1969_SP 51_RCA_Power_Circuits 1969 SP 51 RCA Power Circuits

User Manual: 1969_SP-51_RCA_Power_Circuits

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TECHNICAL SERIES SP·S1

RCA

Power
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Contents
PAGE

SEMICONDUCTOR MATERIALS, JUNCTIONS, AND DEVICES

Semiconductor Materials, Current Flow, N-P-N and P-N-P Structures, Types of Devices

SILICON RECTIFIERS

Theory of Operation, Characteristics and Ratings, Series and Parallel
Rectifier Arrangements, High-Voltage Rectifier Assemblies, Packaging

THYRISTORS
Theory of Operation, Construction, Ratings and Characteristics, Series
and Parallel Operation, Transient Protection

SILICON POWER TRANSISTORS
Design and Fabrication, Basic Transistor Parameters, Maximum
Ratings, Thermal Considerations, Second Breakdown, Safe-Area
Ratings, Small-Signal Analysis, Large-Signal Analysis, Switchi'ng
Service

RECTIFICATION

149

POWER CONVERSION

162

POWER REGULATION

200

Linear Voltage Regulators, Switching Regulator, General Triggering
Considerations, Phase-Control Analysis of SCR's, Motor Controls,
Incandescent Lighting Controls

THYRISTOR AC LINE·VOLTAGE CONTROLS

226

General Considerations, Motor Controls, Heater Controls, Incandescent Lighting Controls

262

HIGH-FREQUENCY POWER AMPLIFIERS •
Design of RF Power Amplifiers, Matching Networks, Marine Radio,
Citizens-Band Transmitters, Mobile Radio, SSB Transmitters, Aircraft Radio, Community-Antenna TV, UHF Military Radio, Microwave Amplifiers and Oscillators, Frequency Multipliers

CONTROL AND LOW-FREQUENCY POWER AMPLIFIERS.

379

General Considerations, Audio-Frequency Power Amplifiers, Ultrasonic Power Sources, Servo Amplifiers

BIBLIOGRAPHY

• 438

INDEX.

440

RCA TECHNICAL PUBLICATIONS

444

Information furnished by RCA is believed to be accurate and reliable.
However, no responsibility is assumed by RCA for its use; nor for any
infringements of patents or other rights of third parties which may
result from its use. No license is granted by implication or otherwise
under any patent or patent rights of RCA.

RCA
Silicon
Power Ci·rcuits
Manual
Manual, like its preceding edition, provides
T hisdesign
information for a broad range of
power circuits using RCA silicon transistors, rectifiers, and thyristors (SCR's and triacs). It includes a brief introduction to semiconductor
physics, as well as descriptions of construction,
theory of operation, and important ratings and
parameters for each type of device. Specific design criteria and procedures are presented for
applications involving rectification and powersupply filtering, power conversion and regulation,
ac line voltage controls, rf power amplifiers, and
control and low-frequency power amplifiers. Design examples are given, and typical practical
circuits are shown and analyzed.

A lthough this Manual is intended primarily

1"1. for circuit and system designers working
with solid-state power devices, portions of it will
also be found useful by educators, students, radio
amateurs, hobbyists, and others interested in the
use of semiconductor devices and circuits.
RCA

I Electronic Components I

Harrison, N.J. 07029

Copyright 1969 by Radio Corporation of America
(All rights reserved under Pan-American Copyright Convention)
Printed in U.S.A. 1/69

RF
Powe r-Transisto r
Packages
JEDEC TO-39

JEDEC TO-60

Molded-Si I icone
Plastic Package

Hermetic Stripline
Ceramic-to-Metal
Package

Coaxial Package

Semiconductor Materials,
Junctions, and Devices
devices are
SEMICONDUCTOR
small but versatile units that
can perform an amazing variety
of control functions in electronic
equipment. Like other electron
devices, they have the ability to
control almost instantly the
movement of charges of electricity. They are used as rectifiers,
detectors, amplifiers, oscillators,
electronic switches, mixers, and
modulators.
In addition, semiconductor devices have many important advantages over other types of
electron devices. They are very
small and light in weight (some
are less than an inch long and
weigh just a fraction of an
ounce). They have no filaments
or heaters, and therefore require
no heating power or warm-up
time. They consume very little
power. They are solid in construction, extremely rugged, free
from microphonics, and can be
made impervious to many severe
environmental conditions.

SEMICONDUCTOR MATERIALS
Unlike other electron devices,
which depend for their functioning on the flow of electric charges
through a vacuum or a gas, semiconductor devices make use of
the flow of current in a solid. In

general. all materials may be
classified into three major categories--conductors, semiconductors, and insulators-depending
upon their ability to conduct an
electric current. As the name indicates, a semiconductor material
has poorer conductivity than a
conductor, but better conductivity than an insulator.
The materials most often used
in semiconductor devices are
germanium and silicon. Germanium has higher electrical conductivity (less resistance to
current flow) than silicon, and is
used in many low- and mediumpower diodes and transistors.
Silicon is more suitable for highpower devices than germanium.
One reason is that it can be used
at much higher temperatures. A
relatively new material which
combines the principal desirable
features of both germanium and
silicon is gallium arsenide. When
further experience with this material has been obtained, it is expected to find much wider use in
semiconductor devices.

Resistivity
The ability of a material to
conduct current (conductivity)
is directly proportional to the
number of free (loosely held)

RCA Silicon Power Circuits Manual

electrons in the material. Good
conductors, such as silver, copper, and aluminum, have large
n umbers of free electrons; their
resistivities are of the order of
a few millionths of an ohm-centimeter. Insulators such as glass,
rubber, and mica, which have
very few loosely held electrons,
have resistivities as high as several million ohm-centimeters.
Semiconductor materials lie in
the range between these two extremes, as shown in Fig. 1. Pure
germanium has a resistivity of
INCREASING RESISTIVITY10-3

10-&
OHM-CM

COPPER

103

shown in Fig. 2. Because such
a structure has no loosely held
electrons, semiconductor materials are poor conductors under
normal conditions. In order to
ELECTRON - PAIR BONOS

~
++

Figure 2.

Crystal lattice structure.

106
I

GERMANiuM SILICON GLASS

. - - - INCREASING CONDUCTIVITY

Figure 1. Resistivity of typical conductor,
. semiconductor, and insulator.

60 ohm-centimeters. Pure silicon
has a considerably higher resistivity, in the order of 60,000
ohm-centimeters. As used in
semiconductor devices, however,
these materials contain carefully
controlled amounts of certain impurities which reduce their
resistivity to about 2 ohm-centimeters at room temperature (this
resistivity decreases rapidly as
the temperature rises).

Impurities
Carefully prepared semiconductor materials have a crystal
structure. In this type of structure, which is called a lattice, the
outer or valence electrons of individual atoms are tightly bound
to the electrons of adjacent
atoms in electron-pair bonds, as

separate the electron-pair bonds
and provide free electrons for
electrical conduction, it would be
necessary to apply high temperature or strong electric fields.
Another way to alter the lattice structure and thereby obtain
free electrons, however, is to add
small amounts of other elements
having a different atomic structure. By the addition of almost
infinitesimal amounts of such
other elements, called "impurities", the basic electrical properties of pure semiconductor materials can be modified and
controlled. The ratio of impurity
to the semiconductor material is
usually extremely small, in the
order of one part in ten million.
When the impurity elements
are added to the semiconductor
material, impurity atoms take the
place of semiconductor atoms in
the lattice structure. If the impurity atoms added have the
same number of valence electrons as the atoms of the original
semiconductor material, they fit
neatly into the lattice, forming
the required number of electron-

Semiconductor Materials, Junctions, and Devices
pair bonds with semiconductor
atoms. In this case, the electrical
properties of the material are
essentially unchanged.
When the impurity atom has
one more valence electron than
the semiconductor atom, however, this extra electron cannot
form an electron-pair bond because no adjacent valence electron is available. The excess
electron is then held very loosely
by the atom, as shown in Fig. 3,
and requires only slight excitation to break away. Consequently,
the presence of such excess electrons makes the material a better conductor, i.e., its resistance
to current flow is reduced.
Impurity elements which are
added to germanium and silicon
crystals to provide excess electrons include phosphorus, arsenic, and antimony. When these
elements are introduced, the resulting material is called n-type
because the excess free electrons
have a negative charge. (It
should be noted, however, that

the semiconductor material is
not changed.)
A different effect is produced
when an impurity atom having
one less valence electron than
the semiconductor atom is substituted in the lattice structure.
Although all the valence electrons of the impurity atom form
electron-pair bonds with electrons of neighboring semiconductor atoms, one of the bonds
in the lattice structure cannot be
completed because the impurity
atom lacks the final valence electron. As a result, a vacancy or
"hole" exists in the lattice, as
shown in Fig. 4. An electron from
an adjacent electron-pair bond
may then absorb enough energy

\ t ..

SEMICONDUCTOR
ATOMS

VACANCY
(HOLE)

Figure 4.

IMPURITY
ATOM

Figure 3.

Lattice structure of n·type
material.

the negative charge of the electrons is balanced by an equivalent positive charge in the center
of the impurity atoms. Therefore, the net electrical charge of

Lattice structure of p-type
material.

to break its bond and move
through the lattice to fill the
hole. As in the case of excess
electrons, the presence of "holes"
encourages the flow of electrons
in the semiconductor material;
consequently, the conductivity is
increased and the resistivity is
reduced.
The vacancy or hole in the
crystal structure is considered to
have a positive electrical charge
because it represents the absence
of an electron. (Again, however,
the net charge of the crystal
is unchanged.)
Semiconductor

RCA Silicon Power Circuits Manual

material which contains these
"holes" or positive charges is
called p-type material. P-type
materials are formed by the addition of boron, aluminum, gallium, or indium.
Although the difference in the
chemical composition of n-type
and p-type materials is slight,
the differences in the electrical
characteristics of the two types
are substantial, and are very important in the operation of semiconductor devices.

P-N JUNCTIONS
When n-type and p-type materials are joined together, as
shown in Fig. 5, an unusual but
very important phenomenon occurs at the interface where the
two materials meet (called the
P- N JUNCTION
P-TYPE MATERIAL

HOLES

Figure 5.

N-TYPE MATERIAL

ELECTRONS

Interaction of holes and electrons
at p-n junction.

p-n junction). An interaction
takes place between the two
types of material at the junction
as a result of the holes in one
material and the excess electrons
in the other.
When a p-n junction is formed,
some of the free electrons from
the n-type material diffuse across
the junction and recombine with
holes in the lattice structure of
the p-type material; similarly,
some of the holes in the p-type
material diffuse across the junction and recombine with free

electrons in the lattice structure
of the n-type material. This interaction or diffusion is brought
into equilibrium by a small
space-charge region (sometimes
called the transition region or
depletion layer). The p-type material thus acquires a slight
negative charge and the n-type
material acquires a slight positive charge.
Thermal energy causes charge
carriers (electrons and holes) to
diffuse from one side of the p-n
junction to the other side; this
flow of charge carriers is called
diffusion current. As a result of
the diffusion process, however, a
potential gradient builds up
across the space-charge region.
This potential gradient can be
represented, as shown in Fig. 6,
by an imaginary battery connected across the p-n junction.
(The battery symbol is used
merely to illustrate internal effects; the potential it represents
is not directly measurable.) The
potential gradient causes a flow
of charge carriers, referred to as
drift current, in the opposite direction to the diffusion current.
Under equilibrium conditions,
the diffusion current is exactly
balanced by the drift current so
JUNCTION

I
I
P

I
I
I
I

I
I
I

I
I

-I}- J

- +

Figure 6.

IMAGINARY
SPACE - CHARGE
EQUIVALENT
BATTERY

Potential gradient across spacecharge region.

Semiconductor Materials, Junctions, and Devices
that the net current across the
p-n junction is zero. In other
words, when no external current
or voltage is applied to the p-n
junction, the potential gradient
forms an energy barrier that prevents further diffusion of charge
carriers across the junction. In
effect, electrons from the n-type
material that tend to diffuse
across the junction are repelled
by the slight negative charge induced in the p-type material by
the potential gradient, and holes
from the p-type material are repelled by the slight positive
charge induced in the n-type material. The potential gradient (or
energy barrier, as it is sometimes
called), therefore, prevents total
interaction between the two
types of materials, and thus preserves the differences in their
characteristics.

CURRENT FLOW
When an external battery is
connected across a p-n junction,
the amount of current flow is determined by the polarity of the
applied voltage and its effect on
the space-charge region. In Fig.
7 (a), the positive terminal of
the battery. is connected to the
n-type material and the negative
terminal to the p-type material.
In this arrangement, the free
electrons in the n-type material
are attracted toward the positive
terminal of the battery and
away from the junction. At the
same time, holes from the p-type
material are attracted toward
the negative terminal of the battery and away from the junction.
As a result, the space-charge region at the junction becomes
effectively wider, and the potential gradient increases until it

approaches the potential of the
external battery. Current flow is
then extremely small because no
voltage difference (electric field)
exists across either the p-type or
the n-type region. Under these
conditions, the p-n junction is
~aid to be reverse-biased.
ELECTRON FLOW

.-----i'I

'11I

'1-----,
I

':.+.;

-II',I-+-------'

L -_ _ _ _ _ _

(a)

REVERSE BIAS

ELECTRON FLOW

.-----i'

•

1: _--,J
N

'1-----,

L'--_-III-'---l-I

L:I~+J

1'11-_-------'

'--_ _ _ _-:-1+

(bJ FORWARD BIAS
Figure 7.

Electron current flow in biased
p·n junctions.

In Fig. 7 (b), the positive
terminal of the external battery
is connected to the p-type material and the negative terminal
to the n-type material. In this
arrangement, electrons in the
p-type material near the positive
terminal of the battery break
their electron-pair bonds and enter the battery, creating new
holes. At the same time, electrons from the negative terminal

RCA Silicon Power Circuits Manual

of the battery enter the n-type
material and diffuse toward the
junction. As a result, the spacecharge region becomes effectively narrower, and the energy
barrier decreases to an insignificant value. Excess electrons
from the n-type material can
then penetrate the space-charge
region, flow across the junction,
and move by way of the holes in
the p-type material toward the
positive terminal of the battery.
This electron flow contiiJ.Ues as
long as the external voltage is
applied. Under these conditions,
the junction is said to be forward-biased.
The generalized voltage-current characteristic for a p-n junction in Fig. 8 shows both the

CURRENT(mAli
FORWARD
CURRENT

REVERSE
CURRENT

Figure 8.

!CURRENT(~Al

Voltage-current characteristic for
a p-n junction.

N-P-N and P-N-P Structures
Fig. 7 shows that a p-n junction biased in the reverse direction is equivalent to a highresistance element (low current
for a given applied voltage), while
a junction biased in the forward
direction is equivalent to a lowresistance element (high current
for a given applied voltage). Because the power developed by a
given current is greater in a highresistance element than in a lowresistance element (P = PR),
power gain can be obtained in a
structure containing two such resistance elements if the current
flow is not materially reduced. A
device containing two p-n junctions biased in opposite directions
can operate in this fashion.
Such a two-junction device is
shown in Fig. 9. The thick end
layers are made of the same type
of material (n-type in this case),
and are separated by a very thin
layer of the opposite type of material (p-type in the device
shown). By means of the external
batteries, the left-hand (n-p)
junction is biased in the forward
direction to provide a low-resistance input circuit, and the righthand (p-n) junction is biased in
OUTPUT

reverse-bias and forward-bias regions. In the forward-bias region, current rises rapidly as the
voltage is increased and is relatively high. Current in the reversebias region is usually much
lower. Excessive voltage (bias)
in either direction is avoided in
normal applications because excessive currents and the resulting high temperatures may
permanently damage the semiconductor device.

Figure 9.

N-P-N structure biased for power
gain.

the reverse direction to provide a
high-resistance output circuit.
Electrons flow easily from the
left-hand n-type region to the cen-

Semiconductor Materials, Junctions, and Devices
ter p-type region as a result of
the forward biasing. Most of these
electrons diffuse through the thin
p-type region, however, and are
attracted by the positive potential
of the external battery across the
right-hand junction. In practical
devices, approximately 95 to 99.5
per cent of the electron current
reaches the right-hand n-type region. This high percentage of current penetration provides power
gain in the high-resistance output
circuit and is the basis for transistor amplification capability.
The operation of p-n-p devices
is similar to that shown for the
n-p-n device, except that the biasvoltage polarities are reversed, and
electron-current flow is in the opposite direction. (Many discussions of semiconductor theory
assume that the "holes" in semiconductor material constitute the
charge carriers in p-n-p devices,
and discuss "hole currents" for
these devices and "electron currents" for n-p-n devices. Other
texts discuss neither hole current
nor electron current, but rather
"conventional current flow", which
is assumed to travel through a
circuit in a direction from the
positive terminal of the external
battery back to its negative terminal. For the sake of simplicity,
this discussion will be restricted
to the concept of electron current
flow, which travels from a negative to a positive terminal.)

Types of Devices
The simplest type of semiconductor device is the diode, which
is represented by the symbol
shown in Fig. 10. Structurally, the
diode is basically a p-n junction
similar to those shown in Fig. 7.
The n-type material which serves
as the negative electrode is re-

f.erred to as the cathode, and the
p-type material which serves as
the positive electrode is referred
to as the anode. The arrow symbol llsed for the anode represents

Figure 10.

Schematic symbol for a semi·
conductor diode.

the direction of "conventional current flow" mentioned above; electron current flows in a direction
opposite to the arrow.
Because the junction diode conducts current more easily in one
direction than in the other, it is
an effective rectifying device. If
an ac signal is applied, as shown
in Fig. 11, electron current flows
freely during the positive half
cycle, but little or no current

LOAn

Figure 11.

Simple diode rectifying circuit.

flows during the negative half
cycle.
One of the most widely used
types of semiconductor diode is
the silicon rectifier. These devices
are available in a wide range of
current capabilities, ranging from
tenths of an ampere to several
hundred amperes, and are capable of operation at voltages as
high as 1000 volts or more.
Parallel and series arrangements

RCA Silicon Power Circuits Manual

of silicon rectifiers permit even
further extension of current and
voltage limits. These devices are
discussed in detail in the section
on Silicon Rectifiers.
If two p-type and two n-type
semiconductor materials are arranged in a series array that consists of alternate n-type and ptype layers, a device is produced
which behaves as a conventional
rectifier in the reverse direction
and as a series combination of an
electronic switch and a rectifier
in the forward direction. Conduction in the forward direction can
then be controlled or "gated" by
operation of the electronic switch.
These devices, called thyristors,
have control characteristics similar to those of thyratron tubes.
The silicon controlled rectifier
(SCR) and the triac are the most
popular types of thyristors. Fig.

EMITTER

"'J;:

~"!:'",.

Figure 13.

u"TE

:ANODE (CASEI

I
IN"

MAIN

~IGN::rLEI

TERM~·~·':r
~T''''
l.!:/!..l.-:;-'---'--~N
TERMINAL
MAIN

TRIAC

12 shows the junction diagrams
and schematic symbols for the
SCR and triac. Such devices are
discussed in the section on
Thyristors.
" Several variations of the basic
junction-diode structure have been
developed for use in special applications. One of the most important
of these developments is the tunnel diode, which is used for amplification, switching, and pulse
generation. This special diode is
described in the RCA TRANSISTOR MANUAL SC-13 and in
greater detail in the RCA TUNNEL DIODE MANUAL TD-30.
When a second junction is added
to a semiconductor diode to provide power or voltage amplification (as shown in Fig. 9), the
resulting device is called a transistor. The three regions of the
device are called the emitter, the
base, and the collector, as shown
in Fig. "13. In normal operation,

~ERMINAL I

~- ""

MAIN TERMINAL2
(CASEl
Figure 12. Junction diagrams and
schematic symbols for SeR's and triacs.

BASE

COLLECTOR

Functional diagram of transistor
structure.

the emitter-to-base junction is
biased in the forward direction
and the collector-to-base junction
in the reverse direction.
Different symbols are used for
n-p-n and p-n-p transistors to
show the difference in the direction of current flow in the two
types of devices. In the n-p-n
transistor shown in Fig. 14 (a),
electrons flow from the emitter to
the collector. In the p-n-p transistor shown in Fig. 14 (b), electrons
flow from the collector to the emitter. In other words, the direction
of electron current is always opposite to that of the arrow on

Semiconductor Materials, Junctions, and Devices
the emitter lead. (As in the case
of semiconductor diodes, the arrow indicates the direction of
"conventional current flow" in the
circuit.)
The first two letters of the
n-p-n and p-n-p designations indiCOLLECTOR

EMITTER

(0) N-P-N TRANSISTOR

EMITTER

COLLECTOR

(b) P-N-P TRANSISTOR

Figure 14.

Schematic symbols for
transistors.

cate the respective polarities of
the voltages applied to the emitter
and the collector in normal operation. In an n-p-n transistor, the
emitter is made negative with respect to both the collector and the
base, and the collector is made
positive with respect to both the
emitter and the base. In a p-n-p
transistor, the emitter is made
positive with respect to both the
collector and the base, and the collector is made negative with respect to both the emitter and the
base.
The transistor, which is a threeelement device, can be used for a
wide variety of control functions,
including amplification, oscillation, and frequency conversion.
Power-transistor characteristics
and ratings are discussed in detail in the section on Silicon
Power Transistors.

Silicon Rectifiers

SILICON rectifiers can be operated at ambient temperatures
up to 200°C and at current levels
of hundreds of amperes and voltage levels as high as 1000 volts.
In addition, parallel or series arrangements of two or more rectifiers can be used to provide even
higher current or voltage capabilities. Because of their high
forward-to-reverse current ratios,
silicon rectifiers can achieve rectification efficiencies greater than
99 per cent. The rectifiers are very
small and lightweight, and can be
made highly resistant to shock
and other severe environmental
conditions. In addition, they have
excellent life characteristics which
are not affected by aging, moisture, or temperature.

THEORY OF OPERATION
The operation of a silicon rectifier can be conveniently explained
by analysis of the flow of charge
carriers across the p-n junction
under both forward- and reversebias conditions. Alternatively, an
analysis of the potential distribution in the junction for each bias
condition may be used to predict
the behavior of the rectifier.
In a silicon rectifier, the regions adjacent to the metal contacts are heavily doped, one with
p-type dopant and the other with
n-type dopant, to ensure that

nonrectifying ohmic contacts are
formed at the silicon-to-metal
interfaces. A rectifying junction
should exist only within the silicon, at the interface of the ntype and p-type regions. A lightly
doped n-type region between the
heavily doped n- and p-type regions provides the high blocking-voltage capability required
of the rectifier. Because of this
lightly doped region, the more
heavily doped n-type region adjacent to the metal contact is
referred to as the n + region. The
silicon rectifier, therefore, is a
p-n-n + structure.

Carrier-Flow Analysis
The theory of operation of
p-n-n + silicon junctions can be
visualized by use of the diagrams
shown in Fig. 15. In these diagrams, free electrons are represented by dots and free holes by
circles; the movements of electrons and holes are indicated by
arrows.
In equilibrium, as shown in Fig.
15 (b), each region of the crystal
contains approximately the same
number of free electrons or free
holes as the amount of donor
impurities or acceptor impurities,
respectively. The p-type region
contains only holes, the n-type region contains only electrons, and
the metal contacts contain both

Silicon Rectifiers
holes and electrons. The nature of
the metal-to-semiconductor ohmic
contact is such (as explained
later) that only electrons can go
from the metal into the n-type
semiconductor, and only holes can
go from the metal to the p-type
METAL
(CATHODE

METAL
(ANODE

(01 JUNCTION

DIAGRAM

(bl EQUILIBRIUM CONDITION

- -.
(el REDISTRIBUTION OF CHARGE CARRIERS
WHEN REVERSE BIAS IS APPll ED

(d) REVERSE·BIAS CONDITION

(el fORWARD·BIAS CONDITION

Figure 15. Concentrations of electrons
(dots) and holes (circles) in a silicon
rectifier.

semiconductor. The resulting behavior under forward- or reversebias conditions is as follows:
Reverse-Bias Operation-When
a reverse bias is applied (positive

voltage to the n-type region and
negative voltage to the p-type region), a nonequilibrium distribution of holes and electrons occurs
because a region around the p-n
junction is depleted of free charge
carriers. This redistribution occurs because electrons are attracted by the positive voltage
applied to the n-type region and
holes are attracted by the negative voltage applied to the p-type
region so that they are displaced
from the equilibrium positions, as
shown in Fig. 15 (c). The net result is that carriers move away
from both sides of the junction to
create a depletion region or
space-charge region which can
withstand the applied voltage
without further current flow, as
shownin Fig. 15 Cd). Only a very
small leakage current flows because, as noted above, holes from
the metal cannot enter the n-type
region and electrons from the
metal cannot enter the p-type region. This leakage current can be
attributed to thermal generation
of electron-hole pairs within the
depletion layer, as indicated in
Fig. 15 Cd).
Forward -Bias Operation-The
junction is forward-biased when
a positive voltage is applied to the
p-type region and a negative voltage is applied to the n-type region. This bias causes holes and
electrons to move toward and
across the junction. As a result,
the concentration of free charge
carriers in the central region of
the junction is greatly increased,
as shown in Fig. 15(e). Holes
from the left metal contact can
freely enter the p-type region, and
electrons from the opposite metal
contact can freely enter the n-type
region. An abundant supply of
holes and electrons is available,

RCA Silicon Power Circuits Manual

therefore, to replace those, that
move across the junction.

Potential-Hill Analysis
The operation of p-n-n + silicon
junctions may also be visualized
in terms of the potential-energy
diagrams shown in Fig. 16. In
these diagrams, the vertical scale
represents energy. An increase in
electron energy is indicated by the
upward direction from the Fermi
energy level (EF line), and an increase in hole energy is indicated
by the downward direction from
this level. Electrons are always
above the EF line and holes are
always below this line, which represents the ground state or zero
energy level for both types of carriers. Both electrons and holes
tend to "fall" toward this level
unless there is some source of energy to move them away from it.
Thermal energy from the silicon
crystal is one source of energy
that normally causes some of the
carriers to be displaced above and
below the Fermi level, as shown in
Fig. 16 (b).
In the metal contacts, holes and
electrons exist side by side because
there is no forbidden-energy region. In the semiconductor material, however, the Fermi level
lies within a forbidden-energy
region which cannot be penetrated
by holes or electrons. In the ntype semiconductor, the Fermi
level lies near the top of the forbidden-energy region, and there
is ample space for free electrons
to move about. There are no holes
in the n-type region, however, because more energy is required to
force the holes below the forbidden-energy region than can be
supplied by the thermal effects.
Similarly, in the p-type region, the
Fermi level lies close to the bot-

tom of the forbidden-energy region. The holes, therefore, can
easily obtain enough thermal energy to get below this region, but
electrons cannot obtain enough
energy to get above it. As a result,
only holes can enter the p-type

METAL
(CATHODE
CONTACT)

(0) JUNCTION DIAGRAM

..... :.
FORBIDDENENERGY
REGION

(b) EQUILIBRIUM CONDITION

~:-=:~"""""41M',;;.., E

'. F

(e) REVERSE-BIAS CONDITION

- . -.-.... ....... , ,.. ·.. ·.::EF
!
E+" : :•• ' :.

FORBIDDEN-ENERGY
• .. • ...

~:GION

I ••
I

(d) FORWARD·BIAS CONDITION

Figure 16. Potential-hill diagrams for various stages of rectifier operation (upward
direction indicates increasing electron energy; downward direction indicates increasing hole energy).

region from the metal, and only
electrons can enter the n-type region from the metal. Holes can
freely circulate between the metal
and the p-type region, but elec-

Silicon Rectifiers
trons are excluded. Electrons can
freely circulate between the metal
and the n-type region, but holes
are excluded.
In visualizing the operation of
a silicon rectifier by use of the
potential-hill diagrams shown in
Fig. 16, the following factors must
be considered:
1. The shape of the forbiddenenergy region is rigid at the
metal-to-semiconductor contact. The shape is determined by the doping level
(or carrier concentration),
which is extremely high at
the contacts and cannot,
therefore, be changed by the
carriers injected or removed
by applied voltage or current.
2. The shape of the forbiddenenergy region is flexible at
the p-n junction because the
carrier concentration at the
junction is quite low and can
be readily influenced by addition or removal of carriers
by means of an applied bias.
The behavior under forward- and
reverse-biased conditions may
then be explained as follows:
Reverse-Bias Operation-Under reverse-bias conditions, the
potential energy of electrons is
increased on the negatively biased
side of the junction so that the
energy at this end is higher, as
shown in Fig. 16 (c). Although the
applied bias is such that it tends
to push electrons from the metal
into the p-type region and holes
from the metal into the n-type region, no current flows because the
rigidity of the forbidden-energy
region at the contacts prevents
such movements of the charge
carriers. The applied voltage simply increases the height of the
potential hill at the junction be-

15
cause there are no carriers available to move in the direction that
the field would cause them to
move. On both sides, the carriers
have an "uphill" climb to the
junction.
Forward -Bias Operation-The
application of a positive voltage
to the p-type region and a negative voltage to the n-type region
raises the electrons to a higher
potential energy on the n-type
side of the junction, as shown in
Fig. 16(d). This bias must alter
the shape of the forbidden-energy
region so that its ends meet the
changed energy levels of the
metals. Because the shape is
flexible only at the junction, the
applied bias causes the profile of
the forbidden-energy region to be
altered, as shown in Fig. 16 (d),
to reduce the height of the built-in
potential hill. As a result, many
electrons now have sufficient
thermal energy to get over the
hill, and many holes have sufficient
thermal energy to get under it.
Because the height of the hill is
equivalent to about one electronvolt, a forward bias of one volt is
sufficient to allow electrons and
holes to move unimpeded across
the junction; the current is then
limited only by the ohmic resistance of the external circuit.

CHARACTERISTICS
AND RATINGS
The characteristics data and the
ratings given in the manufacturer's specifications on silicon
rectifiers provide an important
guide to the selection of the proper
device for a given circuit application. Characteristics data provide
the information that a circuit
designer needs to predict the performance capabilities of his cir-

RCA Silicon Power Circuits Manual

cuit, and form the basis for the
ratings that define the safe operating limits for the rectifier.

Important Characteristics
Characteristics data given for
silicon rectifiers are based on the
manufacturer's determination of
the inherent qualities and traits
of the device. Characteristics are
usually directly measurable attributes. Of the various rectifier
characteristics for which data are
given, four of the most important
are thermal impedance, forwardvoltage drop, reverse (leakage)
current, and reverse recovery
time. These four characteristics
help determine the performance
and environmental capabilities and
limitations of rectifiers.

Thermal Impedance-Although
silicon rectifiers can operate at
high temperatures, the actual pellet of silicon which performs the
rectification is quite small and has
a very low thermal capacity. During normal operation, the rectifier
p-n junction dissipates approximately 1 watt of power for each
ampere of forward current. The
temperature of the junction rises
rapidly during high-current operation. An increase in junction temperature beyond rated capabilities,
as a result of either high currents
or excessive ambient temperatures, may cause rectifier failure,
either directly because of irreversible material damage as a result
of the high temperature or indirectly because of the effect of the
increased temperature on the reverse-blocking capability of the
rectifier, as described later .. The
heat dissipated in the silicon pellet must be removed rapidly;
therefore, so that the temperature
of the junction is not allowed to

rise above the safe operating
value of 200°C. For this reason,
the silicon pellet is mounted between heavy copper parts in a
symmetrical direct-soldered arrangement that results in uniform
distribution of thermal stresses,
mInImUm thermal fluctuations,
and low thermal resistance.
Fig. 17 shows a cross-sectional
diagram of a typical silicon rectifier. Because of the way in which
the rectifier is constructed, there

Figure 17. Cross·sectional diagram of a
typical silicon rectifier.

is always a thermal "drop" between the p-n junction and the
outside of the rectifier case. This
thermal "drop", which is analogous to the voltage drop across
the various components of an electrical circuit, is caused by the
thermal impedances of the various
components of the internal rectifier structure. These impedances
include both thermal resistance
and thermal capacitance. The
lower side of the silicon pellet is
soldered directly to a heavy copper
stud that provides a low-thermal-

Silicon Rectifiers
resistance path between the pellet
and the rectifier heat sink. The
upper side of the pellet is soldered
to a heavy copper block which, together with the stud, forms a
thermal capacitor.
During long periods of steadystate operation, the thermal capacitance becomes fully charged and
does not affect the operation of
the rectifier. For this reason,
thermal-capacitance values are not
included in manufacturers' specifications on silicon rectifiers. It
is important, however, that the
specifications include the thermal
resistance, expressed in °C per
watt, because this value is used,
together with the power dissipated by the rectifier, to determine the rise in junction
temperature above the case temperature.
The thermal capacitance incorporated into the rectifier structure becomes extremely important
when the rectifier junction is subjected to sudden changes in current, such as may occur during a
fault condition. This capacitance
absorbs heat produced by highcurrent pulses and allows the
heat to flow through the pellet
and stud (low-thermal-resistance
path) during periods of low current. In this way, fluctuations in
junction temperature are held to
a minimum.
Forward-Voltage Drop - The
major source of power loss in a
silicon rectifier arises from the
forward-conduction voltage drop.
This characteristic, therefore, is
the basis for many of the rectifier
ratings.
A silicon rectifier usually requires a forward voltage of 0.4 to
0.8 volt, depending upon the temperature and impurity concentration of the p-n junction, before

17
a significant amount of current
flows through the device. As shown
in Fig. 18, a slight rise in the
forward voltage beyond this point
causes a sharp increase in the forward current. The slope of the
voltage-current characteristic at
voltages above this threshold value
200

175

/ 'II
II II I

100

~ 75

0::

~ 50

o
Figure 18.

1//11125
y
200 C (/1I/ooc
Ilcio~J /J
Ii 1/ r
A/I1.0J /.5
0

fi!

0.5

FORWARD VOLTAGE-V

2.0

Typical forward characteristics
of a silicon rectifier.

represents the dynamic resistance
of the rectifier. Losses that result
from this resistance characteristic increase as the square of the
current and thus increase rapidly
at high current levels. The dynamic resistance is dependent
upon the construction of the rectifier junction and is inversely
proportional to the area of the
silicon pellet.
Fig. 18 also shows that, at any
reasonable current level, the value
of forward voltage required to
initiate current flow through the
rectifier decreases as the temperature of the rectifier junction increases. This voltage-temperature
dependence has a compensatory effect in rectifiers operated at high
currents, but it is a source of difficulty when rectifiers are operated
in parallel.
Reverse Current-When a reverse-bias voltage is applied across
a silicon rectifier, a limited amount

RCA Silicon Power Circuits Manual

of reverse-blocking current flows
through the rectifier. This current
is in the order of only a few
microamperes, as compared to the
milliamperes or amperes of forward current produced when the
rectifier is forward-biased. Initially, as shown in Fig. 19, the
reverse current increases slightly
as the blocking voltage increases,

Figure 19.

Typical reverse characteristics
of a silicon rectifier.

but then tends to remain relatively constant, even though the
blocking voltage is increased significantly. The figure also indicates
that an increase in operating temperature causes a substantial increase in reverse current for a
given reverse voltage. Reverseblocking thermal runaway may occur because of this characteristic
if the reverse dissipation becomes
so large that, as the junction temperature rises, the losses increase
faster than the rate of cooling.
If the reverse blocking voltage
is continuously increased, it eventually reaches a value (which
varies for different types of silicon rectifiers) at which a very
sharp increase in reverse current
occurs. This voltage is called the
breakdown or avalanche (or
Zener) voltage. Although rectifiers can operate safely at the
avalanche point, the rectifier may
be destroyed as a result of thermal
runaway if the reverse voltage increases beyond this point or if

the temperature rises sufficiently
(e.g., a rise in temperature from
25·C to 150·C increases the current by a factor of several hundred) .
Reverse-Recovery Time-After
a silicon rectifier has been operated under forward-bias conditions, some finite time interval (in
the order of a few microseconds)
must elapse before it can return
to the reversecbias condition. This
reverse-recovery time is a direct
consequence of the greatly increased concentration of charge
carriers in the central region that
occurs during forward-bias operation. If the bias is abruptly reversed, these carriers abruptly
change direction and move out in
the reverse direction. Because
there is a finite number of these
carriers in the central region, and
there is no source of additional
charge carriers to replace those
that are removed, the device will
eventually go into the reversebias condition. During the removal
period, however, the charge carriers constitute a reverse current
known as the reverse-recovery
current.
The reverse-recovery time imposes an upper limit on the frequency at which a silicon rectifier
may be used. Any attempt to operate the rectifier at frequencies
above this limit results in a significant decrease in rectification
efficiency and may also cause
severe overheating and resultant
destruction of the rectifier because of power losses during the
recovery period.

