the IROR and
PWAC methods is desirable. The IROR method is used in some transmission studies though seldom directly in this field.
Internal Rate of Return. In the development of IROR analysis, designed to determine the most efficient use of money for each project,
the internal rate of return can be defined as the rate that causes the
present worth of the net cash flows for the project to be zero. The two
main elements of net cash flow are the investment and the recovery;
net cash flow thus involves cash flowing into a project (investment)
and back (revenues less operations costs and taxes). The equation for
IROR is a polynomial that must usually be solved iteratively by trial
and error. While this process may be lengthy and complex, it has been
programmed for computer solution and can be applied where only a
comparison of alternatives is desired. However, roots to the solution
may be numerous or there may be no meaningful, finite roots. The
IROR method cannot provide an evaluation of the profitability of an
al ternati vee

Another disadvantage to the use of the IROR method of analysis is
that as the number of plans is increased, the number of comparisons
that must be made increases even faster. For x number of plans, the
number of comparisons is x (x -1) /2. Where a large number of
plans are being considered, the IROR analysis becomes awkward.
Despite these disadvantages, the IROR method of analysis is used
in certain situations. Capital funds for the construction program in
anyone year are finite and it is sometimes difficult to introduce new
types of facilities that require high initial capital expenditures. Sometimes, these facility costs appear favorable on the basis of a PWE
analysis but are formidible with limited capital funds. The alternatives may then be evaluated on the basis of the IROR. For example,

Chap. 11

Engineering Economy

293

a plan requiring high initial investment may require much lower
operating or maintenance funds in comparison with another plan with
lower initial costs. Benefits of a higher initial capital outlay can thus
be measured by the IROR method to determine the most efficient use
of money for each of the projects so analyzed.
This method of analysis and the
present worth of expenditures method are essentially alike when both
are properly processed. However, in the PWAC approach, certain
parameters are often treated in such a manner that the results are
invalidated. For example, it is difficult in PWAC studies to account
adequately for increasing costs such as those due to inflation and to
increased maintenance with equipment aging. These difficulties result
from using average cost values for broad categories of equipment;
cost changes for individual items can depart significantly from these
average values. Thus, the PW AC method is not recommended.
Present Worth of Annual Costs.

However, this method has been used often because it is possible to
group equipment into categories and to assign average values of life,
salvage, maintenance costs, operating costs, and ad valorem taxes to
each category. From these values, it is a relatively simple procedure
to calculate annual cost rates as percentages of installed costs for each
category. From these costs, study procedures can be used to derive
present worth comparisons rather quickly and simply. The costs may
be converted to equivalent present-worth values by considering them
as annuities and using Equation (11-7) for conversion. A second
reason for working with annual costs is that the treatment of noncoincident equipment placements and retirements is often facilitated.
With noncoincident placements and retirements, two time periods
must be defined and treated independently over the period covered
by the study. The planning period is defined as that between the beginning of the study (T == 0) and the time of the last placement of
equipment. The complernentary period is that time between the last
placement to the time of the last retirement of equipment. The planning period covers those years during which additions, removals, and
changes are planned in order to meet growth forecasts and other
service requirements. The planning period is restricted to the number
of years ahead that judgment dictates is reasonable in terms of predictability of needs and availability of resources. The complementary
period is the span of years beyond the end of the planning period for
which annual costs will continue and will influence present worth
evaluations of costs and revenues.

294

Elements of Transmission Analysis

Vol. 1

Present Worth of Expenditures. This method of analysis may be defined
as the summation of the cash flows for capital expenditures, net
salvage, income taxes, and operation costs (or savings) for a project
after conversion to present worths at the appropriate rate. Equation
(11-4) is used for each of the convers,ions. The method is straightforward, has none of the complications of multiple roots and numerous
comparisons found ill the IROR analysis, and is the method most
often used for engineering economy studies. It is superior to the
PWAC method primarily because average costs are not used. Furthermore, since individual costs must be used, it is a simple matter to include in the analysis the effects of variable factors such as inflation.

Study Assumptions
While the assumptions made for any of the analytic alternatives discussed are similar, those covered here are particularly applicable to
a PWE analysis. The important parameters include equivalency of
service provided by each of the plans, the life of plant (cotermination
or repeated plant), plant retirement effects (sunk costs), and the
elimination of common costs (the inclusion of incremental costs only).
Equivalency of Service. The alternative plans in an engineering economy study must satisfy service needs equally or allowance must be
made for the advantages of one plan relative to another. If the number
of new circuits is insufficient to meet the needs, other subsidiary
facilities must be provided and allowance must be made in the study
for the costs of these additional facilities. Furthermore, the alternative plans should be equivalent in terms of the quality of service each
provides; the reliability and transmission performance of each must
satisfy the overall objectives for the project under study.

One complication arises in respect to the equalization of service
capabilities. Modern transmission systems tend to be broadband and
capable of providing large numbers of voiceband channels. The growth
of demand, on the other hand, tends to be relatively smooth and constant. When growth exceeds capacity, a new system must be installed;
thus, the new system provides an excess of capacity until demand
again increases to the system limit. Alternative plans usually involve
systems of different capacities and costs. These systems fulfill the
needs and provide excess capacities in different proportions. The
analysis may thus be seriously dependent on short-term versus longterm conditions of meeting service needs and the economic comparison
of alternatives must account for the differences.

Chap. 11

Engineering Economy

295

Cotermination and Repeated Plant A~sumptions. Either or both of two
basic assumptions regarding life of plant may be made in preparing
most engineering economy studies. One assumption is for the cotermination of plant and the other is for repeated plant [1]. With cotermination of plant, the retirement dates are identical for all final plant
items; this assumption can result in having atypical service life values
assigned to various plant items in the study. The cotermination assumption would clearly be valid, for example when various plant items
are to be installed in a buiding which is known (or assumed) to have
an end-of-life corresponding with the end of the study period.

When repeated plant is assumed, the life of each asset in the study
is determined by its physical characteristics. Usually, in studies that
involve the repeated plant assumption, the effects of retiring an item
of plant at end-of-life must be taken into account by replacing it with
one at the same cost that permits the provision of equivalent services
over the study period. This replacement must then be evaluated in
terms of its effects over the period of the study.
Circumstances and judgment must determine which of the two
assumptions is the better in a given study situation. Whichever assumption is made, it is .important that the plans be comparable in
quantity and quality of service over the same period of time. In addition, it must be recognized that future decisions (and costs) may be
affected by present decisions. For example, one of the alternative plans
under study might lead to the premature exhaust of building capacity
and new building construction might be required. An evaluation of
such effects must be undertaken as part of the study.
When the appropriate life-of-plant assumption has been established,
the effect of the assumption on costs must also be considered. Average
costs are simple to apply but may not be sufficiently accurate. Explicit
estimates of costs for maintenance, depreciation, return, and taxes
over the expected life span for each item of plant should be included
in an economy study. Thus, in most cases, a PWE analysis is required.
In a period of high inflation, the repeated plant assumption of zero
inflation is invalid because maintenance and replacement costs increase with time. Thus, the coterminated plant assumption may be
more appropriate with all PWE costs properly inflated. An appropriate adjustment in net salvage value is also required. If a PW AC study
is being made, the repeated plant assumption may be modified to
reflect forecasted price changes. Replacement plant costs may be calcu-

296

Elements of Transmission Analysis

Vol. 1

lated for a sufficiently long period into the future so that the last
plant placements have negligible effects on study results.
Retirement of Plant. When the cost of equipment has once been incurred, that cost must be recovered by methods of depreciation accounting whether the item is retired early, at the end of life as originally defined, or at some later time. The cost so incurred is irrelevent
to a new engineering economy study involving other alternatives
even when one of those alternatives is the early retirement of that
item. Such cos,ts are called sunk costs. Sunk costs are irrelevent because they are common to the study alternatives. However, other costs
related to that item cannot be ignored. When plant is retired, many
other costs are affected; property tax, maintenance, rent, energy,
and operating costs are no longer incurred.
Incremental Costs. In most engineering economy studies, costs and
revenues that are common to alternate plans may be neglected because
the comparison of one plan with another involves only the consideration of differences between them. Although the costs (called incremental costs) that meet this criterion are usually easy to define,
their identification sometimes involves the exercise of engineering
judgment.

Revenues can usually be neglected because the selection of plans
for comparison is based on equivalent quantity and quality of service
and, therefore, of revenue. This equivalency must be considered carefully in each study and, where there are significant differences, incremental revenues must also be included in the analysis.
Summary of the Comparison Study Process

Since most of the important elements of engineering economy
studies have been discussed, the step-by-step procedure used in the
conduct of such a study may now be outlined. Such a study starts
with the recognition of a need for new facilities and ends with a decision to proceed with the implementation of a specific plan that has
been demonstrated as economically superior to alternative plans.
Forecasts of demands for new services and new facilities are made
continuously by two kinds of planning groups, one responsible for
long-range (fundamental) planning and one for short-range (current)
planning. Comparison studies may be made in either type of planning
activity. However, comparison studies for current planning activities

Chap. 11

297

Engineering Economy

are of greatest interest here because such studies result in implementation of specific projects in accordance with planning, budgeting, and
control procedures required by the construction program. Thus, the
initiation of an engineering economy study of alternatives is made
in response to a planning-group forecast of needs for new facilities.
After the need for a study has been demonstrated, alternate plans
must be proposed for comparison. The number of alternatives to be
considered depends on the knowledge and judgment of those involved
in the study. Incremental costs (and sometimes revenues) for each of
the plans must be determined and documented.
A time-cost diagram is often prepared as an aid to analysis and
to presenting an orderly comparison of alternative plans. Such a
diagram helps to visualize costs and their times of occurrence; it also
provides a mechanism for checking that all important costs are included for analysis and that each of the alternatives provides service
over the period of time corresponding with the study period. A time·cost diagram is illustrated in Figure 11-4.

FC = $10,000
R & C = $1000

M =
T =

$1000/yr
$1000/yr

5 = $1000

V777ZZZZZZZZZZZZZZZZZVZZZ777ZZZ7ZZZ7Z7Z7
PLAN 1

M =
T =

FC = $5000
R & C = $300

[

$500/yr
$500/yr

5 = $50

WZZZZZZZZ77Z7ZZ
M = $800/yr

FC = $8000
R&C=$500.

T=$800~

5=0

W77Z7ZZ7ZZZZZ771ZZ72l7222Z7J7ZZZZV7VZ2ZZZA
PLAN 2
[

I

o
FC
R& C
M
T
5

M = $800/yr
T
$800 ~r

FC = $8000
$500

R&C =

I

2

I

4

=
.5 = 0
V2Z777Z7VV7727Z7177Z77Z7Z7Z0;l
I

6

= First cost
= Rearrangements and changes
= Maintenance
= Total taxes (ad valorem, income, and property)

=

I

8

I

10

I

12

Years

Salvage

Figure 11-4. Time-cost diagram.

I

14

I

16

I

18

I

20

298

Elements of Transmission Analysis

Vol. 1

After all pertinent data has been gathered, study assumptions must
be established and examined for validity in the specific analysis to be
undertaken. Care must be taken to be sure that alternate plans are
equivalent in terms of quantity and quality of services provided and
that suitable allowances for differences are made where necessary.
The applicability of the coterminated or repeated plant assumption
must be determined. This assumption is of course closely related to
the type of analysis to be carried out (lROR, PWAC, or PWE).
Finally, the best possible judgment must be exercised in evaluating
intangible aspects of a plan; these might include the esthetic effects
of certain designs or the impact of a project on the environment.
Of necessity, economy studies are based on a number of explicit
and implicit assumptions. It is often desirable to broaden the scope
of the study to determine the sensitivity of the results to variations
in the assumptions. For example, the growth rate used in the forecast
that initiated the study might be varied or, if it was assumed to be
uniform, the effect of a nonuniform rate might be evaluated. Sometimes, project studies are complicated by interactions with other
projects. The construction of parallel or crossing routes or succeeding
installations may affect initial costs. Estimates must be made of these
effects and it may be desirable to determine the sensitivity of the
results to variations in the estimates.
When all studies have been completed, the results are compared in
respect to economy, uncertainity, and sensitivity to variations. A
decision is made in favor of a specific plan and a recommendation is
made for management consideration and implementation.
REFERENCES

1. Engineering Department of The American Telephone and Telegraph Company.

Engineering Economy, Third Edition (New York: McGraw-Hill Book Company, Inc. 1977).
2. Grant, E. L. and W. G. Ireson. Principles of Engineering Economy, Fifth
Edition (New York: The Ronald Press Company, 1970).
3. Smith, G. W. Engineering Economy: Analysis of Capital Expenditures, Second
Edition (Ames, Iowa: Iowa State University Press, 1973).

Telecommunications
Transmission
Engineering

Section 3
Signal Characterization
Telecommunications in the Bell System involve the transmission
and, in many cases, the switching of many types of signals which
differ materially from one another. To facilitate the evaluation of
transmission objectives, the nature and magnitude of various impairments, the performance provided by different systems or facilities,
and the manner in which all of these interact, it is necessary that
the various types of signals be described in terms that permit the
expression of mathematical relationships among all these factors.
This section of the book provides such signal characterization for
the principal forms of transmitted signals - speech signals, address
and supervisory signals, data signals, and video signals. It also covers
the characterization of combinations of signals that are found in a
frequency division multiplexed load on an analog carrier system.

Chapter 12 covers the characteristics of speech signals typically
found in a telephone channel, i.e., a loop or trunk. Bandwidth, amplitude, phase, and frequency variations are described for telephone
speech and the characteristics of a multichannel speech signal transmitted on analog carrier systems are described. A brief discussion
of radio and television program signals is also given.
Wherever telecommunications signals must be switched, signals
must be transmitted for the purpose of directing and controlling the
switching apparatus. These signals, called address and supervisory
signals, are of many types. The most important are described in
Chapter 13. The proliferation of this variety of signals has resulted
from the increasing number of switching system types and the increased number of switching features that have been provided. The
signal characterization given in this chapter is provided with a
minimum of discussion of the equipment or switching features
involved.

299

The material in Chapter 14 represents the characterization of a
number of the more important types of data signals found in the
Bell System. These signals are, in many cases, digital in format;
they involve the provision of channels ranging from bandwidths of
tens of hertz to several megahertz. Amplitude, frequency, and phase
shift keying techniques are employed in multilevel formats ranging
from two to fifteen levels. Some signals are analog in nature and
as such, may achieve an infinite number of values over a restricted
but continuous range.
The transmission of video signals is among the telecommunication
services provided by the Bell System. While the number of video
circuits in service is small compared to the number of voice-frequency
circuits, the video circuits utilize a substantial portion of the Bell
System transmission facility capacity because of the large bandwidth
most of them require. Characteristics are described in Chapter 15
for telephoto, video telephone, and black and white and color television signals.
One reason for the extensive and detailed attention given to
signal characterization is the fact that signals and transmission
systems interact in important ways. It is rare that only one type
of signal is to be found in anyone transmission system. This is
especially true in broadband carrier systems which carry simultaneously a large variety of signals. Some of the effects of such signal
combinations are characterized in Chapter 16, where a qualitative
discussion of such combinations is presented.

300

Signal Characterization

Chapter 12

Speech Signals
A message channel in the switched message network or in a private
line network must carry a wide variety of signals; the most common
and, therefore, among the most important is the telephone speech
signal. Much research effort has been devoted to an understanding
of all the details of the processes of speech and hearing [1,2,3,4]. The
concern here, however, is with the electrical signal analog of the
acoustic message. This signal and its characterization are related
primarily to the processes carried out in the transmitter (microphone) of the telephone station set and the effects on the signal produced by interactions between it and the channels on which it is
carried.
The problems of speech signal characterization are made complex
by the large number of variables involved and the resulting difficulties
of defining and measuring important parameters explicitly. To overcome these difficulties, signal parameters are defined in terms of
their statistical properties, such as average values, standard deviations, and activity factors. These parameters are defined first for a
hypothetical single continuous talker of constant volume, VOc. This
value, expressed in vu, is next modified to account for breathing
intervals and intersyUabic gaps and to define the single constantvolume talker in terms of power in dBm, POe.
Variables are next introduced to cover the effects of the sex and
speaking habits of the talkers, circuit losses, the automatic compensation introduced by talkers to overcome impairments, station set
variability, etc. Consideration of these variables introduces the
concept of the variable volume talker, one whose average volume
is VOc and whose volume has a standard deviation, (T.
The definition of these parameters is relatively straightforward,
but the determination of their values by analytic means is not. Meas301

302

Signal Characterization

Vol. 1

urements are usually made in working systems to determine the
values of average and standard deviations. These measurements must
be expressed, of course, in terms of some well-established reference
point, such as 0 TLP.
A continuous talker signal is not ordinarily found in a telephone
message channel. Activity factors associated with the efficiency of
trunk utilization and talk-listen effects must be evaluated. With these
factors accounted for, the statistics of talker signals in multiplexed
broadband systems can be evaluated and used for the determination
of signal-dependent impairments such. as intermodulation noise,
crosstalk, and overload.
12-1

THE SINGLE-CHANNEL SPEECH SIGNAL

Whereas single-frequency signals are easily specified by just a
few numbers - one for frequency, one for amplitude, and in some
cases, one for phase - in addition to a functional expression such as
sine or cosine, a telephone speech signal is not so easily specified or
defined. It consists of many frequencies varying in amplitude and
relative phases. Its average amplitude fluctuates widely, and even
its bandwidth may vary with circumstances. Consider first the speech
signal generated at a telephone station set and the way in which it
is modified by the transmission elements of the channel between the
transmitter and receiver.
Speech Signal Energy Distribution and Channel Response

The electrical analog of the acoustic speech signal is generated in
the station set transmitter. Sound waves from the speaker are impressed on the transmitter of the station set, which typically houses
a small container filled with carbon granules. Common battery direct
current, supplied from the central office over the loop conductors,
passes through these granules. The varying pressure of the speech
waves causes the resistance between granules to vary and, in effect,
to modulate the direct current passing through them.
Human speech contains significant components extending roughly
from 30 to 10,000 Hz. The distribution of the long-term average
energy for continuous speech approximates that shown in Figure 12-1.
The actual spectral energy density and bandwidth are, of course,

Chap. 12

Speech Signals

303

0

~
~

--10

>-

i
1

20

~

~

]

Q)

""

-30

-40
0.1

0.2

0.3

0.4

0.6 0.8 1.0
Frequency

2.0

3.0 4.0

6.0

8.0 10.0

(kHz)

Note: Data averaged and smoothed;
male and female voices included.

Figure 12-1. Approximate long-term average spectral energy density for
continuous speech.

highly variable parameters. Nearly 90 percent of the speech energy
lies below 1 kHz. This part of the spectrum also contains considerable
intelligibility so that speech transmitted through a I-kHz low-pass
filter would be at least partly understandable. However, it would also
be quite unnatural and unpleasant. The listener would have to work
hard to recover intelligibility, and many of the nuances in speech
that permit recognition of the talker would be lost.
In practice, a band extending approximately from about 0.25 to
3.0 kHz has been found to provide commercially acceptable quality
for telephone communications. The transmission response at several
points in a simple connection is depicted in Figure 12-2. In the Bell
System, the transmission band of telephone circuits is defined as that
between points that are 10 dB down from the reference frequency,
usually taken as 1000 Hz. Figure 12-2 shows that, even for the simple

304

Signal Characterization

Vol. 1

Trunk and/or
CO equipment

+20
+10

,

0

-

",..",-

-

~~

-10
-20

iii

~

!lc:
0

9f
...
x:

~

+20
+10
0

~

~

II

>

"a

-10

3lc:

-20

V'"

- r---.

r"""""'"

.... 1iI"""

f

0

9-

II
III:

+20
+10
0
-10
-20

~

o

,/

~

500

-

.-- .......

1000

1500

@

2000

~

f"

2500

~Ito.

"" ~

3000

3500

Frequency (Hz)

Figure 12-2. Transmission response, normalized at 1000 Hz, at points along a
typical connection (trunk and central office equipment assumed
distortion less).

Speech Signals

Chap. 12

305

connection depicted, the band is already restricted to approximately
0.25 to 3.0 kHz.
Single Constant-Volume Talker

To develop an understanding of speech signal characterization
from the point of view of practical applications of transmission
design, layout, and operation, consider first a single continuous
talker of constant volume, a somewhat hypothetical case. The volume
of this talker's telephone speech signal has, by definition, a value of
VOe VUe

A continuous talker is not capable of producing truly continuous
speech signals. Pauses due to the thought process, to breathing intervals, or to intersyllabic gaps in energy result in an activity factor,
T e , of 0.65 to 0.75.
The value of power in dBm in a speech wave is defined as the
value of volume in vu corrected by the activity factor. Thus, the
power for a continuous talker may be written
POe

For example, if

Te

==

== VOe + 10 log Te dBm.

(12-1a)

0.725, the power in such a signal is
POe

== VOe -

1.4 dBm.

(12-1b)

This value agrees with an empirically derived relationship between
vu and dBm for speech signals which is generally accepted.
Sources of Volume Variation

Except under specially controlled circumstances, a constant-volume
talker is a rarity. Consider some of the important sources of volume
variation. First, the telephone speaking habits and sex of the speaker
introduce wide variations. He or she may be loud or soft-spoken
and may hold the telephone transmitter close or at a distance. In
addition, telephone sets have a range of values for the efficiencies with
which they transform acoustic waves to electrical waves and vice
versa. Further, their efficiencies are, by design, variables which depend
on the value of direct current fed to them from the central office. The

306

Signal Characterization

Vol. 1

length of the loop, the wire gauge used, the presence or absence of
irregularities such as bridged taps or bridged stations, and the
possible use of loading on the loop all contribute to variations from
loop to loop. These variations affect the average losses in the loop
and the amount of current fed to the transmitter. In addition,
these variations affect differently the attenuation at different frequencies. Variations in average loss and in frequency-dependent
attenuation are also found in central office wiring and equipment,
trunks, and carrier facilities that may be used in a built-up connection. Furthermore, impairments such as sidetone, echo, circuit noise,
room noise, and crosstalk have subjective effects on speaking habits,
as do distance, trunk loss, and type of call. *
Some of the variable losses involved in a simple interlocal telephone
connection are illustrated in Figure 12-3. Station set efficiencies for
sound pressure to electrical signal conversion and vice versa are such
that, with typical losses in the circuit making up a local connection,
a speaker producing at the microphone a sound pressure of 89.5
dBRAP (dB above reference acoustic pressure) would be heard at
a sound pressure of 81.5 dBRAP. Reference in this case is an
acoustical pressure of 0.0002 dyne per square centimeter. The previously mentioned variables are such that received sound signals
have a wide range of values with a standard deviation of nearly
± 8 dB about the average value of 81.5 dBRAP.
In Figure 12-3, the noise impairments shown as introduced in
loops, central office equipment, and the trunk might be picked up at
any of these points. The figure is illustrative. Room noise at the
speaker's end of the connection enters the circuit through the transmitter and appears at the distant receiver along with the speech
signal. Room noise at the listener's end affects his hearing directly
and, in addition, enters his transmitter and appears in his receiver
by transmission through the sidetone path. The decreasing powers
in the signal and in each noise component, caused by the increasing
circuit loss illustrated at the bottom of the figure, are not assigned
values in the figure because they are so highly variable on different
connections and under differing circumstances. Even though impairments are not discussed here in detail, the noise and loss impairments
are shown qualitatively in Figure 12-3 to illustrate their sources.
*It has been observed that volume increases about 1 vu for each 3 dB of trunk
loss and about 1 vu for each 1000 miles of dis'tance. Volume on business calls
tends to be somewhat higher than on social calls.

("')
':T
Q

l'
~

\
,\~

. Typical
Impairments ---.. Room
noise

B
TalkN

IT

T~t

I

I

I

I

0,,_

I

-'-t"
co

j~

~
U

I

----' I

~

~

loop

I

I

Circuit _
noise

I

-

~STA

(R

Assumed
direction of
transmission

~~~;e

em,,'alk

CO
EQPT

Trunk

_

I

Battery _ _
noise

CO
EQPT

Induced
power hum

loop

I
I

I

I

-', I

I

'1"- - -- - -l,

:

I

i

I

I

I

I

I

I

I

I
""'i------+-""
I

STA~

;iLt

I

I

I

I

---

I '--

I

I

-- -

I

I

Room
noise

TI/\~
RI'\\l~L:J

CJ)

"'0
CD
CD

n

:r
CJ)

I

cO'

I

iii"

I

:::J
Q

I
I
--{"
I
-'-,

Figure 12-3. Circuit losses and impairments in a typical interlocal telephone
connection.

w

~

308

Signal Characterization

Vol. 1

They have an indirect, subjective effect on talker volumes as previously mentioned.

Single Variable-Volume Talker

As has been pointed out, the single constant-volume talker is, in
general, a hypothetical case. The aforementioned variables are so
numerous and so difficult to evaluate precisely that it is necessary
to rely on measured data in order to characterize the single variablevolume talker. The results of the 1960 survey of speech volume measurements, essentially an evaluation of the variable-volume talker, are
summarized in Figure 12-4 [5]. While these are the latest data
available, they are somewhat dated, and consideration is being given
to conducting a new survey. In such a survey, many variables must
be considered, and studies are being made to determine which of
these are important in the present day plant [6, 7].
SPEECH VOLUMES (VU)*
TYPE OF CONNECTION

MEAN

STANDARD DEVIATION

Intrabuilding

-24.8

7.3

Interbuilding

-23.1

7.3

Tandem

-19.6

5.9

Toll

-16.8

6.4

*Measured at transmitting switch, class 5 office.

Figure 12-4. Near-end talker speech volumes, 1960 survey.

A knowledge of the average power per talker of a group of talkers
all of whose volumes vary with time is needed for the design of
broadband carrier systems. Such designs must be based on total
signal power, determined from the mean value and standard deviation of each of the speech signals to be carried. These signals do not
combine statistically as normal distributions, even though each is
normal in dB. The average power values must be added; this requires
conversion from dBm to milliwatts, determination of the average
value, addition of the averages in milliwatts, and reconversion of the
result to dBm.

309

Speech Signals

Chap. 12

Consider a probability density function, normal in dB, having
an average value of 0 dBm and standard deviation of 3 dB (these
values are illustrative, not typical). Such a function is plotted in
Figure 12-5 (a). If the dBm values are converted to milliwatts, the
density function of Figure 12-5 (b) results. Note that this function
is skewed and that its mean value is greater than 1 mW. The difference, 8, between the average value in dBm (0 dBm or 1 mW) and
the mean value of the distribut.ion increases as a- increases. The
necessary correction to express the power under a log normal probability density function has been derived elsewhere and is equal to
O.115a-2 [8]; i.e., to obtain the average power in dBm, 0.115a-2 must
be added to the mean value.

-9

-6

-3

0
dBm

3

6

9

o

2345678
mW

(b) Log-normal in mW

(a) Normal in dB

Figure 12-5. Density functions.

Thus, the average power of a variable-volume talker signal having
a log normal density function and a standard deviation of a- may be
expressed by

P()p == POe

+ 0.115a-2 == VOe -

1.4

+ 0.115a-

2

dBm.

(12-2)

This equation is derived from Equation (12-1b) and from the discussion above which relates the average value of power to the mean
value of the density curve, normal in dB.
The mean value of volume for toll calls is given on the last line of
Figure 12-4, but further manipulation is necessary to make the data
useful for toll system analysis. The first step is to translate the

310

Vol. 1

Signal Characterization

data from the outgoing switch of the class 5, or end office, where the
measurements were made, to a comparable point in a toll sy~tem.
Between the point of measurement and the entrance to the toll portion
of the network are, for each connection, a toll connecting trunk and
certain items of central office equipment. These have a loss of
(VNL + 2.5) dB, which includes 2 dB assigned to the trunk and
0.5-dB allowance for the central office equipment. If 0.5 dB is allowed
for the VNL (a typical value), the average -16.8 vu volume for toll
calls shown in Figure 12-4 may be translated to toll system values
(at the -2 dB TLP) as
V toll == -16.8 - (2.0

+ 0.5 + 0.5) == -16.8 -

3.0 == -19.8 vu.

Typically, the losses of toll connecting trunks have a standard deviation of 1 dB. Thus, when combined with the standard deviation of
measured toll volumes at the end office, the standard deviation of
vol ume on the toll system is
CTtoll

== yl6.42 + 12 == 6.47 vu.

For the values of toll call volumes, the average continuous talker
power is

POp == -19.8 - 1.4 + 0.115CT2 == -19.8 - 1.4 + 4.8 = -16.5 dBm.
One further correction is needed. Recall from Chapter 3 that the
outgoing switch at which a toll trunk is terminated is defined as a
-2 dB TLP. Therefore, the toll average power must be converted to
a value at 0 TLP by adding 2 dB ; i.e.,
P()p == -16.5

+ 2 == -14.5 dBmO.

All of the above discussion relates to volume and power averaged
subjectively over an interval of 3 to 10 seconds. In reading the
volume indicator, occasional very high and very low readings are
ignored. High peaks, however, do occur, and their magnitude is
sometimes of considerable interest. The peak factor for a typical
continuous talker is approximately 19 dB. For a talker of lower
activity, peak magnitudes are not affected, but the average power is
reduced relative to the continuous talker.

Speech Signals

Chap. 12
12-2

311

MULTICHANNEL SPEECH

The need for characterizing the speech signals in multichannel
systems arises primarily from the need to control overload performance in analog systems. The characteristics of a multiplexed
combination of speech signals are determined by extrapolation of
the analysis of single speech signal characteristics.
If there are a number, N a , of independent continuous talker signals
of distributed volumes simultaneously present in a broadband system,
each signal occupying a different frequency band but at the same
TLP, the total power represented by the N a signals is

+ 10 log Na
== VOc - 1.4 + 0.115cr + 10 log Na

P av == POp

dBm.

(12-3)

In a system containing N channels, the maximum number of simultaneous signals that could be present is Na == N; however, such an
event is extremely unlikely, especially when N is large. Thus, it is
necessary now to examine the factors that enter into an evaluation
of the probable number of simultaneous talkers in such a system.
The speech activity factor for a continuous talker, T c , was included
in Equation (12-1) for the evaluation of Poe. In evaluating P av
[Equation (12-3)], other forms of activity must be taken into
account. The assumption is made that, on the average, during a
conversation the person using a telephone talks half the time and
listens half the time. Thus, the value of the talk-listen activity factor,
1'8, may be taken as 0.5. More trunks are provided than are needed,
even during the busy hour when traffic is heaviest, because the
number of call rejections due to busy circuits must be held to an
acceptable minimum. Furthermore, during the time a call is being
set up, there is low speech activity on the trunk. These effects may
be accounted for by a trunk efficiency factor, Te. For domestic circuits, Te is usually taken as 0.7. For overseas calls, this value may
be as high as 0.9.
The two activity factors discussed above are usually combined
into a single telephone load activity factor,
'TL

== T8Te == 0.5 X 0.7 == 0.35.

Signal Characterization

312

Vol. 1

Other activity considerations not specifically evaluated have led to
a commonly accepted value of TL = 0.25 for domestic telephone
systems. A higher value (usually TL = 0.35) is used for transatlantic
or transpacific systems. It must be remembered, however, that these
are average busy-hour values. The number of speech signals simultaneously present during the busy hour, when such load considerations are important, varies considerably.
For an N-channel system having a load activity factor TL, the
number of independent continuous talker signals, N a , is a variable
whose mean value is NTL. A system designed to carry just NTL continuous talkers would be overloaded half the time. A system designed
to carry N continuous talkers would be impractical because such a
signal load would occur only a very small percentage of the time.

It is necessary, therefore, to establish the statistical distribution
of channels that would carry continuous talker signal power as a
function of time. The variable representing this distribution may be
called N s • The probability that the number of channels carrying
continuous talker power is N s may be found from
N'
N
N-N
P (Ns) = N s ! (N ~ N s) ! TL s (1 - Td
s
This is a binomial distribution that approaches a normal distribution
having a mean value of NTL and a standard deviation ylNTL (1-TL)
if NTL > 5.
For design purposes, the number of talkers assumed to generate
speech energy simultaneously is the number that may be present
one percent of the time. This value, chosen on the basis of experience, shows adequate balance between performance and cost. Thus,
Na is the value of Ns exceeded one percent of the time. From the
values of areas under a normal curve (Figure 9-15), this value is
Na ~ NTL
2.33 ylNTL (1- TL).

+

Examination of this equation shows that the mean, NTL, increases
more rapidly than the standard deviation, ylNTL (1 - Td, as N
becomes larger. Thus, for large values of N, Na approaches NTL.
Also, it can be seen that the larger the value of TL, the smaller N
need be for this approximation to be valid. Note that for TL = 1,
1 - TL = 0, and Na = NTL.

Speech Signals

Chap. 12

313

Thus, for large values of N, Equation (12-3) can be rewritten

P av

~ VOe -

1.4

+ 0.115u + 10 log N + 10 log
2

TL

dBm.

This approximation can be made an equality, even for systems of
small N, by defining a term which takes into account the deviation
of Na from NTL. This term is defined*
Na

del

(12-4)

= 10 I og - N .
TL

When'terms are rearranged, this may be written
10 log Na

= del + 10 log N + 10 log TL

and substituted in Equation (12-3) to give

P av =

VOe -

1.4

+ 0.115u2 + 10 log + 10 log N + del
TL

dBm.
(12-5)

For the two values of TL given previously (0.25 and 0.35), the relationships among N a , NTL, and del are shown in Figure 12-6 for
systems of various sizes. The value of ~el is shown to become small
as N gets larger. It is often ignored in systems in which N > 2000
channels.
If VOe is evaluated at 0 TLP, the value of P av in Equation (12-3)
is in dBmO. In the total speech load of N signals, P av is the average
power at 0 TLP exceeded during one percent of the busy hour when
all N channels are busy. (A channel is considered busy when a talking connection is established; speech signals need not be present.)
From Equations (12-2) and (12-5), the long-time average load
per channel may be determined (by substituting the previously derived values P(}p
-14.5 dBmO and TL
0.25) for broadband toll
systems as

=

Pav/chan = P(}p

=

+ 10 log + dd
TL

dBmO.

*Other near-equivalent definitions of del are given in Reference 9, pages 227
and 229. The definition given here, however, is commonly used; its value is
conveniently determined and nearly always accurate enough for engineering
purposes.

Vol. 1

Signal Characterization

314

TL
N
Na

=

0.25

NTL

TL
Na

Acl' dB

=

0.35

NTL

Aclt dB

6

4.84

1.5

5.1

5.60

2.1

4.3

12

7.37

3.0

3.9

8.78

4.2

3.2

24

11.80

6.0

2.9

14.59

8.4

2.4

36

15.88

9.0

2.5

19.94

12.6

2.0

48

19.84

12.0

2.2

25.19

16.8

1.8

96

34.74

24.0

1.6

45.18

33.6

1.3

300

93.32

75.0

0.9

124.92

105.0

0.7

600

175.55

150.0

0.7

237.89

210.0

0.5

2000

545.91

500.0

0.4

750.34

700.0

0.3

Figure 12-6. Number of active channels and Acl.

For very broadband systems (N
the load is

Pav/chan

>

== -14.5 -

2000), Ad approaches zero and

6

== -20.5 dBmO

for a telephone signal load of variable volume talkers. *

12-3

LOAD CAPACITY OF SYSTEMS

The load capacity of a multichannel telephone transmission system
is the peak power generated by the total number of speech signals
the system can carry without producing an undue amount of distortion or noise or otherwise affecting system performance or
reliability. The maximum signal amplitude impress·ed on the system
depends on the average talker volume, the distribution of volumes,
and the talker activity. Overload may be the result of the signal
amplitude exceeding the dynamic range of an amplifier or other active
device, of frequency deviations exceeding the bandwidth of an anglemoduled system, or of voltages exceeding the quantizing range of a
*N one of the material in this chapter considers the effects of address, supervisory, or data signals on average channel loading. These effects are covered in
Chapter 16.

315

Speech Sig na Is

Chap. 12

digital quantizer. A system is often said to be overloaded when the
overload point of the system is exceeded by peaks of the transmitted
signal more than 0.001 percent of the time. (It is not then said to be
overloaded 0.001 percent of the time.)

Multichannel Speech and Overload
Overload is defined in a number of ways in Chapter 7. These definitions all basically relate to the signal amplitude at which performance
is no longer linear enough to satisfy performance objectives. In
any of these definitions, it is convenient to use P s dBmO to express the average power of a single-frequency signal that causes
system overload. The peak instantaneous power of this sinusoid is
(Ps
3) dBmO.

+

Most systems do not overload on average power but rather when
instantaneous peaks exceed so.me thresho.ld. A multichannel telephone
system with P av == P s overlo.ads severely because the multichannel
signal has a peak facto.r much larger than the 3-dB peak facto.r for
the single frequency, P s • The peak facto.r for multichannel speech
is 13 to. 18 dB, depending on the number of channels in the system.
It has been fo.und that performance is usually satisfactory if the
peak Po.wer of the multichannel Io.ad exceeded 0.001 percent of the
time is set equal to. or less than the peak Po.wer o.f the sinusoid,
(P s
3) dBmO. This may be written

+

Ps

+ 3 == P av + ac

2

dBmO

Ps

== P av + .1c2 -

3

dBmO,

or
(12-6)

where ac2 is the peak signal amplitude exceeded 0.001 percent o.f
the time. The value o.f ac2 has been determined and is plotted in
Figure 12-7. This figure shows that as the number of active channels,
N a , increases, the peak factor asymptotically appro.aches 13 dB.

Vol. 1

Signal Characterization

316
20
~

0

18

I11III

III

Q.a;-

]~

c: ..
..c: u

16

~

~

0.2

.~~

14

r--- .....

"3
~

12
10

1

5

10

50

100

500

1000

Number of active channels, Nu

Figure 12-7. Peak factor, ~c2, exceeded 0.001 % of time for speech channels.

This value corresponds closely to that for random noise.
If Equation (12-5) is substituted in Equation (12-6),
P s == V Oc

-

1.4

+ 0.1150"2 + 10 log + 10 log N
TL

+ ~cl + ~c2 3 dBmO
or, with ~c == ~c1 + ~c2 3,
Ps == V
1.4 + 0.1150"2 + 10 log + 10 log N
-

(12-7a)

-

TL

Oc -

(12-7b)

dBmO.

The term ~c is known as the multichannel load factor. It is plotted
in Figure 12-8 as a function of N and several values of (J" for an
assumed value of TL == 0.25. For other values of 0" or TL, ~c can be
found from the empirically derived formula
~c == 10.5

+

400"

NTL

+ 5 yl20"

dB.

(12-8)

Single-frequency signals are used in the analysis of system load
capacity, but they are seldom used in load testing. A band of Gaussian
noise is frequently used in system testing to simulate a multichannel
signal.
Effect of Shaped TLP Characteristics
The discussion of the multichannel speech signal load and its relation to overload phenomena has been carried out in terms of 0 TLP
characterizations of speech signals. Implied in the discussion is the

Speech Signals

Chap. 12

23
22
21
20
iii'

:s

~ ... u= 6dB

',-"

I\..

16

g

:;
~

~

", "

0

0

u=5dB

\.

~
.2 17
~

~
o+:

\..

" ",,-" ,
"- ""

18

Qi

""-

~~

19

~

of!

317

u= 4dB'

~

15

,~

'~ "-.-, ~"
~~

14

'"

"'- .....'"

13
12
11

10

20

so

100

',~

"

~

t-- """'-

........ r---1Iooo,.."

"'::::-- r--

-~

500

200

Number of channels in system,

~~ ~ ...

1000

2000

N

Figure 12-8. The multichannel load factor, Ll c , for

'TL

= 0.25.

assumption that the transmission from 0 TLP to the point of
interest where overload may occur (for example, at the output of a
line repeater) is flat with frequency and thus the same for all channels
in the broadband system. This is not necessarily so. Noise advantage
in the system can frequently be obtained by shaping the transmission
between the two points. In this case, the TLP at the point of interest
is not flat with frequency; as a result, the volume distribution at the
point of interest is modified according to the line frequencies of the
individual channels and the transmission characteristic between the
two points.
The average power of such a shaped signal load may be determined [9] at the point of interest by
iT

P'av = P av

10C(f)/lOdl
IB

+ 10 log J IT _
iB

dBm.

(12-9)

318

Signal Characterization

Vol. 1

Here, IT and IB are the top and bottom frequencies, respectively, of
the signal spectrum at the point of interest, and C (I) is the gain
shape in dB between 0 TLP and the point of interest.
With shaping between 0 TLP and the overload point, the peak
factor, and hence ~c, are more complex. The effects of signal shaping
on overload have been studied, using a computer, for normally distributed talker volumes having various gain characteristics over the
multiplexed band. It has thus been found empirically that, for the
same overload condition (0.001 percent), the value that should be
used for ~c is very well approximated if the system is assumed to
have 'Y} channels instead of N channels. The value for 'Y} is taken as
that number of channels whose TLPs are within 6 dB of the channel
having the highest TLP at the point where overload occurs.
12-4

PROGRAM SIGNALS

Program transmission is a nationwide service provided by the
Bell System to transmit the audio programs of radio and television
broadcasters between points of program origination and one or
more transmitting stations. In addition, "wired music" material is
also transmitted for distribution to customers subscribing to such
services. Other program services include conference calls and calls
connected to public address systems for a large audience. While such
signals are audio signals, regular telephone circuits cannot be used
for program transmission because of the more stringent objectives
generally applicable to program service. The more stringent objectives arise from the necessity of transmitting music and from the
need for higher fidelity speech when the receiver is not a telephone
set receiver.
At the present time, the majority of program circuits used in toll
transmission systems employs a band of frequencies from about 50
to 5000 Hz. For special broadcasts in which the program is speech
alone, such as newscasts, the broadcaster may use specially conditioned message circuits that transmit a band of frequencies from
200 to 3500 Hz. Other program services, less frequently used, cover
frequency ranges of 50 to 8000 Hz and 35 to 15,000 Hz. The latter
two are used primarily to transmit high quality music for FM and
FM-stereo broadcasts in local areas and to satisfy the needs of
educational television services.

Chap. 12

Speech Signals

319

The bandwidth is specified differently for program facilities than
for telephone speech. The bandwidth of program circuits is defined
as that between the frequencies at which the response is 1 dB below
the I-kHz response, as contrasted with lO-dB response points for
message circuits. Program circuit filters must roll off more gently
than message circuit filters because program signals are more susceptible to delay distortion impairments than are ordinary message
signals. Program channel equipment is often provided with a modest
amount of delay distortion equalization.
The energy distribution in program signals is difficult to specify
because of the wide range of program material transmitted - speech,
drama with sound effects, music of different varieties, etc. No
generally accepted program spectrum has been established.
The average volume and the dynamic range of program signals
are somewhat higher than for telephone speech. There are relatively
few program channels, however, and contributions to system load
effects are generally small enough to be ignored. A possible exception
is the coverage often given to special events such as a presidential
speech or a political convention. All program facilities leaving one
location may be carrying the identical program. Careful study is
necessary to guard against overload of systems in these circumstances.
REFERENCES

1. Dudley, H. "The Carrier Nature of Speech," Bell System Tech. J., Vol. 19
(Oct. 1940), pp. 495-515.

2. French, N. R. and J. C. Steinberg. "Factors Governing the Intelligibility of
Speech Sounds," The Journal of the Acoustical Society of America (Jan.
1947) .

3. Potter, R. K. and J. C. Steinberg. "Towards the Specification of Speech," The
Journal of the Acoustical Society of America (Nov. 1950).
4. Sullivan, J. L. "A Laboratory System for Measuring Loudness Loss of Telephone Connections," Bell System Tech. J., Vol. 50 (Oct. 1971), pp. 2663-2739.

5. McAdoo, Kathryn L. "Speech Volumes on Bell System Message Circuits1960 Survey," Bell System Tech. J., Vol. 42 (Sept. 1963), pp. 1999-2012.
6. Sen, T. K. "Subjective Effects of Noise and Loss in Telephone Transmission,"
Conference Record, IEEE, International Conference on Communications, 1971.

7. Brady, P. T. "Equivalent Peak Level: A Threshold-Independent Speech Level
Measure," The Journal of the Acoustical Society of America, Vol. 44 (Sept.
1968), pp. 695-699.

320

Signal Characterization

Vol. 1

8. Bennett, W. R. "Cross-Modulation Requirements on Multichannel Amplifiers
Below Overload," Bell System Tech. J., Vol. 19 (Oct. 1940), pp. 587-610.
9. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston'-Salem, N. C.: Western Electric
Company, Inc., 1970), Chapter 9.
10. Holbrook, B. D. and J. T. Dixon. "Load Rating Theory for Multichannel
Amplifiers," Bell System Tech. J., Vol. 18 (Oct. 1939), pp. 624-644.

Signal Characterization

Chapter 13

Signalling
Signalling involves the generation, transmission, reception, and
application of a class of signals needed for directing and controlling
automatic switching machines and conveying to telephone system
users information needed for using the network. Such signals may
be functionally categorized as follows:
(1) Address signals

(2) Supervisory signals *
(3) Alerting signals

(4) Information signals
(5) Test signals.

Address signals are used to set up connections (Le., to route calls)
by controlling the operation of automatic switching machines. Such
signals may be generated at station sets, switchboards, or switching
machines. Many types of address signals are used on both loops
and trunks.
Supervisory signals are used to convey, to a switching machine or
to an operator, information regarding the status of a loop or trunk.
The four service conditions that supervisory signals convey are as
follows:
(1) Idle circuit, which is indicated by the combination of an on-

hook signal and the absence of any connection in the central
office between the loop and another loop or trunk.

*Although address and supervisory signals are both used to control switching
machines, they are considered separately in this chapter.
321

322

Signal Characterization

Vol. 1

(2) Busy circuit, which is indicated by an off-hook signal and a
connection to a trunk or another loop.

(3) Seizure, or call for service, which is indicated by an off-hook
signal and the absence of any connection to another loop or
trunk.
(4) Disconnect, which is indicated by an on-hook signal and a
connection to a trunk or another loop.
The terms on-hook and off-hook are derived from supervisory conditions that exist on a loop. If the station set is on-hook, it is idle;
if it is off-hook, it is busy. The terms are so descriptive that they
are commonly applied to trunks as well as to loops. Supervisory
signals must be extended over a connection to the point at which
billing information can be used by a message accounting machine or
by an operator. Details of how such signals are used are beyond the
scope of this chapter.
Alerting signals are those whose primary function is to alert an
operator or a customer to some need. Included in this group are such
signals as flashing, ringing, rering, recall, and receiver-off-hook
signals.
Information signals include machine announcements, audible ring,
busy tone, and dial tone. While many of these signals are normally
transmitted at low enough amplitudes or are used infrequently enough
that they have little impact on transmission, the reverse is not true.
For example, machine announcement arrangements, such as the
Automatic Intercept System, have been carefully engineered so that
the customer hears the announcement at about the same amplitude
as he would hear an operator. This avoids contrast and ensures a
good overall grade of service. Also, in order to be compatible with
acceptable transmission standards, the design of tone generators for
dial tone, audible ringing, busy tone, etc., is controlled by a precise
tone plan which specifies the frequencies and amplitudes of all such
tones.
Test signals are of many types. They are not covered in detail
in this chapter, but discussions of several types of test signals are
found elsewhere in the text.

Chap. 13

Signalling

323

The characterization of signals covered in this chapter is important from a transmission point of view for a number of reasons.
There is a great variety of such signals and some are used frequently,
in large numbers, and for long periods of time. It is important to
know their characteristics if they are likely to affect the transmission
performance of other signals sharing the same facility or transmission medium. Furthermore, such signals sometimes have transmission requirements that are more stringent than other "pay-load"
types of signals and, as a result, may be a controlling factor in
establishing overall design limits for transmission facilities. In
addition, the signalling circuits interconnect with transmission cir. cuits and may contribute to transmission loss and distortion. Finally,
on loops, the signalling circuits affect the amount of current that is
delivered to the station set transmitter.
The incompatibilities between signalling and transmission circuits
could cause distortion of the address signals. Pulse splitting, a serious
form of mutilation that can make a single pulse look like two, is an
example. It can occur in four-wire terminating sets as a result of
spurious low-frequency oscillation caused by parallel resonance between a transmission capacitor and the inductance of a signalling
relay. This type of problem must be avoided in the design of
signalling-transmission interface circuits. Typically, a nonlinear device, e.g., a diode, may be connected in series with the oscillatory
elements to break up the low-frequency oscillations.
13-1

SIGNALLING ON LOOPS

Three aspects of signalling on loops are important from a transmission standpoint. These are supervision, addressing, and customer
alerting. All of these aspects of signalling on loops are related to
what is known as common battery operation.
Common Battery Operation

Most of the equipment associated with an individual telephone
central office is operated from a single large centralized battery. *
Current supplied from such a battery to the loops connected to the
*Some local battery operation and manual switchboards may still be found in
rural areas. This type of operation and the signalling arrangements required are
rapidly becoming obsolete and are not covered here.

Vol. 1

Signal Characterization

324

central office is modulated by speech in the transmitter to form the
speech signal. The same battery current is used to implement
signalling functions that must be provided from the station set
toward the central office equipment.
One type of connection of loops to the common battery supply is
illustrated in Figure 13-1. Three loops and station sets are shown

,---------------,
I
'>
I
I

I
I
loop

STA

IT

Common
battery

-

I

II +

Bus
bars

I

I
I

~

:---1

I

I

I
I
I
I
I

I

---0

Trunk to
distant

CO

I
I
L ___ .J
Switches

I
Loop
STA
set

I

IT

r----,
I

I

I

STA
set

I
I

\

I

I
I
I ~ ___ J
I
L ______________ ~
Central office equipment

Figure 13-1. Common battery connections - repeat coil circuits.

Loop

325

Signalling

Chap. 13

with the tip loop conductors, T, connected to the grounded positiveside bus bar of the battery. The ring conductors, R, are connected
to the ungrounded negative side of the battery. The repeat coils (or
transformers) and capacitors in each of the battery feed circuits to
which the loops are connected couple the transmission from the
loops into the switches to complete connections to trunks or to
other loops. Another circuit configuration commonly used as a battery
feed circuit is known as a bridged-impedance-type circuit. This circuit, shown in Figure 13-2, couples the loop to the switches by
capacitors rather than repeat coils. Both types of battery feed circuits
are designed to minimize the transmission of speech or noise signals
from the loops into the common battery. These are oversimplified
schematics that do not show details of the signalling functions.

Supervision on Loops and PBX-CO Trunks

During various stages of a call (call for service, dial tone, dialing,
connecting, ringing, talking, etc.), battery and ground are supplied
to the loop or Private Branch Exchange (PBX)-central office (CO)

Switches

r----,
I
I
I

T

I
I

I

Station
set

I

I
I
I

I..

P

I
I

-4BV

I

I
I

II

I

I

L

I

':'"

-4BV
line
circuit

I

I
-I

To other
switches
and
trunk

I

L
I

I L ___ ...J I

I
1

I
I

I
I

R

I

I

I

I

I
I

I
I

I

1

I..

EfI
1

Trunk
circuit

-I

Figure 13-2. Transfer of loop supervision - bridged impedance battery feed.

326

Signal Characterization

Vol. 1

trunk* by a circuit somewhat like those illustrated in Figure 13-l.
The battery supply may be a different circuit, however, for each
stage of the call and may be different for either an incoming call or
an outgoing call. Furthermore, while idle loops always have negative
battery on the ring conductor, the battery-ground connections to a
calling party may be reversed during the progress of setting up a
call. In the talking condition, either calling or called party loops may
have the polarity reversed, particularly when served by a step-by-step
switching machine. Each battery supply circuit must include a relay
or other device which can. respond to changes in the signalling or
supervisory condition on the loop and, in responding, extend the
information regarding the changed conditions to other circuits.
Figure 13-2 illustrates the process for an outgoing call. When the
station set is on-hook, battery and ground are connected to the loop
conductors through the windings of the L relay in the loop circuit
and the closed cutoff relay contacts. Operation of the L relay, caused
by the flow of current through its windings when the station set
changes to an off-hook condition (call for service), results in switching system operations which disconnect the L relay from the loop
(by operating the cutoff relay) and which connect the loop to a
trunk circuit. Thus, during the first part of the call sequence, supervision of the loop is provided by the flow of current through the
L relay; during the second part of this sequence, supervision is
provided by the S relay in the trunk circuit through whose windings
current is supplied to the loop.
It should be stressed that the circuits of Figures 13-1 and 13-2
and the sequence of operation just described are illustrative only.
Although many variations exist in different types of switching
systems, the basic function of loop supervision is performed in all
systems by circuits very similar to those described.
The process just described is known as the loop-start process.
Another process used to initiate a call is known as ground-start. In
some cases, for example on certain dial-selected PBX trunks, the
calling sequence is started by applying a ground to the ring side of
the line. In such cases, the line relay is wired to accept only this
call-for-service signal and responds accordingly. It is used in this
application in order to minimize the probability of simultaneous
*In many respects PBX-CO trunks are functionally similar to loops.

Chap. 13

Signalling

327

seizure of a trunk from both ends for an incoming and an outgoing
call. The simultaneous seizure of a trunk from both ends, a condition
called glare, would be a serious problem on dial-selected PBX trunks
because there can be an interval of 4 seconds after an incoming call
is connected to the trunk before it is rung. Additional time may pass
until the incoming call is answered and the trunk is made busy at
the PBX. With ground-start operation, the trunk, while in the idle
state, has no ground on the tip conductor. Upon seizure by the central
office equipment, ground is applied to the tip conductor, a condition
used immediately to make the trunk busy at the PBX; removal of
the tip ground is recognized by the PBX as a disconnect signal. When
a call is originated at the PBX, ground is placed on the ring conductor. When a central office connection is established, the normal
battery and ground connections to ring and tip are made. Either state
(ground on ring or loop closure) is recognized immediately by the
central office equipment as a trunk seizure. The. central office equipment later recognizes the opening of the loop as the disconnect signal.
The parameters that enter into the calculation of loop supervision
relationships include the resistance of the station set, the resistance
of the loop conductors, the resistance of the central office equipment
and wiring, the resistance of the battery supply circuit (nominally
400 ohms in most central offices), the sensitivity of the relay or
other device that must respond to changes in loop status, and the
battery voltage itself. These parameters all vary within their respective ranges. The station set resistance has manufacturing variations and, in addition, is designed to be a function of the loop current.
The resistance of the loop conductors is dependent on the distance
of the station set from the central office and the gauge of wire employed. The resistance of the central office wiring is also dependent
on length and wire gauge. In addition, the resistance of the paths
through the CO equipment is different according to the circuit type
and type of switching machine and must be accounted for along with
manufacturing tolerances. Allowance must also be made for loop
conductor leakage currents.
The battery voltage has, in most central offices, a nominal value
of -48 volts; it varies approximately ±4 volts about the nominal.
Provision is sometimes made to increase the supply voltage to 72 volts
for groups of long loops designed for operation on a single relatively
small gauge of cable (Unigauge design) or when dial long line equipment is used to extend loop length.

328

Signal Characterization

Vol. 1

The large number of variables involved in supervisory signal computations makes it necessary to apply a set of rules that can be used
universally to determine if signalling or some other function limits
loop performance. One such rule for laying out loop plant is that
the conductor loop resistance must be equal to or less than the
signalling limit or 1300 ohms, whichever is lower (in most cases,
loop resistance may exceed 1300 ohms for signalling). The 1300-ohm
limit has been established to assure adequate transmission. Other
rules apply to loading, allowable number of bridged taps, etc.
Signalling limits must be determined for each case.

Address Signalling on Loops

Two modes of generating address signals are used at common
battery telephone station sets operating in a machine switching
environment. These are dial pulsing and TOUCH-TONE signalling.
They are described in some detail because different transmission
problems are related to each.
Dial Pulsing. Address signalling occurs when a rotary dial is moved
to its off-normal position and then released. The signals consist of
pulses which result from interruption of the loop current by the
pulsing contacts of the dial. The number of pulses corresponds to the
digit dialed. The central office equipment responds to the dialed digits
to establish the desired connection.

Timing relationships are important in this process in a number
of ways. Note first that the dial pulse signals differ from supervisory
signals on a loop only in respect to timing. On-hook and off-hook
supervisory signals are of long duration while dial pulsing signals
are measured in small fractions of a second. The process of transferring address information from the station set dial to the central
office equipment is dependent on these timing relationships and on
the des'igns of the dials, the central office equipment, and the loops.
Some basic time relationships are shown in Figure 13-3, where the
digits 2 and 3 are assumed to have been dialed sequentially. The
first of these time relationships is illustrated by the first pulse in
Figure 13-3. The complete pulse cycle is made up of a break interval
during which the pulse contacts of the dial are open, and a make

329

Signalling

Chap. 13

interval during which the pulse contacts are closed. The two intervals
are related by the expression
B

01.
/0

rea

k

Break interval X 100
B rea k
rnake 'Int ervaI s

==

+

The percent break used in Bell System dials is 58 to 64 percent.
The second time relationship of importance is the pulse repetition
rate or number of pulse cycles per second that can be successfully
transmitted. Most dials used on station sets are designed to operate
at 10 pulses per second (pps). While many parameters influence the
maximum, the pulse rate of these dials is primarily set by the operating speed capabilities of step-by-step switching equipment. The
dials used at PBX or manual central office switchboard positions are
often of a 20-pps design. The higher pulse rate is used to achieve
higher operating efficiency. The higher speed dials can only be used
where tie trunks or foreign exchange trunks on the PBX do not
involve DX or SF signalling arrangements. These signalling systems,
described later, are not capable of operating at the higher speeds. In
addition, the switching system involved must be capable of responding
to the higher pulse rate; step-by-step systems are generally not
capable of such operation. The use of the higher speed dials is
facilitated by the lack of bridged ringers on PBX trunks and the
short trunk length usually associated with PBX operation.
The two timing relationships given so far, percent break and pulse
repetition rate, are governed largely by the operate and release char-

i

g~
--'

~

I

1f

O~~

Break

Digit

__

21+- Inte~~;ital i+---

~~

__

I

~

________

~

__

Digit 3

1

~~~~

__

~

Time - - - .

Mo',

CYCler
Figure 13-3. Dial pulsing of digits 2 and 3.

Open
____

loop

330

Signal Characterization

Vol. 1

acteristics of central office equipment as they are affected by the loop
characteristics. The pulse waveforms of Figure 13-3 are highly
idealized. As illustrated in Figure 13-4, impedance characteristics
of the loop, station set, and ringer circuits cause distortions of the
pulses that must be taken into account when station set signalling
problems are being considered. The dashed-line pulses in Figure 13-4
are again highly idealized; the solid-line pulses show how one form
of distortion (caused by ringer and cable capacitance charge and
discharge) causes changes in the percent break of the repeated pulses.
Margins for such distortion must be provided in the design of central
office control circuits.

OPER

t f,-j L

t::::±::t:2.i:::==t:i;;;;;;;;;;iti::::========±::l;;;;;J.i=====

o'"ok

break

Nominal
interdigital
time

j

Figure 13-4. Effect of pulse distortion on dial pulse time relationships.

The third timing relationship in dial pulsing is shown in
Figures 13-3 and 13-4 as the interdigital time. This is the time that
the loop is closed after a digit has been dialed until the first pulse
of the next digit. It includes the time required by the customer or
operator to search for the next digit, to pull the dial around to its
stop, and to release it to start pulsing the next digit. The central
office equipment must contain timing circuits to recognize this interval
with allowances (or margins) for pulse distortion caused by the loop
and other equipment.
TOUCH-TON E Signalling. A second form of address signalling used
on station sets is implemented by a set of pushbuttons rather than
by a rotary dial. This form of signalling, called TOUCH-TONE, is
usually superior to conventional dial pulsing because it is more
accurate, more convenient, and faster. (It is also somewhat more
costly.) Operation of any pushbutton results in the generation of
two single-frequency tones which are transmitted as long as the

Chap. 13

331

Signalling

button is depressed. Oscillators, activated by pushbutton operation,
are powered by the line current furnished from the central office.
While a button is depressed, the telephone transmitter circuit is
opened, and a resistor is inserted in series with the receiver so that
the tones are heard in the receiver at a comfortable sound amplitude.
The layout of the standard 12-button TOUCH-TONE matrix pad
and the frequencies generated by each button are depicted in
Figure 13-5. If the number 7 pushbutton is operated, for example,

1477 Hz

1633 Hz (spare)

1209 Hz

1336 Hz

cb

IA~I ~697!'

IG:I! IJ~L! ~770HZ
Ip;s! IT~vl Iw:vr-

852 Hz

G

F~Ej

@-941HZ

Figure 13-5. Pushbutton layout on TOUCH-TONE station set pad showing signalling
frequencies.

the 1209-Hz and 852-Hz frequencies are generated. Central office
equipment, different from that used to receive dial pulse signals,
recognizes these tones as representing the numeral 7. This equipment,
called TOUCH-TONE converters, translates the oscillator signals to
digital signals similar to dial pulse signals for machine switching
recognition and operation. The pushbuttons marked * and # are
used for certain special signalling. Some 10-button sets, lacking the
* and # pushbuttons, are still in service. A 16-button set (4-by-4
matrix) is also available for use in private line network service
provided to the U.S. government.
The signals in the low-frequency group, 697 to 941 Hz, are transmitted nominally at -6 dBm; those in the high-frequency group are
transmitted nominally at -4 dBm. The actual amplitudes are de-

332

Signal Characterization

Vol. 1

pendent on the amount of loop current. These high signal amplitudes,
and the fact that this type of signalling is not as susceptible to distortion caused by the medium as are dial pulse signals, make the design
of pulse receiving equipment at the central office quite straightforward. Although these amplitudes are higher than those of many other
signals transmitted in the voiceband, they are considered acceptable
because they have a low duty cycle; i.e., they are transmitted only
occasionally and they are of short duration. Nevertheless, these amplitudes are being reviewed for a possible downward adjustment which
may result in somewhat more stringent sensitivity requirements for
the pulse receivers. Since TOUCH-TONE signals fall in the voiceband,
they may be transmitted through the switched message network.
Thus, they may be used as a form of data communication.
Alerting Signals on Loops

There are two types of alerting signals transmitted towards the
station set that are considered here, namely, ringing signals and the
receiver-off-hook signal used to alert a customer that his receiver has
been left off-hook.
Ringing. Conceptually, the alerting signal used to ring the station
set bell is simple. * However, details of signal generation, coding for
party-line operation, variables that may affect the ringing process,
and instrumentalities used to achieve ringing objectives make a
conceptually simple process rather complex in practice.

The ringing signal is used mainly on loops, although some 20-Hz
signalling is used on ring-down (manual) trunks, and as a ring-back
and ring-forward signal on other types of trunks. On loops, it is
usually applied at the central office** as a composite ac and dc signal.
The forward-ringing ac component has a frequency of 20 Hz. In
some types of switching machines, an ac component of about 420 Hz
is superimposed; this component is fed back to the calling party to
serve as an audible ring, giving assurance that the called number
is being rung. The dc component of the ringing signal may be of
either polarity with respect to ground.
*In addition to the complexities discussed here, the alerting of a customer to
an incoming call is sometimes accomplished by in-band, coded tone signals. Such
signals are used primarily in special service arrangements.
**One exception, for example, is in the Subscriber Loop Multiplex System in
which the ringing signal is applied to the loop at a terminal remote from the
central office.

Chap. 13

Signalling

333

It would, of course, be possible to ring the station bell continuously
until the station set is answered. Early tests, however, indicated that
continuous ringing would be undesirable and irritating. The standard
central9ffice ringing cycle has been set as a 2-second ringing interval followed by a 4-second silent interval. This cycle is sometimes
modified to provide coded ringing to alert the desired one of several
party-line stations on a single line. The standard ringing cycle used
at PBXs is a I-second ringing interval followed by a 3-second silent
interval.
I t is des.irable to set the magnitude of ringing signals as high as
possible in order to maximize the length of loop over which station
sets operate satisfactorily. However, since the telephone plant is
designed generally to operate at low currents and voltages, the maximum ringing-signal voltages are limited to values that do not operate
protective devices, cause dielectric failure or overheating of equipment, or present a hazard to operating personnel.
The station set ringer may be connected to the loop in a number
of ways, depending on the type of service. On individual lines, the
ringer is normally connected across the line in series with a capacitor,
as illustrated in Figure 13-6 (a). With the types of high-impedance
ringers presently used, a total of five ringers can be connected in
parallel as illustrated by Figure 13-6 (a). The number is limited by
ringing and dial pulsing requirements. Ringing ranges vary with the
number of ringers used and with the characteristics of the switching
system involved; they are less than dialing and supervisory ranges
when the number of ringers is a maximum.
For party-line service, other types of ringer connections are required. One is illustrated in Figure 13-6 (b). The types of service
include 2-party, 4-party, and 8-party service in many suburban and
rural areas. In more remote rural areas, 10- and 20-party service is
sometimes provided. Full selective ringing (only the called party hears
the ring) can be provided on 2-party and 4-party lines. Semiselective
ringing (where only a limited number of parties hear each ring) is
provided on some 4-party lines and all 8-party lines. Nonselective
or semiselective code ringing is provided on the rural lines with large
numbers of parties.
As shown in Figure 13-6 (b), party-line ringing often involves
ringer connections between one side of the line and ground. Due to

Signal Characterization

334

,---l r----l
T

I

I

I I

I

Extension
station

I

I I

I

I
I

I

I
I

I

L ___ --.J

I

I
L _ _ _ .J

(a) Bridged ringing on
an individual line

Vol. 1

I-------:l

CE fill
,---E
I
L __

Hp

~ation

___

I

~

c :reo

--~

I

L

_

';09
~ation

_

_

I

~

(b) Two-party full selective
grounded ringing

Figure 13-6. Two common types of station set ringer connections.

unbalanced conditions that might exist on such lines, caused by different numbers of ringers on each side or very different loop lengths
to each, such lines may be quite noisy and may cause crosstalk due
to interference currents. In these cases it may be necessary to use
gas tubes or solid-state ringer isolator circuits which balance the
lines so that induced currents are not converted to excessively large
interferences. Care must be used in the application of such circuits
so that additional noise impairments caused by gas-tube breakdown
are not introduced.
Receiver-Off-Hook Signal. When a station set is left in the off-hook
condition, a tone may be applied to the loop to attract the attention
of someone at the station to this condition. The tone used was at
one time known as a howler. The howler, a very high-amplitude signal
in the voiceband, proved to be unsatisfactory for use with the 500-type
station set because of the clipping action of the equalizer in the set.
Furthermore, when the howler signal was transmitted over telephone
lines using carrier facilities, there was danger of seriously overloading
some transmission paths.

The howler signal has been almost universally replaced by a signal
called the receiver-off-hook (ROH) tone. The signal is made up of a
combination of 1400, 2060, 2450, and 2600 -Hz. When applied automatically, the ROH signal appears on the loop for' about 50 seconds.
It is interrupted at a rate of five times per second. It can also be
applied manually from the local test desk as a continuous or
interrupted signal.

Chap. 13
13-2

Signalling

335

SIGNALLING ON TRUNKS

While there are significant differences in detail, most of the same
general functions of signalling must be accomplished on interoffice
trunks as on loops. These functions include addressing, supervision,
alerting, transfer of information, and testing. As may be expected,
many of the characteristics of signals used on trunks are similar or
identical to those used on loops.
Signals that relate directly to station operation, such as ringing
and ROH signals, are not generally used on interoffice trunks. * On
the other hand, the types of switching systems that must be controlled and the functional characteristics of the trunks themselves
are so diverse that the variety of signals used on trunks is considerably greater than on loops. Two general types of signals are
described; they are classified as dc or ac signals. Under each type
there are many variations.
The address information required to route a call must be forwarded
from the originating central office through various toll offices to the
terminating central office. In general, dc signals are used within the
switching machines. Such signals are often unsuitable for transmission over trunks, and it is necessary to transform the signals at one
end of a trunk to a form more suitable for transmission and then
back to the original form at the other end of the trunk. If the trunk
length exceeds the range limits of the dc systems or if the trunk cannot pass dc, ac or'derived dc techniques must be used. These conversions require equipment which is described elsewhere.
One form of signalling interface is used frequently for both dc and
ac signalling. The name, E and M lead signalling, is derived from
lead designations historically used on applicable circuit drawings.
The E and M lead interface between a signalling path on a transmission facility and a switching system trunk circuit is shown in
Figure 13-7. The circuit conditions on the E and M leads are standard
in all systems employing this method of connection. (Some later systems utilize paired leads rather than single-wire leads to reduce interferences; these applications involve some departures from the simple
E and M lead circuit conditions.) The manner in which signals are
*Ring-forward and ring-back signals are transmitted over operators' trunks to
the local office where they are then applied in appropriate form to the loop.

336

Vol. 1

Signal Characterization
LOCAL CENTRAL OFFICE

r----,

Transmission
2-wire or 4-wire

I

I

I

To
distant
central
office

Interoffice
transmission
facilities

I
Interface
equipment

To
switches
and
switch
control

I
I

--. I

I

I
Signalling

Signalling

,--I

Trunk
circuit

L ___

I

L_

-

_J

E

......-

TRUNK AND LEAD STATUS
NEAR END
On hook
Off hook

MLEAD
Ground
Battery

FAR END
On hook
Off hook

E LEAD
Open
Ground

M
~

Figure 13-7. E and M leads.

converted to dc or ac types for transmission over the trunk, the
characteristics of the transmitted signals, and the method of combining the signalling path with the transmission path vary widely.
Systems that employ E and M leads have the advantage that signals
can be transmitted independently in both directions on a trunk.
DC Loop Signalling on Trunks

Since the transfer of address and supervisory signalling information is most economically accomplished by dc signalling, such methods
are used whenever technically feasible. There are two forms of dc
signalling. The first is called loop signalling, a name which is derived
from the fact that a dc circuit, or loop, is available between the two
ends of a trunk. (It is not related to the loop that connects a station
set to the central office.) The second form of dc signalling, called
derived dc signalling, is discussed subsequently. One or the other
of these dc signalling arrangements is used extensively for all interlocal, toll connecting, or toll trunks that operate at voice frequency
and that are short enough to permit their application.
The dc loop signalling systems operate generally by altering the
direct current flow in the trunk conductors. At one end of a trunk,
the current may be changed between high and low values, it may be

Chap. 13

Signalling

337

interrupted, or its polarity (direction of flow) may
These changes are detected by suitable relays or other
paratus at the other end of the trunk. The signalling
known as reverse-battery, battery and ground, high-low,

be reversed.
types of apsystems are
and wet-dry.

Signals cannot be transmitted in both directions independently in
dc loop systems. Thus, such systems are used on one-way trunks,
primarily on' local and on toll connecting trunks.
Reverse Battery Signalling. Because of its economy and reliability,
this is the most widely used dc loop signalling method on local
trunks. Battery and ground for signalling purposes are furnished
through the windings of the A relay at the terminating end of the
trunk as shown on Figure 13-8. Supervision is provided at the
originating end of the trunk, usually by opening (on-hook) or closing
(off-hook) contacts in the trunk transmission path under the control
of the originating station set through relay S1. At the terminating
end of the trunk, supervision is provided by the station set and
relay S2. Normal battery and ground are connected to the trunk conductors for the on-hook signal and are reversed by operating the
T relay to represent the off-hook condition. Address signals may be
under the control of the calling station set or under the control of
dial pulsing equipment in the originating central office.

To

To

loop

loop

I
L __

Terminating

-=n~u~

Figure l3-8. Reverse battery signalling.

338

Signal Characterization

Vol. 1

Battery and Ground Signalling. This mode of signalling is used to
extend the range of loop signalling. It is accomplished by connecting
battery and ground at both ends of the loop in a series aiding configuration. This type of connection, illustrated in Figure 13-9, is
usually provided only during the period that addressing information
is being transmitted.

The current available for signalling is nearly doubled as compared
with the ordinary dc loop connection with battery and ground at one
end only. For supervision, the battery and ground at the originating
office is usually removed, and a dry polar bridge is substituted to
function with the reverse-battery supervision signal from the terminating end. However, reverse-battery supervision can also be provided
in the battery and ground arrangement of Figure 13-9; the battery
and ground must be reversed at both ends of the trunk.
Miscellaneous DC Loop Arrangements. A number of other dc loop
signalling arrangements are used to provide address or supervisory
signalling information on voice-frequency trunks. Most are being
replaced by the reverse-battery or battery and ground systems previously discussed or have so little impact on transmission problems
that detailed discussion here is not justified. These include wet-dry
signalling and high-low signalling. Both of these signalling methods
utilize dial pulsing or ac signalling for the transmission of address
information and may thus be considered primarily as supervisory
systems. Wet-dry signalling provides dc loop supervision in the form
of presence or absence of battery and ground. The trunk is wet
(battery and ground connected) for one set of supervisory states

r-?

I

Originating office

III

I

w.

0

I

r-LLI __

Pulsing
relay

I

!_n___ ~
I

Trunk

n_

Terminating office

~III

-~-~j
I
I

Receiving
relay

Figure 13-9. Battery and ground pulsing.

Chap. 13

Signalling

339

and dry (battery and ground disconnected) for the opposite. High-low
signalling refers to the impedance bridged across the trunk, high
impedance being used for one set of supervisory conditions, low impedance for the other. This method is still used occasionally to provide supervision at the originating ends of reverse-battery signalling
systems.
Panel Call Indicator (PCI) System

This system utilizes a 4-bit code to transmit address information.
Originally, the system was designed to transmit address information
from a panel-type switching machine to an operator position at a
manual B-type switchboard. The use has been extended to signalling
between panel-type switching machines and manual switchboards,
between crossbar switching machines and manual switchboards, between panel or crossbar switching machines and other panel or
crossbar machines, and in specialized applications within panel or
crossbar machines.
At the receiving end of a PCI system, the called number may be
displayed on a lamp field before an operator, or the transmitted
address may directly drive switching system registers. In either
case, supervisory information must be transmitted by another means.
The 4-bit code in PCI signalling is designed so that the first and
third hits of each digit code are defined by open-circuit or light positive pulses, and the second and fourth bits by light or heavy negative
pulses. The negative pulses in the second and fourth time slots are
used to synchronize the receiving with the sending end of the trunk
and to advance a register to successive digits. Four decimal digits,
sent consecutively with no pause in between, require a total transmission time of about 1 second. A heavy positive pulse is transmitted
to indicate end of pulsing. Thus, the complete system consists of a
five-state signalling system. Figure 13-10 gives the various permissible signal conditions; Figure 13-11 gives the complete PCI code;
Figure 13-12 shows a portion of a typical transmitted signal.
Revertive Pulsing

As in the case of PCI, revertive pulsing was developed to satisfy
the signalling needs of panel-type switching systems. It was later
adopted for use with certain crossbar systems because it is capable

340

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Signal Characterization
LOOP CONDITION

SYMBOLS

-

Open, zero current
Light positive current
Light negative current
Heavy negative current
Heavy positive current

p
n
N
P

(Polarities are ring relative to tip.)
BASIC PSI CODE CYCLE

B,
n
N

A

Time slot (interval)
Normal
Permissible

p

D
n
N

C

p

Figure 13-10. PCI signal conditions.

HUNDREDS TENS AND UNITS
DIGIT

0
1
2

3
4
5
6
7
8
9

A

B

C

D

-

p

n
n
N
N
n
n
n
N
N

-

p
-

n

n
n
n
n
n
N
N
N
N
N

p
p

--

p

-

p

THOUSANDS
A

B

-

n

p
p

n
n
n

-

-

p
p

-

-

N
N
N
N
n
n

C

-

D

n

N
n

N

-

n

p
p

n

N
n

N
N

Figure 13-11. PCI codes.

of operating somewhat faster (up to 22 pps in crossbar and 32 pps
in panel) than more conventional dial pulse systems and because the
crossbar systems, designed to replace the panel, had to interconnect
with existing panel systems. This mode of signalling is no longer
recommended for new installations, although many revertive pulsing
systems are still in operation.'
The mode of operation is quite different from other systems; address signals with different functions are transmitted in both directions, as shown in Figure 13-13. The terminating office, which may

Signalling

Chap. 13

14-- Digit 7 -+t

Io+-Digit 3-.!
I
I

p

p

~

"

I'

--'!

==-!

341

I

/

I

-----------

! ,1
r,'

!I

N ---I

I I I I I
IAIBICID'
I I I I I

JE---n r----------JI'

I

i

End of
pulsing

U

u=

I
I
I
I
IAIBICIDI
I
I
I
I
I

Figure 13-12. Typical PCI pulse signals - digits 3 and 7 in hundreds, tens, or units
position.

be of the panel, crossbar, or ESS type, receives a start signal from
the originating office. Equipment at the terminating office generates
pulses in accordance with its operation. These pulses are sent back
to the originating office, and when the number of pulses received at
the originating office corresponds to the digit being transmitted, a
stop signal is sent to the terminating office to end that phase of the
operation. After the appropriate number of digits has been recorded
in the terminating office equipment, an incoming advance pulse is
returned to the originating office; the trunk is then ready to be connected through to the talking paths at each end. As can be seen in
Figure 13-13, revertive pulsing requires three signalling states for
its operation, two to convey the pulsing count and one for the incoming
advance signal.

Revertive pulses
Start

Stop

+
+
0---,---------

r-

Incoming advance

~

L- ___ ---1

Sent forward ----.

(a) Originating office

+--

Sent back

(b) Terminating office

Figure 13-13. Revertive pulsing signals.

Vol. 1

Signal Characterization

342

Derived DC Signalling on Trunks

Derived dc signalling paths are used for many long local trunks
and short-haul toll connecting and intertoll trunks where a complete
dc loop is not available or where extended ranges are desired for
dc signalling. In these cases, dc signalling paths are sometimes derived
from the transmission path, which, of course, must be a physical
facility. Derived systems utilize E and M lead connections and, as a
result, may be used on one-way or two-way trunks. The types of
derived paths now in use include simplex (SX), composite (eX),
and duplex (DX) circuits, all of which may be used to transmit both
supervisory and address signals.
Simplex Signalling. The method of connecting a simplex signalling
circuit to a voice-frequency trunk is illustrated in Figure 13-14. By
feeding the signalling currents through the center taps of line transformers, signalling current flux is cancelled in the transformers and
the signals are not transmitted beyond the transformers in either
direction. However, the trunk resistance is halved by paralleling the
two conductors, thus extending the range compared to loop signalling.
Simplex signalling has largely been superseded by DX signalling.

Trunk

r---------- - - -

-----------~

Voice
channel

Voice
channel

~----~~

---~---------

t~

Signal
transmitting
relay

_________

Signal
receiving
relay

Figure 13-14. Simplex signalling connections.

Chap. 13

343

Signalling

Composite Signalling. This method of signalling consists essentially
of combining a voice transmission path with dc signalling paths by
means of a high-pass, low-pass filter arrangement as illustrated in
Figure 13-15. The dc address and supervisory signals are transmitted
between central offices over one wire of the transmission circuit with
ground return. Where necessary, the second conductor of the transmission path can be used to compensate for differences in earth
potential between the two offices.

The crossover frequency of the filter characteristics is approximately 100 Hz. Thus, interference from signalling currents is blocked
from the voice-frequency band.
One arrangement of such a composite signalling system is shown
in Figure 13-16. The connection through the P windings of the
ex relays is used for earth potential compensation. The arrangement may be extended to several other signalling circuits, each using
the same trunk conductor, by wiring the P windings of the ex relays
in series with the ones shown in the figure. Thus, the signalling and
transmission are not necessarily associated; signalling on a given
trunk transmission path may be associated with a different trunk.

---1 ~(---1111

CX circuit 1 4 - - - - - -____

~

Central
office

\

VF,,"o'

~~High pass

-II-(--~III
CX circuit 2

Figure 13-15. Composite signalling circuit for one end of a trunk pair.

344

Vol. 1

Signal Characterization

line

line

r-~I~~----~--

line

-+------~

u
-

cx

- o:L

S2

."""+-----1

p

-

+ -

~¥~
ex

legs

T
Biasing
potentiometer

Biasing
potentiometer

Figure 13-16. Composite signalling circuit - one voice channel.

Duplex Signalling. Duplex signalling, illustrated in Figure 13-17, is
based on the use of a symmetrical and balanced circuit that is
identical at both ends of the trunk. The circuit and its mode of operation are patterned after those used in ex signalling, but a composite set is not required. Signalling and transmission are on the
same transmission path and hence do not occur simultaneously. One
wire of the trunk conductor pair is used for signalling and the other
for ground potential compensation. Its chief advantage is that it can
operate on circuits having loop resistance higher than can be tolerated
by other systems, i.e., up to 5000 ohms.

n

::r
Q

l'
Office 1

I

\

Trunk circuit

T

Transformer

r------ - -

--1---

-- -

\

Trunk circuit
-

-

-

I
I

,T
--T
I

I

rill

I

-=-

I

CAl

Office 2

I

Trunk
cable
pair

I

II~
~

11dj;-----

:~I

I
A

~

-

+

MA

- --,
E1 I

I I:

I

I
CJ)

cO'
::J
Q

::J

(Q

-:
M

I
I
I

I
1
_I

1

Balancing
network

L __

~as

~.::.J

OX signalling circuit

-=-

-=-

OX signalling circuit

Figure 13-17. Duplex signalling system.

w
,a:..
Ot

346

Signal Characterization

Vol. 1

AC Signalling on Trunks

Use of ac signalling may be dictated by the limitations of distance
on dc systems or by the inability to transmit dc signals over commonly
used carrier systems. Thus, even though conversion equipment and
ac generators are required, such systems are a necessity in the
telephone plant.

It is theoretically possible to transmit ac signals for address and
supervisory information at any frequency in the voiceband, defined
for these purposes as approximately 200 Hz to 3500 Hz. Carrier
transmission systems usually provide 4000 Hz spacing between channel carriers. Present voice-frequency signalling systems operate in
the range of 500 to 2600 Hz.
A number of ac signalling systems have been designed to operate
by using inband frequencies. Two are commonly used at present, the
2600-Hz single-frequency system and the multifrequency pulsing
system.
Inband 2600-Hz Signalling. This system is commonly referred to as
single-frequency (SF) signalling. With certain adaptations that involve other single-frequency signals, the system may be used to
transmit address and supervisory signals in both directions on most
types of trunks.

One of the design considerations in voice-frequency signalling is the
prevention of mutual interference between transmission and signalling
systems. Voice-frequency signals are audible; consequently, signalling must not take place during conversation. In most applications
of this type of system, the presence of a 2600-Hz signal corresponds
to the on-hook condition and the absence of 2600 Hz corresponds to
the off-hook condition. Thus, there is no 2600-Hz tone normally
present on the line during conversation. Signal receiving equipment,
however, must remain connected during conversation in anticipation
of incoming signals and may be subject to false operation due to
sp~ech signal components that resemble the tones used for signalling.
Several methods are used to protect against false operation of
signalling circuits:
(1) Where possible, signal tones of a character not likely to occur
in normal speech are chosen.

Chap. 13

Signalling

347

(2) Time delay is used in the signalling and trunk circuits so that
normal speech currents are ignored.
(3) Speech signal energy, when detected at frequencies other
than the signalling frequency, is used to inhibit operation of
the circuits in the signalling receiver.
This system may be used to signal independently in both directions
on four-wire facilities. When a 2600-Hz SF signal is being transmitted to reflect the on-hook, steady-state supervisory condition, it
is applied to the trunk at an amplitude of -20 dBmO. Thus, the
steady-state load effect of such a signal is somewhat below the long
term average speech power in a telephone channel. When being used
to transmit address information, however, the 2600-Hz signal is
increased in amplitude by 12 dB to -8 dBmO. Such a high signal
amplitude is permissible because of the short duration of the address
signal pulses and because of the low probability of large numbers of
such high-amplitude signals being simultaneously present in a
transmission system.
There are a number of SF signalling characteristics that interact
importantly with transmission systems. These have particularly
serious implications in their interactions with carrier systems.
Problems arise as a result of two conditions: (1) a majority of trunks
utilizing a carrier system may be equipped with SF signalling, and
(2) most of these trunks may originate at the same office. In the
latter case, there may be high coherence in the relative phases of
the many 2600-Hz signals. As a result, the way in which these signals
combine may cause overload or excessive peaks of intermodulation
noise at certain frequencies and at unpredictable times. In such situations, action must be taken to break up phase coherence among
2600-Hz signals in different channels.
Furthermore, where large numbers of trunks in a carrier system
employ SF signalling and terminate in the same office, serious disruption of the switching system operations can occur as a result of
carrier system failure. If most of the trunks are in the idle condition,
the carrier system failure causes the sudden interruption of all of
the 2600-Hz signals. This is interpreted by the switching machine
as simultaneous calls for service from many trunks. As a result, the
switching machine is momentarily overloaded until it can dispose

348

Signal Characterization

Vol. 1

of the disabled trunks. Some carrier systems employ trunk conditioning circuits which cause all affected trunks to appear busy so
they will not be seized until after repairs have been made; the
conQ,itioning circuits then remove the busy condition and restore the
trunks to service.
~

Another adaption of SF signalling (really a two-frequency system)
is used for selective signalling in a multistation four-wire privateline network such as might be used as an order-wire facility for
carrier systems or for private customer communications networks
interconnecting separate locations. Dial pulses are used to signal
selectively anyone of a maximum of 81 stations. The dc dial pulses
are converted, at the customer's premises or at the central office, to
a frequency shift format utilizing 2600 Hz and 2400 Hz.
Multifrequency Pulsing. Multifrequency (MF) pulsing signals are
used to transmit address information on trunks. Signalling is accomplished by the transmission of combinations of two, and only
two, of six frequencies in the voiceband. The principal advantages
of this system are speed, accuracy, and range. However, this system
is not capable of transmitting supervisory signals and, as a result,
supervision must be provided by. another system such as DX, loop,
or SF.

13-3

OUT-Of-BAND SIGNALLING

Any signalling arrangement that utilizes frequencies out of the
voiceband of the trunk over which signalling is taking place may be
considered as an out-of-band signalling system. By such a broad definition, de systems and a common channel interoffice signalling (CCIS)
system would be considered out-of-band systems. However, it has been
convenient to discuss dc systems as a separate class of systems. In
the eCIS system, signalling information is transmitted on a voicefrequency data channel independent of the trunks involved in the
connection.
Out-of-band systems that are in current use include early N1, 0,
and ON carrier systems, which use a single-frequency signal at
3700 Hz in the voice channel, and the digital signalling arrangements
used in the time division multiplex T -type systems. In addition,
systems like the 43A1 Carrier Telegraph System are sometimes used
(as in submarine cable operation) to signal over a channel separate
from the voice channel.

Chap. 13

Signalling

349

Out-of-Band SF Signalling

The out-of-band signal at 3700 Hz falls in the passband of a voicefrequency channel but at a high enough frequency that it is above
the cutoff of the channel filters, hence above the band occupied by
speech energy. This mode of operation has the advantages that no
provision need be made for protection against inadvertent voice
operation of the signalling circuits; in addition, signalling can take
place during the talking interval if required.
During the trunk idle condition, the 3700-Hz signals are present
in both directions of transmission; trunk control, supervisory, and
address signals are transmitted by interrupting the 3700-Hz signal
in a fashion similar to that described for 2600-Hz inband signalling.
Interconnection between the transmission system signalling and
other transmission circuits is made by E and M lead facilities.
The 3700-Hz signals are applied to the high-frequency line of the
carrier system at the transmitting end of the carrier system after
the compressor portion of the compandor. Thus, compandor action
has no effect on the 3700-Hz signals.
Out-of-Band Digital Systems

In the coding of PCM signals for transmission over T -type carrier
lines, address and supervisory signals are assigned specified bits in
the carrier pulse stream. In some cases, this assignment of bits
is permanent; as a result, a significant portion of the system's
theoretical channel capacity is assigned to signalling. In other cases,
the address and supervisory bits are assigned on a borrowed basis
in such a way that speech transmission is of higher quality than
would otherwise be possible. The signalling bits are used for speech
coding when not required for signalling.
13-4

SPECIAL SERVICES SIGNALLING

Most of the discussion of signalling and the characterization of
alerting, address, and supervisory signals that have been given in
this chapter apply equally to signalling in the switched message
network and to special service arrangements. However, there are
some significant differences; some are due to the nature of special
service circuits themselves, and some are due to the manner in
which the special services are administered.

350

Signal Characterization

Vol. 1

Tandem Signalling Links

In the switched message network, the tandem connection of a
number of trunks usually involves the regeneration of address
signals at the point of interconnection. Thus, in signalling over long
distances through a combination of trunk types and transmission
system types, the signalling equipment and signal transmission
impairments need only be considered on a trunk-by-trunk basis.
One type of special service trunk (by definition) is the PBXcentral office trunk. A PBX station, connected through the PBX
trunk to the central office must signal by dial pulsing through the
PBX station line and PBX trunk without regeneration. This situation
may be further compounded by the need to signal through an intermediate PBX tie trunk. These conditions often result in marginal
signalling conditions in PBX station signalling over tie trunks and
PBX-central office trunks.
Service Demands and Plant Complexities

Many special service circuits must traverse parts of the plant in
which a mix of trunk plant and loop plant occurs. One example is a
foreign exchange (FX) line whose station set is located in one
central office area but whose home central office may be many miles
away. The final loop connection is from the local central office, but
the loop must then be extended through cables normally used for
interoffice trunks to the distant serving office. Another example is
an off-premise extension from a PBX that may require a transmission path involving connections through both loop and trunk cables.
Inward and outward W ATS (wide area telephone service) lines
provide additional examples.
REFERENCES

1. Breen, C. and C. A. Dahlbom. "Signalling Systems for Control of Telephone
Switching," Bell System Tech. J., Vol. 39 (Nov. 1960), pp. 1381-1444.

2. Weaver, A. and N. A. Newell. "Inband Single-Frequency Signalling," Bell
System Tech. J., Vol. 33 (Nov. 1954), pp. 1309-1330.

Signal Characterization

Chapter 14

Data Signals
The transmission of data signals in the Bell System involves the
transmission of coded information between machines or between
man and a machine. In some cases the transmitted information is
coded into some digital form that is convenient to the operation of
a machine, such as a computer, and also convenient to the necessary
interpre~tion by man at the input and output of the machine. In
other cases, the transmitted signal is more conveniently coded as a
direct electrical analog of the information and digital encoding is
not utilized. Thus, there are two important forms of data signals,
digital and analog. Digital signals are those that can assume only
discrete values of the parameter that is varied to convey information;
analog signals can assume a continuum of values between given
maxima and minima. A common application of digital transmission
techniques requires digital data signal characterization for transmission over analog systems. Other digital signals and and certain forms
of analog data signals must also be characterized.
Digital data signals are transmitted at signalling rates that
range from a few bits per second to millions of bits per second.
The most commonly used rates, several thousand bits per second,
are those compatible with voiceband circuits. In many private line
applications and in the switched public network, transmission circuits
that are normally used for voice communications are alternatively
used for digital or analog data signal transmission.
In many cases of interest here, data signals are those used by
computers; they are usually binary signals transmitted serially on
a pair of conductors, but they are seldom in a form convenient for
transmission over Bell System facilities. Processing to transform a
signal to a suitable format often takes place at two locations - first
at the station set to make the signal suitable for transmission on
telephone loops, and then at carrier terminals to prepare the signal
351

352

Signal Characterization

Vol. 1

for transmission over a carrier system in a form suitable for
modulating and multiplexing with other types of signals. The processing may involve special coding for error detection and correction.
Each of the processes must be reversed so that the signal delivered
at the receiving end of the circuit is a faithful replica of the signal
accepted from customer equipment. These processes are similar to
those described in Chapter 8.
Since many existing transmission systems were designed as
analog facilities for the transmission of analog speech signals, the
processing of a data signal for transmission over these systems must
be such as to make the signal compatible with the transmission
system. This compatibility involves loading effects, channel characterization, and intermodulation and signal-to-noise performance. Thus,
the nature of the processes must be described here in some detail.
Processing of data signals for transmission over digital transmission systems is not covered here because the coding is unique to each
digital system and the operation of the digital system is not materially
affected by the characteristics of the signals. On the other hand, the
line signal of a digital transmission system (suitably processed) is
sometimes transmitted over an analog transmission system. The
analytic treatment of digital data signals and digital line signals is
identical when they are transmitted over analog systems, and both
must be characterized. Hereafter, they are generally referred to
simply as digital signals.

14-1

DIGITAL SIGNAL TRANMISSION CONSIDERATIONS

A number of considerations related to digital signal transmission
on analog facilities have had important effects on the design of signal
formats. These include restrictions on signal amplitudes, signal-tonoise ratios and error rates, and the relationships between signal
and channel characteristics.
Signal Amplitudes

A number of criteria must be considered in setting the amplitude
of a digital signal using the switched public network or sharing
facilities with the network. One such consideration is that the power
in the signal should not cause excessive intermodulation or overload
in transmission systems, especially in analog carrier systems where

Chap. 14

Data Signals

353

service to many other customers might be jeopardized. The established requirement is that signals operating in the voiceband are to
be limited to -13 dBmO*, defined as the maximum allowable power
averaged over a 3-second interval. When the activity factors and
other statistics of data transmission are accounted for (e.g., the
number of operating half-duplex versus full-duplex channels), this
value is equivalent to a long-term average power of -16 dBmO per
4-kHz channel.
The signal amplitude requirement for narrowband data signals,
several of which may be multiplexed in a single voice channel, is
also -16 dBmO, or a 3-second maximum of -13 dBmO, for the composite signal. The power of each individual signal must be sufficiently
lower so that the total power in th~ channel does not exceed the
objective.
For a wideband digital signal, one occupying more than a 4-kHz
channel, the amplitude criterion is sometimes expressed somewhat
differently, namely, that the signal power may not exceed the total
power of the displaced channels.
The gain of some analog transmission system repeaters is regulated by the power in the transmitted signal. When wideband digital
signals are processed for transmission over this type of system, the
power in the transmitted carrier and its sidebands must be essentially
constant at a value equal to that of the displaced message channel
carriers and their sidebands.
Irrespective of its form or the bandwidth it occupies, one more
constraint is imposed on a wideband digital signal. No singlefrequency component may exceed an average power of -14 dBmO [1].
This limit, established to avoid the generation of intelligible crosstalk
intermodulation products in analog carrier systems, may sometimes
be exceeded on the basis of low probability of occurrence or because
of the short duration involved. Where danger of intelligible crosstalk
exists, a scrambler or other means of reducing single-frequency
components must be used [2].
Signal components at frequencies above the nominal band must
be limited in amplitude to low values that can not interfere with
adj acent channels in a carrier system, or interfere through any
*This value is equivalent to -12 dBm as measured at the serving central office.

354

Signal Characterization

Vol. 1

crosstalk path with some other wider band signal or a cable carrier
system that might share the same facility. For example, these unwanted signal component amplitudes are specified for voiceband
signals at frequencies of 3995 Hz and higher [3]. In addition, it is
required that the power in the band between 2450 and 2750 Hz not
exceed that in the band between 800 and 2450 Hz in order to minimize
interference with single-frequency signalling systems.
Error Rate and Signal-to-Noise Ratio
Unlike speech or video signals, which must be evaluated on a subjective basis because of human responses to various types of signal
impairment, digital signals are evaluated objectively. The evaluation
of digital signal transmission is often expressed in terms of error
rate, i.e., the number of errors in a given number of transmitted
bits (e.g., one error in 106 bits or an error rate of 10- 6 ). It is sometimes convenient, however, to evaluate performance in terms of the
signal-to-noise ratio because signal and noise amplitudes are easy
to measure. When this is done, the noise characteristics must be
specified; usually the Gaussian distribution (see Chapter 17) is
used because there is a definite and demonstrable relationship between
Gaussian noise and error rate.
While the effects of impairments other than noise (such as gain
distortion or delay distortion) may also be expressed in terms of
error rate, transmission studies are often facilitated by converting
the impairment into an equivalent signal-to-noise ratio. This is done
by evaluating the error rate for the impairment being studied and,
from that error rate, determining the reduction in signal-to-noise
ratio that would produce the same error rate in an unimpaired
channel compared with the impaired channel. The reduction in
signal-to-noise ratio is called noise impairment. While noise impairments cannot be added directly to give an overall impairment or
error rate, the technique provides a convenient method of comparing
the merits of one mode of transmission with another over a real
channel.
Consideration is being given to the possibility of using a figure of
merit other than signal-to-noise ratio or error rate. In practice,
errors often occur in bursts that produce a high error density for
only a small portion of the time involved in transmitting a digital
signal; the remaining time may be error-free. Such a burst may

Chap. 14

Data Signals

355

cause a high apparent error rate, yet have little effect on the efficiency
of transmission. One possibility being considered as a figure-of-merit
involves calculating or counting the percentage of data blocks (time
intervals) in which error-free transmission occurs. Another involves
the number of error-free seconds per minute or per hour.

Channel Characteristics

The format into which a digital signal is to be processed for transmission on a analog channel must represent a compromise between
maximizing the rate of information transmitted (bits per second per
hertz of bandwidth) and minimizing the impairments due to extraneous noise or -intersymbol interference. The transmission characteristics of the channel bear an important relationship to the design compromises that are made, as does the cost of the terminal equipment.
For a transmitted pulse to retain a rectangular shape, the bandwidth of the transmission channel would have to be very great
(theoretically infinite). Bandwidth is expensive and, furthermore, the
wide band would admit interference from noise or other perturbations
appearing at frequencies outside the band which contains the maj or
portion of the signal energy. It is desirable, therefore, to curtail the
signal spectrum as much as possible without undue impairment of
the signal. Nyquist's criteria' (1) and (2), defined in Chapter 10, give
important leads to how the band may be limited and pulses shaped
to minimize errors at the receiver. There are several satisfactory ways
of shaping the pulses by appropriate design of the channel characteristic [4]. One is the raised cosine characteristic; it has the virtues
of meeting simultaneously Nyquist's criteria (1) and (2) in response
to an applied impulse and does so without undue penalty in added
bandwidth. It tends to produce less noise iInJ>airment than other
channel characteirstics and also has the virtue of being physically
realizable to a close approximation by straightforward design techniques. The raised cosine channel characteristic, near optimum for
transmission of an impulse, requires some modification to accommodate commonly transmitted rectangular pulses.
Figure 14-1 (a) shows an idealized channel characteristic, curve p.
Curves rand s are modifications that follow cosine-shaped roll-off
characteristics at the high end of the band. They are symmetrical

356

Vol. 1

Signal Characterization

c:

o

.~

.~

c:
~

I-

O~-----r------+-----~----=-~----

o

/1/2
Frequency

--+

(a) Channel characteristics, raised cosine roll-offs
X/sin

X

~
~'
-,;"t'
~

::x::

... -----'

1.0 - - ...... : : . ---.

c:

o

'=
.~

~"
"

0.5

c:

c

S

~

'-<

S(x/sinx)

/1/2
Frequency

--+

(b) Modified raised cosine characteristic

Figure 14-1. Channel shaping.

about the frequency 11 where their values are 0.5 relative to the
values at zero frequency. These raised cosine channels are said to
have Nyquist shaping. If the characteristic yields zero transmission
at frequency 3/t/2 (curve r approximately), it has a 50 percent rolloff. If the characteristic yields zero transmission at 21 (curve s
approximately), it has a 100 percent roll-off. Roll-off is thus defined
as excess bandwidth expressed as a percentage of the theoretically
minimum requirement.
If the bandwidth is extended beyond It and the roll-off characteristic has Nyquist shaping, a linear phase/frequency characteristic
can be closely approximated in practice. When these characteristics

Chap. 14

Data Signals

357

(cosine roll-off and linear phase) are provided, the zero amplitude
crossings of output pulses resulting from applied impulses still occur
at times corresponding to ±n/ (2/d. If the roll-off extends to 2ft, the
raised cosine pulses at the output have additional zero crossings at
odd multiples of one half the intervals that occur in the idealized
channel transmission.
Rectangular pulses, transmitted through a channel having any of
the characteristics in Figure 14-1 (a), cannot be readily detected
because excessive intersymbol distortion occurs. As discussed in
Chapter 6, the (sin x) /x channel response results from the application of an impulse, a signal which has a flat energy distribution. To
make the channel respond in the desired fashion to rectangular
pulses-that is, so that output pulse waveforms have the desired
(sin x) /x format-it is necessary thai the spectrum of the applied
rectangular pulses be modified to approach the flat spectrum of an
impulse. The normal spectrum of the applied rectangular pulse has
a (sin x) /x spectrum. To make the spectrum appear flat, the pulse
must be multiplied by the inverse function, x/sin x.
The desired modification of the signal can be accomplished by
modifying the raised cosine channel by an x/sin x function. In
practice, only the first lobe of the x/sin x function need be considered. Figure 14-1 (b) illustrates. Since the (sin x) /x function
becomes zero at 2/1, x/sin x theoretically becomes infinity at this
frequency. It can be shown, however, that the product of the x/sin x
function and the cosine function representing curve s also becomes
zero at 2/1•
A stream of rectangular puls.es having a 100 percent duty
cycle (T == T) transmitted over a channel having a characteristic,
s (x/sin x), like that of Figure 14-1 (b), appears at the channel
output as shown in Figure 14-2 (b) where T == 1/ (2ft). The time delay between the input, Figure 14-2 (a), and the output, Figure 14-2(b),
is ignored. Note that the (sin x)/x form of each output pulse is such
that the zero crossings correspond to the sampling points of successive
pulse intervals.
The interval, 1/ (2ft), is known as the Nyquist interval. In channels
having sharp cutoffs, the signalling interval, T, must closely approximate this interval in order to minimize intersymbol interference.

358

Signal Characterization

o

--0 :....

Vol. 1

0

j4T"'T~

,..,I
I

~

(a) Input pulses

I
I
I

0

I
I
'

(b) Output pulses, "raised cosine filter"

o
o

T

1/(2/,)

2T

3T

4T

1//, 3/(2/d 2//,

5T
5/(2/,)
Time

-+

Figure 14-2. Effects of a cosine channel on pulse shaping.

With a 100 percent roll-off characteristic, larger departures from
T == 1/(2fd can be tolerated than in a channel having a sharp cutoff.
The shaping of the channel characteristic may be placed at any
point in the channel. If the characteristic of the medium is predictable, its characteristic can be incorporated in the overall channel
characteristic. Since there are a number of places where shaping may
be used, the detailed effect on characterization of the transmitted
signal cannot be generalized.
14-2

DIGITAL SIGNAL CHARACTERISTICS

A large number of different digital signal formats are possible
and have been used in the Bell System. Many formats have been tried
and found unsatisfactory because of low efficiency or susceptibility to
various forms of impairment and are now considered obsolete. An
important stimulus to continued development, in addition to the
burgeoning demands of the business machine and computer industries,
is the desire to make signal transmission more economical by increasing efficiency, i.e., by increasing the number of transmitted bits

Chap. 14

Data Signals

359

per second per hertz of available bandwidth at less cost per unit of
information transmitted.
Amplitude Shift Keyed Signals

Initially, the generation of digital information was by amplitude
shift keying (ASK) techniques in a binary baseband mode. This
mode, basically that used to operate computers, is still used in many
telephone network signalling systems. Because of its simplicity, the
ASK binary baseband mode is used for transmission of digital data
signal~ over Bell System facilities, but only for relatively short
distances. The binary baseband signal format is neither as efficient
for a given bandwidth as other formats nor is it suitable for transmission on facilities which provide no dc continuity or are subject
to quadrature distortion, low-frequency cutoff, or significant envelope
delay distortion. As a result, where these restrictions are important
and signal-to-noise performance is adequate, equipment is installed
to process the binary baseband signals into forms more suitable to
the environment.
The nature of ASK signals is such that when they are used as
baseband signals in the form of simple on-off pulses with average
amplitude of zero, low- and zero-frequency components are important to their characterization and to their recovery by detection
circuits in the receivers. Because of their nature, such signals may
be regarded as formed by a process of modulation of a direct current.
The difficulties associated with transmission of zero- and very-Iowfrequency components through transmission facilities and networks
are among the important reasons for the infrequent use of ASK
modes of signal transmission without additional processing for transmission over Bell System facilities. When an ASK mode is used,
special provision must be made to eliminate the low- and zerofrequency components of the signal at the transmitter and at the
outputs of regenerative repeaters and to restore these components
at the repeater inputs and at the receiver.
Terminal equipment in the form of station sets, sometimes called
data sets, has been developed by the Bell System and many other
manufacturers to process data signals in a variety of ways. Some
of this equipment was initially arranged to have the binary data
signal amplitude-modulate a carrier in a 4-kHz voiceband channel.

360

Signal Characterization

Vol. 1

A signalling rate of 750 bits per second was achieved by using
double sideband modulation with transmitted carrier, and a rate of
1600 bits per second was achieved by using vestigial sideband techniques. These AM techniques provide frequency translation to eliminate the dc continuity and low-frequency cutoff problems. The
transmitted carrier is recovered for demodulation at the receiver in
proper frequency and phase to eliminate quadrature distortion impairment from the received signal.
ASK Signal Waveforms. Digital symbols may be represented by any
of a large variety of electrical signal formats. As previously mentioned, the control of computers usually involves the use of binary
ASK signals. Logically, the operation of computers relates to the 0 and
1 representation of binary numbers which in turn correspond to the
two states of a binary signal. Some alternate ways of representing
these two states are illustrated by the formats shown in Figure 14-3.

The waveforms of Figure 14-3 have several features in common.
First, all of the waveforms represent the same sequence of digits,
namely, 0110001101. Each of the waves depicted represents a
synchronous system in which the receiving equipment is timed by
some mechanism so that the incoming signal is sampled at the instants indicated. The sampling is required in most cases in order to
determine if the signal amplitude at the sampling instant is above
or below one or more of the decision thresholds indicated. In
Figure 14-3 (f), the sampling would take the form of a zero-crossing
detector since, in that case, Os are represented by transitions in the
signal and 1 s by no transitions. Finally, the peak-to-peak amplitudes
of the signals are all shown as equal to two units of voltage, V.
Figure 14-3 (a) illustrates the simplest of these signal formats.
A 1 is represented by the presence of a voltage, and a 0 by the
absence of voltage. If the wave is between half and full amplitude at
a sampling instant, it represents a 1; if it is between zero and half
amplitude, it represents a O. Thus, the half-amplitude value is the
decision threshold.
Figure 14-3 (b) is similar in all respects to Figure 14-3 (a) except
that opposite polarities of voltage are used to represent 0 and 1
instead of voltage and no-voltage. The decision threshold in this
case is zero volts. The polar form illustrated here is sometimes
adapted to the transmission of nonsynchronous digital signals.

Chap. 14

Data Signals

(0)

T~-I~I

V

361

:]-J-----t------f----tf
'!I~'~I!I!'!I~'~ '!I~'

(b)

Po~'

...-"..I

V

':

~-j---+-u--+---tf

,!,

- 1.0

21·.00

V

(c) Return-to-zero

~ I~

!

I! I! I ! I ~ I ~ I I ~ I

rL__
'+0 '+1 '+1 ,\ 1+01+0 '+1 '+1 '+01+1 ,

(d) Polar return-to-zero

V

1.°0~-

__.~____..-.__

-1.0

'+0 '+1 '+1 '+0 1+0 '+0 '+1 '+1 '+0 1+1 ,
V

(e) Bipolar

1.00

~

-1.0

'+0 '+1 '+1 '+01+0 '+0 '+1 '+1 '+0 '+1 ,
V

(f) Differentially encoded

1.°0~_
-1.0

- - -

- -

+ + + • • • • • • • •
101111

1010101111

1011

I

1.0
0.67

- - - -

- - - -- -- -

- - - -

- - - -

- - - --

0.33

(g) Four-level

V
-0.33

t t t

-0.67

----------.

---- ----------

= Sampling instants
-1.0

= Decision thresholds

•

01

•
10

+

00

Time--+

Figure 14-3. Basic ASK waveforms.

• •
11

01

362

Signal Characterization

Vol. 1

Figure 14-3 (c), called return-to-zero, differs from the first two in
that pulse length for a symbol is less than the time allotted to the
symbol interval. The extent to which the pulse length differs from
the symbol interval determines the duty cycle, defined as 100'T/T percent where 'T is the pulse length and T is the symbol interval. As in
Figure 14-3 (a), voltage is use1 to represent a 1 and no-voltage to
represent a 0 for the return-to-zero signal.
Figure 14-3 (d) is the return-to-zero counterpart of the polar twolevel signal of Figure 14-3 (b). Note that the polar return-to-zero
signal is really a three-level signal having less than a 100 percent
duty cycle. * However, since only two of the values, plus-voltage
and minus-voltage, are used to represent the digital information in
the signal, it may be regarded as a binary signal. Note that each
symbol, whether a 1 or a 0, is associated with the presence of a pulse.
For this reason, the synchronization of the receiving equipment may
be accomplished by using the information in the signal, thus making
the receiver self-clocking. This feature allows this signal format to
be used for the transmission of nonsynchronous data.
The bipolar signal of Figure 14-3 (e) has valuable properties that
have caused it to be the format chosen for the line signal for the
T1 Carrier System. The symbol 0 is represented by zero voltage and
the symbol 1 is represented by the presence of voltage. However,
the polarity of voltage for successive 1 symbols is alternated. Two
important results are achieved. First, the dc component of the signal
is virtually eliminated. This permits transformer coupling of the
repeater to the line, facilitates the separation of the signal from
dc power, and makes decision threshold circuits more practical by
effectively eliminating the phenomenon known as baseline wander
caused by a varying dc signal component. Second, the concentration
of energy in the signal is shifted from the frequency corresponding
to the baud rate to one-half the baud rate. This reduces near-end
crosstalk coupling, reduces the required bandwidth to about one-half
of that needed for a polar signal of the same duty cycle and repetition rate, and makes the design of timing recovery circuits more
practical.
In Figure 14-3 (f), the information is coded in terms of transitions
that occur in the transmitted signal. Successive pulse intervals are
*The polar return-to-zero and bipolar signals are sometimes called pseudo
three-level signals.

Chap. 14

Data Signals

363

compared. If they are identical, a 1 was transmitted in the original
signal; if successive intervals show a transition, a 0 was transmitted.
The signals of Figures 14-3 (a) through 14-3 (f) may all be considered binary, either in the number of values of voltage transmitted
or in the significant number of values used to represent binary information. Figure 14-3 (g) is not binary; it is illustrative of a class
of signals which can be used to transmit data quite efficiently when
the signal-to-noise ratio that can be realized is high enough to permit
signal detection at a number of different decision threshold values
that generally are smaller than those for the binary signals previously
discussed.
The signals of Figure 14-3 are used in many ways. In some cases,
they are the signals delivered to the station set by the customer and
in other cases they represent the signals transmitted over Bell System
facilities. The several forms commonly used may be characterized
somewhat more fully to illustrate their use.
Wideband Binary ASK Signals. A limited number of applications of
this signal format are used for digital data transmission in the
Bell System. Data station and carrier terminal facilities are available
to permit the transmission of a polar form of signal, somewhat like
that of 14-3 (b), at synchronous rates of 19.2, 50.0, or 230.4 kb/s;
for nonsynchronous service, the signal elements must have corresponding minimum durations of 52.0, 20.0, and 4.0 /LS. The three
arrangements have been developed to permit wideband data transmission in 24-kHz, 48-kHz, and 240-kHz bands found in commonly
used FDM equipment. The 50-kb/s arrangement is the one most frequently used; its operation is typical of these arrangements.

As mentioned, the signal is transmitted in a polar form, called
restored polar, different from the format of Figure 14-3 (b) in that
the dc component and some of the low-frequency components are
filtered out at the transmitting data station and restored at the receiver. As a result of the filtering, the transmitted signal is sharply
skewed, as shown in Figure 14-4 (b). This mode of transmission
obviates the need for high fidelity transmission at zero and very low
frequencies.
The power spectral densities for synchronous and nonsynchronous
polar signals and restored polar signals are shown in Figure 14-5.
For the synchronous signal, the spectra are those of a signal having

364

Vol. 1

Signal Characterization

a rate of 50 kbjs (T == 20 JLs) and
random bits having an equal probability of being 1 or 0 (p == 0.5).
The nonsynchronous signal spectra
represent a two-valued facsimile
signal in which the average rate
of black-white transitions is 4000
per second, and pages are 10 percent black and 90 percent white
(the probability of a 1, p == 0.1).
The low-frequency power density
spectra are very similar for the
synchronous and nonsynchronous
signals.

(a) Synchronous or nonsynchronous
polar signal

(b) Same signal in restored
polar format,

Figure 14-4. Restored polar signal.

Thus, Figures 14-4 (b) and 14-5 illustrate, in the time and frequency domains, respectively, the characteristics of the processed
50-kb /s signal as it is transmitted on loops. If a carrier system is
used, further processing is necessary. Two cases are of interest, i.e.,
processing for transmission in the 48-kHz group band of the L-type
multiplex and processing for transmission in the 96-kHz N-type
carrier band. Transmission in both cases is by amplitude modulation
with vestigial sideband (VSB).

-10

II'

I

Polar signal

·~5
CI-

~o

Restored polar line signal
(2-kHz cutoff)

~IO

O-g

,,"-

~

~

I

,,~

Q)

-50

r-....

~,

-40

\

'" ! ~ n ,

~"

~"

~~

Q.. - -

",-

"~~'

-30

00

8. ....
..."'M
'-..
E

............-.,

~

-20

Synchronous
signal

~"

"

.iI"
0.01

0.02

0.05

0.1

0.2

0.5

2
Frequ~ncy

'5

10

J

~

Nonsynchronous
(facsimile) signal

20

50

100

(kHz)

Figure 14-5. Power density spectra of polar and restored polar signals.

200

Chap. 14

365

Data Signals

The frequency allocation, channel characteristic, and resulting
signal spectrum for transmission in L-type multiplex are shown in
Figure 14-6. The channel transmission characteristic and frequency
allocation are shown in Figure 14-6 (a). In the 60- to 108-kHz
spectrum, a speech channel for coordination of operations may be
provided in addition to the data channel for the VSB data signal.
The baseband signal spectrum, shown in Figure 14-6 (b), is the same
as that of Figure 14-5 but modified by the group frequency channel
characteristic; the modification is most notable at high frequencies
where channel characteristics limit the baseband top frequency to
37 kHz. The modulation process results in a VSB signal with the
carrier suppressed. However, the fact that signal components at

t 4 - - - - 37-kHz lower

sideband----~~....,...:_+t

o
60 kHz

100kHz

Frequency ----.

108 kHz

wideband
carrier frequency

(a) Group frequency

Channel characteristic

~

i~~_

1 -

t

1/2 -

,I

",

I

Restored polar line
signal spectrum

Restored polar line
signal spectrum

.~

o

;:

.---J'.... ................,

r ,-

o L -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

~,-------~~----

25 kHz
Frequency~

(b) Baseband

Figure 14-6. Data signals in L-type multiplex at 50 kbjs.

37 kHz

Vol. 1

Signal Characterization

366

zero and low baseband frequencies have been removed at the station
set permits the reinsertion of a low-amplitude carrier component.
This component is recovered at the receiving terminal equipment to
control the phase and frequency of the carrier used in the demodulation process [5].
When the 50-kb/s signal is processed for transmission over an
N -type carrier system, it is modulated into the high group of the
N-type system as shown in Figure 14-7. The modulation process is
VSB with carrier transmitted. Since the nominal bandwidth in
N-type carrier is 96 kHz, the signal is not as severely band limited
as in the L-type multiplex. Two voice channel carriers are transmitted, with or without voiceband modulating signals. These carriers
and the data carrier are not quite sufficient to supply the signal
power for N -carrier line regulation. Therefore, a single-frequency
signal is added at 176 kHz at an amplitude sufficient to make the
total power of the transmitted composite signal equivalent to that
of the normal N -carrier line signal.
As mentioned previously, similar signal formats are provided for
transmission at 19.2 kb/s (one-half group band) and at 230.4 kb/s
(supergroup band). The transmission arrangements are quite similar
except that in the case of 19.2-kb/s transmission the vestigial shaping
is accomplished at the data station instead of the carrier terminal.

12-kHz
vestigial
sideband

j+--

I

1

;

40-kHz
lower
sideband

Q)

'"0

.~
Ci.
E
o

1/2

Q)

.~

'0

Qj
0:::

0
176 kHz
\~

168 kHz

184 kHz

______________- J /
VF carriers

240 kHz

Wideband carrier

Figure 14-7. Data signals in N-type carrier at SO kb/s.

Chap. 14

Data Signals

367

Thus, the 19.2-kb/s signal is transmitted at carrier frequency over
the data loops. The carrier is at 29.6 kHz [1].
Bipolar Line Signals. Bipolar signals find their greatest use in the
Bell System as line signals in T-type carrier systems. The line signal
in the T1 Carrier System is bipolar, like that shown in Figure 14-3 (e),
in all respects. The line signal in the T2 Carrier System is similar,
but with one important exception; in T2, the line signal is prevented
from containing more than five successive Os by a method that
modifies the bipolar signal format. This is accomplished by logic
circuits in the transmitting terminal which examine the line signal
before it is applied to the line. If the signal contains six consecutive
Os and if the last 1 was a
a 0+-0-+ signal is substituted for
the six Os; if the last 1 was a -, a 0-+0+- signal is substituted
for the six Os. The resulting violation of the bipolar rule (alternate
1 s must be of alternate polarity) is a means for recognizing the
need for six Os which must be reinserted in the pulse stream at the
receiving terminal. The substitution is made in order to guarantee
a minimum density of 1s in the line signal.

+,

This code substitution eases the design and increases the accuracy
of repeater timing circuits. The price paid is the additional logic
circuits that must be used to accomplish the substitution and the additional complication of ignoring the substituted codes when bipolar
violations are used as a measure of system performance.
The timing problem in the T1 Carrier System is also solved by
limiting the maximum number of successive Os in the line signal but
in a manner different from that used in the T2 system. In the
T1 line signal, the number of consecutive Os that can be transmitted
is limited to 15. For example, if encoded speech signals are being
transmitted, this limitation is imposed by preventing any 8-bit word
containing all Os from being transmitted to the line. If such a word
is generated, it is modified in the terminal equipment by inserting
a 1 in the seventh digit of the coded word. This is the least significant
digit of the code representing the amplitude sample. The eighth digit
is used for signalling. The code substitution permits the true bipolar
feature to be maintained in the line signal. Its cost is a slight increase
in channel coding noise.
The power spectral densities of the T1 and T2 signals are, of
course, functions of the statistical makeup of transmitted signals and

Signal Characterization

368

Vol. 1

of the signalling rate employed. The power spectral densities of the
two signals are conveniently represented in terms of the probability,
p, of a 1 in the signal sequence. The bipolar signal used in T1 is
represented in Figure 14-8 for a range of p from 0.4 to 0.6. The
T2 signal with code substitution for six successive Os is shown in
Figure 14-9 for the same range of values of p, 0.4 to 0.6. In both
figures the abscissas are normalized to unity, IT = 1, where I is in
hertz and T is the signalling rate.
In the T1 system, the signal is transmitted at 1.544 X 106 bits per
second with a 50 percent duty cycle. The minimum pulse width is
then T
1/ (2 X 1.544 X 106 ), or about 0.324 JLs. In the T2 system,
the signal is transmitted at 6.312 X 106 bits per second, also
with a 50 percent duty cycle. For T2, the minimum pulse width is
6
T = 1/ (2 X 6.312 X 10 ), or about 0.079 JLs.

=

The bipolar nature of the two signals and the coding sequence
employed result in negligibly small discrete frequency components

p=006
1.5

..s::.

-t;

°i

~
a

.0

1.0

°c
:;)

;

a.
C!)

01

~

"0
>

C!)

0
!r
:;)

005

c:

a
C!)
~

o
o

1.0

005
Normalized frequency,

IT

Figure 14-8. Power spectra for T1 bipolar signals.

Chap. 14

369

Data Sig no Is

of

-g

'i

-g

c:

.8

1.0

'2

:;)

~

Q,

o

0.5
Normalized frequency,

1.0

IT

Figure 14-9. Power spectra for T2 bipolar signals coded for restricted number of
sequential zeros.

and nulls in the spectrum at zero frequency and at integral multiples
of frequencies corresponding to the signalling rate. For each system,
the losses above the frequency corresponding to the signalling rate
are high; as a result, the spectra of Figures 14-8 and 14-9 may
be ignored above the signalling frequency. In Tl carrier, the top
transmitted frequency then may be regarded as f == 1/ (2T) ==
1/ (2 X 0.324) == 1.544 MHz; in T2 carrier, the top transmitted
frequency is f == 1/(2T) == 1/(2 X 0.079) == 6.312 MHz.
Signal amplitudes vary widely through the system in both Tl
and T2. One reference point often used is the output of a line
(regenerative) repeater. Even here, the amplitude varies somewhat.
The nominal value in Tl is 3 volts, peak; in T2, 4.2 volts, peak.
Multilevel ASK Signals. The ASK signals described thus far have
been two-level or, at most, three-level (Tl and T2 line signals).

Vol. 1

Signal Characterization

370

Where channels and transmission facilities exhibit a high signal-tonoise ratio and have well controlled transmission characteristics
(gain/frequency and phase/frequency), the efficiency of transmitting
information can be significantly improved by coding the digital signal
into a multilevel ASK format such as the four-level signal illustrated in Figure 14-3 (g). Such multilevel signals are used in the
voiceband [6] and in the mastergroup band of broadband carrier
systems [1]. In addition, a system is being introduced that permits
the coding of a 1.544-megabit-per-second line signal, such as that
used in T1 carrier, into a multilevel signal that can be transmitted
over microwave radio systems at frequencies below the normal frequencies allocated to message channels [7]. The multilevel ASK
signals presently transmitted in the Bell System are listed in
Figure 14-10.
The first four groups of signals, those transmitted at 1.8, 2.4, 3.2,
and 3.6 kilobauds, are transmitted in the voiceband. The signalling
BAUD RATE

BIT RATE

(kilobauds)

(kb/s)

1.8

2.4

3.2

3.6

772

NO. OF
LEVElS

BANDWIDTH

1.8

2*

Voice

3.6

4

Voice

5.4

8

Voice

2.4

2*

Voice

4.8

4

Voice

7.2

8

Voice

3.2

2*

Voice

6.4

4

Voice

9.6

8

Voice

3.6

2*

Voice

7.2

4

Voice

10.8

8

Voice

1,544

7

440 kHz

*Optional binary mode.
Figure 14-10. Multilevel ASK signals in the Bell System.

Chap. 14

371

Data Signals

rates are optional and are provided to the customer in accordance
with appropriate tariffs which govern the extent to which transmission facilities are equalized to provide adequate transmission
quality. Note that for these signals a general rule may be applied;
i.e., if n-valued coding is used at a rate of x bauds, the transmitted
information rate may be expressed as x log2 n bits per second.
The signal transmitted at the 772-kilobaud rate is the digital line
signal used for transmission over microwave radio systems. The rate
at which information is transmitted for this signal cannot be computed by the expression previously given for voiceband rates because
the method of coding is different. The mode involves what is known
as class IV coding for partial response transmission [8, 9], for which
the transmission rate is x log2 (n
1) /2 bits per second, where x
again represents the baud rate and n represents the number of values.