Ratings
Ratings for silicon rectifiers
are determined by the manufacturer on the basis of extensive

Silicon Rectifiers

testing. These ratings express the
manufacturer's judgment of the
maximum stress levels to which
the rectifiers may be subjected
without endangering the operating
capability of the unit. The following list includes various factors for which silicon rectifiers
must be rated: peak reverse
voltage, forward current, surge
(or fault) current, operating
and storage temperatures, amperes squared-seconds, and mounting torque.
Peak Reverse Voltage-Peak
reverse voltage (PRV) is the rating used by the manufacturer to
define the maximum allowable reverse voltage that can be applied
across a rectifier. This rating is
less than the avalanche breakdown
level on the reverse characteristic. With present-day diffused
junctions, the power dissipation at
peak reverse voltage is a small
percentage of the total losses in
the rectifier for operation at the
maximum rated current and temperature levels. The reverse dissipation may increase sharply,
, however, as temperature or blocking voltage is increased to a point
beyond that for which the device
is capable of reliable operation.
It is important, therefore, to operate within ratings.
A transient reverse voltage rating may be assigned when it has
been determined that increased
voltage stress can be withstood
for a short time duration provided
that the device returns to normal
operating conditions when the
overvoltage is removed. This condition is illustrated in Fig. 20.
Peak-reverse voltage ratings for
single-junction silicon rectifiers
range from 50 to 1500 volts and
for mUltiple-junction silicon-recti-

fier stacks may be as high as several hundred thousands of volts.

--f---------

--t-r ---- -TRANSIENT PRV

L._ REPETITIVE

PRV

Figure 20. Typical waveform of repetitive
and transient reverse voltal1es applied
across a silicon rectifier.

Forward Current-The current
rating assigned to a rectifier is
expressed as a maximum value of
forward current at a specific case
temperature. For these conditions,
the power dissipation and internal
temperature gradient through the
thermal impedance from junction
to case are such that the junction
is at or near the maximum operating temperature for which the
blocking-voltage rating can be
maintained. At current levels
above this maximum rating, the
internal and external leads and
terminals of the device may experience excessive temperatures,
regardless of the heat sink provided for the pellet itself. The
current rating can be described
more fully in the form of a curve
such as that shown in Fig. 21.

TYPE OF OPERATION:
A-DIRECT CURRENT
B-SINGLE PHASE
C-THREE PHASE
D-SIX PHASE
A

r-...
..It 1'--."
sp:...C
D f""'...: 1"-..""
3

r- I'" ~

2
1

950

160

"'"

----

170
180
190 200 210 220
CASE TEMPERATURE - ·C

Figure 21. Currellt rating chart ·for a 12·
ampere silicon rectifier.

RCA Silicon Power Circuits Manual

Because the current through a
rectifier is not normally a smooth
flow, current ratings are usually
expressed in terms of average current (Iayg) , peak current (Ipk) ,
and rms current (Irm.). Each of
these currents may be expressed
in terms of the other two currents.
The average current through a
rectifier in half-sine-wave service
is related to the peak current by
the following equation:

_ [1..1071" Ipk sin wt dCwt)]

Iavg -

I
Ip k
7r

(Ia)

Iavg

(Ib)

or
Ipk

= 7r

The relationship between the
peak current and rms current of
a rectifier in half-sine-wave service can be expressed as follows:

[
I rm •

10" Ipk2 sin2 wt dcwt)]l
+ i 0 dCwt)l

27r

=! Ipk

(2a)

or
Ipk

2 I rm•

(2b)

Table I-Relationship of Iavg, I rm .,
and Ipk
Ipk
1T Iavg
3.14 Iavg
Iavg
(1/1T) Ipk
0.32 Ipk
Ipk = 2 Irms
I rm"
'h Ipk
Iavg
(2/1T) Irma
0.64 Irma
I rm •
(1T /2) Invg
1.57 Iavg

=
=
=
=
=

=
=

Published data for rectifiers
usually list maximum limits for
average current and for repetitive
peak current. The maximum average forward-current rating is·
the maximum average value of
current that is allowed to flow
through the rectifier in the forward direction under stated conditions. The repetitive peak
forward-current rating is the
maximum instantaneous value of
repetitive forward current permitted under stated conditions.
The dual maximum ratings are
required because, under certain
conditions (e.g., when a high
capacitive load is used), it is possible for the average current to
be low and for the peak current
to be high enough to cause overheating of the rectifier. The approximate expression for power
losses P in a silicon rectifier,
given by the following equation,
can be used to explain how this
type of operation is possible:
P (watts)

=
(Vde Ide)

Table I summarizes the relationships expressed by Eqs. (1)
and (2). As discussed later, certain of these relationships are
used to determine the power dissipated in a rectifier. The relationships for average, peak, and
rms currents are applicable only
when the rectifier is used in halfsine-wave service.

+ (Irms2 Rdyn )

(3)

where the voltage Vile is 0.4 to
0.9 volt depending upon the junction temperature; the direct current Ide is equivalent to the average current Iavg; the current I rm •
is the true rms current and, for
a fixed average current, increases
as the peak current increases;
and Rdyn is the dynamic resistance

Silicon Rectifiers

of the rectifier over the current
range considered.
An analysis of Eq. (3) shows
that if the peak current is increased and the conduction time
is decreased so that the average
current is held constant, the rms
current and, therefore, the power
dissipated in the rectifier CIrms 2
R dyn ) are also increased. This behavior explains why the maximum
permissible value of average current in multiple-phase circuits is
reduced as the number of phases
is increased and the conduction
period is reduced. Fig. 21 shows
the effect of the number of phases
on the variation in average current with case temperature.

used to limit the duration of the
surges. In some cases, a rectifier
that has a higher surge rating
than average current requirements
indicate to be necessary may be
used to meet surge requirements
UPPLY' 60 Hz SINE WAVE
CASE TEMPERATURE =150' C
RESISTIVE OR INDUCTIVE LOAD

"'"

f---

25C f - - - RMS ~m·Ju~~~~ED VALUE

r--

""- ~

AVERAGE FORWARD CURRENT=
MAXIMUM RATED VALUE

200

""-

"""'-.... ..........
2

•

SURGE-CURRENT DURATION-CYCLES

•

100

(a)

Surge Current-A third maximum-current limit given in the
manufacturer's data on silicon
rectifiers is the surge (or fault)
current rating. During operation,
unusually high surges of current
may result from in-rush current
at turn-on, load switching, and
short circuits. A rectifier can absorb a limited amount of increased
dissipation that results from
short-duration high surges of current without any effect except a
momentary rise in junction temperature. If the surges become
too high, however, the temperature of the junction may be raised
beyond the maximum capability
of the device. The rectifier may
then be driven into thermay runaway and, consequently, be destroyed. Fig. 22 (a) shows a typical surge-current rating curve
for a silicon rectifier.
If the value and duration of
anticipated current surges exceed
the rating of the rectifier, impedance may be added to the circuit to limit the magnitude of the
surge current, or fuses may be

4
I

!
u

[\A

I00

8
6

'\\
'\
,,\:

r" .... ~
-..........:
0.01

0.1

::::-

1.0

SURGE DURATION-S

(b)

Figure 22. (a) Peak-surge-current rating
chart for a 12-ampere silicon rectifier;
(b) coordination chart that relates rectifier
surge-current ratin~ (curve A), opening
characteristics of circuit fuses (curve B),
and maximum available surge current in
a circuit (curve C).

of the circuit. This technique
eliminates the need for additional
circuit impedance elements or
special fusing.
If fuses are used to protect the
rectifiers, a coordination chart,
such as that shown in Fig. 22(b),
should be constructed. This chart
shows the surge rating of the rectifier (curve A), the opening char-

RCA Silicon Power Circuits Manual

acteristics of the fuse (curve B),
and the maximum surge current
available in the circuit (curve C).
In the construction of a coordination chart for a particular rectifier, the rms value of the surge
current can be obtained from a
universal surge-rating chart, such
as that shown in Fig. 23. The
opening characteristics of the fuse

For half-wave service, the peak
surge current (Is = I pk ) can be
converted to rms current by use
of the relationships given in
Table I, as follows:

137.6
-2-' or 68.8 amperes

600

500

i 40 1\
~

40A

l:!0:: 30o \

::>

::;
0::

10or---..

t--

0
0.01

VI 120A

~:2A
-<"I I 15A

lO.5A

~_r2

0.1
SURGE DURATION-S

Note: The rms current given by this curve is a
partial surge rating and should be added to the
normal rms current to determine the total surge

rating.

Figure 23. Universal surge-current rating
chart for RCA silicon rectifiers.

can be obtained from the manufacturer's published data, and the
maximum surge current can be
calculated.
The coordination chart shown
in Fig. 22 (b) was prepared for a
12-ampere silicon rectifier operated in half-wave service from a
220-volt rms ac source and protected by a fuse having opening
characteristics as shown by
curve B. If the total shortcircuit impedance of all the rectifier elements is determined to
be 2.25 ohms, the peak surge
current Is for full-wave operation can be calculated as follows:
I _ 220 Vrms X 1.41
s 2.25
=

137.6 amperes

Curve A of Fig. 22 (b), which is
merely a reproduction of the 12ampere curve on the universal rating chart shown in Fig. 23, gives
the surge-current rating of the
12-ampere silicon rectifier, but
does not consider the normal rms
value of current that the rectifier
can handle. This normal value of
rms current must be subtracted
from the total surge current to
determine the actual overcurrent
of the fault. First, the relationships in Table I are used to convert the average-current rating of
the rectifier to the normal rms
value, as follows:
I rms

1.57 Iavg

1.57 X 12, or 18.8 amperes

The overcurrent is then determined from the following calculation:
IBurge - Inormal

68.8 -18.8,

or 50 amperes
The 50-ampere fault current is
represented on the coordination
chart in Fig. 22 (b) by the
straight-line curve C. The 12ampere rectifier can sustain a
fault current of this magnitude
for 51 milliseconds, as indicated

Silicon Rectifiers
by the point of intersection of
curves A and C. The fuse, however, opens and interrupts the
flow of current in the circuit
after 43 milliseconds, as indicated by the point of intersection of curves Band C, and the
rectifier is protected.
Amperes Squared-Seconds (Pt)
-The amperes squared-seconds
rating of a silicon rectifier provides information on the maximum subcycle surge current that
the rectifier can sustain when it
is used with extremely fast circuit-interrupting devices or is
operated in nonsinusoidal rectifier
applications. In the manufacturer's published data, the rating
is usually given for operation at
60 Hz and is calculated from the
maximum peak surge current that
the rectifier can sustain over the
period of one cycle (16.67 milliseconds), as follows:
J2t

(one-CYcle surg~-current rating) 2
X 16.67 X 10-3

I=Jf
=

(5)

1240 amperes squared-seconds

'\J

3 X 10- 3 seconds

283 amperes

If a half-cycle sine wave of cur-

rent is passed through the rectifier instead of the square wave of
current, the peak value of the
maximum permissible current is
determined by use of the relationship in Table I, as follows:

(4)

The peak value of surge current
that can be sustained by a 12ampere silicon rectifier is given
by the curve shown in Fig. 22 (a)
as 240 amperes. The amperes
squared-seconds rating for the
rectifier is then determined from
the following calculation:

J2t

maximum surge current can be
calculated for any time between
0.83 millisecond and 8.3 milliseconds (i.e., from 5 to 50 per
cent of the period of one cycle).
For example, if a square wave of
current is to be passed through
the 12-ampere rectifier for 3 milliseconds, the maximum current
that can be tolerated is determined
as follows:

e~o

240 amperes squared-seconds

X 16.67 X 10-3

From the value obtained for
the Pt rating, the rms value of the

I pk

2 I rms

2 X 283, or 566 amperes

SERIES AND PARALLEL
RECTIFIER ARRANGEMENTS
Two or more silicon rectifiers
can be used in parallel or series
arrangements to extend current
and voltage capabilities beyond
the limits attainable from a single
rectifier. Some basic considerations for multiple connections of
silicon rectifiers are discussed in
the following paragraphs.

RCA Silicon Power Circuits Manual

Parallel Arrangements
When two or more silicon rectifiers are connected in parallel,
the current-handling capability of
the combined units is substantially
greater than that of a single rectifier of the same type. It is often
more practical, however, to obtain
the greater current capability by
use of a multi phase circuit or by
selection of a single higher-current rectifier, if available, that
can provide the capabilities required.
When rectifiers are to be used
in parallel arrangements, the main
concern is the forward-voltage
characteristics of the rectifiers
selected. If the forward-voltage
characteristics of the rectifiers are
not closely matched, an unbalance
in the current division among the
rectifiers occurs. The rectifier that
has the lower forward-voltage
drop receives a larger share of
the total current. The higher current causes a greater heating of
this rectifier which further increases the current. This regenerative effect can result in destruction of the rectifier and can lead
to progressive destruction of all
the rectifiers in the parallel array. In parallel operation of
silicon rectifiers, therefore, the
circuit configuration should assure
that the rectifiers receive equal
shares of the total current, forward-voltage characteristics of
the rectifiers should be closely
matched, or a combination of
both techniques should be used.
An equal division of current
among the rectifiers can be fOl'ced
by use of resistors or balancing
inductors in series with each rectifier. The major disadvantage to
the use of series resistors is that
they introduce large power losses

that reduce rectifier efficiency. The
major disadvantage of balancing
reactors is the relatively high cost
of these components.
The best method to assure equal
division of current through parallel rectifiers is to select rectifiers
on the basis of the match in their
forward-voltage
characteristics.
This selection can be made more
easily when a large number of
parallel circuits is to be constructed, because the rectifiers can
then be graded into different voltage-drop categories and units
from only one category selected
for a given parallel circuit. Because the forward voltage drop of
a silicon rectifier is dependent
upon the temperature, rectifiers
used in a parallel array should be
maintained at the same temperature. One technique that may be
used to assure that temperature
deviations among the rectifiers
will be held to a minimum is to
mount all the units in the parallel
array on the same heat sink.
When silicon rectifiers are connected in parallel arrangements,
all contacts should have a low resistance, the wires used should be
large enough so that their resistance is negligible, and in highcurrent arrays the wiring should
be arranged so that a mIlllmum
unbalance in inductive effects is
achieved.

Series Arrangements
Two or more silicon rectifiers
may be connected in series arrangements when voltage requirements exceed the capabilities of
a single rectifier. The main con"
cern when rectifiers are to be
operated in series is that the reverse voltage be divided equally
across each rectifier. The use of

Silicon Rectifiers
resistance-capacitance equalizing
networks and the selection of rectifiers that have matched reverse
characteristics are the two most
common techniques employed to
assure equal voltage division.
These techniques are discussed in
greater detail later in connection
with High-Voltage Rectifier Assemblies.
A third technique that may be
employed when rectifiers are connected in series is the use of
transformers that have multiple
secondary windings. Each secondary winding is connected across
one of the rectifiers in the series
array. This technique is practical
when only a few rectifiers are to
be connected in series. For a large
number of rectifiers, the cost and
complexity of the multiple-secondary approach become prohibitive.

HIGH-VOLTAGE
RECTIFIER ASSEMBLIES
A series-stack arrangement of
rectifier units is used when voltages higher than those obtainable
from a single rectifier are required. Several methods have been
used to equalize the voltage distribution across series rectifiers for high-voltage assemblies.
Among these methods the two
most common are RC compensation and selection of matched rectifiers for uncompensated assemblies.

RC·Compensated Assemblies
In the RC-compensated highvoltage stack, a resistor and a capacitor are placed across each
rectifier unit. These resistors and
capacitors force an equal division
of reverse voltage across each unit
in the series string if their values
are chosen so that, under all op-

erating conditions, these components, and not the rectifiers,
control the distribution of the voltage. The resistors control the voltage division during dc operation.
The capacitors control the voltage
division during high-frequency operation or when transient voltages
are applied. Both the. resistor and
the capacitor control the voltage
division during normal low-frequency operation.
The stray capacitance from the
rectifiers to ground, C" in Fig. 24,
tends to cause an unequal distribution of voltage across the rectifiers. The disruptive effect of
this stray capacitance is one rea-

o~~~
c~ c~ c~ c~

II TI T
I

T'I
I

_..L_-L _..L __ .L_

_.1. __

GROUND PLANE

Figure 24. High-voltage rectifier assembly
using shunt capaCitors (C,) to compensate
for stray capacitances (Cg) and to equalize
the reverse-recovery times of the
rectifier un its.

son for the use of a shunt capaci·
tor Cs across each rectifier.
The effect of the stray capacitance is greatest during transient
conditions. When a step reverse
voltage is applied to the rectifier
terminal farthest from ground,
most of this voltage appears
across the first rectifier in the
series stack. This condition occurs
because the junction capacitance
of that rectifier is small and has
a large reactance compared to the
capacitance to ground of the remainder of the rectifiers in the
stack. If a shunt capacitor C"
which is large in comparison to
the stray capacitance C", is connected across each rectifier, an

RCA Silicon Power Circuits Manual

equal voltage distribution can be
firmly established among all the
rectifiers in the series stack.
The shunt capacitors are also
used to equalize reverse-recovery
time. As mentioned in the section
on Characteristics and Ratings,
reverse recovery of a rectifier is
basically the result of two effects:
(1) minority carriers are swept
out of the junction by reverse current, and (2) minority carriers
recombine in. the junction area.
Of these two effects, the faster one
is the sweeping out of minority
carriers by reverse current.
In any string of rectifiers, the
reverse' recovery time of the individual units differs slightly. If
the rectifiers are not specially
graded for recovery times, then
those units which recover first
must either block the total reapplied voltage or pass reverse
current. When these faster units
recover, they stop the flow of reverse current and thereby slow
down the recovery time of the remaining units. The shunt capacitors bypass reverse current
around the recovered rectifiers
and thereby speed up the recovery of the slower rectifiers.

Uncompensated Rectifier
Assemblies
In an uncompensated high-voltage rectifier stack, the characteristics of the series rectifiers are
matched to provide an equal division of voltage among individual
units in the stack. The characteristiCs considered for this voltage
division are reverse-recovery time,
avalanche voltage, and reversedissipation capability. The effects
of these characteristics are all
interrelated and must be considered together.

When rectifiers have been sorted
into recovery-time groupings, they
can be used more reliably in series
arrangement because all of them
will recover their blocking ability
at about the same time. Any
charge which flows into the capacitance Cg is partially supplied
while all the rectifiers are still in
an "ON" state. Any current that
flows during this time passes
through units which are in a lowimpedance state; the power dissipated across them, therefore, is
small. In addition, if all the units
have matched recovery-time characteristics, the main mode of reverse reGovery results from a
sweeping out of minority carriers,
and all the rectifiers recover by
the faster recovery method. Any
unbalance in recovery time is
small, therefore, and the units
which recover first have to block
excess voltage for only a very
short period of time.
A rectifier in an externally uncompensated series stack that recovers before the other rectifiers
in the stack immediately begins to
block all the voltage; as a result,
the blocking-voltage capability of
this rectifier may be exceeded
sufficiently to cause failure of the
device.
In effect, matching of recoverytime and avalanche characteristics
of rectifiers performs the same
function as the capacitor and resistor in RC-compensated series
stacks. The reverse-dissipation
capability of the rectifier takes
the place of the capacitor in the
RC-compensated series stack.· The
use of matched avalanche characteristics provides the same .results
as the compensating resistor during dc operation. The match in
the reverse-dissipation capability
of the rectifiers assures that there
is no decrease in reliahility of the

Silicon Rectifiers

unit as a result of the avalanche
action.
Packaging

There are generally three methods of packaging high-voltage rectifier assemblies: encapsulation;
open exposure to air; and immersion in a special high-voltage atmosphere, such as transformer oil
or the newer gaseous insulating
mediums. Each of these systems
has its advantages and disadvantages.
When encapsulation is used, a
high packing density can .be
achieved. The encapsulant protects
the rectifier stack from harmful
atmospheres, such as those encountered in high-humidity areas.
The encapsulant further protects
the stack from accumulations of
dust and dirt which can cause
leakage 'paths and upset voltage
division among the rectifiers. On
the other hand, the encapsulant
acts as a barrier to the checking
of individual units in the stack
so that a rectifier failure cannot
be repaired, even if it can be detected; any deterioration of the
stack which is detected by an overall check of the total assembly
can be corrected only by replacement of the total stack. In addition, the encapsulation of highcurrent assemblies results in a
serious loss of heat-dissipating
ability.
For these reasons, it is not advisable to encapsulate very large
or expensive assemblies. If a highvoltage, low-current assembly is
to be encapsulated, some thought
should be given to the use of several encapsulated sections, so
that if deterioration does take
place in a part of the stack, only
that part need be replaced. In
general, only those assemblies

27
which .can be advantageously replaced as a whole should be encapsulated.
Open assemblies directly exposed to the atmosphere have several advantages. They are fairly
easy to install, and cooling can be
accomplished by convection and
radiation or, for high dissipation,
by forced air. All the rectifiers are
exposed and can be checked for
deterioration. If a rectifier is
found to have deteriorated, it can
be replaced individually, and it is
not necessary to discard the whole
stack. Open construction permits
efficient use of large heat sinks
and allows the designer to make
fuller use of the capability of the
rectifier.
The features which make encapsulation attractive are the features which are disadvantages in
the open stack. A low packing
density is required because of isolation requirements. Harmful atmospheres or high humidity can
affect operation. Accumulations of
dust and dirt can result in leakage paths which upset the voltage
division among the rectifiers, and
during high-voltage operation
corona may develop if care is not
taken.
Oil-immersed assemblies offer
some of the advantages of both encapsulated and open assemblies,
plus a few additional advantages.
When oil is used as an insulating
medium, a fairly good packing
density can be obtained. The intimate contact between the oil and
the rectifier heat sinks aids rectifier cooling. The closed oil system
tends to reduce any accumulation
of dirt. The dielectric properties
of the oil reduce or eliminate
corona problems. In addition, the
rectifier stacks can be removed
from the oil for testing and maintenance.

RCA Silicon Power Circuits Manual

The disadvantages of oil immersion outweigh the advantages
in many applications, e.g., in
lower-voltage installations. The
use of oil immersion requires an
oil tank with high-voltage bushings. The added weight of the
system may create a floor-loading
problem. When large quantities of
power are being dissipated by the
rectifiers, additional cooling is required. The use of a heat ex-

changer to remove the heat from
the oil or of a radiator with a
fan through which the oil can circulate may be necessary. If care
is not taken, the oil can become
contaminated with moisture and
dirt, with the result that arcing
and corona may occur. Although
testing and maintenance of an oilimmersed system are possible,
removal of the assembly from the
oil is often a difficult operation.

Thyristors
T HE

term thyristor is the generic name for semiconductor
devices that have characteristics
similar to those of thyratron
tubes. Basically, this group includes bistable semiconductor devices that have three or more
junctions (i.e., four or more semiconductor layers) and that can
be switched between conducting
states (from OFF to ON or from
ON to OFF) within at least one
quadrant of the principal voltagecurrent characteristic. There are
several different types of thyristors, which differ primarily in the
number of electrode terminals and
in their operating characteristics
in the third quadrant of the voltage-current characteristic,
as
shown in Table II. Reverse-blocking triode thyristors, commonly
called silicon controlled rectifiers
(SCR's), and bidirectional triode
thyristors, usually r~ferred to as
Table II-Different Types of
Thyristors
No. of
Terminals

Third-Quadrant Operation
Blocking

Conducting

Switching

Reverseblocking
diode
thyristor

Reverseconducting
diode
thyristor

Bidirectional
diode
thyristor

Reverseblocking
triode
thyristor

Reverseconducting
triode
thyristor

Bidirectional
triode
thyristor

triacs, are the most popular types.
The discussions in this section
deal primarily with these two
thyristor devices.

THEORY OF OPERATION
A silicon controlled rectifier
(SCR) is basically a four-layer
p-n-p-n device that has three electrodes (a cathode, an anode, and
a control electrode called the
gate). Fig. 25 shows the junction
diagram, principal voltage-current
characteristic, and schematic symbol for an SCR. A triac also has
three electrodes (main terminal
No.1, main terminal No.2, and
gate) and may be considered as
two parallel p-n-p-n structures
oriented in opposite directions to
provide symmetrical bidirectional
electrical characteristics. Fig. 26
shows the junction diagram, voltage-current characteristic, and
schematic symbol for a triac. An
analysis of the voltage-current
characteristics of SCR's and triacs
and of the charge-carrier interactions that make possible the
switching transitions indicated by
these characteristics provides useful information concerning the
operation and possible applications of these devices.

Voltage-Current Characteristics
As shown in Fig. 25 (b), the
operation of an SCR under re-

RCA Silicon Power Circuits Manual

(a)

FIRST QUADRANT
ANODE(+)

"ON" STATE

REVER~~A~1:°CKING

HOLDING CURRENT Ih
/

~!l~~I$Qy'~R_YOLTAGE

~~====r=~~~V
,

"OFF"STATE

REVERSE
BREAKDOWN
VOLTAGE

THIRD QUADRANT
ANODE(-)

f
(b)

breakdown voltage differs for individual SCR types.
During forward-bias operation
(anode positive with respect to
cathode), the p-n-p-n structure of
the SCR is electrically bistable
and may exhibit either a very high
impedance (forward-blocking or
OFF state) or a very low impedance (forward-conducting or ON
state). In the forward-blocking
state, a small forward current,
called the forward OFF-state current, flows through the SCR. The
magnitude of this current is approximately the same as that of
the reverse-blocking current that
flows under reverse-bias conditions. As the forward bias is increased, a voltage point is reached

ATHODE

SCR

GATE

MAIN

TER~P

MAIN

Ip~:~1

ANODE (CASE)

FIRST QUADRANT
MAIN TERMINAL 2(+)

(e)

Figure 25. (a) Junction diagram, (b) principal voltage·current characteristic, and
(c) schematic symbol for an SCR thyristor.

verse-bias conditions (anode negative with respect to cathode) is
very similar to that of reversebiased silicon rectifiers or other
semiconductor diodes. In this bias
mode, the SCR exhibits a very
high internal impedance, and only
a slight amount of reverse current, called the reverse blocking
current, flows through the p-n-p-n
structure. This current is very
small until the reverse voltage exceeds the reverse breakdown voltage; beyond this point, however,
the reverse current increases
rapidly. The value of the reverse

TERMINAL

(a)

. =======+~~~=-V
-:::

"OFF" STATE

BREA~:v-~-::~:::l
THIRD QUADRANT
MAIN TERMINAL 2(-)

I
(b)

~:::"
TRIAC!

MAIN TERMINAL 2
(CASE)
(e)

Figure 26. (a) Junction diagram, (b) principal voltage-current characteristic, and
(C) schematic symbol for a triac thyristor.

Thyristors
at which the forward current increases rapidly, and the SCR
switches to the ON state. This
value of voltage is called the forward breakover voltage.
When the forward voltage exceeds the breakover value, the
voltage drop across the SCR
abruptly decreases to a very low
value, referred to as the forward
ON-state voltage. When an SCR
is in the ON state, the forward
current is limited primarily by
the impedance of the external circuit. Increases in forward current
are accompanied by only slight increases in forward voltage when
the SCR is in the state of high
forward conduction.
As shown in Fig. 26 (b), a triac
exhibits the forward-blocking, forward-conducting voltage-current
characteristic of a p-n-p-n structure for either direction of applied
voltage. This bidirectional switching capability results because, as
mentioned previously, a triac consists essentially of two p-n-p-n
devices of opposite orientation
built into the same crystal. The
device, therefore, operates basically as two SCR's connected in
parallel, but with the anode and
cathode of one SCR connected to
the cathode and anode, respectively, of the other SCR. As a result,
the operating characteristics of the
triac in the first and third quadrants of the voltage-current characteristics are the same, except for
the direction of current flow and
applied voltage. The triac characteristics in these quadrants are
essentially identical to those of
an SCR operated in the first quadrant. For the triac, however, the
high-impedance state in the third
quadrant is referred to as the
OFF state rather than as the reverse-blocking state. Because of

31
the symmetrical construction of
the triac, the terms forward and
reverse are not used in reference
to this device.
In triacs, the gate-triggerpulse polarity is usually measured with respect to main
terminal No.1, which is comparable to the cathode terminal of
an SCR. The triac can be triggered by a gate-trigger pulse
which is either positive or negative with respect to main terminal
No.1 when main terminal No.2 is
either positive or negative with
respect to main terminal No. 1.
The triac, therefore, can be triggered in any of four operating
modes, as summarized in Table
III. The quadrant designations refer to the operating quadrant on
Table III-Triac Triggering
Modes
Gate·to-MainTerminal-No.1
Voltage

Main-Terminal-No.2to-Main-Terminal-No.1

Operating
Quadrant*

Voltage

Positive

1(+)

Negative

Positive

1(-)

Positive

Negative

111(+)

Negative

'" (-)

* Positive (+) and negative (-J signs indicate polarity of gate trigger pulse.

the principal voltage-current characteristics, shown in Fig. 26 (b)
(either I or III), and the polarity
symbol represents the gate-tomain-terminal-N o. 1 voltage. Fig.
27 shows the flow of current in
a triac for each of the four triggering modes.
The gate-trigger requirements
of the triac are different in each
operating mode. The I (+) mode
(gate positive with respect to
main terminal No. 1 and main

RCA Silicon Power Circuits Manual

MTI

1(+)
(a)

MTI

Figure 27.

MTI

IH
(b)

MT I

m(+)

(el

(d)

Current flow in the four triggering modes of a triac: (a) Mode 1(+);
(b) Mode I(~); (c) Mode 111(+); (d) Mode 111(-).

terminal No. 2 positive with respect to main terminal No.1),
which is comparable to equivalent
SCR operation, is usually the most
sensitive. The smallest gate current is required to trigger the
triac in this mode. The other three
operating modes require larger
gate-trigger currents. For RCA
triacs, the maximum trigger-current rating in the published data
is the largest value of gate current
that is required to trigger the selected device in any operating
mode.
Thyristors are ideal for switching applications. When the working voltage of a thyristor is below
the breakover point, the current

through the device is extremely
small and the thyristor is effectively an open switch. When the
voltage across the main terminals
increases to a value exceeding the
breakover point, the thyristor
switches to its high-conduction
state and is effectively a closed
switch. The thyristor remains in
the ON state until the current
through the main terminals drops
below a value which is called the
holding current. When the source
voltage of the main-terminal circuit cannot support a current equal
to the holding current, the thyristor reverts back to the high-impedance OFF state.
The breakover voltage of a thy-

Thyristors

ristor can be varied, or controlled,
by injection of a signal at the
gate, as indicated by the family
of curves shown in Fig. 28. Although this family of curves is
shown in the first quadrant typical of SCR operation, a similar set

~REAKOVER

L_/-_ --

.r--=--:: I -

VOLTAG

I
I

v•

I93> I 92> I91=O
Figure 28. Curves. showing breakover characteristics of a thyristor for different values·
of gate current.

of curves can also be drawn for
the third quadrant to represent
triac operation. When the gate
current is zero, the principal voltage must reach the breakover
val ue V (lIOl of the device before
breakover occurs. As the gate current is increased, however, the
value of breakover voltage becomes less until the curve closely
resembles that of a rectifier. In
normal operation, thyristors are
operated with critical values well
below the break over voltage and
are made to switch ON by gate
signals of sufficient amplitude to
assure that the device is switched
to the ON state at the instant desired.
After the thyristor is triggered
by the gate signal, the current
through the device is independent
of gate voltage or gate current.
The thyristor remains in the ON
state until the principal current
is reduced to a level below that
required to sustain conduction.

Charge-Carrier Interactions

The electron-hole interactions
that make possible the switching
transitions in p-n-p-n semiconductor structures are represented
graphically by the potential-energy diagrams shown in Figs. 29,
30, and 31. These diagrams show
the potential energies of holes and
electrons as a function of distance
through the crystal. The upward direction indicates increasing levels of electron energy, and
the downward direction indicates
increasing levels of hole energy .
The dots in the diagrams represent free electrons, and the circles
represent free holes.
The electrons in a solid can occupy only specific energy levels or
electron states. Each existing state'
can be occupied by only one electron. The Fermi energy level EF
is the dividing line above which
most of the existing electron states
are empty and below which most
state-s are full. Conduction in a
solid occurs only by movement of
free charge carriers, i.e., free electrons or free holes. A free electron
is an electron which is at an energy level for which most of the
existing states are empty, and a
free hole is an empty state at an
energy level for which most of the
existing states are filled. Free
electrons exist therefore, only at
energy levels above E F, and free
holes exist only at levels below
E F . Because electrons and holes
tend to seek the lowest available
energy levels, they both move
toward E j .-, which is the zeroenergy level for both types of
charge carriers. On the potentialhill diagrams, electrons always
tend to "fall", and holes always
tend to "rise". If the charge carriers were not affected by outside

RCA Silicon Power Circuits Manual

influences, therefore, all free electrons and holes would eventually
reach the Fermi level and disappear. A distribution of free
electrons above E F , however, is
maintained by thermal energy of
the lattice which constantly agitates the electrons to non-zero energy levels.
In the metal contact regions,
there is a continuous distribution
of electron states about the Fermi
energy level so that free holes and
free electrons exist simultaneously
side by side. In the semiconductor
regions, there is a band of energy,
called the forbidden region, in
which no electron states exist.
As a free carrier tries to move
through the system of metal to
semiconductor to metal, it finds
that it can move freely through
the metal, but when it reaches the
semiconductor it encounters an
obstacle, the forbidden-energy region, which it must go over or
under depending upon whether it
is a free electron or a free hole.
The carrier must obtain sufficient
energy so that it is displaced far
enough from the Fermi level to
go over or under the forbiddenenergy region. If sufficient energy,
such as thermal agitation or an
applied voltage, is not available,
the carrier is reflected back to its
origin.
In silicon crystal, the forbidden
region is wide enough so that, at
ordinary temperatures, there is
not sufficient thermal energy
available to distribute carriers
both above and below the band.
If the Fermi energy level is close
to the top of the band, thermal
energy is sufficient to lift electrons
into states on top of the forbidden
region, but is not sufficient to push
holes into states below this region. As a result, the material

contains many free electrons, but
very few free holes, and is referred to as an n-type semiconductor because it contains mostly
negative-charge carriers.
Similarly, a p-type region in the
semiconductor, which contains
mostly positive-charge carriers,
results when the Fermi level is
close to the bottom of the forbidden band. For this condition,
thermal energy is sufficient to
excite holes into states below the
band, but is not sufficient to excite electrons into states above
the band.
The position of the Fermi level
in the forbidden region is determined by the carrier concentration. This concentration, in turn,
is determined by both the dopant
concentration and the concentration of injected carriers.
At the metal-to-semiconductor
interfaces, the dopant concentration is very high. At such interfaces, the carrier concentration
cannot be changed significantly
by injected carriers, and the position of the Fermi level in the
forbidden region is firmly fixed.
In the inner semiconductor regions and near the junctions, the
dopant concentration is relatively low so that the total carrier concentration and, therefore,
the position of the Fermi level
in the forbidden region can be
changed by injection of carriers
from surrounding regions. These
factors make the forbiddenenergy region appear flexible
within the body of the semiconductor but rigid at the
metal-to-semiconductor contacts.
This rigidity of the potential hill
at the contacts prevents electrons
in the metal from entering the
p-type semiconductor, but allows
holes to circulate freely between

Thyristors
the metal and the p-type region;
similarly, electrons can circulate
freely between metal and the ntype region but holes cannot cross
the metal-to-n-type-semiconductor
interface.

METAL
(CATHODE
CONTACT)

f~'1 ~i'm(. :'
JI

Forward-Blocking State-The
sequence of diagrams in Fig. 29
illustrates the transition of the
thyristor from the equilibrium
(zero-bias) condition to the forward-blocking state. In the equilibrium condition, the concentration of charge carriers (electrons
and holes) is determined primarily by dopant concentrations.
For this condition, which is represented by the potential-hill diagram shown in Fig. 29 (b), there
is approximately one free carrier
for each dopant atom.
VVhen the cathode side of the
thyristor is biased negatively with
respect to the anode side, the potential energy of the electrons is
increased in the cathode region
and that of the holes is increased
in the anode region. Because of
the difference in energy level from
cathode to anode, the shape of the
forbidden-energy region is altered
in the most lightly doped section
(i.e., the n-type base) so that the
height of the potential hill of the
central junction is increased. As
.shown in Fig. 29 (c), any electrons
that exist in this region "fall
down" the resultant hill, and any
holes in this region "rise" to the
top of the hill. In this way, all
free charge carriers are removed,
and the hill becomes a depletion
region, as shown in Fig. 29 (d).
The movement of charge carriers with an increase in the forward voltage resl.lts in a charging,
or displacement, current similar
to the current (i = Cdv/dt) that
charges a capacitor. This displace-

METAL
(ANODE
CONTACT)

"'T. I

(a) JUNCTION DIAGRAM

EMPTY ELECTRON
STATES

o~~\..~
FILLED ELECTRON
FORBIDDEN-ENERGY
STATES
REGION
(b) EQUILIBRIUM CONDITION

(e) CHANGE

IN POTENTIAL CONFIGURATION
WHEN FORWARD BIAS IS APPLIED

(d) FORWARD·BLOCKING STATE

~ L

(d)

(b)
TIME-

I~ ~
(b)

Cd)

TIME-

(e) VOLTAGE AND CURRENT WAVEFORMS OUR.

ING TRANSITION FROM EQUILIBRIUM CONDI·
TION TO FORWARD·BLOCKING STATE

Figure 29. Potential·hill diagrams for vari·
ous stages of thyristor transition from
equilibrium condition to forward-blocking
condition (electron energy increases up·
ward, hole energy increases downward).