+

Signal Spectra. Binary baseband signals are coded into the multilevel format in a data set or in terminal equipment associated with
a carrier system. All of the multilevel signals listed in Figure 14-10
are transmitted in a partial response format and have an energy
distribution as shown in Figure 14-11. Energy above frequency /1,
the Nyquist frequency, is removed by an appropriate cutoff filter
which leaves only a vestige of the second lobe, as illustrated in
Figure 14-12. A timing signal, P t , is added to facilitate recovery of
the synchronizing, or timing, information at the receiver.

When multilevel baseband signal transmission is appropriate,
the signal of Figure 14-12 may
be transmitted directly. Note that
there is no energy at zero frequency and that low-frequency
components are of low amplitude.
Only slight signal impairment is
suffered when such a signal is
transmitted over baseband facilities which cannot pass direct
current and low-frequency components. This mode of transmission
(baseband) is used for transmit-

Frequency

-+

Figure 14-11. Spectral energy distribution, multilevel partial
response signal.

372

Signal Characterization

Vol. 1

ting the 772-kilobaud signal of
Figure 14-10 on microwave radio
systems. It is frequency modulated
in the FM transmitter along with
whatever speech channels are carried by the system.

Frequency ~

Figure 14-12. Partial response signal high-frequency lobes removed - timing signal
added at fl.

All signals in Figure 14-10 other
than the 772-kilobaud signal are
transmitted by VSB techniques.
These may be upper or lower sideband; a lower sideband version
with a vestigial upper sideband is
illustrated in Figure 14-13.
Phase Shift Keyed Signals

Signal transmission by phase
shift keying (PSK) techniques is
accomplished in the voiceband by
the use of data sets which code incoming binary signals into multilevel phase shifts of appropriate
carrier signals. In PSK transmission, sideband frequencies are
Frequency ---+
generated by the modulating signal
so that the bandwidth required is
Figure 14-13. Partial response signal
at carrier frequency _
equal to twice the highest frevestigial upper sideband. quency component in the modulating signal. The distribution of
energy in the modulated carrier wave follows a pattern like that
illustrated in F~gure 14-14.
Phase shift keying has advantage over other modes in certain
situations. In a band-limited channel, PSK signals are relatively
immuneto amplitude changes. The signal is transmitted at essentially
constant power. The mode lends itself well to the recovery of a
clock signal at the receiver and offers speed advantages by multilevel coding techniques. This mode has the disadvantage of being
sensitive to phase distortions, phase jitter, and impulse noise. These
impairments may affect the zero crossings of the signal.

Chap. 14

Data Signals

Ie

= carrier frequency

II

= highest frequency in

373

modulating signal

Figure 14-14. Power spectral s:fensity of a PSK data signal.

A number of successful PSK data sets and types of terminal equipment have been developed. One such arrangement is used to transmit
a number of telegraph signals simultaneously in a single voiceband.
Each signal is modulated to a separate part of the voiceband, and
the signals are combined by FDM methods. Some four-phase voiceband systems provide for the transmission of data at rates up to
2400 bits per second. The baseband signal phase-modulates a carrier
by -+-45 degrees and -+-135 degrees relative to its nominal zero-phase
condition. (Such a system, no longer used extensively, was also
developed to transmit digital data at 40.8 kb/s.) A newer voiceband
system using eight-phase modulation transmits data at 4800 and
9600 bits per second [11, 12].

frequency Shift Keyed Signals
Data sets have been developed to exploit the use of frequency shift
keying (FSK) techniques. In one such system 1200 Hz and 2200 Hz
were used to represent the "space" (no pulse) and "mark" (pulse)
signals, respectively. (Space and mark are terms handed down from
telegraph usage.) This system operated at about 1200 bits per second
over the switched public network and up to 1800 bits per second on
conditioned private lines. Later, more sophisticated terminal equipment utilized FSK techniques to achieve 2400 bits per second.

374

Signal Characterization

Vol. 1

These arrangements display most of the advantages of the PSK
mode of transmission and have the additional advantage of being
relatively simple to implement; circuits are readily designed. However, FSK signals have the usual feature of achieving high immunity
to noise at the cost of wider required bandwidths. As a result, the
FSK systems are commonly used in voice bands or less at low
signalling rates relative to those achievable with multivalued PSK
and ASK arrangements.
Many private line and switched network telegraph and
typewriter services are provided by FSK techniques. In
tion, some moderate-speed voiceband data is also transmitted
TOUCH-TONE signalling as a means of data transmission
effect, also a form of FSK.

teleaddiFSK.
is, in

Telegraph Signals. Telegraph signals are commonly transmitted at
various rates, including 75 and 150 bauds, by FSK techniques in
narrow channels which are combined into a voiceband by frequency
division multiplex techniques. Seventeen separate channels can be
provided with frequencies as given in the top portion of Figure 14-15
to transmit 75-baud telegraph signals. For 150-baud signals, the
channel assignments are shown at the bottom of the figure.

The binary (1 and 0) input signals are translated into FSK
signals at the terminal equipment. A 1, or mark, signal corresponds
to a frequency in the passband of the channel 35 Hz (for 75-baud
signals) or 70 Hz (for 150-baud signals) above the channel center
frequency. The 0, or space, signal is represented by a frequency
35 (or 70) Hz below the channel center frequency. The center frequency is not transmitted as a discrete signal.
Low-Speed Voiceband Data. Low-speed teletypewriter signals are provided in the voiceband by FSK techniques using 1070 and 1270 Hz
as the mark and space signals, respectively, for transmitting in one
direction, and 2025 and 2225 Hz for signalling in the opposite direction. This arrangement, in effect, provides equivalent four-wire
transmission and allows full duplex operation. Data rates vary from
about 100 bauds to 300 bauds.
Medium-Speed Data. Data at rates up to 1800 bits per second can be
transmitted in a voiceband by an arrangement that uses 1200 Hz
and 2200 Hz as the mark and space frequencies, respectively.

375

Data Signals

Chap. 14

SINGLE BANDWIDTH
Channel
number

1
2
3
4
5
6
7
8
9
10
11

12
13
14
15
16
17

Space
frequency

390
560
730
900
1070
1240
1410
1580
1750
1920
2090
2260
2430
2600
2770
2940
3110

Center
frequency

425
595
765
935
1105
1275
1445
1615
1785
1955
2125
2295
2465
2635
2805
2975
3145

Mark
frequency

460
630
800
970
1140
1310
1480
1650
1820
1990
2160
2330
2500
2670
2840
3010
3180

DOUBLE BANDWIDTH

21
22
23
24
25
26
27
28

610
950
1290
1630
1970
2310
2650
2990

680
1020
1360
1700
2040
2380
2720
3060

750
1090
1430
1770
2110
2450
2790
3130

Figure 14-15. Voice-frequency carrier data channel assignments.

TOUCH-TONE Signalling. TOUGH-TONE signalling, described briefly
in Chapter 13, was introduced initially as a means for transmitting
address signals from telephone station sets to the central office
switching machine. These signals may be impressed on the telephone
line while a connection is established. Since the TOUCH-TONE signals
fall in the voice-frequency band, they offer the possibility of being
used to transmit data [13]. Special receivers are provided for data
transmitted by TOUCH-TONE signalling.
14-3

ANALOG DATA SIGNALS

A number of voiceband analog data signals are transmitted by
FM techniques. Three of these are found in the plant in sufficient

376

Signal Characterization

Vol. 1

quantity to warrant individual description. In each case, signal
power is limited to -16 dBmO, long-term average. Many other signals
are transmitted in quantities too small to warrant individual characterization. Among these are several types of telemetry and telewriter
signals.
Medium-Speed Voiceband Data

One type of analog data signal transmission involves the translation of a 0 to +7 volt continuous signal from the customer to an
FM signal which is transmitted over telephone facilities in the voiceband. A zero-volt input signal is transmitted as a 1500-Hz signal on
the line, and a +7 volt signal is transmitted as a 2450-Hz signal on
the line; intermediate input voltages and line frequencies are linearly
related. The baseband signal may contain components from zero
frequency up to about 1000 Hz.
In the direction of transmission opposite to that used for data
transmission, a 60 ± 1 Hz signal is sent for synchronization. This
signal is translated to 600 Hz for transmission over the line. The
powers contained in the data and synchronizing signals are equal.
The data signal can be used for facsimile transmission with resolution equivalent to 100 lines per inch and at speeds of up to 180 lines
per minute for copy reproduced on 8-1/2 by 11 inch paper.
Low-Speed Medica I Data

Medical data such as electrocardiagrams and electroencephalograms can be transmitted over telephone facilities by FM techniques.
Input signals are accepted with components from zero to about
100 Hz and with amplitudes of -2 to +2 volts. Such signals
frequency-modulate a carrier at 1988 Hz; the carrier frequency
varies linearly with the input voltage at frequencies between -262
and +262 Hz relative to the carrier. A signal at 387 Hz is transmitted in the opposite direction to permit signalling from the receiver
to the transmitter.
One feature of this type of transmission that is different from
others is that the signal generated in medical electronic equipment
may be coupled to the telephone line electronically or acoustically.
The latter method has the virtue of allowing for portable equipment.

Chap. 14

Data Signals

377

The signal can be coupled to the line at any telephone connected to
the network.
low-Speed Ana log Data

Multichannel analog data transmission is provided in the voiceband at low speed by an FM arrangement utilizing carriers at 1075,
1935, and 2365 Hz. Each of these carriers may be frequency-modulated
by baseband signals having components from zero to 105 Hz and
amplitudes between -2.5 and +2.5 volts. A reverse direction signal
is used to permit the receiver to communicate with the transmitter
during data transmission. This arrangement is used to transmit
medical or other types of analog data.
REFERENCES

1. Mahoney, J. J., Jr. "Transmission Plan for General Purpose Wideband
Services," IEEE Transactions on Communications Technology, Vol. COM-14,
No.5 (Oct. 1966), pp. 641-648.
2. Fracassi, R. D. and F. E. Froehlich. "A Wideband Data Station," IEEE
Transactions on Communications Technology, Vol. COM-14, No.5 (Oct. 1966),
pp. 648-654.
3. Bell System Technical Reference PUB41005, Data Communications Using
the Switched Telecommunications Network (American Telephone and Telegraph Company, May 1971).
4. Bennett, W. R. and J. R. Davey. Data Transmission (New York: McGrawHill Book Company, Inc., 1965).
5. Ronne, J. S. "Transmission Facilities for General Purpose Wideband Services
on Analog Carrier Systems," IEEE Transactions on Communications Technology, Vol. COM-14, No.5 (Oct. 1966), pp. 655-659.
6. Bell System Technical Reference PUB21204, Data Set 203-Type (American
Telephone and Telegraph Company, June 1970).
7. Seastrand, K. L. and L. L. Sheets. "Digital Transmission over Analog Microwave Radio Systems," IEEE International Conference on Communications,
June 19-21, 1972.
8. Gerrish, A. M. and R. D. Howson. "Multilevel Partial-Response Signaling,"
IEEE Conference on Communications Digest, 1967.
9. Kretzmer, E. R. "Generalization of a Technique for Binary Data Communication," IEEE Transactions on Communications Technology, Vol. COM-14,
No_ 1 (Feb. 1966), pp. 67-68.
10. Bell System Technical Reference PUB41301, Data Set 301B - Interface
Specification (American Telephone and Telegraph Company, Mar. 1967).

378

Signa I Characterization

Vol. 1

11. Baker, P. A. "Phas&oModulation Data Sets for Serial Transmission at 2,000
and 2,400 Bits per Second," AlEE Transactions, Part 1, Communications and
Electronics, No. 61 (July 1962), pp. 166-171.
12. Schilling, D. L. and H. Taub. Principles of Communications Systems (New
York: McGraw-Hill Book Company, Inc., 1971).
13. Bell System Technical Reference PUB41802A, Data Couplers CBS and CBT
for Automatic Terminals (American Telephone and Telegraph Company,
Mar. 1971).

Signal Characterization

Chapter 15

Video Signals
A wide variety of video services is provided over the transmission
facilities of the Bell System. These vary from narrowband telephotograph service, operating in the voiceband, to multimegahertz
bandwidth television services provided for the television broadcast
industry and for educational, industrial, and private distribution
systems.
As in the transmission of other types of information, the transmitting and receiving equipment at both ends of a video transmission path must include transducers capable of translating one form
of energy to another. In this case, different values of luminance (light
intensity), together with color information in the transmission of
color television signals, are converted to electrical signals at the
transmitter; at the receiver, the transducer must translate the
electrical signal back to light signals so that the transmitted image
can be viewed or recorded on film or paper.
Many natural characteristics of the human recipients of video
information have influenced the design of transmitting and receiving
equipment as well as the design of the transmitted video signals.
Among these are the persistence of vision, the preferred viewing
distance of visual images, the resolution capability of the eye, the
human tolerance to departures from accurate color rendition, and
the effects on viewing preferences of ambient conditions such as
lighting [1]. These human factors have influenced the rate at which
picture images are transmitted; the format of color television signals;
the resolution and, therefore, the bandwidth of signals; and many
other aspects of video signal transmission.
15-1

TELEVISION SIGNALS

In 1970, the Bell System operated well over 100,000 route miles
of part-time and full-time television circuits. The majority of these

379

380

Signal Characterization

Vol. 1

were provided for network television broadcast signals* [2]. As a
convenience, the black and white (monochrome) signal is used here
as the basis of television signal description even though most television signals now transmitted in the United States are color. The
chrominance information in a color signal is regarded as being
superimposed on the monochrome signal and is so described.
Standard Monochrome Baseband Signals

Intra-urban transmission needs are nearly always provided in the
Bell System by baseband facilities. Interurban needs are usually provided by long-haul or short-haul microwave relay facilities; these are
usually fed by baseband facilities which interconnect the broadcaster's equipment and the terminals of the microwave radio system.t
The baseband signal received at the microwave system terminal
frequency-modulates the microwave carrier. Only the baseband
signal is characterized in detail here, although some attention is
subsequently given to the signal format used in commercial television
broadcasting.
The conversion of light signals to electrical signals and the reconversion to light signals at the receiver involves a scanning operation
which differs in details for different systems. However, all systems
must provide, in the scanning operation, for the synchronization of
the receiver with the transmitter (a coding process) ; they must also
provide for the conversion from luminance variations to electrical
signal variations (a modulation process).
Scanning and Synchronization. Figure 15-1 illustrates the scanning
pattern used for broadcast television signals in the United States.
The scanning mechanism causes the exploring element and the reproducing spot to move in synchronism across the image field and
the receiving field (picture tube) in nearly horizontal lines from
left to right. The scanning lines are started at the top; successive
*The signals described here have been standardized in the United States. Other
standards have been estabilshed elsewhere; e.g., 625-line, 50 frame-per-second
signals are used in Europe. As a result of satellite transmission, Bell System
facilities are being adapted for transmission of such signals. Conversion of the
signal to the USA standard is presently the responsibility of the broadcaster.
tCoaxial cable systems were once used for televislion signal transmission, but
they are no longer used for this purpose in the Bell System.

Chap. 15

Video Signals

Image
field

Received
image

\

I

381

luminance

Exploring
element

information

,r----------------,\

Reproducing
spot

t

Scanning synchronizing information

Scanning
pattern
generator

_--J

'",,'a,.d H.'d,
Vertical flyback

Figure 15- 1. Broadcast te,levision scanning process.

scans are made at successively lower parts of the field until the bottom
is reached. The spots are then returned to the top to begin a second
field. Succeeding scans in alternate fields are interlaced. The interlaced
scans of two successive fields make up a frame.
The exploring element at the transmitter is caused to scan the
image field by the scanning pattern generator. The scanning pattern
must cover every part of the image in a systematic and specified
manner. Information regarding the location of the exploring spot
and the direction in which it is being moved are coded at the transmitter and sent to the receiver so that the reproducing spot can be
located in the received image field at a position corresponding to
that of the exploring element in the transmitter. This process of
synchronizing the receiver to the transmitter is also illustrated
functionally in Figure 15-1.

382

Signal Characterization

Vol. 1

While Figure 15-1 shows the transmission of scanning/synchronizing
and luminance information over separate channels, the information
is in reality combined into one composite signal for transmission or
broadcast. The two kinds of information, separated in polarity and
time, are illustrated in Figures 15-2, 15-3, and 15-4.

r

Horizontal line

scanning interval
H= 63.5 fls

~

j.-

Picture signal
interval (52.3 fls)

- - - - Picture white

_ _- 1 - _

Blanking pulse

Horizontal
line synchronizing
pulse (4.8 fls)

Black

Picture signal

Figure 15-2. Monochrome television horizontal line scanning and synchronization.

Equalizing
pulses

Vertical
synchronizing.
pulses

Equalizing
pulses

Figure 15-3. Monochrome television vertical synchronization.

383

Video Signals

Chap. 15

Maximum luminance,
reference white

100
80


]

60

a..

40

0

20

Picture signal

E

.~
(;

Qi

c:::

_

0

_ _

-- -

Minimum luminonce,
reference black
Blanking

-20
-40

Time (not to scale) ----.

Figure 15-4. Monochrome television signal, relative amplitudes.

Consider first the horizontal line scanning function illustrated in
Figure 15-2. The total line scanning interval, H, is 63.5 JI-s, equivalent
to about 15,750 line scans per second. Of this interval, 11.2 ,us are
assigned to a blanking pulse. The blanking pulse interval is divided
into a 1.6-,us front porch interval, a 4.8-,us back porch interval, and
a 4.8-,us horizontal synchronizing pulse interval. The porches isolate
the synchronizing pulse from transients or overshoots of the picture
signal. The synchronizing pulse, recognized at the receiver by its
polarity and duration, triggers circuits that drive the reproducing
spot at the receiver to the left side of the image field (flyback).
During the blanking pulse interval, the receiving tube is normally
blanked out; the luminance of its reproducing spot is driven into
the ultrablack region so that the synchronizing pulse and the flyback
of the spot are not visible. After each blanking pulse fnterval, the
scanning circuits drive the exploring and reproducing spots in
synchronism across the image from left to right.
When the last line of a field scan is completed, the scanning pattern
enters a vertical blanking interval as shown in Figure 15-3. This
interval is about 1200 JI-s long, equivalent to the duration of about
20 horizontal sc·an intervals. During a part of this interval, a number
of vertical synchronizing pulses, each about 25 p,s long, drive the

384

Signal Characterization

Vol. 1

spot to the top of the screen (vertical flyback) to begin a new field
scan. A series of horizontal pulses (called equalizing pulses), transmitted at twice the normal line scan rate, precede and follow the
vertical synchronizing pulses. Following the second burst of these
equalizing pulses is a series of horizontal synchronizing pulses transmitted at the normal scan rate as a part of the vertical blanking
interval. The equalizing and normal horizontal synchronizing pulses
transmitted during the vertical blanking interval are provided to
condition the synchronization circuits of the transmitter and receiver
so that the two are indeed in synchronism and to guarantee that the
interlace pattern is properly implemented in successive field scans.
The timing of the vertical blanking intervals is such that a field
is produced every 1/60 second. The interlacing of the next field with
the first makes up a frame, one of which is produced each 1/30 second.
This 30-per-second frame rate, combined with the 15,750 horizontal
line rate, results in a picture nominally formed of 525 lines per frame.
Luminance Signal. As shown in Figure 15-1, an exploring element
measures the intensity of the light at a given spot on the image to
be transmitted. The light intensity is converted to an electrical
signal whose amplitude is a specified function of the measured
intensity. This electrical analog of the light intensity is transmitted
to the receiver where the inverse process, the conversion of the
electrical signal to appropriate light intensity value,s, takes place.
The reproducing spot at the receiver then illuminates the receiving
mechanism to the proper intensity.

If the image being scanned at the transmitter is one having no
motion, the light intensity at a given paint and its electrical signal
counterpart depend only on the position of the exploring element.
Thus, the signal can be regarded as a function of two variables
which describe the two-dimensional image field. If the image at any
spot involves time variations of light intensity, say due to motion,
the luminance signal is a function of time also, and the corresponding
electrical signal is a function of three independent variables.
The electrical signal amplitude is defined by a scale that was
originally standardized by the IRE (now IEEE). The scale*, used
as a convenience in examining television waveforms on an oscilloscope, is illustrated in Figure 15-4.
*This scale can be derived from Figure 7, Reference 2.

Chap. 15

Video Signals

385

Bandwidth and Resolution. During the development of television, subjective viewing tests were used to determine that a bandwidth of
about 4.2 MHz results in a satisfactory received television image.
This conclusion involved the combined evaluation of many parameters
such as acceptable vertical and horizontal resolution, frame and field
rates, equipment costs, etc. Bandwidth in excess of 4.2 MHz does
provide somewhat better performance, but the improvement is
considered uneconomical.

Low-frequency transmission requirements are set primarily by the
low rate of 60 fields per second. Vertical blanking pulses appear in
the complex signal waveform at that rate, and due to the complexity
of the signal, there are also sideband components around that frequency. As a result, good transmission response must be provided
to nearly zero frequency in order to maintain good phase response
at and near 60 Hz.
As mentioned, the required bandwidth was determined by subjective tests. These were, in turn, conducted on the basis of previous
judgments regarding the desirable vertical and horizontal resolution
that was to be provided. These parameters, bandwidth and resolution,
are importantly and intimately related.

Vertical Resolution. As previously described, the scanning process
produces a standard pattern of 525 horizontal lines per frame. The
picture width is 4/3 its height. This ratio is defined as the aspect
ratio. Horizontal lines are lost during the vertical blanking period,
reducing the effective (visible) number of lines to about 93 percent
of the total. Further loss of resolution, inherent in the scanning
process, is due to the finite width of the scanning line and to the
shape of the scanning spot. The relative position of horizontal image
lines and scanning lines affects reproduction. In the extreme, if the
image has alternate black and white lines of the same width as the
scanning lines and coincident with them, a faithful reproduction
results; however, if the same scanned lines were centered on the
boundary between scanning lines, they would produce a flat gray
picture. On the average, this effect decreases vertical resolution to
about 70 percent. The net effect, then, is that the number of vertical
elements which can be resolved is

nv

== 525 X 0.93 X 0.7 ~ 342.

386

Signal Characterization

Vol. 1

Horizontal Resolution. Horizontal resolution is determined by the
highest frequency component that can be resolved along a line.
Assume that a simple sinusoid generates a series of black and white
dots along the line. If spot size is not limiting, the finest detail that
can be resolved is determined by the highest frequency that can be
transmitted. If the horizontal resolution is to be about equal to the
vertical resolution, the number of picture elements per line scan
should be nh == 342 X 4/3 == 456 (the multiplier of 4/3 is used to
account for the aspect ratio).
A sinusoid that would generate 456 alternate black and white dots
would go through 228 cycles along a line. As shown in Figure 15-2,
the duration of the visible portion of a line scan is about 52.3 J-ts.
Thus, to satisfy the criterion that horizontal resolution should be about
equal to vertical resolution, the top transmitted frequency should be
It == 228/52.3 ~ 4.3 MHz, a value close to that mentioned earlier,
4.2 MHz, obtained from subjective tests.
Spectrum. The line scanning rate of a monochrome television signal
determines to a great extent the distribution of energy in the
signal spectrum. Thus, strong signal components are found in the
signal at 15,750 Hz; since the signal waveform is complex, many
harmonics of this fundamental are also produced. The spectral distribution is illustrated in Figure 15-5. Each component varies with
time by approximately ±3 d'B according to picture content and
motion; average values are illustrated. No voltage is shown at zero
frequency because the amplitude of that component is under design
control and is related to the design of the transmission circuits used.
However, it is customary to clamp the signal so that the dc component is relatively constant in order to avoid excessive base-line
wander [3]. Note that the envelope of the distribution decreases
at a rate of 6 dB per octave; i.e., for each doubling of the frequency,
the line scan component is about 6 dB lower (one-half the voltage).

The 60-per-second field frequency generated by the vertical blanking pulses also influences signal energy distribution. These blanking
pulses produce upper and lower sidebands of 60 Hz and 60-Hz
harmonics about each multiple of the line scanning frequency.
Signal Amplitudes. In television signal transmission, amplitudes are
limited by signal-to-noise and system overload considerations just as
in any other form of signal traJ?smission. These limitations are ex-

Chap. 15

387

Video Signals
"0c

Cl
... 'Ii;
II> 0
Q.II>

_"'0

(5 '>
>-

-20
-30

.. 0

E.=

... 0
~

..Q

-40

>

~-""

g

-50

II> Q.

6

..0
co";'
"'0 -""
C

II>
Q.

-60
-70
10

100

1000

10,000

Frequency (kHz)

"0c
~

Cl

(a) Envelope
-20

';n
II> 0
Q.II>

.=72
o >

>-

.. 0

-30

E.=

... 0

>

~-""

~i6

-40

..0
co";'
"'0-><

cII>

Q.

-50

5

10

15

20

25

Frequency in multiples of
line scan frequency

(b) Typical spectrum

Figure 15-5. Monochrome television signal voltage spectrum.

pressed in terms of average, peak, or single-frequency power at
specific TLPs in the telephone system if the signal parameter can
be translated to the voiceband. However, TLP relationships cannot
usually be directly applied if the signal is wideband (as in television),
i.e., if it occupies more than a telephone channel bandwidth.
Generally, television signal amplitude measurements are more
conveniently expressed in voltage than in power. It is important,
therefore, to recognize the voltage-impedance-power relationships
that exist in television circuits and to recognize the complications
inherent in properly translating the voltage expressions and their
points of application to the TLPs used in telephone system operation.
Television signal transmission in the Bell System is controlled
from a television operating center (TOe), where signals are re-

388

Vol. 1

Signal Characterization

ceived at baseband from the broadcasters. It is from such a center
that signals may be switched to other baseband circuits for local distribution or pick-up and/or to terminal locations for transmission
over the microwave radio channels used in the makeup of the television network in the United States. The relation of the TOe to the
network is illustrated in Figure 15-6.
In order that the baseband and microwave radio transmission
system designs may properly take into account the amplitudebandwidth-spectral energy distribution relationships, television signal
amplitude is maintained at one volt peak-to-peak into 124 ohms at
the TOe. While it is never referred to as such, this point is somewhat
analogous to the O-dB TLP in the telephone network. It is sometimes
called the O-dBV point.
Baseband Color Signals
The National Television System Committee (NTSC) was formed
by the television industry during the early 1950s [4] for the purpose

Studio

Microwave
terminal

-< .........1---

Broadcaster's
radio
transmitter

-{>Studio

Microwave
terminal

Figure 15-6. Typical intracity television network layout.

Mobile
studio

Baseband
transmission
facility

Chap. 15

389

Video Signals

of developing a set of color television standards that would be compatible with existing mO:Qochrome standards. The signal format that
finally evolved is one that superimposes information regarding the
image color content on the monochrome luminance signal.
While luminance is transmitted as previously described for a
monochrome picture signal, chrominance (hue and saturation) must
be coded for transmission and is accomplished by modulating a carrier
signal at 3.579545 MHz. The amplitudes and relative phases of this
carrier and its sideband components are carefully controlled and
together carry the necessary color information.
Scanning and Synchronization. The scanning process is identical to
that used for monochrome signal transmission. The color carrier at
the receiver is synchronized to that of the transmitter by means of a
burst of the color carrier freqlfency superimposed at a reference
phase on the back porch of each horizontal synchronizing pulse. The
burst signal contains about nine full cycles of carrier frequency (a
minimum of eight) as shown in Figure 15-7. The phase relationship
of the color carrier and its sidebands with respect to these color
bursts determines the hue of the color. A scanned line is also
illustrated in Figure 15-7 to show how the color information modifies
the normal monochrome luminance signal.
Spectrum. Concentrations of energy are found at line scan fr€quency multiples above and below
the color carrier. The color signal
carrier, 3.579545 MHz, was chosen
as an odd multiple of one-half the
monochrome line rate *, so that the
color signal components fall in the
spectral spaces between components of the luminance signal. The
power in chrominance signal components is 10 to 15 dB lower than
in the corresponding components of
the luminance signal. The spectrum
of a color signal is illustrated in
Figure 15-8.

luminance
Color burst
(8 cycles minimum)

Horizontal
line synchronizing
pulse

Figure 15-7. Color television signal
waveform.

*For color signals, the line rate is 15.734264 kHz. This frequency is used to
avoid a high-frequency multiple of 60 Hz.

Signal Characterization

390

Vol. 1

Note:
Spacing and amplitudes of line
scan components are not to scale.

t

_

1

Color
subcarrier

luminance signal

IZ2ZZZZZI Chrominance signal

Q)

]
·c

Ol
0

E

.~
-0

a;
0::

0

2

3.58

4

Frequency (MHz)

Figure 15-8. NTSC color TV spectrum illustrating interleaving of monochrome and
color line scan components.

Broadcast Sig na Is
Baseband monochrome or color television signals are processed for
broadcasting in accordance with standards specified by the FCC [2].
The baseband audio signal, which frequency-modulates a carrier at
5.75 MHz, is added to the bas·eband video signal; the composite
video jaudio signal is then used to amplitude-modulate a carrier of
assigned frequency in the radio-frequency spectrum. The channel
assignments in the RF spectrum, each 6 MHz wide, are shown in
Figure 15-9. The assigned carrier frequency for each channel is
located 1.25 MHz above the bottom frequency assigned to the channel.
The transmitted signal is a truncated double-sideband, amplitudemodulated signal with transmitted carrier as illustrated in
Figure 15-10: The overall transmission plan specified is one involving
vestigial sideband transmission. As shown in Figure 15-10, there is
no vestigial roll-off shaping at the transmitter. Thus, vestigial
shaping must be provided in each television receiver. This mode of
transmission tends to optimize overall signal-to-noise performance
in the channel.
At present, it is general practice in the Bell System to transmit
the audio signal over facilities separate from those used for the video
signal. Several methods of combining the signals have been tried, in-

Video Signals

Chap. 15

FREQUENCY
BAND
(MHz)

CHANNEL NO.

..
2. . . . . . .
.....
3 ........ .
.... . ... . .... .
4
........... .
5
. . . . . . . . . . . ..
6
...
7
8 .... . ....... .. .
9 . . . . .. . . . . . . . . .
10.

.

.

.

'

0.,

11.

12
13.
14.
15
16
17.
18
19.
20.
2122.
23
24.
25.
26.
27.
28
29
30
31
32
33
34

...
..........

.

..
......

•

.

.

......... .

...... . . . . . . . . . . ..
.. .
...... . . .. ... .
.. . . . . . . . . . . . . . . . .
.. .
.. .
. .....
.. .
.. .
.. .
.........

.

..... .
..... . . . . .

..

.

.

..

.

......... . ...

.

. ...

. ....

.

54-60
60-66
66-72
76-82
82-88
174-180
180-186
186-192
192-198
198-204
204-210
210-216
470-476
476-482
482-488
488-494
494-500
500-506
506-512
512-518
518-524
524-530
530-536
536-542
542-548
548-554
554-560
5€0-566
566-572
572-578
578-584
584-590
590-596

391

CHANNEL NO.

35 . . . . . . . . . . . . . . . . . . .
. .........
36 .
. . . . . .
37 .
38 . . ..
. ....... . ...
39 .
40
41
Li2 .. . . .... .
...... . ... . . ...
43.
44
. . . . . . ...
45 .
46. .. . . . . . . . . .
. ....
47. .. .
..........
48
49. .. . . . . . . . . . . . . . .
50 .. ....
. ....... .
51- . . ... . .. .
52. .. . . ..... . . . . . .
...
53
. .....
54. .. .
. . . . . . ' . ........
55
56. .. . . . . . . . . . . . . . . . . .
. . . . . . . ...
57.
58 . .. . ...... . . . . . . . . . .
59 . . ..
60
. . ...
. ....
61
62.
. . . . . . . ...
63 ..
..........
64
.....
65
.........
66
67 . .. . . . . . . . . . ...
68
.'

,

.'

'

'"

.

.

FREQUENCY
BAND
(MHz)

596-602
602-608
608-614
614-620
620-626
626-632
632-638
638-644
644-650
650-656
656-662
662-668
668-674
674-680
680-686
686-692
692-698
698-704
704-710
710-716
716-722
722-728
728-734
734-740
740-746
746-752
752-758
758-764
764-770
770-776
776-782
782-788
788-794
794-800

Figure 15-9. FCC radio spectrum broadcast television channel assignments.

eluding one that involves the pulse amplitude modulation of the audio
signal and its super-position on the front porch of the video signal.
N one of these has proved to be satisfactory. Practical means are still
being explored so that the two signals may be transmitted on the same
facility without undue penalty in cost, performance, or bandwidth.

Signal Characterization

392

Vol. 1

1.0

~

.2

II

d;
o ...

-0

.~

... 0

E
::>
E

U

~
::>

';C,-g

o a.
E~

0.0 ----~-r___'L..---..-----_r_---_r_--~_r_...1.--.3Io.-_ro

o

0.5

-+t

1.25

2

4

~;~i!~1:---3.579545MHZ~~1

.

5.45
II

5.75 6
II

t==::::::~..._

~-----------6MHz-----------~~.

Note: Not drawn to scale

Figure 15-10. Idealized televis,ion channel amplitude characteristic - transmitter.

Closed Circuit Signals

The Bell System transmits a variety of closed circuit signals such
as industrial television (lTV) and educational television (ETV) as
well as broadcast-type signals transmitted over community antenna
television (CATV) systems. Because these are closed circuit arrangements, FCC standards need not always be met in all respects; however, the signal format is sometimes designed to meet FCC standards
so that standard television receivers can be used for viewing.
Industrial Television. Industrial television systems are always operated on a closed circuit basis; that is, lTV signals are not transmitted
over normal broadcast facilities. Because of this, the scanning and
synchronizing mechanisms for lTV transmitting and receiving equipment are often l'ess sophisticated than those required for broadcast
television, and less operating margin may be provided. Interlaced
scanning is often not used because transmission objectives are less

Chap. 15

Video Signals

393

stringent than in other types of services. However, the bandwidth
provided is usually about equal to that used for broadcast quality
service. Amplitude control is provided at a TOC or equivalent when
such signals are transmitted over Bell System facilities.
The overall effect is that for transmission analysis, an lTV signal
may safely be assumed to be equivalent to a broadcast quality television signal. Audio signals are transmitted only as required and
usually not in accordance with FCC standards for broadcast TV
signals.
Educational Television. While -educational television network arrangements may be quite different from standard broadcast TV network
arrangements, the receiving equipment is often a standard television
receiver; therefore, the signal format is usually identical to the
standard signal previously described. Sometimes, ETV signals are
transmitted over cable systems which provide six channels. At the
viewing locations, carrier-to-baseband converters are used with baseband viewing sets.
Community Antenna Television. In CATV systems, broadcast signals
are received at a common point and distributed by cable distribution
arrangements to CATV subscribers. In such systems the signal
format is again generally constrained to the standard broadcast
format by the use of standard television viewing sets. Two exceptions
are found. First, the distribution system need not have the same
total band as is assigned in the radio spectrum although the FCC
does prescribe a minimum of 20 channels. Thus, a limited number of
channels might be distributed to the CATV subscribers. Second, to
ease the design of amplifiers in the distribution system, the sound
signal is usually transmitted at a lower amplitude relative to the
video signal than in normal broadcast practice. This is accomplished
at the antenna location ("head end") of the CATV system by
separating the two signals, demodulating the audio signal, and then
remodulating and recombining at the new relative amplitudes.

15-2

PICTUREPHONE SIGNALS

PICTUREPHONE service is now being introduced in the Bell
System. A signal format has evolved that provides satisfactory results, but bandwidth requirements are high. Evaluations of all aspects
of this service are continuing with the objective of providing

394

Signal Characterization

Vol. 1

more economical modes of transmission. A brief description of the
PICTUREPHONE signal as it is presently constituted is given
here [5]. Significant changes in the signal format are likely in the
future.
The basic methods of transducing a picture to an electrical
signal and then back to picture information are very similar in
PICTUREPHONE service and in television. The differences are in
the details. The standards that have been established to date provide
full motion capability (adequate, for example, for lip reading);
resolution is sufficient for a life-like image of the face.
Figures 15-11 and 15-12 depict the baseband PICTUREPHONE
signal. One significant difference in the treatment of this signal is
that high-frequency energy in the video signal (not in the synchronizing pulses) is pre-emphasized in the transmitting station set and
de-emphasized in the receiving station set. As a result, the received
signal-to-noise ratio is significantly improved, but there are overshoots in the signal which must be considered when PICTURE PHONE
signal transmission analyses are undertaken. Margin must be provided so that these overshoots do not overload carrier systems, and
clipping levels must be carefully established so that the picture quality
is not excessively degraded.
Scanning

The scanning process for PICTURE PHONE signals follows that
used for television in that the image is scanned from !tft to right
and lines are formed from the top of the image to the bottom. The
detailed dimensions of the scanning pattern are given in Figure 15-11.
There are nominally 60 fields per second with alternate fields Band
A interlaced, thus providing 30 frames per second. Note that there
are 125.5 active lines per field and the equivalent of eight horizontal
lines per vertical synchronizing pulse interval. The total number of
horizontal scans, then, is 267 per frame.
Modulation

Picture signal modulation of a scanned line is illustrated in
Figure 15-12. The relative amplitudes of synchronizing and picture
signals are shown on a relative amplitude scale similar to that used
for television (see Figure 15-4). However, the peaking effect of

n

:r
Q

l'
I.

~I.

Field B

I

125.5 active
1.........- - - video lines

Vertical blanking
(8 lines)

~ •

I
~

•

~I

Field A

I
• •

125.5 active lines

01

Vertical blanking
(8 lines)

~

I

Receiver
vertical retrace

··ri

)'
luminance
information
Top of scene

<
a:
CD
o

(J)

cO·

Overshoot
due to
pre·emphasis

:::l
Q

Horizontal sync pulse

Vi"

Bottom of scene

Time

--+

Front~/

porch

2.93 JLS

Back
porch

1 r-I·.· I •I
8.79 JLs

~.

7.78 JLs

Figure 15-11. Composite PICTUREPHONE video signal showing scanning intervals.

w
~

396

Vol. 1

Signal Characterization

I/
Clipping
voltage......

1.4

Pre-emphasized video

•
I

line rate

\+-------+--- (125 p.,s) - - - + I
....._ _ _ _ _+ - _ Scanned video - - +
(111.3 p.,s)

Transmitted video ~
(105.5 p.s)

-0

~

'5
Il-

'5
o

g

Sync
pulse
tip---+-

0.2

Black--'

o

2.93 p.s

.2

.S
Q)

-0

.~

~

E

c

.~

White ~ -0.6

Video blanking pulse
(19.5 p.s)

o

a;
co:

Clipping
_ 1.9
voltage ......

Figure 15-12. PICTUREPHONE slgnal line format.

pre-emphasis, previously mentioned, is seen to cause signal excursions
well in excess of the normal sync-tip-to-reference-white voltage.
Amplitude

The PICTUREPHONE signal amplitude is controlled at the O-dB
PICTUREPHONE transmission level point (0 PTLP). For this
service, the 0 PTLP is defined as the output of the central office loop
equalizer in the direction of transmission from the station set to the
central office. At the 0 PTLP, the signal is maintained at a nominal
value of 0_8 volts peak-to-peak across 100 ohms. *
*This value is subject to interpretation due to the fact that the signal is preemphasized at the 'Station set. Amplitudes, such as that given, are based on the
equivalent, de-emphasized signal format.

Chap. 15
15-3

Video Signals

397

TElEPHOTOGRAPH SIGNALS

In spite of the fact that telephotograph is one of the oldest of the
video services in the Bell System, dating back to the early 1930s,
and in spite of the fact that little new development work has been
done in recent years, many thousands of miles of telephoto graph
circuits are still in operation. These are used primarily to satisfy
the needs of the news photo services [6].
Several different equipment types are currently in use, but the
signal format is sufficiently similar that one general description
should suffice. The systems of interest operate on private line voiceband circuits that are equalized to meet the necessary transmission
requirements for satisfactory picture transmission and reception.
Scanning

In telephotograph systems, the light beam used to scan the image
is held in a constant position. The picture being scanned is wrapped
around and fastened to a cylinder which is rotated and advanced
axially by a synchronous motor.
The scanning light beam, modulated by the various shades in
the picture, is reflected from the image surface into a photoelectric
cell. The scanning density and rate achieved by the optical mechanism
are 100 lines per inch and 20 inches per second (circumferentially),
respectively. One vertical inch of picture, up to 11 inches wide, is
scanned in one minute.
Synchronism is achieved by absolute control of the motor speed
at the transmitter and at the many receivers which can be operated
simultaneously. The control is maintained by a 300-Hz tuning fork
which is housed in a temperature-controlled enclosure. The accuracy
of synchronization is maintained to within a few parts per million.
The holding bar used to clamp the image picture in place on its
cylinder is made of highly polished metal. The high-amplitude pulse
resulting from the reflected light from this bar is used to make the
initial adjustment of the receiver to start the receiver motor in step
with the motor at the transmitter.

398

Signal Characterization

Vol. 1

Bandwidth

The scanning and modulation processes just described are accomplished by the intensity modulation of a light beam which is itself
varied by a sine wave function at a rate of 2000 Hz in some systems
and 2400 Hz in others. The resulting modulated electrical signal at
the output of the photoelectric cell is then transmitted as, a doublesideband signal (2000-Hz carrier) or a vestigial-sideband signal
(2400-Hz carrier). Double-sideband signals are transmitted at a
somewhat lower rate than that given previously which applied to
the VSB mode of transmission. The band must be gain and delay
equalized between 1000 Hz and 2800 Hz. This useful band, l?OO Hz
wide, is capable of producing the resolution demanded by the scanning
rates given.
REFERENCES

1. Glasford, G. M. Fundamentals of Television Engineering
McGraw-Hill Book Company, Inc., 1955).

(New York:

2. Federal Communications Commission. Rules and Regulations, Vol. III (March
1968), pp. 234 B, C, and D, and 259-267.

3. Doba, S., Jr. and J. W. Rieke. "Clampers in Video Transmission," Trans.
AlEE, Part I, Vol. 69 (1950), pp. 477-487.
4. Fink, D. G., Editor. "Color Television Standards," Selected Papers and Records
of the National Television System Committee (New York: McGraw-Hill Book
Company, Inc., 1955).

5. Baird, J. A. et al. "The PICTUREPHONE System," Bell System Tech. J.,
Vol. 50 (Feb. 1971).
6. Reynolds, F. W. "A New Telephotograph System," Bell System Tech. J.,
Vol. 15 (Oct. 1936), pp. 549-573.

Signal Characterization

Chapter 16

Mixed Signal Loading
The signals described in Chapters 12 through 15 are found in
various facilities of the Bell System, but seldom is anyone
type of signal the only one ever found at any given location or
facility. In some instances, a variety of signal types are simultaneously transmitted on the same facility; in other instances, the type
of signal transmitted on the facility changes with time. Broadband
carrier systems, for example, may simultaneously carry speech,
narrowband and wideband data, facsimile, PICTUREPHONE, and
address and supervisory signals. A single trunk, on the other hand,
may carry speech, data, facsimile, and address and supervisory
signals at different times.
Important combinations or mixtures of signals must be characterized primarily so that the composite signal may be properly
related to overload phenomena in carrier transmission systems. In
some cases, overload effects are relatively minor, causing only partial
deterioration of performance. However, the effects are accentuated
with increased signal amplitudes so that transmission may be seriously
impaired and, ultimately, the entire system may fail. Any study
of mixed signal loading must then be concerned with the characterization of signals known to be transmitted simultaneously in
today's environment. In addition, the characterization must be in
terms that permit continuous re-evaluation of signals to account for
the effects of new technology, the introduction of new instrumentalities or new services, or the implementation of new policies such
as interconnection with customer-provided equipment.
Since a very large number of combinations of signal loads may
occur in broadband systems, it is extremely difficult to characterize
mixed signal loading effects explicitly. Intermodulation phenomena,
whose effects are accentuated as signal amplitudes increase, can
produce noise, crosstalk, or other distortions such as signal com-

399

400

Signal Characterization

Vol. 1

pression. These are due to the nonlinear input/output characteristics
of active circuits and devices, such as the amplifiers used to compensate for media losses in transmission systems. All transmitted signal
components interact to form new, unwanted signals. In some cases,
these combine to form a noise-like impairment. In other cases, components of the interference signal fall directly upon and in phase
with the components of a particular wanted signal so that its internal
magnitude relationships become distorted due to the fact that some
components are more distorted (compressed) than others. Sometimes, signal components combine with pilot or controi frequencies
to fall into other channels as intelligible crosstalk.
16·1

MIXED SIGNALS AND OVERLOAD

As previously mentioned, the effects of intermodulation are sometimes relatively minor and result in only partial deterioration of
performance; but as amplitudes increase, transmission may be
seriously impaired. To avoid this, the signal load on a system must
be carefully controlled and limited to well-defined maximum values.
When distortion or noise results from excess amplitudes and performance is seriously impaired, a transmission system is said to be
overloaded. If the effects are so serious that communication is impossible, the phenomenon is sometimes called hard overload. Often,
the effects of overload must be evaluated statistically. Signal and
system characteristics interact in ways that are strongly dependent
on how long and by how much a signal exceeds its nominal value,
how the system responds to the signal, and how quickly the system
recovers from the overload condition.
Signal load criteria have been established to guard against overload. In general, the simplest statement of these criteria for signals
transmitted in the Bell System is that the long-term average power
in any 4-kHz band shall not exceed -16 dBmO. The statistical
properties of individual types of signals are applied to specific
situations to allow higher' amplitudes for short time intervals. The
most important of these statistical properties are the variations of
signal amplitude with time and the activity factors that may properly
be applied to various modes of transmission for each signal typesimplex, half duplex, or duplex.
The same broad criterion is applied to signals requiring more than
a 4-kHz frequency allocation, but it is expressed somewhat differently.

401

Mixed Signal Loading

Chap. 16

In this case, the total power in the signal may be no greater than
the long-term average power resulting from a signal of -16 dBmO
in each of the displaced 4-kHz channels. Again, the random nature
of the broadband signal amplitude variations sometimes permits
excess amplitudes for short periods of time or in restricted portions
of the band.
Since many of the more serious problems relating to system loading are experienced in wideband systems capable of transmitting
signals in 600-channel blocks (a mastergroup) or more, the following considerations of signal loading are mastergroup-oriented. For
comparison purposes, the mastergroup speech signal load is first
analyzed, and mixed signal loads are then compared to this analysis.
For systems wider or narrower than one mastergroup, the same
approach may be used by extrapolation and with appropriate care
in the treatment of variables that are functions of system capacity.
16-2

MASTERGROUP SPEECH SIGNAL LOAD

Consider a 600-channel mastergroup loaded with speech signals only.
To determine overload relationships, it is necessary to know the average power and the peak power in the composite signal. The average
power at 0 TLP (that exceeded no more than 1 percent of the time
during the busy hour) may be computed by using Equation (12-5):
P av

== VOc -

1.4 + 0.1150-2 + 10 log TL + 10 log N + del

dBmO.

From Figure 12-4, the average value of VOc for toll calls is -16.8 VUe
Since this value must be converted to its equivalent value at 0 TLP,
allowances of -3 dB for toll connecting trunk loss (VNL + 2.5 dB)
and + 2 dB for conversion from the outgoing toll switch (-2 dB
TLP) are added. Thus, VOc == -17.8 vu and, from Figure 12-4, it
has a standard deviation of 6.4 VUe A standard deviation of 1 dB is
also allowed for toll connecting trunk loss variations. Thus, (}" ==
Y6.42 + 12 == 6.47 vu, and 0.115 (}"2 == 4.8 VUe The activity, TL, is taken
as 25 percent; thus 10 log TL == -6 dB. The number of channels, N,
is 600; 10 log 600 == 27.8 dB. The value of del, which accounts for the
maximum number of active channels, is found in Figure 12-6 to be
+0.7 dB for a 600-channel mastergroup. If these values are summed,
the average power in a mastergroup of 600 telephone channels
carrying speech only is found to be
P av == - 17.8 - 1.4 + 4.8 - 6 + 27.8 + 0.7 == + 8.1

dBmO.

402

Vol. 1

Signal Characterization

The peak power can be determined from the average power by
adding a correction factor, Ac 2, which represents the rms signal
amplitude exceeded 0.001 percent of the time. Thus,

P max

== P av + Ac2

(16-1)

dBmO.

For N == 600 channels and TL == 25 percent, the number of active
channels exceeded no more than 0.001 percent of the time is found
from Figure 12-6 to be Na == 175.55. From Figure 12-7 the corresponding value of AC2 is about 13 dB. The 0.001 percent peak, then,
is found from Equation (16-1) as
P max

== P av +

Ac2

~

+ 8.1 + 13

~

+ 21.1

dBmO.

Note in Figure 12-7 that for large numbers of active channels
(Na > 100), Ac2 approaches a constant value of about 13 dB. This
relationship permits the use of Gaussian noise, which has the same
peak factor, as an excellent simulation for a busy hour, multichannel
telephone load for large systems.
The peak power capacity required of a transmission system
== P max - 3 dB) is usually expressed in terms of the peak power
of a single-frequency sinusoid applied at 0 TLP [see Equations (12-6)
and (12-7)].
(P s

16-3

MASTERGROUP MIXED SIGNAL lOAD

In the present plant, no mastergroup can be expected to carry
speech signals only. Thus, it is necessary to consider the effects of
mixing various other types of signals with speech signals.
Speech and Idle Channel Signals

The signalling system most commonly used on trunks employing
broadband carrier facilities is the 2,600-Hz SF system described in
Chapter 13. When a trunk that is so equipped is idle, 2600 Hz is
transmitted continuously as a supervisory signal at an amplitude
of -20 dBmO. Thus, theoretically, a mastergroup may carry 600
such randomly phased idle channel signals (translated to carrier
frequencies). In this case, the total average power in the mastergroup would be equal to - 20 + 10 log 600 == +7.8 dBmO, about
the same as the previously determined average power in a master-

Mixed Signal Loading

Chap. 16

403

group carrying only speech signals. However, activity factors affect
the mastergroup signal in a complicated manner when the combined
speech and idle channel signal load is considered.
Average Mastergroup Power. It was shown previously that the busyhour speech (only) load is +8.1 dBmO if the speech activity factor,
TL, is 0.25. That value of TL is, in turn, based on a trunk efficiency
factor, Te, of 0.7. Thus, 180 trunks [600 (1 - 0.7)] may carry
idle channel supervisory signals. The power in these signals totals
-20 + 10 log 180 == +2.6 dBmO. When this power is combined
with the speech power by power addition (Figure 3-5), the total
busy-hour load may be found as 2.6 +" 8.1 ~ 9.0 dBmO.
II

While the ratio of speech and idle channel signals in a mastergroup varies from the busy hour to the nonbusy hour, the total
power in a mastergroup remains relatively constant (from a maximum of 9.0 dBmO to a minimum of 7.8 dBmO).
To illustrate the way in which the 600-channel mastergroup
loading varies with time, consider the load when the busy-hour effect
has been reduced so that the equivalent speech load is that of a
300-channel system. The speech load for N == 300 channels may be
computed by the same method as that previously used; its value
is found to be +5.3 dBmO. It is assumed that the other 300 channels
carry idle channel signals; the power in these signals is -20 +
10 log 300 == +4.8 dBmO. The remaining 300 channels are subject to
the trunk efficiency factor, Te == 0.7. Thus an additional 300 (1 0.7) == 90 channels carry idle channel signals. The power in these
additional signals is -20 + 10 log 90 == -0.5 dBmO. The total power
is thus 5.3 +" 4.8" +" (-0.5) == 8.7 dBmO.
II

Average Channel Power. In Chapter 12, it was shown that the longtime average (or rms) load per channel in a broadband toll system
is about -20.5 dBmO when speech signals only are considered. The
mastergroup power for speech was found to be about +8 dBmO
during the busy hour. When single-frequency signal loading is
included with the speech load, the average mastergroup busy-hour
load is 1 dB higher, +9 dBmO. Theref{)re, it may be concluded
that the long-time rms channel load is also 1 dB higher, or about
-19.5 dBmO. This value is the long-term average channel power
based on the average speech volume of -16.8 vu for toll calls
measured in the 1960 survey, which also indicated a tendency for

404

Signal Characterization

Vol. 1

volumes to increase slightly on longer toll calls [1]. Thus, the speech
load on long-haul systems could increase by about 1 dB. Even with
the I-dB allowance there appears to be some margin between the
speech load with present station sets and the design objective of
-16 dBmO. In the future this margin may be used to permit somewhat greater transmitter efficiency in new telephone sets, particularly
on longer loops. Therefore, long range planning should be based on
the assumption that both speech and data signals eventually may
have a long-term average of approximately -16 dBmO.
Maximum Mastergroup Power. In a mastergroup made up only of
speech signals, the value of power that is exceeded 0.001 percent of
the time may be found by Equation (16-1),

P max == P av

+

Ac2

dBmO.

It is now desirable to determine this maximum power value for a
mastergroup having a speech and idle channel signal load. It has
been shown that the average value of a composite busy-hour mastergroup load is +9 dBmO. A value of AC2 for the composite signal
remains to be determined.
As shown in Figure 12-7, Ac2 is equal to about 13 dB for speech
signal loads in excess of about 75 active channels. It can be shown [2]
that the instantaneous value of the sum of n sine waves of equal
amplitude, different frequencies, and random phase relationships
also exceeds the rms value of the n signals by about 13 dB 0.001
percent of the time for values of n in excess of 100. Thus, in a
combined signal, one part consisting of 300 channels containing
speech signals and one part consisting of 300 single-frequency supervisory signals, each having approximately the same peak factor, it
can be safely assumed that the total also has a peak factor of 13 dB.
Thus, the maximum power in a mastergroup carrying 300 speech
signals and 300 idle channel signals is
P max == 9 + 13

== +22

dBmO.

( 16-2)

This result depends on the assumption that the 2600-Hz signals
are randomly related to one another in phase. Suppose, for example,
that the phases of the 300 single-frequency signals assumed in
developing Equation (16-2) were coherent so that their peak amplitudes coincided 0.001 percent of the time (an unlikely event). The

Chap. 16

405

Mixed Signal Loading

peak voltage of the 300 signals then would be 300 times the peak
voltage of one, and the peak power would be 300 2 == 90,000 times
the power of one such signal. Thus, the peak power would be
-20 + 10 log 90,000

== -20 +

49.5

== +29.5

dBmO.

This is a peak value 7.5 dB higher than that of Equation (16-2),
a value that would surely be expected to cause overload.
Phase coherence would not be expected under past field operating
conditions and design practices. A multiplicity of 2600-Hz oscillators
and a random physical association of signalling equipment and
transmission multiplexing equipment caused a dispersion of frequency and phase relationships that prevented any significant effects
due to coherence. More recent trends in the layout of office equipment
and in equipment design practices provide fixed wiring patterns
between a single supervisory signal generator and many carrier
channels. Special wiring patterns with controlled phase reversals
must be designed to guarantee partial cancellation of composite
signal peaks.

Speech and Address Signals
Address signals are transmitted at amplitudes higher than the
-16 dBmO long-term average power objective for a channel, but
the statistics of these signals do not cause the average power
objective to be exceeded. High-amplitude speech signal bursts of
short duration also occur; these are limited to a maximum of
+3 to +10 dBmO, depending on the system, by channel terminal
equipment. The limiting has negligible effect on the individual
speech signal; the distortion is masked by other distortions such
as that in the carbon transmitter of the station set.
Under normal operating conditions, these high-amplitude address
and speech signals do not seriously affect carrier system operation.
Their amplitudes are low compared to the total signal power in a
mastergroup (+9 dBmO), and/or the frequency of occurrence is so
low that such signals do not usually cause trouble. However, abnormal operating conditions or system designs which change the
statistical relationships can lead to serious overload troubles related
to the transmission of these high-amplitude signals. The maladjustment of channel equipment, operating errors (for example, the

406

Signal Characterization

Vol. 1

improper application of a test tone to a circuit), or the improper
maintenance of a carrier system (which might result in some frequencies being transmitted at much higher amplitude than the
designed values) are all trouble conditions to guard against. A
system design which requires the use of shaped TLP characteristics,
such as the pre-emphasis used in microwave radio systems and the
signal shaping used in coaxial systems, results in peak factors that
are equivalent to those in systems of fewer channels than are provided in the design (see Chapter 12-3). Thus, peak factors are higher,
the effective signal band is smaller, and even a single channel carrying
an inordinately high signal can cause system overload.
Speech and Data Signals

Carrier system speech channels are frequently used for the transmission of data signals. These signals are sometimes tranmitted
over trunks which are parts of the switched public network or
switched private line networks and sometimes over dedicated,
point-to-point private line circuits. Any of these circuits may involve
interconnection with customer-provided equipment through a Bell
System connecting arrangement. The control of signal amplitudes
tends to vary somewhat depending on the source of the signal.
As discussed in Chapter 14, the maximum amplitudes of voiceband
digital data signals are specified not to exceed -13 dBmO when
averaged over a 3-second interval. Allowing for channel activity
factors and a mix of duplex and half-duplex operation, the resulting
long-term average should not exceed -16 dBmO. Modern systems
are designed to operate satisfactorily over a range of data and
speech signal combinations that meet the -16 dBmO objective. However, a heavy concentration of private line duplex data channels
applied to a given system could cause this average to be exceeded
and should be avoided by dispersion of these channels over several
systems.
Data signals, as transmitted over carrier systems, may be regarded
simply as single-frequency signals insofar as their overloading effect
is concerned. Therefore, a peak factor of 13 dB for multichannel
systems (mastergroup or higher) may be safely assumed, since the
peak factors for all contributors - speech, data., and supervisory
signals - are equal.

Chap. 16

Mixed Signal Loading

407

Speech and Video Signals

While several broadband carrier systems were initially designed
to carry a combined signal consisting of voice and broadcast television signals, none of them are so used today primarily because of
difficulties encountered in controlling intermodulation products between the two types of signal. Therefore, the characterization of
such a combined signal is of no consequence and is not discussed.
PICTUREPHONE service has not yet been provided in any
significant amount on systems that transmit combinations of speech
and analog PICTUREPHONE signals. Studies are now under way
to determine how such signals interact and how the combined signals
may affect the systems over which they are transmitted.

16-4

SYSTEM-SIGNAL INTERACTIONS

The characterization of signals in this chapter has been presented
to relate the average and peak powers of the signals to carrier system
overload. In some cases, system type, design, operation, or maintenance interacts with the transmitted signal to change its characteristics so that overload effects may be accentuated or mitigated.
System Misalignment

Multirepeatered broadband analog systems are designed so that
the gain of a repeater compensates for the loss of the preceding
section of the transmission medium. Because the compensation is
not perfect, the signal amplitudes depart from their nominal values.
These departures are called misalignment; they may be positive at
some frequencies, causing the signals to be higher than nominal,
and negative at other frequencies, causing the corresponding signal
components to be lower than nominal. The effects on signal characteristics can be negligible for small misalignment, or they may be
quite significant. The analysis of such effects is similar to that
relating to the shaped TLP concept of Chapter 12.
Carrier and Pilot Signals

The discussion of phase coherence among single-frequency supervisory signals and the importance of guaranteeing random phase
relationships among such signals applies also to carrier signals

408

Signal Characterization

Vol. 1

(such as may be transmitted in a DSBTC system) or to singlefrequency pilot signals. Special wiring designs must sometimes be
used to introduce phase reversals in order to produce partial cancellation of signal peaks.
Compandors

The advantage in individual channel signal-to-noise performance
gained by using syllabic compandors results from the fact that the
range of signal amplitudes is substantially reduced for transmission
over the medium. The reduction, called the compression ratio, is
usually on the order of 2 to 1; a signal amplitude range of 50 dB
is reduced to 25 dB, and its standard deviation is also reduced by
a factor of 2 to 1 from 6 to 3 dB. The average signal amplitude
is a system design parameter. Thus, in a given cable carrier
system using compandors, the value corresponding to Vo for a noncompandored channel must be selected by the designer to optimize
performance. The optimization must take into account the fact that
the use of compandors generally results in a higher average power
per channel.
Sometimes, when the mUltiplexed signal of a compandored carrier
system is applied as a portion of the signal to another system of
higher capacity which does not normally use compandors, precautions must be taken to avoid overload in the higher capacity system.
Two effects must be taken into account: one is the higher average
power in a voice channel due to the compandor action; the other is
the high power represented by the transmitted carriers in most Bell
System compandored systems. The requirements of the high-capacity
system may be met by reducing its channel capacity, by lowering
the amplitude of the total applied compandored signal load, or by
lowering the relative amplitudes of the carrier components. In some
instances, some of the compand or advantage may be lost. This loss
is usually not important because the high-capacity systems are less
noisy (by design) than the systems for which compandors are
provided.
TASI
Time assignment speech interpolation, discussed briefly in Chapter 2,
has as its principal effect on broadband signal characterization an
increase in the activity factor for each speech circuit. The amount
of increase is a function of the TAS! system design, which must

Chap. 16

Mixed Signal Loading

409

take into account the number of trunks between terminals, the
number of lines being served, the ratio of the two, the allowable
degradation due to freeze-out, and the syllabic content of the language being used. (Freeze-out is an effect that leads to clipping of
initial speech bursts due to the fact that all trunks are active and
therefore busy.) In T AS! systems, the trunk activity factor may
increase from 25 or 30 percent to 90 or 95 percent.
Microwave Radio Systems
The Federal Communications Commission specifies that the frequency deviation of a frequency-modulated microwave carrier be
confined to the allocated band [3]. Modern microwave systems, while
designed to carry a long-term average per-channel signal power
load of -16 dBmO, are tested by noise loading techniques with a
load equivalent to -15 dBmO per 4-kHz channel. This approach
provides some margin against peak excursions of composite signals
which produce the extremes of the microwave frequency deviations.
At the same time, signal-to-noise objectives are met for the system
when operated at a load value equivalent to -16 dBmO per channel.
REFERENCES

1. McAdoo, Kathryn L. "Speech Volumes on Bell System Message Circuits1960 Survey," Bell System Tech. J., Vol. 42 (Sept. 1963), pp. 1999-2012.

2. Bennett, W. R. "Distribution of the Sum of Randomly Phased Components,"
Quarterly of Applied Mathematics, Vol. 5 (Jan. 1948), pp. 385-393.
3. Federal Communications Commission. Rules and Regulations, Vol. 2 (Aug.
1969).

Telecommunications
Transmission
Engineering

Section 4Impairments and Their Measurement
The next six chapters contain descriptions and definitions of impairments suffered by telecommunication signals as they are transmitted through various channels and media. These descriptions,
qualitative for the most part, are related to the sources of impairment, the manner in which the impairments are measured, and the
units in which the measurements are expressed.
Signal transmission is subject to impairment by a number of imperfections in channels; thus, signal impairment may be regarded as
resulting from channel impairment. The channel imperfections include interferences induced from external sources, interferences that
are signal-dependent and caused by nonlinear channel input/output
characteristics, distortions of the channel transmission characteristics,
and indirect effects such as timing and synchronization errors.
Transmission irregularities affect various types of signals differently. Consider, for example, the transmission of a variety of
signals over imperfect voiceband channels. In one case, carrier signal
generating equipment may produce jitter which is scarcely noticeable
in speech signal reception but which causes disastrous impairment
of voiceband data signals. In another case, the channels under consideration may have impedance discontinuities that produce intolerable echoes from the point of view of speech signal transmission but
which may have negligible effects on data signal transmission.
Sometimes impairments may be dealt with in the design process.
For instance, if a particular type of signal is intolerant of frequency
shift, the effect can be eliminated by using a method of transmission
that permits recovery of the transmitted carrier frequency and
phase. Signals sensitive to frequency shift impairment should usually
not be transmitted by suppressed-carrier methods.

410

Occasionally, somewhat degraded performance may be tolerated in
time of trouble. Such a situation would be typified by an increase
in noise, for example, while major troubles are being corrected. The
ability to furnish some service, even though below normal, may be
preferable to furnishing no service at all.
Some impairments are evaluated subjectively and others objectively. Sometimes the same impairment may be evaluated both ways
depending on the type of signal to be transmitted. For example,
random noise must be evaluated in terms of its annoying effect in
speech or video signal transmission and in terms of the number of
errors it causes in digital data signal transmission. In either case,
the ultimate expression must be in terms that can be stated quantitatively so that meaningful values may later be established for
objectives and requirements.
Chapter 17 deals with various types and sources of noise and
crosstalk. Some forms of noise are induced in transmission channels
from external sources by a number of different coupling mechanisms.
Some have their sources within the channel of interest. Some forms
of noise are independent of the signal transmitted, while others are
functions of the transmitted signal.
Signal transmission may be seriously impaired by departures from
desired amplitude/frequency channel characteristics. These characteristics and some departures from ideal are discussed in Chapter 18
in relation to typical signals and channels.
A discussion of timing and frequency synchronizing relationships
is found in Chapter 19. Impairments that relate to such functions
are seldom controlling in baseband systems. They appear in carrier
systems or when signals are otherwise processed by time or frequency
functions.
Chapter 20 discusses the effects of echoes in a telephone message
channel. Echoes cause serious impairment to speech and telephotograph signals. The impairing effects are a complex combination of
echo amplitude and the amount of delay difference between the signal
and its echo.
Delay distortion has a number of adverse effects on signal transmission, particularly on video and data signals. Chapter 21 treats
the impairments caused by delay distortion in channels of any
bandwidth that may carry signals sensitive to delay distortion.
411

The ultimate deterioration of signals occurs when transmission
is cut off by a failure. Chapter 22 considers the design, construction,
layout, and operation of the transmission plant from the point of
view of its reliability. Protection switching arrangements, emergency restoration, and diversity of routing are subjects of discussion.
Deterioration of transmission need not be total, however. Poor maintenance practices and/or inadequate support equipment and support
systems may bring about a gradual circuit deterioration that causes
impairments to increase with time. These subjects are also discussed
in Chapter 22.

412

Impairments and Their Measurement

Chapter 17

Noise and Crosstalk
The transmission of telecommunications signals is degraded by
the limitations of practical channels and by the existence of various
types of interference in the channel of interest. Interference may
be induced from a source outside the channel of interest (e.g., power
line noise picked up by a voice-frequency circuit), or it may be
generated from within (e.g., intermodulation noise caused by nonlinear input/output characteristics of repeaters in an analog
transmission system).
The effects of some interferences depend on the type of signal
affected. For example, bursts of impulse noise are usually of little
consequence in the transmission and reception of speech signals
because of the use of amplitude limiters and the relative insensitivity
of the human ear to this type of impairment. However, impulse
noise can seriously impair digital signal transmission. Some other
types of interference, such as thermal noise, degrade the transmission
of all types of signals. Unwanted signals and interferences, their
sources, means of controlling the sources and coupling paths, the
nature of the impairments incurred, and the methods of measurement
are all basic to an understanding of impairments suffered in the transmission of signals in the telecommunications network.
17-1

COUPLING

Almost all transmission circuits are exposed to external influences
and forces by virtue of proximity to other circuits. For example, a
loop or trunk is usually physically close to other circuits in cables or
on pole lines; multiplexed message channels share a wide bandwidth;
any circuit passing through a central office is exposed to sizable
switching transients; and many circuits have power transmission
lines paralleling part of their routes. The exposure to electromagnetic
fields created by the currents in these nearby circuits results in many
possible interference coupling paths from a disturbing circuit to the
circuit of interest, the disturbed circuit.
413

414

Impairments and Their Measurement

Vol. 1

Currents and Circuit Relationships

The extent of interference caused by coupling is dependent on
the symmetry, or balance, of the disturbed circuit and on the type
of current (longitudinal or metallic) that results from the coupling.
Currents that flow in the same direction in the two conductors of
a pair of wires are called longitudinal currents, while currents that
flow in opposite directions in the two conductors are called metallic
currents. Both types are illustrated in Figure 17-1. The voltage
sources, E with internal impedance ZG, are coupled to the transmission line by some form of coupling mechanism designated as Z c.
The resulting currents are transmitted through the central office,
typically through common battery circuits which include impedances
Zs as illustrated, to the load impedance, ZL. The Zs impedances may
represent a number of components such as supervisory relays,
transformers, common battery supply leads, etc.
In Figure 17-1 (a), the currents through ZL are exactly equal
and opposite (net zero) if all the networks and the transmission
line are exactly balanced, i.e., electrically alike and symmetrical
wIth respect to ground. In this event, an interference voltage coupled
as in Figure 17-1 (a) causes no interference current in ZL. However,
if the Zc and Zs networks are not balanced, unequal currents flow in
the two sides of the circuit. The difference between them is a
metallic current that appears in the load, Z L, as interference. This
metallic component of the current can be represented as originating
in an equivalent circuit like that of Figure 17-1(b), where E may
represent the source of unbalance current, some system-generated
interference, or a wanted signal source.
The common battery does not cause appreciable unbalance because
the internal impedance of a central office battery is extremely low,
typically a small fraction of an ohm. However, other parts of the
connection, those represented by impedances Zs, are often unequal and
and create an unbalanced circuit unless carefully controlled.
The circuits and currents of Figure 17-1 may be defined in terms
of balanced and unbalanced conditions since the grounds located
between impedances Zs and between impedances Zc provide references with respect to which circuit symmetry can be evaluated and
direction of current flow can be determined. If the disturbed circuit
has no ground or common return, a plane of symmetry cannot be
established, and longitudinal currents are not generated.

Chap. 17

Noise and Crosstalk

415

j.--- Transmission line-....... . - - - - Central office - - - - I
I
I
--~

--+
(a) Longitudinal current

I+--

Transmission

line--1.~"---

Central office - - - - -

I

I
I

1

(b) Metallic current

Figure 17-1. Currents in a two-wire telephone line.

416

Vol. 1

Impairments and Their Measurement

Coupling Paths and Their Control

The coupling path from a disturbing to a disturbed circuit may
result from electromagnetic, electric (dir~ct), or intermodulation
phenomena. These phenomena and the resulting coupling paths are
typical of interference problems found in telecommunications systems.
Coupling path losses must be controlled so that transmission impairments may be held to tolerable values.
Electromagnetic Coupling Paths. A coupling path is involved when an
electromagnetic field resulting from an alternating current carried
in one conductor causes a voltage to be induced in another conductor [1, 2]. The induced voltage may result from either the magnetic
or the electric field, whichever is dominant.

Figure 17-2 illustrates a simple and idealized case of magnetic
coupling where A is one conductor of a disturbing circuit equidistant
from the two conductors of disturbed circuit B. The magnetic field
produced by current 10 in conductor A induces voltages El and E2
in B. The resulting longitudinal currents, 11 and 12 , in the two conductors of the disturbed circuit are exactly equal and of opposite
polarity. Thus, they cancel one another, and there is zero net metallic
current; i.e., 13 == O. Departures from the idealized conditions assumed in Figure 17-2 may cause the induced currents in the two

A

I

10 - - - .

8
~Il

4-12

ZG/2

ZG/2

Figure 17-2. Circuit relationships - magnetic coupling.

ZL/2

Chap. 17

Noise and Crosstalk

417

conductors of the disturbed circuit to be different in magnitude,
phase, or instantaneous direction of flow; the result would be a
net metallic current in the disturbed circuit. This may occur if the
couplings from conductor A to the conductors of circuit Bare
unequal or if the impedances to ground in the disturbed circuit are
unequal, as would be the case if Zu were in the circuit. In either
case, Is =F= O.
Among the measures employed to control the magnetic coupling
between circuits is shielding. Others include separation, orientation,
and balance. Magnetic shielding is employed in braided or other
forms of iron shields to cover the copper conductors to be used for
the transmission of signals that are particularly susceptible to
magnetically induced interferences. An example is the use of specially
shielded wires for intracity television baseband signal transmission.
More commonly, shielding is used on circuit packs having areas of
high component density, especially where magnetic components
(inductors and transformers) are used. Where transmission lines
are shielded against magnetic coupling, the shields (such as cable
sheaths) must be grounded at both ends.
Electric field coupling is the result of capacitance between adjacent parallel conductors. This form of coupling, resulting from
the electric field produced by voltages in the disturbing circuit, is
among the most important and most prevalent in communication
systems. Capacitive coupling loss is a maximum at low frequency
and tends to decrease at a rate of 6 dB per octave of frequency.
If the capacitance from a disturbing conductor to each of the two
wires of a disturbed circuit is different, the current flowing in each
of the disturbed conductors is different, and a resultant metallic
current flows. Similarly, if the two currents are equal but the impedances of the two disturbed conductors are unequal (for example,
due to a shunt impedance to ground on one conductor only), a
resultant metallic current also flows.
Many of the guidelines that govern the relationships between
and disturbed paths in magnetic coupling apply to electric
field coupling also. Electrostatic shielding of conductors (by iron,
copper, or aluminum shields), separation between disturbing and
disturbed circuits, orientation of one circuit with respect to another,
and balance of the impedances affect the control of electric field
coupling paths.
di~turbing

418

Impairments and Their Measurement

Vol. 1

Electric Coupling Paths. Electric coupling paths are those produced
by impedances that are common to two or more otherwise independent circuits. These paths, which include common batteries and
their supply leads and terminal multiplex equipment filters whose
pass bands are adjacent or overlap, are normally controlled in design;
they are little affected by system application and maintenance.
The manner in which the common battery impedance can become a
source of interference is illustrated by Figure 17-3. In Figure 17-3 (a) ,
two telephone station sets are shown with independent connections
to trunks or other station sets. The two local station sets, ST A 1 and
STA 2, receive current from the common battery supply having
internal impedance Zbo The connections from the station sets are
over loops and through central office battery supply and supervisory
circuits designated Z So The transmission circuits are coupled by
transformers. In Figure 17-3 (b), the station set, loop, transformer,
and supervisory circuit impedances of the two circuits are lumped
together as Z1 and Z2. The battery impedance is shown as Zb, and
the transmitter at STA 1 is shown as a voltage generator, E. This
simplified schematic shows clearly how STA 1 and STA 2 are coupled
by Zb. The following numerical example illustrates how interference
from STA 1 to STA 2 is limited, or controlled, by maintaining Z b
at a low value.

Example 17-1: Electric Coupling Path Control
To simplify the example, assume that
(a) Z1 and Z2 in Figure 17-3 (b) are both 1000 ohms.
(b) the interfering current, 12 , resulting from the voltage,
E, must be at least 80 dB below the desired current, 11 ;
i.e., 20 log 11/12 > 80 dB.
What value of Zb will produce this result?
The voltage relationships in the right-hand mesh of
Figure 17-3 (b) may be written, by using Kirchoff's second law as
shown in Equation (4-3), as
100012

-

(11 - 12 ) Zb

== 0

or

+

1000
Zb
Zb
If 20 log 11/12 > 80 dB, 11/12 > 10,000
11

--y; ==

Thus, Zb

<:

0.1 ohm.

Chap. 17

Noise and Crosstalk

~J

STA 1

419

~

To trunk or
another station set

c]

To trunk or
another station set

R

STA 2

(a) Two common battery station set connections

(b) Simplified schematic

Figure 17-3. Electric coupling through the common battery impedance.

420

Vol. 1

Impairments and Their Measurement

While somewhat oversimplified, this example illustrates how two
circuits may be coupled by a common impedance such as Zb and
how the coupling may be controlled in design by holding the common
impedance to a much lower value than the coupled transmission
circuit impedances. In a real case, the internal battery impedance
tends to be very low, typically less than 0.01 ohm, and coupling becomes a problem only where long power leads are common to a
number of otherwise independent circuits. Their impedance adds to
Zb to give an effective value, Z'b, that can introduce excessive
coupling. In this case, the complex impedances of all the involved
circuits must be taken into consideration. Sometimes, decentralized
battery filters must be used to bypass the interference currents to
ground. Although the common dc impedance remains high, these
filters reduce the complex impedance at signal frequencies to low
values.
In a large office, many interference currents such as I I - 12 in
Figure 17-3 (b) are carried in the common battery. Even though
each is small, there may be several thousand such signals simultaneously present. Together, they form a significant source of noise that
must be carefully controlled by battery lead layout and appropriate
filtering.
Figure 17-4 illustrates how carrier system terminal equipment
filters may provide an electric coupling path. Two 4-kHz baseband
input connections are shown at the left. The input signals modulate
carriers at frequencies tel and te2 (where te2 == tel
4 kHz) and
produce double-sideband signals over bands ±4 kHz about the
carriers. These double-sideband signals then pass through bandpass
filters which pass their lower sidebands and suppress their upper
sidebands. At the filter outputs, the two signals are combined. Note
that the suppressed upper-sideband signal from Input 1 falls directly
into the band occupied by the lower-sideband signal of Input 2. This
form of coupling can sometimes be avoided by selecting carrier
frequencies such that the overlap does not occur; however, bandwidth
is wasted. Control is usually attained by designing the filters so
that adequate suppression is obtained and interference currents are
at an acceptably low amplitude, 50 to 80 dB below the wanted signal
currents.

+

Intermodulation Coupling. The coupling that results from intermodulation among signals in an FDM carrier system cannot be described

o

421

Noise and Crosstalk

Chap. 17

4 kHz

tel

MOD

Input 1

Input 2

~

o

4 kHz

l_m
tc2

l_~
tC2

tc2 = tel + 4 kHz
Figure 17-4. Electric coupling in multiplex terminal equipment.

in the same physical sense as the electromagnetic and electric coupling
paths just discussed. Intermodulation is inextricably involved in the
mathematics of the no.nlinear input/o.utput characteristics o.f the
devices; therefo.re, a detailed discussio.n o.f this type o.f co.upling is
deferred to. a later part o.f this chapter.
17-2

INDUCED NOISE AND CROSSTALK

The so.urces o.f many types o.f no.ise and cro.sstalk are o.utside the
disturbed channel. Such interferences are co.upled into. the disturbed
channel by co.upling mechanisms and thro.ugh the types o.f co.upling
paths discussed abo.ve. Here, so.me specific induced interferences and
methods of co.ntrol are described.
Power System Noise

Pro.blems invo.lving inductive coupling arise where facilities fo.r
the Po.wer industry and the communicatio.ns industry share the same
undergro.und o.r Po.le line enviro.nment. Communicatio.ns channels
carrying signals having co.mpo.nents that extend do.wn to. o.r clo.se to
zero frequency are particularly susceptible to. interference fro.m the
high-strength magnetic and electric fields generated by Po.wer systems.

422

Impairments and Their Measurement

Vol. 1

Nature of Impairments. The characteristics of the 60-Hz wave present
in most power distribution systems are high energy, high harmonic
content (especially odd harmonics), and large differences between
the currents carried by different conductors of the power line, i.e.,
high unbalance currents. The 60-Hz fundamental component is at
such a low frequency that speech transmission is seldom impaired
since most voice-frequency circuits and all carrier circuits have high
attenuation at 60 Hz. However, high-amplitude odd harmonics of
60 Hz often cause an unpleasant hum in voice-frequency speech
transmission systems.

The 60-Hz and harmonic components can also cause bar pattern
interferences in television, PICTUREPHONE, or other video channels. Video signals require a flat attenuation/frequency response to
essentially zero frequency; thus extraneous signals at low frequencies
can cause picture impairment.
Data signals transmitted at baseband and requiring good response
at low frequencies may also be seriously impaired by 60-Hz and
harmonic interference. The impairment takes the form of increased
error rate.
Inductive Coordination. This term is applied to the cooperative efforts
of the power industry (represented by the Edison Electric Institute),
other utilities, and the Bell System to solve problems that arise where
facilities for different types of service share the same environment.
In considering problems of interferences in communication circuits
due to coupling from power circuits, three conditions are considered.
These are influence, coupling, and susceptibility. Influence refers
to those characteristics of power circuits and associated apparatus
that determine the character and intensity of the fields they produce.
Coupling covers the electric and magnetic interrelations between
power and communication circuits. Susceptibility refers to the characteristics of communication circuits and associated apparatus,
which determine the extent of any adverse effects from nearby
power circuits. These three conditions form the basis of inductive
coordination.

A large unbalance of the currents carried on the individual conductors of a multiphase power distribution circuit is a source of
influence on communication circuits. A reduction of power line influence may be accomplished by transposing the power line conductors

Chap. 17

Noise and Crosstalk

423

and by balancing load currents. The influence reduction results from
a cancellation of fields caused by the unbalanced currents. In addition to reducing influence, load balancing makes power distribution
more efficient and, therefore, more economical.
The distance between power and communication circuits and their
mutual orientation are among the factors that must be considered
in order to control coupling. On shared facilities the separation
between the potentially interfering source and each communication
circuit conductor must be as large as practicable, and the distance
between the communication paired conductors must be as small as
possible. When power and communication circuits must cross one
another, a 90-degree crossing minimizes coupling between the lines.
The susceptibility of communication circuits can be reduced in a
number of ways. The proximity of conductors subject to power line
influence is effectively accomplished by twisting the conductors of
each pair together where possible. Twisting of pairs is specified in
the design of multiconductor cables and some open-wire pairs. This
tends to equalize the distance from the conductor pair to each power
conductor so that induced voltages are made nearly equal and metallic
interference currents are minimized. Where twisted pairs cannot
be used, the disturbed conductors are transposed, or frogged, at
regular intervals to reduce susceptibility. Impedance balance to
ground of the disturbed circuit is then an effective deterrent to the
conversion of longitudinal to metallic current. Finally, good shielding~
i.e., maintaining cable sheath continuity, offers some protection to
communication circuits when they are in cables.
Some coordination problems are structural and, as such, may
result in danger to personnel or communication equipment from
high energy coupled from the power source into the communications
circuits. While most systems are 60-Hz ac, some high-voltage dc
power systems are also in use. Stray direct currents from the latter
may cause noise or corrosion problems if structural problems and
appropriate grounding arrangements are overlooked.
Impulse Noise

Impulse noise consists of spikes of energy of short duration which
have approximately flat spectra in the band of interest. The flat
spectra are shaped by channel response characteristics so that,

424

Impairments and Their Measurement

Vol. 1

typically, the average spectrum of a large number of observed impulses approximates the frequency response of the channel on which
the measurements are made [3]. Some of the more important sources
of impulse noise are: (1) corona discharges in transmission lines
simultaneously powering remote repeaters, (2) lightning, (3) electrical and electroacoustic transients associated with the termination
of a call at a station set, (4) relay operations associated with switching and alarm functions, (5) microwave radio fading phenomena
and the associated protection switching operations, and (6) many
other transmission system operating and maintenance procedures.
In speech transmission, impulse noise causes little impairment.
Above a certain threshold value, acoustic shock caused by impulse
noise might be painful; however, circuits are designed to limit amplitudes well below the threshold, and acoustic shock is seldom experienced. At amplitudes below the limiting values, the human ear is
quite tolerant of impulse noise.
In video transmission, the impairment takes the form of shortduration interferences such as small light or dark flickers in the
picture (sometimes called pigeons) or, in extreme cases, a shortduration loss of synchronization that causes the picture to tear
horizontally or to roll vertically. While all of these impairments are
objectionable, such events are tolerated if they occur only occasionally.
The most serious effect of impulse noise is found in digital signal
transmission. The interfering impulses are short compared with the
time between them and, as a result, the receiving circuits resolve
them as independent events. Depending on the impulse amplitude,
polarity, duration, and time of occurrence, individual signal components or blocks of data symbols may be obliterated, resulting in
errors in the received signal.
Single-Frequency Interference

Single-frequency signals or wideband signals having discrete
single-frequency components can be excessively annoying when
coupled into a telephone channel. If they are of sufficient amplitude
and fall between 200 and 3500 Hz, they may produce audible tones
in the telephone receiver. Single-frequency interferences can also
disturb SF signalling systems, produce bar patterns in video receivers,
and cause high error rates in data transmission systems.

Chap. 17

Noise and Crosstalk

425

Crosstalk

Crosstalk was initially used to designate the presence in a telephone receiver of unwanted speech sounds from another telephone
conversation. The term has been extended in its application to
designate interference in one communication channel or circuit caused
by signals present in other communication channels. Consideration is
limited here to the interference to one signal by another signal of
the same general type-e.g., speech interfering with speech, video
with video, digital with digital, etc. It should be pointed out, however,
that crosstalk coupling of one signal type to another is often significant in establishing transmission level points for communication
systems.
Crosstalk Coupling and the TLP. As discussed in Chapter 3, many of
the complexities of system design and operation are made tractable
by the concept of TLPs. The importance of any coupling path is
strongly dependent on the relative magnitudes of the wanted signal
and the unwanted interference. It is really a question of the signalto-interference ratio, which is difficult to define in telephone practice;
the TLP approach is found to be a useful way of dealing with signalto-interference problems.

With this approach, the interference is defined in terms of its
value at a specific TLP, and the coupling is expressed as equal level
coupling loss (ELCL). The ELCL is defined as the ratio of signal
power at some known TLP in the disturbing circuit to the induced
power measured at an equal TLP in the disturbed circuit. The ELCL
concept is illustrated in Figure 17-5 where two repeatered voicefrequency circuits are depicted as transmitting from left to right.
A coupling path having 80-dB loss is shown from the output of the
repeater in the disturbing circuit to the input of the repeater in the
disturbed circuit. Thus, ·the coupling path loss must be adjusted by
the gain of the repeater in the disturbed circuit (30 dB) to give a
value of ELCL of 50 dB. Note that the ELCL is independent of
signal amplitude and of the particular TLP used in its determination.
Near-End, Far-End, and Interaction Crosstalk Coupling. These forms of
coupling, abbreviated NEXT, FEXT, and IXT, respectively, are
subclasses of coupling modes that exist between communication
channels or circuits. Although any of these forms of crosstalk
coupling may cause impairment, NEXT and FEXT tend to be predominant. With NEXT coupling, the interference energy in the

426

Impairments and Their Measurement

Vol. 1

Disturbing channel

J'

""'-

Coupling path

~

"\
'\

-40 dB TLP

,

/ ' Direction of transmission---...

SOdB

/

/

50 dB ELCL

/
Disturbed channel

~

\

/

-10 dB TLP

Figure 17-5. Coupling path loss and equal level coupling loss.

disturbed circuit is transmitted in the directio.n o.ppo.site to. that o.f
the signal energy in the disturbing circuit. With FEXT co.upling,
the signal and interference travel in the same directio.n. Interactio.n cro.sstalk o.ccurs when energy is co.upled to. a tertiary path,
pro.pagates alo.ng that path, and then is co.upled to. the disturbed
circuit. The two. stages o.f co.upling may be o.f the near-end o.r far-end
type o.r a co.mbinatio.n o.f bo.th.
Speech Crosstalk. When an unwanted speech signal is co.upled into.
ano.ther speech channel, the interfering signal may be intelligible
or it may be unintelligible but have syllabic characteristics so that
a listener thinks it may be intelligible. Such interferences are particularly objectionable because of the real or fancied loss of privacy.
Even when they are clearly not intelligible, they tend to be highly
annoying because of the syllabic content. Stringent objectives to.
minimize these interferences are applied in transmission systems.

When many unwanted speech signals appear in a disturbed channel
simultaneously, each at such a low amplitude that neither intelligence
nor syllabic variatio.ns are co.nveyed, the net effect may resemble
random noise. In rare circumstances, the metallic co.upling of large
numbers of speech signals through common battery circuits in a
central office might produce such an impairment. Ho.wever, coupling
losses through battery feed circuits are kept at high values by design.

Chap. 17

Noise and Crosstalk

427

Video Crosstalk. When a picture signal is coupled to another video
channel, the interfering picture signal may be superimposed on the
disturbed picture receiver. This form of interference is rare, however. The two signals are usually not synchronized, and the coupling
path usually has a loss/frequency characteristic that distorts the
interfering signal. A more common effect of such a coupling is known
as the windshield wiper effect. The synchronizing pulses of the
disturbing signal create a bar pattern across the disturbed picture.
Since the two signals are normally unsynchronized, the bar pattern
moves across the picture with a windshield wiper effect.
Digital Signal Crosstalk. As in most cases of interference to digital
signals, crosstalk produces errors. Below some threshold essentially
no errors are made, although a disturbing signal amplitude just
slightly higher than the threshold value causes a very sharp increase
in error rate.

In the design of digital transmission systems, the crosstalk due to
the presence of the line signals of many systems in one cable is
often the limiting factor in the spacing of regenerative repeaters.
17-3

SYSTEM-GENERATED NOISE AND CROSSTALK

Many sources of noise and crosstalk exist within a channel or
within a transmission system. Such interferences are controlled
by circuit design and, within the constraints of a particular design,
by signal amplitude manipulation since the ultimate interfering
effect is a matter of the signal-to-noise ratio. If interferences are
independent of the signal amplitude, the signal-to-noise ratio is improved by raising the transmitted signal amplitude. If interferences
are signal-dependent, the signal-to-noise ratio is generally improved
by reducing the transmitted signal amplitude because this type of
interference generally changes more rapidly than the signal amplitude. Thus, performance optimization in analog transmission systems
involves the selection of optimum signal amplitudes because both
types of noise are usually present.
Random Noise

Random noise is an impairment that appears in all circuits as a
result of physical phenomena that occur within the affected circuit
or channel. The complete characterization of random noise types
that are commonly found in transmission channels is beyond the

428

Impairments and Their Measurement

Vol. 1

scope of this chapter; but the important noise sources are briefly
described, the resulting impairments to various telecommunication
signals are discussed, and methods employed to measure and evaluate
these types of interferences are described [4].
The terms white noise and Gaussian noise, often used to describe
random noise characteristics, must be defined. The term white noise
has become well established to mean a uniform distribution of noise
power versus frequency, i.e., a constant power spectral density in
the band of interest. The Gaussian noise distribution, discussed in
Chapter 9, is the limiting form for the distribution function of the
sum of a large number of independent quantities which individually
may have a variety of different distributions. A number of random
noise phenomena produce noise having this Gaussian amplitude
distribution function.
By definition, Gaussian noise has a finite probability of exceeding
any given magnitude, no matter how large. In practice, however,
consideration can sometimes be limited to the magnitude attained
0.01 percent of the time. Thus, it is convenient to define the peak
factor for random noise having a Gaussian distribution at 3.89 UN
where UN is the rms value of the noise.* The peak factor is then
11.8 dB above the rms value (usually rounded to 12 dB for convenience). In cases where the value attained 0.001 percent of the
time must be used, the peak factor is 13 dB.
Several types of signal independent random noise are encountered
sufficiently often to warrant discussion. These include thermal noise,
shot noise, l/t noise, and Rayleigh noise. Since each of these types
of noise has random characteristics, the total power in multiple
sources, such as those encountered in multirepeatered analog transmission systems,may be computed simply by summing the powers.
There is no amplitude or phase correlation between components
from independent sources.

Thermal Noise. According to the kinetic theory of heat, electrons
in a conductor are in a continual random motion which leads to an
electrical voltage whose average value is zero but which has ac
components of random amplitude and duration. The phenomenon
produces an interference signal called thermal noise.
*The noise has an average value of zero, having random positive and negative
excursions. The rms value can be shown as equal to the standard deviation, UN.

429

Noise and Crosstalk

Chap. 17

It is shown [5, 6] that for thermal noise the available noise
power is

== kTwattsjHz
k == Boltzmann's constant == 1.3805 (10- 23 )
PN(f)

(17-1)

where
joule/K, and T is
the absolute temperature of the thermal noise source in Kelvins. At
room temperature, 17°C or 290 K, the available noise power is
PN(f) == 4.0(10- 21 ) watts/Hz or -174.0 dBm/Hz.
In theory, the thermal noise spectrum eventually drops to zero;
actually, however, it is flat over all frequencies of practical interest
from zero to the highest microwave frequencies used and can be
termed white noise. Also, the available noise power is directly proportional to bandwidth and absolute temperature. Thus,
pa

== kTB watts

(17-2)

where B is the bandwidth of the system or detector in hertz. This
may be expressed in dBm as

Pa

== -174 + 10 log B

dbm.

(17-8)

While thermal noise has a flat power spectrum and a Gaussian
amplitude distribution, it should not be concluded that white and
Gaussian are synonymous; they are not.

load,

Sometimes it is desirable to determine the voltage generated by
a thermal noise source. This may
be accomplished by considering an
equivalent circuit like that of
Figure 17...16. The equivalent circuit
assumes a noise voltage generator,
EN, in series with a hypothetically
Figure 17-6. Equivalent circuit of a
noiseless resistor of R ohms. If
noisy resistor.
this noise source is connected to a
load resistor, R L, and if RL is equal to R, the maximum power will
be delivered to R L • This maximum deliverable power is Pa == E;/4R.
As previously shown, the available noise power from a thermal noise
source is pa == kTB. Equating these two powers and solving for the
rms voltage of the equivalent Thevenin generator yields
EN

== yl4kTBR

volts.

(17-4)

430

Impairments and Their Measurement

Vol. 1

Shot Noise. This type of random noise is found in most active
devices. It is similar to thermal noise in that it has a Gaussian distribution and a flat power spectrum. However, it differs from
thermal noise in the following two respects:

(1) The magnitude of thermal noise is proportional to absolute
temperature, whereas shot noise is not directly affected by
temperature.
(2) The magnitude of shot noise is proportional to the square
root of the direct current through the device. Thus, the shot
noise magnitude may be a function of signal amplitude if the
signal has a dc component.
For fixed conditions in a particular design, it is often convenient
to combine shot noise with thermal noise into a single equivalent
noise source. The way in which the two combine depends on the
particular circuit arrangement.
Shot noise may be computed as an rms current by
i

== v'2qI

ampere

(17-5)

where q == charge of the electron == 1.6 (10- 19 ) coulomb, and I is the
direct current through the device.
Low-Frequency (1/1) Noise. This noise is associated with contact and
surface irregularities in semiconductors and in the cathodes of
electron tube devices. The noise has a Gaussian distribution, and in
a given band (between /1 and /2) may be computed by
12

P=

I~

dl = K (In 12 - In It)

(17-6)

11

Evaluation of the constant K depends on specific devices and circuit
conditions. The evaluation given by Equation (17-6) would result in
infinite noise if the band were to extend down to zero frequency or
up to infinite frequency. This is not to be expected, and the equation
holds only for finite bandwidths which do not extend to either extreme.

Chap. 17

Noise and Crosstalk

431

Rayleigh Noise. When the bandwidth of the circuit or channel under
consideration is small compared with its midband frequency, the
noise in the band is considered as narrowband noise. If the noise has
a Gaussian distribution, it appears to have the characteristic of a
midband sinusoidal carrier modulated by a low-frequency signal
whose highest frequency component is dependent on the bandwidth.
The result is a noise which, when detected, has an envelope with a
Rayleigh amplitude distribution.

Subjectively, there is little distinction between noises having a
Gaussian or Rayleigh distribution. However, the peak factor of the
Rayleigh distribution, the value exceeded 0.01 percent of the time,
is 9.64 dB; this is more than 2 dB below that for a noise having a
Gaussian distribution. This must sometimes be taken into account
in circuit design or in system performance evaluation.
Intermodulation Noise and Crosstalk
Intermodulation, caused by nonlinear input/output characteristics
of analog system repeaters, may result in many different types of
interference, all of which are in some way signal-dependent. The
process is very complex and has many variables that need not be
fully evaluated here [4]. However, a brief review of the principles
is given.
The nonlinear characteristics may be expressed as a power series
having an infinite number of terms. Usually, terms higher than third
order are small enough to be ignored and the equation is written
(17-7)
Consider an input signal, ei = A cos at + B cos f3t + C cos yt. If
this signal is substituted in Equation (17 -7) and expanded by
trigonometric substitution, many interference frequencies are found
in the output in addition to the wanted signals. All these components
are given in Figure 17-7 except the dc term, aOei~ which is usually
of little interest; it is filtered out, in most cases, and causes no
interference.
Random Intermodulation Noise. If all the signals involved in the
intermodulation phenomenon are speech signals, the result is an
interference very similar to random noise. If a signal is carried

FREQUENCIES AND RELATIVE MAGNITUDES TO BE FOUND IN OUTPUT, eo = alei 1 + ~ei2
FROM APPLIED SIGNAL, ei = A cos at + B-cos {3t + C cos yt
TERM 1
de
First
order
Second
order

Third
order

TERM 2
1/2

~(A2

.a=..

+ aaeia,

(,J
~

TERM 3

+ B2 + C2)
3/4 aaA (A2 + 2B2 + 2C2) cosat
+ 3/4 aaB(B2 + 2C2 + 2A2) cos{3t
+ 3/4 aaC(C2 + 2A2 + 2B2) eosyt

alAcosat + alBcos{3t
+ alCcosyt

3"

"0
Q

1/ 2 a2 (A 2cos2a t + B2cos2{3t + C2cos2yt)
+ ~AB[cos(a+{3)t + cos (a-{3)t]
+ ~BC[cos ({3+y) t + cos ({3-y) t]
+ ~AC[cos(a+y)t + cos(a-y)t]

~.

3

CD
::J

ur
1/4 ag(A3cos3at + B3cos3f3t + C"cos3yt) ~l
A2B [cos (2a+{3) t + cos (2a-{3) t]
A2C[cos(2a+y)t + cos(2a-y)t]
B2A [cos (2{3+a) t + cos (2{3-a) t] >
+ 3/4 a3 -<, B2C[cos(2{3+y)t + cos(2{3-y)t]
!f:A[COS(2y+a)t + cos(2y-a)t]
C2B[cos (2y+{3) t + cos (2y-{3)t];
+ 3/2 a3A C[cos(a+{3+y)t + cos(a+{3-y)t
+ cos(a-/3+y)t + cos(a-/3-y)t]

Note: Observe that if in the applied signal A = B, then the amplitude of the ex + f3 product, which is at the frequency ·ex + {3, is 6 dB greater than the 2a product. Similarly, ex - /3 is 6 dB greater than the 2a product, and
2a - {3 (and similar terms) are 9.6 dB greater than 3a. If A = B = C, then the a + {3 - y term and similar!
terms (but do not confuse with 2a - {3 type) are 15.6 dB greater than 3a. The compression, or first-order component, arising from the c,3 term is at least 9.6 dB greater than 3a and may be much greater, depending on t::
number of signals applied; for the three-frequency input given above, it is 23.5 dB greater. If the an's are functions
of frequency, the frequency effects must be added to the aforementioned effects to determine. the amplitude differences
between products.
i

I

Q

::J

a...
-4

:r
CD

~.

~

CD

Q

(II

..,c
CD

3

CD
::J

....

i

Figure 17-7. Expansion of power series for three-sinusoid input.

<
~

Chap. 17

Noise and Crosstalk

433

in a speech channel, each fundamental signal (cos at, cos {3t, etc.)
may be considered as a band of energy 4 kHz wide. As a result, it
can be seen that the frequency band of the intermodulation product
(the interference) is 8 kHz wide for the second-order products shown
in Figure 17-7 and 12 kHz for the third-order products. Thus, more
than one channel can be disturbed by the interferences.
If a broadband signal has a large number of fundamentals, the
number of disturbing products that can be produced is very large.
For example, in a system of 10,000 channels, a disturbed channel
may have well over one million third-order products. The probabilistic
combination of the large number of contributors, together with the
basic characteristics of each fundamental speech signal, generates
an interference that is Gaussian in its amplitude distribution and
has a flat power spectrum over the band of a disturbed channel.
Many other detailed characteristics of speech signals must be
evaluated in determining the effects of random intermodulation noise.
In addition to the speech signal characteristics, system characteristics must also be considered. For example, in analog cable
systems, modulation products of different types accumulate from
repeater to repeater according to different laws which are determined by the phase correlation between repeater sections. In microwave radio systems, the intermodulation phenomenon is as important
as in cable systems but results from different basic causes. Intermodulation noise in AM systems is a function of signal amplitude,
but in FM systems it is a function of the frequency deviation. In
AM systems, the noise results directly from the nonlinear input/
output characteristic of amplifiers as illustrated by Equation (17-7).
In FM systems, it results from gain and phase deviations in the
transmission medium. The end result, provided the number of
channels in the system is large, is essentially the same - a nearly
flat spectrum of noise having a Gaussian distribution (see Chapters
12 and 16).
Intermodulation Crosstalk. The transmission of FDM signals over
analog transmission systems produces interchannel coupling which
may also yield intelligible crosstalk in a disturbed channel.

The nature of the coupling mechanism may be demonstrated by
considering a simple illustration of two signals, A. cos at and B cos {3t,
transmitted simultaneously through a repeater whose input/output
characteristic may be represented by the truncated power series of

434

Impairments and Their Measurement

Vol. 1

Equation (17-7). The first term on the right side of Equation (17-7)
is a dc term. The second term yields the wanted output signal, a
reproduction of the input signal, e/, multiplied by the gain, at. The
third term (together with higher order terms) represents the inherent nonlinearity of analog repeaters. In this illustration, it is the
third and fourth terms which can produce intelligible crosstalk
through intermodulation.
For example, if the input signal is
ei

== A cos wd + B cos 

8

0

6

1-1--

V'j 11'/ V
1/ 1// V

Iii

~
~

4
2

If~

J. rfI

V

ViiI
/,W
4
If!J V
2 rlIJ
rtf

o rJ
o

20

40

60

80

100

120

Round trip echo path delay (milliseconds)

Figure 20-7. One-way loss for satisfactory echo in 99 percent of connections.

loss of one additional end-to-end transit of the four-wire circuit.
An exception, relatively rare and yet important where encountered,
is found in large multi station private line circuits. Here, listener
echo is often controlling, and special care must be taken in designing
this type of circuit.
There is a close relationship between listener echo and near-singing
of a circuit. Both conditions are caused by currents circulating within
a transmission path. Circuit instability, or singing, and singing
margins were discussed in Chapter 4. Interestingly, transmission
impairment occurs before singing actually takes place. If the singing
margin is too low, the near-singing condition of the circuit causes
voice signals to sound hollow, somewhat like talking into a barrel.
To avoid this effect, singing margin is maintained at 10 dB or more
in 95 percent of all connections and seldom, if ever, less than 4 dB.

Chap. 20

Echo in Telephone Channels

491

Digital Data Signals

When digital data signals are transmitted over telephone channels,
there is greater concern with listener echo than with talker echo.
Listener echo is usually very low in amplitude when talker echo is
well enough controlled to satisfy speech signal transmission but some
built-up connections in a switched network, public or private, may
have poor return losses at both ends of a four-wire intermediate link.
As a result, echo performance may be poor, and digital data echoes
may be generated at high enough amplitudes to interfere with reception. Circuits designed for dedicated data signal transmission may be
controlled so that listener echo is of low amplitude.
Data signalling rates between 1000 and nearly 10,000 bits per
second are commonly used. Thus, a listener echo delayed by 0.1 to
1.0 millisecond or more appears at the receiver as an unwanted
interfering signal having relatively little correlation with the wanted
signal. The magnitude of such an interference may be high enough
to be a serious source of data errors.
Talker echo is usually far less disturbing to data signal transmission than is listener echo. In certain instances, when a data terminal
is switched from send to receive, a talker echo resulting from the
end of a transmitted signal may appear as the leading edge of an
unwanted received signal. This may be confused with the expected
reply to the transmitted signal.
When data signal transmission equipment is designed for use on
the channels of a switched network, the problems relating to echo
must be solved by terminal design. Adequate signal-to-noise margin
must be provided in the receiver to cope with listener echo effects.
Timing circuits must be provided to avoid talker echo effects in
terminal equipment which may serve as both transmitter and receiver. However, the amount of time delay allowed for in engineering
design (called turnaround time) reduces the data transmission
efficiency, or throughput rate. When this is critical, full duplex
four-wire private line operation may be required or full duplex
operation may be established over the switched network by using
two separate connections.
TeJephotograph Signals

Telephotograph signals are very susceptible to echo impairment in
the form of a "ghost" of the desired picture. The echo elements are

492

Impairments and Their Measurement

Vol. 1

detached from the signal elements by an amount proportional to the
delay in the echo path. The echo may be positive or negative, depending on phase relationships between the signal and its echo. Since
most telephoto graph transmission is over dedicated channels where
impedances can be better controlled, echo is a serious problem only
when switched network channels are used.
20-3

ECHO MEASUREMENT AND CONTROL

The measurement of echoes in telephone channels is accomplished
primarily by return loss measurements. Echo performance is controlled by impedance adjustments and by the use of echo suppressors
on long circuits having delays in excess of 45 milliseconds. Private
line, or dedicated, channels are often provided as four-wire facilities
in order to avoid the echo problem. Even where some two-wire links
are necessary, the performance of such channels can usually be
made satisfactory by design control at the two-wire-to-four-wire
interface.
Echo Return Loss

Return loss, discussed in Chapter 4, is usually used as a measure
of echo performance resulting from an impedance discontinuity such
as that found at a four-wire terminating set in a telephone channel.
Return loss is defined rigidly in terms of the ratio of the sum and
difference of the complex impedances at the discontinuity. However,
the complexity of phase relationships in the incident and reflected
voltage or current waves makes it impractical to express return loss
over a band of frequencies except by averaging the performance over
the band of interest. A suitably weighted power average is used. This
. average, called echo return loss (ERL), is applied to the band from
500 to 2500 Hz.
This type of measurement is sometimes made by applying random
noise to the 500 to 2500 Hz band, sometimes by using a sweeping
frequency that covers this band and sometimes by measuring a
number of single-frequency return losses across the band. The
weighting is applied by the inclusion of appropriate networks in the
test equipment or by the manner in which the results are processed.
Several weightings are used (including flat weighting), none of
which is universally accepted.

Chap. 20

493

Echo in Telephone Channels

Echo return loss evaluation may be illustrated by considering
return loss measurements at a number of single frequencies. Typically,
measurements are made at frequencies /1 = 500, /2 = 1000, /a = 1500,
/4 == 2000, and /s
2500 Hz. These measurements may be regarded
as applying to the edges of four equal frequency bands, designated
B l , B 2 , B a, and B 4 • The plane geometry rule for finding the area of a
trapezoid may be applied by analogy to the determination of the
average return loss over the four bands of interest. This rule, as
applied here, yields an echo return loss value,

=

ERL

B (RL/12+ RLf5 + RL/2 + RLfa + R Lf4 )
== -10 log 4B

dB (20-3)

where B is the bandwidth of each of the four bands of interest
(500 Hz), and RLfn is the return luss at each of the five frequencies
expressed as a power ratio. This equation has the effect of weighting
the return losses at the band edges (500 and 2500 Hz) to one-half
the effectiveness of the return losses at 1000, 1500, and 2000 Hz.
The following table, which gives return loss values that might
be measured at the five frequencies of interest, provides a summary
of how the data would be analyzed.
RATIOS

FREQUENCY,
Hz

RETURN
LOSS, dB

CURRENT

POWER

WEIGHTED
POWER RATIO

500
1000
1500
2000
2500

25.0
30.0
25.0
22.0
18.0

0.056
0.032
0.056
0.079
0.126

0.00316
0.00100
0.00316
0.00631
0.01583

0.00158
0.00100
0.00316
0.00631
0.00792

The last column, which represents the five return loss terms in
Equation (20-3), totals 0.01997. When divided by 4, this yields a
value of 0.00499. Then,
ERL

== -

10 log 0.00499

== 23.0 dB.

If a straightforward averaging of the five power ratios in the
next-to-last column had been made, the echo return loss would be
calculated as
ERL

== -

10 log 0.0~946

== 22.3 dB.

494

Impairments and Their Measurement

Vol. 1

While the difference between these approaches, 0.7 dB, appears to
be small, it is significant and there is evidence that the weighted
value more nearly represents the subjective effect of echoes as
evaluated by return loss measurements.
In the switched network, ERL measurements are made at various
switching offices; impedance adjustments are made to guarantee the
echo performance at each office involved. The measurements and
adjustments are usually made with some standard value of impedance
as a reference. The measurements are called through balance or
terminal balance measurements.
Singing Return loss

As previously discussed, margin must be provided against instability or singing. Singing return loss measurements, made to give
assurance of the necessary stability, must be made at all frequencies
at which a circuit might become unstable. Experience has shown that
the important bands are those from 200 to 500 Hz and from 2500 to
3200 Hz. Below 200 Hz and above 3200 Hz, telephone circuits usually
have sufficient loss to suppress any tendency towards instability.
Frequencies in the 500 to 2500 Hz range are usually satisfactory
from the standpoint of singing return loss if they meet echo return
loss requirements.
The singing return losses or the singing margins are measured in
the field by sweep frequency or random noise techniques or in the
laboratory by point-by...;point methods. Impedance adjustments are
specified to guarantee satisfactory performance; the adjustments
specified in echo return loss tests generally tend to improve singing
return loss performance.
Echo Suppressors

Figure 20-7 shows that the overall connection loss must be increased SUbstantially as echo delay becomes greater. However, as
transmission loss increases, talker volume at the listener's station
set decreases; loss of volume may become a serious 'impairment.
Experience has shown that the loss associated with a 45-millisecond
echo delay (one-way loss of about 9 to 11 dB) IS about as much
as can be tolerated and still produce satisfactory received volume.

Chap. 20

Echo in Telephone Channels

495

Thus, circuits with echo delays in excess of 45 milliseconds are
equipped with echo suppressors. These devices, used on four-wire
trunks, insert high loss in the return direction when speech energy
is being transmitted and permit a lower insertion loss on trunks that
are so equipped.
REFERENCES

1. Huntley, H. R. "Transmission Design of Intertoll Telephone Trunks," Bell
System Tech. J., Vol. 32 (Sept. 1953), pp. 1019-1036.
2. Clement, M. A. Transmission (Chicago: Telephony Publishing Corporation,
1969) .

Impairments and Their Measurement

Chapter 21

Phase Distortion
Some signals, such as digital and video signals, are particularly
sensitive to departures from linear input/output phase characteristics
in the channels over which they are transmitted. Speech signals are
not adversely affected by these irregularities because the human
hearing mechanism resolves signal components at different frequencies in a way that has little phase dependence; thus, little attention was originally given to phase irregularities in telephone channels.
However, with the increased use of such channels for the transmission of other types of signals, the necessity for understanding and
coping with phase-related impairments has continually increased.
The characterization and control of wideband channels are also
increasingly necessary because they are largely used by types of
signals most sensitive to departures from linear input/output phase
characteristics.
21-1

PHASE/FREQUENCY MATHEMATICAL CHARACTERIZATION

In Chapter 6 the breakdown of a square wave into its Fourier components was discussed, and the necessity of maintaining proper
amplitude and phase relations among the signal components was
mentioned. Impairments caused by departures from ideal (flat)
amplitude/frequency response were considered in Chapter 18. Here,
consideration is given to the impairments resulting from departures
from the ideal (linear) phase/frequency characteristic in a channel.
Departure from Linear Phase

Consider first, the simple square wave of Figure 21-1 (a). As
pointed out in Chapter 6, this wave can be synthesized from an
infinite number of odd harmonics of its fundamental frequency. These
harmonics and the fundamental must be controlled in both amplitude
and phase. Figure 21-1 (b) shows the dc, fundamental, and thirdharmonic signal components of the idealized square wave of

496

Chap. 21

(a)

Phase Distortion

~:R I I
o

.

I.- T/2---.1

I

~l/wo=Tsec~

1.0

(b)

0.5 ~-~--+---+---~k----+-----

497

Impairments and Their Measurement

498

Vol. 1

Figure 21-1 (a) in the phase and amplitude relationships they must
bear to one another to form the original square wave. Figure 21-1 (c)
shows how these add ,to approximate the square wave.
If the channel over which these components are transmitted has
a linear phase/frequency characteristic (for example, phase shift at
3wo is three times that at tuo), the time relationship between components is unaffected by transmission. (For this discussion, the
channel is assumed to have flat gain equal to 0 dB over the entire
spectrum.) Since the delay is the same at all frequencies, the approximated square wave is identical at the output to that at the
input (the absolute time delay is neglected).
N ow consider the effect of phase distortion, i.e., a departure from
linear of the phase/frequency characteristic. Assume that the phase
shift at radian· frequency 3wo is not linearly related to that at tuo.
The fundamental may be written cos (0

(a)

a;

.::

(b) ~

-0
OIl

Q.

~

0

a;

/32

0
.z;

>
c
w

D.

WI

Radian frequency, w

W2

Radian frequency, w

Figure 21-3. Phase shift derived from envelope delay.

(21-6)

501

Phase Distortion

Chap. 21
Envelope Delay Distortion

Envelope delay distortion, or relative envelope delay, is the difference between the envelope delay at any frequency and that at a reference frequency. The reference is usually taken as the frequency at
which the envelope delay is a minimum. Thus, envelope delay distortion may be written

EDD
where

=

::! - (::!) seconds
1

(21-7)

(::!) is the envelope delay at the reference frequency.
1

Illustrative Characteristics
Figure 21-4 illustrates the various expressions for the phase distortion characteristics previously discussed. Three kinds of channel
characteristic are illustrated, namely, an ideal linear phase characteristic (one that can only be approached in practice), a low-pass
characteristic typically found in baseband cable transmission facilities, and a bandpass characteristic typically found in FDM carrier
transmission facilities. The characteristics are displayed qualitatively
to show their general shapes. In each sketch, the curve from w = 0
to W =Wt illustrates the general shape of the inband channel characteristic. Above the top channel frequency, 'Wt, the trend of the
out-of-band characteristic is illustrated for each case in a general
sense. Exact characteristics vary widely according to design. The
bandpass characteristic is illustrated in terms of its baseband
equivalent.

Intercept Distortion
Some signals transmitted over a channel having a certain type of
phase characteristic may suffer from a form of distortion known
as intercept distortion. This distortion may occur even though the
phase characteristic is linear over the useful part of the band, i.e.,
the part carrying all significant components of the transmitted signal.
This form of distortion may be illustrated mathematically with the
help of Figure 21-5.

502

Impairments and Their Measurement
IDEAL

1

BANDPASS

lOW· PASS

,/

51

(a)

Vol. 1

1c.
Cli.

0

w,

0

0

Wt

w----+

Wt

u

!

>-

0
Qj
"0

(b)

,

51

"\

0

.J:.

c.

I,

~"

I \

\

~ (/3/wh
<:Q.

0

WI

0

w----+

W,

0

WI

0

WI

>-

0
Qj
"0

(c)

,:21

3..'!.
"'-.c

S:f
~ o~
"'-."0

<:Q.

0
0

w,

0

w----+

Wt

I,,

'U
Gl

..'!.

>-

0
Gj

-0

8.
0

(d)

1
Gl

~
(d(3/dwh
"'-.
~

0

~Wt

0

Wt

0

Wt

W----+
u

"\ "

51

..::::~

~

Of
~~
-~
I >-

(e)

~ ~
"-.

Gl

~

~

~]c

Gl

0
0

W,

0

w----+

Wt

0

Figure 21-4. ~hase distortionahd related parameters.

w,

Phase Distortion

Chap. 21

503

--,----I

::0-

g

>.

c
"'ii
~

Boc

~

C

1
=

n21T

f

c

..t:
~

BOA =0

o
Radian frequency,

ill

Figure 21-5. Phase delay characteristics to illustrate intercept distortion.

The three characteristic curves in Figure 21-5 are all linear in the
region from CUI to Seth == CUa. Curve A is an ideal linear phase curve;
curves Band C are bandpass phase characteristics that typify transmission through a bandpass channel such as those found in FDM
equipment. The characteristics have been translated (shifted in frequency) to their baseband equivalents. The dotted extrapolations of
the· low-frequency ends of curves Band C are straight-line extrapolations of the linear portions of those curves down to zero frequency.
The familiar analytic geometry expression for a straight line,
mx + b, may be used as the equation for any of the characteristics, A, B, or C, at least up to frequency Wa. The expression, for
present purposes, is
y

==

13 == mcu + /30

(21-8)

where po is the zero-frequency phase intercept of the straight line
with the 13 axis, W is the radian frequency, and m is the slope of the
straight line.
Now, consider two components of a simple input signal
Al cos wtt

+ Aa cos SCUlt == Al cos

WIt

+ A3 cos cust

Impairments and Their Measurement

504

Vol. 1

where 

IT

!I!

~
Q)

-c
.~

Q.

E

0
Qj

c
c
0
...c
U

(e)

0.5

o
-0.5
Radian frequency, cu ----..

Figure 21-6. Amplitude/frequency responses for vestigial-sideband transmission.

508

Vol. 1

Impairments and Their Measurement

The amplitude of
filter. By further
and multiplication
Equation (21-13)

== [A

the carrier component is halved by the vestigial
trigonometric expansion of the (We - Wi) term
of the right side by 2 (assumed flat amplification),
may now be written as

+ P ( t )] cos wet + Q ( t)

sin wet

(21-14)

where P(t) == ai cos Wit and Q(t) == ~ sin Wit. Note that P(t), the
wanted component, and Q (t), the quadrature component, are both
equal to the input signal but that Q (t) is shifted in phase by
1T/2 radians relative to P(t). Equation (21-14) also shows that P(t)
and Q (t) may be regarded as modulating carriers of the same
frequency, We, again separated by 7T/2 radians.
The signal components of Equation (21-14) are shown vectorially
in Figure 21-7. Note that the amplitude of the resultant vector, equal
to the envelope of the signal, is determined by
1SSSB 1== V (A

+

1PI) 2

+ 1Q 12

(21-15)

The distorting effect of the quadrature component is illustrated in
Figure 21-8. The amplitude of the peak in the illustration can be
estimated from Equations (21-14) and (21-15). If there is no dc component, A, the amplitudes of P(t) and Q (t) are equal and the peak
excursion of the signal of Figure 21-8 is 1.7 times the amplitude of the
step. If a dc component is added, the influence of the quadrature term

In-phase components, P(t)

Figure 21-7. Analysis of SSB signal into in-phase and quadrature components.

,I

509

Phase Distortion

Chap. 21

i:

1\

Distorted
output
signal

I

,

~~----OJ

]

I

a.
E

Ideal input

/

«

/

signal

/

-----_..../_-...
Time

---+-

Figure 21-8. Effect of quadrature distortion on signal characteristic.

is reduced, as can be seen by examination of Equation (21-15). The
shape of the modified step transition in Figure 21-8 is influenced by
the ratio of the vestigial to the principal sidebands and the shaping
of the characteristic through the vestigial region.
Differential Phase

I

~

In a video transmission system, differential phase is defined as
the difference in output phase of a low-amplitude, high-frequency
sine-wave signal at two stated amplitudes of the low-frequency signal
on which the high-frequency signal is superimposed. Since color
television is the only signal significantly affected by the phenomenon,
the definition of differential phase is in terms pertinent to
color signal characteristics. Differential phase measurements are
made using a 3.579545-MHz low-amplitude signal to simulate the
color carrier in an NTSC color signal. The low-frequency signal used
is usually a 15.75-kHz sine wave simulating the fundamental line scan
frequency of the luminance component of a standard color signal.
Other low frequencies are also sometimes used.
Mathematically, the generation of differential phase can be demonstrated by considering the intermodulation of the two test signals
due to nonlinearity in the circuit being evaluated. Let {3 represent
the low frequency and a represent the high frequency. The input
signal then may be represented by ein == A cos .at
B cos {3t. Also,
let the input/output characteristic of the circuit be represented by

+

eout

= ao + al~n + lli2ein + as~n + ...
2

3

(21-16)

510

Vol. 1

Impairments and Their Measurement

To simplify the illustration, consider only the wanted output term,
alein, and the distortion term, a3e 3in. When the input signal is substituted in these terms, the output may be written
elout

== al

(A cos at

+ B cos f3t) + a3 (A cos at + B cos f3t)3.

(21-17)

N ow, with respect to the definition of differential phase, attention
may be concentrated on just three of the terms that can be derived
by expanding Equation (21-17).* These may be written
~out

3
== alAcosat + -a3 AB2 cos
4

+

(a+2f3) t

43 a3 AB2 cos (a-2f3) t.

(21-18)

The signal of Equation (21-18) may be regarded as an amplitudemodulated version of the desired output component, al A cos at, with
sidebands at frequencies (a+2f3) and (a-2f3). Amplitude and phase
relations among the signal at frequency a and its sidebands determine the nature and magnitude of the impairment. If the sideband
components combine in phase with al A cos at, the impairment is
differential gain, discussed in Chapter 18; if the sideband energy is
at 1T/2 radians relative to the wanted signal, the impairment is
essentially all differential phase. If the sidebands combine and lie
between 0 and 1T/2 radians relative to the wanted signal, the impairment is a combination of the two.
e(a + 2/1)
Differential phase is illustrated
2/1)
ea
/
by the phasor diagram, Figure 21-9.
-~
~1'r<
If the phasors, e(a+2/3) and e(a-2/3h
are small compared to ea, the
magnitude of the resultant, er , is
nearly constant and equal to ea. Figure 21-9. Phasor diagram iIIustraAlso, the differential phase shift,
ing differential phase.
measured by the angle CPd, is a
maximum when e(a+2/H is in phase with e(a-2/n. Thus, the differential
phase is equal to
'\..

e(a -

-:~..--J

(21-19)

* The complete expansion of a 3-component input signal through a nonlinear
power series like that of Equation (21-16) is given in Chapter 17 (Figure 17-7).

Chap. 21
21-2

Phase Distortion

511

PHASE DISTORTION IN TELEPHONE CHANNELS

All forms of phase distortion described so far may occur in standard 4-kHz channels used for telephone signal transmission. With
the exception of differential phase, all may impair the signals typically
transmitted in these channels. The sources of signal impairments
are largely departures from linear phase/frequency characteristics,
the resultant generation of echoes, and signal-dependent distortion
such as quadrature distortion. The effects on various types of signals
may be quite different depending on the nature of the transmitted
information [1].
Phase/Frequency Impairments
Phase/frequency impairments may result from many sources of
distortion in a telephone channel. The two most common sources are
those related to the transmission characteristics of loaded cable
circuits and those related to the cutoff characteristics of filters in
FDM equipment.
The transmission characteristics of loaded cable are similar to
those of a low-pass filter. The phase/frequency characteristic of a
low-pass filter is illustrated qualitatively in Figure 21-4. The exact
shape and magnitude of the channel distortion and the extent of the
impairment to signal transmission depend on many interrelated
parameters such as the type of cable and loading, the lengths of line
and end section, the impedance match of the source and load to the
line, and the characteristics and susceptibility of the transmitted
signal.
The effects of bandpass channel filters are also illustrated in
Figure 21-4. The shape and magnitude of the channel distortions
and the resulting signal impairments are significantly influenced
both by the number of filters that may be connected in tandem in
various situations and by the transmitted signal characteristics.
Digital Signals. As in the case of other forms of impairment, the
effect of phase/frequency distortion on digital signals is conveniently
expressed in terms of an increase in error rate or in terms of an
equivalent signal-to-noise impairment. One simple form of signal
impairment, iIIustrated in Figure 21-1, results from an assumed
simple type of phase/frequency distortion. More complex forms of
channel distortion cause more complex forms of signal distortion.