RCA Silicon Power Circuits Manual

ment current ceases when the forward ,voltage reaches a steady
value because there are no additional carriers for' the field to
move. Although there are many
electrons available on the cathode
side of the thyristor and many
holes available on the anode side,
these carriers cannot enter the depletion region because they do not
have sufficient energy to "climb"
the 0.8- to 1.0-volt potential hills
at junctions J 1 and J B •
The current and voltage waveforms during the transition from
the equilibrium to the forwardblocking state are shown in Fig.

METAL
(CATHODE
CONTACT)

METAL
(ANODE
CONTACT)
METAL (GATE CONTACT)

N-BASE

P-

EMITTER

J3
(a) JUNCTION DIAGRAM

(b) FORWARD·BLOCKING STATE

29 (e).

Forward-Conducting StateThe transition in a thyristor from
the forward-blocking state to the
forward-conducting state is illusboated by the potential-hill diagrams shown in Fig. 30. When a
thyristor is in the forward-blocking state, shown in Fig. 30 (b),
application of a positive bias to
the gate causes the potential energy of electrons in this region
to be reduced so that the height
of the potential hill at junction
J 1 is decreased, as shown in Fig.
30 (c). A positive gate bias of
0.8 to 1.0 volt reduces the barrier of J 1 sufficiently so that electrons from the n-type emitter can
move across the p-type base into
the depletion region. The electric
field then sweeps them across this
region, as indicated in Fig. 30 (c).
Electrons accumulate in the
"well" at the bottom of the depletion region until their combined negative charge increases
the potential electron energy sufficiently to cause the potential hill
at junction J: l to disappear. Holes
can then move from the p-type
emitter across the n-type base into

FORBIDDEN-ENERGY
REGION

(e) CHANGE IN POTENTIAL CONFIGURATION

WHEN POSITIVE BIAS IS APPLIED TO GATE

(d) POTENTIAL CONFIGURATION AS FORWARD
BlAS BEG I NS TO INCREASE

(e) FORWARD-CONDUCTING STATE

GATE

CURRENT
ANODE-TO-!
CATHODE
CURRENT
ANODE - TO- !
CATHODE
VOLTAGE

~1-r::;:==t:~~~~
F=$==-=i==:~--i--

L _ _ _-=~;:;:;;;;f:,;,==
TIME

(I) CURRENT AND VOLTAGE WAVEFORMS DURING TURN-ON TRANSITION

Figure 30. Potential-hill diagrams for various stages of thyristor transition from
forward-blocking state to forward-conducting state.

Thyristors
the depletion region. These holes
then immediately "climb" the potential hill at J 2 , as shown in Fig.
30 (d).
The increased supply of holes
to the p-type base further depresses the potential hill at J 1 so
that the n-type emitter can inject
an even greater number of electrons into the depletion layer.
This action, in turn, increases the
injection of holes from the p-type
emitter. As a result of these regenerative effects, the current
through the thyristor increa.ses
rapidly, and the depletion region
collapses to complete the transition to the forward-conducting
state. Fig. 30(e) illustrates this
condition. In this state, the concentrations of both holes and electrons are greatly increased over
the equilibrium concentrations.
The thyristor can be sustained in
the forward-conducting state by
an anode-to-cathode forward-voltage drop of approximately 1 volt,
anq the thyristor current is
limited only by the impedance
of the external circuit.
'l'hecurrent and voltage waveforms·during the transition from
the forward-blocking to the forwat~d"'Cond\H!ting state are shown
in Fig. 30 (f) .
Turn-OIf~The
transition in
the thyristor from the forwardconducting state back to the forward~blocking state is illustrated
in Fig. 31. This transition is accomplished either by momentary
reduction of the anode current to
zero, or by momentary reversal
of the anode-to-cathode voltage.
In the conducting state, carrier
concentrations far in excess of the
equilibrium level are injected into
the n- and p-type regions. These
excess carriers remain for a finite

37
METAL
(CATHODE
CONTACT)

METAL
(ANODE
CONTACT)

P
P-

BASE
JI
J2
N-EMITTER

P+

N
N-BASE
J3

P-EMITTER

(0) JUNCTION DIAGRAM

(b) FORWARD-CONDUCTING STATE

(e) POTENTIAL CONFIGURATION AS ZERO-BIAS

DEPLETION LAYER REBUILDS AT JUNCTION Jl;
N-TYPE BASE STILL CONTAINS MANY EXCESS
CHARGE CARRIERS

(d) POTENTIAL CONFIGURATION AS DEPLETION
LAYER BEGINS TO BUILD AT JUNCTION J2.

(e) THYRISTOR APPROACHES REVERSE-BLOCKING·

STATE, BUT DEPLETION LAYER BUln UP IN" NTYPE BASE STILL CONTAINS SOME EXCESS.
CHARGE CARRI ERS.

.-n

(f) REVERSE-BLOCKING STATE

FORBIDDENENERGY REGION

O~"""-/~O
(g) EQUILIBRIUM CONDITION

Figure 31. Potential-hili diagrams for various stages of thyristor transition from
forward-conducting state to turn-off.

RCA Silicon Power Circuits Manual

time after the anode current is
reduced to zero. If the forward
bias is re-applied before these excess carriers are removed, the
device simply returns to the conducting state and does not switch
to the blocking condition. After
the excess carriers are removed
and the device is returned to
equilibrium, the potential hills rebuild, and the device can return
to the forward-blocking state, as
shown in Fig. 29.
The removal of excess carriers
can be accomplished if the anode
current is reduced to zero until
the excess carriers recombine or
move out of the depletion region.
This removal corresponds to a direct transition from the conditions
shown in Fig. 31 (c) to those
shown in Fig. 31 (g). The potential hill at junction J 1 rebuilds
first because it is in the more
heavily doped region of the device, but the hills at J!.l and J a also
rebuild as .the excess carriers disappear during the zero-anodecurrent condition.
A more rapid removal of the
excess carriers can be accomplishedby a momentary reversal
. of . the anode-to-cathode voltage.
This transition is shown in Figs.
31 (d) through 31 (f). As the reverse voltage increases, carriers
are pulled. out of the device in the
direction opposite to that in which
they were injected so that a substantial reverse current results.
The removal of carriers is aided
as a potential hill and a depletion
region begin to build at junction
J:j , as shown in Fig. 31 (d). As the
remaining quantity of excess carriers is reduced, the reverse current decreases, and reverse voltage
builds up. At the stage shown in
Fig. 31 (e), the reverse depletion
region has built up, but the unde-

pleted n-type base region still contains some excess carriers which
prevent the potential hill at J 2
from rebuilding, and which continue to flow out as reverse current. At the stage shown in Fig.
31 (f), the excess carriers have all
been removed, and device has
reached its steady-state reverseblocking condition. In Fig. 31 (g),
the reverse bias has been removed,
all regions return to the equilibrium zero-bias carrier concentrations, and the device is ready for
return to the forward-blocking
condition.
Current and voltage waveforms
corresponding to the various conditions described in Figs. 29, 30,
and 31 are shown in Fig. 32.

CONSTRUCTION
Construction details for typical
RCA thyristors are shown in Figs.
33 through 37. Fig. 33 shows details for the 2-lead TO-5 package.
This compact package is designed
for applications in which mounting space is limited and can be
attached to a wide variety of heat
sinks with sizes and shapes to
fit the available space. A typical
heat-sink arrangement for an insulating mounting of this package
is shown in Fig. 34. (Various
types of thyristor heat-sink arrangements are described in RCA
Application Note AN-3822, "Thermal Considerations in Mounting
of RCA Thyristors.") This package is used at current levels up
to 7 amperes.
In higher-current applications
the TO-66, TO-3, and press-fit and
stud-mounted TO-48 packages are
used. Internal construction details
of the press-fit package are shown
in Fig. 35.

Thyristors

TlME29 (bl

29 (dll30 Cbl

29 (el

I
I

III

I
I

30 ( 1.31 ( I
30 Cdl.-_+-_...,. 31(el

30 (el

31 (el

29 (el

I 31 Cdl 131 (fl

I I I I

I I

Figure 32. Voltage and current waveforms
for thyristor switching transitions shown
in Figs. 29, 30, and 31.

Construction details of a typical
SCR pellet are shown in Fig. 36.
The shorted-emitter construction
used in RCA SCR's can be recognized by the metallic cathode electrode in direct contact with the
p-type base layer around the periphery of the pellet. The gate, at
the center of the pellet, also makes
direct metallic contact to the pGATE

Figure 33. Cross-section of RCA two-lead
TO-S thyristor package.

type base so that the portion of
this layer under the n-type emitter
acts as an ohmic path for current
flow between gate and cathode.
Because this ohmic path is in
parallel with the n-type emitter
junction, current preferentially
takes the ohmic path until the IR
drop in this path reaches the
junction threshold voltage of about
0.8 volt. When the gate voltage
exceeds this value, the junction
current increases rapidly, and injection of electrons by the n-type

Figure 34. Typical heat-sink isolation technique for a chassis-mounted two-lead
TO-S thyristor.

RCA Silicon Power Circuits Manual
voltage is applied. Because the
c~arging, or displacement, current
(1 ~ Cdv/dt) into this capacitor

Figure 35.

Cross-seotion of RCA press-fit
thyristor package.

emitter reaches a level high
enough tQ turn on the device.
In' addition to providing a precisely controlled' gate current, the
shorted-emitter construction also
improves the high-temperature
and dv/dt (maximum allowable
rate of rise of OFF-state voltage)
capabilities of the device. The
junction depletion layer acts as
a par.allel-plate capacitor which
must be charged when blocking

ANODE
ELECTRODE
Figure 36.

Cross-section of a typical
SCR pellet.

vanes as the rate of rise of forw.ard voltage (dv/dt), a very
hIgh dv/dt can result in a high
current between anode and cathode. If this current crosses the
n-type emitter junction and is of
the same order of magnitude as
the gat€ current, it can trigger'the
device into the conducting state.
Such,unwanted.triggering is minimized by the shorted-emitter construction because the peripheral
contact of the p-type base to
the cathode, electrode provides a
large-area parallel path by which
the dv/dt current can reach the
cathode electrode without crossing the n-type emitter junction.
The center-gate construction of
the SCR pellet llrovides 'fast
t?rn-on ,and high di/ dt ,capabilitIes. In an SCR, conduction is
initiated in the .cathode region immediately adjacent to the gate contact and must then propagate to
the more remote regions of the
cathode. Switching losses are influenced by the rate of propagation of conduction and the distance
conduction must propagate from
the gate. With a central gate all
regions of the cathode are in dIose
proximity to the initially conducting region so that propagation
distance is significantly ·decreased ;
as a result, switching losses are
minimized.
Construction of a typical RCA
triac pellet is shown in Fig. 37.
In this device, the main-terminalNo.1 electrode makes ohmic contact to a p-typeemitter as well
as to an n-type emitter. Similarly,
the, main-terminal-No.2 electrode
also makes ohmic contact to both
types of emitter, but the p-type
emitter of the main-terminal-No.

Thyristors

N-EMITTER
P-EMITTER

GATE

P-BASE
MAIN-TERMINALI ELECTRODE

N
P
N

MAIN-TERMINAL-No. 2
ELECTRODE

Figure 37.

Cross-section of a typical ,triac
pellet.

then acts as the n-type emitter of
a grounded-base n-p-n transistor.
Electrons injected from this region enter the n-type base and
cause a forward bias on one of
the p-type emitters, depending on
which is at the positive end of the
voltage between the main-terminal
electrodes.
As shown in Figs. 36 and 37,
the cathode of an SCR and the
main terminal No. 1 of a triac
are fully covered by a relatively
heavy metallic, electrode. This electrode provides a low-resistance
path to distribute current evenly
over the cathode or main-terminalNo. 1 area and serves as a thermal
capacitor to absorb heat generated
by high surge or overload currents. Junction-temperature excursions that result from such
conditions are, therefore, held to
a minimum.

2 side is located opposite the ntype emitter of the main-terminalNo. 1 side, and the main-terminalNo. 2 n-type emitter is opposite
the main-terminal-No. 1 p-type
RATrNGS'AND
emitter. The net result is two fourCHARACTERISTICS
layer switches in parallel, but
oriented in opposite directions, in
Thyristors must be operated
one silicon pellet. This type of within the maximum ratings
construction makes it possible for specified by the manufacturer to
a triac either to block or to con- assure best results in terms of perduct current in either direction formance, life, and reliability.
between main terminal No.1 and These ratings define limiting
main .terminal No.2.
values,determined on the basis of
The gate electrode also makes extensive tests, that repr,esent the
contact to both n- and p4ype re- best judgment of the manufacgions. As a result, the deviee can turer of the safe operating capabe triggered by either positive or bility of the device. The manufacnegative gate signals, for either turer also specifies a number of
polarity of voltage between the 'device parameters, called charmain-terminal electrodes. When acteristics, which are directly
the triac is trigg,ered by a positive measurable properties that define
gate signal, conduction is ini- the inherent qualities and traits
tiated, as in the SCR, by injection of the thyristor. Some of these
of electrons from the main-termi- characteristics are important facnal-No. 1 n-type emitter, and the tors in the determination of the
gate n-type region is passive. The maximum ratings and in the pregate n-type region becomes active diction -of the performance, life,
when the triac is triggered by a and reliability that the thyristor
negative gate signal, because it can provide in a given application.

RCA Silicon Power Circuits Manual
Voltage and
Temperature Ratings

The voltage ratings of thyristors are given for both steadystate and transient operation and
for both forward- and reverseblocking conditions. For SCR's,
voltages are considered to be in
the forward or positive direction
when the anode is positive with
respect to the cathode. Negative
voltages for SCR's are referred to
as reverse-blocking voltages. For
triacs, voltages are considered to
be positive when main terminal
No.2 is positive with respect to
main terminal No. 1. Alternatively, this condition may be refen'ed to as operation in the first
quadrant.
When the voltage applied to a
thyristor is in the polarity for
which switching to the ON state
is possible, the voltage-blocking
capability of the device is temperature-sensitive. The maximum
junction temperature for thyristors is usually between 100°C and
150°C. The selection of the maximum operating temperature represents a compromise which assures that a sufficient number of
devices provide the required
blocking-voltage capability (for
which a low junction temperature
is desirable) and which allows the
highest possible current rating for
the thyristors (for which a high
.iunction temperature is desirable). Increases in .iunction temperature above this maximum
value result in a greater reliability
stress and adversely affect the
switching characteristics of thyristors.

OFF-State Voltage-The repetitive peak OFF-state voltage
V PIDr is the maximum value of

OFF-state voltage, either transient or steady-state, that the
thyristor should be required to
block under the stated conditions of temperature and gate-tocathode resistance. If this voltage
is exceeded, the thyristor may
switch to the ON state. The circuit designer should insure that
the VDn:lr rating is not exceeded
to assure proper operation of the
thyristor.
The effect of increased temperature is accentuated in thyristors
because of the regenerative action
upon which the operation of these
devices is dependent. Thermally
generated currents tend to be multiplied. If this blocking current
crosses the gate-to-cathode junction, its effect on the thyristor is
similar to that of the gate current
and thus tends to reduce the
breakover voltage V BO ' For this
reason, OFF-state voltage ratings
are specified at the maximum
rated junction temperature.
A gate-to-cathode shunting resistance can be used to provide a
path for the blocking current that
bypasses the gate-to-cathode junction. The use of this shunt resistance improves the OFF-state
blocking capability, but reduces
the gate sensitivity. OFF-state
voltage ratings, therefore, are
specified with no external gate-tocathode impedance to represent
worst-case conditions.
Under relaxed conditions of
temperature or gate impedance, or
when the blocking capability of
the thyristor exceeds the specified
rating, it may be found that a
thyristor can block voltages far in
excess of its repetitive OFF-state
voltage rating Vn]Dr. Because the
application of an excessive voltage to a thyristor may produce
irreversible effects, an absolute

Thyristors
upper limit should be imposed on
the amount of voltage that may
be applied to the main terminals
of the device. This voltage rating
is referred to as the peak OFFstate voltage VIm. It should be
noted that the peak OFF-state
voltage has a single rating irrespective of the voltage grade of
the thyristor. This rating is a
function of the construction of the
thyristor and of the surface properties of the pellet. The V m[ rating should not be exceeded under
either continuous or transient
conditions.
Fig. 38 shows a simple, inexpensive test circuit that may be
used to evaluate the OFF-state
voltage capabilities of thyristors.

Figure 38. Test circuit used to determine
dc forward- and reverse-voltage-blocking
capabilities and leakage current of
thyristors.

(The circuit may also be used for
reverse-blocking and leakage tests
of thyristors.) Resistor Rr and
capacitor C r are included in the
test circuit to limit the rate of
rise of applied voltage to the thyristor under test. Resistor R"
limits the discharge of capacito;
C r through the thyristor in the
event that the thyristor is turned
on during the test. Resistor Ra
provides a discharge path for
capacitor Cr.
Reverse Voltages (For Reverse-Blocking Thyristors)-Reverse-voltage ratings are given
for SCR's to provide operating
guidance in the third quadrant,
or reverse-blocking mode. There

43
are two voltage ratings for SCR's
in the reverse-blocking mode:
repetitive peak reverse voltage
(VnlDr ) and nonrepetitive peak
reverse voltage (Vns )[).
The repetitive peak reverse
voltage is the maximum allowable
value of reverse voltage, including all repetitive transient voltages, that may be applied to the
SCR. Because reverse power dissipation is small at this voltage, the
rise in junction temperature because of this reverse dissipation
is very slight and is accounted
for in the rating of the SCR.
The non repetitive peak reverse
voltage is the maximum allowable
value of any nonrepetitive transient reverse voltage which may
be applied to the SCR. These nonrepetitive transient voltages are
allowed to exceed the steady-state
ratings, even though the instantaneous power dissipation can be
significant. While the transient
voltage is applied, the junction
temperature may increase, but removal of the transient voltage in
a specified time allows the junction temperature to return to its
steady-state operating temperature before a thermal runaway
occurs.
The test circuit shown in Fig.
38 may be used for reverse-voltage tests of an SCR.
ON-State Voltage-When a thyristor is in a high-conduction
state, the voltage drop across the
device is no different in nature
from the forward-conduction voltage drop of a rectifier, although
the magnitude may be slightly
higher. As in rectifiers, the ONstate voltage-drop characteristic
is the major source of power losses
in the operation of the thyristor,
and the temperature produced

RCA Silicon Power Circuits Manual

becomes a limiting factor in the
rating of the device.

Fig. 39 shows curves of the
maximum average forward power
dissipation for the RCA-2N3873

Thermal Resistance
6

The thermal resistance of a thyristor is an indication of the ability of the device to remove heat
that is generated internally within
the pellet. If a thyristor has a low
thermal resistance, the junction
temperature does not rise as high
for a given conduction current or
junction power dissipation. The
most common or useful thyristor
thermal resistance specified is the
value from the junction to a particular point on the case. This
valll-e is referred to as the junction-to-case thermal resistance,
fh-c. The next value of thermal
resistance that is necessary for
proper use of the thyristor is the
thermal resistance from the heat
sink, which is usually attached to
the thyristor, to the ambient air,
OC-A. If the thermal resistance of
the total path from the junction to
the ambient air and the power
dissipated within the device are
known, the average temperature
can be calculated.

Current Ratings
Thyristor current ratings define
maximum values for normal or
repetitive currents and for surge
or nonrepetitive currents. These
maximum ratings are determined
on the basis of the maximum
junction-temperature ratillg, the
junction-to-case thermal resistance, the internal power dissipation that results from the current
flow through the thyristor, and
the ambient temperature. The effect of these factors in the determination of current ratings is
illustrated by the following example.

CURRENT WAVEFORM- SINUSOIDAL
INDUCTIVE
LOAD- RESISITIVE

Of--

0~180°

CONDUCTION
ANGLE

f---0

Ii/

CONDUCTION

ANGL~"i./

w/14
tJ

900

,i7JV7

()c:..

300

/1 W

I/iJ t?'
~

AVERAGE FORWARD CURRENT-A

Figure 39. Power-dissipation rating chart
for the RCA-2N3873 SCR,

SCR as a function of average forward current for dc operation and
for various conduction angles. For
the 2N3873, the junction-to-case
thermal resistance OJ-O is 0.92°C
per watt and the maximum operating junction temperature T J is
100°C. If the maximum case temperature TO(lllaxl is assumed to be
65°C, the maximum average forward power dissipation can be determined as follows:
P

AVG(max)

TJ(max) -

TC(max)

8 J --c
(100 - 65) °C
0.92 °C/watt

il8 watt!"

._-

(6)

Thyristors
The maximum average forward
current rating for the specified
conditions can then be determined
from the rating curves shown in
Fig. 39. For example, if a conduction angle of 180 degrees is assumed, the average forward current rating for a maximum dissipation of 38 watts is found to be
22 amperes.
These calculations assume that
the temperature is uniform
throughout the pellet and the case.
The junction temperature, however, increases and decreases under conditions of transient loading
or periodic currents, depending
upon the instantaneous power dissipated within the thyristor. The
current rating must take these
variations into account.
ON-State Current-The ONstate current ratings for a thyristor indicate the maximum values
of average, rms, and peak (surge)
current that should be allowed to
flow through the main terminals
of the device, under stated conditions, when the thyristor is in the
ON state. For heat-sink-mounted
thyristors, these maximum ratings
are based on the case temperature; for lead-mounted thyristors,
the ratings are based on the ambient temperature.
The example used to show the
effect of various factors on maximum current ratings pointed out
that these ratings are determined
on the basis of the internal power
dissipation, the junction-to-case
thermal resistance, and the difference between the maximum operating junction temperature and
the maximum case temperature.
Because the maximum operating
junction temperature is fixed, the
maximum ON-state current ratings may be given by curves that

relate current to case temperature.
The maximum allowable current
approaches zero as the case temperature approaches the maximum
operating junction temperature
because this current is directly
proportional to the ratio of the
difference between case and junction temperatures to the junctionto-case thermal resistance.
The maximum average ONstate current rating is usually
specified for a half-sine-wave current at a particular frequency.
Fig. 40 shows curves of the maximum allowable average ON-state
current I T1.·(",",,) for the RCA2N3873 SCR family as a function
of case temperature. Because peak
and rms currents may be high for
small conduction angles, the curves
in Fig. 40 also show maximum allowable average currents as a
function of conduction angle. The
maximum operating junction temperature for the 2N3873 is 100·C.
CURRENT WAVEFORM-SINUSOIDAL
LOAD- RESISTIVE OR INDUCTIVE,

100

Q- -

0 1<--r-+1180'

,~-r.--CONDUCTION~'~~/
ANGLE

~I
~f~ ,~

Cl~ ""~

~:9~~~

90'

,'(~

60'

IJO'\\.

P'~- f--

,0.

1\ '"
\

\
~

AVERAGE FORWARD CURRENT-A

Figure 40.

Current rating chart for the
RCA-2N3873 SCR.

RCA Silicon Power Circuits Manual

The rating curves indicate, for a
given case temperature, the maximum average ON-state current for
which the average temperature of
the pellet will not exceed the maximum allowable value. The rating
curves may be used for only resistive or inductive loads. When capacitive loads are used, the currents produced by the charge or
discharge of the capacitor through
the thyristor may be excessively
high, and a resistance should be
used in series with the capacitor
to limit the current to the rating
of the thyristor.
The ratio of rms to average
values for a sinusoidal current
waveform through an SCR is 1.57.
The maximum average ON-state
current rating I'l'F(nw:l, therefore,
can be readily converted to the
maximum rms ON-state current
rating ITF(rmRl' For example, as
may be determined from Fig. 40,
the maximum average ON-state
current for the 2N3873 is 22 amperes for a conduction angle of 180
degrees and a maximum case temperature of 65°C. For these same
conditions, the rms current rating
may be determined as follows:

X 1.57
22 amperes X 1.57

35 amperes

hF(rms) =

hF(avg)

The dashed-line curve in Fig. 40
shows the rms current rating for
the 2N3873 as a function of case
temperature for a conduction angle
of 180 degrees.
The ON-state current rating for
a triac is given only in rms values
because these devices normally
conduct alternating current. Fig.
41 shows an rms ON-state current
rating curve for a typical triac as

CURRENT WAVEFORM=SINUSOIDAL
LOAD= RESISTIVE OR INDUCTIVE
RATING APPLIES FOR ALL CONDUCTION
ANGLES .

....

{~~

'"C'3~

~ ....I 110
en
~'!l

3!q100

«_II"
....

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

~!i 90

Figure 41.

o 180·"U36O!-

..........

I'-- .......
I

CONR~JLT~ON
=Sr' ~

456

RMS CONDUCTION CURRENT-A

Current rating curve for a typical RCA triac.

a function of case temperature. As
with the SCR, the triac curve is
derated to zero current when the
case temperature rises to the maximum operating junction temperature. Triac current ratings are
given for full-wave conduction under resistive or inductive loads.
Precautions should be taken to
limit the peak current to tolerable
levels when capacitive loads are
used.
The surge ON-state current
rating I~~F(,urge) indicates the maximum peak value of a short-duration current pulse that should be
allowed to flow through a thyristor
during one ON-state cycle, under
stated conditions. This rating is
applicable for any rated load condition. During normal operation,
the junction temperature of a thyristor may rise to the maximum
allowable value; if the surge occurs at this time, the maximum
limit is exceeded. For this reason,
a thyristor is not rated to block
OFF-state voltage immediately following the occurrence of a current
surge. Sufficient time must be allowed to permit the junction temperature to return to the normal
operating value before gate control
is restored to the thyristor. Fig.
42 shows a surge-current rating
curve for the 2N3873 SCR. This

Thyristors

SUPPLY=60-Hz SINE WAVE
CASE
TURE=65"C
LOADREPET
REVERSE VOLTAGE
M RATED VALUE
.. 400
AVERAGE FORWARD CURRENT
I
MAXIMUM RATED VALUE

I\. .

....z

i:!30 0
II:

::>

ljlZO0
II:

::>

.......

..
Ul

><100

0
2

6 6

•• 6

10
100
1000
SURGE CURRENT OURATION-CYCLES

Figure 42.

Surge-current rating curve for
the RCA-2N3873 SCR.

curve shows peak values of halfsine-wave forward (ON-state)
current as a function of overload
duration measured in cycles of the
60-Hz current. Fig. 43 shows
surge-current rating curves for a
typical triac. For triacs, the rating
curve shows peak values for a fullsine-wave current as a function of
the number of cycles of overload
duration. Multicycle surge curves
are the basis for the selection of
circuit breakers and fuses that
are used to prevent damage to the
thyristor in the event of accidental
short-circuit of the device. The
number of surges permitted over
the life of the thyristor should be
limited to prevent device degradation.

SUPPLY=60HZ SINE WAVE
LOAD' RESISTIVE
CASE TEMPERATURE=+75"C
01'-,.
GATE CONTROL MAY BE LOST
DURING AND IMMEDIATELY
f"'...
0
FOLLOWING SURGE CURRENT
INTERVAL.

OVERLOAD MAY NOT BE RE(

t--di/dt=200 A/,.s
I

1"'41°O~f--- i

O.5iF=

0--

:~~~ -~-----------------~

:-0-'1"11'1

.........

~~~~~~A~~~~ ~~~C~~~URNED

WITHIN STEADY-STATE RATED
VALUE.
4 66
4 6 6
4 .6
I
2
10 2
100 2
1000
SURGE CURRENT DURATION-FULL CYCLES

Figure 43.

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

Figure 44. Voltage and current waveforms
used to determine di/dt rating of the
RCA-2N3873 SCR.

I'...

Critical Rate of Rise of ONState Current (di/dt)-In a thyristor, the load current is initially
concentrated in a small area of
the pellet when load current first
begins to flow. This small area
effectively limits the amount of
current that the device can handle
and results in a high voltage drop
across the pellet in the first microsecond after the thyristor is triggered. If the rate of rise of current
is not maintained within the rating of the thyristor, localized hot
spots may occur within the pellet
and permanent damage to the device may result. The waveshape
for testing the di/dt capability of
the RCA 2N3873 is shown in Fig.
44. The critical rate of rise of ONstate current is dependent upon

Surge-current rating chart for
a typical triac.

the size of the cathode area that
begins to conduct initially, and the
size of this area is increased for
larger values of gate trigger current. For this reason, the di/dt
rating is specified for a specific
value of gate trigger current.

RCA Silicon Power Circuits Manual

Holding and Latching Currents
-After a thyristor has been
switched to the ON-state condition, a certain minimum value of
anode current is required to maintain the thyristor in this low-impedance state. If the anode current
is reduced below this critical holding-current value, the thyristor
cannot maintain regeneration and
reverts to the OFF or high-impedance state. Because the holding current (In) is sensitive to
changes in temperature (increases
as tempreature decreases), this
rating is specified at room temperature with the gate open.
The latching-current rating of a
thyriHtorspecifies a value of anode
current, sHghtly higher than the
holding current, which is the-minimum amount required to sustain
conduction immediately after the
thyristor is switched from the OFF
state to the ON state and the gate
signal is removed. Once the latching current (rr,) is reached, the
thyristor remains in the ON, or
low-impedance, state until its anode current is decreased below the
holding-current value. The latch"
ing-current rating-is an important
consideration when a thyristor is
to be used with an inductive load
because the inductance limits the
rate of rise of the anode current.
Precautions should be taken to insure that, under such conditions,
the gate signal is present until the
anode current rises to the latching
value so that complete turn-on of
the thyristor is assured.
Fig. 45 shows a simple test circuit that may be used to determine
the holding and latching currents
of thyristors. For the holdingcurrent tests, the value of potentiometer Rl is adjusted toapproximately 50 ohms, and the

Figure 45. Test circuit used to determine
holding and latching currents of thyr.istors.

spring-loaded push-button switch
PB I is momentarily depressed _to
turn on the thyristor. The value
of RI is then gradually increased
to the point at which the thyristor
turns off.
For the latching-current test,
the value of potentiometer Rl is
initially adjusted so-that the mainterminal current is less than the
holding level. The value of Rl is
then decreased. as push-button
switch PB I is alternately depressed and released; until the thyristor latches on.
Critical Rate of Rise of OFFState Voltage (dv/dt)-Because
of the internal capacitance of a
thyristor, the forward-blocking
capability of the device is sensitive
to the rate at which the forward
voltage is applied. A steep rising'
voltage impressed across the main.
terminals of a thyristor causes a
capacitive charging current to'
flow through the device. This
charging current (i = Cdv/dt) is
a function of the rate of rise of
the OFF-state voltage.
If the rate of rise of the forward voltage exceeds a critical
value, the capacitive charging current may become large enough to
trigger the thyristor. The steeper
the wavefront of applied forward
voltage, the smaller the value of
the breakover voltage becomes.
The use of the shorted emitter
construction in RCA SCR's has

Thyristors

resulted in a substantial increase
in the dv/dt capability of these
devices by providing a shunt
path around the gate-to-cathode
junction. Typical units can withstand rates of voltage rise up to
200 volts per microsecond under
worst-case conditions. The dv/dt
capability of a thyristor decreases as the temperature rises
and is increased by the addition
of an external resistance from
gate to reference terminal. The
dv/dt rating, therefore, is given
for the maximum junction temperature with the gate open,
i.e., for worst-case conditions.
Fig. 46 (a) shows a simple test
circuit that may be used to determine the dv/dt capability of a
thyristor. The curves in Fig.
46 (b) define the critical values
for linear and exponential rates of
increase in reapplied forward
OFF-state voltage for an SCR.
The critical value for the exponential rate of rise of forward
SW,

anode supply

=
relay

volt~

dv
dt -

able res.stor

== discharge resistor
== current-limiting reMl == oscilloscope
R2
R3

sistor

noninductive veri(a)

TIME
(b)

Figure 46. (a) Test circuit and (b) waveforms used to determine dv/dt capability
of a thyristor.

rated value of
thyris~or voltage (Vllo) XO.632
RC time constant

(7)
The dv/dt rating allows a circuit designer to design an RC
time-constant network that can be
used to limit the rate of rise of a
transient voltage below the critical value of the thyristor.
It has been found in many applications that simple circuit additions, such as shown in Fig. 47,
can be used to reduce the dv/dt

POWER
SOURCE

~SCR

age (variable)
SWl
mercury-wetted

voltage is the rating given in the
manufacturer's test specifications.
This rating is determined from
the following equation:

Figure 47. Diagram showing. use of- RC
network to improve the dv/dt capability
of an seR.

stress on the thyristor. The- dv/dt
capability is also increased by application of reverse bias to the
gate during the rise of OFF-state
voltage.
Switching Characteristics

The ratings of thyristors are
based primarily upon the amount
of heat generated within the device pellet and the ability of the
device package to transfer the internal heat to the external case.
For high-frequency applications in
which the peak-to-average current
ratio is high, or for high-performance applications that require
large peak values but narrow current pulses, the energy lost during

RCA Silicon Power Circuits Manual

the turn-on process may be the
main cause of heat generation'
within the thyristor. The switch- .'
ing properties of the device must
be known, therefore, to determine
power dissipation which may limit
the device performance.
Turn-on Time-When a thyristor is triggered by a gate signal,
the turn-on time of the device consists of two stages, a delay time td
and a rise time tn as shown in
Fig. 48. The total turn-on time tgt
is_defined as the time interval between the initiation of the gate

peak OFF-state voltage and the
peak ON-state current level, it is
influenced primarily by the magnitude of the gate-trigger current
pulse. Fig. 49 shows the variation
in turn-on time with gate-trigger
current for the RCA-2N3873 SCR.
4

~ 3

w
::;;

>= Z
z

o
I

i=1

r--- r---

o
ANODE
CURRENT

0,1

Figure 48. Gate current and voltage turn-on
waveforms for a thyristor.

signal and the time when the resulting current through the thyristor reaches 90 per cent of its
maximum value with a resistive
load. The delay time td is defined
as the time interval between the
10-per-cent point of the leading
edge of the gate-trigger voltage
and the 10-per-cent point of the
resulting current with a resistive
load. The rise time tr is the time
interval required for the principal
current to rise from 10 to 90 per
cent of its maximum value. The
total turn-on time, therefore, is
the sum of both the delay and
rise times of the thyristor.
Although the turn-on time is
affected to some extent by the

0.5

0.7

0.9

1.1

GATE CURRENT-A

Figure 49.

GATE TRIGGER
PULSE

0.3

Turn-on time characteristics for
the RCA-2N3873 SCR.

When larger currents are available
from the gate-trigger pulses, the
delay-time portion of the turn-on
period is reduced, and the over-all
turn-on time is decreased. When
it is desirable to reduce the variation in turn-on time among devices of the same type, higher
gate-drive signals should be used.
Fig. 50 shows a simple test circuit used to determine turn-on
times of thyristors. The value of
resistor Rl is chosen so that the
rated value of current flows
through the thyristor. Turn-on
time is specified by the thyristor
manufacturer at the rated blocking voltage.

cE3

I g t- 200 mA
O.ll's RISE TIME .1\.

6V-

Figure 50. Test circuit used to determine
turn-on time of thyristors.

Thyristors
When a thyristor is turned on
by a gate-current pulse, current
does not start to flow throughout
the entire junction instantaneously; instead, the current is confined initially to a small area
adjacent to the gate. The voltage
drop across the thyristor at this
time is large because the current
density in the small area that is
turned on is high. As the conduction area increases, the current
density is reduced, and the voltage drop across the thyristor becomes smaller. Eventually, the
boundaries of the high-currentdensity region propagate across
the entire junction area. The time
required for completion of this
action is considerably longer than
the specified turn-on time. For
resistive loads, the turn-on time
can be defined as the time interval
between the 10-per-cent point at
the beginning of the gate voltage
and the instant at which the applied blocking voltage decreases
to 10 per cent of its original
value.
For thyristors operated at low
blocking voltages, the 10-per-cent
value is insignificant from the
standpoint of device dissipation.
For thyristors operated at blocking voltages in the order of hundreds of volts, however, 10 per
cent is sufficiently high in magnitude to represent an appreciable amount of device dissipation.
Moreover, the typical turn-on
time, as defined for certain gate
drives, may be in the order of
2 to 3 microseconds, while the
time required for conduction to
spread over the entire junction
area may be in the order of 20
microseconds. During this spreading time, the dynamic voltage drop
is high, and the current density
can produce localized hot spots in

the pellet area in conduction. In
order to guarantee reliable operation and to provide guidance for
equipment designers in applications having short conduction
periods, published data for RCA
thyristors give the voltage drop
at a given instantaneous forward
current and at a specified time
after turn-on from an OFF-state
condition. The wave-shapes for
the initial ON-state voltage for
the RCA-2N3873 SCR are shown
in Fig. 51. This initial voltage,
together with the time required
for reduction of the dynamic
forward voltage drop during the
spreading time, is an indication
of the current-switching capability of the thyristor.

1 __

--l--r--VT(I)

I
I

ITM=300A

__~ __
~
~

1__

t=2ps

Figure 51. Initial ON-state voltage and
current waveforms for the 2N3873 SCR.

When the entire junction area
of a thyristor is not in conduction, the current through that
fraction of the pellet area in conduction may result in large instantaneous power losses. These
turn-on switching losses are pro-

RCA Silicon Power Circuits Manual

portional to the current and the
voltage from cathode to anode of
the device, together with the repetition rate of the gate-trigger
pulses. The instantaneous power
dissipated in a thyristor under
such conditions is shown in Fig.
52. The curves shown in this figure indicate that- the peak power
dissipation occurs in the short interval immediately after the deI
I
I
I
I

V(BO)F

I
I

+--------I

I
I

I
I
I

PEAK
FORWARD
POWER
DISSIPATION
I

REVERSE
- POWER
DISSIPATION

voltage is re-applied to the device.
The transient temperature rise
may have a major effect on the
turn-off time of a thyristor. As a
result, when transient effects have
to be considered, turn-off time
measurements should be made under pulsed conditions.
Turn-Off Time-The turn-off
time of an SCR also consists of
two stages, a reverse-recovery
time and a gate-recovery time, as
shown in Fig. 53. When the forward current of an SCR is reduced to zero at the end of a
conduction period, application of
reverse voltage between the anode
and cathode terminals causes reverse current to flow in the SCR
until the reverse-blocking junction
establishes a depletion region. The
time interval between the application of reverse voltage and the
time that the reverse current
passes its peak value to a steadystate level is called the reverserecovery time tIT' A second recovery period, called the gate-recovery time tg,., must then elapse for
the forward-blocking ,iunction to

Figure 52. Instantaneous power dissipation in a thyristor during turn-on.

vice starts to conduct, usually in
the first microsecond. During this
time interval, the peak junction
temperature may exceed the maximum operating temperature given
in the manufacturer's data; in
this case, the thyristor should not
be required to block voltages immediately after the conduction interval. If the thyristor must block
voltages immediately following the
conduction interval, the junctiontemperature rating must not be
exceeded, and sufficient time must
elapse to allow the junction temperature to decrease to the operating temperature before blocking

dVp/c1t --r-/

-""""'1 - - - - - I
I
I

dir/dt~
IT

..L --I
I
trr--l

V(BO)F

---1VRM

-:l==---fl.........= = I

I--1

I---

tgr

I
I

---l

Figure 53. Circuit-commutated turn-off
voltage and current waveforms for
a thyristor.

Thyristors
establish a forward-depletion region so that forward blocking voltage can be re-applied and successfully blocked by the SCR.
The gate-recovery time of an
SCR is usually much longer than
the reverse-recovery time. The total time from the instant reverserecovery current begins to flow to
the start of the re-applied forward-blocking voltage is referred
to as the circuit commutated
turn-off time t ... The turn-off time
is dependent upon a number of
circuit parameters, including the
ON -state current prior to turnoff, the rate of change of current
during the forward-to-reverse
transition, the reverse-blocking
voltage, the rate of change of the
re-applied forward voltage, the
gate trigg-er level, the gate bias,
and the junction temperature. The
junction temperature and the ONstate current, however, have a
more significant effect on turn-off
time than any of the other factors.
Because the turn-off time of an
. SCR depends upon a number of
. . circuit parameters, the manufac. turer's turn-off time specification
is meaningful only if these critical
parameters are listed and the test
circuit used for the measurement
is indicated.
Fig. 54 shows a simple test
circuit used to measure turn-off
time. The circuit subjects the
SCR to current and voltage waveforms similar to those encountered
in most typical applications. In
the circuit diagram, SCR 1 is the
device under test. Initially, both
SCR's are in the OFF-state; pushbutton switch SW 1 is momentarily
closed to start the test. This action turns on SCR 1 and load current flows through this SCR and
resistor R~. Capacitor C1 charges
through resistor RH to the voltage

R" R,
R2

100 ohms

variable resistor,

0.7 to 50 ohms
R. = 5000 ohms
R5

variable

resistor,

0.1 to 1 ohm
C1

variable capacitor,
0.1 to 1 p.F, 150 V
SCRl = SCR under test
SCR2 = RCA·40378

FACTORY TESTED r-VFB RATED

~~''''~

L1(

LS2 CLOSED

SICLOSED

Figure 54. Test circuit and voltage waveforms used to determine turn-off times
of thyristors.

developed across R 2 • If the second push-button switch SW2 is
then closed, SCR 2 is turned on.
SCR 1 is then reverse-biased by the
voltage across capacitor Cl' The
discharge of this capacitor causes
a short pulse of reverse current to
flow through SCR 1 until this device recovers its reverse-blocking
capability. At some time t l , the
anode-to-cathode voltage of SCR]
passes through zero and starts to
build up in a forward direction
at a rate dependent upon the time
constant of C1 and R 2 • The peak
value of the reverse current during the recovery period can be
controlled by adjustment of potentiometer R". If the turn-off time
of SCR l is less than the time
t 1 • the device will turn off. The
turn-off interval tl can be measured by observation of the anodeto-cathode voltage of SCR 1 with
a high-speed oscilloscope. A typical waveform is shown in Fig,
54.

RCA Silicon Power Circuits Manual

Gate Characteristics
SCR's and triacs are specifically
designed to be triggered by a signal applied to the gate terminal.
The manufacturer's specifications
indicate the magnitudes of gate
current and voltage required to
turn on these devices. Gate characteristics, h{)wever, vary from
device to device even among devices within the same family. For
this reason, manufacturer's specifications on gating characteristics
provide a range of values in the
form of characteristic diagrams.
A diagram such as that shown in
Fig. 55 is given to define the
limits of gate currents and voltages that may be used to trigger
any given device of a specific
family. The boundary lines of
maximum and minimum gate impedance on this characteristic diagram represent the loci of all
possible triggering points for thyristors in this family. The curve
OA represents the gate characteristic of a specific device that is
triggered within the shaded area.
5~~------------~--~

REQUIREMENTS TO TRIGGER
ALL UNiTS AT THESE
TEMPERATURES

3i+---+----1I---Y--t----+---

Trigger Level-The magnitude
of gate current and voltage required to trigger a thyristor
varies inversely with junction
temperature. As the junction temperature increases, the level of
gate signal required to trigger
the thyristor becomes smaller.
Worst-case triggering conditions
occur, therefore, at the minimum
operating junction temperature.
The maximum value of gate
voltage below the level required
to trigger any unit of a specific
thyristor family is also an important gate characteristic. At
high operating temperatures, the
level of gate voltage required to
trigger a thyristor approaches the
minimum value, and undesirable
noise signals may inadvertently
trigger the device. The maximum
nontriggering gate voltage at the
maximum operating junction temperature of the device, therefore,
is a measure of the noise-rejection
level of a thyristor.
The gate voltage and current required to switch a thyristor to its
low-impedance state at maximum
rated forward anode current can
be determined from the circuit
shown in Fig. 56. The value of
resistor R2 is chosens{) that maximum anode current, as specified
in the manufacturer's current rating, flows when the device latches
into its low-impedance state. The
value of resistor R1 is gradually
decreased until the device under
test is switched from its high-

> 2!-t----=--=1-~~~~
III

li
C>

GATE CURRENT-rnA

Figure 55.

Gate-characteristics curves for
a typical RCA SCR.

ctEJ

6V=

~"
V

Figure 56. Test circuit used to determine
gate-trigger-pulse requirements of
thyristors.

Thyristors
impedance state to its low-impedance state. The values of gate
current and gate voltage immediately prior to switching are the
gate voltage and current required
to trigger the thyristor.
The gate nontrigger voltage
Vgnt is the maximum dc gate voltage that may be applied between
gate and cathode of the thyristor
for which the device can maintain
its rated blocking voltage. This
voltage is usually specified at
the rated operating temperature
(lOO·C) of the thyristor. Noise
signals in the gate circuit should
be maintained below this level to
prevent unwanted triggering of
the thyristor.
Pulse Triggering-When very
precise triggering of a thyristor
is desired, the thyristor gate must
be overdriven by a pulse of current much larger than the dc gate
current required to trigger the
device. The use of a large current
pulse reduces variations in turnon time, minimizes the effect of
temperature variations on triggering characteristics, and makes
possible very short switching
times.
In the past, the maximum value
of gate signal that could be ,used
to trigger a thyristor was severely
restricted by minimum dc triggering requirements and limitations on maximum gate power.
The coaxial gate structure and
the "shorted-emitter" construction techniques now used in RCA
thyristors, however, has greatly
extended the range of limiting
gate characteristics. As a result,
the gate-dissipation ratings of
RCA thyristors are compatible
with the power-handling capabilities of other elements of these de-

55
vices. Advantage can be taken of
the higher peak-power capability
of the gate to improve dynamic
performance, increase di/dt capability, minimize interpulse jitter,
and reduce switching losses. This
higher peak-power capability also
allows greater interchangeability
of thyristors in high-performance
applications.
The "shorted-emitter" technique
makes use of the resistance path
within the gate layer which is in
direct contact with the cathode
electrode of the thyristor. When
gate current is first initiated, most
of the current bypasses the gateto-cathode junction and flows from
the resistive gate layer to the
cathode contact. When the IR drop
in this gate layer exceeds the
threshold voltage of the gate-tocathode junction, the current
across this junction increases until
the thyristor is triggered.
When an SCR is triggered by
a gate signal just sufficient to turn
on the device, the entire junction
area does not start to conduct instantaneously. Instead, as pointed
out in the discussion on Switching Characteristics, the device
current is confined to a small area,
which is usually the most sensitive part of the cathode. The remaining cathode area turns on as
the anode current increases. When
a much larger signal is applied
to the gate, a greater part of the
cathode is turned on initially and
the time to complete the turn-on
process is reduced. The peak amplitude of gate-trigger currents
must be large, therefore, when
thyristors have to be turned on
completely in a short period of
time. Under such conditions, the
peak gate power is high, and pulse
triggering is required to keep the
average gate dissipation within

RCA Silicon Po.werCircuits Manual

the values given -in the manufacturer's specifications. New gate
ratings, therefore, are required
for this type of application.
The forward gate characteristics for thyristors, shown in Fig.
57, indicate the maximum allowable pulse widths for various peak
values of gate input power. The
pulse width is determined by the
relationship that exists between
gate power input and the increase
in the .temperature of the thyristor pellet that results from the application of gate pewer. The
curves shown in Fig. 57 (a) are for
RCA SCR'sthat have relatively
small current ratings (2N4101,
2N4102, and 40379 families), and
the curves. shown in Fig. 57 (b)
are for RCA SCR's that have
larger current ratings (2N3670,
2N3873, and 2N3899 families).
Because the higher-current thyristors have larger pellets, they also
have greater thermal capacities
> 40
I

'" 32

.",

~~".I.s'~
~~~
+,.