512

Impairments and Their Measurement

Vol. 1

Some are amenable to theoretical analysis and evaluation, but in
field situations they usually are most easily evaluated by error rate
or eye diagram measurements. One useful type of analysis involves
expressing the effect of channel impairments in terms of the generation of signal echoes. This work is particularly useful in the evaluation
of analog signal distortion but can be adapted to digital signal
impairment in some cases [2].
Analog Signals. While speech signals are not adversely affected by
phase/frequency distortion, analog data signals and particularly
telephoto graph signals transmitted over telephone channels may be
severely impaired by echoes that result from this form of distortion.

In the telephoto graph picture, an echo appears as a low-amplitude
reproduction of the picture or portions of the picture displaced from
the picture signal itself. The amount of displacement and the faithfulness of reproduction in the echo depend on the magnitude and
nature of the distortion. If the displacement is small, picture details
may simply be blurred or distorted; if the displacement is large, the
impairment may more nearly appear as a faint reproduction of the
picture with positive or negative polarity.
Detailed analyses of echo phenomena have been made in order to
provide quantitative evaluation of such impairments [3]. One type
of analysis that has proved to be valuable for all forms of video
signal transmission utilizes the concept of an echo rating. While
applicable to any form of video signal transmission, the concept was
first applied to television signal transmission and later used to
analyze transmission over a PTCTUREPHONE channel [4].
Quadrature Distortion

As illustrated in Figure 21-8, quadrature distortion causes unwanted changes in a signal shape at a point where there is a sharp
transition in the signal amplitude. Digital data signals and telephotograph signals commonly contain such sharp transitions and
are thus particularly susceptible to quadrature distortion. In a
carrier signal, the impairment must be evaluated in terms of possible
overload effects. Peak factors such as those illustrated in Figure 21-8
may cause overload in carrier equipment and result in clipping of
the signal peaks or in an increase in intermodulation or both. Intermodulation may cause deterioration of the signal itself or of other
signals sharing the same medium.

I

,

Chap. 21

Phase Distortion

513

While quadrature distortion is most evident in carrier signal waveforms, its effects may also appear in the signal after detection.
These effects may increase the error rate for digital signals or may
cause blurring or smearing of portions of a telephotograph signal
in areas where there are large and sudden changes in the luminance
of the image.
21-3

PHASE DISTORTION IN BROADBAND CHANNELS

Broadband channels are provided primarily for the transmission
of television, PICTUREPHONE, and wideband digital signals, all of
which are particularly sensitive to phase distortion. All of the general
comments and discussion relating to phase distortion in telephone
channels apply equally well to transmission in broadband channels.
In addition, quadrature distortion and differential phase have particularly serious effects on the transmission of wideband signals.
Phase/ Frequency Distortion

Minimizing phase/frequency distortion in broadband channels
through equalization techniques is made difficult by the multiplicity
of phase/frequency characteristic shapes encountered across the band
in a long transmission facility. This difficulty is a result of the many
modulation stages and tandem application of connectors and/or
blocking filters that may be found in long systems.

r

Quadrature Distortion

Quadrature distortion effects on wideband digital signal transmission are similar to the effects on voiceband digital signal transmission. Signal peaking must be controlled to avoid clipping and
transmission system overload. The loss of margin, or increase in
error rate, caused by quadrature distortion of the detected signal
usually can not be tolerated; therefore, this form of distortion must
be carefully controlled in the received signal. Often some form of
vestigial sideband modulation is chosen so that the carrier can be
recovered in proper phase at the demodulator.
Quadrature distortion of PICTUREPHONE and television signals
must also be carefully controlled to limit the blurring or smearing
of the picture at sharp luminance transitions. There has been little
PICTUREPHONE transmission by SSB or VSB techniques so
that the quadrature distortion problem has not really been faced.
Considerable effort was made to limit quadrature distortion in the

514

Impairments and Their Measurement

Vol. 1

transmission of television signals over Ll and L3 Coaxial Carrier
Systems [5, 6].
Differential Phase

Differential phase, as discussed previously, is of importance only
in the transmission of NTSC color signals. When this distortion is
encountered, the phase relationships among color signal components
transmitted at high video frequencies vary with respect to one
another. The result is a change in the hue of various colors. If the
distortion is excessive, colors may change completely as the luminance
of the picture varies.
21-4

MEASUREMENT, EVALUATION, AND CONTROL OF PHASE
DISTORTION

Most of the impairments discussed in earlier chapters can be
measured by relatively straightforward methods and by the use of
conceptually simple test equipment such as signal generators and
detectors. Phase distortion, however, is somewhat more difficult to
measure and evaluate, partly because of the difficulty of defining
and measuring a reference phase. As a result, most measurements
are made in terms of relative phase. These observations apply equally
to voiceband and broadband measurements; and while different test
set designs are used for different bandwidths, the theory of operation
is often independent of the bandwidth.
Phase/Frequency Measurement and Evaluation

Phase/frequency measurements are seldom made in the field on
voiceband circuits because of the inherent difficulty of establishing
a reference phase. In addition, the complexities of measuring and
evaluating even relative phase (delay distortion or envelope delay
distortion) are great enough that time-domain measurements are
usually favored. Time-domain measurements have the advantage of
relative simplicity and speed, but they have the disadvantage that
the effects of individual impairments are difficult to separate from
one another. When poor performance is indicated, the time-domain
measurements must usually be supplemented by frequency-domain
measurements in order to identify specific sources of impairment.
The common time-domain methods of measurement and evaluation
include error rate measurements by means of pseudo-random data
messages and eye-diagram presentations on a cathode-ray oscilloscope.
Another method involves the use of the PIAR system of measurement.

Phase Distortion

Chap. 21

515

The PI AR System. The peak-to-average ratio (P /AR) provides a
single number measure of the overall quality of circuits used for
the transmission of voiceband data signals [7]. A P / AR generator
transmits a precise, repetitive pulse through the system. The pulses,
dispersed by all of the impairments in the channel, are then delivered to the P / AR receiver which responds to the pulse envelope
peak and the pulse envelope full-wave average. A meter in the
receiver is used to indicate the ratio of these two parameters. The
ratio, called the P / AR rating, appears on the meter in a form
determined by

.

P/AR ratIng

== 100

[E
(pk)
2 E(FWA)

-1

J.

(21-20)

where E (pk) is the normalized peak value of the pulse envelope
and E (FWA) is the normalized full-wave rectified average value of
the envelope.
The P / AR approach to voiceband circuit evaluation is valuable
because of its simplicity and speed. It also lends itself well to analytical evaluation based on measured or estimated amplitude/frequency
and phase/frequency channel characteristics. Computer programs
have been developed to accomplish this evaluation [8].
Envelope Delay Distortion Measurements. While phase measurements
per se are seldom made, envelope delay measurments can be made
without excessive complexity of test equipment, measuring technique, or interpretation. The results of these measurements can
then be converted to a phase shift
'characteristic when needed. Usually, however, the envelope delay
distortion curve suffices for evaluation of a circuit.
~
c

The usual method of measuring :;;envelope delay can be described
/3u
with the assistance of Figure 21-10, l. /3c
which illustrates the inband phase/
/31
frequency characteristic of a bandpass channel translated to baseband. Envelope delay can be
Radian frequency, w
measured to a close approximation
at radian frequency We by transFigure 21-10. A phase/frequency
mitting a carrier frequency signal
characteristic.

i

516

Impairments and Their Measurement

Vol. 1

at

We modulated by a signal which places sidebands at frequencies
and 'Wu. If the modulating frequency is chosen so that the phase
characteristic between Wz and Wu is approximately linear, the phase
difference between the carrier and the two sideband frequencies may
be written
.
Wz

The envelope delay may then be determined as the slope of the
phase curve at the carrier frequency, (de, used for the measurement.
Equation (21-5) may then be applied to this measuring technique:
(21-21)
The modulating frequency must be quite low to make
Equation (21-21) a reasonable approximation. In Bell System voiceband measuring sets, the modulating frequency is 83-1/3 Hz. Sets
designed for wideband channel measurements use proportionately
higher carrier and modulating frequencies.
Measurements of the type just described may be made on a pointby-point basis by adjusting (de manually and measuring the phase
differences at each setting. The measurement may be automated by
sweeping the band with a continuously varying We and displaying
the envelope delay on an oscilloscope or other recording device.
Echo Observations. Sometimes, gross evaluation of channel performance can be accomplished by transmission of test signals and
examination of the received signal on an oscilloscope or, in the case
of video circuits, on a television or PICTUREPHONE receiver. More
precise analysis or measurement by other techniques is then necessary.

Phase Distortion Control

The control of phase/frequency characteristics, quadrature distortion, and differential phase must all be considered in the design and/or
operation of telecommunication facilities.
Phase/Frequency Characteristic Control. The necessity of controlling
high-frequency and low-frequency cutoff characteristics has been
previously discussed from the point of view of satisfying Nyquist's
criteria. These cutoff characteristics must generally be designed to

Chap. 21

Phase Distortion

517

have linear phase/frequency characteristics, most nearly achievable
if the roll-offs are gradual. Sharp channel cutoffs are to be avoided.
Where channels are to be used for digital signal transmission,
their design may involve a conflict which must be resolved by
carefully determined compromises. To make transmission efficiency
as high as possible, it is tempting to design for the absolute maximum
rate of transmission that a channel can theoretically accommodate.
This design approach usually produces significant amounts of energy
near the band edges where characteristics are hardest to control.
Generally, it is advisable to restrict the bit rate to something below
the maximum in order to provide operating margin.
Another means of controlling the phase/frequency characteristic
is by equalizing the channel to produce a near linear phase/frequency
characteristic. Many types of delay (phase) equalizers are used for
this purpose. If a channel is dedicated to the transmission of a
limited number of signal types, specific designs of equalizers may
be used to equalize that channel for satisfactory performance. If the
channel is partly dedicated and partly switched, fixed equalizers
may be provided for the dedicated portion of the circuit and for some
average characteristic representing the switched portion. Adjustable
equalizers may also be provided in both dedicated and switched
channels in order to compensate for seasonal or other time-varying
phenomena. Finally, adaptive equalizers have been designed to adjust
themselves automatically to gain and delay impairments on the basis
of certain signal characteristics. These equalizers are usually of the
tapped delay line type [9].
Quadrature Distortion Control. There are a number of design-related
ways of controlling quadrature distortion. These include several that,
of necessity, involve design compromises. For example, the wider
the vestigial sideband, the less the quadrature distortion; however,
the decrease in distortion can only be achieved at the expense of a
greater total bandwidth or a reduction of the width of the wanted
sideband.

The index of modulation is another design parameter that may
be used to reduce quadrature distortion. The amplitude of the component A cos wet in Equation (21-14) is related to the index of
modulation, as discussed in Chapter 8. The larger this component

518

Impairments and Their Measurement

Vol. 1

(low index of modulation), the more nearly the total transmitted
signal is in phase with the wanted signalP (t) cos wet; the quadrature component, Q (t), then has less effect, as can be seen by examination of Figure 21-7. However, this means of reducing quadrature
distortion can only be accomplished at the expense of overall signalto-noise ratio. For a given maximum magnitude of transmitted
modulated signal, the higher the index of modulation, the better the
resulting signal-to-noise ratio.
The last important factor involves the use of product demodulation rather than envelope detection at the receiver. As previously
described, quadrature distortion is first evident in the SSB or VSB
carrier frequency signal. If this distorted signal is envelope-detected,
the quadrature distortion is carried through the receiving equipment
and appears in the output signal. If product demodulation is used
at the receiver and the distorted carrier frequency signal has not
been clipped or limited in any way, the quadrature distortion does
not appear in the output signal, provided the phase of the demodulating carrier is very close to that of the received carrier [6].
Differential Phose Control. This form of distortion cannot be controlled in operation except by ensuring that signal amplitude does
not exceed the design value. This distortion can only be controlled in
the integrated signal-system design process, which must result in
satisfactory performance-both signal-to-noise and differential phase
performance-in the face of natural nonlinearities in the channel
transmission equipment.
REFERENCES

1. Bell System Technical Reference PUB41004, Transmission Specifications for
Voice Grade Private Line Data Channels (American Telephone and Telegraph
Company, Oct. 1973).

2. Mahoney, J. J., Jr. "Transmission Plan for General Purpose Wideband
Services-Appendix A," IEEE Transactions on Communications Technology,
Vol. COM-14 (Oct. 1966), pp. 647 and 648.
3. Wheeler, H. A. "The Interpretation of Amplitude and Phase Distortion in
Terms of Paired Echoes," Proceedings of the IRE (June 1939), pp. 359-385.
4. Crater, T. V. "The PICTUREPHONE System: Service Standards," Bell
System Tech. J., Vol. 50 (Feb. 1971), pp. 255-258.
5. Morrison, L. W. "Television Terminals for Coaxial Systems," Transactions of
the AlEE, Part II, Vol. 68 (1949), pp.1193-1199.

Chap. 21

Phase Distortion

519

6. Rieke, J. W. and R. S. Graham. "The L3 Coaxial System-Television Terminals," Bell SY8tem Tech. J., Vol. 32 (July 1953), pp. 915-942.
7. Campbell, L. W. Jr. "The PAR Meter: Characteristics of a New Voiceband
Rating System," IEEE Transactions on Communication Technology, Vol.
COM-18 (Apr. 1970), pp. 147-153.
8. Fennick, J. H. "The PAR Meter: Applications in Telecommunications Systems," IEEE Transactions on Communication Technology, Vol. COM-18 (Feb.
1970) , pp. 68-73.
9. Lucky, R. W. "Techniques for Adaptive Equalization of Digital Communication Systems," Bell System Tech. J., Vol. 45 (Feb. 1966), pp. 255-286.

Impairments and Their Measurement

Chapter 22

Maintenance and Reliability
This chapter relates the basic principles and general application
of maintenance and reliability to transmission and service impairments. Serious impairment to transmission or service can occur
when poor maintenance design' practices are followed, when maintenance procedures are inadequate, or when unreliable equipment,
apparatus, and facilities are used. Maintenance and reliability are
interrelated; in the extreme, poor maintenance can lead to the
ultimate impairment, system failure.
While maintainability and reliability must be carefully planned
during the design, development, and installation of all equipment
and systems, maintenance must also be a continuing concern throughout the service life of each system or item of equipment so that
performance standards continue to be met. A wareness of and
familiarity with all facets of maintenance systems, maintenance support systems, and test equipment are maj or elements in the control
of network transmission performance.
The reliability aspects of transmission systems vary widely in
accordance with such factors as accessibility, availability of protection switching and emergency broadband restoration facilities, and
the impact of service outages on the kinds of circuits to be routed
over the system. A balance must be sought among such factors as
the degree of reliability improvement obtained, the cost of the improvement, the time allowance for temporary outage deemed acceptable to the customer, and the cost of service restoration when
outages do occur.
Economics plays a large role in the design, development, and
operation of maintenance and reliability aspects of equipment and
systems. One example may be found in submarine cable system
design and operation. The cables and repeaters in these systems are
placed in a highly isolated and stable environment, the ocean floor.
520

Chap. 22

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521

However, when failure occurs, the recovery of cables and repeaters
for repair is a very time-consuming and costly operation. The
revenue lost during system outages can also represent a substantial
financial penalty. For these reasons, it is economical in submarine
cable systems to spend large sums to provide high system reliability
and accurate fault-location equipment in spite of the favorable
environment.
22-1

MAINTENANCE

Maintenance work is carried out either to correct an existing
trouble or to minimize or avoid the occurrence of trouble. In the
first case, there are various indications of trouble conditions, which
alert maintenance personnel to the need for repairs. The indications
may come directly from a customer, an operator, or other observer
of a malfunction; or trouble may be indicated by local or remote
alarms or measurements which reveal that some parameter fails to
meet requirements.
The second case, preventive maintenance, is performed on a routine
basis for the purpose of recognizing, limiting, or preventing the deterioration of transmission performance and minimizing the likelihood of service failure. Preventive maintenance activities may involve
only measurements; if no trouble is indicated by the measurements,
further action may be unnecessary.

r

Many transmission parameters, such as noise, loss or gain, balance,
etc., are measured periodically under various environmental conditions. The results of the measurements are reported to a central
point where the data are analyzed and combined. From these analyses,
indices are derived and published both as a means of comparing performance with other organizational units for which similar indices
are derived and as a means of determining trends in performance. By
using these indices as guides, it is often possible to see where and
when preventive maintenance routines are not being followed or are
inadequate or incomplete and where their application must be
strengthened. In many cases, routine maintenance procedures are
prescribed in which a system is temporarily removed from service at
specific intervals so that it can be realigned for optimum performance.
Requirements for preventive maintenance and periodic performance
measurements have greatly increased since direct distance dialing
has become widespread. In the past, most long distance calls and

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Impairments and Their Measurement

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many local calls were established with the help of an operator. When
transmission was unsatisfactory or when there was a service failure,
it was usually possible for the operator to identify the defective
circuit and to report it to maintenance personnel. Now, the customer
often fails to report troubles, particularly those of a marginal nature;
and even when a report is made, it is difficult to identify the source
of trouble. In addition, the tremendous plant growth and the need to
improve the productivity of plant maintenance personnel has added
continuing emphasis to the need for preventive maintenance routines.

Sources of Deterioration and Failure

Causes of performance deterioration are numerous. As d.evices
age, they often perform less efficiently and cause changes in critical
parameters. Aging effects are, of course, more pronounced in equipment employing electron tubes than in equipment employing solidstate devices; but all devices, active and passive, display some form
of deterioration with age. This is most apparent where high
mechanical, thermal, or electrical stresses exist.
Where moving parts are involved, electrical performance and reliability deteriorate due to mechanical wear. This type of deterioration
is most often found in electromechanical switching systems; also,
transmission paths through relay and plug-in unit contacts, etc., are
often adversely affected by increases in noise or loss.
Each year, millions of telephone connections are changed because
people move, equipment is rearranged, and facilities are changed.
The resulting plant rearrangements often cause performance deterioration since undesired bridged taps may be left on cable pairs,
impedance relationships may change at interface points to produce
changes in return loss and echo, and defective workmanship can cause
unwanted grounds or circuit crosses.
Weather changes may also cause deterioration of transmission
performance. Seasonal changes make it necessary in some carrier
systems to readjust equalizers to compensate for changes in transmission characteristics. Moisture due to rain or humidity can produce
trouble conditions in the loop and trunk plant, particularly if there
are numerous open-wire circuits or cable sheaths that have deteriorated so that they are no longer waterproof.

Chap. 22
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Maintenance and Reliability

523

Finally, equipment defects are also a source of impairment or unreliability. These may result from poor quality control or manufacturing errors, poor workmanship (including installer errors) in the
field, damage in transport or in service, unusual stress, and many
other causes.

Maintenance Systems and Equipment
Maintenance arrangements are provided for transmission systems
as required to meet best the demands of satisfactory cost and service
relationships. Sometimes the maintenance equipment is built into the
transmission system as a subsystem. In other cases the maintenance
or monitoring equipment may be centralized and applied to several
transmission systems. Maintenance operations may be automatic or
manual, locally or remotely controlled, and may involve the use of
fixed or portable test equipment. All these options depend on specific
applications to the purpose to be served.
Integrated Designs. Where continued satisfactory operation of a
transmission system depends on the frequent adj ustment of system
components or where efficient fault-location procedures must be provided in order to minimize the cost of service failure and repair,
maintenance equipment is often built in as a subsystem of a transmission system.

An example of integrated maintenance equipment is found in the
L5 Coaxial Carrier System. In L5, a transmission surveillance center
is provided at certain main repeater stations. This equipment provides the capability of measuring remotely the gain-frequency characteristics of a large number of coaxial transmission systems or
selected parts of systems. In addition, fault-location equipment may
be activated from the surveillance center to assist in the identification and isolation of troubles in remote repeaters. Protection switching
functions can also be activated from the surveillance center.
Adjunct Designs. Many designs of maintenance equipment and complete maintenance systems have been provided as adjuncts to transmission systems or to the switched networks. These are maintenance
faciliti€s that interconnect manually or automatically with transmission systems or with large groups of trunks. Their functions range
from simple manual or automatically sequenced measurements of
loop-to-ground resistance to complex series of automatic loss and

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Impairments and Their Measurement

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noise measurements of both directions of transmission on interoffice
trunks. Special test bays are provided to measure automatically or
manually the performance of circuits dedicated to the transmission
of specialized types of signals such as digital data and video signals .

.

The provision of adjunct test facilities has been stimulated by the
expanding plant. The large number of circuits that require testing
has led to considerable automation; time, cost, and manpower limitations simply do not permit manual testing. The expansion of types
of services has created a demand for well designed test facilities
and orderly procedures for their use. For example, the increased use
of telephone channels for data transmission and the increased interconnection of customer-provided data transmission equipment have
led to the design of test facilities that can be located in a telephone
central office and yet test the circuits in both directions of transmission ("loop-around testing"). This mode of testing has the
added advantages of minimizing the number of visits that must be
made to remote locations to test such circuits and minimizing the
amount of portable test equipment that must be carried to customer
locations, thus making the maintenance job more economical.
A wide variety of portable test equipment is also required for
various phases of the maintenance task-prevention, identification,
isolation, and repair. Portable adjunct equipment includes signal
generators and detectors, noise measuring sets, and delay distortion
measuring sets. They may be used sporadically in investigating
trouble situations or periodically in preventive maintenance procedures. Most central office transmission paths, for example, are tested
periodically for noise and, against standard terminations, for adequate
return loss.
Maintenance Support Systems. Systems that may be regarded as in
the maintenance support category are those that provide communication service for maintenance personnel (order wires), local and
remote alarm and telemetry arrangements, and system features that
are adapted to the maintenance function. These support arrangements may be integrated into the transmission system or may be
provided as adj uncts.

Consider first the communication facilities needed by maintenance
personnel. In some instances, the equipment may be simply a telephone connected to the public switched network to permit direct

Chap. 22
II
I

Maintenance and Reliability

525

dialing by the maintenance man at a remote location to his home
base or to another remote location. In other cases, typically in coaxial
system operations, private channels (called order wires) are installed.
These use interstitial wire pairs in the cable or may even be assigned
separate facilities in order to increase reliability. Order-wire systems
have become quite sophisticated and may include switching arrangements and alternate use for data transmission. Such facilities may
also be integrated with the transmission system. An example is found
in the TH radio system which includes an order-wire circuit in the
basic system desi,gn.
Alarms are provided in every system to alert maintenance personnel to real or incipient trouble conditions. This type of maintenance
support equipment also varies widely in design and application. An
alarm may be as simple as a local alarm actuated when a fuse operates
to light a lamp and/or to sound a bell or buzzer. Alarm information
may be extended from remote, unattended locations to a manned
central location. The extension of the alarm may again be very
simple-for example, the connection of the alarm indicator to the
remote location over a pair of wires-or the connection may be over
a data transmission system that collects alarm information from
many remote locations and forwards it to the central location. This
type of system may even provide for the remote control from the
central location of certain maintenance functions at the remote
stations. For example, in certain versions of the TH-3 Microwave
Radio System, equipment is built into the radio equipment bays to
provide for some remote control maintenance functions and to report
to a central location the existence of alarms and other forms of
trouble indication at the remote radio repeater stations.
Automatic protection switching systems are often provided so that
a hot standby facility is switched into service in the event of failure
of a working system. These switching facilities often provide a
maintenance support function. When it is necessary to perform
maintenance, measurement, or repair of a working system, service
may be temporarily transferred to the spare facility while the maintenance work proceeds. Even where protection switching facilities
are not available, this function is sometimes accomplished by patching
to spare facilities.
Documentation. The description of maintenance equipment and the
specification of tests and testing intervals are important aspects of

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Impairments and Their Measurement

Vol. 1

maintenance operations. For tests to be meaningful, the test equipment must be properly calibrated and personnel must be trained in
its use.
In the Bell System, many internal operating and maintenance
documents are devoted to descriptions of all types of test equipment
and to their calibration and use. Sections devoted to descriptions of
transmission systems and their operation have parts which contain
directions and suggestions on system maintenance procedures and
intervals. When these guides are not faithfully followed, system
deterioration may accelerate.

22-2

RELIABILITY

Reliability may be considered with respect to a device, a circuit,
a transmission system, or service to the customer. * The reliability
of a device is defined as the probability that the device will continue
to function satisfactorily during some specified interval, normally
its useful life. Where repair and replacement of failed devices (Le.,
maintenance) is feasible, reliability is defined for a system comprised
of discrete devices as the percentage of time the system is expected
to operate satisfactorily over a given time interval.
The opposite of reliability is the probability of failure during a
specified time interval. For systems, this measure of unreliability is
often expressed as the outage time over a given time period. Shortterm and long-term outages and intervals between which outage
times are measured may all be important, as in the case of microwave
radio systems where short-term outages due to fading differ in their
effect from longer outages due to gross equipment failures. Typically,
the objectives for system outage are expressed as minutes per year.
Since systems are comprised of many de.vices, overall system
failure rates and reliabilities are functions of many complex combinations of individual device reliabilities. The laws of probability,
discussed in Chapter 9, are used to evaluate these combinations.
In general, combinations of devices in series are more unreliable than
the least reliable device; parallel combinations are more reliable
than the most reliable device. Increased reliability of parallel com-

* An even broader term, survivability, is used to describe the ability of the
network to function in the event of enemy attack on the contiguous 48 states.
This subject is not covered here since it is only indirectly related to transmission.

Chap. 22

Maintenance and Reliability

527

binations is the justification for providing diversity for critical
systems or components of systems.
Sources of Failure

The sources, causes, and mechanisms of service failure may be
categorized in many ways. The principal categories can be defined
as external and internal; within each of these, there are natural and
man-made categories. These categories may be considered briefly and
their effects on the deterioration of service and signal transmission
may be qualitatively evaluated.
External Sources. Among the most common external sources of
failure are the effects of weather and other natural phenomena.
Lightning, in its direct impact, causes serious damage even to wellprotected cables and equipment. Indirectly, it is a source of impulse
noise, static in radio transmission, and induced currents in wire
circuits that can cause damage and system outage. Ice, snow, wind,
and water can also be destructive. Ice on microwave system antennas
causes serious deterioration of transmission performance. Ice, snow,
and wind often bring down aerial wire and cable. They make access
difficult where remote equipment and facilities are necessarily exposed. Water does tremendous damage when flooding occurs, but
even relatively light rain or humidity can cause deterioration of
service where insulation is exposed and weakened by age and the
elements. Rain attenuation of some microwave radio signals is a
serious source of impairment. Atmospheric layers not broken up by
convection or winds are a source of refractive fading in microwave
radio systems.

Other natural phenomena, such as sunspot eruptions and the aurora
borealis, can create -earth currents that temporarily disable cable
system operations or create inoperable conditions in high-frequency
radio transmission. Finally, communications systems are in no way
immune to the devastation caused by earthquakes, landslides, and fire.
Among man-made sources of failure are the environmental hazards
created by nearby power transmission systems. These systems may
induce interference currents into communication circuits or, in the
event of certain power system faults, may produce damaging currents
and expose personnel to high voltages. If communications circuits are
exposed to dc power systems, still found in traction company operations, the damaging effects of electrolysis must be considered.

528

Impairments and Their Measurement

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Construction, installation, and maintenance are also frequent causes
of failure. Outside plant may be damaged by workmen pursuing highway or building construction activities or service may be disrupted
inadvertently during normal outside plant operations. Sometimes,
service outages are a result of automobile accidents.
While little damage has occurred to Bell System plant as a result
of enemy action in time of war, this potential source of failure must
be of great concern to all those responsible for the design, development, and operation of all parts of the plant. Little can be done to
protect against direct hits of even conventional weapons. The possibility of direct damage and the effects of electromagnetic pulses due
to near misses of atomic explosives are given much consideration in
the design of portions of the present-day plant which carry critical
services.
Internal Sources. Within systems, circuits, and devices there are
a number of natural or man-made stresses that may be causes or
sources of unreliability. Among these stresses are high voltage (which
may produce noise or failure by breakdown), heat (which accelerates
the aging process and may cause fire), and mechanical stress (which
may cause fatigue failure or breakage due to mechanical shock or
long-term vibration in transport or service). Natural aging is, of
course, also a source of performance degradation and, ultimately,
failure.

Defects due to manufacture, handling, design, or improper installation may cause failure or deterioration. Such defects are sometimes
hard to control because they are so unpredictable.
Another form of internal stress is that of overload. At least two
forms of overload can cause transmission impairments. One form,
which results when signal amplitudes exceed design values, produces
serious transmission performance impairments due primarily to
intermodulation and, in the extreme, can cause transmission system
failure. This form of overload sometimes occurs when test signals
are misapplied or when high noise amplitudes are introduced by a
feeding system that has failed. The second form of overload, excessively high traffic, has its greatest impact on switching system
operation. This form of overload causes blocking of calls and a
breakdown of service. It can impair transmission performance only
indirectly by imposing higher than average loads on affected systems.

Chap. 22
Ii

Maintenance and Reliability

529

Designs for Reliability

I

'"

Reliability in a telecommunication network hinges on the design
of all elements in the network. Examples are cited of apparatus,
circuit, system, and manufactur.ing designs that have had a direct
impact on reliability performance.
III

Apparatus. Certain types of apparatus are commonly used to protect
circuits and systems from, failure due to high-voltage that may result
from lightning or contact with power systems, or excessive currents
caused by power system faults. Protective apparatus includes carbonblock, gas-tube, or solid-state (diode) protectors which break down
when subjected to excess voltage and carry fault currents safely to
ground. These devices are themselves sometimes sources of transmission impairments; when lightning or other faults cause partial
breakdown, low resistance to ground or high resistance or opens in
one conductor path may result, impairing the circuit by excessive
attenuation, noise, distortion, or crosstalk.

II'
I

H,eat coils are used on many circuits to protect personnel and
equipment from power sources which have voltages too low to operate
carbon-block or gas-tube protectors and which produce currents to
ground (through office equipment) too low to operate normal fuses
or circuit breakers. Heat coils are designed to operate when fault
currents exceeding specified values continue to flow on a communications conductor for time periods sufficient to cause excessive heating
and/or fire in the equipment. Operation of the device serves to ground
the offending conductor permanently. The heat coil must be replaced
when the fault has been cleared.
Fuses and circuit breakers are devices which also operate to protect personnel and equipment from excessive voltage or current.
These devices operate to open the offending circuit.
Circuits. A few examples of the many circuit arrangements furnished to provide reliable operation are cited here. Among the most
important is the central office battery arrangement that is used to
furnish common battery to all or most switching, signalling, and
transmission systems associated with each office. The battery supply
circuits are designed so that in normal operation the load is supplied
from the primary commercial source with a charging current supplied
to the battery. The size and capacity of the battery are determined

530

Impairments and Their Measurement

Vol. 1

by the load that must be carried by the battery alone in the event
of primary power failure and by the amount of time the battery
alone must carry the load without service failure.
Power distribution circuits within communications systems must
also be designed to guarantee maximum overall system reliability.
The design problems involve size of conductors, division of load
among the battery feed conductors, and the location and capacity of
fuses. The circuits must be arranged so that a fault in one part of a
system is contained and the whole system is not taken out of service.
Grounding of cable sheaths, apparatus cases, and other outside
plant items must be carefully controlled to minimize corrosion effects
due to electrolysis, especially where dc power systems are used.
Systems. Perhaps the most common feature of system design for
reliability involves the "hot spare," i.e., the provision of spare
equipment that is powered and ready to operate. Service from a
failed line or piece of equipment is transferred to the spare. The
transfer may take place automatically, by action of a switching
arrangement designed to recognize failure and to substitute the
spare facility, or manually, by patching in the spare equipment.
Coaxial transmission systems, microwave radio systems, and frequency division multiplex terminal equipment are usually provided
with automatic switching facilities. Reliability improvement hinges
on the reliability of the protection switch, which may lie idle for long
periods of time before it is called into action. New designs of highspeed digital transmission- systems are also provided with sophisticated monitoring and switching arrangements. Some short-haul
carrier systems and most of the voice-frequency trunk plant are
provided with flexible patching arrangements. The degree of protection in each case is determined by the reliability of the component
parts of the system and the resulting effect on the overall end-to-end
reliability of the circuits routed over the system.

Emergency broadband restoration is a procedure designed to maintain service on a broader scale than the switching and patching
arrangements just discussed. Restoration arrangements are set up
primarily to provide temporary service over spare facilities in the
event of any kind of failure that is not automatically restored, including failure resulting from the cutting of a coaxial cable or the
loss of a microwave repeater tower. Restoration patching and
switching bays have been provided in many locations so that transmission systems may be patched together in a flexible manner. Band-

~

'I
I

Chap. 22

Maintenance and Reliability

531

I

widths and transmission level points are critical parameters in the
design of these bays.
II'

Arrangements are also provided for physically replacing damaged
plant on an emergency basis. Portable microwave radio repeaters
and towers, coaxial cable lengths and splicing arrangements, gasolinedriven power supplies, and trailer-mounted PBXs and central office
switching machines are all kept in storage, available on quick demand
to furnish emergency service.
"Hardened" systems have also been installed in recent years to
increase reliability of the network, especially in the event of enemy
attack. Cables, structures, and buildings have been built or installed
to meet stringent blast-resistant requirements, and equipment is
often shock-mounted. Shielding is used on cables, structures, equipment, and buildings to minimize the possibility of service failure in
the event of exposure to electromagnetic pulses that accompany
nuclear blasts.

~'I

Manufacturing Designs. The reliability of apparatus, circuits, and
systems is related to the design of manufacturing processes used.
Mechanical, thermal, or electrical stresses can often be avoided by
proper design of the manufacturing process. Reliability can be improved by proper test and inspection methods. All these, however,
must be brought into economic balance. Manufacturing costs are
.increased by more stringent reliability requirements, and they can
only be justified by savings realized in field operation-reduced
maintenance, less outage time, reduced cost of repairs, etc.

Network Operating Methods and Procedures
Reliability of service is related finally to network operating methods
and procedures in the field environment. An important element in
the layout of facilities for reliable operation is the provision of
diverse routes and facilities. In the long distance plant, for example,
diversity of trunking between distant cities is often achieved by
dividing the trunks between coaxial systems and microwave radio
systems so that some service will remain in the event either type
system fails. Such diversity may well be further increased as domestic
satellite systems are brought into operation.

532

Impairments and Their Measurement

Vol. 1

The alternate routing features of the local and toll portions of the
message network provide a great measure of reliability. If a route
is blocked as a result of trouble or excessive amounts of traffic,
alternate routes can usually be found to satisfy most service needs.
Many features of route layouts can be selected to maximize reliability. Hardened long-haul transmission systems are laid out so
that the backbone route that carries the bulk of the traffic bypasses
large cities. These routes are thus less vulnerable to damage by
enemy attack. Service into the cities is carried by sideleg systems
which are usually smaller in capacity and less well-protected against
damage.
In certain environments, the provision of appropriate maintenance
vehicles is an important element in system reliability. Access to outside plant facilities may be hampered by snow or other vagaries of
the weather, long water crossings, or mountainous terrain. Trucks,
snowmobiles, barges (for river work), and helicopters all find their
places in route maintenance and reliability work, not only for repair
activities but also for patrolling so that new construction work or
other sources of trouble along the route may be anticipated.
Another environmental factor influencing reliability is out-of-sight
plant; cable may be buried directly or placed .in conduit. In recent
years, there has been increased emphasis on the part of the public
to improve and beautify our environment, one result of which is increased desirability of out-of-sight plant. While in many cases higher
capital costs have resulted, some added benefits in reliability and
lower maintenance costs have been realized. Generally, out-of-sight
plant is less susceptible to damage by people, ice, snow, wind, rain,
and lightning. It has also resulted in somewhat fewer outages due
to cable damage. Offsetting the latter advantage, however, is the fact
that outages tend to be of somewhat longer duration.

Telecommunications
Transmission
Engineering

Section 5
Objectives and Criteria
The design, installation, operation, and maintenance of transmission facilities must be based on logically and scientifically established
objectives that can be applied throughout the useful life of the
facilities. The objectives must also be realistic in that, when met,
they lead to customer satisfaction at a reasonable cost. Objectives are
dynamic. They must be changed to accommodate changing customer
opinion and the introduction of new services. However, the degree
of change and adjustment of objectives must be tempered by economic
considerations. If objectives are too stringent, excessive costs may
be incurred for new system designs and for maintenance of existing
systems. If objectives are too lenient, performance may be so poor
that customer satisfaction may be low, and an excessive number of
service complaints may be received. T'o avoid either extreme, objectives are continually re-examined and re-established.
There are occasions when relaxation of objectives must be considered for economic and/or plant reasons. The importance of the
service, a complete understanding of the basis of the objective, and
a firm plan to correct the situation are required before relaxation
can be implemented. It is sometimes tempting, for example, to apply
objectives lower than optimum in the case of a new service on
the basis that the new service is temporary or limited in application.
If this approach is taken, there is danger that concentrations of
the new serviee may occur to the extent that damaging effects cannot
easily be overcome. There is also the danger that the demand for
the service will increase and that problems first introduced as a
result of poor judgment win proliferate and then require years of
effort to correct.
Many objectives are determined by a process of subjective testing
because impairment judgments are based on the sight or hearing
mechanisms of the users. Subjective testing is not much used in the
operating cOlnpanies; it is carried out primarily under controlled

533

laboratory conditions. A knowledge of subjective testing techniques
and methods is desirable, however, in order that results can be
properly interpreted and used. Information about this type of testing
is covered in Chapter 23.
Customer satisfaction with the transmission performance of the
switched network is conveniently expressed in terms of grade of
service, a measure of the expected percentage of telephone users who
rate the quality of telephone connections excellent, good, fair, poor,
or unsatisfactory when the connections include the effects of a given
class of transmission impairments. The grade-of-service concept is
described in Chapter 24, and several applications of the concept are
discussed.
Transmission objectives are subject to considerable manipulation
to make them applicable to various operational situations. After the
objectives have been determined, a number of ways of interpreting
them must be considered to account for such factors as variability of
an impairment and the probability of its occurrence. Also, objectives
must be translated into firm requirements for system or circuit performance; then the requirements must be allocated to different parts
of the network and to different impairments. These m·ethods of
treating objectives are considered in Chapter 25.
Chapter 26 discusses a number of specific transmission objectives.
As related to the message network, many of these have been accepted
for general application. Others, including many that apply to other
services, have only provisional status; and in some cases, objectives
have not yet been established. The chapter contains some general
discussion to indicate the nature of the problems involved when
objectives are not established.
The economic tradeoffs that must be considered as engineering
compromises in the design, application, and operation of transmission
facilities are interrelated and involve judicious application of transmission objectives. These relationships are discussed and illustrated
by significant examples in Chapter 27.
The North American telecommunications network must interconnect with and operate with the networks of many other countries
and thus may be regarded as part of a world-wide telecommunications network. The coordination of the many facets of international
534

operation is guided primarily by the International Telecommunication Union (I.T.U.), a specialized agency of the United Nations for
telecommunications. The International Telegraph and Telephone
Consultative Committee (C.C.I.T.T.), and the International Radio
Consultative Committee (C.C.I.R.) are two permanent organs of the
I.T.U. and are concerned with international coordination of operations. Chapter 28 describes some of the significant ways in which the
Bell System and the telecommunications industry of the U.S.A. interact with these international bodies, stressing the relationships that
have evolved in respect to transmission objectives as they are expressed in the Bell System and by the international organizations.

535

Objectives and Criteria

Chapter 23

Subjective Testing
Clearly defined transmission objectives must be established for
use in setting performance standards and maintenance limits for
existing systems and in setting design and development requirements
for new systems. The performance standards and maintenance limits
must be adjusted to achieve -economically feasible performance that
yields satisfaction for the majority of customers.
Various methods of subjective testing have been developed for the
purpose of measuring customer opinion as to the disturbing effects
of transmission impairments. The data thus acquired can be used
by the application of statistical principles to establish relationships
between transmission impairment measurements, the subjective effects of the impairments, and overall customer satisfaction. These
relationships can then be applied to the establishment of transmission
obj ectives.
Transmission objectives should be reviewed frequently and brought
up to date so that they reflect changes resulting from the introduction of new transmission technology, the introduction of new signals
or services, and the slowly evolving customer responses to these
changes. If customer opinion and objectives are not reviewed
regularly, there is the danger that they may be accepted as a matter
of habit and thus become traditional.
Some objectives, whether old or new, can be established or revised
in a discrete or quantitative manner because they relate only to
machine and equipment performance; some, such as the signal-to-noise
objectives for digital signal transmission, can be stated discretely
because performance thresholds are sharply defined; other impairments, however, must be judged by subjective testing; and in many
cases objectives and performance must be expressed statistically.
In these instances, one of a number of available test methods must
be selected, the purposes of the tests must be well-defined, and the

536

Chap. 23

II ~

Subiective Testing

537

test environment must be well-controlled. Also, it must be possible
to quantify and express the results in useful terms for application
to system design and operation. In addition, objectives are also related
to transmission grade and grade of service for use in transmission
management. Subjective testing does not provide the answers to many
of the questions relating to objectives or grade of service, but it is
often the starting point.
23-1

SUBJECTIVE TEST METHODS

Subjective tests of communication system phenomena fall generally
into one of three categories: (1) threshold tests to determine threshold values of impairment; (2) pair-comparison tests to compare
interfering effects of two different forms of impairment; and
(3) category judgment tests to establish subjective reactions to a
wide range of impairments (including intelligibility of telephone
circuits), a range that spreads from threshold values to unusable
values. Circumstances determine selection of the category to be used.
Threshold Testing

!II

In the determination of an impairment threshold, the test procedures are arranged so that each participant, or observer, is given
the opportunity to establish a value of impairment magnitude at
which the stimulus is "just perceptible" or "just not perceptible."
Threshold measurements are often made at the beginning of more
extensive test procedures in order to establish a base from which
other work may proceed. Threshold measurements are also valuable
in determining the sensitivity of observers to a particular type of
impairment, i.e., to determine if the variation of reactions shows
a large or small standard deviation. This information is useful in
assessing the importance of other parameters that may affect the
result by masking or enhancement.
Threshold measurements may also be used to determine the importance of some newly observed impairment phenomenon. If, in the
normal course of development or operation, the impairment is well
below the threshold value, it may sometimes be safely ignored; if it
is at or above the threshold value, its importance is increased and
more extensive testing is indicated.
Threshold testing is usually easier to carry out than other types
of subjective testing programs. In many cases, the broad judgments

Obiectives and Criteria

538

Vol. 1

involved and the fact that designs are seldom based on threshold
values make it unnecessary to perform threshold tests with the
attention to detail required for useful results in other types of
testing. Threshold measurements also need only a few test subjects
since opinions are not involved.

Pair-Comparison Testing

Occasionally, a new form of impairment can be evaluated by a
test procedure, called pair-comparison testing, designed to establish
a magnitude that makes the impairment being tested as disturbing
as another type of impairment for which objectives are well defined.
Two typical arrangements for this type of testing, also called isopreference testing, are illustrated in Figure 23-1. In Figure 23-1 (a) the
Signal
source

I
Impairment
A

1
-

An. (

Receiver
A

/

I
Impairment
B

An.!

Receiver
B

/
(a) Two-receiver arrangement

Signal
source

I

Impairment
A

An.!
/

I

L. . .- Impa~- - 'ment~I {I
An.

7(b)

, "'"

r

Receiver

Single receiver arrangement

Figure 23-1. Experimental arrangements for pair-comparison testing.

~
I

Chap. 23

Subjective Testing

539

signal source is connected to the two receivers which are adjusted
to be as nearly alike as possible with no impairments present. Attenuator A is then adjusted to impress on receiver A an impairment
such as random noise. The test subject is then asked to adj ust A TT B
so that in his judgment the ,disturbing effect of impairment B (for
example, a single frequency interference) is as disturbing on receiver
B as impairment A is on receiver A.
In Figure 23-1 (b) the same procedure is followed except that only
one receiver is used. The test subject adjusts ATT B in the same
manner as previously described but makes the comparison between
impairments by switching back and forth between the two disturbing
sources. In the second procedure the uncertainty of the equivalence
of the two receivers is removed. However, other uncertainties exist
such as the effects of switching transients and, in telephone testing,
tlte coupling-decoupling between the ear and telephone receivers.
Hence, there is little choice between the procedures.
The pair-comparison method of testing may be used for either
visual or hearing tests. The results are generally considered more
valid, or at least more useful, than threshold test results; however,
all the statistical aspects of observer reactions are not included.
Impairment evaluation is most valid when the impairment is rated
relative to some standardized scale that can be applied to all kinds
of impairments.

Comment Scale Testing -

Category Judgments

The two types of service for which subjective testing has been
conducted widely are telephone and television. For each of these,
there has evolved a mode of subjective testing which involves a
scale that permits quantitative evaluation of judgments of the disturbing effects of impairments. The two scales are different, though
they have certain similarities, and they are used somewhat differently.
Telephone Impairment Testing. Bandwidth limitation was one of the
first types of telephone transmission impairment for which objectives
were established by subjective testing. The test method that evolved,
known as articulation testing, measured intelligibility of received
speech. The test procedure involved the preparation of stimuli in the
form of standard lists of vowel and consonant sounds, syllable sounds,
real and nonsense words, and sentences. These stimuli were trans-

540

Objectives and Criteria

Vol. 1

mitted by a number of speakers to various listeners who recorded
what they heard. Errors in their records were used as the basis of
evaluating the effects of variations in the high-frequency or lowfrequency cutoffs or in the overall bandwidth of the circuit [1, 2,
3, 4, 5, 6]. Such lists are still used in some related types of testing [71.
Category judgment evaluations have been applied analytically to
the results of articulation tests. At present, other kinds of impairments to the transmission of speech signals over message channels
are often evaluated directly by subjective tests in which participants
rate specific transmission conditions excellent, good, fair, poor, or
unsatisfactory. The tests are conducted in such a manner that various
impairments are rated under listening conditions selected to be as
representative as possible of operating conditions.
Usually, these tests are carried out to evaluate a specific impairment - for example, a single frequency tone. Other impairments
either are suppressed or are impressed on the listening circuits at
values typical of those found in practice. Ultimately, objectives must
be established for combinations of impairments which are evaluated
to establish a grade of service.
Television Impairment Testing. Subjective testing of television impairments has followed the complete cycle of threshold testing, comparative testing, and comment scale testing. The cornment scale shown
in Figure 23-2 was adapted for use in the Bell System and was
selected after many efforts to find suitable terms that would adequately describe a wide range of impairments.
COMMENT NUMBER

COMMENT DeSCRIPTION

1

Not perceptible.

2

Just perceptible.

3

Definitely perceptible, but only slight impairment to
picture.

4

Impairment to picture, but not objectionable.

5

Somewhat objectionable.

6

Deiinitely objectionable.

7

Extremely objectionable.

Figure 23-2. Seven-grade comment scale for rating television impairments.

Chap. 23

Subjective Testing

541

In this type of test, a minimum of ten observers are usually used.
The observers are persons (usually technically trained) having good
eyesight, experience in judging television picture impairments, and
proven consistency in their evaluations over a reasonable period
of time.
23;.2

TEST PLAN AND PROCEDURES

The design and administration of a subjective test program involves
careful planning and preparation. To have maximum value, such
tests must have well-defined goals and must be carefully controlled
throughout. The nature of the goals often influences the choice of
test method, determines the details and sophistication of test arrangements, establishes the importance of providing appropriate and
well-designed environmental test conditions, and helps to establish
the number and qualifications of observers.

Setting Goals
Some carefully considered questions - by definition, the right
questions - are involved in the determination of the goals of a
subjective test program. The determination of the right questions is
sometimes an iterative process, because they are not automatically
known. However, if the attempt is not made to ask the right questions, the risk is high of getting the right answers to the wrong
questions and then to set off in the wrong direction. To illustrate,
consider the problem of determining how much frequency offset can
be tolerated in FDM channels. If a subjective test program is conducted in which only speech signals are used, the results would
indicate listener tolerance of tens of hertz to this impairment. Early
considerations, however, should have included a preliminary investigation to determine what type of signal is most susceptible to frequencyoffset. The preliminary tests would quickly have shown that
certain types of music are most susceptible, and a subjective test
program would then have been designed around the criteria of satisfying critical listeners to musical programs; speech signal testing could
have been limited to that which would assure that speech transmission would be acceptable when objectives for music were satisfied.
Who is to be pleased and to what degree are two other questions
that must be answered. For television signals; transmission objectives
that satisfy home viewers may not satisfy the broadcasters or the

542

Obiectives and Criteria

Vol. 1

advertisers. Transmission objectives must be set to satisfy the most
critical of these groups, and it is often necessary to set objectives at
threshold or near-threshold values.
Test Locale

Subjective tests may be conducted in the field or in the laboratory,
with the choice normally determined by the test goals and by the
relative advantages and disadvantages of each locale.
Field Tests. The principal advantages of conducting tests in the field
are that the normal, uncontrolled environment of the operating plant
is used and that the test subjects (observers) are the customers who
normally use the service. Thus, realistic appraisals of various
phenomena can be made under operating conditions.

The same parameters that are judged to be advantages of field
testing are also the greatest disadvantages when considered from
another point of view. The inability to control the test environment
and the observers makes it difficult to achieve accuracy and precision
in the test results. Service impairments such as slow dial tone and
all circuits busy conditions can be evaluated best in the field environment. The subjective evaluation of transmission impairments, however, seldom falls within the framework of broad judgments and
evaluations of service.
Laboratory Tests. Most subjective testing of transmission impairments is carried out in the laboratory where test conditions can be
controlled and where observers can be selected and trained. Sometimes the entire test program is carried out in the spirit of a
laboratory experiment, with all facets of the program (impairment
simulation, environment, procedure, etc.) carefully designed and
controlled.

In other cases, a laboratory test program may be designed to
simulate the field environment but in a controlled manner. One such
test program, for example, involved the introduction of computercontrolled time delays (with and without echo suppressors) into
working telephone circuits for the purpose of simulating very long
transmission circuits and evaluating the effect of echo. The observers,
selected laboratory personnel, evaluated the effects of the impair-

Chap. 23

Subjective Testing

543

ment during actual conversations and reported to the computer by
prescribed station set dial operation [8].
Normally, laboratory tests of transmission impairments are greatly
preferred over field tests. Better simulation of the impairment under
test can usually be made in the laboratory, test results are less likely
to be influenced by external factors, and better control can be exercised over the program. Also, laboratory testing is usually less
expensive than field testing.
Test Conditions

After the initial test plans have been formulated and the procedure
has been decided upon, the next step is to establish all test conditions
and facilities. It must be decided whether the tests are to be made
under laboratory or field conditions; a source of the impairment (real
or simulated) must be provided; the circuits required for conducting
the test must be selected or designed; and the necessary test equipment
must be procured.

W

Laboratory Environment. The process of laboratory subjective testing
must involve careful control of the test environment, including both
the physical environment in which the test is conducted and the
environment induced by circuit conditions and arrangements. In both
cases, the laboratory environment must realistically simulate the
environment in which the impairment actually occurs and must be
consistent with the stated goals of the test program.

Physical Environment. It is not possible to specify the nature of
control necessary over the physical environment in any given situation; however, the physical environment must be consistent with
the goals of the test. If, for some reason, the threshold value of a
stimulus must be determined under the most stringent conditions,
external distractions must be minimized. For example, if a listening
test is required, the environment must be something in the nature of
a soundproof room; if a visual test is required, the environment must
be a darkened room.
On the other hand, if a stimulus is to be evaluated by categoryjudgment-type testing with normal observing conditions, it may be
desirable to create a noisy environment by playing recorded street
sounds or room noise at appropriate sound levels. If the tests involve
television viewing, appropriate ambient lighting may be used.

544

Obiectives and Criteria

Vol. 1

Circuit Conditions. Circuit conditions that are provided for subjective tests are perhaps even more variable than physical conditions,
but they must also be consistent with pre-established goals. Some
examples may be given.
If telephone listening tests are to be made, a number of questions
must be answered. First - would the purposes of the tests be served
in the presence of impairments other than the one under test (multiple
impairment testing) ; and if so, how loud should they be? For example,
if echoes are being evaluated, should there be noise on the test circuits
or should they be as quiet as possible? Impairments are interdependent; while subjective test results may apply to one or a combination of several impairments, other interrelated impairments must
always be kept in mind. Second-should there be a normal signal
present, and if so, what kind of signal? If a particular noise impairment is under test, for example, should the observers listen to a
simulated conversation while evaluating the noise? Or would it be
better to have the observers listen to continuous speech? Or perhaps
there should be no speech signal on the circuit at all.
If television viewing tests are involved, the same kinds of questions
must be answered. For significant results, should a picture be present
or should the screen be blank? Should the picture be one with large
flat areas of constant brightness or should it be "busy" with a lot
of high-frequency components present in the signal? Should other
impairments be present in the picture during the tests?
These questions have no general answers and therefore must be
considered both separately and collectively. The answers can often
be determined from the results of preliminary testing carried out to
establish procedures and to determine which parameters affect the
results sought.
Source of Impairment. Introduction into the test circuit of the impairment to be evaluated is, of course, a prerequisite to subjective testing.
Sometimes this is straightforward, particularly when the impairment
is well-defined and easy to simulate. For example, a signal generator
to produce a single frequency interference or a random noise generator to introduce random noise into the test circuit may well suffice.

On the other hand, it is often necessary to record the impairment
and then to use the recording as the source during the test. This

"I,
'

I

I

Chap. 23

545

Subjective Testing

',1

li,11

[I

approach is used in cases where the impairment is intermittent or
has some other unusual characteristic that is not easily reproduced
except under carefully controlled conditions. An example is the
evaluation of interference falling into a telephone channel due to
cross-modulation between multifrequency signalling tones and television signal components where combined system (telephone-television)
operation is contemplated. In this situation, the interference falls at
different frequencies in the disturbed channels, has highly variable
amplitude characteristics, is randomly intermittent, and has a complex and variable spectrum. Recordings of such an impairment are
the only way that the impairment can be adequately simulated for
test purposes, and great care must be taken that the recordings
adequately represent the variables mentioned.
Test Circuits. The principal requirement of test circuits used in
subjective testing is that they must be capable of delivering signals
and impairments to the test area without introducing distortion that
might mask the results of the test. It is essential, therefore, that all
transmission, distribution, and control circuits be thoroughly tested
under all conditions to which they will be subjected in the test
program.
\

Test Equipment. The selection of test equipment is as important as
the selection of test circuits. The test equipment must be available
before the test program is begun, and effort must be expended to
assure that its capabilities and accuracies are appropriate to the
task. Consideration must be given to the human engineering of the
tests so that the selected test equipment can be used conveniently.
Consideration must also be given to the need for and availability of
automated measurements and recordings of measurements.

Test Procedures

The actual conduct of the test program finally must be worked out
in detail. Only general guidelines can be given here because the procedure may be different for each test. In most situations, ten or
more observers (sometimes expert and sometimes non-expert) are
asked to participate, particularly when comment scale testing is to
be used. For these purposes, an expert observer is defined as a person
with good vision (for television) or hearing (for telephone) with
experience in judging impairments, who has exhibited consistency
in his evaluations over a reasonable period of time. Frequently, television testing involves the use of expert observers; for telephone

546

Objectives and Criteria

Vol. 1

testing, nonexpert observers are chosen to be a representative sample
of all users.
Usually, a test program is begun by training the observers. The
training involves first an exposure to the impairment under test so
that each observer knows what to look for or listen for. If test
arrangements are such that other impairments are present and
cannot be eliminated, the observers may be told to try to ignore them
and judge only the impairment under test. The observers then are
given the scale of comments to be used in judging the impairment.
Often, a few trial runs are used to give the observers a sense of
understanding of the test process.
Some pitfalls are to be guarded against. One is the introduction
of observer bias such as the bias that might result from presenting
an ordered sequence, like best-to-worst or worst-to-best test conditions, to all observers in all test sequences. Randomizing the sequence
of presentation is desirable. Another pitfall to be avoided is observer
fatigue. This condition can sometimes be identified in preliminary
testing; experienced observers may become inconsistent after a period
of observing, and that period of time may then be used for the
duration of final testing.
Before actual testing begins, every step of the procedure should
be rehearsed, and every effort must be made to ensure that all observers are exposed to the same or very similar viewing or listening
conditions. The circuits, test equipment, television pictures or telephone signals, and impairment sources should be checked and calibrated before each test in order to eliminate unwanted and unexplained variations. In short, the entire procedure must be conducted
with great care and precision to ensure valid results.
23-3

DATA ANALYSIS

For a subjective test program to produce useful results, the accumulated data must be analyzed and presented so that they may
be related to performance criteria. For these purposes the subjective
test data and performance criteria are often expressed in terms of
mean values and standard deviations.
Methods of analysis have improved as subjective testing procedures
have become more scientific and as the importance of test results has
become more widely appreciated. The progress made with respect to

Chap. 23

Subjective Testing

547

the evaluation, analysis, and presentation of the results of subjective
testing of television impairments is a case in point. In the middle and
late 1940s, when the television industry was growing rapidly, most
of the development and research emphasis was placed on gaining an
understanding of the fundamentals of television camera, transmission, and reproduction processes. Later, experiment and analysis were
devoted to the evaluation of various impairments.
One study exemplifying this type of analysis involved the evaluation of random noise impairment of television pictures [9]. In this
study, the similarity of random noise effects to the graininess of
photographs was noted, and the number of spots or grains that
could be expected from noise was compared with the graininess of
photographic pictures. The analysis had to take into account the size
of the grains (due to the duration of noise bursts) , all of the television
signal processes (camera and viewing tuhe spot sizes and shapes,
scanning process, brightness-voltage relationships), viewing distance,
etc. ; furthermore, all of these parameters had to be expressed mathematically. The analysis was closely tied to earlier observations that
the ratio of the minimum perceptible change of a stimulus to the
value of the stimulus tends to be constant over a wide range of
stimulus values (the Weber-Fechner law).

I

~'I

i

Later work in evaluating television impairments extended the
ideas of comparison testing and introduced the comment-scale method
of impairment evaluation. For example, one series of tests was based
on the comparison of echo and random noise impairments with high
quality, projected lantern slides of photographs impaired by defocusing the projection system by known amounts [10]. The comparisons made between defocused lantern slides and impaired television pictures involved the use of a unit called the limen, or liminal
unit. (One liminal unit indicates a 75 percent observer vote preference
for one picture condition over another.) The analysis of the preference
votes approximately followed a normal distribution. It was also
shown that the difference from one comment to another is approximately one limen where the comment scale used was the same as that
given in Figure 23-2, with one minor exception-the present definition
of comment 7 is "extremely objectionable," while that used in the
earlier tests was "not usable." The results of these tests were plotted
in various ways to determine the usefulness of the data for engineering purposes. One such plot is illustrated in Figure 23-3, in which
echo attenuation is plotted as a function of the percent of observa-

Obiectives and Criteria

548

Vol. 1

50

40
iii'

~

c

30

0

'.;:

0

:::I
C

!0
0

20

~

.H
10

10

25 50

75 90

99

99.9

Percent of observations for given echo attenuation

Figure 23-3. Illustrative plot of echo impairment characterization.

tions indicated for each value of attenuation. A separate plot is given
for each comment number. Test data were smoothed for these plots.
As the emphasis shifted to comment scale testing, data analysis
techniques have been improved, and data have been subjected to more
and more critical evaluations. In early studies [11], data that had
been smoothed by eye was often presented for engineering use. More
recently, the smoothing process and methods of presentation have
been derived by more systematic procedures and more analytic
methods [12]. Further improvements in analysis are under study.
The analysis of subjective test results of telephone impairments
has evolved in a somewhat similar manner. Some indication of how
such analyses are currently made is illustrated by a report on the
derivation of modern message circuit noise objectives [13]. One
useful product of these tests and analyses is illustrated by Figure 23-4,
which shows the variation of observer reaction to various amounts
of noise on a telephone circuit, expressed in terms of comment scale
testing.

549

Subjective Testing

Chap. 23
100
90

Slc
:!
GI

0

a-

i! f
GI

70

""'0
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GI

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-

u

~]
...u til
..
GI

~

50

c
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indicate 50% point
and standard deviation

c

.21
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20

Received volume
constant, -28 vu
0

15

20

25

30

35

40

45

50

55

60

65

Noise at line terminals of station set (dBrnc)

Figure 23-4. Noise opinion curves.

REFERENCES

1. Fletcher, H. and J. C. Steinberg. "Articulation Testing Methods," Bell System
Tech. J., Vol. 8 (Oct. 1929).

2. French, N. R., C. W. Carter, Jr., and W. Koenig, Jr. "The Words and Sounds
of T'elephone Conversations," Bell System Tech. J., Vol. 9 (Apr. 1930).
3. Castner, T. G. and C. W. Carter, Jr. "Developments in the Application of
Articulation Testing," Bell System Tech. J., Vol. 12 (July 1933).
4. French, N. R. and J. C. Steinberg. "Factors Governing the Intelligibility of
Speech Sounds," The Journal of the Acoustical Society of America, Vol. 19
(Jan. 1947).

5. Martin, W. H. "Rating the Transmission Performance of Telephone Circuits,"
Bell System Tech. J., Vol. 10 (Jan. 1931).
6. McKown, F. W. and J. W. Emling. "A System of Effective Transmission Data
for Rating Telephone Circuits," Bell System Tech. J., Vol. 12 (July 1933).
7. "IEEE Recommended Practice for Speech Quality Measurements" (New
York: The Institute of Electrical and Electronics Engineers, Inc., 1969),
Standard # 297.

8. Riesz, R. R. and E. T. Klemmer. "Subjective Evaluation of Delay and Echo
Suppressors in T'elephone Communications," Bell System Tech. J., Vol. 42
(Nov. 1963), pp. 2919-2941.
9. Mertz, P. "Perception of Television Random Noise," Journal of the Society
of Motion Picture Engineers, Vol. 54 (Jan. 1950), pp. 8-34.

10. Mertz, P., A. D. Fowler, and H. N. Christopher. "Quality Rating of Television
Images," Proceedings of the Institute of Radio Engineers, Vol. 38 (Nov.
1950) , pp. 1269-1283.

550

Objectives and Criteria

Vol. 1

11. Fowler, A. D. "Observer Reaction to Low-Frequency Interference in Television Pictures," Proceedings of the Institute of Radio Engineers, Vol. 39
(Oct. 1951), pp. 1332-1336.
12. Lessman, A. M. "The Subjective Effects of Echoes in 525-Line Monochrome
and NTSC Color Television and the Resulting Echo Time Weighting,"
Journal of the Society of Motion Picture and Television Engineers, Vol. 81
(Dec. 1972), pp. 907-916.
13. Lewinski, D. A. "A New Objective for Message Circuit Noise," Bell System
Tech. J., Vol. 43 (Mar. 1964), pp. 719-740.
14. Guilford, J. P. Psychometric Methods (New York: McGraw-Hill Book Company, Inc., 1954).

Objectives and Criteria

Chapter 24

Grade of Service
Transmission grade of service is a measure of the expected percentage of telephone users who rate the quality of telephone connections excellent, good, fair, poor, or unsatisfactory when the
connections include the effects of a given class of transmission impairments. It combines the distribution of customer opinions with
the distribution of plant performance parameters to obtain the expected percentage of customer opinions in a given category or
categories. While the term is usually applied to overall communication service, the grade-of-service concept can be. applied in theory to
one aspect of communications such as transmission; to one specific
impairment such as noise, loss, or echo; or to various combinations
of these impairments. It is usually expressed in terms such as a
noise grade of service of 95 percent good or better or a noise/loss
grade of service of 3 percent poor or worse. Among the impairments that tend to degrade speech signal transmission performance,
noise, loss, and echo are predominant.
Transmission management of the telecommunications network involves the establishment of transmission objectives, the measurement
of transmission performance, and the measurement of customer
opinions of the quality of service rendered. The grade-of-service
concept is a useful tool for fulfilling these responsibilities. While the
concept is usually used directly in establishing objectives, it is also
sometimes used in inverse applications to determine what performance must be achieved to meet established grade-of-service
objectives.

II

24-1

A GRAPHIC DERIVATION OF GRADE Of SERVICE

The transmission grade of service is usually determined by mathematical derivation from opinion and performance survey data. A
simplified graphical analysis is offered first in order to 'illustrate the
551

552

Vol. 1

Obiectives and Criteria

basic concept as an aid to an understanding and interpretation of
the mathematical derivation. This analysis is, of course, hypothetical
and uses values of opinion and performance parameters that represent a typical problem of loss grade of service.

Customer Opinion Distributions

The distribution of customer opInIOns would normally be determined by a subjective test program in which the distributions of
connection losses and talker volumes are inherently combined. For
a loss grade-of-service analysis, the combined distribution would
then have to be interpreted in terms of loss only. Assume that the
results of the subjective tests are finally expressed as the percentage
of observers that rate connections with each of seven loss values
(0 through 6 dB, inclusive) according to the standard rating scaleexcellent, good, fair, poor, unsatisfactory. For this impairment, the
unsatisfactory category is increased by those observations that the
received volume is considered too loud when the connection loss is low.
The distribution of good ratings is plotted as a histogram in
Figure 24-1. In the analysis it might be found that observers rated
more than one value of loss in a given category, and the total number
of observations in that category might then exceed 100 percent.
To avoid this ambiguity, assume that for each observer only the
highest value of loss rated in a given category is used; thus, the
ordinate in Figure 24-1 is really in terms of the threshold of good
ratings.

60

~
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40

D

~

91

.Jl
0
"0
0
0

20

(!)

0
0

3

2

Loss

4

5

6

(dB)

Figure 24-1. Histogram of good ratings of loss.

553

Grade of Service

Chap. 24

This manner of displaying the results of the subjective tests may
now be extended to show how the connection is rated by all the
observers for each value of loss. Figure 24-2 illustrates the cumulative
opinions of good or better and too loud, and fair or worse. The cumulative opinions of good or better never reach 100 percent because the
low losses result in some opinions of too loud which must be subtracted
from the total.

Relation of Connection losses to Subjective Test Results
To determine the grade of service, the losses of the connections
being evaluated must be measured and plotted. Figure 24-3, a
histogram of the distribution of such losses, represents the probability of encountering a given connection loss. Similarly, Figure 24-1
represents the probability that a connection loss of a given value
is rated good by a random sample of observers. These distributions
may now be combined as a product of the probabilities at each loss
value to obtain the probability of a connection of a given loss rated
good. The resulting probabilities are plotted as the distribution
shown in Figure 24-4. Thus, of all possible combinations of con-

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0

TL

0

-c:;)
...2

60

40

0

C

E

40

60

20

*

5/

0

9
80 ·0

...

E

-c
0
0

(!)

~

.B
~

4i
:=

GI
..D

~
0

.£

-c
c:

~
II>

..D

G

0

100
4

3

2

0

loss

5

(dB)

Legend:
G- good
E -excellent
TL-too loud

Figure 24-2. Overall ratings of loss.

6

554

Objectives and Criteria

Vol. 1

60

~..
c

.40

0

~

~

0

u

20

0
0

3

.4

5

6

Loss (dB)

Figure 24-3. Histogram of connection losses.

~
::00

10

0)

8

0

"tI

.!!

6

~

.4

E
0

"ij
GI

2

0

0

~

u

0

2

3

.4

5

6

Loss (dB)

Figure 24-4. Histogram of connections rated good.

nections and observers, just 20 percent (the sum of the entries in
the histogram in Figure 24-4) would be rated good.
Another, somewhat more detailed process may be used to combine
the distributions of Figures 24-1 and 24-3. This approach involves
finding the probability that the difference between the two is a
certain number of dB for every possible combination of opinion and
connection loss. The process is illustrated in Figure 24-5 where the
values of Z are the differences in loss values from Figure 24-1 and
Figure 24-3. The total probability of the loss difference, (Y -X) =Z,
is the sum of the products of all the ordinates at loss values with
differences equal to Z.
Coincidence of the good threshold and connection loss values
(i.e., 5,5; 4,4; 3,3; 2,2) is shown at Z = O. As in Figure 24-4, the
percentage of connections rated good by observers is again 20 per-

I

Chap. 24

Grade of Service

555

30

X
25
III

Y

~
tsl

15

Q;

10

_X_,_Y_ 1,2

= loss value from

histogram of
connection losses,
Figure 24-3

20

II
~
I

= loss value from

opinion histogram,
Figure 24-1

I,

_ _......--1,3

2,2

;:...

5

0

-6
5,2

Z (dB)

5,6

1,6

Figure 24-5. Histogram of dB differences between loss and loss rated good.

cent. When trunk losses are lower than the good threshold of each
observer, the connection is rated good, excellent or too loud. When
trunk losses are higher than the good threshold, the connection is
rated fair or worse.
This general approach can be pursued further to extract from
the result those combinations of connection losses and observer
opinions that would result in a net judgment of too loud. Notice,
however, that in the example chosen, the only connections for which
too loud ratings are given are those having 0 or 1 dB of loss
(Figure 24-2). The assumed distribution of connection losses
(Figure 24-3) shows that there are no connections in the study
having less than 2 dB of loss. Therefore, the resultant distribution
is not affected by the too loud category of opinions.
If the distribution of the parameter Z, shown in Figure 24-5, were
plotted as a cumulative distribution histogram, Figure 24-6 would
result. Since there are no too loud ratings, Figure 24-6 shows that
37 percent (Z == 0 dB) of the connections are rated good or better.
The remainder, 63 percent, are rated fair or worse. It may be said,
then, that the example demonstrates a 37 percent good-or-better loss
grade of service.

556

Obiectives and Criteria

Vol. 1

100

80

~~
VII

:g

60

..c~

e~

0..1

~ ~

.~ ~

40

"5
E
~

u

20

-6

-5

-4

-3

-2

-1

0

Z

2

3

4

56

(dB)

Figure 24-6. Histogram of cumulative distribution of

Z.

For actual distributions of observer opInIOns and losses (and
other impairments such as noise and echo which must be evaluated
simultaneously), such a simplified approach using histograms and
direct multiplication and summing of probabilities is impractical because the distributions are, or at least approach, continuous distributions. However, as pointed out in Chapter 9, distributions of these
parameters are normal or may safely be assumed normal. In addition,
the results of subjective tests are usually represented by normal
distribution functions such as those illustrated in Chapter 23 (see
Figure 23-4). Therefore, the combination of impairment and opinion
distributions may be treated mathematically by using representative
values for their means and standard deviations. As covered in
Chapter 9, the combined distribution can be determined for two
independent distributions by subtracting their mean values and
adding their variances.
24-2

MATHEMATICAL DERIVATION OF GRADE OF SERVICE

As previously mentioned, grade of service can be computed from
mathematical expressions of measured performance parameters and
of user opinions of performance. While manipulation of grade-ofservice relationships has seldom been necessary in the operating
companies, the concept is becoming more widely applied as more use is

Chap. 24

557

Grade of Service

made of c()mputer programs, such as GOSCAL (grade-of-servke
calculation). Such programs will be made available for field applications. The mathematical grade-of-service relationships may be used
to determine the expected grade of service for certain combinations of
performance parameter measurements and user opinions.
To describe grade of service mathematically, * let R denote the
rating assigned by an individual selected at random whose telephone
connection is subject to an impairment designated X. Also, for convenience, assign numerical values, designated Cj, to the 5-category
comment scale as follows:

Excellent ==
Good ==
Fair ==
Poor ==
Unsatisfactory ==

5
4
3
2
1.

N ext, suppose that connections are made and rated by each of a
random sample of k customers; their corresponding ratings are
designated Rl, R 2 , • • • , Rk. Then, the fraction who rate their connections in any category, Cj, is
k

2:

(11k)

i

1) (Ri

- Ci)

== 1

where

and
1)

(Ri - c;)

== 0 when Ri #

Cj.

Thus, the expected .fraction is
k

E{

(11k)

i

2:

8 (Ri -

Cj)

== 1

* Mr.N. A. Marlow, Bell Telephone Laboratories, Holmdel, N. J., .provided this
mathematical treatment of the grade-of-:service relationships in an unpublished
memorandum.

558

Vol. 1

Objectives and Criteria

The corresponding grade of service for category Cj, i.e., the expected
percentage of customers who would place their connections in
category Cj, is then lOOP {R==cj} percent. The discussion to this point
is general in that the impairment, X, either can be fixed or can vary
randomly according to a given distribution.
To obtain an expression for the probability P{R==cj}, which explicitly reflects both the variability of customer rating for a given
impairment value and the variability of impairment values, let
P{R==cj \ X==x} denote the conditional probability that the rating is
Cj, given a fixed value x of the impairment X. If Ix (x) denotes the
density of X, it follows from the law of total probability that

f

00

P{R=c;}

=

P{R=cj I X=x}!x(x)dx

(24-1)

By writing gj (x) == P{R==cj \ X==x} and fixing a particular value
of x, it follows that as Cj varies, gj(x) is a conditional (discrete)
distribution of customer opinion which can be estimated by subjective
testing in a controlled laboratory environment.
To illustrate a particular application of Equation (24-1), suppose
that the rating category under consideration is good or better; i.e.,
R == 4 or 5. The corresponding grade of service is

100P{R=4 or 5}

= 100

f

00

P{R=4 or 5 I X=xl!x(x)dx

(24-2)

where
P{R==4 or 5 \ X==x} == P{R==4\ X==x}

+ P{R==5\ X==x}

==g4(X) +g5(X)

Suppose also that X is normally distributed with mean value, JJ-, and
standard deviation, u. Then, by substitution in Equation (24-2), the
grade of service becomes
100P{R==4 or 5}

==

100
ay'21T

f

co

2

2

P{R==4 or 5 I X==x}e- x I X==x}

== P{T> x}

,

and it follows from the law of total probability that

PIT > Xl

=
=

J

00

PIT > x I X=xj /x(x)dx

J

00

PIT>

xl /x(x)dx

(24-7)

where ix(x) is the density of the impairment X. On the other hand,
if X ::::: x, a good-or-better rating occurs if and only if T > x; hence
P{T > x}

== P{T >

x I X==x}

== P{R==4 or 5 I X==x}

(24-8)

Thus, the distribution of thresholds among individuals is given by
the function
peT

< x) == 1 -

P{R==4 or 5 I X==x}

,

(24-9)

and substitution into Equation (24-8) gives the grade of service.
To illustrate, suppose again that X is normally distributed with
mean, p-, and standard deviation, (7, and assume that

( a-x)

P{R==4 or 51 X=x} = Fz - b -

where
1 /-0 2
e- /2dy
( a-x) == y21T
a-x

Fz - b -

Y

562

Objectives and Criteria

Vol. 1

From Equation (24-9),
P{T

< x}

( a-x)
=:Fz (-x-a)
b-

=:

1 - Fz - b -

Thus, T is normally distributed with a mean a and standard deviation b. To determine the good-or-better grade of service, write
P{X

< T}

=:

P {X - T

< O}

(24-10)

Since X and T are both normally distributed and independent, it
follows that X - T =: S is normal with mean, IL-a, and standard deb 2 • Thus, if d is any real number,
viation, O"s =: yw

+

P{X - T

< d}

=:

Fs (

d- (jL-a) )

yu2+b 2

(24-11)

where F s (s) is the normal distribution function.
In particular, setting d

=:

0,

(24-12)

Consider now a simple but useful application of these concepts
to the determination of a noise grade of service. The function f (S) ,
is plotted in Figure 24-7 as a normal probability density function
representing the combined distribution of noise and customer opinions. Its median value is shown as (J-L-a). The O-db value is by
definition the value at which the stimulus just meets the given rating,
good. The O-db point is related, for a particular set of conditions, to
the median value by a value proportional to the standard deviation,
KO"s, in the figure. Noise is more disturbing as its magnitude increases, and so it is necessary to express the integral f (8) so that

563

Grade of Service

Chap. 24

/

~­

C~
0

(p,-a)

8 (dB)---+

Figure 24-7. Normal probability density function for noise grade-of-service
determ ination.

the area to the left of the O-dB point in Figure (24-7) represents
the good-or-better grade of service. That is,

f

00

Grade of service
=1good or better

!s(s) ds

o

The process of combining the noise distribution and opinion distribution functions to determine the grade of service can be conveniently carried out by using arithmetic probability paper. Suppose,
for example, that the distribution of noise for a group of trunks, as
measured and translated to the station set terminals, is found to have
a mean value of 36 dBrnc and a standard deviation of 4 dB. Also,
suppose that subjective tests have been conducted, that the results
show that the median value of noise rated good or better at the
station set is 39 dBrnc, and that opinions vary normally with a
standard deviation of 6 dB (see Figure 23-4). The two functions
are plotted in Figure 24-8.

Ir

To determine the good-or-better noise grade of service provided
by these trunks, the two functions of Figure 24-8 may be combined
and plotted as in Figure 24-9. Here, the mean value of the combined
distribution is the difference between the means of the two distributions of Figure 24-8 (36 - 39 == -3 dB) and the standard deviation
I

1\

Vol. 1

Obiectives and Criteria

564

.........-,__.........,

99.99r-----,r-"'II~-....,...-_r_-

99.B .-..--t----ft---t---+--++--+____i

90.-..--t--+-~-~-+--+____i

j

*g

-c

01

.
I

c

o
·c
.a.

o

G)

t

j

o

0.2

0.01

I----I--+-f--+---I--+--++_~

I - - - - I_ _ _--'-_.....L..._...L...-_.LL..---I

o

10

20

30

40

50

60

70

Noise at station set (dBrnc)

Figure 24-8. Illustrative probability density functions for noise and noise ratings.

of the combined distribution is the square root of the sum of the
squares of the two standard deviations (V42
62 == 7.2 dB). The
resulting distribution crosses the O-dB value, the value of noise
relative to that rated good or better, at the 62 percent point on the
ordinate. Thus, these trunks yield a noise grade of service of 62
percent good or better.

+

To determine a probability density function needed to achieve ,a
given grade of service, such as 95 percent, the inverse process must
be used. The resulting function might then be used to set equipment
performance criteria. The process would be an iterative one in which
the density function of Figure 24-7 would first be assumed. The O-dB

II
'\,1
"

Chap. 24

Grade of Service

565

99.99

99.8

/

99

~
Gi

II

90

t;

..a

.,0
0
0

.,

0)

j

50

J!!

2
III

C

0

J

~
CD
C

c

0

u

10

1I

V

V

~

J

0.2

0.01
-'50

V

)

I

V

-40

-30 -20 -10

0

10

20

30

40

Connection noise relative to noise rated good or better (dB)

figure 24·9. Combined probability density function for grade-of-service rating of
illustrative trunk group.

point would be determined by referring to Figure 9-15 to determine
the value of KG's for which the area to the left of the O-dB point is
95 percent of the total (1.65 O"s). Achievable performance curves
would then be studied to be sure they would fit the assumed conditions. By continuing the measurement of performance, it is possible
to verify that the 95 percent grade-of-service criterion is still being
satisfied.
.
The preceding discussion has been confined to the grade-of-service
evaluation of a single impairment; in reality a number of impair-

566

Obiectives and Criteria

Vol. 1

ments always coexist. This type of evaluation is sometimes made with
the assumption that other impairments are held constant or that the
impairment of interest is dominant. To e·stablish overall transmission
grade-of-service evaluations, all important impairments must be considered. Many evaluations of telephone circuits now .are based on
composite grades of service combining the effects of more than one
impairment. The loss/noise grade of service is an example [1, 2].
Techniques are also now available to extend the concept to loss/noise
and echo grade of service. For such evaluations, equations like (24-5)
must be evaluated as multiple integrals. Computer programs such as
GOSCAL are useful as an aid in evaluating these integrals.
24-3

USES Of THE GRADE-Of-SERVICE CONCEPT

Alternate solutions to many transmission engineering problems
can be compared by using the grade-of-service concept. The information obtained by such analyses often provides the basis for making
engineering compromises in establishing or allocating objectives,
identifying weak spots in performance, evaluating improvements,
showing the effects of time on services rendered, or conducting a
subjective test program or a field performance survey. Grade of
service is also used to evaluate combinations of service parameters
and to optimize performance with respect to such combinations so
that no single parameter is allowed to dominate.
Engineering Compromises

Solutions to engineering problems almost always involve compromise when requirements conflict. One of the more obvious conflicts
is achievement versus cost; performance can nearly always be
improved if costs are ignored.
Grade-of-service relationships can often be used to determine what
compromises are most appropriate and most economical. As an
example, consider a study to determine the allocation of noise objectives to long-haul and short-haul carrier systems. The allocations
were derived to satisfy customer-to-customer grade-of-service opinions of 95 percent good or better for 1000- to 4000-mile connections
made up of combinations of long-haul and short-haul trunks having
various assumed noise density functions. The resulting noise values
were translated through a representative loop loss distribution to
equivalent values at the station set for which grade-of-service

I
I'

I

Chap. 24

Grade of Service

567

opinions had been established by subjective testing. Throughout the
study, the noise values were determined for each assumed trunk
length from measured data. The standard deviation was assumed
constant at 4 dB, independent of trunk length. One overall result of
the study, shown in Figure 24-10, was a curve showing the locus of
points for which combinations of long-haul and short-haul trunk
noise satisfied a constant criterion of 95 percent good or better. Other
curves, not shown, were determined for the other percentages, 97,
93, etc.
40

~
£:

38

~
~

!

£:

.......

36

·0
...

E~

.!! E

!§

34

""" ~

;:)..-

0

..c

C.
£:

...2

32

~
~
\

£:

0

GI

~

30

28

22

24

26

28

30

32

34

Mean short-haul system noise (dBrncO)
60 miles

Figure 24-10. Noise allocation study results.

I

The choice of objectives, shown to be 34 dBrncO for long-haul and
28 dBrncO for short-haul systems, was made on the basis of considerations of expected noise performance of systems under development at the time of the study and the economics of reducing the
noise in those systems. Figure 24-10 shows that a 2-dB relaxation
of the long-haul objective to 36 dBrncO would require a 4-dB more
stringent short-haul objective in order to maintain the 95 percent
good-or-better grade of service. Also, if the short-haul objective were
relaxed by 2 dB to 30 dBrncO, the long-haul objective would have to
be made more stringent by about 2.5 dB.

I

Another example of how grade of service might be used to solve
an engineering problem involves the design of a group of new

568

Objectives and Criteria

Vol. 1

circuits needed to provide service to some remote location. If the
most inexpensive design were applied, circuit losses, would be
significantly higher than the objective mean value. The reduction of
these losses to meet the objective would necessitate the use of gain
devices whose cost would make the project appear economically unattractive. There might even be a third alternative in which losses
might be reduced to values somewhat short of the obj ective at only a
modest cost increase. The three alternatives could be analyzed to
determine how the losses in each case would affect the overall grade
of service. The results might be evaluated economically by making
a present worth of annual cost analysis, and then the final decision
could be made as a compromise in which the reduction in grade of
service could be evaluated in terms of cost to the company. Any of
the alternatives might be a reasonable solution to the problem, provided the overall grade of service remained within the satisfactory
range.
Performance Evaluation

Two aspects of performance can be studied conveniently by using
grade-of-service concepts. These are the identification of performance
weak spots in a geographical :area and the evaluation of performance
improvements that have been introduced (evaluated by measurement)
or proposed (evaluated by analysis).
Consider as an example of weak spot identification a situation in
which transmission performance in an administrative unit (for
example, a district or division) is shown to be deteriorating by a
succession of dropping indices or an increasing number of customer
complaints. Usually, the source of trouble can be identified by direct
analysis of the index data, but in some cases it may be necessary to
make measurments and then to compute the grade of service for loss,
noise, and echo (return loss). The results might show that the falling
index and/or the basis of complaints is a result of deteriorating echo
performance. Further investigation might reveal that balance measurements have not been made according to schedule in just one central
office, and with concurrent rearrangements in that office, the resulting
impedance mismatches are the cause of performance deterioration.
Performance improvements that are introduced in the system or
in some part of the system (a central office, a district, a division)
may be evaluated by making a grade-of-service comparison using
data obtained by measurements taken before and after the improve-

I
'I,ll

I

II,

Chap. 24

Grade of Service

569

ment is introduced. * This type of evaluation might include an analysis
of the expected improvement,based on predicted performance before
implementation, and a comparison of the measured results with
those predicted.
Time Effects on Grade of Service

Grade-of-service evaluations have their greatest value when they
are made periodically. Variations and trends can be observed by
comparing results of succeeding evaluations. Such comparisons are
most informative in situations where poor maintenance practices,
aging plant, or uncontrolled rearrangements lead to the introduction
of increasing impairments, though the trends can often he observed
and the cause of deterioration identified by direct analysis of indices.
Improvements in overall plant performance are also best evaluated
by making periodic grade-of-service evaluations. Design changes
cannot generally be made in the field instantaneously, and the periodic
monitoring of performance can be used to verify that an improvement
program is having the desired effect.

~I

Similarly, the introduction of a more stringent transmission objective cannot be expected to result in a rapid improvement in overall
performance. It is often uneconomical or technically unfeasible to
introduce the necessary improvements in existing systems, apparatus,
or equipment. The introduction of new systems designed to meet the
new objectives also takes time; years often pass before customer
satisfaction (as measured by appropriate performance indices) reflects the results of introducing such new systems.
Finally, communication system customers appear always to expect
improved service with time [3]. The response of communication
networks to increased public demands is necessarily a matter of
considerable time.
Sometimes a grade-of-service evaluation shows the need for a new
subjective test program or for a field survey of performance. When
customer satisfaction with transmission performance appears to de*Caution must be observed when making a grade-of-service analysis on a small
data base. The percentages obtained are valid on an absolute basis only for large
universes. However, observations of the change in good-or-better or poor-orworse percentages with changes in transmission parameters for one or more
subcomponents are valid even for small data bases.

570

()biectives and Criteria

Vol. 1

teriorate with time (as indicated by survey results, for example) and
no performance degradation can be identified, the cause may be a
result of changing public opinion regarding acceptable performance;
and new subjective tests may be needed to establish the new bases
of opinion.
With the introduction of new services and systems, there is also
the possibility that unexpected changes in performance are the cause
of deteriorating customer satisfaction. A survey might show the deterioration of customer satisfaction, and the change in plant performance might be reflected in the results of transmission measurements.
When this occurs, a new survey of plant performance may be needed.
24-4

LOSS-NOISE-ECHO GRADE OF SERVICE

Grade of service is being used increasingly to establish transmission objectives, to relate performance to objectives, and to evaluate
given performance parameters through the use of performance indices. In a number of these applications, grade of service provides a
link between the subjective evaluation of an impairment and the
establishment of an objective.
As discussed previously, grade of service can be applied to one
specific impairment (such as loss, noise, or echo) or to combinations
of these impairments. One important combination of impairments is
reflected in the combined loss-noise grade of service recently developed.
Earlier work had resulted in a model based on received volume; this
was followed by work on a model to incorporate both received volume
and idle circuit noise. These models were replaced as a result of more
recent work on loss and noise. Finally, effects of talker echo, obtained
in combination with loss and noise, resulted in models of the subjective effects of loss, noise, and talker echo on telephone connections [4].
These models have provided a basis for performance evaluation in
terms of combined loss-noise-echo grade of service.
In the analysis of subjective test results, it was recognized that
different tests yielded somewhat different results even when the same
impairments were tested. This complicated the combining of results
from different tests into a composite model of subjective opinion and
led to the concept of a general transmission rating scale, referred to
as the R-scale, which assigned a single numerical value to any specific
impairment.

Grade of Service

Chap. 24

571

In this concept of the R-scale, it was recognized that subjective
test results can be affected by various factors such as the subject
group, type of test, and range of conditions included in the test. This
could cause difficulties in trying to establish unique relationships between impairments and subjective opinion. The introduction of the
R-scale tended to reduce this difficulty by looking at the problem in
two parts. First, the transmission rating as a function of the impairment was anchored for two specific impairment conditions which
tended to lessen the dependence on individual tests. Second, the subjective opinions could still be displayed for the individual test base
from the R-scale results plus the reverse transformation.

Connection Loudness Loss and Noise Model
The loss-noise grade of service has been recognized for some time
as a valuable element in the evaluation of transmission performance.
Therefore, loss and noise were first treated together as a step toward
the larger result of a loss-noise-echo grade of service. This loss-noise
work led to the establishment of the anchor points for the R-scale
shown in Figure 24-11. These two points were selected to be well
separated in quality. One point is typical of a short intertoll connection and the other represents an extreme condition of loss and noise
which should rarely occur even on long intertoll connections between
long loops.
LOSS, LE
(dB)

NOISE

TRANSMISSION

(dBrnc)

RATING

15
30

25
40

80
40

Figure 24-11. Transmission rating anchor points.

Results from a number of different subjective tests were used in
deriving the loss-noise subjective opinion model. The loss values from
these tests were expressed in terms of loudness loss values which
represent the acoustic-to-acoustic transfer efficiency of overall telephone connections in terms of the Electro-Acoustic Rating System
(EARS) method [5]. Noise values used in the model are expressed at
the line terminals of a telephone set having a reference receiving
efficiency of 26 dB based on the EARS method. This efficiency value

572

Objectives and Criteria

Vol. 1

is approximately the receiving efficiency of a loop made up of a
500-type telephone set, a short line facility, and a standard central
office battery feeding bridge.
The R-scale representation of subjective opinion for connection loudness loss and noise is denoted RLN and'is given in Equation (24-14).
Curves generated from the equation for RLN are plotted in
Figure 24-12.
RLN

= 147.76 - 2.257Y(Le -7.2)2 + 1 - 2.009NF

+ 0.02037 LeNF

(24-14)

100

90

80

70

Z

~

60

C»

c

'';:

I:!
c

.:
0

50

'~

c

.-I:!

40

30

20
Anchor conditions:
Loss

10
•
•

Noise

15dB
30 dB

25 dBrnc
40 dBrnc

10

15

0
5

20

25

30

Connection loudness 1055, LE (dB)

Figure 24-12. Transmission rating for loss and noise.

35

573

Grade of Service

Chap. 24

In Equation (24-14), Le is the acoustic-to-acoustic connection loudness loss (in dB) of an overall telephone connection and N F is the
power addition of the circuit noise, N, and 27.37 dBrnc where N is
expressed in dBrnc at the line terminals of a telephone set with a
reference receiving efficiency of 26 dB based on the EARS method.

Talker Echo Model
The R-scale representation of subjective opinion for talker echo,
denoted R E , is given in Equation (24-15).

RE

= 95.01 -

53.45 log [

1+D

V1 +

(D/480)2

]

+ 2.277E.

(24-15)

In this equation, D is the round-trip echo path delay in milliseconds
and E is the round-trip acoustic-to-acoustic loudness loss in dB of
the echo path. Curves generated from Equation (24-15) are plotted
in Figure 24-13 for a range of echo path delay and echo path loss
values.

Loss-Noise-Echo Model
The R-scale representation of subjective opinion for the combined
impairments of loss, noise, and talker echo is denoted R LNE ; it is related to RLN and RE as shown in Equation (24-16) where RLN and RE
are given in Equations (24-14) and (24-15) respectively.

(24-16)

Transmission rating for loss, noise, and talker echo, (R LNE ) is
shown plotted in Figure 24-14 as a function of echo path loudness
loss for a range of round-trip echo path delay values with a connection loudness loss value of 15 dB and a circuit noise value of 30 dBrnc.
The asymptotic limits of the curves at large values of echo path loud-

574

Objectives and Criteria

Vol. 1

80

70
[;l

~

60

01

c

-2
c
0

.=

so

.~

c

I:!

40

t-

30

20

10

so

30
Echo path loudness loss,

E (dB)

Figure 24-13. Transmission rating for talker echo.

ness loss vary with connection loudness loss and circuit noise in
accordance with the curves of Figure 24-12.
Subjective Opinion Models
The transmission rating scale was selected so that most telephone
connections have positive ratings between 40 and 100 with higher
ratings denoting better quality. One important feature of the transmission rating is that ratings can be computed without reference to
any particular subjective test. As users become more familiar with
the R-scale, the test-independent measure of subjective quality may
replace the presently used measures such as percent good or better,
percent poor or worse, etc., which are test dependent.

t

I

Grade of Service

Chap. 24-

575

100
II"

90

80

10
~
2:

-.l

'5

60

DI

c

-e
c
0

50

.=

.~

c

e

40

I-

30

20

10

J.+-+--4-+--____.~_A_____.,....,.-_+_---

Connection loudness loss,
I.E = 15 dB
Circuit noise, N
30 dBrnc

=

0
I

r

0

10

20

30

40

50

60

Echo path loudness loss, E (dB)

Figure 24-14. Transmission rating for loss, noise, and talker echo.

For present use, relationships have been established between the
R-scale and the subjective opinions for specific subjective tests. For
example, contours of constant percent good or better and poor or
worse are shown in Figure 24-15 for a specific set of loss-noise subjective tests performed in 1965. The results of these tests have been
widely used and thus represent a subjective test data base that is
well known [6].
REFERENCES

1. Lewinski, D. A. "A New Objective for Message Circuit Noise," Bell System
Tech. J., Vol. 43 (Mar. 1964), pp. 719-740.

Vol. 1

Obiectives and Criteria

576

30r---------r-----~~~~------~----~~_r------~_r----~--~

25

co

~
IOl

o..:l

20

=.2
:::

G)

c

"C

~

.2
c
0

"e

15

G)

c
c
0

u

10

5

~

15

________

~

________

20

~

25

________

~

__

~

____

30

~~

35

____

~~_A~~~~

40

45

Circuit noise, N (dBrnc)
Good or better
-

-

-

Poor or worse

Figure 24-15. Constant percent contours.

2. Sen, T. K. "Subjective Effects of Noise and Loss in Telephone Transmission,"
I.E.E.E. Transactions on Communication Technology, Vol. COM-19 (Dec.
1971), pp. 1229-1233.
3. MacAdam, W. K. "A Basis for Transmission Performance Objectives in a
Telephone Communication System," A.I.E.E. Transactions, Part 1, Communications and Electronics, Vol. 77 (1958) pp. 205-209.
4. Cavanaugh, J. R., R. W. Hatch, and J. L. Sullivan. "Models for the Subjective
Effects of Loss, Noise and Talker Echo on Telephone Connections," Bell
System Tech. J., Vol. 55 (Nov. 1976), pp. 1319-1371.
5. Sullivan, J. L. "A Laboratory System for Measuring Loudness Loss of Telephone Con,nections," Bell System Tech. J., Vol. 50 (Oct. 1971) pp. 2663-2739.
6. Spang, T. C. "Loss-Noise Echo Study of the Direct Distance Dialing Network,"
Bell System Tech. J., Vol. 55, (Jan. 1976), pp. 1-36.

Objectives and Criteria

Chapter 25

Determination and Application of Objectives
Transmission objectives must be processed in a number of ways to
make them useful in system design and operation. They can be
considered as goals that are established and used as criteria for the
achievement of a quality of service that is economical and ultimately
satisfactory to nearly all customers. The processes to which objectives
are submitted produce a set of requirements, i.e., performance
parameters that must be satisfied if the objectives are to be met.
Ambiguity between the terms objectives and requirements may be
noted. The distinction may be a matter of definition, point of view,
or terminology. When an expression such as "a 95 percent good-orbetter grade-of-service objective" is used, there can hardly be any
doubt that an objective is being discussed. If it is stated that "the
transistor must have a single-frequency fundamental-to-third harmonic ratio for a milliwatt output," there is little doubt that a
requirement is being stated. In between, there are many uncertainties
and shades of meaning. The processing of requirement and objective
data, therefore, is often similar and involves what shall here be
called determination, interpretation, allocation, and translation.
These subjects are all broad in nature. It is not the intent here to
discuss them in detail with respect to the many possible applications.
Rather, general considerations of the processing are reviewed and
several examples are given. It must be recognized, also, that the
processes are generally reversible. The measurement of performance
of devices, circuits, and parts of systems can often be extrapolated
to determine or estimate the overall performance of a transmission
system.
25-1

DETERMINATION

The determination of transmission objectives most often begins
with a subjective test program designed to establish the relationship

577

578

Objectives and Criteria

Vol. 1

between an impairment (or combination of impairments) and observer opinions of the effects of various amounts of the impairment.
The data representing the test results are then combined with
performance parameters so that the combination can be expressed
in terms of grade of service. Finally, the grade-of-service relationships
are analyzed through engineering economy studies to determine
relative costs of furnishing various grades of service. On the basis
of these studies, a value for the objective can be selected that represents a reasonable compromise between providing customer satisfaction and the cost of providing the service.
Another way of processing data in order to form an objective is to
derive an objective index for a given impairment; an index is a
single number, based on a scale of 1 to 100, which can be used as a
broad measure of plant performance. Indices are used mainly as
tools for transmission management; they are particularly valuable
in showing trends of performance for large geographical or administrative units of the plant. The objective indices are always expressed
according to the following scale:

99 - 100
96 - 98
90 - 95
Below 90

Excellent
Fully satisfactory
Fair to mediocre
Unsatisfactory

Requirements that must be met in order to satisfy the established
objectives are usually derived from the objectives. The dependency
of the one upon the other distinguishes requirements from objectives.
An objective is a goal; a requirement must be met to satisfy the goal.
25-2

INTERPRETATION

In whatever form it may be stated, an objective is subject to a
great deal of interpretation to make it applicable to a particular set
of circumstances. The interpretive treatment of objectives may
call for identification of the following: (1) the static characteristics
of the impairment (for example, a pure single frequency versus one
having high sideband content or intelligible crosstalk versus nonintelligible crosstalk); (2) the probabilistic phenomena which might

I

II

I

Chap. 25

Determination and Application of Objectives

579

,,:'

cover the probability of occurrence or the statistical properties of a
varying impairment; (3) the simultaneous effects of multiple impairments of the same or different types; (4) the way of expressing
the impairment and the objective for various types of signals; (5) the
establishment of a requirement in terms of a limit. The term limit
implies -that some form of corrective action must be implemented
if the requirement is exceeded.
Static Impairment Characteristics
The interpretation of an objective often depends on some characteristic of the impairment. For example, the transmission of television signals in the presence of speech signals introduced new types
of interference to telephone transmission. Some of these interferences
may be regarded as single-frequency interferences for which objectives have long been established. However, since they result from line
scan frequency components of the television signal, there is sideband
energy at multiples of 30 and 60 Hertz on both sides of each line scan
frequency multiple. These sidebands produce a subjective effect that
makes the single-frequency interference sound distorted. The objective for this distorted single-frequency interference is a matter of
interpretation and had to be established by subjective tests designed
to compare the interfering effect of the distorted tone with that of a
pure single frequency. The distorted tone was found to be less interfering than the pure single frequency, so that 2 dB more interference
power can be tolerated. Thus, the single-frequency interference objective may be interpreted for application to television tone interferences so that if the single-frequency objective is x dBrncO, the
television tone objective is x +2 dBrncO.
Another example of interpretation concerns crosstalk objectives,
usually expressed in terms of minimum allowable crosstalk coupling
loss derived from crosstalk indices. In some cases, the nature of the
coupling path results in nonintelligible crosstalk due to some phenomenon such as frequency inversion. In the past, the objectives applied
to nonintelligible crosstalk were the same as those applied to intelligible crosstalk. The reason for this interpretation was that when
nonintelligible crosstalk is heard, the syllabic character of the interference is quite recognizable, and the listener finds it as annoying as
if it were intelligible. More recently, this type of crosstalk has been
treated as noise, with the objective made about 3 dB more stringent
than that for random noise.

580

Obiectives and Criteria

Vol. 1

Probabilistic Characteristics
A statement of objectives for impairments having probabilistic
characteristics must include appropriately qualifying phrases to
account for the variability. Several examples may be cited.
In digital signal transmission, one of the most common ways to
express transmission impairment is in terms of error rate. When the
effect of impulse noise is evaluated, performance must be related to
error rate in such a way that the rate of signal transmission, the
amplitude distribution of the interference, the probability of occurrence of the interference, and certain characteristics of the transmitted signal must all be considered. Simplistic statements of an
error rate objective are often inadequate; block error rates, or the
expected percentage of unimpaired transmitted blocks of information, are sometimes more meaningful because error detection codes
and the basic coding of the signal often permit retransmission of
impaired blocks. A burst of errors might completely ruin a single
block of information, causing an apparently excessive error rate.
The result, however, might be the retransmission of that single block
of information, one of many perfect blocks. Thus, an error rate
objective simply expressed as an objective of 10- 6 must be further
interpreted to account for signals and interferences having various
parameters.
Impulse noise may also impair television signals. Here again, any
expression of an impulse noise objective must take into account the
statistical variation of impulse amplitudes and the probability of
occurrence.
Interference, though continuously present, may also vary in amplitude and/or in frequency and in the subjective effect of one or the
other. The previously cited example, comparing the interfering
effects of television signal components and single frequencies, involved subjective tests that included amplitude variations (due to
changes in picture content) and frequency variations (due to frequency drift in power sources) in addition to the sideband distortion
components discussed. The interpretation of the final objective had
to recognize that the mean amplitude value and the nominal frequency were represented.
Very low-frequency interference in television signals sometimes
has the same subjective effect as a flickering of the picture. Careful

Chap. 25

Determinatlon and Application of Objectives

581

interpretation of subjective test results must be made to insure that
both bar pattern and flicker effects are covered by the objective.
Multiple Impairments
Another situation that involves interpretation of objectives occurs
when multiple impairments are simultaneously present. When they
are of different types, a portion of the objective must be allocated
to each impairment. If the impairments are of the same type, the
objectives are usually established 0)" interpreted in terms of the
combined effect.
One illustration of the way multiple impairments may be treated
is the handling of multiple sources of intelligible crosstalk. The performance and objectives for intelligible crosstalk are usually expressed in terms of the crosstalk index. As discussed in Chapter 17,
the crosstalk index is derived by mathematical relationships which
include the probability of hearing intelligible crosstalk. If the sources
are independent, the number of sources is included as a parameter
in the derivation. If the crosstalk paths can cause simultaneous
exposures to the same source, the coupling is increased by 10 log N
or 20 log N (N is the number of paths), as appropriate, and the
crosstalk is treated as if it were from a single source.
Sometimes there are multiple interferences of a random nature
whose combined interfering effect is best evaluated by summing the
powers of the individual contributors. In multichannel analog transmission systems, for example, the combined effect of thermal noise
and interchannel modulation noise is determined by adding the
powers of the two contributors. The objective must be interpreted as
applying to the sum of the interferences.
Objectives, Requirements, and Limits
There is a multitude of expressions used for performance, objectives, and requirements in telecommunications. These expressions
are all subject to interpretation according to the nature of the impairment, the characteristics of the channel and the signal, or the
manner in which these characteristics interact. Depending on circumstances, digital signal transmission performance or objectives
may be expressed in terms of signal-to-noise ratio, noise impairment,

582

Objectives and Criteria

Vol. 1

error rate, or percentage of eye closure. Television impairments are
usually expressed in terms of signal-to..;interference ratios where the
signal is measured in peak-to-peak volts; however, the interference
may be expressed in rms, peak, or peak-to-peak volts. Random noise
and echoes are weighted by frequency and/or time delay. Telephone
objectives and requirements are often expressed in terms of absolute
values of interference as measured at specified transmission level
points.
All these expressions must be thoroughly understood since often
it is necessary to interpret one in terms of another or to derive one
from another. Part of the interpretation process requires a thorough
understanding of the transmission level point concept. When the
concept is properly applied, telephone system noise in dBrncO, for
example, -can easily be interpreted as a signal-to-noise ratio for data
signal transmission analysis.
Objectives have been defined as desired goals. Requirements are
performance parameters that must be met if objectives are to be
satisfied. Limits are performance parameters that, when exceeded,
indicate a need for some form of corrective action and, in som,e cases,
removal of a circuit from service until the corrective action is
completed.
When a new transmission system is being developed, design objectives are applied to guide the generation of design requirements
that must be met. The design requirements are maximum or minimum
values that must be met in the controlled development environment
if the design objectives are to be met.
When a system is installed in the field, engineering objectives are
those that are recommended for the application or layout of the system
in the field environment. After installation and during the useful life
of a transmission system, trunks and other transmission channels
are connected through the system. When these circuits are connected
and before they are released for service, they are subjected to a
series of tests specified on the circuit order to ensure that all the
equipment is properly aligned and to verify that the circuit meets
its engineering objectives. The minimum and maximum values established for these tests are sometimes called circuit order requirements.

Maintenance requirements are intended to reflect performance
that is practical to obtain in the field environment using existing

t

I

Chap. 25

Determination and Application of Objectives

583

I'

'I I

equipment and operating procedures. Maintenance limits are those
within which performance 'is satisfactory; when the limits are exceeded, maintenance action is required. A maintenance limit may be
established at some value which, if exceeded, requires that a circuit
be taken out of service. Such a limit is sometimes called a turn-down
limit.
25-3

ALLOCATION

Objectives are usually established and applied in a format that
expresses the performance goal for overall systems or broad categories of service. To be useful in development, design, or operation,
these broad objectives must be appropriately allocated to a variety
of impairments, to portions of the plant or parts of systems.
Allocation Assuming Power Addition

11'11

The allocation process requires the exercise of considerable judgment and a knowledge of many system performance parameters and
cost relationships. The process is seldom arbitrary, but in the absence
of data indicating otherwise, it is common to assume that different
types of impairments add according to their powers and that like
impairments from different parts of a system also add by power.
It does not necessarily follow that the several impairments are given
equal weight. If economic factors or system parameters are significant, the impairments may be allocated different proportions of an
overall objective.
An overall objective for a single impairment may also be allocated
to different parts of the plant or to different elements of connections
according to the assumption of power addition. Allocations of noise
to a hypothetical layout of video circuits may be used to illustrate
this technique. Figure 25-1 shows the principal elements in a
4000-mile layout. The elements include a toll transmission circuit or
circuits, local transmission circuits, carrier switching centers, video
television operating centers (TOes), and intraoffice trunks. The
number of each of the various elements must be assumed or determined from engineering studies of the service needs.
If the layout is known and power addition is assumed, the allocation of the objective is a straightforward process of dividing the
power of the interference that just meets the objective among the

Objectives and Criteria

584

Vol. 1

Overall c:ircuif {4000 miles}

I------I~

1'----.

Toll circuit

t

Breaks down into individual links, hops, or miles
of toll facility making up the 4OOO-mile circuit.

Local circuit

t

Assume 12 local links in several cities on route.
Assume 3 of these are maximum length
and the remaining 9 average 10 dB better performance.

' - - - -... Switching circuit
Carrier switching

t
Assume 3 switching centers.

4

t

•

Video switching

+

Assume 3 TOes and 4 intraoffice trunks,
all with equal weight.

Figure 25-1. Assumed configuration of the overall circuit for objective allocations.

elements that may make up a 4000-mile overall connection. This
breakdown is illustrated by Figure 25-2. Allocation such as that
illustrated cannot be rigidly followed because some degradations are
present only in certain sections of the overall connection and are
completely absent in other sections. Thus, it is often necessary or
desirable to reallocate larger portions of the objective to the troublesome sections.
Cost Effects

When allocation to various parts of the plant or system is considered, the relative costs of .achieving the allocated objective must
be carefully weighed. The relationships between allocations, the
characteristics of different parts of the plant, and the relative extent
to which the parts of the plant are used must be considered. Two
illustrations, taken from a study of message circuit noise allocations,
show how these parameters interact [1].
The study, which culminated in grade-of-service calculations for
telephone connections over all distances, showed that the overall
noise grade of service was about 97 percent good or better. Yet, for

I

I .

['

Chap. 25

585

Determination and Application of Obiectives

II

Overall objective

XdBm

1"1

Toll objective
X-2 dBm
Switching objective

~

X-13dBm

Per mile
(4000 miles)
X-38 dBm

Carrier switching
objective

X-16dBm

Per switching
center
(3 centers)
X-21 dBm

+

Per TOe
(3 centers)
X-25 dBm

Video switching

x-r

objective
m

Per intra-office
trunk
(4 trunks)
X-25 dBm

Local objective

X-5dBm

Per link
(3 max. length links)
X-ll dBm

Per link
(9 short links)
X-21 dBm

Notes:
(1) All noise values in weighted
dBm referred to the same
video transmission level point.
(2) Allocations rounded to the
nearest dB.

I

Figure 25-2. Noise objectives for a 4000-mile circuit aJ/ocated on the assumption
of power law addition.

'"
I

longer connections the grade of service was calculated to be below
90 percent due to the fact that noise increases at a rate of about
3 dB for each doubling of the distance. The relatively poor performance on long connections had little effect on the overall grade of
service because the number of calls decreases rapidly with distance.

III
I

The conclusion from this part of the study was that noise objectives for longer systems should be made more stringent by 3 to 4 dB
to improve the grade of service on long connections. It was recognized,
however, that the achievement of 3 to 4 dB improvement in noise on
existing systems would not be economically feasible, so the more
stringent objectives are applied only to newly designed systems.
The second observation made in the study was that noise from
short- and long-haul trunks influenced the overall noise at the station

586

Vol. 1

Obiectives and Criteria

set to the extent that a reduction of loop noise below 20 dBrnc could
not be justified. Regardless of money or effort expended to reduce
this noise contribution, the grade of service would not be significantly
improved. Thus, loop noise in excess of 20 dBrnc would be observed
as a degradation in grade of service. These results are illustrated in
Figure 25-3. As a result of these studies, an overall loop noise
objectiv4:} of 20 dBrnc was adopted.
Allocation for Digital Transmission
Allocation problems for digital signal transmission are the same
in principle as those encountered in analog signal transmission. How-

100
Medium
Long

t

2:

Jl

(;

1

90

Intercontinental

01
~

~
l-

80

1.2
Loop nOise
• I"Imlt ........

I

1
(;

0.8

0
D.

~
GI

t

Intercontinental

D-

004
Long
Medium

o

5

10

15

20

25

30

Noise at line terminals of station set (dBrncl

Figure 25-3. Grade of service for connection obiective as a function of loop noise.

t

Chap. 25

Determination and Application of Obiectives

587

ever, the problems differ in detail because of the discrete nature of
the signal, the regenerative processes used in digital transmission
system repeaters, and the properties of time division signal multiplexing. Digital signal impairments include errors, jitter, and
misframes.
In a regenerative repeater system, it is assumed that transmission
line noise impairments are noncumulative because, in theory, signal
pulses are perfectly reconstructed at each repeater. However, margin
must be provided to guard against pulse distortion to the point where
errors may occur since, at that point, performance deteriorates very
rapidly.
Because of the precipitous nature of performance· degradation,
digital system components, such as repeaters and multiplex equipment, normally operate at an error rate that is near zero. A high
system error, rate is often due to a single repeater operating with
excessive pulse distortion or with insufficient margin. Therefore, it is
common practice to assign the same error rate objective to parts of
a system as that assigned to the whole system. The probabi1ity of
exceeding this error rate is then allocated among the parts.
Certain impairments are cumulative and careful attention must be
given to these when objectives are being allocated. Timing problems
(jitter) are cumulative along a repeatered 1ine. Therefore, the total
objective must be allocated so that relatively large margins are
maintained.
Misframes occur when the demultiplexing terminal loses synchronism with the incoming bit stream. Communication on all channels
is interrupted until synchronism is recovered. The effect is usually
noted at all levels of the digital hierarchy below that at which it
occurs. Thus, misframe impairments must be allocated among the
various multiplex levels.
Another class of impairments that may accumulate has its source
in the terminal e ui ment used- to convert analo s· nals to a (fl"gftil
:(oiiiiat.
e coding process produces noise that is called quantizing
l!.oise, an impairment that increases with the number of times the
signal is so processed. Care must be taken to allocate objectives
realistically in relation to laws of accumulation that may pertain to
given situations.

588
25-4

Obiectives and Criteria

Vol. 1

TRANSLATION

The translation of objectives from one set of parameters to another
(for example, from a broad objective to a specific requirement) or
from one transmission level point to another frequently requires a
knowledge of how systems operate or how they can be organized to
adapt them to an assumed process of translation. Three examples of
system operating parameters are the laws of addition of intermodulation products in a series of analog cable system repeaters, the effects
of frogging on system performance, and the relationships among
various noise contributors in an optimized system design.
Obiectives to Requirements

Requirements are generally derived from objectives by a process
that may be regarded as translation. Many examples could be used
to illustrate the process. Consider two that relate to the generation
of intermodulation noise in analog systems.
In an analog cable system proposed for use up to 4000 miles, a system design objective is established as a goal to satisfy overall noise
grade-of-service objectives. A number of interpretation and allocation
processes are carried out so that the translation is finally carried to a
point such that it is possible to specify the permissible magnitudes of
second-harmonic and third-harmonic products for a 0 dBmO signal
in the 800 miles between frogging points. These new values may now
be regarded as system design requirements that .must be met in the
800-mile link if the initial overall noise objective is to be satisfied.
In a microwave radio system, a noise objective consistent with
overall Bell System noise grade-of-service objectives .is similarly
established for 4000-mile transmission. Through interpretation and
allocation, this objective is processed so that it is possible to determine the maximum permissible value of interchannel modulation noise
generated in one radio repeater. This value ,might be regarded as a
requirement itself, but further translfttion may al~o be applied so that
the requirement can be expressed in terms of return...loss values for
the waveguide sections of the radio repeater. (InFM systems reflections due to low return losses produce intermodulation among the
signal components.) Thus, the overall noise obj ective for the system
is translated into return-loss requirements for the individual repeater
waveguide sections.

Chap. 25

Determination and Application of Obiectives

589

Transmission Level Point Translations

Objectives and requirements are often expressed in reference to
a specific transmission level point, generally 0 TLP. Sometimes it is
necessary to express the same objective in reference to some other
TLP. This translation process is usually straightforward but care
must be taken to make the translation properly.
Consider the previous discussion of the translation of an overall
noise grade-of-service objective to the second and third harmonic
requirements for an analog cable system. To illustrate the further
translation to a different TLP, assume that the 800-mile requirements are a maximum second harmonic of -40 dBmO and a maximum
third harmonic of -50 dBmO for a 0 dBmO fundamental signal.
(These values are illustrative only and are not necessarily representative.) Now, suppose that a convenient point of measurement of
system performance is at a -10 dB TLP. A 0 dBmO signal translates
to a -10 dBm signal at the -10 dB TLP, the second-harmonic requirement translates to - 40 -10 == -50 dBm, and the third-order
requirement translates to -50 -10 == -60 dBm.

I

II

I

N ow suppose that these 800-mile requirements must be expressed
in terms that are consistent with the magnitude of a test signal
specified as -16 dBmO. At the 0 TLP, the second-harmonic requirement is then - 40 -2 (16) == -72 dBmO; translated to the -10 dB
TLP, the requirement is -72 -10 == -82 dBm. Similarly, the thirdharmonic requirement at 0 TLP is -50 -3 (16) == -98 dBmO or
-98 -10 == -108 dBm at the -10 dB TLP. (Recall that the second
and third harmonics vary in dB by 2:1 and 3 :1, respectively, relative
to the fundamental.)
The processes are similar when objectives or requirements are
translated between transmission level points in video systems. However, the situation is further complicated by the fact that television
objectives are usually expressed in volts or in dB relative to volts
(rms, peak, or peak-to-peak) and the expression of the objectives
and their translation must therefore take into consideration the impedances at the points of interest as well as the appropriate voltages.
Indices

Objectives and requirements are used in the field as standards
against which measured performance can be compared. One aspect
of this process involves transmission management. The vastness of

590

Obiectives and Criteria

Vol. 1

the plant and the many parameters to be evaluated have led to the
concept of transmission indices. These are single-number evaluations
of a large sector of plant which are derived from grade-of-service
objectives and expressed in such a way that performance measurements can easily be translated into indices. Such indices are used
extensively as· a transmission management tool.
System Parameter Effects

Three analog cable system parameters were previously mentioned
for their significant impact on the translation of objectives or requirements. These include the laws of addition of intermodulation
products, the effects of frogging, and the interrelationships among
noise contributors in an optimized system design. Many other parameters could be mentioned, but these illustrate the importance of
system effects on translation processes.
laws of Addition. It can be shown that second-order and many thirdorder intermodulation products tend to accumulate in successive
repeaters of an analog cable system by a law of power addition [2].
Also, some types of third-order products (usually termed 2A-B
and A+B-C products) tend to add systematically (by voltage) in
successive repeaters. The translation of objectives must take these
facts into account.

The hypothetical set of objectives for second and third harmonics,
previously suggested as illustrative, can be used again here; for a
o dBmO fundamental signal, the second- and third-harmonic requirements were -40 dBmO and -50 dBmO. Assume that the system under
consideration requires 250 tandem repeaters in an 800-mile link. The
translation of the harmonic distortion requirements to per-repeater
requirements can be accomplished by taking these laws of addition
into account. Thus, a per-repeater second-harmonic requirement may
be obtained from the 800-mile requirement by subtracting the power
of the other repeater contributions. For a 0 dBmO fundamental, then,
the per-repeater requirement for second harmonic is
-40 -10 log 250

== -40 -24 == -64 dBmO.

For the third harmonic, the per-repeater requirement is
-50 -20 log 250

== -50 -48 == -98 dBmO.

These values may be further adjusted for the TLP appropriate to
the repeater and for the magnitude of the test signal.

Chap. 25

Determination and Application of Objectives

591

A peculiarity in computing the third-harmonic requirement must
be explained. Third-harmonic intermodulation products accumulate
by a power law. The requirement is derived on the basis of voltage
addition because the dominant (2A-B and A+B-C) third-order
products add by voltage and the same nonlinear coefficient applies
to both third harmonics and the dominant products. Thus, it is a convenient fiction to assume voltage addition for third harmonics. The
requirement must ultimately be translated into a per-repeater modulation coefficient requirement and, beyond that, into requirements
on device linearity and amplifier feedback.
Frogging. Frequency frogging of telephone channels is specified in
long analog cable systems to accomplish two principal goals: (1) to
break up the systematic addition of third-order modulation products
and (2) to break up systematic departures from ideal (flat) transmission in the system amplitude/frequency response. Both of these
advantages are sought in order to ease the requirements on linearity
and equalization of repeaters in short sections of line. The effectiveness of frogging can be seen by examining the translation from
4000-mile to 800-mile objectives and then examining how the resulting linearity requirements would have been made more stringent if
the frogging advantage could not be realized.

The effect of in-phase addition on the third-harmonic requirement
for a single repeater in an 800-mile link was previously noted. The
-50 dBmO requirement for an 800-mile link (from which the singlerepeater requirement was derived) was, by inference, derived by
translation from the 4000-mile objective and included the assumption
of power addition between 800-mile links. If it had been necessary
to assume in-phase or voltage addition between 800-mile links, the
800-mile requirement would have been -43 -20 log 5 == -57 dBmO
for the third harmonic of a 0 dBmO fundamental. The assumption of
frogging and power addition of 800-mile links eased the 800-mile and
per-repeater requirements by 57 -50 == 7 dB.
Signal-to-Noise Optimization. Transmission system design analysis
has shown that if the predominant source of intermodulation noise
in an analog cable system is a result of second-order nonlinearity,
the optimum signal-to-noise performance is obtained when signa1
amplitudes are adjusted so that the intermodulation noise is equal
to the thermal noise in the system [2]. If the predominant intermodulation noise is due to third-order nonlinearity, the optimum perfor-

592

Obiectives and Criteria

Vol. 1

mance is obtained when signal amplitudes are adjusted so that the
intermodulation noise is 3 dB less than the thermal noise.
These relatively simple theoretical relationships are made complex
by many of the detailed design parameters that enter into an actual
computation and the resulting iterative process that must take place
during design and development. The result of the design process is
that one type of intermodulation phenomenon tends to dominate the
other. The translation process, from objectives to device and circuit
requirements, must then be applied rigidly to the dominant parameter. The extent to which the requirements on parameters of less
importance can be relaxed depends on the amount of margin exhibited.
Some parameters can be safely ignored in spite of their potentially
harmful effects on performance. In the analysis of intermodulation
phenomena, for example, the second- and third-order nonlinearity
terms of an input/output function are so dominant that terms higher
than third order are usually ignored. During design and development
the higher order terms must be checked, but they are usually found
to be insignificant. Exceptions are found occasionally in the design
of nonlinear modulator circuits used in multiplex equipment.
REFERENCES

1. Lewinski, D. A. "A New Objective for Message Circuit Noise," Bell System
Tech. J., Vol. 43 (Mar. 1964), pp. 719-740.

2. Technical Staff of Bell Telephone Laboratories. Transmission Systems for
Communications, Fourth Edition (Winston-Salem, N.C.: Western Electric
Company, Inc., 1970), Chapter 13.

Objectives and Criteria

Chapter 26

Transmission Objectives
Transmission objectives, derived from grade-of-service analyses
of the results of subjective tests and performance measurements, are
stated in terms of design, performance, or maintenance objectives.
Requirements, derived from the objectives, are also given in these
same terms and additionally in terms of maintenance limits. These
limits define points at which performance is so poor and service is
so adversely affected that circuits must be repaired or, in the extreme,
taken out of service until repairs or adjustments can be made.
The objectives are continuously studied and modified to adapt to
the changing environment caused by the introduction of new equipment and systems, new technology, new services, and by changes in
customer opinions. The objectives are often established as overall
values applicable to terminal-to-terminal connections. They are then
allocated in various ways to appropriate portions of the plant, to
various impairments, or to a particular type of service.
This chapter discusses well-established objectives, with numerical
values given wherever possible. Where objectives have not become
standard, only general discussion is included to indicate the nature
of transmission problems involved. Space does not permit a comprehensive listing of objectives for all types of signals, systems, or
services. Furthermore, the changing nature of transmission objectives
might make the material obsolete within a short time.
26-1

VOICE-FREQUENCY CHANNEL OBJECTIVES

Transmission objectives for voice-frequency channels in the
switched message network were initially established to satisfy the
needs of speech transmission. As new types of signals and services
have evolved and as new technology has been applied to all parts of
the system, existing objectives have been modified and new objectives
have been developed where necessary.