II.,

.. "0
+.
8 ~~~~-

I-

~l~~~~SISTANCE

GATE CORRENT-A

1-\'0

,,"-/

ll: 32

~
~

~-&

~~",-ey

624 ~~t~"

l!!
~

1·6
8

~r -

V
o

i":

......I• .s'~ ___ ~
"01$;.0
"00
~

ffi

-.!....

-32 t--i--7r--i

MINIMUM
GATE RESISTANCE

-16I---HH-/---+.

~ -241-11-1-1;

I.'

1"1000
2
4

. -8~~~-+-r-r~~'
'"'"

:::-

(a)

>40

(a)

.~j

'"~-16
~-20
'"
'">
'"0:-24

=t;f
/
- ,;;t.~&'/

~
g
24 -'*~t;."'YI
.~ 16

than the smaller-current devices.
Wider gate trigger pulses can
therefore be used on these devices
for the same peak value of gr.te
input power.
Because of the resistive nature
of the "shorted-emitter" construction, similar volt-ampere curves
can be constructed for reverse
gate voltages and currents, with
maximum allowable pulse widths
for various peak-power values, as
shown in Fig. 58. These curves
indicate that reverse dissipations
do not exceed the maximum allowable power dissipation for the device.

GATE CURRENT-A

(b)
Figure 57. Forward-gate characteristics for
pulse triggering of RCA SCR's: (a) lowcurrent types, (b) high-current types.

-4~'::.0:--'---=o!-:.e:--'---=0!-:.6'->---':O~.4-'---':O:>!.2c'-'--'
REVERSE GATE CURRENT-A

(b)

·Figure 58. Reverse gate characteristics of
RCA SCR's: (a) low-current types, (b) highcurrent types.

Thyristors
Trigger-Circuit Requirements
-The basic gate trigger circuit
for a thyristor can be represented
by a voltage source and a series
resistance, as shown in Fig. 59.
The series resistance should include both the external circuit
resistance and the internal generator resistance. With this type of
equivalent circuit, the conventional load-line approach to gate
trigger-circuit design can be used.

., 4

i'w

T=25°C

\
f\

:;;

~
I

~ 2
:::>

I
CIRCUIT RESISTANCE

SCR
RC

'" "

---.... ""-

~ 3
z

~ 2

:::>
t-

.........

1000

T=25°C

With ,pulse triggering, it is assumed initially that the' turn-on
time required to trigger all thyristors of the same type is known,
and that the maximum allowable
gate trigger-pulse widths for specific gate-power inputs are to be
determined.
The magnitude of gate-trigger
current required to turn on all
SCR's ofa given type can be determined from the turn-on characteristics shown in Fig. 60. The
spread or band of turn-on characteristics for the same gate current
results from the variation of gatetrigger characte·ristics among devices of the same family. Because
of the greater over-drive factor
involved, the same gate current
applied to a device obviously turns
on a low-gate-current device in
much less time than that required
to turn on a higher-gate-current

"--

200
400
600
BOO
GATE CURRENT-rnA
(a)

5
Figure 59. 'Equivalent 'diagram of the basic
gate·trigger circuit for a thyristor.

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

--.

--. I---

200
400
600
BOO
GATE CURRENT-rnA
(b)

1000

Figure 60. Turn-on time distribution among
RCA SCR's: (a) low-current types,
(b) high·current types.

device. For example, a gate-trigger current of 100 milliamperes
overdrives an SCR that requires
a trigger current of only 2 milliamperes by a factQr of 50 and
causes the device to turn on very
quickly, while an SCR that requires 10 milliamperes of trigger
current is overdriven by a factor
of 10 and is turned on more

RCA Silicon Power Circuits Manual

slowly. As the gate current increases, the band of turn-on characteristics becomes narrower, and
an increase in gate current does
not effectively decrease the turn-on
time.
The following example, in which
an RCA-2N3873 SCR is to be
turned on in 2.5 microseconds,
demonstrates the use of the various characteristics in the solution
of a typical triggering problem:
The turn-on characteristics
shown in Fig. 60 indicate that a
gate-trigger current of 1 ampere
is required to insure that all devices of this type will turn on in
2.5 microseconds (the 2.5-microsecond ordinate level intersects the
upper curve at 1000 milliamperes).
In addition, the width of the gatetrigger pulse should be at least
2.5 microseconds to ensure that
the SCR remains on after it is
triggered. Actually, the minimum
requirement is that the pulse
width be wide enough for the
SCR anode current to achieve
the latching value. Conservative
design, however, requires the
pulse width to be at least equal
to the turn-on time. For inductive loads, the turn-on time is
larger than indicated in the characteristics curves because of the
slow rise of current through the
inductance.
A straight load line can then be
plotted on the pulse triggering
characteristics, as shown in Fig.
6l. The two points that determine
the position of this line are the
source voltage (20 volts) and a
point slightly above the intersection of the required gate current
(1 ampere) and the curve of maximum gate resistance. The load
line should lie below the pulsewidth curve required to trigger
all SCR's (in this example, the

1'32
!!l241----t-:r-t--'"

j:!
oJ

Figure 61. Forward gate characteristics of
typical RCA SCR's showing load line for a
source of 20 volts and a required gate
current of 1 ampere.

2.5-microsecond curve). The maximum allowable pulse width is obtained by estimation of the pulsewidth curve tangent to the load
line. In this example, the pulse
width is estimated to be 30 microseconds (the pulse-width curves
are logarithmically spaced). The
load line intersects the abscissa
at the 4-ampere point. The maximum circuit resistance, therefore,
is 5 ohms. The peak gate power is
the product of gate voltage and
gate current at the point of tangency of the pulse-width curve,
and is approximately 20 watts (10
volts x 2 amperes).
When gate pulses are used to
trigger SCR's, the maximum allowable operating frequency f is dependent upon the average power
rating of the gate P g(Uyg) and can
be determined from the following
equation:
f = Pg(avg)/Pg(pk)XPW g
(8)
where P g(pk) is the peak gate
power and PWg is the gate pulse
width.
If it is assumed that only half
the total average gate-dissipation
rating of the RCA-2N3873, or 0.25
watt, is used to trigger the device, then the maximum allowable
operating frequency is determined
as follows:

Thyristors

0.25W
20W X 2.5 X 1O-6second
= 5000 Hz
If there is no reverse gate power
dissipation, the maximum allowable frequency can be 10,000 Hz.
If the maximum allowable pulse
width is 30 microseconds the
maximum allowable operatin~ frequency is proportionately reduced
to 416 Hz.
The trigger-circuit design is
usually fixed by the requirements
for reliable triggering, and reverse gate dissipation is considered after the values of source
voltage and circuit resistance have
been determined. Reverse gate
power dissipation results from reverse gate-bias conditions or circuit reaction caused by some
switching function. As in the case
of the forward gate characteristics, a load-line approach can also
be used to determine the reverse
gate characteristics. The maximum anticipated value of reverse
gate potential is used as the
source voltage, and the external
circuit resistance is used to determine the slope of the load line.
The load line on the reverse gate
characteristics shown in Fig. 62
represents a reverse gate-source
voltage ·of 24 volts and an external-circuit resistance of 5 ohms.
From the relationship that exists
among pulse width, average gate
power, peak gate power, and frequency, a maximum pulse width
can be calculated for the actual
operating frequency. For a reverse
gate dissipation of 0.25 watt, peak
gate power of 10 watts, and a frequency of 5000 Hz, the maximum
allowable pulse width PW is calculated as follows:
f=

PW=
=

0.25W
5000 Hz X lOW
5 microseconds

(9)

This reverse gate-pulse width
should be less than the maximum
allowable pulse width as determined by the curve th~t lies just
below the load line on Fig. 62. In
this example, the maximum allowable pulse width for reverse dissipation is 100 microseconds.

1- 8 -

~-16

(!)

-24

~-32

-40~

-1.0

~~'
x-

sfg

__~____~1--L-i__~~~~~
-0.8
-0.6
-0.4
-0.2
·0
REVERSE GATE CURRENT-A

Fig!Jre 62. Reverse gate characteristics for
tYPical RCA SCR's showing load line for
a reverse gate·source voltage of 24 volts
and an external circuit resistance of
5 ohms.

The total average dissipation
caused by gate-trigger pulses is
the sum of the average forward
and reverse dissipations. This total dissipation should correspond
to the average gate power dissipation shown in the published data
for the selected SCR. If the average gate dissipation exceeds the
maximum published value, as the
result of high forward gate-trigger pulses and transient or steadystat~ reverse gate biasing, the
maXImum allowable forward-conduction-current rating of the device must be reduced to compensate for the increased rise of
junction temperature caused by
the increased gate power dissipation.
The trigger-circuit design considerations described for RCA

RCA Silicon Power Circuits Manual

SCR's also apply to RCA triacs.
Although both types of devices
are triggered in the same manner,
the triac can be triggered by
either positive or negative gatetrigger pulses independent of the
polarity of the voltage between
the main terminals.

SERIES AND
PARALLEL OPERATION
The voltage or current capabilities of a single thyristor can be
extended by use of two or more
thyristors of the same type in
series or parallel arrangements,
respectively. The following paragraphs discuss basic considerations important to the successful
operation of thyristors used in
multiple connections.

Series Connections
When thyristors are connected
in series for higher-voltage operation, certain procedures should be
followed. These procedures usually
depend upon the typical electrical
characteristics of the thyristors
lised and the requirements of the
circuit application.
The most important consideration in series connections of thyristors is to assure that voltages
are divided equally across the individual units in the series string.
One technique that may be used
to obtain the desired voltage distribution is to select units that
are matched with respect to such
characteristics as OFF-state voltage breakdown, reverse voltage
and current, and temperature effects. The use of a resistor across
each unit in the stack is also
recommended for improvE:d series
operation of thyristors. The value
of the resistors should be some

fraction of the maximum OFFstate resistance of the thyristor to
force equal voltage division among
the devices.
When SCR's are used in series
arl'angements, differences in the
reverse-recovery times of the units
have an important bearing on the
voltage division. Variation in internal capacitances of thyristors
and in stray capacitances between
thyristors and ground can also result in an unequal voltage division
among the various units. The use
of capacitive voltage dividers is
recommended to eliminate the effects of such conditions. When
capacitive voltage dividers are
used, however, a damping resistor
should be connected in series with
each capacitor to restrict peakcurrent values when the thyristors are switched to the ON state
while the OFF-state voltage is
present on the capacitor.
When thyristors are connected
in series, the gate-trigger circuit
used to turn on the various units
requires special consideration. Because of differences in the delay
and rise times of thyristors, gatetrigger currents that have a fast
rise time must be used to turn on
the units in the series string. The
use of large gate-trigger currents
minimizes turn-on differences. If
large, quick-rising trigger currents are not used, the voltage
across units that have longer turnon times may exceed peak-voltage
ratings.

Parallel Connections
Thyristors are connected in
parallel to obtain output currents
higher than the current ratings
of an individual thyristor. The
main consideration for this type

Thyristors
of operation is that the current
must be divided equally among the
parallel thyristors. One technique
that is used to assure proper current division is to connect an
identical balancing resistor in
series with each thyristor. The
value of these resistors should be
several times larger than the
maximum ON-state impedance of
the thyristors so that the current
through each thyristor will be essentially the same even though
the ON-state impedances of the
thyristors are different. The addition of a balancing resistor to
each conduction path, however,
increases the power dissipation
and, consequently, decreases the
over-all efficiency of the circuit.
The efficiency of the circuit is improved if reactors, rather than
resistors, are used to achieve
balanced currents.
Another technique used in the
parallel connection of thyristors
is to select matched devices on the
basis of specific conduction characteristics. When this technique
is employed, circuit and load impedances must be carefully designed to assure an equal impedance for each conduction path
in the parallel array. When factory-matched units are employed,
care must be taken to insure that
all units are operated at essentially the same case temperature.
Because the forward voltage drop
of a thyristor is temperaturedependent, differences in case
temperature can result in unequal
current sharing. All thyristors in
the parallel array, therefore,
should be mounted on a common
heat sink to assure that the operating junction temperature of
each device is the same.
When thyristors are connected
in parallel, it is preferable to use

61
a continuous gate drive to turn
on the devices because of the differences in the latching levels of
individual thyristors. Continuous
gate drive is particularly important when inductive loads are used
because such loads produce slowrising output currents, and the
continuous drive assures that gate
current is present throughout the
full conduction period. If pulse
triggering is employed, the duration of the gate-trigger pulse must
be sufficient to allow the conduction currents through all the thyristors to build up to values
greater than the latching values
to assure that all thyristors are
completely turned on. The .gatetrigger pulses should be fast-rising, high-amplitude pulses to assure good current sharing among
the parallel thyristors during the
turn-on interval.
Consideration should be given
in parallel arrays to the possibility
that one thyristor may be inadvertently turned on from some
extraneous source, e.g., a high rate
of rise of OFF-state voltage
(dv/dt). Under such conditions, it
is possible that an excessive
amount of current may flow
through this thyristor.
TRANSIENT PROTECTION
Voltage transients occur in
electrical systems when some disturbance disrupts the normal
operation of the system. These
disturbances may be produced by
various sources (such as lightning surges, energizing transformers, and load switching) and
may generate voltages which exceed the rating of the thyristors.
In addition, transients generally
have a fast rate of rise that is
usually greater than the critical

RCA Silicon Power Circuits Manual

value for the rate of rise of
the thyristor OFF-state voltage
(static dv/dt).
If transient voltages have magnitudes far greater than the device rating, the thyristor may
switch from the OFF state to the
ON state; the excess voltage is
then transferred from the thyristor to the load. Because the internal resistance of the thyristor
is high during the OFF state, the
transients may cause considerable energy to be dissipated in
the thyristor before break over
occurs. In such instances, the
transient voltage exceeds the
maximum allowable voltage rating, and irreversible damage to
the thyristor may occur.
Even if the magnitude of a
transient voltage is within the
maximum allowable voltage rating of the thyristor, the rate of
rise of the transient may exceed
the static dv/dt capability of the
thyristor and cause th~ device to
switch from the OFF state to the
ON state. In this case, thyristor
switching from the OFF state
to the ON state occurs because
of the fast rate of rise of OFFstate voltage (dv/dt) and the
thyristor capacitance (e), which
result in a turn-on current i =
edv/dt. Thyristor switching produced in this way is free from
high-energy dissipation, and
turn-on is not destructive provided that the load current that
results is within the device
capability.
In either case, transient suppression techniques are employed
to minimize the effects of turn-on
because of overvoltage or because
the thyristor dv/dt capability is
exceeded.
One of the obvious solutions to
insure that transients do not ex-

ceed the maximum allowable
voltage rating is to provide a
thyristor with a voltage rating
greater than the highest transient voltage expected in a system. This technique, however,
does not represent an economical
solution because, in most cases,
the transient magnitude, which
is dependent on the source of
transient generation, is not easily
defined. (Transient voltages as
high as 2600 volts have resulted
from lightning disturbances on a
120-volt residential power line.)
Usually, the best solution is to
specify devices that can withstand voltage from 2 to 3 times
the steady-state value. This technique provides a reasonable
safety factor. The effects of voltage transients can further be
minimized by use of external circuit elements, such as a series
Re network, across the thyristor
terminals, as shown in Fig. 63.

POWER

INPUT

Figure 63. Diagram showing use of RC
network for transient suppression in
thyristor circuits.

The rate at which the voltage
rises at the thyristor terminal is
a function of both the load impedance and the values of the
resistor R and the capacitor e.
Because the load impedance is
usually variable, the preferred
approach is to assume a worstcase condition for the load and,
through actual transient mea-

Thyristors

surement, to select a value of
C that provides the minimum
rate of rise at the thyristor
terminals. The resistance R
should be selected to minimize
the capacitor discharge currents
during turn-on.
For applications in which it is
necessary to minimize false turnon because of transients, the addition of a coil in series with the
load, as shown in Fig. 64, is very
effective for reduction of the
rate of voltage rise at the thyristor terminals. For example, if
a transient of infinite rise time
is assumed to occur at the input
terminals and if the effects of the
load impedance are neglected, the
rise time of the transient at
the thyristor terminals is approximately equal to El'lj VLC. If the
value of the added inductor L is
100 microhenries and the value
of the snubber capacitor C is 0.1
microfarad, the infinite rate of
rise of the transient at the thyristor terminals is reduced by a
factor of 3. For a filter network
consisting of L = 100 microhenries, C = 0.22 microfarad, and
R = 47 ohms, a 1000-volt-permicrosecond transient that appears at the input terminals is
suppressed by a factor of 6 at the
thyristor terminals.
L

POWER

INPUT

Figure 64. Diagram showing use of RC
network for transient suppression and an
inductance to prevent false turn-on because of transients in thyristor circuits.

COMMUTATING dv/dt
CONSIDERATIONS
In ac power control, a triac
must switch from the conducting
state to the blocking state at
each zero current point, or twice
per cycle. This action is called
commutation. If the triac fails
to block the circuit voltage following the zero-current point,
control of the load power is lost.
This action is not damaging to
the triac. Commutation for resistive loading presents no special problems because the voltage and current are essentially
in phase. For inductive loading,
however, the current lags the
voltage so that, following the
zero-current point, an applied
voltage opposite to the current
and equal to the peak of the ac
line voltage occurs across the
thyristor. The maximum rate of
rise of this voltage which can
be blocked by the triac without
reverting to the ON state is
termed the critical rate of rise
of commutation voltage for the
triac or the commutating dv/ dt.
SCR's do not experience commutation limitations
because
turn-on is not possible for the
polarity of voltage opposite to
current flow.
The triac may be considered as
two SCR's in an inverse-parallel
connection with the exception
that the high-voltage blocking
function is common to both
SCR's. In the circuit shown in
Fig. 65, during the zero-current
crossover (point A), the half of
the triac in conduction starts to
commutate when the main current flow falls below the holding
current. At the instant the conducting half of the triac turns
off, an applied voltage opposite

RCA Silicon Power Circuits Manual

to the previous current polarity
is applied across the triac. When
this voltage is applied, a displacement current results from
the formation of a depletion region at the junction. The portion
of this displacement current
which crosses the n-type emitter
junction of the other side of the
triac may be sufficient to trigger
the device into the ON state in
that' direction. The over-all result is loss of power control to
the load. The rate of decrease of
current prior to the zerO-Gurrent
point and,the rate of application
of voltage in the opposite- polarity determine th'e commutating
duty on the triac.

The most economical approach
to reduction of the dv/dt stress
so that it is within the capability
of the triac is the use of a series
RC network across the triac. The
rate of change of re-applied
voltage is then dependent on the
inductance and capacitance of
the load and the impedance of
the network. The magnitude of
added capacitance is determined
by the load impedance and the
dv/dt limitation of the triac.
The value of the added resistance
R should be sufficient both to
damp the LC oscillation and to
maintain the capacitor discharge
currents dhlring triac turn-on
within acceptable limits.

SOURCE VOLTAGE
LOAD

/ @

Figure 65. Simplified diagram and voltage and current waveforms for operation of a
triac in a circuit that has an inductive load and a lagging-current power factor.

Silicon Power Transistors
HE performance of power tranTsistors
in electronic equipment

depends on many factors besides
the basic characteristics of the
semiconductor material. The two
most important factors are the
design and fabrication of the transistor structure and the manner
in which power is dissipated from
the device. Other factors that must
also be considered are maximum
ratings, basic parameters, reliability, and types of service in
which power transistors are used.

DESIGN AND FABRICATION
The ultimate aim of all transistor fabrication techniques is the
construction of two parallel p-n
junctions with controlled spacing
between the junctions and controlled impurity levels on both
sides of each junction. A variety
of structures has been developed
in the course of transistor evolution.
The earliest transistors made
were of the point-contact type.
In this type of structure, two
pointed wires are placed next to
each other on an n-type block
of semiconductor material, and the
p-n junctions are formed by electrical pulsing of the wires. This
type has been superseded by junction transistors, which are fabricated by various alloy, diffusion,
and crystal-growth techniques.
In grown-junction transistors,
the impurity content of the semiconductor material is changed during the growth of the original

crystal ingot to provide the p-n-p
or n-p-n regions. The grown crystal is then sliced into a large number of small-area devices, and
contacts are made to each region
of the devices. Fig. 66 shows a
cross section of a grown-junction
transistor.
ASELEAD

SOLDER!
EMITTER
CONTACT

Figure 66.

~SOLDER
COLLECTOR
CONTACT

BASE
REGION

Cross-section of grown-junction
transistor.

In alloy-junction transistors,
two small "dots" of a p-type or
n-type impurity element are placed
on opposite sides of a thin wafer
of n-type or p-type semiconductor
material, respectively, as shown
in Fig. 67. After proper heating,
the impurity "dots" alloy with the
ORIGINAL
SEMICONDUCTOR
MATERIAL-BASE
EMITTER DOT
REGION

~
S()L[)ERCcoillc

CONTACT

DOT

Figure 67.

Cross·section of alloy-junction
transistor.

semiconductor material to form
the regions for the emitter and
collector junctions. The base connection in this structure is made
to the original semiconductor
wafer.
The drift-field transistor is a
modified alloy-junction device in

RCA Silicon Power Circuits Manual

which the impurity concentration
in the base wafer is diffused or
graded, as shown in Fig. 68. Two
advantages are derived from this
structure: (a) the resultant builtin voltage or "drift field" speeds
current flow, and (b) the ability
to use a heavy impurity concentration in the vicinity of the emitter
DIFFUSED
BASE REGION

SOLDER
~~RI~~~~I:~~t
COLLECTOR SEMICONDUCTOR
DOT
MATERIAL

Figure 68.

Cross·section of drift·field transistor.

and a light concentration in the
vicinity of the collector makes it
possible to minimize capacitive
charging times. Both these advantages lead to a substantial extension of the frequency performance
over that of the alloy-junction device.
The diffused-junction transistor represents a major advance in
transistor technology. The increased control over junction spacings and impurity levels made
possible by the diffusion technique has led to significant improvements in transistor performance capabilities.
The first diffused-junction silicon power transistor was the single-diffused "hometaxial" structure shown in Fig. 69. The
hometaxial transistor is fabricated

by a simultaneous diffusion of impurity from each side of a homogeneously doped slice of silicon.
A mesa is etched on one side of
the slice in an intricate design to
define the transistor emitter and
expose the base region to facilitate
application of metal contacts to the
semiconductor. Large amounts of
heat can be dissipated from a
hometaxial structure through the
highly conductive solder joint between the semiconductor material
and the device header. This structure results in a high-performance, rugged power transistor
that has a very low collector resistance.
The double-diffused transistor
provides a structure which has
an additional degree of freedom
for selection of the impurity levels
and junction spacings of the base,
emitter, and collector. This structure makes possible high voltage
capability through a lightly doped
collector region without compromise of the junction spacings
which determine device frequency
response and other important
characteristics. Fig. 70 shows
a typical double-diffused silicon
transistor. In this type of transistor, the emitter and base junctions
are formed on the same side of
the silicon slice by photolithographic and silicon-dioxide maskeASE LEAD
METAL FILM
CONTACT
SOLDER

EMITTER METAL

EMITTER LEAD
DIFFUSED EMITTER
DIFFUSED BASE
HEADER

UNDI FUSED
COLLECTOR

Figure 70. Cross-section of double-diffused
silicon power transistor.

UNDIFFUSED BASE

(HOMOGENOUS)

Figure

69. Cross-section of hometaxialbase silicon power transistor.

ing and solid-state diffusion. A
mesa is usually etched through the
base region to reduce the collector area at the base-to-collector
junction and to provide a rugged,
stable semiconductor surface.

Silicon Power Transistors
The double-diffused silicon
planar transistor provides the inherent advantages of the doublediffused design together with the
added advantage of protection or
passivation of the emitter-to-base
and collector-to-base junction surfaces. Fig. 71 shows a typical
double-diffused silicon planar transistor. The base and emitter regions terminate at the top surface
of the semiconductor slice under

collector resistance. The structure
and characteristics of this type of
transistor are similar to those
of the triple-diffused transistor
shown in Fig. 72. The epitaxial
structure differs fundamentally
only in the way the collector region is fabricated. The lightly
SILICON DIOXIDE
DIFFUSED EMITTER
DIFFUSED
BASE
E
SOLDER

DIFFUSEDI_~~~~f?:J
BASE

UNDIFFUSED
COLLECTOR

DIFFUSED
EMITTER

Figure 71. Cross-section of double-diffused
silicon planar power transistor.

the protection of a layer of silicon
dioxide_ Photolithographic techniques and silicon-dioxide masking
are used to provide for diffusion
of both base and emitter impurities in selective areas of the silicon slice.
The triple-diffused transistor
structure provides the advantages
of the double-diffused design without the disadvantage of high collector resistance. This structure
has a heavily doped region diffused
from the bottom of the silicon
slice which effectively reduces the
thickness of the lightly doped collector region to a value dictated
only by electric-field considerations. This design thus minimizes
the thickness of the lightly doped
or high-resistivity portion of the
collector to obtain a low collector
resistance. A low collector resistance is a particularly important
advantage in high-current applications. Fig. 72 shows a section of
a triple-diffused planar structure.
A triple-diffused mesa structure
could also be fabricated.
The epitaxial double-diffused
transistor structure also has a low

UNDIFFUSED
COLLECTOR

C
HEADER

DIFFUSED
COLLECTOR
HEAVILY DOPED

Figure 72. Cross-section of triple-diffused
silicon planar power transistor.

doped collector portion of the epitaxial structure is grown on top
of a heavily doped silicon slice in
a high-temperature reaction chamber. This growth proceeds atom
by atom and is a perfect extension
of the crystal lattice of the heavily
doped silicon slice on which it is
grown. In contrast, the triplediffused structure starts with a
lightly doped region and has a
heavily doped region diffused into
a portion of it. Both techniques
provide the low collector resistance
required for high-current or highpower circuit applications.
The epitaxial-base transistor
has a structure in which a lightly
doped base region is deposited by
epitaxial techniques on a heavily
doped silicon slice of opposite-type
dopant. Photolithographic and silicon-dioxide masking and a single
impurity diffusion are used to define the emitter region, as shown
in Fig. 73. This structure offers
the advantage of low collector resistance and ease of controlling
DIFFUSED EMITTER
....t5~~~~..!!EPITAXIAL
BASE

Figure 73. Cross-section of epitaxial-base
silicon power transistor.

RCA Silicon Power Circuits Manual

impurity spacings and emitter
geometry, for high-current and
moderate-frequency performance.
A variation of this structure uses
two epitaxial layers. A thin lightly
doped epitaxial layer, which is
used for the collector, is deposited
over the heavily doped silicon slice
prior to the epitaxial deposition of
the base region. The collector epitaxial layer is of opposite-type
dopant to the epitaxial base layer.
This structure, shown in Fig. 74,
has the advantages of the epitaxialbase device, with an added advantage of higher voltage ratings provided by the epitaxial collector
layer.
CONTACT METAL

SILICON
DIOXIDE

r~te~~~~~~~l.DIFFUSED
EMITTER

DIFFUSED EMITTER

EPITAXIAL l~~~~~~....!'EPITAXIAL
COLLECTOR
BASE

-A~~~~~.c~~~~5Y
SOLDER

ratio and reduces the charging
time constants without compromise of the transistor current and
power-handling capability. The
overlay transistor is fabricated by
exceptionally well controlled diffusions and very precise photolithographic and silicon-dioxide
masking operation. Fig. 76 shows
a section through a typical overlay emitter region.

COLLECTOR

Figure 74. Cross-section of dual-epitaxiallayer si licon power transistor.

The overlay transistor is a
double-diffused epitaxial device
which employs a unique emitter
structure. In this structure, a
large number of separate emitters
are tied together by diffused and
metalized regions, as shown in
Fig. 75. This design concept increases the emitter edge-to-area

Figure 76.

Cross-section of overlay transistor.

Power-transistor designs differ
fundamentally from signal-level
transistors in the way that the
semiconductor element is packaged to provide for high thermal
conductivity and low-resistance
electrical contacts. The power
semiconductor element is usually
soldered or gold-alloyed to a solid
metal header, as shown in Fig.
77. For the high-power types, the
header is generally constructed
from copper or laminated copper
and steel for improved heat transfer. Low-resistance contacts are
soldered or metal-bonded from the
EMITTER CONTACT

EMITTER
LEAD

Figure 75.

Emitter structure of an overlay
transistor.

Figure 77.

BASE
LEAD

Assembly details for high-power
si licon transistor.

Silicon Power Transistors
emitter or base metalizing contacts to the appropriate package
leads. This packaging concept results in a simple structure that
can be readily attached to a
variety of circuit heat sinks and
that can safely withstand power
dissipations of hundreds of watts
and currents of tens of amperes.
A few high-performance power
transistors are packaged with
electrical isolation of the collector. This isolation is achieved,
without compromise of thermal
dissipation, by gold-alloying of the
semiconductor element to a metalized ceramic disc. This disc, which
is usually beryllium oxide, is
brazed to the package header to
provide a low thermal-resistance
path to the circuit heat sink.

69
current gain from base to collector.
2. alpha (a)-general term for
current gain from emitter to col:
lector.
3. hfc-ac gain from base to
collector.
4. hFE-dc gain from base to
collector.
The input impedance rill of a
transistor also affects the power
output, as indicated by the equations shown in Fig. 78. The input impedance is not usually specified directly because of the large

BASIC TRANSISTOR
PARAMETERS
A transistor is usually employed
to obtain a power gain by use of
a small control signal to produce
larger signal variations in the
output current. In a vacuum tube,
the most common gain parameter
is the voltage amplification factor
(fJ,) from the grid to the plate.
In a transistor, the most commonly specified gain parameter is
the current gain ({3) from the
base to the collector. Power gain
of a transistor operated in the
common-emitter circuit configuration is proportional to the square
of the current gain multiplied by
the load resistance divided by the
input resistance, as indicated in
Fig. 78.
The current gain (or current
transfer ratio) of a transistor is
expressed by many symbols; the
following are some of the most
common, together with their particular shades of meaning:
1. beta ({3) -general term for

ic = ibfl

INPUT CURRENT

INPUT VOLTAGE

OUTPUT CURRENT

= i, = h.(3

OUTPUT VOLTAGE

R'n

= i"Rr. = ibfin.

INPUT POWER

ib 2

OUTPUT POWER

i c2 Rr.

POWER GAIN

=
=

power output/power

ib 2,82 rL/ib 2r1n

(32rL/fln

R'n

ib' (32 rIo

input

Figure 78. Test circuit and
simplified
power-gain calculation for a transistor operated in a common-emitter configuration.

number of components of which it
is comprised, but is usually specified as a maximum base-to-emitter
voltage Vile under specified inputcurrent conditions.

RCA Silicon Power Circuits Manual

Other low-frequency electrical
characteristics commonly specified
for transistors are those needed
to verify the maximum ratings
and the leakage currents. Leakage
currents are important because
they affect biasing in amplifier
applications and represent the
"OFF" condition for transistors
used in switching applications.
Several different leakage currents
are commonly specified. The most
basic specification is I CBO, which
indicates the leakage from collector to base with the emitter open.
This leakage, which is simply the
reverse current of the collectorto-base diode, is composed of two
components, a saturation current
that doubles in value for approximately every 8°C increase in temperature and a surface-leakage
component that is not directly related to temperature. In a silicon
transistor, the saturation current
is normally small; at room temperature, only the surface leakage
is measurable. High-temperature
leakage currents are usually specified in the published data for a
transistor.
In addition to the I cBo ratings,
ICEY, ICEO' and ICER ratings are
often specified for transistors.
I CEV is the leakage from the collector to emitter with the base-toemitter junction reverse-biased.
ICER is the leakage current from
the collector to the emitter with
the base and emitter connected
by a specified resistance. I CEO is
the leakage current from collector
to emitter with the base open.
I CEV differs from I CBO only very
slightly and in most transistors
the two parameters can be considered equal. (This equality is not
maintained in symmetrical transistors.) I CEO is simply the product
of I CBO at the voltage specified
and the hFE of the transistor at

a base current equal to I CBO . I CEO
is of course the largest leakage
current normally specified. ICER
is intermediate in value between
I CEV and I CEO .
When transistors are used at
higher frequencies, their gain decreases. This condition is discussed more completely in the section on High-Frequency Power
Amplifiers. The hr. decreases with
frequency in a predictable way, as
shown in Fig. 79.

FALLS OFF
AT
jdBlOCTAVE

FREQUENCY (LOGARITHMIC)

Figure 79. Transistor current·gain parameter h .. as a function of frequency.

Because of the regular decrease
at high frequencies (6 dB per octave), a measurement of the gain
at any frequency on the 6-dBper-octave slope multiplied by the
frequency at which beta is measured results in approximately the
same value. This value, called the
gain-bandwidth product fT' is indicative of the high-frequency
capability of a transistor. Other
parameters which affect high-frequency performance are the capacitance or resistance which
shunts the load and the input impedance, the effect of which is
shown by the equations of Fig.
78.

The specification of all the characteristics which affect high-frequency performance is so complex

Silicon Power Transistors
that often a manufacturer does
not specify all the parameters but
instead specifies transistor performance in an rf-amplifier circuit. This information is very
useful when the transistor is operated under conditions very similar to those of the test circuit,
but is difficult to apply when the
transistor is used in a widely different application. Some manufachIrers also specify transistor performance characterisetics as a
function of frequency, which alleviates these problems.
The power-dissipation capability
of a transistor is usually given by
a dissipation derating curve, a
thermal-resistance specification,
and a maximum junction temperature, or a safe-area curve. Thermal
resistance is the increase in temperature of the junction of a transistor (with respect to some reference) divided by the power
dissipated. In power transistors,
the thermal resistance is normally
measured from the pellet of the
transistor to the case. The user
is then required to determine the
remainder of the heat-flow path.
Thermal resistance is usually
measured by operation of the transistor in a pulsed type of service
in which power is dissipated in
the transistor during most of the
operating cycle. During the remainder of the cycle, a temperattu'e-sensitive parameter of the
transistor is monitored to determine the junction temperature.
The parameter usually monitored
to determine junction temperature
is the forward-voltage drop across
the base-to-emitter diode junction.
For optimum accuracy, the thermal resistance of each transistor
must be determined individually.
The test, therefore, is very slow
and expensive. There is an additional disadvantage to thermal-

resistance testing in that the
measurement is based on the average junction temperature and
does not indicate the maximum
temperature attained within the
device if temperature distribution
across the pellet is not uniform.
Safe-area curves are normally
verified with a power rating test.
In this type of test, the transistor
is subjected to a high-level pulse
of power (usually equal to the
power ratings of the transistor at
25°C) for a period of time that is
long compared to the transistor
internal time constant, but short
compared to the thermal time constant of the case. The voltage
across the transistor is monitored.
A failing unit momentarily shorts
because of localized overheating.
During the test, this overheating
is detected by a sensing circuit,
and power is removed. In an actual
application, the transistor would
be destroyed. A safe-area rating
curve indicates whether a transistor can withstand a given power
level without excessive localized
overheating.

MAXIMUM RATINGS
All semiconductor devices undergo irreversible changes if
their temperature is increased beyond some critical limit. A number
of ratings are given for power
transistors, therefore, to assure
that this critical temperature limit
will not be exceeded on even a
very small part of the silicon chip.
The ratings for power transistors
normally specify the maximum
voltages, maximum current, maximum and minimum storage temperature, and maximum power
dissipation that the transistor
can safely withstand.

RCA Silicon Power Circuits Manual

72
Voltage Ratings

Maximum voltage ratings are
normally given for both the collector and the emitter junctions of
a transistor. A V BEO rating, which
indicates the maximum emitterto-base voltage with the collector
open, is usually specified. The collector-junction voltage capability
is usually given with respect to
the emitter, which is used as the
common terminal in most transistor circuits. This capability may
be expressed in several ways. A
VCEO rating specifies the maximum reverse collector-to-emitter
voltage with the base open ; ~
VCEll rating for this voltage implies that the base is returned to
the emitter through a specified
resistor; a VCES rating gives the
maximum reverse voltage when
the base is shorted to the emitter;
and a V CEV rating indicates the
maximum voltage when the base
is reverse-biased with respect to
the emitter by a specified voltage.
A V(,EX rating may also be given
to indicate the maximum collectorto-emitter voltage when a resistor
and voltage are both connected
between base and emitter.
If a maximum voltage rating
is exceeded, the transistor may
"break down" and pass current in
the reverse direction. The breakdown across the junction is usually
not uniform, and the current may
be localized in one or more small
areas. The small area becomes
overheated unless the current is
limited to a low value, and the
transistor may then be destroyed.

Current Ratings
The maximum current rating of
a transistor indicates the highest
current at which, in the manufacturer's judgment, the device is

useful. This current limit may be
established by setting an arbitrary minimum current gain or
may be determined by the fusing
current of an internal connecting
wire. A current that exceeds the
rating, therefore, may result in
a low current gain or in the destruction of the transistor.

Storage and Operating
Temperature Ratings
The basic materials in a silicon
transistor allow transistor action at temperatures greater than
300°C. Practical transistors, however, are limited to lower temperatures by mounting systems and
surface contamination. If the
maximum rated storage or operating temperature is exceeded,
irreversible changes in leakage
current and in current-gain characteristics of the transistor result.

Power Ratings
A transistor is heated by the
electrical power dissipated in it. A
maximum power rating is given,
therefore, to assure that the temperature in all parts of a transistor
is maintained below a value that
will result in detrimental changes
in the device. This rating may be
given with respect to case temperature (for transistors mounted
on heat sinks) or with respect to
"free-air ambient" temperature.
Case temperature is measured
with a small thermocouple or other
low-heat-conducting thermometer
attached to the outside of the case
or preferably inserted in a very
small blind hole in the base so that
the measurement is taken as close
to the transistor chip as possible.
Very short pulses of power do not
heat the transistor to the temperature which it would attain if the

Silicon Power Transistors
power level was continued indefinitely. Ratings of maximum power
consider this factor and allow
higher power dissipation for very
short pulses.
The dissipation in a transistor
is not uniformly distributed across
the semiconductor wafer. At
higher voltages, the current concentrations become more severe,
and hot spots may be developed
within the transistor pellet. As a
result, the power-handling capability of a transistor is reduced at
high voltages. The power rating
of a transistor may be presented
most easily by a limiting curve
that indicates a peak-power safe
operating region. This curve
shows power-handling capability
as a function of voltage for various time durations. The factors
that determine the boundaries defined by the safe-area curve and
the use of this curve are discussed
in the following sections.

THERMAL CONSIDERATIONS
The physical mechanisms related to basic transistor action are
temperature-sensitive. If the bias
is not temperature-compensated,
the transistor may develop a regenerative condition, known as
thermal runaway, in which the
thermally generated carrier concentration approaches the impurity carrier concentration. [Experimental data for silicon show
that, at temperatures up to 700 o K,
the thermally generated carrier
concentration nj is determined as
follows: nl = 3.87 X 10 16 X T X
(3/2) exp (-1.21/2kT).J When
this condition becomes extreme,
transistor action ceases, the collector-to-emitter voltage VCE collapses to a low value, and the current increases and is limited only
by the external circuit.

If there is no current limiting,
the increased current can melt the
silicon and produce a collector-toemitter short. This condition can
occur as a result of a large-area
average temperature effect, or
in a small area that produces
hot spots or localized thermal
runaway. In either case, if the
intrinsic temperature of a semiconductor is defined as the temperature at which the thermally
generated carrier concentration is
equal to the doped impurity concentration, the absolute maximum
temperature for transistor action
can be established.
The intrinsic temperature of a
semiconductor is a function of the
impurity concentration, and the
limiting intrinsic temperature for
a transistor is determined by the
most lightly doped region. It must
be emphasized, however, that the
intrinsic temperature acts only
as an upper limit for transistor
action. The maximum operating
junction temperature (power) is
established by additional factors
such as the efficiency of heat removal, the yield point and melting
point of the solder used in fabrication, and the temperature at
which permanent changes in the
junction properties occur.

Thermal Resistance
The methods of rating power
transistors under steady-state conditions are embodied in the following definition of thermal resistance: The thermal resistance
of a semiconductor device is the
quotient of the temperature drop
and the heat generated through
internal power dissipation under
steady-state conditions, the temperature drop being measured between the region of heat generation and some reference point.

RCA Silicon Power Circuits Manual

It should be noted that thermal
resistance is defined for steadystate conditions. If a uniform
temperature over the entire semiconductor junction is assumed, the
power dissipation required to raise
the junction temperature to a predetermined value, consistent with
reliable operation, can be determined. Under conditions of intermittent or switching loads,
however, such design is unnecessarily conservative and expensive.
In the next section, the problem
of transient thermal response is
investigated and the concept of
thermal capacitance is introduced.

Junction-to-Case Thermal Impedance-The heat-flow problem
in a transistor may be analyzed
in terms of the simple electrical
analog shown in Fig. 80. The
model uses an energy-storage element C, which introduces the concept of thermal capacitance, to
explain the transient thermal
properties of transistors. Although this model may be conveniently used to predict the rise
of junction temperature that results from a unit step or pulse
input of power, the two-element
equivalent circuit is an extreme
over-simplification.

For example, in the doublediffused epitaxial planar transistor shown in Fig. 81, the major
DIFFUSED BASE

Figure 81.

physical source of heat is the collector-to-base junction. Fig. 82
shows the thermal equivalent circuit for this transistor. In general, the thermal-resistance elements shown to the left of the
junction are so large that the
power flow through this path is
negligible. In addition, the heat
energy introduced by the bulkresistance terms for moderate current levels may be considered
small in comparison to the heat
injected at the collector-to-base
junction.
If these simplifications are
made, the thermal equivalent circuit may be reduced to the form

THERMAL CIRCUIT
ELEMENT

Figure 80.

ELECTRICAL EQUIVALENT

SYMBOL UNITS

TIME
HEAT FLOW
POWER
TEMPERATURE
THERMAL RESISTANCE
THERMAL CAPACITANCE

PIt)
TIt)

Structure of double-diffused epitaxial planar transistor.

SECONDS
WATTS
JOULES/SECOND
'C
'C/WATT
WATT.SECONDS!'C

ELEMENT

SYMBOL

UNITS

TIME
CURRENT

I(t)

SECONDS
AMPERES

VOLTAGE
RESISTANCE
CAPACITANCE

VIt)
R
C

VOLTS
OHMS
FARADS

Electrical analog representation of the heat-flow path of a transistor: (a)
thermal circuit; (b) electrical equivalent of thermal circuit.

Silicon Power Transistors
HEAT FLOW
TOWARD
_

f~~bt~~

BASE AND

E~~11~R

HEAT DISSIPATED
AT COLLECTOR JUNCTION
BULK AND CONTACT
RESISTANCE HEATING

BULK
RESISTANCE HEATING

HEAT FLOW
TOWARD
AMBIENT
THROUGH
BULK

([ -1 I vvv-.-Ivv',.......vv'-IJ'''''rOI~'''''~J-J]
""l" AMBIENT

Figure 82.

Thermal equivalent circuit for transistor structure shown in Fig. 81.

shown in Fig. 83. It should be
noted that the elements of this
circuit are complex quantities
which are dependent upon the
operating conditions of the transistor. At high current levels, current-crowding effects cause the
current-flow paths from emitter
to collector junction to be modified. The modified current-flow
paths tend to concentrate the heat
in a small portion of the collector
junction area and thus to create
hot spots. As these conditions develop, the thermal equivalent circuit must also be modified to
account for the restricted heatflow paths. It should be obvious
from this discussion that a complete thermal equivalent circuit is
very complex.
However, the response of this
complex system to a given input
can be determined as follows: If
the model is restricted to sufficiently low currents and the dependence of the thermal resistance
on the operating point is neglected, the simple equivalent
shown in Fig. 84 may be used

Figure 83.

~_",9AS i rt-~9,\sl\,,0LI\DrE_R"'-~--iCASE
9CASE
CCASE
AMBIENT

(al

(bl
Figure 84. Simplified equivalent circuits
for a small-si~nal medium-power transistor:
(al thermal cIrcuit; (bl electrical analog of
thermal circuit.

for a small-signal medium-power
transistor. Representative values
for the thermal parameters in a
typical transistor are as follows:
8s i
= 15°C/W
8so1der = 0.4 °C/W
8 ease = 19.6 °C/W
CS i
= 0.18 X 10-3 (W-sec);oC
Csolder = 0.04 X 10-3 (W-sec);oC
C ense = 285 X 10- 3 (W-sec);oC

Because of the difference in the
magnitude of these elements, the
equivalent circuit may be further
simplified in the time domain.

Simplified equivalent circuit for transistor structure shown in Fig. 81.'

RCA Silicon Power Circuits Manual

For very short times (t < < Oease X
Cease), the thermal impedance to
the right of C.old,. in Fig. 84 is
approximately an open circuit, and
the equivalent circuit appears as
shown in Fig. 85. The electrical
JUNCTION

·85i

'ttp'"''''
':' AMBIENT

Figure 85. Simplified thermal equivalent
circuit for a transistor when the duration
of applied voltage and current is very short
(i.e., t
0... , C.a •• ).

analog of such a circuit can be
used to show that the response to
a step input of power P is given
by the following expression:
TJ (t)

P
(CSi + Csolder)

TJ(t) =TJ
=

P (BSi + esolder + Bease)

+ Tamb

(12)

There is no time dependence implicit in this equation, which is
identical to the solution for the
steady-state condition.
At intermediate times such that
OSiCB < < t < OeaRe Cease> the effective equivalent circuit can be represented as shown in Fig. 86. The
electrical analog can again be
used to show that the r~sponse
JUNCTION

85i + 9S0LDER

't@'CA"
':'

AMBIENT

Figure 86. Simplified thermal equivalent
circuit for a transistor for OSI Cm
t

[ eSi (Csolder - CE)

(l-eXPB~~E+t)J

+ Tamb

of the thermal capacitors are
charged, and the junction temperature is determined as follows:

(10)

< (Jease Cease.
of this circuit to a step input of
power, under these conditions, is
given by the following equation:

T J (t) = [P (BSi + Bsolder) X
Ui (t)] + P eease X
[1- exp (- t/B eRse Cease)] (13)
where T J is the junction temperature, and the other parameters are
evident from Fig. 85.
Eq. (10) shows that initially
the junction temperature rises
faster than an exponential because
of the linearly increasing t term.
For time durations greater than
five thermal time constants (t ~
5 OSiCE), the exponential term exp
(-t/OSiC E) approaches zero, and
the junction temperature rises
linearly.
If the response is analyzed a
long time after the application of
the step of power, some definite
statements can be made. All

where the unit step function U l (t)
is zero for t < 0 and unity
for t > O.
Eq. (13) indicates that when
OSiCE « t < Oease Cease> the junction temperature rises exponentially from a constant value, and
reaches another constant value in
approximately five time constants.
The response of the circuit in
Fig. 84 has been predicted during'
two transient periods for steadystate conditions. The response
must then be determined for intermediate times between the two
transient responses given by Eqs.
(10) and (13). Because it is assumed that the analog model

Silicon Power Transistors
contains only linear elements,
superposition may be used. The
response of the circuit in Fig.
84, therefore, may be determined
by addition of the responses defined by Eqs. (10) and (13) with
appropriate summing factors. This
summation can be performed
graphically; the results of such
an analysis based upon the numerical values given previously
are shown in Fig. 87. The ordinate
value is the thermal impedance,
or transient thermal resistance
40 TRANSISTOR MOUNTED ON

TC=2~C

INFINITE HEAT SINK

p'30

'"<.>z

~20

0::

..J

:i
:z:
'"
...

0::

10-4

/
V

10-3

10 2

10 1

102

103

TIME-S

Figure 87. Graphical representation of
transient thermal resistance curve.

OT' The value of OT is determined
by the pulse width and may be
used to calculate the peak pulse
power PI" as follows:

TJ (max) -

Tamb

(14)

8T (Tp)

where TJl is the pulse width.
The heating and cooling curves
are conjugates, and may be related by the following equation:
Tc

= .:lTn - Tn = PRT

Th (15)

where Tr is the cooling response
and Til is the heating response.
It is apparent, therefore, that the
()T for a given device can be determined if the junction temperature is monitored as a function
of time after the removal of a
steady-state load.

In a power transistor, it is
often desirable to mount the silicon pellet on a copper pedestal
so that the heat spreads over a
wider area before it reaches the
steel case. This dispersal of heat
introduces two more elements in
the equivalent circuit to account
for the thermal resistance and
capacitance of the copper pedestal. In practice, 0('11 is very small
and Cell is comparable to Cen"e'
As a first approximation, 0('11 may
be neglected, and C('II and Crnse
can be lumped together. The
equivalent circuit is then shown
in Fig. 84, and the thermal response is shown in Fig. 87.
In this analysis, a simple
thermal equivalent circuit has
been used to predict the junctiontemperature response to a suddenly applied pulse of power.
Although the elements of the
equivalent circuit are dependent
upon the operating conditions,
this dependence has been neglected
to simplify the problem to obtain
some insight to the response. Fig.
87 does not present an actual
transient thermal response of a
transistor, but is a graphical
presentation of the result obtained from the application of a
step function of input power to
the approximate model developed.
Thermal Impedances External
to the Transistor-The thermal
equivalent circuits for a transistor discussed in the preceding section considered only the thermal
paths from junction to case. For
power transistors in which the
silicon pellet is mounted directly
on the header or pedestal, the
total internal thermal resistance
from junction to case O.T_(' varies
from 50°C per watt to less than
1°C per watt. If the transistor is
not mounted on a heat sink, the

RCA Silicon Power Circuits Manual

thermal resistance from case to
ambient air {)C-A is so large in
comparison to that from junction
to case that the net over-all
thermal resistance from junction
to ambient air is primarily the
result of the {)C-A term_ Table IV
lists values of case-to-air thermal
resistance for popular JEDEC
cases. Beyond the limit of a few
hundred milliwatts, it becomes impractical to increase the size of
Table IV-Case-to-Free-Air
Thermal Resistance for Popular
JEDEC Cases
Case
()C_A('C/W)
TO-18
300
TO-46
300
TO-5
150
TO-39
150
TO-8
75
TO-66
60
TO-60
70
30
TO-3
TO-36
25
the case to make the {)C-A term
comparable to the {)J-C term. As
a result, most power transistors
are designed for use on an external heat sink.
The primary purpose of a heat
sink is to increase the effective
heat-dissipation area. The effect
on the thermal equivalent circuit
is shown in Fig. 88. From the
electrical analog, the effective resistance of the two parallel
thermal paths is smaller than
JUNCTION 6s;

6S0LDER
CSOLDER
CCASE
AMBIENT

Figure 88. Thermal equivalent circuit for
a transistor mounted on a heat sink.

that of either of the paths. The
effect of the heat sink is to pro-

vide an additional low-thermalresistance path from case to ambient air. The heat-sink thermal
resistance actually consists of two
series elements, the thermal resistance from case to heat sink
that results from conduction
({)c-s) and the thermal resistance
from heat sink to ambient air
caused by convection and radiation ({)S-A).
In practice, the case must be
electrically isolated from the heat
sink except for grounded-collector
circuits. The thermal resistance
from case to heat sink, therefore,
includes two components. One
component is caused by surface
irregularities and can be minimized by use of silicone grease
compounds; the other component
is introduced by the electrical insulating washer required. The
thermal capacitance of these two
elements is very small and can be
neglected.
If the full power-handing capability of a transistor, as determined by {)J-C, is to be realized,
there should be no temperature
differential between the case and
ambient air. This condition can
occur only when the thermal resistance of the heat sink is zero, i.e.,
when the transistor is mounted on
an infinite heat sink. Although an
infinite heat sink can never be realized in practice, the greater the
ratio {)J-c/{)c-A> the closer is the
approximation, and the nearer the
maximum power limit defined by
{)J-C can be approached. When a
power transistor is used with a
heat sink, the heat loss by convection and radiation through the
case is very small compared to the
loss through the heat sink. If
{)enRe and CeaRe are neglected, or at
worst combined with {)heat sink and
Chent Rink' the thermal equivalent
circuit for the transistor can be

Silicon Power Transistors
represented as shown in Fig. 89.
The form of the equivalent circuits shown in Figs. 84 and 89 is
the same, and their response characteristics are similar.
9Si

9S0LDER

79
In natural convection, the medium
moves because of differences in
density. Both forced and natural
convection are used for transistor
cooling. The following equation defines the thermal resistance of
vertical plates freely suspended in
free air at ground level:
Bennv

(2300jA) (Lj'l's -

Tam!»l

(17)
AMBIENT
CE

Ccase

Cheat sink

Ohcat sink (fJcase)
8he:lt sink
Oease

Oheat sink

Figure 89. Simplified thermal equivalent
circuit for a transistor mounted on a heat
sink.

Heat Removal
Heat may be transferred by
three basic processes: conduction,
convection, and radiation. Each of
these processes is used in the removal of heat from silicon power
transistors.
Conduction is a process of heat
transfer in which heat energy is
passed from one atom to the next,
while the actual atoms involved in
the transfer remain in their original positions. If a known amount
of power flows through a material,
the thermal resistance which may
be attributed to conduction is determined by the following equation:
Bcone!

t/4.186 kA °C per watt (16)

where t is the length of the thermal path in centimeters, k is the
thermal conductivity in CALI
(sec) (em) (DC), A is the area perpendicular to the thermal path t
in square centimeters, and the
conversion factor 4.186 is given in
(watt) (sec) ICAL.
.
Convection is a term applied to
the transfer of heat by the physical motion of hot material. In
forced convection, the medium of
heat transfer is moved by a fan.

where A is the total exposed area
(twice the area of one side) in
square centimeters, T, is the surface temperature of the heat sink
in 'c, T"llll> is the ambient temperature in DC, and L is the height of
the heat sink in centimeters.
The third process by which heat
may be transferred is radiation.
The rate of emission from a surface can be found from Stefan's
law. In accordance with this law,
the equation for radiation thermal
resistance may be written as follows:
1793 X lOs
Brad = Ali' ('I' 2 _ l' [lmh 2) (1', - l' nlBb)
_J

(18)

where A is the total exposed area
in square centimeters, E is the
emissivity (a function of the surface finish), T, is the surface temperature in 'c, and Tamil is the
ambient temperature in 'C.

Selection and Use of
External Heat Sinks
The sources of thermal resistance both internal and external
to the transistor have been discussed, and the processes which
may be used for heat removal have
been explained briefly. A power
transistor is normally designed to
be used with an external heat sink.
This section discusses the factors
involved in the selection of an external heat sink.

RCA Silicon Power Circuits Manual

Types of Heat Sinks-Heat
sinks are produced in various
sizes, shapes, colors, and materials; the manufacturer should be
contacted for exact design data. It
is convenient for discussion purposes to group heat sinks into
three categories as shown below:
1. Flat vertical-finned types are
normally aluminum extrusions with or without an anodized black finish. They are
unexcelled for natural convection cooling and provide reasonable thermal resistance at
moderate air-flow rates for
forced convection.
2. Cylindrical or radial verticalfinned types are normally cast
aluminum with an anodized
black finish. They are used
when maximum cooling in
minimum lateral displace-

ment is required, using natural convection.
3. Cylindrical horizontal-finned
types are normally fabricated from sheet-metal rings
and have a painted black
matte finish. They are used
in confined spaces for maximum cooling in minimum displaced volume.
It is also common practice to
use the existing mechanical structure or chassis as a heat sink. The
design equations and curves for
such heat sinks based upon convection and radiation are shown
in Figs. 90, 91, and 92.
A useful nomograph which considers heat removal by both convection and radiation is given in
Fig. 93. This nomograph applies
for natural bright finish on the
copper or aluminum.

2800

2600

=WQX(_L_ 10.25
A
Ts-Ta

B'
Be= :

N 2400
E
u
><

tii

UJ
It:
..J
<--'<+--+_'~

12001---+--'<~-~~ -r--+--~--~
10001---+--~-~~~--+-~~~

BOO~_~_~_-L_-L_~_~_~

20
40
60
BO
TSURFACE -TAMBIENT -

100

120

140

Figure 90. Convection thermal resistance as a function of temperature drop from the
surface of the heat sink to free air for heat sinks of various heights. (Reprinted from
Control Engineering, October 1956.)

Silicon Power Transistors

~ S'R
u

1793 xl0 8

SR=

~2000~--4---~---4----~--~---+--~

Ae (Ti+ To2)(Ts+To)

Sil

.....

• Ae ·C/WATT

~
<
ILl
U

iii

~ 1200~~d-~~~~----~--~---+---4
..J

;::

«
~
z

;::

a:0

:I:

...J

<.>

II:

THICKNESS

AREA
OF ONE
SIDE OF
HEAT
SINK OR
CHASSIS
(SQUARE
INCHES)

INSTRUCTION FOR USE, SELECT THE HEAT-SINK AREA AT LEFT AND DRAW A HORIZONTAL LINE
ACROSS THE CHART FROM THIS VALUE. READ THE VALUE OF MAXIMUM THERMAL RESISTANCE DEPENDING ON THE THICKNESS OF THE MATERIAL, TYPE Of MATERIAL, AND MOUNTING POSITION.

Figure 93.

Thermal resistance as a function of heat-sink dimensions. (Nomograph reprinted from Electronic Design, August 16, 1961.)

removal, a vertically mounted heat
sink provides a thermal resistance
that is approximately 30 per cent
lower than that obtained with horizontal mounting_
In restricted areas, it may be
necessary to use forced-convection
cooling to reduce the effective
thermal resistance of the heat
sink On the basis of the improved
reliability of cooling fans, it can
be shown that the over-all reliability of a system may actually be
improved by use of forced-convection cooling because the number
of components required is reduced.

Economic factors are also important in the selection of heat
sinks_ It is often more economical
to use one heat sink with several
properly placed transistors than to
use individual heat sinks_ It can
be shown that the cooling efficiency
increases and the unit cost decreases under such conditions.

Selection and Use of Insulators
As pointed out previously, when
transistors are to be mounted on
heat sinks, some form of electrical
isolation must be provided between

Silicon Power Transistors

the case and the heat sink. Unfortunately, however, good electrical
insulators usually are also good
thermal insulators. It is difficult,
therefore, to provide electrical insulation without introduction of
significant thermal resistance between case and heat sink. The best
materials for this application are
mica, beryllium oxide (Beryllia),
and anodized aluminum. A comparison of the properties of these
three materials for case-to-heatsink isolation of the TO-3 package
is shown in Table V. If the area
of the seating plane, the thickness
of the material, and the thermal
conductivity are known, the caseto-heat-sink thermal resistance

good method for thermal isolation
of the collector from a metal chassis or printed-circuit board is by
means of a beryllium-oxide washer. The use of a zinc-oxide-filled
silicone compound between the
washer and the chassis, together
with a moderate amount of pressure from the top of the transistor,
helps to decrease thermal resistance. Fin-type heat sinks, which
are commercially available, are
also suitable, especially when
transistors are mounted in Teflon
sockets which provide no thermal
conduction to the chassis or
printed-circuit board. Fig. 94 illustrates both types of mounting.

Table V-Comparison of Insulating Washers Used for Electrical
Isolation of Transistor TO-3
Case from Heat Sink
Material
Mica
Anodized
Aluminum
Beryllia

Thickness
(inches)

(OC/W)

Capacitance
(pF)

0.002

0.4

0.016
0.063

0.35
0.25

110
15

e~_"

Oc.p, can be readily calculated by

use of Eq. (16). In all cases, this
calculation should be experimentally verified. Irregularities on the
bottom of the transistor seating
plane or on the face of the heat
sink or insulating washer may result in contact over only a very
small area unless a filling compound is used. Although silicone
grease has been used for years, recently newer compounds with zinc
oxide fillers (e.g., Dow Corning
#340 or Wakefield #120) have
been found to be even more effective.
For small general-purpose transistors, such as the 2N2102, which
use a JEDEC TO-5 package, a

Ca)

0
TO -5 PACKAGE
WELDED TO
HEAT-RADIATOR

2 HOLES

Dn
Cb!
Figure 94. Suggested mounting arrangements for transistors having a JEDEC TO-5
package: (a) without heat sink; (b) with
fin-type heat sink.

At frequencies of 100 MHz and
higher, the effects of stray capacitances and inductances and of
ground paths and feedback coupling have a pronounced effect on
the gain and power-output capabilities of transistors. As a result,

RCA Silicon Power Circuits Manual

physical aspects such as mechanical layout, shielding, and heat-sink
considerations are important in
the design of rf amplifiers and oscillators. In particular, it should
be noted that the insulating washer necessary for isolation introduces coupling capacitance from
collector to chassis which may seriously limit circuit performance.