593

594

Obiectives and Criteria

Vol. 1

Bandwidth
The bandwidth of telephone loops and trunks has evolved without
a specific and consistent set of objectives. Initially, deficiencies in
the bandwidth of such circuits were masked by station set limitations.
The necessity for establishing an acceptable channel bandwidth
allocation and carrier separation was recognized when AM carrier
systems were introduced. At that time, the single sideband (SSB)
mode of transmission was established; also, the 4-kHz s'pacing of
carriers was deemed adequate in view of practical bandwidth limitations and in view of articulation tests conducted for the purpose of
establishing bandwidth requirements for intelligibility and naturalness of speech.
As new systems have been introduced and as design technology
has improved, efforts have continued to make the effective bandwidth
of network channels as wide as is economically feasible within the
constraints of (1) the 4-kHz carrier separation and achievable filter
designs and (2) the unavoidably low singing return losses of loaded
cable facilities near the high-frequency cutoff region.
More recently, subjective tests have shown that the preferred
bandwidth for voice communications is approximately from 200 to
3200 Hz. As a result of these tests and technological advances, efforts
are being made to establish standard design objectives for the bandwidth of each major portion of the network so that overall connections
can meet the bandwidth objective. The natural increase in attenuation with higher frequencies for nonloaded cable and the sharp highfrequency cutoff of loaded facilities cause both types of facilities to
exert considerable influence over the effective bandwidth of loops
and VF trunks in an overall connection. Economics must be considered for making ()bjectives for each portion of the network as
stringent as possible, yet balanced with other portions. When finally
established, the design objective may be expected to be close to the
preferred bandwidth.
While this discussion centers about the transmission of speech
signals, it should be pointed out that as new voiceband data services
are introduced, the continued pressure to transmit at higher data
rates creates additional demand for wider bandwidths.
Frequency Response Characteristic Distortion
Formal message network objectives for inband amplitude and
phase distortion are not generally available (except for the case of

Chap. 26

Transmission Objectives

595

conditioned data loops). However, the same factors that tend to make
the effective telephone channel bandwidth as wide as possible also
work to make the inband response as uniform as possible. The
difficulties have been to express the objective values in a generally
acceptable manner and to allocate channel impairment requirements
optimally among the many contributors.
Amplitude/Frequency Distortion. The only message network design
objective for this impairment that has general acceptance applies to
loops for DA T APHONE® service or to data access arrangement
(DAA) loops for speeds of 300 bits per second or higher. The objective is that the loss at 2800 Hz shall be no more than 3 dB greater
than the loss at 1000 Hz [1].

Other portions of the network for which amplitude/frequency
response objectives are being studied include trunks, carrier- and
cable-derived facilities, and central office equipment including the
transmission paths through switching machines. Maintenance objectives are also under study for these parts of the network. Some
installation requirements for allowable slope are available in terms
of 400-Hz and 2800-Hz deviations from 1000-Hz loss values. The
limits depend on the type of facility used.
Phase/Frequency Distortion. Message network phase/frequency distortion objectives, usually expressed in terms of envelope delay distortion, are applied to loops and other special-service circuits conditioned
for data transmission [1]. If a loop is conditioned for data transmission at a rate of 300 bits per second or higher, a performance
objective applies of no more than 100 microseconds of differential delay between any two frequencies over the band from 1000 to 2400 Hz.

Phase/frequency distortion objectives are under study for application to other parts of the plant. These studies are likely to result in
an objective .for signal peak-to-average ratio (P / AR); the P / AR
meter method of expressing impairments is discussed in Chapters 18
and 21. This approach has considerable merit in its simplicity but
has the undesirable attribute of evaluating all impairments simultaneously [2]. Thus, it can be used for expressing delay distortion
objectives only where delay distortion is known to be the predominant
impairment.

Network Loss Design Plans
Echo and loss result from different impairing mechanisms and
have different subjective effects on listeners. However, they are closely

596

Objectives and Criteria

Vol. 1

related in that a practical way of reducing echo effects is to in·
crease loss. Since a loss increase introduces impairment (reduced
received volume), a compromise must be sought that maintains circuit
losses at satisfactory values, yet reduces echo effects to acceptable
values.
Ideally, it might seem to be desirable to operate telephone circuits
with no echo and no loss between end offices, but such ideal designs
are impractical and can be achieved only in the laboratory or on
selected circuits under well-controlled operating conditions. In a large
complex network involving switching, the nature of the variables
makes such a mode of operation uneconomical and impractical. Echofree transmission implies high return loss at interfaces such as
four-wire to two-wire conversion points. Lossless transmission implies
stable operation of electronic circuits in the face of highly variable
terminating impedances.

The transmission objectives for loss and echo in the toll portion
of the network have been established on the basis of the via net loss
concept [8 t 4]. This concept and the resultant objectives, while still
applicable to the network t are subject to continuous study, and details
change from time to time. For example, echo suppressor application
rules were recently revised. In addition, with the introduction of
time-division switching arrangements in the toll portion of the network, a fixed-loss design is being considered for replacing or supplementing the VNL plan. Such a new plan is required where digital
switching and digital transmission techniques are combined and where
they must be integrated with the existing analog network.

Via Net Loss Design Plan. A significant factor related to echo impairment is the propagation time involved in a connection, echo path
delay, which can be predicted from known parameters of the types
of facilities used in making up a connection. The loss and propagation time of the echo path can be predicted only statistically because
of the variations in facility properties and in return loss at the
distant end office. Similarly, reaction to talker echo (the third controlling parameter in judging echo performance) can be predicted
only statistically because of the variation in customer tolerance.

Chap. 26

Transmission Obiectives

597

The required one-way overall connection loss for satisfactory echo
is plotted in Figure 26-1 as a function of the round-trip echo delay
and of the number of trunks in the connection. Also shown is a linear
approximation for one trunk that proved useful in the evolving concept of VNL operation. This approximation was derived empirically
by considering (1) the need for increased loss at low delays to prevent singing or near-singing; (2) the need to control noise, crosstalk,
and transmission system loading; (3) the compromise between sufficient loss to control the effect of echo and the degradation introduced
by echo suppressors; and (4) the analytical advantage of having the
loss expressed as a linear function of echo path delay.
Linear approximations for more than one trunk may be derived by
adding 0.4 dB for each additional trunk to the loss required for a
single trunk. This loss is approximately the difference between loss
curves at 45 milliseconds delay. The linear approximations may be
drawn from the equation,

=

+

+

OCL O.102D O.4N 4.0
dB
(26-1)
where OCL is the overall connection loss, D is the echo path delay
in milliseconds, and N is the number of trunks in the connection.
Note that 0.102 is the slope of the dashed line of Figure 26-1 and
that (O.4N and 4.0) dB is the zero-delay intercept of this line for
various values of N. Equation (26-1) is used for connections involving round-trip delays up to 45 milliseconds. For delays in excess
of 45 milliseconds,. one of the trunks is equipped with an echo
suppressor.

The final step in the VNL design process is to assign trunk losses
so that each type of trunk in a connection operates at the lowest
practicable loss consistent with its length and the type of facility
used. In Equation (26-1), 2 dB of the constant is assigned to each
toll connecting trunk, and the remainder is assigned to each trunk
in the connection, including toll connecting trunks. The amount added
to each trunk is in proportion to the echo path delay of the trunk
and is defined as via net loss. * It is
(26-2)
dB
VNL = 0.102D + 0.4
where D is the echo path delay in milliseconds.

* The recent change in the method of defining toll connecting trunk loss, which
involved the assignment of an additional 0.5 dB of loss (for central office equipment) to the toll connecting trunk, resulted in a design value of VNL + 2.5 dB.
This added loss was previously assigned to the loop; thus, the customer-tocustomer loss has not changed.

598

Vol. 1

Obiectives and Criteria
20

18

Number of trunksin tandem

~6

/

16

/ / V~2
~1

/

/

V/ /~ V'l

~4~"
V~
~V/ ~/

14

/~ V/ ~I

12

V
/ //V/

/.4~

'"
.2

~

I If~ ~

c:

on0
:g
c:
8

~4

10

VI rr~

~Q)

r

r\

' Linear approximation
for one trunk , I
slope
0.102 dB/ms

=

/ VA

<5

V~ If!
1: ~

6

/

4

2

o

1i1V

V·J 1//

Ih fj

flJJ
rI/
V

o

20

40

80

60

Round-trip echo path delay

100

120

(ms)

Figure 26-1. One-way loss for satisfactory echo in 99 percent of connections.

II

I

Chap. 26

599

Transmission Obiectives

Since the echo path delay is directly related to the length of the
circuit, Equation (26-2) is usually written in terms of length and a
via net loss factor (VNLF).
VNL = VNLF (d)

+ 0.4

(26-3)

dB

where d is the distance in miles. The VNLF is
VNLF

= 2 X 0.102

(26-4)

'V

where v is the velocity of propagation in miles per millisecond. The
velocity of propagation used in Equation (26-4) must allow for the
delay in an average number of terminals as well as for the delay of
the medium. Accepted values of VNLF are given in Figure 26-2 for
commonly used facilities.

VIA NET LOSS FACTOR, dB! MILE
TYPE OF FACILITY

TWO-WIRE
CIRCUITS

FOUR-WIRE
CIRCUITS

Toll cable (quadded low-capacity)
19H172-62, 16H172-63

0.04

0.020

19B88-50

0.04

0.020

19H88-50

0.03

0.014

19H44-25, 16H44-25

0.02

0.010

0.01

-

-

0.0015

0.04

0.017

VF open wire
Carrier (cable, open wire,
microwave radio)
VF local cable (loaded or nonloaded)

Figure 26-2. Via net loss factors.

Fixed Loss Design Pion. With the introduction of No. 4 ESS and with
the expected evolution from analog to digital methods of transmis-

600

Obiectives and Criteria

Vol. 1

sion, a new loss plan for the toll portion of the network is needed
because of the difficulty of associating circuit loss with digital signal
processing. The introduction of controlled toll trunk losses in an
all-digital network would require (1) the conversion of digital signals
to their analog equivalents, insertion of the required losses, and reconversion to the digital format or (2) changing the encoded signal
amplitude by some digital process. Either method would be costly
and would introduce impairments.
A fixed l088 plan is now being introduced for use in an all-digital
toll network. This· plan specifies a 6-dB trunk loss between class 5
offices, regardless of connection mileage, to provide a good compromise between loss/noise and echo performance over a wide range of
connection lengths. and loop losses. Under this plan, each toll connecting trunk is allocated a loss of 3 dB; all-digital intertoll trunks
(digital facilities interconnecting digital toll switches) are operated
at a loss of 0 dB.
Connections in an all-digital toll network will have lower trunk
losses than similar connections in the present analog network. In
addition, noise will be reduced because of the use of digital facilities
and the elimination of channel banks at intermediate toll offices.
Loss/noise and echo grade-of-service studies have shown that full
implementation of an all-digital toll network will result in a significant improvement in transmission quality; the large improvement in
loss/noise grade of service due to lower loss and noise will more than
offset the slight degradation in echo grade of service due to lower
loss. These conclusions are based on the assumed application of echo
suppressors on trunks longer than 1850 miles and a 4-dB increase in
the requirements on terminal balance for two-wire toll connecting
trunks.
The fixed loss plan strictly applies only to an all-digital network.
It will take many years for the present predominantly analog network to be converted to a predominantly digital network. Therefore,
an operating plan to cover the transition period must be provided
in order to assure satisfactory performance when analog and digital
switching machines are interconnected.
The plan being implemented is designed to make the combined
analog-digital network conform closely to the characteristics of the

Chap. 26

Transm ission Objectives

601

present analog network. The fixed loss plan will be implemented as
portions of the network are converted to all-digital facilities. Following are the principal characteristics and constraints of the combined
network:
(1) The expected measured loss and the inserted connection loss
of each trunk must be the same in both directions of transmission.
(2) The -2 dB TLP at the outgoing side of analog toll switches

and the 0 dB TLP at class 5 offices are retained and a
-3 dB TLP is established for digital toll offices.
(3) The -16 dB and +7 dB TLPs at carrier system input and
output are retained.
(4) Existing test and lineup procedures for digital channel banks
are retained.
(5) Combination intertoll trunks, those terminating in digital
terminals at a digital (No.4 ESS) switching machine at
one end and in D-type channel banks at an analog switching machine at the other end, are designed to have 1-dB
inserted connection loss.
11

11'

(6) Analog intertoll trunks are designed according to the via
net loss plan.

Echo Obiectives

One way to express the network echo design objective is that trunk
loss designs should be such that talker echo (the dominant impairment) is satisfactorily low on more than 99 percent of all telephone
connections which encounter the maximum delay likely to be experi:enced. This way of expressing the overall objective recognizes:
(1) that echo performance can be controlled by controlling trunk
losses, (2) that the control of echo on connections implies further
oontrol of echo on the trunks used to form customer-to-customer connections, and (3) that echo impairment is a function of the amount
of delay in the connection.

602

Obiectives and Criteria

Vol. 1

The parameters of echo amplitude and echo delay contribute
significantly to echo performance in the network. Echo amplitude
depends on the impedance relations at circuit interfaces and the
losses of the involved circuits. The phenomenon is treated in terms
of return loss and trunk losses that combine to produce echo path
loss. On long circuits, minimum echo delay can be obtained by using
carrier facilities where the velocity of propagation is much higher
than in voice-frequency facilities. Carrier facilities are used for
economic reasons (larger circuit cross sections and lower unit costs)
as well as for echo delay control.
The most serious source of echo is low return loss found at class 5
offices where connections are made between loops and toll connecting
trunks. While reasonable control of toll connecting trunk impedance
can be exerc.ised, the impedances of the randomly connected loops
vary widely due to varying lengths and circuit make-up.
The distribution of echo return losses (ERLs) at class 5 offices,
calculated from loop survey data, has a mean value of 11 dB and
a standard deviation of 3 dB [5]. The distribution of singing return loss (SRL) has a mean value of 6 dB and a standard deviation
of 2 dB. These return loss distributions are used in the overall
process of establishing echo and loss objectives for other parts of
the network.
Return loss objectives are specified for connection points in the
toll portion of the network; generally the echo and singing return
loss objectives for these points are more stringent than for the local
portion since toll trunk parameters are more controllable. The
following objectives are typical, but not all-inclu.sive.
(1) For four-wire trunks terminating at two-wire switches in

class 1, 2, or 3 switching offices, the ERL objective is
27 dB (minimum 21 dB); the SRL objective is 20 dB
(minimum 14 dB).
(2) For the interface between four-wire intertoll trunks and

most two-wire toll connecting trunks at class 1, 2, 3, or
4 switching offices, the ERL objective is 18 dB (minimum 13 dB). For four-wire toll connecting trunks, the
objective is 22 dB (minimum 16 dB). For both two-wire
and four-wire trunks, the SRL objective is 10 dB (minimum
6 dB).

Chap. 26

Transmission Obiectives

603

These return losses are measured against standard terminations, the
values of which depend on the type of switching office involved. The
measurement process and the complexity of impedance adj ustment
procedures that permit these return loss objectives to be met have
led to the expression of objectives in terms of through balance and
terminal balance requirements applied for many types of trunks at
various types of toll switching offices.
Echo return loss objectives have less influence in the design of
local trunks than in the design of toll trunks because echo problems
are negligible for short trunk lengths. The objectives for singing
return loss on these trunks are not firmly established, but the return
losses are usually held to about 10 dB.

Loss Objectives
The echo path loss involved in determining echo amplitude is made
up of the return loss and twice the circuit loss between the speaker
and the point of reflection. These circuit losses must be well controlled;
they must be low enough to satisfy the requirements on talker volume
and to avoid excessive contrast in volume from call to call yet they
must be high enough to attenuate echoes to tolerable values.

Volume. The basic problem in telephone transmission is to provide
a satisfactory signal amplitude at the receiver. The received signal
amplitude is a function of many interacting parameters, starting with
the transmitted signal amplitude. The latter depends on telephone
speaking habits, station set efficiency of conversion from acoustic
to electric signal energy, sidetone circuit design of the station set,
and losses in the circuits between the transmitter and the receiver.
Received volume differs from many other quality parameters in
that its effects are double-ended; volume can either be too low,
causing difficulty in understanding the received message; or it can
be too high, causing listener discomfort. Subjective tests have been
made to determine listener reactions to different volumes. The results of one series of such tests, plotted in Figure 26-3, clearly show
the double-ended nature of this parameter. Volumes to the left of
the two left-hand curves are judged to be too low to satisfy listeners
while volumes to the right of the right-hand curve are too high to
satisfy listeners. Each of the curves, which divide regions of volume
rated poor, fair, good, etc., is approximately normal with a standard

604

Obiectives and Criteria

100
90
80

"" \ r'\ ~
~

Poor

70

~region

~

CD

30

~

A..

20

Poor or
worse ...

I

10

\

~

0

-60

-50

~v

'.

~

~

~

~

Too loud
region_

1
1
I
,I

\
\

\

~

L

l

Good region

region ,

,

50

!

V Too low to be good
(fair or worse)

~' '"1'\
\ ~

40

60

'ECD

_

'.

/

Vol. 1

j

~~

.l:

Too loud

~ to be good
..l

V~

-40
-30
-20
Received volume at SOO-type set (vu)

-10

o

Figure 26-3. Judgment of received volume from subjective tests.

deviation of about 5 dB. The curves show a fairly wide range (from
about -43 vu to about -12 vu at the median values) over which
received volumes are rated good.
Data of the type shown in Figure 26-3 have been used to help
establish allowable circuit losses in end-to-end customer connections.
The total loss allowance is allocated to the various parts of the plant
in accordance with the results of economic studies and with a satisfactory noise-loss-echo grade of service established by subjective
testing.
Loss Allocations. Transmission objectives for loop loss have been
derived on the basis of satisfying an overall loss/noise grade-ofservice objective [3, 6]. Control of loop loss is accomplished by the
application of carefully specified rules in the design and layout that
produce a satisfactory distribution of losses. The three sets of rules
are parts of the resistance, unigauge, and long route design plans.
These three design plans permit straightforward application of the

Chap. 26

Transmission Obiectives

605

rules to the installation of new cables, of inductive loading, and of
electronic equipment so that overall loss objectives are met because
the objectives are built-in, integral parts of the plans. When the
plans are properly applied, the resulting distribution of loop losses
has a maximum value of about 9 dB (including the effects of bridged
taps). The mean value and the standard deviation of the loss distribution depend on the geographical area served and on the concentration of customers within the area. For the Bell System, an average
1000-Hz value of 3.8 dB and a standard deviation of 2.3 dB are
typical; these values are used in the determination of network loss
obj ecti ves and grade of service.
The above values of loop losses were determined on the basis of
measurements made in 1960 and 1964 [5]. Subsequent studies of
losses and grade-of-service objectives resulted in some tightening
of the objectives, particularly in the long route design plan.
Since a numerical loss objective (other than the maximum) is not
expressed for individual loops, special treatment must be applied
(1) when a loop is assigned to data transmission or another special
service need and (2) when transmission complaints still exist after
it has been verified that the loops involved have been installed according to appropriate design procedures.
II

~

Loss objectives for transmission circuits through switching
machines have not been firmly established, but a loss of less than
1 dB is generally allowed for these circuits. Losses of various types
of trunks constitute the remaining maj or allocation to parts of the
plant, and for purposes of network administration, trunk losses are
now defined in such a way as to include average switching system
loss. Many of the loss values are given in terms of via net loss
which varies according to the length and type of facility.
Losses allocated to trunks depend on the position of the trunk type
in the switching hierarchy and the probability of encountering tandem
connections of such trunks in an end-to-end telephone connection. In
the toll portion of the network, interregional intertoll trunks are
designed on the basis of maximum round-trip echo delay that can
occur on connections involving the interregional trunks. If the delay
can exceed 45 milliseconds, the interregional trunks are equipped
with echo suppressors and the trunks are operated at 0 to 0.5 dB loss.
(Losses high enough to satisfy echo requirements would generally be

606

Obiectives and Criteria

Vol. 1

too high to satisfy volume and contrast objectives.) If the round-trip
echo delays are less than 45 milliseconds, the interregional trunks
are operated at VNL, with a maximum of 2.9 dB.
High-usage intertoll trunk groups are operated at via net loss
where the value of loss is VNL < 2.9 dB, equivalent to a maximum
trunk l~ngth of about 1850 miles on carrier facilities. If echo
requirements call for a loss greater than 2.9 dB, the trunks are
operated at 0 dB loss and are equipped with echo suppressors unless
they are in a final routing chain. To avoid having more than one echo
suppressor in a connection, echo suppressors are generally permitted
only in final groups between regional centers. Secondary intertoll
trunks are operated as close to 0 dB as possible, with a maximum of
0.5 dB. Final intertoll trunk groups are operated at via net loss, but
at a maximum of 1.4 dB loss.
Toll connecting trunks are usually operated at VNL + 2.5 dB loss
with a maximum loss- of 4.0 dB. An alternate design allows a trunk
to have 3.0 dB to 4.0 dB loss provided it contains less than 15 miles
of VF cable facilities or less than 200 miles of carrier facilities. On
long end-office trunks (usually interregional) between class 4 and
class 5 offices where echo requirements indicate the need for loss
greater than 4 dB, an echo suppressor may be added and the loss
set at 3 dB.
In the local portion of the network, direct trunks are designed to
a nominal loss of 3 dB with a maximum of 5 dB. Tandem trunks are
operated at a nominal loss of 3 dB and a maximum of 4 dB, and
intertandem trunks are operated at via net loss. Loss values are assigned similarly to all service and miscellaneous trunks used in the
network. Long interregional direct trunks (between class 5 offices)
may be operated without echo suppressors at VNL + 6 dB loss
(maximum 8.9 dB) over distances of up to 4000 miles.
Loss Maintenance Limits
In order to maintain network performance, 1000-Hz measurements
of trunk losses are made periodically in accordance with maintenance
programs described in Volume 3. The objectives are set in accordance
with indices which have been derived in relation to grade-of-service
objectives. The percentage of measurements showing deviations from
design values in excess of 0.7 or 1.7 dB (the larger deviations carry

Transmission Obiectives

Chap. 26

607

heavier weighting) determines the index for the group of trunks
under study. If the index is 96 or higher, performance is satisfactory
and no action is necessary. If the index is below 96, investigation and
corrective action are indicated. If the loss of any trunk deviates
gom jts desj gn value by 3,7 dB .'or more,".=it~I!!~~_be re!p-~..r.Q..ID_
service.

Message Circuit Noise
Message circuit noise is defined as the short-term average noise
measured by means of a 3A noise measuring set or its equivalent [7J.
Objectives for message circuit noise, allocated to various parts of
the network, are based on subjective tests in which noise was evaluated by telephone listeners in the presence of speech signals held at
a constant volume. Noise and volume were expressed in dBrnc and vu,
respectively, at the line terminals of the station set; observers were
asked to rate the performance in the usual manner (excellent, good,
fair, poor, or unsatisfactory) for a wide range of noise values. The
results of these tests are shown in Figure 26-4.
Loop Noise Objectives. The message circuit noise objective applied
to loops is that noise measured at the line terminals of the station
set shall not exceed 20 dBrnc. * Noise at or below this value has little
effect on grade of service, but noise in excess of 20 dBrnc deteriorates
grade of service appreciably.
I

~1

III
c

0

a-

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100
90

"0

80

8

70

2

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50

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30

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10

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l

Noise at line terminals of station set (dBrnc)

Figure 26-4. Noise opinion curves.

* Most
o dBrnc.

loops have measured noise well below this value. The average is about

608

Obiectives and Criteria

Vol. 1

In recognition of the special circumstances relating to long routes
(those in excess of 1300 ohms controlled by resistance design and
those extended by the unigauge design, both discussed in Volume 3),
the noise objective is made somewhat more lenient. For long routes
the noise objective is administered at 30 dBrnc. For routes on which
the limit of 30 dBrnc is exceeded, special treatment (shielding,
separation from power lines, balancing, etc.) must be employed according to circumstances.
Trunk Noise Objectives. The performance objectives for trunk noise
have been allocated to allow for the tendency of noise to accumulate
with distance and the smaller number of calls of very long distances
compared with intermediate and short distances. To give weighting
to these two factors, trunk noise objectives have been selected to
achieve a 99 percent good-or-better grade of service for short toll
connections (0 to 180 miles, airline distance), 97 percent good or
better for medium length toll connections (180 to 720 miles), and
95 percent good or better for long toll connections (over 720 miles).
Consistent with these overall objectives, allocations have been made
for short-haul carrier facilities (for use on trunks less than 250 miles
long), and long-haul carrier facilities (for use on trunks over 2EO
miles long). These allocations, which recognize the inherent variability of performance in the field environment, are expressed in terms
of mean values and standard deviations. For short-haul carrier, the
mean value of the objective is 28 dBrncO at 60 route miles and for
long-haul carrier, 34 dBrncO at 1000 route miles. The standard deviation is (T == 4 dB in each case. These allocations allow for a 3 dB increase in noise for each doubling of the distance. This increase is
typical of analog carrier system performance but is not usually experienced in pulse-type carrier systems. Design objectives for carrier
systems are based on these performance objectives but are normally
expressed in terms of worst channel noise in a nominal environment.
The current design objective for 4000-mile coaxial cable systems, including multiplex equipment, is 40 dBrncO. The design objective for
microwave radio systems is approximately 1 dB higher [3]. Generally,
where these message circuit noise objectives are met for speech transmission, objectives for voiceband data transmission are also met.

Impulse Noise
Impulse noise is any burst of noise that produces a voltage in
excess of about 12 dB above the rms noise as measured by a 3-type

Chap. 26

Transmission Objectives

609

noise measuring set with C-message weighting; in a speech channel,
these bursts are usually less than 5 but may very rarely be as
long as 45 or 50 milliseconds in duration. The ratio of the voltage
excess to the rms noise voltage is nominally at least 12 dB for a
3-kHz bandwidth; it may be as great as 40 dB in some systems,
particularly microwave radio. Impulse noise is usually viewed as
superimposed on background message circuit noise [8]. Objectives
are dominated by requirements for digital data signal transmission,
and circuits that are satisfactory for data are generally satisfactory
for speech signal transmission.
Impulse noise objectives are usually established on the basis of the
number of counts obtained on a 6-type impulse noise counter during
a prescribed measurement interval and may be expressed for
loops, trunks, or customer-to-customer connections. The application
of acceptable objectives to station sets and central office equipment
is under study.

I

r

The objective for any loop or single voice channel is that there
should be no more. than 15 impulse noise counts in 15 minutes at a
given threshold. For a sampled trunk group, there should be a maximum of 5 counts in 5 minutes at a given threshold. Sampling plans
are specified and the noise thresholds are set at different values for
loops, for VF trunks, and for compandored and noncompandored
carrier trunks. The threshold values are also weighted to take into
account the expected increase of noise with distance in carrier
systems. The trunk impulse noise thresholds are shown in Figure 26-5.
The loop impulse noise threshold is 50 dBrnC referred to the local
central office.
Intelligible Crosstalk
Intelligible crosstalk objectives are generally expressed in terms
of the crosstalk index, a measure of the probability of receiving
intelligible crosstalk. The derivation of the crosstalk index, its relationship to the impairing effects of intelligible crosstalk, and the use
of generalized crosstalk index charts are presented in Chapter 17.
Objectives have been established for most types of trunks. A
maximum crosstalk index of 1 is used for intertoll and secondary
intertoll trunks. An index of 0.5 is applied to toll connecting, direct,
tandem, and intertandem trunks. No index objective has yet been
established for loops.

610

Vol. 1

Objectives and Criteria
FACILITY TYPE
VF TRUNKS,
dBrncO

COMPANDORED*
CARRIER AND MIXED
COMPANDOREDNONCOMPANDORED,
dBrncO

NONCOMPANDORED
CARRIER,
dBrncO

0-60

54

68

58

60-125

54

68

58

125-250

54

68

59

250-500

68

59

500-1000

68

59

1000-2000

68

61

over 2000

68

64

TRUNK LENGTH
(MILES)

* Compandored

trunks, including those with D-type channel banks, are measured
with a -10 dBmO tone transmitted from the far end and filtered out ahead
of the measuring set by a C-notched filter or equivalent. The C-notched filter
is a C-message weighting network with a narrowband suppression section to
provide at least 30 dB of attenuation at the tone frequency.
Figure 26-5. Impulse noise thresholds for trunks.

Crosstalk objectives for central office equipment are usually expressed in terms of equal level coupling loss. In four-wire offices, the
objective for minimum coupling loss between the two sides of one
circuit is 65 dB. The coupling objective for different circuits is
80 dB in two-wire and four-wire offices.
Si ng Ie-Frequency Interference

Well documented and generally accepted transmission objectives
for single-frequency interferences are not now available. When new
systems have been designed, design objectives have been applied in
a generally conservative manner. The factors that have made
it difficult to derive acceptable objectives include the frequency and
amplitude of the interference, the stability or variability of frequency
and amplitude, the harmonic content of the interference, the presence
or absence of masking message circuit noise or other interferences,
the possible presence of other single frequencies, and the constancy
or intermittency of the interference. As a rule of thumb, singlefrequency interferences must be well below other noise in the circuit.

f

I

Chap. 26

Transmission Objectives

611

The most conservative estimate, one that makes single-frequency
noise inaudible to nearly everyone, is that the interference should be
30 dB below message circuit noise. More lenient estimates have led
to design objectives of 10 to 12 dB below message circuit noise. These
objectives apply to speech signal transmission and, when met, usually
result in satisfactory transmission of other voiceband signals.
Frequency Offset

Frequency offset objectives are set primarily to satisfy the needs
of program signal transmission. While the determination of the
threshold for frequency offset is as critical to speech transmission
as it is to music transmission, subjective tests have shown that
listeners are more tolerant of offset in speech signals than in music
signals. The overall performance objective for offset is a maximum
value of -+- 2 Hz; the maintenance objective is ± 5 Hz.
Overload

Over load of broadband or single-channel electronic systems produces signal impairments in the form of noise and distortion. The
objective for overload is expressed as a degradation of the grade of
service in an individual channel. While objectives have not been
firmly established, a reduction of about 1 percent in good-or-better
and an increase of about 0.1 percent in poor-or-worse grades of
service appear to be reasonable performance objectives for the overload phenomenon. These criteria, when applied to D-type channel
banks used with T-type carrier systems, have resulted in the objective
that these banks transmit a +3 dBmO sine wave signal without
causing overload impairment.
A signal transmitted at higher amplitude than the design value
may cause intelligible crosstalk or single-frequency tone interference
as a result of intermodulation or other crosstalk paths. This impairment is not considered as overload unless it is so extreme that the
entire system is affected.
Miscellaneous Impajrments

A number of miscellaneous impairments are recognized as having
potentially serious degrading effects on voice-frequency channel
transmission; they include phase and gain hits, phase and gain jitter,
incidental frequency modulation, and dropouts. Formal objectives for
these types. of impairments have not been established.

612

Obiectives and Criteria

Vol. 1

Telephone Station Sets

The transmission performance of station sets is controlled primarily by design, and there are no specific transmission performance
or maintenance objectives. The great majority of sets in service are
the 500-type, which were developed to meet a set of stringent design
objectives [9]. There are no transmission options or adjustments on
these sets. Therefore, where troubles can be identified with the
station set or where trouble complaints cannot be identified with
other parts of the local connection, the transmitter, the receiver, or
the entire set may be replaced and returned to the manufacturer.
A unique consideration is involved in operator and auxiliary
services wherein the operator headset (receiver and microphone)
must be regarded as the station set. One of the more stringent objectives that must be met by these circuits is that pertaining to
sidetone. In this case, sidetone is a design parameter of the access
circuits rather than the headset circuits. The objectives are commonly
expressed in terms of the acoustic sidetone path loss, which is defined as the ratio in dB of the loudness-weighted acoustic sound
pressure produced by the receiver for a given loudness-weighted
acoustic sound pressure input to the transmitter (or microphone).
The objective for this loss is 12 dB, an optimum determined by
subjective tests; values as Jow as 8 dB and as high as 16 dB are
considered tolerable.

26-2

WIDEBAND DIGITAL SIGNAL TRANSMISSION OBJECTIVES

As in the case of transmission objectives for voice-frequency channels, the expanding use of existing channels for new types of signals
and services has made it necessary to refine and redefine channel
transmission objectives. Similarly, the adaptation of analog systems
and portions of analog systems for wideband digital signal transmission has led to new obj ectives for wideband channel applications.
Frequency bands that were originally provided only as parts of the
voice transmission network are being adapted for wideband digital
signal transmission, and as a result, transmission objectives for the
wider bands and new signals are in process of refinement and redefinition. In addition, digital transmission systems are being developed
and introduced into the network, thereby requiring that objectives
be established for their design and operation.

Chap. 26

Transmission Obiectives

613

The transmission objectives to be established and the manner of
adapting systems and signals for compatibility depend on the signal
format, the sensitivity of the signal to various impairments, and the
characteristics of the system or channel involved. The parameters
involved include load capacity, bandwidth, signal-to-noise performance, jitter, error rates, and the rate of digital transmission.
The wide range of bandwidths, signal formats, impairments,
services, and digital systems makes it difficult to present a complete
set of wideband digital transmission objectives. Therefore, this discussion is limited to a number of examples of objectives that have
been established for specific signal formats and to the approach used
.in several digital system designs. In most cases, the determination
of the objective ultimately rests on subjective judgment of the required grade of service.

I

There are two types of wideband digital signals commonly transmitted on analog systems: the 1A Radio Digital System (lA-RDS)
signal, a 1.544 Mb/s signal transmitted at baseband (0 through
500 kHz) over microwave radio systems in a multilevel signal format
containing seven discrete levels and a family of binary digital data
signals that may be transmitted at 19.2 kb/s, 50.0 kb/s, or 230.4 kb/s
in the half-group, group, or supergroup bands, respectively, of the
L-multiplex (FDM) equipment [10, 11]. Transmission objectives
.for these signals and for digital transmission systems are evolving
as the technology advances.

Performance Evaluation
Transmission objectives for wideband digital signals are expressed
variously in terms of error rate, noise impairment, and eye diagram parameters. In addition, objectives must be expressed for
signal power when digital signals are to be transmitted on analog
systems.
Error Rate. A commonly used design objective for wideband digital
signal transmission, one that has not been sanctioned for general
application, is an error rate of 10- 6 ; Le., the terminal-to-terminal

614

Obiectives and Criteria

Vol. 1

error rate shall not exceed one error in 106 bits. Error rate counters,
or violation counters as they are sometimes more properly called, are
used with many systems to determine error performance for the
complete end-to-end connection or for some link in the connection.
Violations of a predetermined code format are counted and compared
with the objective which must be expressed in the same terms. The
objective must be that value allocated to the particular link under
surveillance.
Noise Impairment. The expression of an objective in terms of noise
impairment is used to equate the degradation of channel performance
by various impairments to an equivalent degradation due to Gaussian
noise. This equivalence can be explained in another way. A certain
error rate can be expected from a given channel whose characteristics
are ideal in all respects except for the presence of Gaussian noise.
The noise impairment due to the introduction of some other degradation, such as delay distortion, is measured by the improvement in
Gaussian noise (improved signal-to-noise ratio) that would be required for the same channel performance as in the channel impaired
only by the original value of Gaussian noise.

Two goals are met by expressing objectives in terms of noise impairment. First, objectives can be allocated to a variety of impairments in an orderly manner that lends itself readily to changes
necessary to meet specific conditions. Second, a straightforward
method is provided for determining how good the channel signal-tonoise ratio must be to meet a specified error rate objective. Both
advantages are especially desirable for studies of digital signal
transmission on analog channels.
Eye Diagram Closure. When a random stream of digital pulses is
properly impressed on an oscilloscope, the successive pulses can be
made to form a pattern, called an eye diagram. As the pulse stream
is impaired by channel imperfections (such as noise, gain and delay
distortion, and crosstalk), the opening in the eye (or eyes for multilevel signals) is reduced by predictable amounts. Thus, the eye
pattern may be used as a measure for performance, and transmission
objectives can be expressed in terms of the percentage of eye closure.

This manner of stating objectives has not proved to be useful in
operating and maintaining systems, but it has found considerable
use in system design where measurements are made under laboratory

',1

1
I

I"II

I'
I
"

I

II',

Chap. 26

Transmission Obiectives

615

conditions [12, 13]. The approach has been used to compare performance and objectives; it has also been used as a means of
allocating objectives among a number of different impairments, each
being allowed a certain percentage of eye closure in the horizontal
(timing) or vertical (amplitude) dimensions or in both.
Signal Power. When a signal is impressed upon a transmission
channel, the channel must be capable of transmitting the signal satisfactorily; in addition, the signal cannot be allowed to degrade other
signals that may share the same transmission system. Overload
performance is one criterion that must be satisfied in both respects.

The impressed signal amplitude must be limited so that the signal
itself is not degraded by the overload characteristics of the channel.
The degradation would fall between two extremes, one in the form
of peak clipping that might be relatively innocuous and the other
in the form of excessive distortion that would render the signal
useless. The limiting value depends in each case on the characteristics
of the channel or system to be used.
Simultaneous transmission of digital and other kinds of signals on
analog facilities further requires that the load imposed by the digital
signals does not seriously impair the other signals. The usual criteria
for the loading objective are (1) that the average power in the
digital signal shall not exceed the average power allotted to the displaced speech channels (-16 dBmO per 4-kHz band), and (2) that
any single-frequency component of the digital signal shall not exceed
-14 dBmO. The latter criterion is sometimes relaxed if the component
is not a multiple of 4 kHz or if the amplitude variability results in
a low probabiilty of its exceeding -14 dBmO.

Design Applications
Since most transmission objectives for wideband digital signals
have not yet been formally accepted or generally applied, it is best
to illustrate for specific cases the ways objectives evolve, are derived,
and are applied.
Bit Rate and Bandwidth. In the design of a new digital transmission
system or the adaptation of analog facilities to the transmission of
digital signals, the first consideration is the overall system design
problem of relating available bandwidth to the desired transmission
rate. First-order effects on the design include: (1) the achievable

616

Objectives and Criteria

Vol. 1

signal-to-noise ratio of the proposed facility, (2) the desirability of
designing a synchronous system that permits regeneration, (3) the
cost involved in terminal and signal regeneration equipment, (4) the
feasibility and cost of equalizing the medium, and (5) the transmission objectives that must be satisfied if the service needs are to
be met. While the concern here is primarily with the objectives, all
of these effects interact in ways that make discussion of objectives
meaningless unless the interactions are explored as well.
The need for digital signal transmission over the analog microwave
radio network evolved partly from the Digital Data System (DDS)
development program. The feasibility of transmitting a DS-1 signal
on a TD-type radio system was established but this possibility was
deemed undesirable because the DS-1 signal carries significant energy
at frequencies up to 1.544 MHz. A substantial number of telephone
channels would thus have to be dropped to accommodate the digital
signal. It was also shown that the upper half of the DS-1 spectrum
might be filtered or the signal might be coded as a 3-level, class IV,
partial response signal with spectral nulls at 0 and 772 kHz. The
former approach was more theoretical than practical; the latter still
appeared too costly because about 120 message channels would have
to be dropped to provide a roll-off band.
A 7-level, class IV, partial response signal with a 15 percent roll-off
band was chosen and is now used in the 1A Radio Dig,ital System
(lA-RDS) which provides a digital facility for DDS. The signal has
spectral nulls at 0 and 386 kHz and extends only to 444 kHz, well
below the 564-kHz multiplex low-end frequency. Thus, no message
channels are displaced.
Performance Objectives. Objectives for 1A-RDS were derived from
those established for DDS. They were based on a leve1 of performance
which was judged would provide a high-quality service at the customer sub-rates of 56 kb/ s and below. The basic criterion was stated
in terms of percentage of error-free seconds. Allowances were included for known sources of hits, such as those caused by protection
switching initiated by maintenance activities and fading. A sub-set
of objectives covers the number of errored-seconds that occur in
shorter periods of time and the number and length of error bursts.

Chap. 26

I.

Transmission Obiectives

617

Designs Based on Noise Impairments. In setting objectives for transmitting wideband digital data signals in the half-group, group,and
supergroup bands of the L multiplex equipment, a major concern was
the equalization of gain and delay distortion in those bands. The objectives for these services were derived initially from the basic goal
of achieving an error rate of 10- 6 or better (between terminals) 95
percent of the time. Portions of this objective were then allocated to
various well-defined impairments (random and impulse noise, for
example), and the remainder was allocated to misequalization, data
set and terminal limitations, net loss variations, and jitter.
These allocations first involved the derivation of a required
signal-to-noise ratio of 12.7 dB. After noise impairments had been
assigned to each of the principal sources of degradation anticipated,
it was concluded that an overall signal-to-noise ratio (Gaussian noise)
of 22 dB would be required to meet the service objective; this
signal-to-noise ratio was used as a design objective.

26-3 VIDEO TRANSMISSION OBJECTIVES
The Bell System transmits three types of video signals that might
be reviewed in detail in terms of applicable transmission objectives:
broadcast television signals, closed circuit television signals, and
PICTUREPHONE signals. Only broadcast television signals are
covered, however, since closed circuit television and PICTURE PHONE
objectives are not well established. Generally, closed circuit television
objectives tend to be somewhat more lenient than those for broadcast
quality signals. Thus, it is usually safe to use broadcast objectives;
if there appears to be serious difficulty in meeting them, the case
must be considered separately. For PICTURE PHONE, only some
early design objectives have been used in preliminary studies and
experimental work [14].
The objectives to be discussed are, for the most part, expressed in
terms of overall 4000-mile objectives. These, of course, must be
allocated to different parts of the plant in accordance with some
logical procedure, as outlined in Chapter 25. Most of the objectives
given are design objectives, and each must be interpreted carefully
and applied judiciously when operational variations and limits are
considered for use as performance and maintenance objectives.

Random Noise
The degree of noise impairment to television signals is a complex
function of the distribution of noise power versus frequency and the
characteristics of the impaired signal (for example, whether it is a

618

Obiectives and Criteria

Vol. 1

monochrome or a color signal). When the noise is at a high enough
amplitude, it may appear as fine, closely packed dots in rapid, random
motion. When observed in monochrome signal transmission, the dots
appear to have the characteristics of a swirling snowstorm; as a
result, the impairment has commonly been referred to as "snow."
If the noise is concentrated at the lower video frequencies, the dots
are relatively large or may appear as streaks in the picture. If the
noise is concentrated at high frequencies, the dots are much finer
and harder to see. Hence, equal powers of noise are judged to be more
annoying at low than at high frequencies. When the noise is concentrated in relatively narrow bands, it produces fleeting herringbone
patterns in the received pictures. If the band is made narrower, the
pattern approaches that of a single-frequency interference. Thus,
equal powers of noise tend to be more objectionable as the bandwidth
of the noise is decreased.
These observations have led to the expression of random noise
objectives in terms of a single weighted value applicable to monochrome or color signals. The weighting, which takes into account the
more objectionable nature of low-frequency noise, makes possible the
use of a single number as an objective; i.e., equal measured values
mean equal subjective effects, regardless of the type of noise. The
effect of narrowband noise is accounted for simply by weighting its
effect with that of broadband noise on the basis of total power. Thus,
if single-frequency interference is present in a channel, the random
noise objective must be made more stringent by an amount that
makes the power sum of random and single-frequency noises meet
the random noise objective. In addition, the single-frequency objective
must also be met.
The random noise weighting characteristic is shown in Figure 26-6.
In spite of some differences in annoying effects in monochrome and
color signal transmission, it is found that satisfactory results are
obtained when this single weighting curve is used to evaluate noise
on facilities used for both types of signals [15]. The objective
generally applied is that the noise introduced by a 4000-miIe system
produce a signal-to-noise ratio of 53 dB or better. This ratio is expressed in terms of the peak-to-peak composite signal voltage (including synchronizing pulses) to the weighted rms noise voltage in
the frequency range of 4 kHz to 4.2 MHz. The noise from zero to
4 kHz is treated separately.

i,

I
1,1

619

Transmission Obiectives

Chap. 26

I

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-12
-14
-16

\-

-

20

-

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30 40 50

I I

70

I

100

200
Frequency

I

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300 400 500 700 1000

I
2000

3000

-

5000

(kHz)

Figure 26-6. Monochrome and color random noise weighting for broadcast
television signals.

Low-Frequency Noise

Noise in the band from zero to 4 kHz is measured in a manner
similar to that for random noise. It is treated separately because of
the likely presence of power-frequency interference (hum in telephone circuits), which can cause bar pattern interference in the received picture. If hum is not present, the low-frequency random noise
is simply added to the broadband random noise.
The objective for low-frequency interference is expressed in terms
of the ratio of the peak-to-peak signal voltage to the rms interference
voltage in the band from 0 to 4 kHz. The objective for a 4000-mile
circuit is a 50 dB signal-to-noise ratio.
Impulse Noise

The characteristics of impulse noise are not well-defined for evaluation as a television impairment. Generally, impulse noise is any
interference that affects a small portion of the received picture for
only a short interva.l of time.
The objectives for impulse noise are also not well-defined. A ratio
of the peak-to-peak composite signal voltage to the peak impulse

620

Objectives and Criteria

Vol. 1

voltage of 20 dB is sometimes considered to be an acceptable objective.
It is applied specifically to interferences that occur at a rate of about
one per minute. No quantitative data are available for impulses of
different durations or for other frequencies of occurrence.
Single-Frequency Interference

A single-frequency interference usually appears on a television
receiver as a discernible bar pattern that may be stationary or in
motion. If the interference is an integral multiple of the nominal
60-Hz field frequency, it appears as a broad, stationary, horizontal
pattern. If the interference differs slightly from a 60-Hz multiple,
the bars travel up or down the picture. If the interference is weak,
the impairment may more nearly resemble a flickering than a bar
pattern, an impairment much more annoying than a stationary
pattern. The effect depends on the flicker rate.
For frequencies at or near multiples of the line scanning frequency,
the patterns are stationary or moving, vertical or diagonal bars. The
bar structures become finer as the interfering frequency increases;
the most critical frequencies are in the range of 100 to 300 kHz.
Similar phenomena are produced by single frequencies near the
color carrier frequency. The high- and low-frequency characteristics
must be determined as high or low frequencies relative to (i.e., displaced from) the color carrier frequency of 3.579545 MHz.
While there is a wide variation of subjective reaction to singlefrequency interferences according to their frequency, stability, multiplicity, etc., the objective is usually stated as two simple numbers.
First, the objective for a single interferer is taken as a signal-tonoise ratio of 69 dB where the signal amplitude is expressed in
peak-to-peak volts (including the synchronizing pulse) and the interference is expressed as an rms voltage. The second expression for
the interference is that the total weighted interference (including
random noise) is to be 53 dB below the signal, the same value as
that given previously for weighted random noise.

Echo
Echo refers to a signal produced by reflection at one or more points
in a transmission path or generated by transmission irregularities
and having sufficient magnitude and time difference to be perceived as

Chap. 26

Transmission Obiectives

621

distinct from the signal received over the primary transmission path.
Echoes may lead or lag the main signal and have characteristics that
are described by four different picture impairments.
Types of Picture Impairments. A number of different picture impairments may occur as a result of reflections at points of discontinuity
in the transmission path or as a result of transmission irregularities.
All such picture impairments are subject (at least in theory) to control and reduction by some form of transmission equalization. These
impairments are discussed in Chapter 18 but are mentioned again
here to stress the facts that all are due to transmission discontinuities
or departures from ideal transmission characteristics and may be
dealt with in terms of echoes.

St'reaking and Smearing. These are often considered separately
but, for convenience, are considered here as one type of impairment.
Both are described as unwanted lines or areas of brightness, usually
observed to the right of a sharp brightness change in a picture, extending toward the right edge of the picture. Streaking extends
undiminished to the right-hand edge; smearing diminishes substantially toward the edge of the picture. Both result from transmission irregularities at frequencies in the region of the field
repetition rate (60 Hz), frequencies in the region of the line scanning
frequency (15.75 kHz), and the first 10 to 15 harmonics of each.
Ringing. An oscillatory transient, called ringing, may occur in a
signal at the output of a system as a result of a sudden amplitude
change of the input signal. This results in closely spaced multiple
repetitions of some picture elements whose reproduction requires
frequency components approximating either the cutoff frequency of
the system or the frequency of a sharp discontinuity within the passband. The ringing occurs at approximately the frequency of the discontinuity or of the band edge and is often accentuated by a rising
gain characteristic preceding the discontinuity or band edge. Performance can be improved by extending delay equalization through
the cutoff region.
Overshoot. This impairment is due to an excessive response to a
sudden change in signal amplitude. It appears as a black outline to
the right of white objects and as a white outline to the right of black
objects. A sharp overshoot may be referred to as a spike; it is
caused by excessive gain at high frequencies.

Vol. 1

Obiectives and Criteria

622

Flat and Differentiated Echoes. Echoes are complex phenomena
whose interfering effects depend on echo amplitude, time separation
from the main signal, the nature of the original signal, and the frequency characteristic of the echo source. If the echo essentially
covers the entire transmitted band, it is referred to as a flat echo.
If it has a sharp frequency characteristic, usually with stronger
reflections at high frequencies, it is known as a differentiated echo.
Differentiated echoes are generally less interfering than flat echoes.
If the echo path accentuates the high frequency echo components at
a rate of 6 dB per octave, the echo is less interfering than flat echo
by about 15 dB.
Echo Objective. The echo objective for video transmission is a 40 dB
signal-to-echo ratio. It is expressed in terms of a single, well-defined,
long delayed (lOlLS or more) echo. In practice, many echoes are
usually present, and each component echo must be weighted in accordance with a weighting function that represents the change in
subjective effect with the time displacement of the echo. The weighted
components are then combined on a power basis for comparison with
the objective. A typical time-weighting function is shown in
Figure 26-7. Recent analysis of subjective test data has shown that
the function also varies according to picture content and the polarity
of the echo [16].

ai'

:s
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c

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~

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Gi

40
35
30
25

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CD

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:)

20

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E
c
0

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alf

15

",

10
5

",

,,'" '"

""

o~~~~~~

.02 .08

.05 .07

.1

",'"

__~~~~~~~__~~~~~~~__~
.2

.3

.5.7
Echo delay

2

3

5

7

10

(p,sec)

Figure 26-7. Single flat echo objectives (echo time weighting curve).

20

Chap. 26

Transmission Obiectives

623

Any departure from flat amplitude response or linear phase response of a transmission channel can be expressed in terms of the
Fourier components of the response functions. These components
are expressed as cosinusoidal functions of the amplitude response
and as sinusoidal functions of the phase response. The Fourier components can then be regarded as generating echoes which may be
summed by power after the weighting function has been applied.
Crosstalk

Video crosstalk occurs when an undesired signal interferes with
a desired signal. The objectives for crosstalk are expressed in terms
of dB of loss in the coupling path between the two signals at 4.2 MHz
at equal transmission level points. When the coupling path is flat
with frequency, the crosstalk is called flat crosstalk. When the crosstalk path loss decreases with frequency at a specified rate in dB per
octave, the coupling is called x dB differentiated crosstalk where x
is the rate of loss decrease.
Where crosstalk can be seen, the interference appears as an image
of the unwanted picture moving erratically across the wanted picture.
The motion occurs because of the lack of synchronization between
independent signals. As the crosstalk image moves across the picture,
it appears to be framed. The apparent framing is formed by the
synchronizing pulses of the interfering signal. The framing tends
to be more noticeable than any feature in the image. The side frames,
which extend from the top to the bottom of the wanted picture,
interfere with the total wanted picture. The effect is similar to a
windshield wiper moving across the picture; the term "windshield
wiper effect" i~ sometimes applied.
If the crosstalk is weak (high coupling loss), neither the frame
nor the image is discernible. At such a near-threshold point, only a
slight flicker can be seen as the frame moves across certain portions
of the desired picture. The subjective effect is more dependent on
flicker rate than on crosstalk magnitude.
If the coupling loss varies with frequency, resulting in differentiated crosstalk, the interfering image may appear to be in basrelief. However, the synchronizing pulses are still the most prominent
feature in the crosstalk image since they have the largest rate of
change.

Vol. 1

Obiectives and Criteria

624

The overall objective for crosstalk coupling loss between equal
level points is dependent on the nature of the coupling path. Some
typical path characteristics that may be encountered in practice are
illustrated in Figure 26-8. The applicable objectives, expressed in dB
of loss at 4.2 MHz, are as follows:
OBJECTIVE, dB

CROSSTALK PATH

Flat crosstalk
6 dB/octave
12 dB/octave
24 dB/octave

58
37

21
17.5

Flat
0

I

6 dB/octave

10
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~

.2
CJ)

foe

20
foe

."",...... ~

30

.5

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~

40

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60

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V

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~

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I

V

I

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I

24 dBJoctave/'

I

/
/

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70

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to
80
.1

~

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.2

.3

I

. ..

1.0
.5
.7
Frequency (MHz)

.1
2

3

4.2 5

.
7

Figure 26-8. Coupling path loss characteristics.

Differential Gain and Phase
These impairments, which have serious effects on color television
signal transmission, are described in Chapters 18 and 21, respectively.
The objective for differential gain, which may produce undesired
changes in color saturation, is 1.4 dB. The objective for differential
phase, which produces changes in color hue, is 50.
Audio/Video Delay
It is customary in the Bell System to transmit video and associated
sound signals over separate transmission paths. If the difference in

Chap. 26

Transmission Obiectives

625

absolute delay between the two paths is excessive, an impairment
results because the picture and sound are out of synchronism; the
sound is heard before or after the producing action in the picture.
The objective is that the delays in the two transmission paths differ
by no more than 55 milliseconds.
Luminance/Chrominance Delay

While the luminance and chrominance information in a video signal
is transmitted over the same channel, the dominant components of
one part of the signal are so far removed in frequency (over 3 l\tIHz)
from the other part that there can be a significant delay difference
between the two. When this delay difference is excessive, the color
portions of the signal are shifted relative to the luminance portions;
i.e., there is a misregistration of color. Such an effect is most noticeable at sharp vertical edges of highly saturated color areas that are
bounded by low-saturated color areas relatively free of detail [17].
The objective for the delay difference is 50 nanoseconds. It is expressed as the difference in delay between 3.6 MHz and frequencies
below 200 kHz. Since the delay below 200 kHz tends to be constant,
measurements are usually made at 200 kHz and 3.6 MHz to evaluate
performance relative to the 50 ns objective.
REFERENCES

1. Bell System Technical Reference PUB 41005, Data Communications Using

the Switched Telecommunications Network (American Telephone and Telegraph Company, May 1971).
2. Campbell, L. W. "The PAR Meter-Characteristics of a New Voiceband
Rating System," IEEE Transactions on Communications Technology, Vol.
COM-18 (Apr. 1970), pp. 147-153.
3. Andrews, F. T., Jr. and R. W. Hatch. "National Telephone Network Transmission Planing in the American Telephone and Telegraph Company,"
IEEE Transactions on Communications Technology, Vol. COM-19 (June
1971) , pp. 302-314.
4. Huntley, H. R. "Transmission Design of Intertoll Trunks," Bell System Tech.
J., Vol. 32 (Sept. 1953), pp. 1019-1036.
5. Gresh, P. A. "Physical and Transmission Characteristics of Customer Loop
Plant," Bell System Tech. J., Vol. 48 (Dec. 1969), pp. 3337-3385.
6. Lewinski, D. A. "A New Objective for Message Circuit Noise," Bell System
Tech. J., Vol. 43 (Mar. 1964), pp. 719-740.
7. Cochran, W. T. and D. A. Lewinski. "A New Measuring Set for Message
Circuit Noise," Bell SY.'3tem Tech. J., Vol. 39 (JuI. 1960), pp. 911-931.

626

Objectives and Criteria

Vol. 1

8. Fennick, J. H. "Amplitude Distributions of Telephone Channel Noise and a
Model for Impulse Noise," Bell System Tech. J., Vol. 48 (Dec. 1969), pp.
3243-3263.
9. Inglis, A. H. and W. L. Tuffnell. "An Improved TelephO'ne Set," Bell System
Tech. J., Vol. 51 (Apr. 1951), pp. 239-270.
10. Seastrand, K. L., and L. L. Sheets. "Digital Transmission O'ver Analog
Microwave Radio Systems," IEEE International Conference on Communications, June 19, 20, 21,' 1972, Philadelphia.
11. MahO'ney, J. J., Jr. "Transmission Plan for General Purpose Wideband
Services," IEEE Transactions on Communications Technology, Vol. COM-14
(Oct. 1966), pp. 641-648.
12. Technical Staff of Bell Telephone Laboratories, Transmission Systems for
Communications, Fourth EditiO'n (Winston-S'alem, N.C.: Western Electric
Gomp.any, Inc., 1970) Chapter 27.
13. MayO', J. S. "A Bipolar Repeater for Pulse Code Modulation 8ignals." Bell
System Tech. J., VO'I. 41 (Jan. 1962), pp. 25-97.
14. Baird, J. A. et al- "The PICTUREPHONE System," Bell System Tech. J.,
Vol. 50 (Feb. 1971), Special Issue.
15. Cavanaugh, J. R. "A Single Weighting Characteristic for Random Noise in
Monochrome and NTSC Color Television," Journal SMPTE, Vol. 79 (Feb.
1970) , pp. 105-109.
16. Lessman, A. M. "The Subjective Effects of Echoes in 525-Line Monochrome
and NTSC Color Television and the Resulting Echo-Time Weighting," Journal
of the SMPTE, VO'I. 81 (Dec. 1972), pp. 907-916.
17. Lessman, A. M. "Subjective Effects of Delay Difference Between Luminance
and Chrominance Information of the NTSC Color Television Signal," Journal
of the SMPTE, Vol. 80 (Aug. 1971), pp. 620-624.

I
I'

Objectives and Criteria

I'

Chapter 27

Economic Factors
The quality of service provided by a telecommunications network
must be based on an appropriate balance between customer satisfaction and the cost of service. To make service objectives meet the
criterion of reasonable cost, compromises must often be made among
the objectives themselves or between objectives and system development or application parameters.
A number of compromises may be used to illustrate the process of
adjusting designs, applications, and objectives for economic reasons.
There are, of course, no unchanging and absolute relationships among
these factors. Guidelines tend to change with time because new systems, new services, and changing customer opinions bring about
changes in the objectives. Furthermore, economic relationships are
significantly affected by local and national economic factors such as
inflation.
27-1

OBJECTIVES

The derivation and application of transmission objectives often
involve judgment as to what can be accomplished within reasonable
cost constraints, the compromises that result from such judgments,
the reconciliation of one set of objectives with another, and the existing economic, environmental, and human resources factors. Consider
first the determination of transmission objectives and the economic
factors involved.
Determination of Objectives

I.

The determination of telephone transmission objectives requires
the use of subjective testing to establish the relationship between an
impairment and observer opinions of its effect. The test results
are then related to measured or derived performance parameters
to obtain values for the grade of service that can be expected for
627

628

Obiectives and Criteria

Vol. 1

the combination of parameters involved. It is often possible at this
point to determine the cost of achieving this grade of service and
the effects of changing the objectives or the performance parameters.
These changes can then be evaluated economically by comparing the
results with the initial cost.
Qualitatively, the results are usually predictable. In nearly all
cases, costs increase when objectives are made more stringent or
when performance is improved. The characteristics of a cost/gradeof-service curve are obviously important, and the judgment that must
be exercised in establishing the objectives is influenced by the nature
of this curve.
In Figure 27-1, curve A shows a gradual increase in cost with
improving grade of service and demonstrates many situations in
which the simple prediction of increasing cost with improving grade
of service is verified. Since the simple prediction does little to support
engineering judgment, the establishment of the objective must be
based on other criteria. On the other hand, curves B-B' and B-B"
represent very different sets of circumstances.
Curve B-B' shows that a relatively small increase in cost yields a
substantial improvement in grade of service up to a good-or-better
rating of 97 percent and that, regardless of cost, the grade of service
cannot be increased beyond 98 percent. Thus, from the point of view

8.0

4.0

1;;

S

2.0

~

·fi
Gi
~

1.0

0.5

88

i
I
I
I
I
98
92
94
96
90
Good-or-better grade of service (percent)

Figure 27-1. Typical cost curves.

i
100

Chap. 27

Economic Factors

629

of economic effects, any attempt to achieve higher than a 97 percent
good-or-better grade of service would be wasteful.
Curve B-B" shows another type of relationship in which costs
increase somewhat faster above 95 percent good-or-better grade of
service than below. The change is not nearly as abrupt as for
Curve B-B', and the achievement of a 96 or 97 percent grade of
service (considered satisfactory) would be justified. The important
point to note is that the derivation of cost curves such ,as those
illustrated often provides strong support for determining objectives,
either in terms of grade of service or more directly in terms of
transmission objectives. Such curves may also be used to judge the
cost of making desired improvements in performance.

Allocation of Objectives

As described in Chapter 25, objectives may be allocated to different
sources of an impairment, the total objective for one type of impairment may be allocated to different parts of the plant (e.g., local or
toll), or the total objective may be allocated to various parts of a
transmission system. Each method of allocation is either directly
dependent on or indirectly tempered by economic factors.
An illustration of how economic factors can affect the allocation
of an objective to different sources of the impairment is seen in the
design of analog submarine cable transmission systems. In most
analog cable systems for land application, signal amplitudes are adjusted to produce optimum signal-to-noise performance. In submarine
cable system design, the cost of cable repairs enters into the problem
of noise allocation to various sources. If cable laying, aging, or other
phenomena cause unanticipated misalignment of signal amplitudes
in the positive (overload) direction, the increase in intermodulation
noise might necessitate installation of additional equalizers in the
cable, a costly operation. To guard against this possibility, submarine
systems are usually operated at low signal amplitudes. The results
are high margin against overload and the allocation of most of the
message circuit noise objective to thermal noise. Intermodulation is
seldom a controlling source of message circuit noise in submarine
cable systems.