Effect of Thermal Factors on
Dissipation Capability
The effects of the heat sink and
the insulating washer between
case and heat sink can be clarified
by sample calculations of the maximum allowable power dissipation
in a transistor. In these calculations, the dissipation capability is
determined for a 2N3055 silicon
power transistor operating at an
ambient temperature of 50°C for
steady-state conditions and for
both repetitive and non repetitive
transient conditions. It is assumed
that the transistor is attached to
a 3-inch-by-4.25-inch, verticalfinned, extruded aluminum heat
sink having a natural finish. This
heat sink has a thermal resistance
OS-A of 2.5°C per watt. The transistor is electrically insulated from
the heat sink by a 0.002-inch-thick
mica washer, which is coated with
a zinc-oxide-filled silicone grease.
The effective thermal resistance
Oo-s of the washer and silicone
grease is 0.5°C per watt.
Steady-State Operation-The
maximum dissipation capability of
a transistor under steady-state
conditions depends on the sum of
the series thermal resistances
from the transistor junction to
ambient air, the maximum junction temperature T J (max), and
the ambient temperature T amb at

which the transistor is operated.
The sum of the series thermal resistances can be determined from
the following relationship:
8 J-

= 8 J -0 + 80-s + 8s-A (19)

The maximum value of the junction-to-case thermal resistance
OJ-O for ,.the 2N3055 transistor, as
given in the manufacturer's specifications, is 1.5°C per watt. For
the thermal system specified, the
sum of the series thermal resistance can then be determined, as
follows:
8 J -A = 1.5 + 0.5 + 2.5
= 4.5 °C per watt
The maximum junction temperature of the 2N3055, as specified
in the manufacturer's rating, is
200°C. For operation at an ambient temperature of 50°C, the
maximum dissipation capability of
the 2N3055 transistor, under
steady-state conditions, is calculated as follows:
TJ (max) - T"mb
P •• (max=
)
(20)
8
J-A

(200-50)/4.5
33.3 watts

The case temperature of the
2N3055 transistor that results
from the maximum steady-state
dissipation is calculated from the
following equation:
To

= P ss (8

0 - A)

+ Tomb

(21)

The term OO-A represents the total
thermal resistance from case to
ambient air (i.e., OO-A
OO-S +
OS-A = ,3°C per watt). The case
temperature, then, can be calculated as follows:

Tc = 33.3 (3) + 50 = 150°C
Single-Pulse Operation-When
a transistor is operated in response to a single, nonrepetitive,

Silicon Power Transistors
short-duration pulse of power, the
maximum allowable power dissipation during this transient period
is substantially greater than the
steady-state dissipation capability
of the transistor. In the following
calculations, the dissipation capability of the 2N3055 transistor
operated in the specified thermal
system from a single I-millisecond
pulse of power is determined.
Before the maximum dissipation
capability of the transistor can be
determined, the transient thermal
resistance of the transistor must
be known. The transient thermal
resistance is usually obtained from
the transistor maximum-operating-area curve, shown in Fig. 95,
in the form of a normalized power
multiplier M. For a I-millisecond

,
1'c - 25°C
'I DF = 1- 1'J (max) _ 250C

(22)

For the system specified, the
thermal capacitance of the heat
sink is so large that the temperature of the heat sink does not
change during the I-millisecond
duration of the pulse. The case
temperature T e , therefore, is essentially the same as the ambient
temperature (50°C).
The data given above, together
with the maximum steady-state
dissipation rating of the transistor (Pm8x = 115 watts at a case
temperature of 25°C), are used to
determine the maximum allowable
dissipation P "I) for the 2N3055
transistor during the I-millisecond period of the pulse, as follows:
P.P = 1\1: (TDF) (Pmax )

(23)

Tc - 25

)
=::Vl ( 1 - TJ (max)-25 (P m • x )

810
4
•
COLLECTOR-TO-EMITTER VOLTAGE-V

8100

Figure 95. Maximum·operating·area curves
Tor the 2N3055 silicon power transistor.

pulse, the normalized power multiplier for the 2N3055, given for a
case temperature of 25°C, is 3. At
higher case temperatures, the
power multiplier M must be linearly derated so that it is reduced to
zero at the maximum allowable
junction temperature (200°C) for
the transistor. The temperature
derating factor TDF is determined
as follows:

50 - 25)
3 ( 1 - 200 _ 25 (115)

296 watts

Repetitive-Pulse OperatioDWhen a transistor is operated in
a repetitive pulse mode, the previous analysis must be modified to
take into account the rise in case
temperature caused by the average
power dissipation. In the following
example, it is assumed that the
2N3055 transistor operates in response to a train of I-millisecond
power pulses at a repetition rate
of 100 Hz. The calculations are
based on the same thermal system
as that specified for steady-state
and single-pulse calculations.
For repetitive-pulse operation,
the average power dissipation P • log
in the transistor is determined by
the following relationship:
(24)

RCA Silicon Power Circuits Manual

where P pk is the peak pulse power
dissipated in the transistor and d
is the duty cycle.
The effective case temperature
that results from this average dissipation is determined from the
following expression:
Tc(eff)

+ P"Vg 8 J-A
= To + Pa,.g 9 J _ O

Tamb

(25)

Substitution of Eq. (24) into Eq.
(25) yields the following result:
Tc(eff)

Tamb

+ Ppk(d) 8 J- A (26)

If the effective case temperature

To (eff), as defined by Eq. (26), is
substituted for the case temperature To in Eq. (23), the following
expression is obtained for the
maximum allowable power dissipation P rp for repetitive pulses:
P _

M [TJ(max) - Tambl P max
25 J\1dPmax 8J-A

rp- TJ(max) -

(27)

On the basis of the definition
given in the section on Thermal
Resistance, junction-to-case thermal resistance may be expressed
by the following equation:
8J-O = TJ(max) - 25
P max

(28)

If the relationship expressed by
Eq. (28) is used, Eq. (27) can be
simplified to the following form:

P rp

= M

('TJ(maX) - Tamb) (29)
8 J -o
M d 8J-A

For the numerical example considered, the following values were
previously assumed:
d

(1 ms/l0 ms) X 100

= 10 per cent
== 200°C

T J (max)
Tamb
= 50°C
8J-o
= 1.5°C/watt

M
8J-A

=3
= 4.5°C/watt

When these values are substituted
in Eq. (27), the maximum allowable power dissipation in the
2N3055 under repetitive pulse conditions is calculated as follows:
3(200 - 50)
P rp = 1.5 + 3(0.1)4.5 = 158 watts
Repetitive pulsing with a IO-percent duty factor reduces the peakpower capability in this case to
about 50 per cent of the singlepulse peak-power capability.
When a transistor is to be subjected to irregularly shaped repetitive pulses, the following procedure may be used to obtain a conservative design:
1. The maximum allowable average power for the irregular
pulse is calculated on the basis of the pulse width T p' the
period between the leading
edges of successive pulses t,
and the maximum steadystate dissipation p. o (max),
as follows:
P avg

P s.(max) (T pit)

(30)

2. The ratio of peak power to average power (N P pk/Pavg)
and the average case temperature (To = po. OS-A + Tomb)
are then used to determine
the effective pulse width
(Tp' = Tp/N).
3. The maximum power capability is then calculated from
the following equation:

_ TJ(max) - To(avg)
8J-O'

tr -

(31)

where OJ-O' is the effective
junction-to-case thermal resistance as determined from
the manufacturer's specifications for the effective pulse
width TI'"

Silicon Power Transistors

SECOND BREAKDOWN
Second breakdown (Sib) is a
potentially destructive phenomenon that occurs in all bipolar
(n-p-n and p-n-p) transistors.
This phenomenon results when the
energy absorbed by a transistor
exceeds a critical level, and causes
localized hot spots within the
transistor pellet. The start of second breakdown is characterized by
an abrupt decrease in collector-toemitter voltage with a small dynamic resistance in the secondbreakdown region, as shown in
Fig. 96.
Although second breakdown may
result from several modes of transistor operation, this phenomenon
can be broadly categorized into
two major classes: (1) forwardbiased emitter-to-base second
breakdown, which occurs when the
transistor operates in the active
region, and (2) reverse-biased
emitter-to-base second breakdown,
which occurs during the cutoff
mode of transistor operation.

.9r-+-t-..:.,-+7_......... DIRECTION OF
"F
TRANSVERSE
FIELD

r£--+----''''''''=--+_:!::!!io.- c

Figure 97. Cross-section of power transistor under forward-bias conditions.

power-transistor pellet. When the
transistor is heavily forward-biased into the active region, a
transverse electric field is produced in the base region, and a
space-charge layer is formed at
the base-to-collector junction. As
current flows from emitter to collector, the transverse field focuses
the current into a narrow region
below the emitter edge. When the
current flows through the spacecharge layer, a significant amount
of heat is generated. With the
current focused into a small area,
the heating effect is localized in
this area, and hot spots (circled
areas in Fig. 97) may be formed
within the silicon pellet. If unchecked, these hot spots initiate
a regenerative cycle of high-

Forward-Bias Second Breakdown
Fig. 97 shows a cross section of
a typical silicon diffused-junction

DC SECOND-BREAKDOWN LOCUS
COMMON-EMITTER AVALANCHE
SUSTAINING REGION
t::.MARY BREAKDOWN

,. 1',
I I

Figure 96.

ICBO LOCUS

,JI

, " COLLECTOR-BASE
--L... AVALANCHE BREAKDOWN

Transistor collector characteristics.

RCASUicon -Power Circuits Manual

density current which results in
forward-biased second breakdown
in the transistor.
The carrier concentration in the
pellet and, consequently, the severity of the hotspots are determined mainly by the magnitude of
the transverse base field and by
the applied collector voltage, which
determines the intensity of the
electric field across the spacecharge layer formed at the baseto-collector junction. The magnitude of the transverse base field
depends on the width of the transistor base, the base resistance,
and the spreading of the spacecharge layer that results from the
application of collector voltage.
The transverse base field increases
with increases in base current that
result from higher injection levels
and reduced current gain at the
higher injection levels.
The severity of the hot spots is
inversely proportional to the width
of the transistor base and directly
proportional to the magnitude of
the applied collector voltage. As a
result, the current level 1s/h at
which second breakdown occurs
decreases rapidly with an increase
in applied collector voltage. The
1~;/b capability is also decreased as
the transistor frequency capability
is increased (Le., as the width of
the base is decreased). Figs. 98
and 99 show variation in 1s/b capability as a function of frequency
capability f'r and collector voltage
VCE, respectively. The curves
shown in these figures are graphical representations of the following empirical relationships:

IS/b:~
(VCE HELD CONSTANT)

IS/b

IT
Figure 98. Variation in forward-bias second-breakdown energy ,level as a 'function
of transistor frequency capability.

where Kl and K2 are constants determined by the device being considered and n is a constant that
ranges from 1.5 to 4 depending
upon the construction of the transistor (Le., graded or abrupt junctions) and other factors.
Eq. (32) suggests that the circuit designer should select the
transistor that has the lowest frequency capability, consistent with
circuit requirements, to achieve
the maximum resistance to second
breakdown. Eq. (33) indicates
that supply voltage should be as
small as possible and that highvoltage transients should be restricted as much as possible to

1. Frequency relationship:
ISlh

= K1/y'fT

(32)

2. Voltage relationship:
h/h =

KdVCE n

(33)

Figure 99. Variation in forward-bias second-breakdown energy level as a function
of collector voltage.

Silicon Power Transistors
achieve second-breakdown protection.
The thermal capacitance of the
transistor pellet results in a localized thermal time constant that
restricts instantaneous formation
of hot spots. As a result, the 11'/1>
capability of a transistor is increased when the time duration of
applied current and voltage is very
short. Fig. 100 shows the variation
in 1'/1> capability with pulse width.
VARIOUS PULSE WIDTHS
Ie MAX___
l.!':!eR~AS~Q TIME

IS/b

•

Figure 100. Variation in forward-bias second-breakdown energy level as a function
of pulse width.

Reverse-Bias Second Breakdown
When current flows through a
power transistor in which the
emitter-to-base junction is reversebiased, the direction of the transverse base field is opposite from
that produced in a forward-biased
transistor. As a result, the emitter
current is focused into a small region at or near the center of the
emitter. Because the current is
crowded into a smaller region under reverse-bias conditions, reverse-bias second breakdown can
be encountered at substantially
lower energy levels than those at
which forward-bias second breakdown occurs. Fig. 101 shows a
cross section of a typical powertransistor pellet under reversebias conditions.

SPACREE-GCIOHNARGE E

MINORITY

'l"c;;;;;:;;;[;;(tIONCENTRATION
CARRIER

I I

-L:-:'J7'' '""",,-_--:"'-_~~'=--=--=--=-~-"'I--ou:ECTlON OF

TRANSVERSE
FIELD

Figure 101. Cross-section of power transistor under reverse-bias conditions.

The resistance of a transistor to
reverse-bias second breakdown is
reduced by any design alteration
that increases current density or
prevents spreading of emitter current_ In power transistors that
have a narrow base, an accelerating base field, or insufficient emitter size for their operating current, second breakdown generally
occurs at lower energy levels than
in transistors without these factors_
Reverse-bias second breakdown
is usually described in terms of
energy because voltage, curllent,
and pulse duration are interdependent when the emitter-to-base
junction is reverse-biased_ The
transverse base field in the transistor depends, to a large extent,
on the turn-off base current and
turn-off voltage_ It is natural,
therefore, to assume that the energy level at which second breakdown takes place is a strong function of the input-circuit turn-off
voltage VIlE and the series resistance R IlE - Fig. 102 shows the variation in second-breakdown energy
level as a function of VBE and
Rm; for a typical power transistor. As shown in this figure, if
Rm; is increased and VBE is decreased, the turn-off base current
and the transverse base field are
both reduced, and the secondbreakdown energy level is raised.
Because turn-off time is an in-

"RCA-Silicon Power Circuits Manual

verse function of base currents,
the circuit d~signer must compromise between transistor turn-off
speed and second-breakdown considerations.

ReE,veE
Figure 102. Variation in reverse-bias second-breakdown energy level as a function
of VB" and RBE.

Second-Breakdown
Evaluation Techniques
'.Ghe ability of a power transistor to withstand second breakdown
under either forward or reversebias conditions can be verified easily by testing the devices
to destruction. The establishment
of meaningful second-breakdown
limits on power transistors, however, requires the use of nondestructive verification tests. Such
nondestructive tests are described
briefly in the following paragraphs.
Forward-Bias Is/" Test-Fig.
103 shows the block diagram of a
typical nondestructive IS/b test
set. In this test set, the transistor
under test is in series with a pass
transistor. The transistor under
test is driven by a differential amplifier to provide a preselected
value of test current at a level independent of transistor current

gain. The pass transistor is operated below saturation so that fast
turn-off is possible. A second differential amplifier senses the voltage across the pass transistor and
a I-ohm resistor in series with
this transistor. This voltage is
maintained at a constant value
throughout the test to improve the
accuracy of the Is/b test voltage.
The circuit is arranged so that
only the collector current of the
transistor under test passes
through the I-ohm resistor. The
voltage across this resistor, therefore, is an accurate indication of
collector current.
The onset of second breakdown
is detected by use of the primary
winding of a pulse transformer
which is placed in series with the
collector of the transistor under
test. During second breakdown,
the rapid rate of rise of collector
current induces a voltage L (d;/ d t )
in the transformer which is
coupled to the input circuit of the
series pass transistor. This voltage
turns off the series pass transistor
in one microsecond. The primary
inductance of the transformer also
limits the immediate current rise.
The voltage developed across this
primary inductance is of a polarity
that immediately reduces the voltage across the transistor under
test. These characteristics, together with the protective cut-out
circuit, prevent transistor degradation during the Is/" tests.
The complete cut-out time of the
actual test set is approximately
one microsecond, which is sufficient to prevent degradation of
even the highest-speed power
transistor available in the industry. The pulse width of voltage
and current applied to the transistor under test can be varied from
0.5 millisecond to several seconds.
For dc I~/h tests, a pulse width

Silicon Power Transistors

VARIABLEPULSE-WIDTH
GENERATOR

Figure 103.

Block diagram of typical lsI. test set.

of 1 to 2 seconds is required because the thermal time constant
of the power transistor pellet and
mounting block may be several
tenths of a second.
Forward-Bias Capacitance-Discharge Test-Fig. 104 shows the
schematic diagram of a typical
test circuit used to determine forward-bias second-breakdown energy level. This test circuit operates on the principle of a charged
capacitor that discharges its en-

tL
-

- c

ergy (Ec = CVc2/2) into a power
transistor at a constant current
rate. As long as the initial voltage
across the capacitor is less than
the VCElt (sus) rating of the power
transistor, the collector current of
the transistor is approximately
constant; as a result, collector
voltage decays linearly. The capacitor is charged by constant
current Vcc/R to a value V c' at
which time switch 8 1 is closed.
A constant current Ie, as determined by the combination of
V BB' R B , and R E , then flows
through the transistor until the
capacitor is completely discharged.
If the drop across RE is neglected,
the energy absorbed by the transistor is given by the following
equation:
Eo = C Vo2/2

Figure 104. Capacitive·discharge test cir·
CUlt used to determine forward-bias secondbreakdown energy levels in transistors.

(34)

Current and voltage waveforms of
the 2N3442 silicon power transistor tested in the capacitance

RCA Silicon Power Circuits Manual

discharge test set are shown in
Fig. 105.
C=6000JlF
VCc=IOOV

c
~ 4

Ia=lOOmA

....a:z
a:

;;)

~
~..J

provided that the following limitation is imposed on transistor
turn-off time:
toff« L Ic(max)/VcEx (sus) (35)
The energy that the transistor
absorbs during the Es/ b test can
be determined from the following
equation:
L Ic(max)2

:'S/b =

>,
....

VCEX (sus) ]
[
. VCF.x(sus) - Vcc

II:

l;l 2
..J
..J

1
o~====~----+_----~~
1

I-ms
Figure 106. Test waveforms for a 2N3442
transistor subjected to ES/b inductive energy test.

Silicon Power Transistors

Fig. 107 shows a block diagram
of a test circuit used for nondestructive Es/ b evaluations. The
main feature of this test circuit
is the unique second-breakdown
detection technique. This circuit
provides the rapid second-breakdown detection necessary to prevent damage to the transistor by
an immediate sensing of a largeamplitude rf noise voltage developed at the base of the transistor under test at the onset of
second breakdown.

Basically, the test circuit turns
on the transistor under test and
causes it to operate into a variable series inductance from a constant-current supply. When the
input drive is removed, a reverse
bias, provided by VBE and RBE,
is applied to the base of the transistor under test. The energy
stored in the series inductance
and the constant-current supply
is then absorbed by the transistor. If this energy is sufficient to
drive the transistor into reverseVCC

VARIABLE
CALIBRATED
CURRENT
SOURCE
O.5-20A
+BIAS

CLAMP
(BISTABLE)

Sm.
10 PPS
lOA MAX.

Figure 107.

CLAMP

Block diagram of EH/b test set.

MONOSTABLE

RCA Silicon Power Circuits Manual

bias second breakdown, the detector triggers a protective clamp
circuit in shunt with the transistor under test. The reaction time
of the test circuit is in the order
of only a few hundred nanoseconds.
Reverse-Bias Capacitance-Discharge Test-The reverse-bias
capacitance-discharge test is similar to the forward-bias capacitance-discharge test described previously, except that the capacitor
is charged to a value greater than
the reverse sustaining breakdown
voltage of the transistor under
test. The base of the transistor
is reverse-biased, as shown in Fig.
108.

c1:

- c

Figure 108. Capacitive-discharge test circuit used to determine reverse-bias secondbreakdown energy levels in transistors.

The value of the series resistance is adjusted so that the current through the transistor is
limited to a value below the maximum collector-current rating. The
energy absorbed by the transistor
in this reverse-biased condition
when switch Sl is moved from
position 1 to position 2 is given
by the following equations:
ECS/b=

(VcEx/R) (VCC-VCEX)

e-t/ROdt

(37)

c [VCEX(SUS) Vco
- VCEX(SUS)2j
(38)
These equations assume that the
VCEX(sus) breakdown value of the
transistor does not change with
=

current. Variations in VCEX (sus)
with collector current usually do
not exceed 10 per cent in most
power transistors.

SAFE-AREA RATINGS
Safe-area ratings are given for
power transistors so that the circuit designer can select the proper
type for his application and can
determine the best trade-offs between desired circuit performance
and the actual capabilities of the
device. These ratings must include forward-bias second-breakdown ratings for both dc and
pulsed operation, reverse-bias
second-breakdown ratings for both
inductive and capacitive loads, and
thermal ratings for both steadystate and transient conditions.
Thermal ratings and forward-bias
second-breakdown ratings can be
readily combined into a single
rating system. A separate rating
system is necessary, however, for
reverse-bias conditions.

Forward-Bias
Safe-Area Ratings
Forward-bias safe-area ratings
are displayed on a voltage-current
chart which shows rating curves
for dc operation and for pulsed
operation of various time durations. Eq. (34) in· the section on
Second Breakdown defines the
forward-bias second-breakdown
energy level in a power transistor. On a log-log graph of
the voltage-current curves, the
locus of this equation results in
a linear derating curve that has
a slope equal to the junction constant n. If the safe operating area
of a power transistor is limited
within any portion of the voltagecurrent characteristics by thermal
factors (thermal impedance, maximum junction temperature, or operating case temperature), this

Silicon Power Transistors
limiting is defined by a constantpower hyperbola (I = KV-l)
which can be represented on the
log-log voltage-current curve by
a straight line that has a slope
of -l.
As pointed out in the section on
Second Breakdown, the energy
level at which second breakdown
occurs in a power transistor increases as the time duration of
the applied voltage and current
decreases. The power-handling
capability of the transistor also increases with a decrease in pulse
duration because the thermal mass
of the power-transistor chip and
associated mounting parts imparts
an inherent thermal delay to a
rise in junction temperature. Fig.
109 shows a curve of normalized
thermal resistance Nu as a function of the time duration of applied power for the RCA-2N3442
silicon power transistor. The two
horizontal regions of the curve

/
V

I
/

caused by the thermal impedances
of the case header and the internal
case parts, such as copper, molybdenum blocks, and beryllia.
For a given case temperature
T e, maximum junction temperature T.T (max), and junction-to-case
thermal-resistance rating 9 J _ C ,
together with the value determined for the normalized thermal
impedance N R , the following
equation can be used to calculate
maximum power dissipation as a
function of the duration of an
applied pulse of power:

The absence of a V CE term from
the equation for power dissipation
under pulsed conditions indicates
that this equation also defines a
constant-power curve which can
be represented on a log-log voltage-current curve by a straight
line that has a slope of -l.
Fig. 110 shows a forward-bias
safe-area rating chart fora typical high-speed silicon power transistor, RCA-2N3585, which has a
gain-bandwidth product fT in the

I~ CASE TEMPERATUREo250e
6 Ie MAX.(PlA.SEDl} PULSE .DURATION ,

~ !?,_"--.I. 2 Mlx.(cdNT1N~d~~~)~
~"I:" ~~IJ) -eg-,4.l!~"""''''1J''A'''''
i c;
'" I
~o....... ~.. :"
.. - Ie

10- 4

10- 3

10-2 10-1
TIME-S

100

Figure 109. Normalized thermal resistance
as a function of the duration of applied
power for the 2N3442 silicon power transistor.

show that the 2N3442, as is typical of most power transistors, has
two major thermal time constants.
The shorter time constant results
from the thermal resistance and
capacitance of the silicon chip and
its interface with the transistor
case. The longer time constant is

~"')-'('~"!\.":1-. .'\.

15 •
lli 6

O"'~+"~~~r\M:\"'Wllr+-l
Y5~~r ~W\.
i ~'-fI\w.\.'t'r\
g
(f'J.'fS

6-C-SINGLE NON-REPETITIVE
PULSE

41---1--+-+

<:>-

:c'"
~

2~~--f-+++-1-+--~-H--+-~~
0.01+
4 -!6""'.!rl10f-0-=2--L~4--!.6
1 ---';'--+-~6-l:8+10--+2--7COLLECTOR-TO-EMITTER VOLTAGE-V

Figure 110. Safe-area rating chart for the
2N3585 silicon power transistor.

RCA Silicon Power Circuits Manual

order of 20 MHz. Fig. 111 shows
a similar rating chart for a lowerfrequency silicon power transistor, RCA-2N3442, for which the
f'L' is typically 1 MHz. The bound:..
aries defined by the curves in the
safe-area charts indicate, for both
100

"CASE TEMPERATURE-25"C

4
2

PULSE'OPERATION'!

""Ill

~;vt.~ 7.9r.1~
a'til""~ 1'0~~
12.DN ;::;
"
-'-I

<1:
o~

ILl>

!;to 100
0:: ILl

.... ii:

r::::: f:;;::--r---..,

I--- I---

I-~ 50

D/8~

(OI\t1;,;J
(/4iI }j

Z(J)

~!;t

rO'-.........

0::

ILl

a..

IS/b LIMITED I--

100

150

200

CASE TEMPERATURE--oC
Figure 112. Safe-area temperature-derating
curves for the 2N3585 silicon power transistor.

case temperature than are secondbreakdown ratings. The thermal (dissipation-limited) derating
curve is a graphic representation

Silicon Power Transistors
of Eq. (22) for the temperature
derating factor given in the section on Thermal Considerations.
This curve, as expected, decreases
linearly to zero at the maximum
junction temperature of the transistor [T.T (max) = 200°Cl. The
second-breakdown (IN/iJ-limited)
temperature derating curve, however, is less severe because formation of the high current concentrations that cause second
breakdown is less likely as the
temperature increases.
Because the thermal and secondbreakdown deratings are different,
it may be necessary to use both
curves to determine the proper
derating factor for a voltage-current point that occurs near the
breakpoint of the thermal-limited
and second-breakdown-limited regions on the safe-area curve. For
this condition, a derating factor is
read from each derating curve.
For one of the readings, however,
either the thermal-limited section
of the safe-area curve must be
extrapolated upward in voltage or
the second-breakdown-limited section must be extrapolated downward in voltage, depending upon
which side of the voltage breakpoint the voltage-current point is
located. The smaller of the collector-current values obtained from
the thermal and second-breakdown
deratings must be used as the safe
rating.
The procedure used to derate
a voltage-current point under
repetitive-pulse or continuouswave operation was described
previously in the section on
Thermal Considerations. Basically, this derating requires the
use of an artificially calculated
case temperature (T('(t>ffl = T(' +
O.T_(' P'"'A') with the single-pulse
safe-area ratings and the tempera-

ture derating curves. This calculated cas,e temperature accounts
for the rise in the operating case
temperature that results from
the transistor thermal resistance
8.T_(' and the average power of
the periodic waveform. The value
obtained for TC(eff) is used as the
case-temperature value on the
temperature derating chart to obtain the repetitive-pulse derating
factor for the safe-area curves.
The preceding discussion covers nonrepetitive and repetitive rectangular-pulse operation
only. The following steps must
be used to resolve all other
voltage-current waveforms into
equivalent rectangular pulses before the derating procedure described can be used:
1. Plot the actual voltage-current load line on the appropriate transistor safe-area
chart.
2. Select the voltage-current
point on the load line that
makes the greatest excursion
into the safe-area region.
3. Estimate the total energy
content of the actual voltagecurrent waveform.
This
value can be most easily estimated by graphical integration of the waveforms.
4. Determine an effective pulse
duration to (eff) by dividing
the total energy in the waveforms by the voltage-current
product at the point selected
in Step 2.
The voltage, current, and effective pulse duration computed
above define a rectangular pulse
equivalent to the actual waveforms.

Safe-Area Design Analysis
Two examples of the use of the
forward-bias safe-area system

RCA Silicon Power Circuits Manual

just developed are given below.
The first example requires the
analysis of a typical power inverter under initial turn-on conditions; the second example
applies to the analysis of a directcoupled audio power amplifier
operating at low frequency into
an "inductive speaker" load.

'"t-~

300

:I>

61200

F ....

J:~

~5100

u>
~

OL-~~~r-~__~~

0.1

0.2
0.3
TIME-ma

0.4

(a)

Example 1: Inverter Initial
Turn-On Analysis-A typical
high-speed, high-voltage, 100watt, two-transformer inverter is
shown in Fig. 113. Fig. 114 shows
the collector voltage, collector
current, and peak power of the
inverter as functions of time for
the initial turn-on condition when
the output capacitor Co is uncharged. It is assumed that a circuit designer wants to determine
the ability of the 2N3585 to operate safely in the circuit and, if
safe operation is shown to be
feasible, the maximum permissible case temperature.
The analysis begins with the
plotting of the resistive load line
on the 2N3585 safe-area curve,

o~~~~~~~~~

0.1

0.2
0.3
TIME-ma

150

'"~IOO
~

....a..

Figure 114.

Waveforms for inverter circuit
shown in Fig. 113.

10K

LOAD
300
OHMS

f=25 kHz

Figure 113.

0.4

(b)

High-speed inverter using RCA 2N3585 transistors.

Silicon Power Transistors
as shown in Fig. 115. Because the
circuit being analyzed is a
switching circuit, each pulse has
a different load line associated

duration t,,(eff) is 20 millijoules
divided by 140 watts, or 0.14 millisecond. Because it is assumed that
the initial circuit turn-on is a
nonrepetitive-pulse operation in
this example, the 120-volt, 1.2ampere, 0.14-miIIisecond, nonrepetitive equivalent rectangular
pulse can be applied directly to
the safe-area curve of Fig. 115.
The result is the definition of
point B (V CE
120 volts, Ie
3.4 amperes), the equivalent
safe-area nonrepetitive peak pulse
for t = 0.14 millisecond. The position of point B indicates that the
transistor will operate safely in
the inverter at a case ter.:.,erature of 25°C.
For determination of the maximum case temperature at which
the 2N3585 will continue to perform satisfactorily, the temperature-derating factor must be
calculated. This factor, the ratio
of collector current at point A to
collector current at point B, is
1.2/3.4 = 0.35, or 35 per cent. Because point A is in the dissipation portion of the safe-area
rating curve, the dissipationlimited curve in Fig. 112 is used
to find the maximum case temperature. For a 35-per-cent derating
factor, this temperature is found
to be 130'C. Thus, it is possible
to turn on this inverter safely at
case temperatures up to 130'C.
If the circuit is to be keyed on
and off at some set repetition
rate, a repetitive analysis which
takes into account the effective
case temperature T c (eff) must be
performed and anew and lower
value of maximum case temperature must be determined.

Figure 115. Inverter turn-on load line on
2N3585 safe-area curve.

with it. Initially, the pulses folIowa highly capacitive load line,
but become more resistive as the
output capacitor charges. This
change of pulse character presents no problem in this analysis
because it is being performed for
initial turn-on only. For this reason, the designer need only plot
the turn-on load line of the first
pulse and the locus of peak voltage and current of the remaining
pulses, as shown in Fig. 115.
Point A (VCE = 120 volts and
Ie = 1.2 amperes) is the point of
greatest excursion of the locus of
peak voltage and current into the
safe-area region.
The total energy required during turn-on is determined by
graphical integration, shown in
Fig. 114 (c). The result of the integration indicates that the energy
required during the O.4-millisecond
turn-on is approximately 20 miIlijoules. The peak power at point A
(the product of the voltage and
current coordinates at that point)
is 140 watts, and the effective pulse

Example 2: Analysis of a Direct-Coupled Audio Power Amplifier at Low FrequencyA quasi-compleTJ'p.. tary 70-watt

100

RCA Silicon Power Circuits Manual
3.9K
+42V

100pF
50V

INPUT

!J~'
=

180
R3

5pF
SV +

10K
R4

CRI
NOTE
3

RCA
4040S

2pF,SV
+ -

CR2

,
CR5
TYPES
IN3754
4.7V,IW
NOTE 4

...-r
CR3

ISK
R2

20
5W
RI7

A.F.

~TSUT
O.II'F

lOOK
RS

O.OIPF
C5

10K
R7

4.7K
RS

250pF
SV +

-42V

NOTE I, RESISTORS ARE 1/2 -W TYPES UNLESS OTHERWISE SPECIFIED.
NOTE2·SET BIAS FOR 20mA QUIESCENT CURREN:r (MEASURED AT J WITHOUT LOAD).
NOTE3·THERMALLY CONNECTED TO HEAT SINK FOR OUTPUT TRANSISTORS.
NOTE4'ZENER DIODE-INI519.

Figure l1S.

70-watt, silicon-transistor audio amplifier.

power amplifier is shown in Fig.
116. This amplifier is terminated
in a resistance-inductance series
load circuit in which the inductance is 40 millihenries and resistance is 1 ohm, to simulate a worstcase speaker impedance. The
amplifier is driven at 20 Hz. Voltage, current, and power waveforms
as functions of time are shown in
Fig. 117.
It is assumed that the circuit
designer wants to determine the
ability of the RCA-40411 output
transistor to operate safely in the
circuit with the frequency and
load specified and with a maximum case temperature of 70·C.
The circuit designer may also

want to analyze the circuit at
other load and frequency conditions. The safe-area curve for the
40411 (a 15-ampere silicon power
transistor) and the load line for a
single cycle are given in Fig. 118.
Point A (VCE = 55 volts, Ie = 4.1
amperes, P = 225 watts) represents the point of maximum excursion of the load line into the
safe-area region. Graphical integration of Fig. 117 (c) yields an
equivalent energy of 2.1 joules.
When the equivalent energy is divided by the power at point A, the
effective pulse duration is found
to be 9.3 milliseconds. Thus, a rectangular pulse of 55 volts, 4.1 amperes and 9.3 milliseconds duration

Silicon Power Transistors

101

is equivalent to the actual circuit
waveforms. Point B (VCE
55
volts, Ie 8.2 amperes) is the safearea value for this single, nonrepetitive equivalent pulse at a
case temperature of 25°C. Derating to obtain the safe-area point
for higher case temperature as
well as for repetitive-pulse conditions must then be performed.
Because there is a continuous
20-Hz sine-wave input with a
period of 50 milliseconds to the
amplifier, the duty cycle of this
equivalent pulse is 9.8 milliseconds divided by 50 milliseconds,
or 18.6 per cent. The average

power calculated by dividing the
energy per pulse (2.1 joules) by
the total period (50 milliseconds)
is 42 watts. When these values
are substituted in Eq. (25), the
effective case temperature is
computed as follows:
70'C + 42 W (1.1)

= 70'C

+46'C

where 1.1'C per watt is the junction-to-case thermal resistance
(O.T-C) for the 40411.
The temperature d era tin g
curves for the 40411 are given in
Fig. 119. Because point B falls
within the second-breakdownlimited section of the safe-area
curve, the derating factor is read
from the Is/b-limited curve of Fig.
119. For a Te (eff) of 116'C, the
derating factor is 75 per cent.
When the current is derated at
point B, point C (VCE
55 volts,
Ie = 6.2 amperes) is obtained. If
second-breakdown limitation were
the only consideration in deter,.
mining the ability of the 40411 to
operate satisfactorily in the cir:'
cuit, the location of point C would
indicate that under the specified·
conditions the transistor would
perform as desired. However, be- .
cause the load line in Fig. 118 also
comes close to the dissipationlimiting curve at point A' (VeE
45 volts, Ie
5.4 amperes), it
is necessary to consider transistor dissipation limitations. Point
B' (V CE
45 volts, Ie = 12.5 amperes) is the single-pulse 25'C
case-temperature equivalent. If the
value of 116°C is used for effective
case temperature, as determined
earlier, a temperature-derating
factor of 50 per cent is read from
the dissipation-limited curve of

a:-ca

o.!.

"'z6
/rl1lJ

::1l!§4
0:>
00

2
30

~250

1200

a:
~ 150
0..

'"-c~

100

Figure 117. Audio

50
30

power-amplifier
forms.

wave·

= 116'C

102

RCA Silicon Power Circuits Manual

4r-----_r----~--~r_~~----~----

9.0

II:

.+-~~~~~~~

5.8

'"~

5
:;)

4.0 :lE

II:

~
2.80
Q.

faN

2.2 :J

2·r------+------~--r__r_r----~r_

Figure 118.

4 ' 8 10
2
COLLECTOR-fO-EMITTER VOLTAGE (VCEI-V
Safe-area rating chart for an RCA 40411 transistor.

Fig. 119. This factor yields a point
C' (VCE
45 volts, Ic
6.3 amperes) which is above the point
A' that represents expected circuit
operating limits. This result indicates that dissipation limitations
will not adversely affect transistor
performance in the circuit. The
greater distance between points

~~
~
~()

'-..0

"6 (/"'I'/'.

r-e.. ........... ..........
"<~~a

"'o

1.0 z

100
150
200
50
EFFECTIVE CASE TEMPERATURE OR
CASE TEMPERATURE (TEFF OR TCI-"C
Figure 119. Temperature derating for the
RCA 40411 transistor.

A and C than between points A'
and C' in Fig. 118 indicates that
there is a greater margin of safety
in the second-breakdown region
than in the dissipation region.

Reverse-Bias Safe-Area Ratings
Power transistors are required
to absorb energy under reversebias conditions in a wide variety
of switching circuits including
solenoid drivers, power inverters,
switching regulators, magnetic
deflection circuits, transformercoupled power amplifiers, and
motor and lighting controls. A
characteristic of these circuits is
the presence of series inductance
such as transformer leakage inductance in invertei's and power
amplifiers, solenoid inductance,
motor armature and field inductance, and regulator low-pass
filter inductance. The best means

103

Silicon Power Transistors
for determining the reverse-bias
safe-operation rating for these
circuits makes use of a series
inductance L (without diode
clamp), a turn-off circuit of
series resistance R m;, and a series
voltage VHF;' If the transistor
under test is driven into saturation with a collector current of
I(, (peak) and the forward base
drive is abruptly removed, the
test transistor turns off through
the turn-off circuit and absorbs
an amount of energy equal to the
second-breakdown energy Es/h
given by Eq. (36).
As explained earlier, the second-breakdown energy is a function of R BE , VBE, and series
inductance. Therefore, because it
is possible to resolve all of the
circuits' mentioned above into a
simple series-inductive switch
with a turn-off series resistance
of RilE and a base-to-emitter voltage of V BE' it follows that the
development of a set of curves
defining a minimum energy rating as a function of L, R BE , and
V 1m for this representative circuit will provide an adequate
basis for determining the reversebias safe-operation rating of any
of the more specialized circuits
represented.
A set of curves used to define
reverse-bias safe operation for
the 2N3585 is given in Fig. 120.
These curves, expressed in terms
of peak current I"k' can be readily converted to energy E through
the use of the following relationship:
E = Y2 LI pk2
(40)
The temperature-derating factor
for the reverse-bias condition is
determined in the same manner
as that for the forward-bias second-breakdown condition. That
is, the IR/h-limited portion of the

III

a:
a:

CASE TEMPERATURE=25°C
BASE-TO-EMITTER VOLTAGE=-4V
INDUCTANCE= 100 p.H

I I
I !.
03 r- ~
f-::12
o
~\oA\l\oA
u
C.
1[71-' I I
«"
u

a:4

«,
I-

a:
a:
:>
v3
a:

10
20
30
40
EXTERNAL BASE-TO-EMITTER
RESISTANCE - n
(0)

CASE TEMPERATURE- 25°C
EXTERNAL BASE-TO-EMITTER
RESISTANCE = 20
INDUCTANCE = 100 I',H

I I

J,cl>Y VV

~~
~,~,~

-'
o

u
~I
UJ

'--

-8

lJ?'1
I I

-6

-4

V V

-2

BASE-TO-EMITTER VOLTAGE-V

(b)

«
~
z

a:
a:

CASE TEMPERATURE' 25°
BASE-TO-EMITTER VOLTAGE=-4V
EXTERNAL BASE-TO-EMITTER
RESISTANCE = 20n

a4'~~-r-r-+~--r-+-~~

Figure 120. Reverse-bias energy of the
RCA 2N3585 transistor.

derating curve in Fig. 112 is used.
The use of the reverse-bias second-breakdown rating curves of
Fig. 120 is illustrated below by
analysis of the inverter circuit
shown in Fig. 113. The analysis
assumes that the inverter is in
the turn-off condition.

Analysis of the Inverter in
the Turn-Off Condition
The leakage inductance in the
primary of the output trans-

104

RCA Silicon Power Circuits Manual

former in the inverter shown in
Fig. 113 was measured and found
to be 5 microhenries. However, in
order that the analysis represent
the worst case, the maximum
transformer leakage inductance
was estimated at 100 microhenries.
For use of the rating curves, an
effective value of series inductance Lewan equivalent input
series resistance R BE , and a turnoff voltage V BE must also be determined.
Because the inverter operates
from a constant voltage, the turnoff or second-breakdown energy
Es/b is given by Eq. (36). However, the rating curves in Fig.
120 are based on measurements
made in the Esl b test set with
constant current drive, and on results calculated by use of Eq.
(40). Therefore, an effective
series inductance for the circuit
is obtained by s.etting Eq. (36)
equal to Eq. (40) and solving in
terms of the inductance L or, in
this case, Leff.