630

Obiectives and Criteria

Vol. 1

An illustration was given in Chapter 25 of how economic factors
influence allocation of the objective for one type of impairment to
various parts of the plant. It was pointed out that the 20 dBrnc
maximum noise allocated to loops is such that no amount of expenditure in the loop plant could possibly improve the noise grade of service
unless both loop and trunk objectives are made more stringent. At
present, the noise resulting from trunks (carried predominantly on
carrier systems in the intertoll portion of the network) controls the
grade of service.
Finally, economic factors may affect the allocation of an impairment to different parts of a system. For example, in long analog
cable transmission systems, the design objective for message circuit
noise for a 4000-mile system is 40 dBrncO. A possible allocation of
this objective might be 37 dBrncO to the line repeaters and 37 dBrncO
to terminal multiplex equipment. However, the difficulty and cost of
achieving high quality performance in line repeaters (used in large
numbers compared to the number of terminals) is recognized by a
higher allocation to the line equipment. In most systems, the line
repeaters are allocated 39.4 dBrncO and the terminal equipment
31.2 dBrncO. This allocation, when further translated to individual
units (repeaters or terminal equipment), still results in a per-unit
allocation that is more stringent for a repeater than for the terminal
equipment. However, the economic balance is such that a further
allocation of the objective to the repeater (which already has been
allocated about 87 percent of the total) would not result in significantly lower overall costs.
Economic Obiectives

At certain times and under certain circumstances economic objectives may supersede all others. In times of economic stress, the desirability of improving performance or increasing route capacity may
have to be subordinated to the necessity of reducing capital and operating expenditures. Such circumstances, undesirable as they may seem,
must be recognized and improvements or expansion must be deferred.
In addition to the effects of economic stress, other less dramatic
effects must be considered. Among the most significant of these is
the availability of capital funds versus anticipated revenue. Sometimes it is necessary to keep outmoded equipment in service by paying
for its maintenance from operating funds even though the results

Chap. 27

Economic Factors

631

of engineering economy studies have demonstrated the desirability
of replacing the old equipment with new. When capital funds are in
short supply, it is impossible to update equipment in the desired
manner. This type of situation may be disclosed by engineering
economy studies which compare initial capital outlays and estimated
operating costs to available capital funds and anticipated revenue.
27-2

DESIGN COMPROMISES

Most of the compromises that must be made between objectives
and cost are made during the development and design of new systems
and new equipment. These compromises are made at every stage of
development and design; the type of system to be developed, the
features to be provided, the choice of circuits and physical designs,
and the selection of components all relate to the balance between
objectives (grade of service) and cost.

Circuit Devices
Devices used in electronic circuits include such elements as resistors, capacitors, inductors, transformers, transistors, and diodes.
Each device selected for the circuit under design must obviously meet
the requirements imposed by its function in the circuit. It must be
of the correct value, capable of dissipating a certain amount of
power, characterized by input/output relationships that are adequately linear, sufficiently reliable, etc. Even with these constraints,
there is often a wide choice within which circuit needs can be met.
Making that choice with good judgment involves consideration of
costs and their relationship to the circuit requirements. Two significant factors are the manufacturing costs of the devices used and the
ingenuity of the designer in utilizing a device to serve more than
one function.
The benefits of mass production are evident in the reduced cost
of devices. Also, economic benefits are usually effected when a device
can be made to serve multiple functions, as do many of the devices in
telephone station sets. The quantity of sets manufactured annually
is so high that even a fraction of a cent saved in one device yields a
significant manufacturing cost saving. As a result, a great deal of
effort is devoted to design· and redesign of the station sets and of
each device used. In such applied cost reduction studies, careful
attention must always be given to every aspect of the design, including the environmental conditions that are found in the operating

632

Obiectives and Criteria

Vol. 1

plant (heat, humidity, voltage, handling, etc.) as well as the circuit
requirements.

Circuits
As discussed here, circuits are packaged entities of interconnected
electronic devices that provide some specific function such as modulation, multiplexing, or amplification. A circuit may include electronic
networks, filters, and equalizers, often referred to as apparatus.
The design of circuits has progressed rapidly in recent years from
point-to-point connection of devices through printed wiring techniques
to a gamut of thin film, thick film, and integrated circuit arrangements that have evolved with the development of solid state technology. With the wide choice of circuit arrangements available,
careful attention must again be paid to economic factors. If large
numbers of identical circuits are to be built and close control of
circuit performance is required, integrated circuits are likely to be
a good first choice. Sometimes, the added expense of integrated circuits in small quantities is justified because the reproducibility of
integrated circuit performance is high.
An interesting illustration of circuit selection based on economic
factors hinges on the selection of devices involved in the design of
narrowband elimination or bandpass filters. In cases where the total
available band for achieving prescribed characteristics is wide, the
design may employ electronic devices, but if the efficiency of bandwidth utilization must be high and the available bandwidths are
small, piezoelectric crystals may be needed to achieve the desired
characteristics. The cost of the resistors, capacitors, and inductors
used in an electrical filter design is, in most cases, much lower than
the cost of crystals and the necessary additional devices. The choice
depends on available bandwidth and the stringency of the requirements.
Physical Design

The physical design of equipment and facilities is greatly influenced
by the costs of maintenance and operation as well as by the costs of
manufacture and installation. Recent trends in physical design have
been influenced by the decision to adopt new standards in building
-design and by the recognition that both transmission and operation

Chap. 27

Economic Factors

633

could be improved by integrated designs of equipment bays [1, 2].
These integrated designs, sometimes called unitized bays, include
many more combinations of transmission, signalling, and switching
system interface equipment than were formerly provided in a single
bay. Some of these combinations have been made possible by the
development of miniature devices and some by improved techniques
of bay wiring and functional circuit interconnection. The new designs
result in a significant reduction in office wiring, the elimination of a
number of cross-connect frames, reduced congestion of cable racks
and cross-connect frames, and a reduction in the number of jack fields.
The most significant feature of the new building design standards
is the reduction of ceiling height and the concomitant standardization
of 7-foot equipment bay heights. The packaging of electronic circuits
must now be consistent with the 7-foot bay standard, but in order to
serve existing buildings with reasonable efficiency, bays are also designed to old standards. The necessity for designing equipment for
several bay heights has led to a number of design compromises that
will eventually be unnecessary. As buildings of new design become
predominant, bay designs for the older buildings will no longer be
economically justifiable.
Unitized bay designs have led to a set of design compromises
different from those relating to building design. Facility terminals,
as the new designs are called, contain all voice-frequency terminal
equipment needed for a specific facility. In general, transmission
performance improves, but there may be some minor limitations on
the features that can be provided and the flexibility of equipment use.
The advent of solid-state technology has also led to situations in
which the solutions to design problems have resulted in various
compromises. A transistor dissipates less power than an electron
tube, but transistors are so much smaller that many more can be
packaged into a given volume than electron tubes. The result is higher
heat dissipation per unit of volume for transistor circuits, so temperature control has become a problem in packaging solid-state devices.
Since the higher density of components has lead to higher weight per
unit of volume in many designs, floor loading must be reconsidered.
Thus, physical designs have interacted with circuit and system designs to bring about new adjustments in objectives and design features. The process of adjustment and compromise is continuous and
parallels the development of all aspects of new technology.

634

Vol. 1

Obiectives and Criteria

Systems
The design of systems follows the same pattern of compromise as
has been outlined for components, circuits, and physical designs.
System features and design criteria must be considered in respect to
feasibility and cost. Reliability, maintainability, restoration of service,
automatic versus manual testing, remote control and telemetry, and
many other operational features must all be weighed carefully in
terms of service and cost.
The balance among system alternatives and cost factors plays an
important role in determining whether to develop a new system. An
example, illustrated by Figure 27-2, involves the cost of a carrier
system relative to the cost of copper pairs for voice-frequency transmission. Costs for carrier and voice-frequency transmission are
normalized to a value of unity at the point where the two costs are
equal. As illustrated, the cost of carrier transmission has a base, A,
representing the fixed cost of the terminal equipment. To this base
cost is added the line cost (medium and electronics), which increases
approximately linearly with distance. The cost of voice-frequency
transmission increases linearly from a base of zero except for discontinuities, designated B, introduced by possible gauge changes and
the periodic need for VF repeaters. The slope of the VF facility cost
curve is directly affected by the total cable cost and the number of
pairs per circuit.

A

1.5

B

§

= carrier terminal cost

= VF repeater cost

0.5

~

~

&
2

4

6

8

10

Length of circuit (miles)

Figure 27-2. Comparison of costs for very short circuits.

12

Chap. 27

Economic Factors

635

It can be seen that the cost/distance curve for the carrier system
is already less steep than for voice-frequency transmission. Further,
it is evident that even if this slope is significantly reduced, the cost
of a circuit is not materially affected because of terminal costs. The
conclusion is that only a significant reduction of the terminal
cost, A, can be expected to improve the position of carrier transmission relative to that of voice-frequency transmission. Curve C2
shows the effect of a terminal cost reduction of about ten percent,
a reduction that has no effect on the relative markets for the two
transmission modes because the crossover point of the cost curve is
still at ten miles. However, with a different set of curves and crossover points, a ten percent reduction might be very significant and
lead to a different conclusion.

Curve C3 shows the effect of a terminal cost reduction of about
50 percent. This may well provide encouragement for the development of new carrier terminals if the cost reduction appears to be
possible, because the crossover point of the carrier and voicefrequency transmission cost curve is now at six miles. In addition,
it would be necessary to show that there are large numbers of circuits in the range of six to ten miles and that there could be a high
expectancy of achieving the 50 percent cost reduction by terminal
redesign.
Many studies of the type described have been made to guide the
development of T -type and N -type carrier systems. The curves of
Figure 27-2 are representative but are not based on any specific
study results. Many other details must be included in a transmission
system development study, such as the gauge of wire and the loss
to which the circuits are designed.
A second example of cost factors in transmission design is shown
in Figure 27-3, which illustrates the effect of electronic equipment
costs on the total line costs in long-haul analog cable transmission
systems. The channel capacity or bandwidth of a number of systems
is shown relative to an arbitrarily selected bandwidth taken as unity
and to an arbitrarily selected unit of line cost. The line costs for a
number of systems are then plotted in terms of electronic and
nonelectronic components. Nonelectronic cost components include the
cost of cable, installation, and right-of-way.
Examination of the curves of Figure 27-3 shows that as the
normalized bandwidth increases beyond a value of 3, the cost of

Obiectives and Criteria

636

Vol. 1

6

5

Q)

3

a.
2

Cost of electronics ' \

Relative system bandwidth

Figure 27-3. Electronic and nonelectronic line costs, analog cable systems.

electronic equipment increases gradually. More important, the cost
of nonelectronic components and electronic components is about equal
for a normalized bandwidth of 6. Thus, it may be expected that any
additional increase in bandwidth would show that the total cost
starts to increase, and the development of new systems would be
financially questionable. Other means of transmission should probably
be considered.
27-3 APPLICATION COMPROMISES
Economic factors influence transmission problems in the field much
the same as in the laboratory environment. In the field, the questions
that arise involve long-range and short-range planning activities;
the optimum selection of equipment, transmission media, and systems;
and the allocation of funds to satisfy necessary operating functions.

Components
In the field environment, the word components refers to units of
equipment such as filters, equalizers, amplifiers, or balancing networks. In designing and laying out loops and trunks, the proper
selection of such components plays a significant part in achieving
performance consistent with established objectives and, at the same
time, in satisfying economic constraints.

Chap. 27

Economic Factors

637

In addition to the decisions that must be made to satisfy technical
objectives, the choice of equipment components must often include
consideration of general trade equipment components that can he
purchased outside the Bell System. Many suppliers have introduced
equipment in the market that meets the needs of telephone operating
companies. Thus, a knowledge of outside suppliers' equipment, its
performance capabilities and cost is imperative.

Systems
In an operating company the planning function typically includes
engineering studies that involve system choices in which economic
factors are important. Many economic studies must be made since
the choice of system depends heavily on cost relationships. Cost curves
similar to Figure 27-2 provide a good basis for solving system applications problems as well as design and development problems. By
combining cost curves and a projected distribution of circuit lengths,
it is often a simple process to decide the most economical choice of
facilities. However, where system capacities are large, analysis may
be quite complicated.
In very heavily populated areas, where large circuit cross-sections
are needed, there may be more than the usual choices of systems.
In most cases, the choice is primarily made from several alternate
plans for increasing the amount of paired copper cable, and the use
of T - and N -type carrier systems. In larger metropolitan areas, the
choices may be increased by the possibility of using microwave radio
systems or digital coaxial cable systems. Several such systems are
now available for metropolitan area applications.
Efficient use of maintenance personnel is another economic factor
in choosing a system. A number of equipment types are now available
to make measurements and surveillance tests automatically and even
to control certain operational functions remotely. In any planned
installation or expansion program, the cost of using such equipment
must be compared with the more conventional manual and on-site
maintenance methods.
REFERENCES

1. Pferd, W. "NEBS: Equipment Buildings of the Future," Bell Laboratories
Record (Dec. 1973), pp. 359-364.
2. Giguere, W. J. and F. G. Merrill. "Getting It All Together with Unitized
Terminals," Bell Laboratories Record (Jan. 1973), pp. 13-18.

Db jectives and Criteria

Chapter 28

International Telecommunications
The evolution of telegraph communications, the invention of the
telephone, the development of radio communication, and the expansion
of the total communication network have led to one of the world's
most highly developed telecommunication systems on the North
American continent. Whatever the principal reasons for this tremendous, but isolated growth in the United States and Canada (invention,
corporate organization, common language, few and open international
frontiers, etc.), little need was initially evident for coordination with
other nations or for the establishment of international objectives or
standards of performance. Thus, standards which in some cases, are
quite similar to those now applied internationally, yet in other cases
are quite different, have evolved independently in the United States
and Canada.
When transatlantic telegraph and then radio-telephone communications were established, the need for some form of intercontinental
coordination was recognized for the first time. The need for continuing and expanding coordination has been more evident as submarine cable and satellite communicationS! have become realities.
Today, the U. S. Government, a number of American common
carriers, and American industrial and scientific organizations (including manufacturers) are members and active participants in
international telecommunications organizations. The increasingly
intense use of the radio spectrum, the enlarged international market
and the increasing use of international direct distance dialing are
bringing about increased standardization of international communications. This trend is suppOrted) in part, by the proliferation of
telecommunication equipment manufacturers, whose international
marketing efforts are naturally enhanced when their equipment
satisfies international recommendations and standards. InternatiGnal
transmission planning permits the use of various in~rnal trans-

638

Chap. 28

International Telecommunications

639

I'

mission plans nationally, but international standards are met at
international switching offices and on international circuits.

28-1

THE INTERNATIONAL TELECOMMUNICATION UNION

While international coordination of telecommunications did not
directly affect the development of the North American network, the
need for coordination and cooperation among European nations was
evident as long ago as 1865. At that time, the International Telegraph
Union was formed by a convention in Paris attended by twenty
delegations from different European countries. Today there are nearly
150 members of the International Telecommunication Union (lTU) ,
the modern descendent of the International Telegraph Union. The
ITU engages in worldwide activities and is one of the specialized
agencies of the United Nations, which recognizes it as the sole
specialized agency competent for telecommunications [1, 2, 3].
Three international technical advisory committees were formed to
deal with various aspects of international telecommunications. These
committees were an outgrowth of the International Committee for
Long Distance Telephony*, commonly referred to as the CCI, in aurated in 1924. The three committees were called (1) the International
Consultative Committee for Telegraph (CCIT), the International
Telephone Consultative Committee (CCIF), and the International
Radio ConsultattVe Committee (CCIR). By 1939, when work was
interrupted by World War II, these committees had succeeded in
solving most of the traffic, operating, and radio coordination problems
to the satisfaction of all Administrations [4]. The American Telephone and Telegraph Company participated in the activities of these
early committees, first as an observer and then, after 1929, as a
fully qualified member.
At present, the relationships between the ITU and the U. N. (and
several other specialized agencies of the U. N.) provide for crossrepresentation between organizations, but the ITU has retained its
independence. The ITU acts essentially as a technical advisory and

* The original name of this organization was the Comite Consultatif Inter·national des Communications Tezephonique8 a Grande Distance.

640

Obiectives and Criteria

Vol. 1

administrative body. In 1956, two of its committees, the CCIF and
the CCIT merged into the International Telegraph and Telephone
Consultative Committee (CCITT).
The lTV and its principal organs maintain an active interest in
all aspects of international telecommunications, including the studies
of a wide variety of technical problems and the coordination of international traffic and operating procedures. In addition, a special working party of the CCITT and the CCIR (two of the principal organs
of the lTV) have produced a handbook to assist the administrations
and private operating agencies in an appreciation of the technical
and economic problems involved in the planning of transmission
systems [5]. Other special working parties have prepared handbooks
on national automatic networks and on local networks. These handbooks contain information on current practices in countries that
have highly developed telecommunication facilities and networks and
are intended to help other countries fill their telecommunications
needs.
International cooperation regarding satellite communications has
been fostered by studies and recommendations of the CCIR. With
the advent of launch vehicles capable of placing substantial radio
communication equipment into earth orbit, the CCIR began studies
of the commercial feasibility of international communication satellites
which culminated in recommended criteria for this mode of communication. The radio frequencies required by early satellites were located
in a frequency band bounded by excessive rain absorption above
10 GHz and high galactic noise below about 1.0 GHz. In order to
share the available useful frequencies with existing microwave radio
systems, equitable criteria had to be devised and international agreement obtained. In 1963, an Extraordinary Administrative Radio
Conference (of the lTV), to which the CCIR is the consultative
technical organization, adopted initial sharing criteria (e.g., signal
powers, frequencies, and allowable interference) for satellites, earth
stations, and the terrestrial systems affected. Their conclusions became part of the international radio regulations upon treaty ratification by the various countries involved, including the Vnited States.
The initial criteria prevailed until 1971 when a World Administrative
Radio Conference adopted new criteria and allocated additional frequencies above the earlier 10 GHz maximum. This action was based
,on recommendations resulting from CCIR studies.

Chap. 28

International Telecommunications

641

Organizational Structure of the ITU

The lTD consists of four permanent organs: (1) a General
Secretariat directed by the Secretary-General and a Deputy SecretaryGeneral, (2) the International Frequency Registration Board
(IFRB), (3) the International Radio Consultative Committee, and
(4) the International Telegraph and Telephone Consultative Committee. The General Secretariat provides liaison between Administrations and private operating agencies throughout the world and is
entrusted with the administrative and financial services of the lTD;
it also has a Technical Cooperation Department whose experts
work in various countries to provide technical assistance where
needed [3, 6].
International Frequency Registration Board. The lFRB acts as the recipient of information from the Administrations to record the frequency assignments of certain types of radio stations. It also acts,
wherever possible, to predict potential interference and to adjudicate
complaints of radio interference between Administrations by suggesting solutions to real or incipient problems.
International Radio Consultative Committee. This committee studies
technical questions relating to radio transmission and operations and
issues recommendations based on technical reports resulting from
their studies. The committee is made up of representatives from all
members of the ITU Administrations and recognized private operating agencies. When authorized, industrial and scientific organizations
may participate on a consultative basis. The plenary assembly assigns
work to various study groups and working parties whose reports
are received at plenary assemblies held by the CCIR approximately
every three years. The reports of the study results submitted and of
the resulting actions taken by the plenary assemblies are published
by the lTD.
International Telegraph and Telephone Consultative Committee. The
CCITT, like the CClR, is made up of representatives from all
members of the lTD, some recognized private operating agencies,
and industrial and scientific organizations. The CCITT studies technical, operating, and tariff questions connected with international
telecommunications. The study groups and working parties present
the results of their studies to plenary assemblies of the CCITT, held

642

Obiectives and Criteria

Vol. 1

about every three years. These reports, together with other actions
of the plenary sessions of the CCITT, are published by the lTD ira
volumes whose colors are chosen to be distinctively related to a
particular plenary session. *

Study Groups and Working Parties

Most of the technical work of the CCIR and the CCITT is carried
out by study groups, special study groups, and joint working parties
that are assigned responsibility for specific types of problems or
fields of investigation. These groups meet as required in order to
consider their assigned questions and problems. Figure 28-1 shows
a number of study groups of the CCITT, some of which operate
jointly with the CCIR. Regular study groups are designated by
Roman numerals and, in respect to their responsibilities, they fall
within a functional division of one field of study. Special study
groups, designated by letter, are involved in more than one field of
study. They may be formed of members from the CCIR, the CCITT,
or both. In Figure 28-1, arrows are used to indicate interactions
between special study groups (SP. A, SP. C, and SP. D) and the
functional study groups. Interactions within a field of study are not
shown. Working parties are formed within a study group to study
a particular problem or field of investigation; they may be permanent
or they may exist only for the time necessary to complete an assignment. Study groups have the responsibility of responding to specific
questions assigned by a plenary assembly of the CCIR or CCITT;
these questions and -subsequent recommendations are included in the
official publications of the CCIR or CCITT. The study groups also
prepare a list of questions and study programs for the following
plenary period (the period between plenary assemblies). The questions are proposed by the members of the CCIR or CCITT. Formal
approval by the plenary assembly is required for recommendations
and questions to become official.

* Examples are the Red Books, which cover the meetings of 1958 at Geneva
and 1960 at New Delhi (1st and lInd Plenary Assemblies); the Blue Books,
which cover the meeting of 1964 at Geneva (IIIrd Plenary Assembly) ; the White
Books, which cover the meeting of 1969 at Mar Del Plata (IVth Plenary Assembly) ; and the Green Books, which cover the meeting of 1972 at Geneva (Vth
Plenary Assembly).

(")
:J'

FUNCTIONAL DIVISIONS OF STUDY

Q

FIELDS OF STUDY
TARIFFS

TELEPHONE
OPERATIONS
AND
SWITCHING

/II GENERAL
TARIFF
PRINCIPLES

QUAlITY

MAINTENANCE

SYSTEMS AND
EQUIPMENT

l'
~
Q)

II OPERATIONS
AND TARIFFS

..~

CD
:::J

Q

TRANSMISSION

XII TRANSMISSION
PERFORMANCE

XVI TELEPHONE
CIRCUITS

XV TRANSMISSION
SYSTEMS

c)"

~

9.-

;t
CD
n

SP. C NOISE - RELIABILITY JOINT WITH CCIR

o

3
3
c

:::J

VIII TELEGRAPH
AND DATA
TERMINALS

TELEGRAPH
AND DATA

rr
Q

-

c)"
::J

en
V ELECTRICAL
PROTECTION
PROTECTION
VI CABLE SHEATHS
AND POlES
-~-----

Figure 28-1. CCITT study groups.

~

w

Objectives and Criteria

Vol. 1

Characteristics of International Operations

The major differences between national and international operations of telecommunication networks involve geography, language,
law, and politics. The ITU has performed admirably in solving the
related problems by patient negotiation and by the dedicated services
of the many persons representing its membership. The ITU operates
on the ~asis of voluntary membership with the assumption that it is
in the members' best interests to observe the conventions, regulations,
and recommendations of the Union [7].
28-2

THE EVOLVING INTERNATIONAL NETWORK

The members of the ITU, through recommendations of the CCITT,
have agreed on the goal of providing customer dialing of international
calls on a worldwide basis. A general plan for achieving this goal has
been agreed upon and is being implemented on a step-by-step basis.
Operator and customer dialing of international calls is already a
reality in many countries. The capability for operator and customer
dialing requires all-number calling, already in effect or planned for
most countries.
World Numbering Plan

Worldwide operator and customer dialing requires a worldwide
numbering plan. An appropriate plan, worked out by the CCITT,
divides the world into eight zones, as shown in Figure 28-2. Each
country is given a 1-, 2-, or 3-digit country code number, the first
digit of which identifies the world numbering zone. In the multinational North American zone 1, which is already organized into a
single integrated numbering plan, the single digit 1 is used as the
country code of all the countries in zone 1. Another interesting detail
is that the European zone has so many countries warranting twodigit codes that it has been assigned the initial digits 3 and 4.
For worldwide dialing, a customer or operator must first dial an
international prefix. Ambiguity between national and international
numbers employing the same initial digits is overcome by first dialing
the international prefix. In the North American network, the prefixes
for international dialing are 01 for calls requiring operator assistance
and 011 for other calls. After the international prefix, the country
code and the national number of the called station -are dialed. The
international numbering plan places the restriction that, after the

Chap. 28

645

International Telecommunications

/)

vi

CD

C

+

oN

C)

C

';;:
CD

-0

E
::l

c::

~

""i:

o

~

646

Objectives and Criteria

Vol. 1

international prefix, there may be a maximum of twelve digits in
the international telephone number.
Some of the capabilities implied by the numbering plan just described are yet to be implemented. In some cases, the digit capacity
of registers in local and toll offices must be expanded. Call routing
from an originating office to the appropriate international switching
center must be provided.
Signalling

When serious consideration was first given to direct dialing of
transatlantic calls, it was immediately noted that the European and
North American signalling systems were incompatible. Furthermore,
none of the existing systems were compatible with the needs of the
TASI system designed for use with the early submarine cable
systems.
Early submarine cable operation was carried out by manual ringdown signalling. In 1960, agreement was reached by the British,
French, and German Administrations with the Bell System on a
specification for an intercontinental signalling system. The system,
sometimes called the Atlantic system, was compatible with TASI,
provided for two-way operation of circuits, and provided practical
interfaces with the European and North American signalling systems.
It. used a modified version of the North American multifrequency
pulsing for the transmission of address information and a new
2-frequency system for supervisory signals. In 1960, both of the
latter frequencies were in standard use in Bell System signalling
systems.
The CCITT was requested to study the Atlantic system for
standardization as a recommended intercontinental signalling system.
The system was accepted by the CCITT with some minor changes
and was designated the CCITT Signalling System #5. Subsequently,
the CCITT standardized a common channel signalling system
(CCITT #6), designed to operate with stored program switching
systems and capable of providing features not available in System #5.
Traffic and Operating'

While most international calls were formerly person-to-person,
station-to-station calling is commonly used between many countries

Chap. 28

Internationa I Telecomm unications

647

and is increasingly available for both incoming and outgoing U. S.
international calls. Credit card and collect calls are also accepted for
calls between many countries and are also more widely used in international telephony.
An international operator may sometimes have language difficulties
or be unable to interpret a tone. To alleviate these problems, calling
operators are able to ring forward and bring in an assistance operator
in the terminating country. A language digit is prefixed to the called
number by the switching machine and pulsed forward to prepare
the distant equipment for receipt of a subsequent language-assistance
signal.
Routing Plan

A routing plan that is similar in many ways to the routing plan
used in the North American network has been recommended by the
CCITT. The hierarchical arrangement of the worldwide plan utilizes
three levels of international switching centers (transit centers),
designated CT1, CT2, and CT3; CTl represents the highest rank in
the hierarchy. The plan is shown in Figure 28-3.
High usage trunk groups between any pair of CT offices are established wherever they can be economically justified. Provisions are
made for alternate routing of overflow traffic from high usage groups
to alternate transversal trunk groups and then to the final group.
An example is given in Figure 28-3. For a call from CT3 on the left
to CT3 on the right, attempts would be made first to use the direct
group between these offices. As implied by the arrows, attempts
would be made to route the call to CT2 and then to CTl on the right.
Finally, the call would be offered to the final route.
According to the routing plan, CTl offices are to be interconnected
in pairs by circuit ,groups having low probability of blocking. In
exceptional cases, two CTl offices may be interconnected through an
intermediate transit center of unspecified rank (CTx). This is done
only where significant economies may be realized and only if transmission and other standards of service quality are met.
The CTl offices are important in the world routing plan. Locations
are chosen to satisfy national and international economic considerations as well as technical requirements for switching and trans-

648

Vol. 1

Objectives and Criteria

INTERNATIONAL NETWORK

@

(T1 (first category (T)

®

(T2 (second category (T)

o

(T3 (third category (T)

o

(Tx (unspecified category (T)

International final route
-

-

-

High-usage circuit group
NATIONAL NETWORK

•

o

Toll center (long distance exchange serving a subscriber through a toll connecting
trunk and local center)
Other national centers (Le., (SPs)
Final circuit group

Figure 28-3. International routing plan.

mission. Each country in which a CTI is located must be concerned
with the costs of interconnecting that CTI with all others by direct
circuit groups. The CTI offices are few in number and their recommended locations are strategically chosen on the basis of the in-

Chap. 28

International Telecommunications

649

transit flow of international transit traffic. These offices are concentration points for the traffic from a very large area. A number of
CT1 offices have been designated or proposed by ITU members to
implement the world routing plan.
The maximum recommended number of tandem-connected trunks
that may be used for an international call is fixed by the CCITT at
12, with a maximum of six international circuits. In some cases and
for only a small percentage of calls, the total number of tandem
circuits may be as high as 14; even in these cases, the maximum
number of international circuits is limited to six. An international
call involving six international circuits would be one routed through
transit centers in the following manner: CT3, CT2, CT1, CTx, CT1,
CT2, CT3.
Final route engineering of a worldwide network for efficient
handling of busy-hour traffic poses interesting problems caused by
the concentration of traffic during a few hours of the day due to
time zone differences. The CCITT has initiated a study of solutions
to these problems by flexible routing and some form of network
management.
Transmission and Maintenance

The possibility of 12 or even 14, tandem-connected circuits increases the likelihood that international connections may be impaired
more than domestic connections. In addition to the greater lengths
and increased number of circuits involved, the variation in types of
facilities also increases. These factors increase the probability of
increased loss, loss variation, noise, distortion, and propagation delays. Unless very stringent controls are imposed, there is an increased
likelihood of ·encountering multiple echo suppressors on an international connection. All of these factors make necessary a high
degree of control over transmission design and maintenance.
The procedures involved in ·establishing and maintaining international circuits have been and continue to be the subjects of study
by members of the CCITT. The resulting recommendations cover such
aspects of international circuits as the types of facilities, switching
systems, and signalling arrangements; detailed responsibilities for
control, trouble locating, testing, and maintenance; and procedures
for operating the international network. At the time international

650

Obiectives and Criteria

Vol. 1

circuits are established between two countries, detailed agreements
(largely based on current recommendations of the CCITT) are
reached on all of the specific items involved in maintenance.

28-3

TRANSMISSION PARAMETERS AND OBJECTIVES

The CCIR and CCITT have defined a large number of transmission
parameters and have established or recommended many transmission
objectives for the international telecommunication network. These
are thoroughly covered in documents published by the lTD [8, 9].
Space does not permit a comprehensive discussion here, but transmission level points, noise, and channel loading serve to illustrate the
manner in which transmission problems are treated internationally.
Currently, in the reports published by lTD, transmission parameters are expressed in decibels. Some parameters are also expressed
in decimal units of the international system of units. For example,
noise and noise objectives are expressed in picowatts and picowatts
per kilometer.
International practices and recommendations include the use of
a reference level, a term that is analogous to the 0 TLP used in the
Bell System. The reference level point is sometimes referred to as
o dBr (dB relative level). For four-wire operation, the transmitting
end of the circuit is defined as a -3.5 dBr point at the "virtual"
switching point, a theoretical point whose exact location depends
on national practice.

Noise
The basic unit of noise measurement used in international practice
is the picowatt (pW), i.e., 10- 12 watt. It should be noted that for a
1000-Hz signal, this is the same reference as that used in the Bell
System. In international maintenance practice, the standard test
signal may be 800 or 1000 Hz. The picowatt may be expressed
in decimal or logarithmic terms; the equivalent values are
1 pW = 10- 12 W = 10-9roW = -90 dBm.
Message circuit noise is measured, according to CCITT recommendations, by a noise measuring set called a psophometer. The set
is equipped with a weighting network that has a characteristic

Chap. 28

651

International Telecommunications

somewhat ~imilar to the C-weighting characteristic used in the Bell
System. The two characteristics are shown for comparison in
Figure 28-4. For general conversion purposes, it is usually sufficient
to assume that the psophometric weighting of 3-kHz white noise
decreases the average power by about 2.5 dB (compared with the
2.0-dB factor for C-message weighting). The term psophometric
voltage refers to the rms weighted noise voltage and is usually
expressed in millivolts.
The (rounded) conversion factor recommended by the CCITT for
practical comparison purposes is that 0 dBm of white noise measured
by a psophometer (1951 weighting) is equivalent to 90 dBrn measured
on a 3A-type noise meter with C-message weighting. This conversion, which applies to white noise in the 300 to 3400 Hz band, is not
valid for other noise shapes because of the differences between
psophometric and C-message weighting [10].
The relationships between various CCITT and Bell System noise
units are summarized in Figure 28-5. The data are particularly
useful for conversion from one noise unit to another since an estimate
of the frequency spectrum effects can be obtained by comparing the
three conditions tabulated. The I-kHz values are given for comparison
of the various conditions used. The I-kHz psophometric reading appears 1 dB high because the psophometric reference is 1 pW at
800 Hz. The 0- to 3-kHz band of white noise approximates the noise
obtained from a message channel. The broadband white noise readings are proportional to the total area under the weighting curve and

0

iii

-10

~
~

c

0

-20

~

GI
GO:

-30
-40
100

200

500

1000

2000

5000

Frequency (Hz)

Figure 28-4. Comparison of noise weighting characteristics.

652

Vol. 1

Objectives and Criteria
TOTAL POWER OF 0 dBm
NOISE
UNIT

o TO

3 kHz
WHITE NOISE

1 kHz

dBrnc

WHITE NOISE
OF -4.8 dBm/kHz
NOT BAND-LIMITED

88.0 dBrnc

88.4 dBrnc

dBrn 3 KHz FLAT

90.0 dBrn

88.8 dBrn

90.3 dBrn

dBrn 15 KHZ FLAT

90.0 dBrn

90.0 dBrn

97.3 dBrn

Psophometric
voltage (600 ohms)

870mV

582mV

604 mV

Psophometric emf

1740 mV

pWp

1.26 X

dBp

91.0 dBp

109

1164 mV
pWp

5.62 X

10 8

87.5 dBp

1208 mV
pWp

6.03 X 108 p Wp
87.8 dBp

Figure 28-5. Comparison of noise measurements.

thus give significant information concerning the weighting function
above 3 kHz. Similar data for other conditions or weightings can be
obtained by integrating the appropriate weighting characteristic over
the required frequency band.
Channel Loading

To simplify calculations in carrier system design, the CCITT has
adopted (Recommendation G.223) a conventional value, -15 dBmO,
to represent the mean absolute power of speech and signalling currents [8]. When the -15 dBmO value was established, it was based
on a determination of expected channel signal loads. Analog system
overload is discussed in Chapter 7 where Definition 2 is the CCITTrecommended definition of overload.
The problem of loading has been under further study in recent
years to determine whether the adopted value should be changed to
reflect the transmission of new signal types. The approach that now
appears most promising is that the amplitudes of data and other
types of signals will be made compatible with -15 dBmO. One step
has been to recommend a maximum sending reference equivalent
(minimum loss) from the subscriber to the first international circuit.
Also, several study groups have agreed that data and voice-frequency
telegraph signals are to be reduced to -13 dBmO.

Chap. 28

International Telecommunications

653

REFERENCES

1. Michaelis, A. R. From Semaphore to Satellite (Geneva: International Telecommunication Union, 1965).
2. Leive, D. M. International Telecommunications and International Law: The
Regulation of the Radio Spectrum (Dobbs Ferry, N. Y.: Oceana Publications,
Inc., 1970).
3. Mili, M. "International Jurisdiction in T'elecommunication Matters," Telecommunication Journal, Vol. 40 (April, 1973), pp. 174-182.
4. Timmis, A. C. Compendium of the Technical Recommendations Issued by the
CCIF, the CCIT and the CCIR of the International Telecommunication
Union (Liverpool: Automatic Telephone & Electric Co., Ltd., Aug. 1958),
Chapters 1 and 2.
5. CCIR and CCITT. Economic and Technical Aspects of the Choice of Transmission Systems (Geneva, International Telecommunication Union, 1968).
6. Richards, D. L. Telecommunication by Speech (New York: Halsted Press
Division, John Wiley and Sons, Inc., 1973) , Appendix 2.
7. Cox, R. W., and H. K. Jacobson. The Anatomy of Influence (New Haven:
Yale University Press, 1973), pp. 59-101.
8. CCITT. Vth Plenary Assembly, Geneva, Green Book Volume III (Geneva,
International Telecommunications Union, 1973).
9. CCITT. Vth Plenary Assembly, Geneva, Green Book Volume VI (Geneva,
International Telecommunications Union, 1973), Part II, Chapter VI.
10. CCITT. Vth Plenary Assembly, Geneva, Green Book Volume V (Geneva,
International Telecommunications Union, 1973), Rec. P .53.
11. Mili, M. "International Jurisdiction in Telecommunication Matters," Telecommunication Journal, Vol. 40 (Sept. 1973), pp. 562-566.

INDEX
AC signalling, 346
Accelerated depreciation, 283
Accounting, depreciation, 281
Accounts, Uniform System of, 274
Acoustic shock, 424
Activity factor, 305
Addition, laws of, 590
Address signal, 22, 321
Alarm arrangements, 524
Alerting signal, 22, 321
Alignment charts, 85
Allocation of objectives, 583, 629
Alternate routing, 10
Amplifier stability, 98
Amplitude /frequency distortion,
455,458
Amplitude/frequency objectives, 595
Amplitude
modulation, 189
shift keying (ASK), 359
Analog coaxial cable systems, 31
Analog data signal, 22, 375
Analog signal, 351
Analysis
network, 63
transmission, 64
Analyzer, spectrum, 143
Angle modulation, 203
Apparent power, 77
Arithmetic mean, 250
Articulation testing, 539
ASK signal waveforms, 360
Aspect ratio, 385
Attenuation constant, 39, 119, 140
Attenuation factor, 119, 124
Audible ring, 332
Audio/video delay, 624
Aurora borealis, 527
Available gain, 46
Average, central value, 250

Bar pattern, 581, 620
Battery
common, 323, 414
feed circuits, 325
impedance, 420
Baud, 210
Bel, 39
Bilateral network, 76
Binary digit, 260
Binomial distribution, 244
Bipolar line signals, 367
Bit, 260
Blanking pulse, 383
Boltzmann's 'constant, 429
Book
costs, 283
depreciation, 283
value, 283
Break interval, dial pulse, 328
Bridged tap, 462
Building design, 633
Busy circuit, 322
C-message weighting, 56
Capital
costs, 280
debt,280
equity, 280
expenditures, 281
recovery, 281
Carrier systems, 28
Carson, J.R., 209
Ca tegory judgments, 539
CCI, 639
CCIF, 639
CCIR, 639
eelS, 348
CCIT, 639
CCITT, 183, 640
Central limit theorem, 243
Central values, 250
Channel, 23
discrete, 268
noiseless, 267
one-way, 24
two-way, 24
Channel bandwidth, 456
Channel capacity~ 268

Back porch, 883
Balance
terminal, 494,603
through, 494, 603
Bandwidth
channel, 456
objectives, 594

654

Index
Channel coding, 264
Channel symmetry, 269
Characteristic impedance, 117, 122
Chrominance, 380, 389
Circuit order requirements, 582
Coaxial cable, 139
Coaxial cable systems, analog, 31
Coding, 216
Coding, channel, 264
Coil
hybrid,106
heat, 529
load, 136
repeat, 104
Combining transmission paths, 106
Comment scale testing, 539
Common battery, 323, 414
Common Channel Interoffice Signalling
System, 348
Community antenna television, 393
Comp'andor, 33, 408
instantaneous, 436
syllabic, 408, 449
Compatibility, system, 15
Compensation theorem, 72, 81.
Complement, set, 223
Complementary period, 293
Composite
cost of money, 280
return, 275
signalling, 343
Compounding, 275
Compression ratio, 408
Concentrator, line, 5
Conditional probability, 225
Conditioning, 459
Confidence limits, 254
Connection loss, overal1, 489, 598
Constants
primary, 116
secondary, 116
Construction program, 274, 279
Continuous source, 259
Contrast, 457, 458, 603
Control signal, 22
Convenience rate, 288
Coordination, inductive, 422
Cost
book, 283

655
Cost (cont)
capital, 280
first, 280
incremental, 294
initial, 277
maintenance, 286
operating, 286
plant operations, 285
recurrent, 277, 285
sunk, 294, 296
Cost of money, composite, 280
Cotermination of plant, 294, 295
Coupling, 413, 422
crosstalk, 425
electric field, 417
electromagnetic, 416
intermodulation, 420
magnetic, 416
Coupling loss, 437
Coupling loss, equal level, 425, 438
Crosstalk, 425, 623
differentiated, 623
digital, 427
far-end, 425
fiat, 623
intelligible, 353, 581
interaction, 425
intermodulation, 431, 433
near-end, 425
speech, 426
video, 427, 623
Crosstalk coupling, 425
Crosstalk index, 439, 581, 609
Cumulative distribution function,
230, 240
Current
longitudinal, 414
metallic, 414
Current revenues, 274
Customer loops, 4
Data, wideband digital, 463
Data access arrangement, 595
Data signal, 21
DATAPHONE service, 595
dB, 39
dBm, 40
dBRAP,306
dBrn,58

656

Index

dBrnc,58
dBrncO,58
dBrnO,58
dBV,388
dc signalling, 336
Debt capital, 280
Debt-to-equity ratio, 278
Debt ratio, 280
Decoding, 264
Deferred taxes, 274
Delay
audio/video, 624
envelope, 46, 498, 500
group, 498
luminance/chrominance, 625
phase, 46, 498, 500
Delay distortion, 188, 499
Delay distortion, envelope, 500, 515
Demodulation, 188
Depreciation, 274
accelerated, 283
accounting, 281
book, 283
straight line, 282
Design
objectives, 582, 593
physical, 632
requirements, 582
Determinants, 103
Determination of objectives, 577, 627
Dial pulsing, 328
break interval, 328
make interval, 328
Differential gain, 467, 510, 624
Differential phase, 509, 511, 514, 518,
624
Differential pulse code modulation, 217
Digital data signal, 351
Digital signals, 351
Digital systems, 32
Direct trunks, 606
Disconnect, 322
Discrete channel, 268
Discrete source, 259
Dispersions, 251
Distortion
amplitude, 188
amplitude/frequency, 455, 458
delay, 188, 499

intercept, 198, 501
pha.se, 188,498,513,514
quadrature, 198, 360,505, 511-513,
517
Distribution
binomial, 244
Gaussian, 239
log-normal, 246
normal, 239
Poisson, 243
Rayleigh, 249
rectangular, 247
uniform, 247
Distribution function, normal
cumulative, 241
Diversity of trunking, 531
Domain, set, 221
Double declining balance, 284
Dropouts, 474,480
Duplex, 24
Duplex signalling, 344
Duty cycle, 362
E and M leads, 335
Earnings, retained, 274
EARS, 571
Earth potential, 343
Earthquakes, 527
Echo, 90,92,467, 512,596, 620
differentiated, 622
fiat, 622
listener, 482, 486, 491
objectives, 601, 622
rating, 512
.
return loss, 492, 602
suppressor, 34,494,605
talker, 482, 489,596,601
weighting, 622
Echo path delay, 597
Echo path loss, 603
Economic objectives, 630
Economy studies, engineering, 273, 278
Edison Electric Institute, 422
Educational television, 393
Efficiency, power transfer, 95
Electric field coupling, 417
Electro-Acoustic Rating System, 571
Electrolysis, 527, 530
Electromagnetic coupling, 416

657

Index
Electromagnetic pulses, 528
Emergency broadband restoration, 530
Empty set, 222
End-office trunks, 606
End section, 138
Energy, 286
Engineering economy, 273, 278
Engineering objectives, 582
Entropy, 261
Envelope delay, 46, 498, 5QO
Envelope delay distortion, 500, 515
Equal level coupling loss, 425, 438
Equalization, 31
Equalizer, 170
Equalizing pulses, 384
Equity capital, 280
Equivalent four-wire transmission, 28
Equivocation, 268
Error
correetion, 265
detection, 265
Error rate, 354
Error rate objective, 613, 617
Estimation, sample, 254
Expectation of a function, 234
Expected value of a random variable,
233
Expenditures, capital, 281
Expenses, operating, 285
Expert observer, 545
Eye diagram, 447, 462, 465, 614
Facility terminal, 28, 633
Facsimile signal, 20, 21, 364
Factor, via net loss, 599
Far-end crosstalk, 425
Feedback
bridge-type, 174
hybrid, 175, 186
series, 173
shunt, 173
Field testing, 542
Filter
band-elimination, 111
bandpass, 110
high-pass, 110
low-pass, 110
Fire, 527
First cost, 280

Fixed loss design plan, 599
Flicker, 466, 581, 623
Flyback, television, 383
Fourier
integral, 158, 163
inverse transform, 158
series, 38
series representation, 146
symmetry, 149
transform, 143, 157
Four-wire transmission, 4, 25
Frequency
domain, 142
frogging, 31, 34
modulation, 203
response, 160
Frequency offset, 474
Frequency offset objectives, 611
Frequency shift keyed signals, 373
Frequency weighting, 56
Frogging, 31,33,34,591
Front porch, 383
Full duplex, 24
Gain
available, 46
differential, 467, 510, 623
hits, 479
insertion, 46
power, 47
transducer, 47
Gaussian distribution, 239
Gaussian noise, 428
Geometric mean, 250
Glare, 327
GOSCAL, 557, 566
Grade of service, 220, 239, 551
loss/noise, 571
loss-noise-echo, 570
Ground-start, 326
Group delay, 498
Group velocity, 46
Hardened systems, '531
Harmonic distortion, 171
Heat coils, 529
High-frequency line equipment, 31
High-low signalling, 338
High-usage trunk, 606
Histogram, 252

658
Hits
gain, 479
phase, 479
Holding tone, 436
Horizontal resolution, 386, 465
Hybrid, 482
coil, 106
feedback, 175, 186
Idle circuit, 321
IFRB,641
Image
impedance, 73
transfer efficiency, 77
Impairment, noise, 447, 460, 462
Impedance
characteristic, 117, 122
image, 73
matching, 104, 130
sending-end, 78
Impulse signal, 159
Impulse noise, 423
objectives, 608
Impulse response, 161
Incidental modulation, 474, 479
Income tax, 285
Incremental cost, 294
Index
crosstalk, 439
of modulation, 190, 205, 51.7
Indices, 589, 606
Inductive coordination, 422
Inductive loading, 136
Industrial television, 392
Inflation, 278, 287
Influence, power circuit, 422
Information
signal, 321
theorY,256
unit of, 259
Initial cost, 277
Insertion
gain, 46
loss, 45, 90, 131
phase shift, 45, 90
Intelligible crosstalk, 353, 581
objectives, 609
Interaction crosstalk, 425

Index
Intercept distortion, 198, 501
Interest, 275
Interference, single-frequency, 424, 620
Interlacing, 384
Intermodulation, 171
coupling, 420
crosstalk, 431, 433
noise, 431
Internal rate of return, 291
International Committee for Long
Distance Telephony (CCI), 639
International Consultative Committee
for Telegraph (CCIT), 639
International Frequency Registration
Board (IFRB), 641
International Radio Consultative
Committee (CCIR), 639
International routing plan, 647
International signalling, 646
International Telecommunication
Union (ITU), 639
International Telegraph and
Telephone Consultative Committee
(CCITT), 640
International Telegraph Union, 639
International Telephone Consultative
Committee (CCIF), 639
Interpretation of objectives, 578
Interregional trunks, 605
Intersection of sets, 223
Intertandem trunks, 7, 12, 606
Investment tax credit, 274, 284
Isopreference testing, 538
ITU, 639
Jitter, 474, 479, 587
Joint working parties, 642
Kirchoff's Law, 65
Laboratory tests, 542
Landslides, 527
Laws
Kirchoff's, 65
Ohm's, 64
Lease, 286
Level, 49
reference, 650
Life of plant, 281

659

Index
Lightning, 527
Limen, 547
Liminal unit, 547
Limit, 579, 593
maintenance, 583
turn down, 583
Line concentrator, 5
Listener echo, 482, 486, 491
Load capacity, 314
Load coil, 136
spacing, 138
Loaded lines, 134
Loading
inductive, 136
noise, 450
Log-normal distribution, 246
Longitudinal current, 414
Long route design, 604
Long routes, 606
Loop
cutsomer,4
loss, 604
loss objective, 605
noise objectives, 607
signalling, 336
Loop-around testing, 524
Loop-start, 326
Loss, 461, 465
insertion, 45, 90, 131
loop, 604
objectives, 605
overall connection, 489, 597
reflection, 126
return, 90, 133
Loss changes, 461, 466
Loss/noise grade of service, 571
Loss-noise-echo grade of service, 570
Low-frequency noise, 619
Luminance, 380, 382
signal, 384
Luminance/chrominance delay, 624
Maintenance, 16, 520
costs, 286
limits, 583
objectives, 593
preventive, 521
requirements, 582
support, 16

Make interval, dial pulse, 328
Mapping, 228
Margin
gain, 178
phase, 178
Mastergroup, 401
Matrix analysis, 103
Mean deviation, 251
Median, central value, 250
Medical data, 376
Mesh analysis, 100
Message, 18
circuit noise, 607
signals, 18
Metallic current, 414
Microwave radio systems, 31
Midrange, central value, 250
Misalignment, signal, 407, 629
Miscellaneous taxes, 286
Misframes, 587
Mode, central value, 250
Modulation, 32, 188
amplitude, 189
angle, 203
coefficients, 182
differential pulse code, 217
DSBSC, 190, 197
DSBTC, 192, 193
frequency, 203
incidental, 474, 479
index, 190,205,517
phase, 203
product, 189
pulse, 210
pulse amplitude, 212
pulse code, 215
pulse duration, 214
pulse position, 215
SSB, 192, 197
VSB, 193, 201
Money
composite cost of, 280
time value of, 275
Monochrome signal, 380
Multiburst test signal, 470
Multichannel load factor, 316
Multifrequency signalling, 348
Multilevel ASK signals, 369

660
Multiplexing, 32
frequency division, 33
space division, 32
time division, 33
National Television System
Committee, 388
Near-end crosstalk, 425
Near-singing, 489
Negative feedback, 168
Nepers,39
Net plant, 283
Network
analysis, 63
bilateral, 76
four-terminal, 91
linear, 63
switched message, 3
synchronizing, 481
synthesis, 63
two-port, 37
Nodal analysis, 102
Noise, 56
digital signal, 435
Gaussian, 428
impairment, 354, 447, 460, 462, 465,
614,617
impulse, 4.23
intermodulation, 431
loading, 182, 450
low-frequency, 619
measuring set, 3-type, 56
message-circuit, 607
notched, 450

11/,428,430
power system, 421
quantizing, 435
Rayleigh, 428, 431
shot, 428, 430
thermal, 184, 428
weighting, 618
white, 428
Noise figure, 184
Noise power, available, 429
Noiseless channel, 267
Nonlinear distortion, 180
Normal cumulative distribution
function, 241
Normal distribution, 239

Index
Notched noise, 450
NTSC, 388
Null set, 222
Numbering plan, world, 644
Nyquist
criteria, 258
interval, 211,357
shaping, 356
stability criteria, 179, 355
Objectives
allocation, 583, 629
amplitude/frequency, 595
bandwidth, 594
design, 582, 593
determination, 577, 626
echo, 601,622
economic, 630
engineering, 582
error rate, 613, 617
frequency offset, 611
impulse noise, 608
intelligible crosstalk, 609
interpretation, 578
loop noise, 607
loss, 605
maintenance, 593
overload, 611
performance, 593
phase/frequency, 595
sidetone, 612
single-frequency, 610
translation, 588
transmission, 593
trunk noise, 608
video, 617
wide band digital, 613
Off-hook, 322
Ohm's Law, 41,64
One-way signalling, 7
On-hook, 322
One-and-one-half balance, 284
Operating
costs, 286
expenses, 285
Order wires, 524
Oscilloscope, cathode ray, 143
Outage time, 526
Out-of-sight plant, 532

Index
Overall connection loss, 489, 598
Overload,53,180,182,24~315,40~

512, 528, 615, 652
objectives, 611
Overshoot, 467,469,470,621
Pair-comparison testing, 538
P / AR, 515, 595
meter, 447, 462
rating, 515
Panel call indicator, 339
Peak factor, 310, 315, 402, 404
Percent break, 329
Performance objectives, 593
Period
complementary, 293
planning, 293
Phase
constant, 39, 120
delay, 46, 498, 500
differential, 509, 511, 514, 518
distortion, 188, 498, 513, 514
distortion control, 516
hits, 479
modulation, 203
shift, 45, 90, 498
shift keyed signals, 372
velocity, 46
Phase/frequency objectives, 595
Physical design, 632
PICTUREPHONE
signal, 20, 394, 407
transmission level points, 396
Pilot signal, 170
Planning period, 293
Plant
life, 281
net, 283
opera tions costs, 285
retirement, 295
Poisson distribution, 243
Pollard's theorem, 69
Porch
back, 383
front, 383
Power
addition, 59
circuit influence, 422
gain, 47

661

Power (cont)
system noise, 421
transfer, 94
transfer efficiency, 95
Present worth of annual costs, 291, 293Present worth of expenditures, 291,
294
Preventive maintenance, 521
Primary constants, 116
Probability, 219
conditional, 225
density function, 231
Product modulation, 189
Program signal, 20, 318
Propagation
constant, 120
time, 498, 596
velocity of, 125, 141, 599
Protection line switching, 31
Protectors
carbon-block, 529
diode, 529
gas-tube, 529
Psophometer, 650
Psophometric
voltage, 651
weighting, 651
Pulse modulation
amplitude, 212
code, 215
duration, 214
position, 215
Pulse splitting, 323
PWAC, 291, 293
PWE, 291, 294
Quadrature distortion, 198,360,505,
511-513, 517
Quantization, 260
Quantizing, 216
Quantizing noise, 216, 435
Radio systems, microwave, 31
Rain attenuation, 527
Raised cosine characteristic, 258, 355
Random variable
expected value, 233
sum of, 237
Range of sample, 251

662
Rate
convenience, 288
of return, 275, 280
of return, internal, 292
Rating
P/AR, 515
transmission, 570, 573
Rating System, Electro-Acoustic, 571
Rayleigh
distribution, 249
noise, 428, 431
Receiver off-hook (ROH) signal, 334
Recurrent costs, 277, 285
Rectangular distribution, 247
Reference level, 650
Reflection, 125
coefficient, 90
factor, 127
gain, 128
loss, 126
Regulation, 31
Regulator, 170
Reliability, 15, 520, 526
Rent, 286
Repeat coils, 104
Repeated plant, 295
Repeater
negative impedance, 27
voice-frequency, 27
Requirements, 593
circuit order, 582
design, 582
maintenance, 582
Resistance design, 604
Resolution
horizontal, 386, 465
vertical, 385, 465
Resonance
parallel, 110
series, 110
Resonant circuits, 109
Restoration
emergency broadband, 520, 530
service, 520
Restored polar signals, 363
Retained earnings, 274
Retirement of plant, 296

Index
Return
composite, 275
rate of, 275
Return loss, 90, 133, 602
echo, 492
singing, 494
structural, 134
Return rate, 280
Revenues, current, 274
Reverse battery signalling, 337
Revertive pulsing, 339
Ring, 325
Ringing, 466, 469,470,621
cycle, 333
selective, 333
signal, 22, 332
Root mean square, central value, 250
Routing plan, international, 647
R-scale, 570
Salvage, 281
gross, 282
net, 282
Sample space, 221
Sampling, 211, 252
theorem, 211, 260
Satellite communications, 640
Scanning, 20, 380, 389
pattern, 381
Secondary constants, 116
Secondary intertoll trunks, 606
Secretariat, General, 641
Section, end, 138
Seizure, 322
Separating transmission paths, 106
Service
grade of, 220, 239
restoration, 520
Set domain, 221
Shielding, 417
Shock, acoustic, 424
Shot noise, 428, 430
Sidetone, 486
objectives, 612
Signal
address, 22, 321
alerting, 22, 321
analog, 351
analog data, 22

Index
Signal (cont)
bipolar line, 367
control,22
data, 21
digital, 351
digital data, .351
facsimile, 20, 21, 364
information, 321
message, 18
misalignment, 407, 629
monochrome, 380
multiburst test, 470
PICTUREPHONE, 20, 394
pilot, 170
program, 20
ringing, 22
restored polar, 363
speech, 19~ 302
stairstep test, 470
supervisory, 22, 321
telephotograph, 397, 491
television, 20, 380
test, 321
video, 20
wide band binary ASK, 363
Signal amplitude, digital, 352
Signalling
ac,346
Atlantic system, 646
composite, 343
dc, 336
derived dc, 342
duplex, 344
high-low, 338
international, 646
loop, 336
multifrequency, 348
one-way, 7
out-of-band, 348
PCI,339
reverse battery, 337
revertive pulse, 339
simplex, 342
single-frequency, 346
2600-Hz, 346
two-way, 7
wet-dry, 338
Simplex signa1Iing, 342

663

Singing, 98
margin, 100, 490
return loss, 494, 602
Single-frequency
interference, 424, 620
objectives, 610
signalling, 346
Slip, digital signal, 478
Smearing, video, 467,469,470,621
Snow, 618
Special Services Signalling, 349
Special study groups, 642
Spectrum analyzer, 143
Speech
activity factor, 311
energy, 303
signal, 19, 302
Spot noise figure, 184
Stability
amplifier, 98
index, 99
Stairstep test signal, 470
Standard deviation, 235, 251
Standing wave ratio, 128
Station set, 4, 25
telephone, 25, 612
Statistics, 219, 249
Straight-line depreciation, 282
Streaking, video, 467, 469, 470, 621
Structural return loss, 134
Study groups, 642
Subjective testing, 536, 574
Submarine cable, 28
Subset, sample space, 221
Sum-of-years-digits,284
Sunk cost, 294
Sunspots, 527
Superposition theorem, 70, 81
Supervisory signal, 22, 321
Suppressor, echo, 34
Susceptibility to power impairment,
422
Switched message network, 3
Switching, 8
blocking, 7
local hierarchy, 8
tandem, 8
time domain, 24
toll hierarchy, 8, 10

664
Switching center
primary, 12
regional, 12
sectional, 12
toll, 12
Syllabic compandors, 408, 449
Symmetry
channel, 269
Fourier, 149
Synchronization, 380, 389, 474
Synchronizing network, 481
Synthesis, network, 63
Systems
carrier, 28
compatibility, 15
Talk-listen activity factor, Sll
Talker
constant volume, 305
echo, 482, 489, 596, 601
variable volume, 308
Tandem trunks, 7, 12, 606
T AS! system, 24, 34, 408
Tax credits, investment, 274, 284
Taxes
deferred, 274
income, 285
miscellaneous, 286
Telegraph signals, 374
Telemetry arrangements, 524
Telephone load activity factor, 311
Telephone station set, 25, 612
Telephotograph signals, 397, 491
Teletypewriter signal, 374
Television, 379
channel assignments, 390
community antenna, 393
educational, 393
flyback,383
industrial, 392
signal, 20, 380
Television Operating Center, 17, 387
Terminal balance, 494, 603
Terminals, facility, 28, 633
Test centers, voiceband data, 16
Test facilities
automatic, 16
switchboards, 16
Test pattern, 469

Index
Test signal, 321
Testing, loop-around, 524
Theorems
compensation, 72, 81
Pollard's, 69
superposition, 70, 81
Thevenin's, 69, 79
Thermal noise, 184, 428
Thevenin's theorem, 69,79
Threshold testing, 537
Through balance, 494, 603
Time-cost diagram, 297
Time domain, 142
Time value of money, 275
Tip, 325
Toll connecting trunks, 7, 12, 606
TOUCH.,TONE, signalling, 330, 3-'75-.
Transducer, 38
Transducer gain, 47
Transfer
characteristics, 37
effects, 76
Transform, inverse Fourier, 158
Transformation
71' to T, 67
T to 71',67
Transformers, 104, 130
Translation of objectives, 588
Transmission
analysis, 64
equivalent four-wire, 28
four-wire, 4, 25
level, 48
line, 115
objectives, 593
paths, 3
rating, 570, 573
response, 160
two-wire, 4, 25
voice-frequency, 25
Transmission level point, 48
PICTUREPHONE, 396
Trunk,7
direct, 606
diversity, 531
efficiency factor, 311
end-office, 606
high-usage, 606
interoffice, 7, 12

665

Index
Trunk (cont)
interregional, 605
intertandem, 7, 12,606
intertoll, 7, 12
local, 7
noise objectives, 608
one-way, 7
secondary intertoll, 606
tandem, 7, 12,606
toll connecting, 7, 12, 606
two-way, 7
Trunk conditioning, 348
Trunk groups
final, 12
high-usage, 12
Turnaround time, 491
Turn-down limits, 583
Two-port networks, 37
Two-way signalling, 7
Two-wire transmission, 4, 25
Uniform distribution, 247
Uniform System of Accounts, 274
Uniguage design, 327, 604, 608
Union of sets, 223
United Nations, 639
Unitized bays, 633
Universe, 221
Variance, 234, 251
V-curves, 451
Vector washout, 196
Velocity
group, 46
of propagation, 125, 141, 599
phase, 46
Venn diagram, 221
Vertical interval test signals, 470
Vertical resolution, 385, 465

Via net loss, 596
design, 458
factor, 599
Video
crosstalk, 427, 623
signal, 20
smearing, 467, 469, 470, 621
streaking,467,469,470,621
transmission objectives, 617
Voice-frequency repeaters, 27
Voice-frequency transmission, 25
Voltage
addition, 61
psophometric, 651
standing wave ratio, 130
Volume, 54, 603
constant, 305
indicator, 55
units, 55
Vu meter, 55
VVashout,vector, 196
VVavelength constant, 120
VVeber-Fechner law, 547
VVeighting
C-message, 56
echo, 622
noise, 618
psophometric, 651
VVhite noise, 428
VVideband
binary ASK signals, 363
digital channels, 463
digital data, 464
digital transmission objectives, 613
Windshield wiper effect, 427, 622
"VVired music," 318
VVet-dry signalling, 338
Working parties, 642
W orId numbering plan, 644
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