Lerr

V CEX(SUS)

(41)

]

V cc

Eq. (41) is valid for all circuits
that operate from a constant
supply voltage. For the inverter
circuit of Fig. 113, L
10
microhenries, Vee = 240 volts,
and V(,EX = 400 volts (from
2N3585 published data). The
value of 240 volts for the constant voltage Vee is composed
of the sum of the supply voltage
and the voltage induced across
the primary of the transformer
as one of the transistors in the
circuit is turning off. When
these values are substituted in
Eq. (41), the computed effective
series inductance is found to be
25 microhenries. RBE is calculated at approximately 0.5 ohm,

the equivalent series resistance
of the diode in shunt with the
3A-ohm resistor; VIlE is measured at approximately 5 volts.
A set of rating curves for the
2N3585 is shown in Fig. 120. In
the circuit used to obtain the
curves, RBE
20 ohms, L
100
micro henries, and V Ill': = -4 volts.
The minimum peak current for
these values of VIlE and RBE is
given in Figs. 120(a) and 120(b)
as 2 amperes.
To permit the application of the
curves of Fig. 120 to the RBE and
V BE of the inverter circuit, translation ratios must be calculated
from the slope of the curves in
Figs. 120(a) and 120(b).
For R BE , the translation ratio
is determined from the value of
minimum peak current at an RBE
of 0.5 ohm divided by the value
of minimum peak current at 20
ohms; both values are taken from
Fig. 120 (a). The result is as follows:

RBE

(trans) = ~:~ = 0.35

For V BE , the translation ratio
is determined from the value of
minimum peak current at a V BE
of -5 volts divided by the value of
minimum peak current at -4 volts;
both values are taken from Fig.
120 (b). This ratio is given by
V BE (trans) =

;:~

= 0.75

The minimum peak current for
the series inductance of 25 microhenries is determined from Fig.
120 (c) as 304 amperes. The equivalent minimum peak current for the
inverter circuit is obtained by
translating this value as follows:
Ipk

(3AA) (0.35) (0.75)

= 0.89

amperes

Silicon Power Transistors

105

This peak current can then be on the I'/b-limiting curve. Thus
converted to the second-break- the inverter can be safely turned
down energy of the inverter cir- off at a case temperature of 60'C
o-l'C = 59·C.
cuit, as follows:
As a final check, the actual
K/h = }2 LIp2 = (2) (25 "H)
total energy absorbed by the cir(0.89) 2 = 10 microjoules
cuit under reverse-bias condiThese values of Ipk and ES/b tions should be compared with
are calculated safe-operation- the locus of peak pulse power
area ratings. The actual peak (derated to the 59°C case tempercurrent necessary for inverter a ture and expressed in terms of
turn-off is 0.8 ampere. For this energy) on the forward-bias safecurrent, the turn-off or second- area chart. If the total energy
absorbed exceeds the forwardbreakdown energy is given by
bias energy, additional derating
on a thermal basis should be performed.
= (1) (25 "H) (0.8)'
=

8 microjoules

The average-power contribution
to this turn-off energy is determined by dividing the energy by
the pulse period, as follows:
P avg

8 uJ/40 uS

0.2 W.

Substitution of this value in Eq.
7 yields
To (eff) = To + PMo. flo'/o =
To + (0.2) (5°C/W) = To + 1°C
where 5'C per watt is the junctionto-case thermal resistance for the
2N3585.
The final problem is to determine the maximum case temperature at which the inverter can
safely turn off on a continuous
basis. The temperature derating
factor is calculated by dividing
the actual peak current Ipk (act)
by the maximum safe-area operation value of Ipk (S.A.), as follows:
Ipk(act)
0.8
Ipk(S.A.) = 0.89 = 0.9, or 90%
From Fig. 112, the temperaturederating curve for the transistor
of interest, a 90-per-cent derating
factor indicates a T" (max) of 60'C

SMALL-SIGNAL ANALYSIS OF
POWER TRANSISTORS IN
LINEAR SERVICE
Silicon power transistors may
be used for a wide variety of circuit applications in which the output signal is proportional to an
applied input signal. Such applications are lumped into a broad
category referred to as linear
service. In most linear-service applications, the terminal voltage
and current of a transistor are
small compared to the levels of
voltage and current established by
dc bias conditions. In this mode
of operation, the transistor can
be conveniently analyzed by means
of a small-signal equivalent circuit.

Small-Signal Equivalent Circuits
In a small-signal ac analysis, a
transistor can be represented as
a three-terminal linear network.
From elementary circuit theory,
it is known that a three-terminal
linear network may be considered
as a linear two-port configuration.
as shown in Fig. 121. The terminal
parameters for the two-port net-

RCA Silicon Power Circuits Manual

106

work are defined by six sets of
equations which differ only in the

Figure 121.

Linear two-port network.

parameters that are selected as
dependent variables. Three sets
of these equations have found
some historical use in the analysis
of transistors in common-emitter
circuit configurations. These three
sets of equations are listed below
for both the general two-port network and a transistor used in a
common-emitter (CE) circuit configuration:
1. z-parameter equations:
(42)
General
VI = zuh + zl2h
(43)
CE
Vi = ziei; + zreio
(44)
General
V2 = Z21II + Z22h
(45)
CE
V = zfeii + zoeio
2. y-parameter equations:
General II = yuVI + yI2V2 (46)
CE
ii = YieVi + yreVo (47)
General 12 = Y21VI + y22V2 (48)
CE
(49)
io = YfeVi + YoeVo
3. h-parameter equations:
General VI = hull + h12V2
(50)
CE
Vi = hieii + hreVo
(51)
General h = h21Il + h22V2
(52)
C E i o = hleii + hoeVo
(53)
In the double-subscript notation
used in the common-emitter equations, the first subscript denotes
the parameter function within the
equivalent circuit (Le., "i" denotes
input, "0" denotes output, "f" denotes forward from input to output, and "r" denotes reverse from
output to input), and the second
subscript denotes the terminal
0

common to both the input and output loops for the transistor configuration being employed. The
equations shown are for the common-emitter transistor configuration; equivalent equations, however, can be written for the
common-base and common-collector configurations.
The y terms defined by the equations are short-circuit admittance
parameters, the z terms are opencircuit impedance parameters,
and the h terms are the hybridcircuit parameters, which may be
defined as follows:
short-circuit input impedance

Vi
hie = ii Vo=O
(54)
short-circuit forward-current
transfer ratio
h Ie

= io
-

IVo=O

(55)

open-circuit reverse-voltage
transfer ratio
h re = Vi

Vo ij=O
(56)
open-circuit output conductance
hoe =

Vo ii=O
(57)
The equivalent circuit for these
equations is shown in Fig. 122.
The techniques used to measure
small-signal z, y, and h parameters
are ml)re or less implicit in their
definitions. In general, the parameters most commonly measured

Figure 122. h-parameter equivalent circuit
for a transistor used in a common-emitter
configuration.

Silicon Power Transistors

107

are the short-circuit admittance
parameters.
The z, y, and h parameters are
in general complex quantities and,
therefore, are frequency-dependent. At frequencies above about
100 MHz, these parameters are
extremely difficult to measure because it is hard to produce true
open-circuit or short-circuit conditions. For this reason, another
set of parameters, known as the
"S" or scattering parameters, is
used to derive an alternative model
for transistors which can be employed for high-frequency design.
The following equations define
"S" parameters on the basis of
the signal-flow diagram of the
transistor shown in Fig. 123:
Erl

SUEil

+ S12Ei2

(58)

.
EiI-

521
~

Erl~

5 11

522A~

~
....

""'-Ej 2

-E, 2

Figure 123. Scattering parameters for
linear two-port network.

If Eqs. (58) and (59) are
solved for the scattering parameters, the following results are obtained:

voltage-reflection coefficient at
port 1 with port 2 terminated
in a matched load
Su

Erl
En

I Ei2=0

forward-transmission voltage
ratio with port 2 terminated
in a matched load

(62)

voltage-reflection coefficient at
port 2 with port 1 terminated
in a matched load

(63)

It should be noted that the scatter-

ing parameters are complex numbers that have both magnitude
and phase. The chief advantage of
the scattering parameters is that
they are measured under matchedtermination conditions which are
easier to obtain than a true open
or short circuit .
It sometimes becomes convenient or necessary to convert one
type of network parameter to another. This conversion is readily
achieved if any pair of the parameter equations is solved for a different independent variable, and
the variables are then equated.
The results of such an analysis
are shown in Table VI.
When the transistor is connected in a practical circuit, such
as that shown in Fig. 124, the

(60)

,--_---.+

reverse-transmission voltage
ratio with port 1 terminated
in a matched load

(61)

Figure 124. Terminated h-parameter equivalent circuit for a transistor used in a
common-emitter configuration.

108

RCA Silicon Power Circuits Manual

source and load impedances affect
the terminal properties of the network. This effect can best be
shown by calculation of the network input impedance from the

h-parameter equations, as follows:
Vi = hi.I; + hr.Vo

(51)

io = hl.i; + ho.Vo

(53)

Table VI-Parameter Equivalencies
Z
Zu

Z12

Z
Z21

Z22

-Z12

Y
-Zn

Z11

-Y12

h12

1+8u-822-~8

h22

1- RIl-

-Y21

-h21
h22

YI2

1 -h12
h11 lhr

Y2I

Y22

h21
hu

hll

h11

h12

h21

h22

Y22
~Y

1
h2?

822+~S

2821

2812
1-Su-S22+~8

1- 8u +812-

1-811-822+~8

1-81l-S22+~8

1-811+822-~8

-28 12

1+811+S22+~8

1+S11+S22+~S

-821
1+SI1 +S22+~S

I+S11-822-~S

Z22

ZI2
Z22

1
Yu

-Y12
Yu

-Z21
Z22

1
Z22

Y21
Yll

Y11

SI1

8 21

1+S11+S22+~S

1-Su+S22-~S

2 S12

1-S11-S22+~S

1-S11+S22-~S

1-S11-SI2+~8

-2S21
1-811-822-~8

A=~Z+Z11-z22-1

1- 811+822-

8 12
822

(1-Y11)(1+Y22)-Y12Y21
1+Y11+Y22+~Y

~z+z11+z22+1

D=~Z-Zll+Z22-1
~Z+Zn+Z22+1

~h+hll-h22-1 K
~h+hn+h22+1

(I+Yn)(1-Y22)-Y12Y21 J=
1+Y11+Y22+~Y

2h12
~h+h11+h22+1

-2h21
~h+hll+h22+1

= Z11 Z2~ - ZI2 Z21
= Yn Y22 - YI2 Y21

L= -~h+hn-h22+1
~h+hn+h22+1

109

Silicon Power Transistors
For the terminated network shown
in Fig. 124, Vo may be expressed
by the following relationship:
Vo

-iozL

-io/YL

The voltage gain K,. of the circuit,
as determined from Eqs. (64),
(66) and (67), may be expressed
by the following relationship:

(64)

Eq. (53) then becomes
io

hlcii

+ hoc (-io/YIJ

(65)

or
(66)

Substitution of Eq. (64) in Eq.
(51) yields the following result:
Vi = (hie

+ _hie hr. )
YL + hoe

(67)

If both sides of Eq. (67) are di-

vided by ib the following equation
for the input impedance Zin is
obtained:

z. In -

Vi - h.
ii Ie

re
+ YLhie+hhoe

(68)

In a similar manner, the equation
for the output impedance Zout may
be derived to obtain the following
relationship:

Eq. (66) is rewritten to obtain
the following expression for the
current gain Ki of the circuit
shown in Fig. 124:
Ki =

~o
Ii

hie YL
hoe
YL

(70)

The power gain PG, which is the
product of the current and voltage
gains, may be expressed as follows:
PG = Ki Kv

(72)

This type of analysis can also be
applied to the z and y parameters;
the general results for all three
circuits are shown in Table VII.
In some cases, information is
supplied for the common-emitter
configuration, and it is desired to
find the parameters for the common-base or the common-collector
configuration. This conversion for
the hybrid parameters is shown
in Table VIII.
Common - Emitter Equivalent
Circuit-The hybrid-pi smallsignal circuit has become popular in transistor analyses because
it offers a reasonable compromise
between the "black-box" two-port
representation (y, Z, or h) and the
complex equations derived from
semiconductor physics. In addition, the hybrid-pi equivalent circuit represents a transistor by
parameters which are independent
of the operating frequency and
which can be related to physical
processes that occur within the
transistor. The complete hybridpi equivalent circuit for a transistor in a common-emitter configuration is shown in Fig. 125. The
discrete components have not been

RCA Silicon Power Circuits Manual

110

combined into equivalent components so that the association of
the components with transistor
physical processes can be readily
shown.
When a transistor is con-

nected for normal operation (i.e.,
emitter-to-base junction forwardbiased and collector-to-base junction reverse-biased) and a small
increment of base-to-emitter voltage is applied, this incremental

Table VII-Network Terminal Properties
Parameter

Zin

Zout

Az + Zll ZL
Z22 + ZL

Az + Z22 Zg
Zll + Zg

Zn
Z22 + ZL

Z21 + ZL
Az + Zn ZL

Y22 + YL
Ay + Yn YL

Yn + yg
Ay + Y22 yg

-Y21 YL
Ay + Yn Yr.

-Y21
Y22 + YL

Ah + h n YL
h22 + YL

h n + Zg
Ah + h22 Zg

-h21 YL
h22 + YL

-h21 ZL
h n + Ah ZL

Az = Zu Z22 - Z12 Z21
Ay = Y11 Y22 - Y12 Y21
Ah = h11 h22 - h12 h21

Table VIII-Hybrid Parameter Relationships
CommonEmitter
Circuit

CommonBase
Circuit

h11

hie

hib=hie- 1 + h'e

h12

h re

h21

h'e

hfb =

h22

hoc

h ob= -hoc
-1+ h re

rb -

hieh oe - h

1 + h'e
-h£e

1 + h re

CommonCollector
Circuit
hie

hr. =

hie

1- hr.

h'e = - (l+hl.)

hoc = hoe

Silicon Power Transistors

111
tion of the basic circuit shown in
Fig. 126. Under conditions of
large voltage gain the load impedance is large. The width of the

e
Figure 125. Complete hybrid-pi equivalent
circuit for a transistor used in a commonemitter configuration.

change in base-to-emitter voltage
produces two components of base
current. One component is produced by the incremental increase
of charge recombination in the
base that is caused by the increase
of excess charge stored in the base.
This component i bl can be expressed as follows:
i bl

gb'.

Vbe =

(l/rb'c)

Vbe

(73)

The other base-current component
results from the incremental
change in excess majority carriers
that is required to maintain electrical neutrality over the increased
minority carriers stored in the
base. This component i b2 can be
represented by the following relationship.

•
Figure 126. Elementary small-signal
transistor equivalent circuit.

collector-junction depletion layer
is voltage-dependent. As a result,
the effective width of the transistor base varies with the output voltage. This phenomenon is
known as "base-width modulation." These effects are accounted
for in a transistor equivalent circuit by the addition of two feedback elements, Cd and rb/e> and
one output shunt element ree which
account for the transient and incremental change of collector current Ie because of base-width
modulation. The resulting equivalent circuit is shown in Fig. 127.

(74)

The total base current ib then is
defined by the following equation:
t

where Cb is the base charging
capacitance.
Eq. (75) provides the basis for
a first-order equivalent-circuit approximation of the transistor.
This equivalent circuit, shown in
Fig. 126, represents the basic gain
mechanism in a transistor.
For large voltage gains, a second-order effect requires modi fica-

Figure 127. Elementary small-signal transistor equivalent circuit which includes
components to represent effects of basewidth modulation.

The equivalent circuit is essentially complete from the standpoint of physical mechanisms
within the transistor. It is known,
however, that the emitter and collector junctions have space-chargelayer capacitances, Cje and Cjc ,
which must also be included in

112

RCA Silicon Power Circuits Manual

the equivalent circuit. In addition,
the transverse majority-carrier
base current produces a voltage
drop in the transistor base which
can be represented by addition of
the spreading resistance rbb"
Finally, because of the transverse
voltage drop across rbb' it frequently becomes convenient or
necessary to divide the collector
junction capacitance into two components, the capacitance CjC mentioned previously and a capacitance Coc which is defined as the
overlap capacitance of the collector-to-base junction. This division
is desirable because the capacitance Coc is not charged through
r hh'·

When all the elements discussed
above are combined into one circuit, the complete equivalent of
the transistor, as shown previously
in Fig. 125, is obtained. This
equivalent circuit is rather cumbersome, but when parallel elements are combined the equivalent
circuit is reduced to the more conventional form shown in Fig. 128.

equivalent circuit which are applicable over a limited frequency
range.
As with vacuum-tube amplifiers, it is convenient to use
low-, medium~, and high-frequency
equivalent circuits in the analysis
of a transistor. The range of applicability is determined by the
parameter values of the transistor
represented by the equivalentcircuit model. A numerical example is necessary, therefore, to
assess the relative importance of
the various elements. In a smallsignal analysis of a transistor, it
is important to realize that, although the small-signal response
depends on frequency, this response is also affected by the operating point and the temperature.
In the following paragraphs, the
response of a transistor at low,
medium, and high frequencies is
considered; changes in response
because of variations in operating
point and temperature are discussed later.
The numerical values for the
hybrid-pi parameters of the RCA2N2102 triple-diffused silicon
pla.nar transistor are given in the
equivalent circuit shown in Fig.
129. As the first step in the estimation of the frequency response
for this circuit, it is necessary to

Figure 128 Conventional form of the complete hybrid-pi equivalent circuit shown in
Fig. 125.

le.. -

Even this equivalent circuit may
seem too cumbersome for circuit
analysis. In practice, however,
certain circuit elements are dominant over a portion of the frequency spectrllm, while other elements may have negligible effect
on transistor behavior. It is
permissible, therefore, to make
further simplifications in the

40.4

•

Figure 129. Hybrid-pi equivalent circuit for
the 2N2102 triple-diffused silicon planar
transistor •.

calculate the frElquency fl at
which the resistance rb' e is equal
to the reactance of the capacitance
Ch ' e' This frequency may be cal~
culated as follows:

Silicon Power Transistors

113
(76)

1
6.28 X 300 X 420 X 10-12
= 1.3 MHz
For frequencies much below fl'
the resistance rl,' e is dominant,
and the effect of the capacitance
Cb '. is negligible. If a similar calculation is performed for the feedback elements rl,'c and C1,'c, a frequency f~ is determined, as follows:

__
1__

271"

rb'c

(77)

Cb'c

1
6.28 X 12 X 106 X 10 X 10-12
1.3 kHz

For frequencies below f2' the effect of the feedback capacitance
Cb'c is negligible.
The preceding calculations are
based upon design-center measured values; individual elements,
therefore, may vary somewhat
from one transistor to another.
Because the frequencies fl and
f2 differ by three orders of magnitude, several factors concerning
the transistor operation become
apparent. At frequencies much below f2' both capacitances Cb'e and
eb'c may be neglected, and the lowfrequency equivalent Circuit shown
in Fig. 130 is applicable. At frequencies above f2 but much be-

lent circuit shown in Fig. 131 is
useful. Finally, at frequencies
much above fl' both rb'. and rb'C
are effectively bypassed by the
shunt capacitances. For such
frequencies, the high-frequency
c

Figure 131. Simplified
medium-frequency
hybrid-pi transistor equivalent circuit.

equivalent circuit shown in Fig.
132 should be used to represent
the transistor.
1-..----HDc

ret

Figure 132. Simplified high-frequency hybrid-pi transistor equivalent circuit.

In practice, the mid-frequency
model shown in Fig. 131 is not
very useful. A more useful equivalent circuit is produced if both
capacitors Cb'. and Cb'c are retained in the circuit. Such an
equivalent circuit, shown in Fig.
133, is useful over the middleand high-frequency ranges.
b

Figure 130. Simplified low-frequency hybrid-pi transistor equivalent circuit.

low fl' rb'. and Cb '. are negligible,
and the middle-frequency equiva-

Figure 133. Simplified hybrid-pi transistor
equivalent circuit for use at medium and
high frequencies.

It is apparent from the foregoing discussion that the hybrid-pi
equivalent circuit offers many ad-

RCA Silicon Power Circuits Manual

114

vantages as a broad-band transistor model. If hybrid data are not
specified by the transistor manufacturer, the parameters at a
given operating point can be determined from known information or from simple low-frequency
measurements, as follows:
The transconductance gm can be
calculated from the following
physical relationship:
gm =

k~ I Ie I mhos

(78)

where
q
electronic charge = 1.6 X
10- 19 coulomb
k
Boltzmann's constant
1.38 X 10- 23 watt-sec/oK
T
absolute temperature in
oK
Ie = collector current in amperes.
At room temperature, T
290°K.
Eq. (78) can then be rewritten
as follows:

hf. flo

IV. = - -

(81)

At low frequencies, the resistance r bb' can be determined from
the calculated value for the resistance rb'e and the measured value
for the short-circuit input impedance. Under the conditions required for the measurement, the
short-circuit input impedance for
the low-frequency equivalent-circuit model can be expressed in
terms of the resistances r bb' and
rb'e as follows:

The low-frequency value for the
resistance rbb" therefore, may be
determined from the following relationship:

gm = 0.04

I Ie I mhos

(79)

where the collector current Ie is
given in milliamperes.
The resistance rb'e is calculated
on the basis of the measured value
for the short-circuit current gain
at low frequencies. Under the conditions required to measure the
short-circuit current gain of the
low-frequency equivalent-circuit
. model shown in Fig. 130, the relationship between the resistance
rb'e and the low-frequency current
gain may be expressed as follows:

When this equation is solved for
the resistance rb' e' the following
result is obtained:

It should be realized that the
resistance rbb' is a distributed
component and is, therefore, a
function of frequency. At high
frequencies, the following equation should be used to calculate
this resistance:
l/fbb'

R.(Yi.)

(84)

Eq. (84) is valid for the following condition:

In the calculation of the resistance rb'C' it is first necessary to
measure the open-circuit reversevoltage transfer ratio at low frequencies. For the low-frequency
equivaient-circuit model shown in

Silicon Power Transistors

115

Fig. 130, the open-circuit reversevoltage transfer ratio can be related to the resistance rb'c as
follows:

first approximation, the capacitance Cb'e may be determined as
follows:
(93)

(86)

From practical considerations, it
is known that rb'e is much greater
than r b' •. Eq. (86), therefore, may
be rewritten as follows:

The remaining capacitance Cb'.
may be determined by use of the
high-frequency equivalent circuit
shown in Fig. 133. For this circuit, the short-circuit current gain
is determined from the following
relationship:

or
rb'c=

(88)

h re flo

In most practical applications of
power transistors, the resistance
ree is so large that its effect is
negligible. In those cases for which
the effect of this resistance is significant, however, the following
approximation is valid:
hoe Iflo

lire.

(89)

If the gain-bandwidth product
fT is defined as the frequency at
which hfe 1, the following !requency relationships become apparent:

hfef

(95)

hiew

(96)

or
ree

~--

hoe flo

Before the capacitance Cb'c can
be calculated, the common-base
output capacitance Cob must be
measured. Fig. 125 shows that the
feedback capacitance is shunted by
the diode overlap capacitance Coc
and the header capacitance Cu.
The capacitance Cb'c, therefore,
can be determined from the following relationship:

~'.=

Cob - Coe - Cu

(90)

{92}

For small-signal conditions, it is
frequently possible to neglect the
Coc and Cu terms so that, as a

== WT/hie

(97)

If the relationship expressed by
Eq. (96) is substituted into Eq.
(94), the following result is obtained:

Eqs. (78) through (99) demonstrate how the hybrid-pi parameters may be calculated for a known
operating condition. For convenience and reference, these relations
are summarized in Table IX.

RCA Silicon Power Circuits Manual

116

Vb'. [(l/fb'.) + SCb'.
- Vo (SCb'e) = Ii

Table IX-Hybrid-Pi Parameters
Relationship

Parameter
gill

q II I
KT
.,

lll'c

h f • Iflo
gm

rbb'l flo

hi.lflo -

mb'l fhi

R. (Yie)

m'.

= jwC.

When conductance terms are
substituted for the resistance
terms, the node equations become

Vb'. [gb'. + S(Cb'. + Cb'.)]
- Vo (SCb'.) = Ii
(102)
Vb'. (gm - S~'c)
+ Vo (g•• + GL + sCb'.)

rca
Cb'c

(100)

Vb'. (gm - SCb'.) + Vo [(1/1'••)
+ (l/RL) + sCb'.l = 0
(101)

where s

rb'.

+ sCb'.1

fb'.
hr.lflo
ho.lflo
Cob - Coc

(103)

+Vcc

-CH~Cob

"---OVo

Cb'.

gm _ Cb'.
WT

Equivalent Input Circuits-Because of the differences in the
magnitude of the elements of the
hybrid-pi equivalent circuit, it becomes convenient to use this circuit to derive an equivalent input
circuit for a transistor. If Rb and
C in the amplifier circuit shown in
Fig. 134 are both very large, their
effects are negligible, and the
equivalent circuit is as shown in
Fig. 135. The node equations for
this circuit can be written as follows:

Figure 135.

:Ii

Figure 134.

Common-emitter transistor
amplifier.

Eqs. (102) and (103) may be
further simplified by practical considerations. In the second term of
Eq. (102), the sCb'c element represents feedback from output to input which is necessary and critical.
In Eq. (103), the sCb'c element in

Equivalent circuit for common-emitter amplifier.

Silicon Power Transistors

117

the first term represents signal fed
forward from the input to the output, which is normally negligible
compared to the signal fed forward by the gm Vb'e generator. In
the second term of Eq. (103), the
sCI,'c term represents the loading
of the output node, which is normally negligible. In addition, except for very large load resistances,
gee is much larger than Gr,. Under
such conditions, the gee term can
be neglected. When these facts are
taken into consideration, Eqs.
(102) and (103) may be rewritten
in the following form:

Vb'. [gb'.
s(Cb'.
- Vo (sCb'c) = Ii

+ Cb'c)]
(104)

Eqs. (102) and (103) can be
solved for the internal input admittance Ii/Vh'~ as follows:

Ceq

Ceq"Cb'.+Cb'c U+Vm RLl
Figure 136. Equivalent input circuit
common-emitter amplifier.

for

resistive load; this equation, however, can be generalized so that it
is applicable to a complex load impedance Zr, as follows:
y

gb'e

+ S [Cb'. + Cb'c (1 + gm Zr,)]
(111)

A circuit representation of the
generalized input impedance defined by Eq. (111) is shown in
Fig. 137. The equivalent admit-

Vb'. [gb'e
S(Cb'e
Cb'c)]
+ [(Vb'. gm)/GL! (sCI,'c) = Ii
Vb'c {gb'.
(l

circuit can be represented as
shown in Fig. 136. Eq. (109) was
derived for the case of a purely

+ S[Cb'. + Cb'c
+ gm Rr,)Jl = Ii

(107)
(108)

Figure 137. General equivalent input cirCUIt for a common-emitter amplifier.

tance for this circuit is expressed
by the following equation:
(109)

Eq. (109) represents an equivalent input circuit that consists of
a resistor rb'e in shunt with an
equivalent capacitance expressed
by the following equation:

When the series spreading resistance r.,l.' is added, the total input

(112)

Eqs. (109) and (111) show that
the small feedback capacitance
Cb'e can have a significant effect
on the frequency response of the
amplifier because of the large
equivalent capacitance reflected at
the input. For example, if the component values for the 2N2102
power transistor are used and the
load resistance Rr, is assumed to be
1000 ohms, the reflected capaci-

118

RCA Silicon Power Circuits Manual

tance may be calculated from Eq.
(110) as follows:

+ Cb'c (1 + gm RrJ
420 pF + 10 pF (1 + 0.4 X 1Q3)
420 pF + 4010 pF = 4430 pF

Ceq = Cb'e
=

This calculation shows that the
smalll0-picofarad collector-to-base
capacitance Cb'c is reflected back
to the input terminals as a 4010picofarad capacitance which overshadows the Cb'e term by a factor
of 10. This reflected capacitance
is analogous to the Miller effect in
vacuum-tube triodes where the
grid-to-plate capacitance reflected
back to the input terminals is multiplied by (1 + gm R L ) •
Common-Base Equivalent Circuit-Historically, the commonbase circuit was the first configuration used for transistors. This
circuit configuration, however, offers low input impedance and less
than unity current gain and is no
longer used except in certain specific applications.
Although the hybrid-pi equivalent circuit is still applicable for
the common-base configuration, it
becomes difficult to take into account the effects of base-width
modulation which now produce
coupling from the output to the
common terminal. For small voltage gain, the base-width modulation effects are negligible, and the
hybrid-pi common-emitter equivalent circuit shown in Fig. 128 can
be redrawn for the common-base
configuration as shown in Fig. 138.
By suitable manipulation of the
circuit equations, it can be shown
that this equivalent circuit reduces
to the common-base "T" equivalent circuit shown in Fig. 139. In
this circuit, the resistance r e and

IIm Vb'e

eO>----.--Ll-I~'
-

Cb"

rb'b'

b
Figure 138. Hybrid-pi equivalent circuit for
a transistor used in a common-base configuration (effects of base·width modulation
are neglected).

the current-gain parameter a are
defined as follows:

(114)

Cb"

Irb'b

Cb'c

Figure 139. "T" equivalent circuit for a
transistor used in a common-base configuration when the effects of base-width
modulation are neglected.

Common -Collector Equivalent
Circuit - The common-collector
configuration is sometimes used
because it offers high input impedance and current gain. It is possible to draw the hybrid-pi equivalent circuit for the commoncollector configuration as shown in
Fig. 140. It can be shown that if
the base-modulation, base-spreading, output-loading, and inputloading terms are neglected, the

119

Silicon Power Transistors

fbb'

Figure 140. Hybrid-pi equivalent circuit for
a transistor used in a common-collector
configuration.

common-collector equivalent circuit can be simplified to the form
shown in Fig. 141, in which the
dependent generator is converted
into a current-dependent source.

figurations were described, and the
way that the network terminal
properties (Zln' Zouto K I , and
KyO as defined in Table VII) are
affected by the source and load
impedances was discussed. The
terminal properties of any configuration may be calculated as
a function of ZL and Zg by use of
the equations shown in Table VII.
The calculations are laborious, and
the results are readily available in
the literature. The general qualitative results are shown in Table
X. Because the common-emitter
configuration provides the highest
power gain (KIKy), this type of
configuration is normally used unless the impedance properties of
one of the other two configurations are required.

Frequency Considerations

Figure 141. Simplified form of hybrid-pi
equivalent circuit shown in Fig. 140.

Network Properties
In transistor circuit design, one
of the first decisions to be made is
the type of circuit configuration
(common-base, common-collector,
or common-emitter) to be used. In
the preceding section, the equivalent circuits for each of these con-

In the hybrid-pi model of a
power transistor, the two capacitances Ch ' e and Ch ' c define two
critical frequencies f1 and f2 that
determine the significant elements
in the model at a particular frequency. These two capacitances
also affect the short-circuit current gain. For the medium- and
high-frequency equivalent circuit
shown in Fig. 142, the short-circuit current gain hfe can be determined from the following equations:

Table X-Qualitative Comparison of Transistor
Circuit Configurations
Property
Terminal
Zin
Zout
Ki
Kv

CommonBase
Circuit
low
extremely high
low « 1)
high

CommonCollector
Circuit
high
moderate
high
low « 1)

CommonEmitter
Circuit
moderate
high
high
high

120

RCA Silicon Power Cir::uits Manual
1000

hf8lf,o
100

(116)
io

ij"

(l/Ib'.)

gm
S(Cb'e

""
,,
,ifp

+ Cb'.)

104

105

106

107

r--....

.......

"b'. Cbo.

1"-

Figure 142. Medium- and high-frequency
common-emitter hybrid-pi transistor model
used for calculation of h'e.

and phase. The short-circuit current ratio hre has a low-frequency
value of (gmrb'e), and a single
breakpoint occurs at a frequency
defined by the following equations:
(l/Ib'.)

211" f~ (Cb'e

10 8

Figure 143. Magnitude of hr. as a function
of frequency for the 2N2102 silicon power
transistor.

rbb'

FREQUENCY-Hz

(117)

The s term (s = jwC) in Eq.
(117) shows that hre is a complex
number that has both magnitude

+ Cb'c)

1
211" Ib'. (Cb'.

+ Cb'c)

(118)
(119)

The beta-cutoff frequency f{3 is
the frequency at which the shortcircuit current ratio h re (or /3) is
reduced to 0.707 of its low-frequency value. At this frequency,
the phase angle of h re is -45
This information is used to determine the variations in the magnitude and phase of hfe for the
2N2102 power transistor as a
function of frequency shown in
Figs. 143 and 144. For frequencies
much above f {3, the response curve
becomes asymptotic to a line that
has a slope of -Ion the log-log
0 •

r-2

468

4 68

108

Figure 144. Phase of hr. as a function of
frequency for the 2N2102 silicon power
transistor.

scale shown. Extrapolation of this
asymptote to the frequency at
which h re = 1 defines another critical frequency f'l" which may be expressed by the following equation:

The term fT is called the gainbandwidth product. At any frequency along the -1 asymptote
(i.e., f > 3 f{3), Eq. (120) can
be rewritten in terms of the operating frequency, as follows:
[ hr. [ W

(121)

[ hr. [ f

(122)

121

Silicon Power Transistors

For the hybrid-pi model for the
common-base configuration shown
in Fig. 145, the common-base
short-circuit current gain hth can

Figure 145. High-frequency common-base
hybrid-pi transistor model used for calculation of hrb (transverse voltage drops in the
base are neglected).

be calculated, for the case when
rl>l: = 0, from the following equation:

The s term in Eq. (123) indicates
that htl> is a complex number that
has both magnitude and phase.
This gain parameter has a lowfrequency value of (gm r h ,.) and a
single breakpoint. This breakpoint
occurs at a frequency fa, referred
to as the alpha cutoff frequency,
at which htl> is reduced to 0.707 of
its low-frequency value. The frequency fa is determined as follows:
(124)

Variation of Small-Signal
Parameters

During the discussion of the
small-signal equivalent circuits, it
was mentioned that the transistor

parameters also depend on the
operating conditions, or bias and
temperature. This section provides
a qualitative analysis of this dependence. The hybrid-pi equivalent circuit is particularly useful
for this discussion because the
parameters can be easily related
to physical mechanisms within the
transistor (as given in Table IX),
which in turn can be related to
the properties of the semiconductor material. It should be noted
that the hybrid-pi equivalent circuit was derived as a linear, onedimensional model, based upon an
assumption of low-level injection
of minority carriers. In particular, the model does not take into
account transverse voltage drops,
which have been shown to limit
the useful safe area of operation
of some transistors because of second breakdown. Over a major portion of the normal operating region, however, the model is quite
adequate for the analysis.
Bias Dependence-The general
hybrid-pi equivalent circuit shown
in Fig. 125 includes three parameters that are associated with the
injection of minority carriers and
the basic gain mechanism in transistors. These parameters are gm,
rh'e and eh. Table IX shows that
the transconductance gm may be
defined as follows:

gm =

~ I Ie I
kT

(125)

Eq. (125) indicates that gIll is
directly dependent upon the collector current and is independent
of the collector voltage V c. Table
IX also shows that rb'. may be
determined from the following relationship:

RCA Silicon Power Circuits Manual

122
,
hfe Iflo
rbe = - - =
gm

hfe Iflo
~IIel

EXCESS ELECTRON
CONCENTRATION nl
I
I

(126)
"blo)

EMITTER

This equation shows that rb'e is
inversely proportional to the collector current. The base charging
capacitance Cb is added to the
equivalent-circuit model to account for the incremental change
in the excess majority carriers
stored in the base. This capacitance is defined by the following
equation:
ib2

(Cb d Vbe)/dt

(127)

Eq. (127) may be rewritten in the
following form:
dQb =

ib~t

= CbdVbe

(128)

or
Cb = dQb/d Vbe

(129)

where dQb is the incremental
change in the excess charge stored
in the base.
Because electrical neutrality is
preserved in the base, dQ b must
also be equal to the incremental
change in the excess minority
carriers stored in the base region.
During normal operation, the excess minority charge injected at
the collector is very small compared to that injected at the emitter, and may be neglected. Under
these conditions, the minoritycarrier concentration in the base
region of a uniform-base n-p-n
transistor becomes as shown in
Fig. 146. The total base charge
can be found by integration of
Eq. (128), and for this simple
distribution is represented by the
area inside the triangle. The equation for the total base charge,
therefore, may be written as follows:
Qb

(q n'b(o) WA)/2

(130)

COLLECTOR

I~~~~~~~-+-----+

10
.,.....---.I I--

-l

1
""1.____--,

COLLECTOR-BASE~

LEMITTER-BASE
SPACE-CHARGE
LAYER

SPACE-CHARGE
LAYER

Figure 146. Excess minority·carrier concentration in the base region of a uniform-base
n-p-n transistor.

where q is the electronic charge,
n'b(o) is the concentration of excess electrons at the edge of the
base region (X = 0), W is the
base width, and A is the area perpendicular to the direction of electron injection.
An analysis of the diffusioncurrent mechanism in transistors
indicates that the collector current
may be determined from the following equation:

qDnA [ n'~O) ]

(131)

where Dn is the diffusion constant
for minority-carrier electrons.
In charge-control theory, a term
known as the average base-charge
replacement time, T F, is introduced. This term is defined as follows:
TF

Qb/Ic

W2/2Dn

(132)

Eqs. (129) through (132) are
combined to obtain the following
equation, which can be used to determine the variation in Cb with
incremental changes in Qb:

Silicon Power Transistors

123

It has been shown previously, by
Eq. (125), that gm is directly dependent upon Ic; Eq. (133), there-

fore, shows that the same dependence applies for Qb.
The relationships expressed by
Eqs. (125) through (133) can be
used to predict the effect of collector voltage on each of the three
parameters (i.e., gm, rb/., and Cb)
being considered. Eqs. (125) and
(126) show that gm and rb /• are
independent of Vc. The base width
W is inversely dependent upon
Vc because, as the reverse bias
across the collector-to-base spacecharge layer is increased, the effective base width is decreased.
Eqs. (132) and (133) show that
Cb is directly proportional to T F
and, therefore, is inversely proportional to the square of Vc.
The two junction capacitances
Cje and Cjc in the complete hybridpi equivalent circuit, shown in
Fig. 125, are included to explain
the voltage-dependent charge associated with the dipole spacecharge layer at each junction.
These capacitances are practically
independent of current and vary
with voltage according to the following equation:

ity-carrier currents. At high collector currents, this transverse
voltage tends to concentrate the
emitter injection current at the
emitter edge, an effect termed
"current crowding". The net result is that the effective length of
the path for majority carriers is
shortened, the transverse voltage
drop is reduced, and therefore
rbb' is decreased. At high collector voltages, the collector-to-base
space-charge layer is increased;
as a result, the base width W is
reduced. If rbb' is considered to be
a bulk resistance, then, from Fig.
147 and a knowledge of resistance
effects, rbb' can be expressed as
follows:
fbb' =

Pb XI A

Pb X/WY

(135)

where Y is the transistor dimension perpendicular to the flow of
base current in the plane of A.
Since W is reduced as Vc increases, rbb' should increase with
increased Vc.
COLLECTOR-BASe:
DEFLECTION
LAYER
INJECTED
ELECTRONS

K/(V'/n)

(134)

BASE HOLE
CURRENT
X ' - - - -_ _
_ _---l

where K is the material constant,
V'is the voltage across the spacecharge layer, and n is the junction
constant (for an abrupt junction
n = 2; for a graded junction n

Figure 147. Model of n-p·n transistor showing transverse base field and currentcrowding effect.

The rb/c' ree, and Cd terms in the
hybrid-pi equivalent circuit are
all associated with base-width
modulation effects and are not too
significant in normal applications.
The rbb' term is included in the
hybrid-pi equivalent circuit to account for the voltage drops in the
base caused by transverse major-

Temperature Dependence-The
parameters shown in the hybridpi equivalent circuit are also temperature-dependent. Eq. (113)
shows that gm is inversely proportional to temperature. It can be
determined from Eq. (126) that
rb/e is proportional to hfelf1o(T).
Because the parameter hrelf10 in-

= 3).

Table XI-Summary of Dependence of Model Parameters on Operating Condition. (Except where in parentheses,
statements refer to low-level injection conditions and voltages low enough for no avalanche multiplication effects).

Increasing Ie
R 2 , and
R 3 , together with the input impedance of transistor Ql' combine
to present a matched impedance
to the pulse generator. Resistor
R3 , which is usually much larger
than resistors Rl and R 2 , merely
provides reverse bias· to increase
the switching speed of transistor
Ql. Point X on the test-circuit
schematic represents the origin of
the input pulse to the transistor
under test. This input consists of
only a positive pulse of voltage. If

132

RCA Silicon Power Circuits Manual

3. Storage Time (t.) represents the time for the collector current to go from
its final ON value to 90 per
cent of its final ON value
after the turn-off base pulse
is applied.
4. Fall Time (tf) represents
the time for the collector
current to go from 90 per
cent of its ON value to 10
per cent of its ON value.
Turn-on time Ton and turn-off
time T off are defined by the following equations in terms of the
preceding four components:

Toll

= t. + tl

(152)

If the correlation of switching
times is to be accurate, exact circuits must be used. These circuits
must include all voltages and all
resistors. One reason for this requirement is obvious, if only t.
and tf are considered. These
switching times depend primarily
on I B2 , but the shape of IB2 depends upon how closely IB2 approaches a current generator. As
previously stated, the approximation of IB2 as a current generator
is limited by the BVEBO breakdown rating. Hence, a specification of IBI and IB2 does not totally
define the IB2 source impedance
and, therefore, does not guarantee
equivalent switching times.

Qualitative Description of
Switching Times-All switching
times can be explained in terms
of transistor physics; accurate estimates of switching times from
parameter measurements, however, are more difficult.
Delay time td arises from a
stored charge at the emitter and
collector junctions. The emitter is

reverse-biased by VBE (off); as a
result, charge is stored in the depletion layer around the emitter.
Similarly, the collector is reversebiased by Vee + VBE (off) and has
an associated capacitance. The depletion layers, and thus the capacitance, change when VBE (off)
switches to V BE ( on) . The time required to effect this change in
charge is termed td and can be
considered as the time required to
charge the junction capacitances
to new values.
The rise time tf involves the
same capacitances discussed above,
plus other factors. The junction
capacitances are still changing because the collector voltage is decreasing and V BE (on) is increasing. The rise time is also affected
by the base transit time and the
charging of the collector capacitance through the collector series
resistance.
The storage time t. depends
upon the time required for minority carriers in the base and collector to recombine and produce a
charge distribution that exists
when the transistor is just ready
to come out of saturation.
Fall time tf can be considered
as the reverse process of rise
time; thus, the charges in the
emitter and collector junction capacitances are again important.
Quantitative Relationships for
Switching Times-The concept of
a transistor as a charge-controlled
device is useful for prediction of
switching-time phenomena. This
concept views the transistor as a
device in which the terminal currents (Ie, I B , and IE) are controlled by the charge in the base.
Transistor theory predicts that
Ie, In, and IE are linearly related
to the base charge. As a result,

Silicon Power Transistors

133

three separate time constants can
be defined:

1. Emitter time constant,
TE = (QB/IE)
(153)
2. Base time constant,
TB = (QB/In)

(154)

3. Collector time constant,
TC = (QB/Ic)
(155)

The time constant TB represents
the effective minority-carrier lifetime in the base. This time constant is related to the time constant TF, as follows:
1.

Iadt

lQt
Qo

dQB

(QBdt/rn)

(160)

Eq. (160) states that the charge
delivered to the base is equal to
the change in the base charge
necessary to establish a new current level, plus the charge needed
to maintain Qn against recombination.
The total base-charge variation
can be expressed by the following
equation, which is derived from
the charge-continuity equation
[Eq. (159)]:

For a uniform base,
TF, = TB (1- a) "'" 1.2/Wh (156)

2. For a graded base,
TE = TB

(I-a) "'" 0.6/Wb (157)

where Wh is the base cutoff frequency (Le., the frequency at
which the base transport factor is
0.707 of its original value).
The time constant Tc can be defined in terms of TF, by the following equation:
(158)

The basic equation of charge
continuity for transistors may be
written as follows:

where C~L'e and C'rc are emitter and
collector transition capacitances.
Because Gr. and CTC depend on
VUE and Vcn, respectively, the following assumptions can be made:
CTc = C'Te VBE- t
(162)
(step-junction assumption)

(159)

CTc = C'Tc Vcn- t
(163)
(reasonable assumption for step or
graded junction)

where III is the base current,
dQII/dt is equal to the change in
base charge, and Qn/Tn can be interpreted as the recombination
rate.
Eq. (159) can be integrated
with respect to time to obtain the
following result:

where the prime capacitances indicate a measurement of C'l'e and
C'I'C at a total voltage of 1 volt.
(This total voltage includes the
junction voltage and the junction
contact potential.)
The notations in Eqs. (162) and
(163) are used and the indicated

(dQn/dt)

+ (QB/TB)

134

RCA Silicon Power Circuits Manual

integrations in Eq. (161) are performed to obtain the following
expression:

tionally, charge must be removed
from the collector. The collector
charge depends on the forward
bias at the collector and on the
collector resistivity.
The charge-control equation is
as follows:

(164)

The important conclusions that
can be drawn from Eq. (164) are
that td increases with VBE (off) ,
decreases with increased I B1 , and
depends primarily on the emitter
transition capacitance when Vee
» VBE(off).
Rise time starts at the edge of
conduction and ends just short of
saturation. The charge equation
is given by
In

dQTe + dQTc + dQB + Qn (165)
dt
dt
dt
Tn

After a number of simplifying
assumptions are made the following equation can be obtained:

where IB is the base current, QB
is the base charge required to
maintain Ie, QBS is the excess
stored base charge, dQB/dt is the
current that results from a change
in QB, and dQBs/dt is the current
that results from a change in QBS.
If QB is constant and is equal
to Tele, the derivative dQB/dt is
zero because QB is the charge that
is required to maintain Ie and is
not changed.
If IB2 is substituted for IB in
Eq. (164), the equation may be
rewritten in the following form:
In2

+ QBS + dQBS
TS

(168)

If Eq. (168) is integrated with
(166)

where CUT is the current-gain
bandwidth at the edge of saturation. All terms, except eTC! are
given at the edge of saturation.
The equation indicates that rise
time is reduced for small ratios
of Ie/lB. In addition, transistors
that have a high fT (cutoff frequency) with RL as a load produce
the lowest rise time.
Storage time is determined by
the length of time required to remove excess base charge over that
required to maintain Ie. Addi-

respect to time, the following
equation is obtained:

- ft.

dt
(dQBs/dIB)

(169)

With the additional information
that TeITB is equal to l/hFE and
that dQns/dlB is equal to Ts, the
final expression for ts becomes
ts

= TS

Inl - IB2 were
h IB2·IS
(Ic/hFE) - In2 negative
(170)

135

Silicon Power Transistors
The term 7"s in this equation is
the storage time constant, and its
value depends on the structure of
the transistor. The equations used
to determine 7"s for different transistor types are tabulated below:
1. For alloy-type transistors
having no collector storage charge,
TS

= 2.4/wb(l-a)

(171)

where CUI> is the base cutoff frequency and ex is the grounded-base
current gain, both measured at
the edge of saturation.
2. For diffused-base alloy transistors,
TS =

3/wb(l- a)

(172)

3. For graded-base mesa or
planar transistors,
TS

= (0.6/6lb)

+ (Tmc/2)

From the previous discussion,
it is obvious that a proper choice
of the ratio Ie/In can minimize
switching time for a given transistor. In addition, some circuit
techniques are available that further improve switching speed. Two
common techniques for this purpose are the use of "collectorcatcher" circuits and of speed-up
capacitors.
A typical "collector-catcher"
circuit is shown in Fig. 162. Improvement in switching speed is
obtained because the transistor is
not allowed to go into saturation;
storage time, therefore, is drastically reduced. With no input

(173)

where Tmc is the minority-carrier
lifetime in the collector.
From the equation for 7"., it is
apparent that an increase in In2
causes a decrease in TN> an increase in 1m (more overdrive)
causes an increase in 7"., and the
limiting value for ts is approximately 0.77"s.
The equation for fall time tr can
be derived in a manner similar to
that used to derive the rise-time
equation. The same charges must
be moved, but the limits are different. The result is as follows:

Ie - hFE IIl2
0.1 Ie - hFEIIl2

Switching-Time Reduction
Techniques

(174)

Because IB2 is negative, Eq. (174)
indicates that tr increases with
h~'I'; but decreases as the ratio
11'/1 B~ decreases.

+vee

Figure 162. "Collector-catcher" circuit.

pulse applied to the circuit, the
transistor is initially biased off
by -V nn. A positive pulse of voltage turns the transistor on and
the collector voltage begins to
drop from +Vee toward +VR' If
VR is greater than the sum of
the voltage drop across CR and
VeE just out of saturation, then
the collector is clamped at some
value of voltage which maintains
the transistor out of saturation.
The difficulty with this circuit
is that the maximum Ie is essentially beta-dependent and, be-

RCA Silicon Power Circuits Manual

136

cause beta varies with temperature, this circuit is not very stable.
Burn-out of the diode or transistor
is possible.
More practical circuits are
shown in Figs. 163 (a) and
163 (b). In these circuits, the battery VB and the diode keep the
transistor out of saturation as
before. However, the feedback arrangement tends to keep Ie constant by automatic variation of
the base drive. For example, if
beta increases and Ie tends to
rise, the collector voltage begins
to decrease, but the base drive
is decreased and the circuit is returned to near its original condition.· The only disadvantage of
this circuit is the isolated battery VR •

Figure 164.

Practical "collector-catcher"
circuit.

feedback arrangement. The function of CRa is to keep the transistor turned off under conditions
of low VBE voltage (to reduce delay time). C acts as a speed-up
capacitor. The use of the proper
speed-up capacitor effectively increases turn-on drive and turn-off
drive without supplying large
amounts of "on" base current. As
a result, faster rise times and
faster fall times are achieved
without the penalty of long storage time.
An example of a circuit that
uses a speed-up capacitor is shown
in Fig. 165. Waveforms for this
circuit are shown in Fig. 166.

Figure 163. I·Collector-catcher" circuits in
which feedback is used.

A practical circuit is shown in
Fig. 164. Operation is similar to
that described above. The drop
across CR 2 acts as the VB supply.
The diode pair CR 1 constitutes the

Figure 165. Circuit that uses speed-up
capacitor to reduce transistor switching
times.

Silicon Power Transistors
The optimum value of C for
fastest response can be found experimentally. If V s is large compared to V HE and R2 can be
neglected, then the charge stored
on the capacitor while the transistor is ON is Vc. This charge should
equal the stored base charge for
best response. Practical values for
R 2 , V s, and V HE will modify this
relation.

137
on transient dissipations for the
case where a transistor is continuously turning on and off. Under such conditions, the average
power can be expressed by the
following general equation:
P avg

(liT)

+ (liT)

VCE(sat)

IC(sat)

to
[

VCE (t)off Ic (t)off dt
t!

+ (1 IT)

~-b
I

Figure 166. Waveforms for circuit shown
in Fig. 165: (al source voltage Vs; (bl base
current IB; (cl collector current Ie.

Power Dissipation
An important consideration for
transistors being used in a switching mode is power dissipation.
Dissipation can be handled in four
parts: (1) average dissipation;
(2) saturation dissipation; (3)
cutoff dissipation; (4) switching
transient dissipation.
Average dissipation is the average power that must be handled
over a complete cycle of operation and basically determines the
heat-sink requirements for a
given transistor case temperature.
It is the average of saturation,
turn-off transient, cutoff, and turn-

rto

V CE(off) IC(oll) dt

VCE (t)on Ic (t)on dt

) t.

+ (liT) )t

(175)

T = total switching·
period
t1 = time interval the
transistor is 0 N
t 2 -t1 = turn-off time
t:l-t 2 = time interval the
transistor is OFF
T-ts
turn-on time
VCE (off) = VCE while transistor
is OFF
Ic (off) = current flowing
while transistor is
OFF [I cEx at VCE
(off) ]
VCE(t)on = VCE as a function of
time while transistor
is turning on
Ie (t) on = Ic as a function of
time while transistor
is turning on
VeE (sat) = V CE while transistor
is ON
Ie; (sat) = 10 while transistor is
ON
Vn: (t) off = VOE as a function of
time while transistor is turning off
Ie (t) off
Ic as a function of
time while transistor
is turning off

where

RCA Silicon Power Circuits Manual

138

Base power is usually very small
and is neglected in the equation
for average power. If required,
however, an IBVBE(t) term can be
included for each interval of time.
It should be noted that the. four
integrals in Eq. (174) are, respectively: (1) saturation dissipation,
(2) turn-off dissipation, (3) cutoff dissipation, and (4) turn-on
dissipation.
Evaluation of the four integrals
usually requires the use of simplifying assumptions or a graphical
approach. If a particular circuit
has been constructed and average
power is to be calculated, two approaches are available:
(1) The instantaneous voltagecurrent characteristic can be plotted, and the integrations performed graphically.
(2) The heat-sink temperature
can be measured under normal operation. A controlled source of
power (for example, dc power)
can then be applied to the transistor until the steady-state temperature of the heat sink is equal to
the normal operating temperature.
The amount of power necessary to

establish this heat-sink temperature is the average power.
If average power is to be calculated for a tentative design, some
simplifying assumptions must be
made. For example, if a particular
transistor is used to switch a resistive load with equal turn-on and
turn-off base currents (the idealized waveforms are shown in Fig.
167), the following ·assumptions
can be made:
1. base power is negligible,
2. turn-on and turn-off switching times are equal,
3. collector voltage and current
vary linearly with time
during the switching transient.
On the basis of these assumptions,
P al'g can be determined as follows:
Pavg

= T

itl

VCE(sat)

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

'kl

,-5'
ow
...a:'
w

::lffi

8~
:::I!

Figure 167.

VeE (SOl)

I===r--t----t--~==~----1\

TIME (I)

Idealized collector current and voltage waveforms for a transistor that has
equal turn-on and turn-off currents.

Silicon Power Transistors

+~
T

itt (_t)
Tsw

139

~) dt

Vp (1 -

lsw

analysis can be assumed to be
purely inductive.
A simple test circuit for observation of a load line is shown in
Fig. 168. The current-sensing resistor in the collector circuit
should be non-inductive and should
have a resistance value much

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

TURN-ON

= Ip VCE(sat) Ton

+ ICEX Vp Toff

+ IpVp Tsw

(176)

From Eq. (176), it is obvious
that the average power dissipated
in the transistor can be reduced,
and the efficiency can therefore be
increased, by use of a transistor
that has the following characteristics: low Vem (sat), low leBo, and
fast switching characteristics (i.e.,
minimum T sw) .

Load-Line Analysis
An analysis of the transistor
load line is an important consideration in achievement of maximum
reliability in a high-power switch.
In general, the load is a combination of resistive and reactive elements. It is almost never purely
resistive, and for "worst-case"

Figure 168.

smaller than any other impedance
in series with the transistor. A
typical load line (VeE as a function of Ie) for this circuit is shown
in Fig. 169(a). If the inductance
is reduced so that L(dijdt) <
VCEX(sus), the circuit has a load
line as illustrated in Fig. 169(b).
[The VeEX(SUS) curve in both cases
should be determined under the
bias conditions of the circuit.]
However, in most applications, and
certainly for the worst-case design, the load line of Fig. 169 (a)
is applicable.

(al
>z

I
I

ON
TURN OFF\

(bl

: VeEX (suII

II:

Test circuit used to determine
transistor load lines.

VCEX IIUII
I

\TURN ON
OFF

I
I

_,:j~~~X

L...::::=;:y,~CC=~======:-"

,I
\ TURN ON

__ ~) BVCEX

OFF
VCC

COLLECTOR-TO-EMITT£R VOLTAGE (VCEI

Figure 169.

Inductive load line for the test circuit shown in Fig. 168; (a) typical load
line; (b) load line when L(di/dt)
VCEX(SUS).

RCA Silicon Power Circuits Manual
Fig. 170 shows typical voltage
and current curves as a function
of time for this switch, with the
load line indicated in Fig. 169 (a).
From these curves, the peak and
average power dissipation, voltage
limitations, and secondary-voltagebreakdown energy can be determined, as follows:
Ppk = VCEX

Pav !! =

jtl

(sus)

I pk

(VCEX(sus»

RB"t) dt

dt (178)

Because I cEx and R sat are small,
the following approximation is
valid:

-11.

L di

I CIIX VCEX(sus) -

LIp

Vce

(179)
V Ce

The average power dissipated in
the switch shown in Fig. 168 is
then given by

V CEX(sus) -

ICEx Vcc

11t2tl ;k (Ipk

ft4

(177)

-----v--~

".. -

P a vg

-y,-----/

TURN-ON

l
2

t;ff

(~) V CEX(sus)

(LIp2) [
T

V CEX(sus)
]
V CEX(sus) - V cc

watts
(180)

+ -1
T

The turn-off energy is expressed
by the following equation:

it4 I

(VCEX

(BUB» dt

~----'

TURN-oFF

Etoff

l
2

(LIp 2) [

V CEX(sus)
]
V CEX(sus) V cc

(181)

lal

Ibl

III

I
~

III

j
o

V"
~~

ICEX
u
- -I::::;::;;:;;:::::;"=~":":"i-~=-:r==- WHERE RT" TOTAL
COLLECTOR AND
EMITTER RESISTANCE

Figure 170. Voltage and current waveforms for the switching circuit shown in Fig. 168.

Silicon Power Transistors
This energy must not exceed the
Es/b rating of the transistor.
Preceding discussions have been
directed toward the calculation of
average power. Although this calculation is important, the peak
power during switching is usually
most critical. Whether the transistor can handle the peak power
pulses during switching can be determined from safe-area-of-operation curves.
The general procedure for determination of the safe area of
operation is as follows:
1) The voltage and current are
plotted as a function of time.
2) An average junction temperature is calculated on the basis of average power and
known case temperature.
3)

The safe-area curves are derated on the basis of an effective case temperature which
is equal to true case temperature plus the average junction-to-case temperature.

4) The load line of voltage as a
function of current is plotted
on the derated safe-area
curve, and it is determined
that this load line does not
remain in any area longer
than the safe-area curve indicates.
5) If the voltage at any point
reaches the sustaining region, all power dissipated in
the sustaining region is considered as reverse-bias second-breakdown energy. This
energy should not be allowed
to exceed the Es/b rating.
(See section on Safe-Area
Ratings for clarification of
ES/h and I Rib safe-area
curves.)

141
Analysis of Inductive-Load
Switching
Inductive switching requires
rapid transfer of energy from
the switched inductance to the
switching mechanism, which may
be a relay, a transistor, a commutating diode, or some other device. Often, it is necessary to calculate accurately the energy that
will be dissipated in the switching
device. This type of calculation is
especially important when the
switching element is a semiconductor device that may not be
able to handle the amount of energy involved safely.
Most inductive switching circuits can be represented by the
basic equivalent circuit shown in
Fig. 171 (a). This circuit shows
the situation at the instant of
turn-off. Variation of this basic
circuit for three methods of turnoff are shown in Figs. 171 (b) ,
171(c) and 171(d).
In the circuits of Fig. 171, Vee
is the voltage source in series
with the turn-off device and its inductive load, Rand L are the
series resistance and inductance,
10 is the current flowing at the
instant of turn-off, and V. represents the breakdown voltage of
the turn-off device.
The energy dissipated in the
turn-off device depends on V", Vee,
I", R, and L. For purposes of
analysis, V. is assumed to remain
constant during the turn-off transient [a reasonable assumption
for the circuits of Figs. 171 (b),
171(c), and 171(d)].
Five theoretical cases-The
five cases to be analyzed are
shown in Fig. 172. The energy
equations for each case and corresponding current and voltage

142

RCA Silicon Power Circuits Manual
VCC

R
L

(o)

Vcc

Va
R

r -

:to!

LVCE~
I

OEVK:

.../

I
I

Vs'Vo+Vz

Vee' O

(d) -

Basic switching circuits with inductive loads.

waveforms for the switching device are also shown.
In case 1, shown in Fig. 172(a),
the energy is given by the familiar expression for energy stored
in an inductor, as follows:

El = (1/2) L U

(182)

where El is the energy for case 1,
L is the circuit inductance, and 10
is the initial current.
Case 2, shown in Fig. 172(b),
differs from case 1 in that energy
is supplied to the switching device by the battery during turnoff. For case 2, the turnoff energy,
E 2 , is given by the following expression:
(

I
I
I

Ie) V.aLVCEX

E2 = (1/2) L 102

I
I
I

l? ___ J

TURN-OFFr

I
I
L ___ ---'

Figure 171.

r--,
R

L
TURN-OFF
OEVICEj

(b) V"Vz

Vs
) (183)
V3 - Vee

To show that case 2 is a modification of case 1, a multiplying factor
k2 can be defined as follows:
E.

(1/2) L 102 k2

(183a)

where the factor k2 is given by
k2

1
1 -

Vs
Vs - Vee

(183b)
p

Fig. 173 shows a curve of k2 as a
function of the ratio Vee/V•.
Case 3, shown in Fig. 172 (c),
causes an energy dissipation Ell
given by the following expression:
E3 '"" 10 Vs L
R
[ In

(1 +' (10 R)J(V3 (I oR)/(V 3

Vee»)
V co)

+1]
(184)

143

Silicon Power Transistors

Vee 0

E =1.I V. n '+IoRftVs-Veel
'
3 R 0 s
IoR!(Vs -Veel

loR/Vee

E3=1/2Llb3

2_fyn'+{IoR/~eelpk2+,l
l oRIVec1pk2 j
Vs
,
p=Vee /Vs,k2= V,-Vee = '-p

k ___
3 - oRlVcep

~ , J
In-'-k-

k4'~~+'
p
pk2

Vcc=O
loR"O

"I~

-l ~('+IaRlVsl j..!-

VSD0
~
g
~In(l+IaR/Vsl

-I

ln '+loRNs
2
' +1
=- 5 loRNs loR/V.

12--

CASE 5

Figure 172.

Equivalent circuits, energy equations, and voltage and current waveforms
for the five basic circuit configurations.

144

RCA Silicon Power Circuits Manual

Eq. (184) can be rearranged,
as was Eq. (183), to show that it
is a modification of case 1. This
rearrangement introduces a new
multiplying factor k3' which is a
function of both the voltage ratio
Vee/Vs and the ratio loR/Vee. Eq.
184 then becomes:
Ea

(184a)

(1/2) L U k3

where the factor k3 is defined as
follows:
k.

by k 2. Case 3 then reduces to case
2.
Case 4, shown in Fig. 172(d),
is a special form of case 3. The
condition loR
Vee arises when
there is negligible voltage drop
across the switching device, in
the ON state, and the current is
limited only by the circuit resistance. The energy dissipation
E4 is then given by:

f (loR/Vee, Vec/V.)

CtR/Vee)

(IoR~V r:d kJ +lJ

[ In (1 +
(loR/Vee)

k.
(184b)

Fig. 173 shows curves of k3 as
a function of the ratio Vee/V. for
several values of loR/Vee. When
the ratio loR/Vee becomes less
than 0.01, kg can be approximated
100
CURVE

FACTOR

---..........

K3
K2
K4 aK3

XoRI
Vee
1--1 ;;.0.01

...~. ~
.........

QO I
o

0.2

Q4
f

.........

,--

V ~1.0 f - .......... .-.~

I-1\\
o.1 \ "'.....

f--

5
10

i-lI0 -

0.6 0.8
= VCc/Vs

[ l;{( 1

-~ I02 L

Vee

~y,

+ V o .!
- Vae) ) +1]
Vee/(Va-Vee)
.
(185)

Again, it is convenient to define
a multiplying factor k4 which is
a function of the ratio Vee/V., as
follows:
E. = (1/2) L I,,2 k.
(185a)
where
2 [ In __1___
]
k. = f (p) = -;;(1 ~ k2k2) + 1

(185b)
Fig. 173 includes a curve of
k4 plotted as a function of p. This
curve corresponds to the curve
of k3 for loR/Vee = 1. As Vee approaches V s' the multiplying factor approaches its maximum value
of two. Therefore, for any inductive switch in which Veo loR,
the maximum energy that must be
handled by the switching device
is L I02, or twice the energy of.
(1/2) L I02 for case 1.

100

1.0

Figure 173. Multiplying factors (k2, ka. k.)
as a function of the ratio Vee/V •.

Case 5, shown in Fig. 172(e),
can also be regarded as a special
form of case 3. A practical example of case 5 is shown in Fig.
171(d). Note that there is no volt-

145

Silicon Power Transistors
age source in series with the inductance and the commutating
diodes; therefore Vee = O. For
this case, the energy E5 is given
by

" 1\

",0.8
:.:
II:

~ 0.6

E. = V, 10 Ii

'"z~

0.4

In
1

1
(L,B IV,)

:::l

::Iii

0.2

"- i'

(loR IV,)
(186)
Because Vee = 0, any loR term
gives an infinite loR/Vee ratio.
Therefore, case 5 cannot be plotted by the method used in Fig.
173. However, a new multiplying
factor k5 can be defined in terms
of loR/V. instead of loR/Vee.
When this new independent variable is used, Eq. 186 becomes

I
10
100
RATIO loR/Va
Figure 174. Multiplying factor k" as a
function of the ratio loRIV,.
0.01

constants k 2 , k 3 , k4 and k5 can be
easily determined from Figs. 173
and 174 for most practical circuits.

(186a)

Four practical examples-The
following examples illustrate the
use of the equations given for
the five theoretical cases.

(I~R/V.) + 1]

Example 1: The two circuits
shown in Fig. 175 are identical
except that R2 in Fig. 175(b) is
greater than Rl in Fig. 175(a).
Vee = roR2

where
k5 = f (loR/V.)
=

2
[In 1 +
(loR/Vs)
(loR/V.)

(186b)
Fig. 174 shows a curve of k5 as
a function of the ratio loR/V•.
(Because k5 can be defined as a
function of loR/V", obviously ka
could also have been defined in
terms of p and loR/V., instead of
p and loR/Vee. The choice was
arbitrary, and was made on the
basis that loR/Vee is usually a
more meaningful ratio from a circuit standpoint.)
The preceding analyses show
that energy dissipated in an inductive switch can, in general, be
considered as a modification of
the simple (1/2) Ll02 relationship.
Each specific case requires a differont multiplying factor k. The

la)

Ibl

Figure 175. Circuits used in Example 1 to
demonstrate the use of case-4 equations.

The problem is to decide in
which circuit the switching device must handle the most energy.
Because Vco = loR, case 4 applies
for both circuits. 10 and V. remain

RCA Silicon Power Circuits Manual

146

constant; therefore, (1/2) L 102 is
the same for both circuits.
To determine the switching energy, it is necessary first to determine how k4 varies. Fig. 173
indicates that as Vee/V. increases
(i.e., as Vee increases), k4 also
increases. Because E4 = (1/2) L
102 k4' an increase in Vee increases
the energy requirement of the device. Thus, for a given circuit
with a specified 10 , such as shown
in Fig. 175, minimum energy is
obtained with the lower resistance in series with the inductor
(because a lower Vee is needed to
establish 10 ) .
Example 2: The circuits shown
in Fig. 176 demonstrate the difference between cases 3 and 4.
The circuit of Fig. 176(a) represents a turn-off condition after
the circuit has reached steady
state (because loR = Vee). Therefore, this circuit corresponds to
case 4.

The energy requirement for the
circuit of Fig. 176 (a) is calculated as follows: The ratio Vee/
V. = 70/80 = 0.875. The corresponding k4 multiplying factor
(from Fig. 173) is approximately
1.6. The energy E4 is then given
by
E.

[Calculation of E4 directly from
Eq. (185) yields a value of 393
millijoules.]
To find the energy requirement
for the circuit of Fig. 176(b)
both the VeciV. ratio and the
10R/Vce ratio must be used. The
Vee/V" ratio is again 0.875. The
ratio loR/Vee
3.5/70
0.05.
From Fig. 173 the interpolated
value for ka is approximately 6.5.
From Eq. (184a), the energy for
this circuit is determined as follows:

(a)

(b)

E-1/2L l o2k 4

E-1/2Llo2k 3

loR-Yee

loR

(/)

::;;

(a)

100H--+-t+P~-rTt-t
6
6
4

2 -

50000

106

466

105

466

10 4

466

103

466

102

SURGE OURATION-S

100

(b)

Figure 188. Typical rectifier circuits using
capacitive loads: (a) half-wave rectifier
circuit; (b) voltage doubler.

fier circuits that use capacitive
loads. In such circuits, the low
forward voltage drop of the silicon rectifiers may result in a very

Figure 189.

Universal surge rating charts
for RCA rectifiers.

156

RCA Silicon Power Circuits Manual

00.01

0.1
SURGE DURATION-S

Figure 190. Typical coordination chart for
determination of fusing requirements: Curve
A-surge rating for 20-ampere rectifier:
Curve B--expected surge current in hal-,wave circuit; Curve C--Opening characteristics of protective device; Curve D-resulting surge current in modified circuit.

With a capacitive load, maximum surge current occurs if the
circuit is switched on when the
input voltage is near its peak
value. When the time constant
RsC of the surge loop is much
smaller than the period of the input voltage, the peak current Ipenk
is equal to the peak voltage Epenk
divided by the limiting resistance
R., and the resulting surge approximates an exponentially decaying current with the time constant R.C.
Surge-current ratings for rectifiers are often given in terms of
the rms value of the surge current
and the time duration t of the
surge. For rating purposes, the
surge duration t is defined by the
time constant R.C. The rms surge
current I rllls is then approximated
by the following equations:

on the surge-rating chart, which
has axes labeled I rm • and t. Because R.C is equal to t, any given
value of R. defines a specific time
t, and hence a specific point on the
plot of the equation for I rm • t.
However, R. must be large enough
to make this point fall below the
rating curve for the rectifier used.
The following example illustrates the use of this simplified
procedure for the half-wave rectifier circuit shown in Fig. 188(a),
which has a frequency f of 60
Hz and a peak input voltage Epeak
of 4950 volts. The values shown
for Elleak and C are substituted in
the equation for Il'lllst as follows:
Irmst

=
=

0.7 (4950) (2.5 X 10-6)

0.0086

When this value is plotted on the
surge-rating chart of Fig. 191, the
resulting line intersects the rectifier rating curve at 3.3 x 10- 4 second. The minimum limiting resistance which affords adequate
surge protection is then calculated
as follows:
RaC

3.3 X 10-4

R > 3.3 X 10-4

= 132 ohms

• - 2.5 X 10-6

Irma = 0.7 (EpeakC/R.C)
= 0.7 (EppskC/t)
(187)

and
(18R)
where Epenk and C are the values
specified by the circuit design.
This equation may then be plotted

Figure 191.

Surge rating chart for staCk.
rectifier CR210.

Therefore the value of 150 ohms
shown for R. in Fig. 188(a) provides adequate surge-current protection for the rectifier.

157

Rectification
The design of rectifier circuits
having capacitive loads often requires the determination of rectifier current waveforms in terms of
average, rms, and peak currents.
These waveforms are needed for
calculation of circuit parameters,
selection of components, and
matching of circuit parameters
with rectifier ratings. Although
actual calculation of rectifier current is a rather lengthy process,
the current-relationship charts
shown in Figs. 192 and 193 can be
used to determine peak or rms
current if the average current is
known, or vice versa.
The ratios of peak-to-average
current (I".nk/Iav) and rms-toaverage current (I,.mjI a,.) are
shown in Fig. 177 as functions of
the circuit constants nwCR r, and
R./nRI,. The quantity WCRI, is the
ratio of resistive-to-capacitive reactance in the load, and the quantity RjR r, is the ratio of the

limiting resistance to the load resistance. The factor n, referred to
as the "charge factor," is simply
a multiplier which allows the chart
to be used for various circuit configurations. The value of n is equal
to unity for half-wave circuits, to
0.5 for doubler circuits, and to 2
for full-wave circuits. (These
values actually represent the relative quantity of charge delivered
to the capacitor on each cycle.)
In many silicon rectifier circuits, Rs may be neglected when
compared with the magnitude of
RI,. In such circuits, the calculation of rectifier currents is simplified by use of Fig. 193, which gives
current ratios under the limitation
that Rs/RI, approaches zero. Even
if this condition is not fully satisfied, the use of Fig. 193 merely
indicates a higher peak and higher
rms current than will actually flow
in the circuit, i.e., the rectifiers
will operate more conservatively
100

,.a
H
....

%RS/nRt:

1.57
I
100 r-

...

OfoRS/nRL=

2
05

.5
I
2

2 I
10 5
30

I FOR HALF WAVE SINGLE PHASE RECTIFIER CIRCU ITS
n=
2 FOR FULL-WAVE SINGLE-PHASE RECTIFIER CIRCUITS
112 FOR VOLTAGE-DOUBLING CIRCUITS

3.14

[

C IN FARADS
RL IN OHMS
w=2.".f WHERE f=L1NE FREQUENCY
RS IN OHMS

~05

"...:i:

1000

5
Io
3o
I00

~
10

100

1000

nwCRL

Figure 192.

Relationship of peak, average, and rms rectifier currents in capacitor-input
circuits.

RCA Silicon Power Circuits Manual

158
8
6
4

:to
ray
1/1
1.Lpeak
ray

I/)

I-

8
6
4

z
.....
0:
0:

::>
u

ffilo

ii:

.....

,..........1-""

!i0:10 2

,II

I:peak

8
6

...

I-

2
10-1 2

4 68 I

lI: rms

4 6 10

-I-

I: rms
Lay

III
4 68102 2

4 68103

68 104

EFFECTIVE RATIO OF RESISTIVE TO CAPACITIVE IMPEDANCE (I1OICR)

Figure 193.

Forward-c:urrent ratios for rectifiers in capacitor-input circuits in which R.
is much less than lie.

than calculated. As a result, this
simplified solution can be used
whenever a rough approximation
or a quick check is needed on
whether a particular rectifier will
fit a specific application. When
more exact information is needed,
the chart of Fig. 192 should be
used.
Average output voltage Eav is
another important quantity in capacitor-input rectifier circuits because it can be used to determine
average output current Iav. The
relationships between input and
output voltages for half-wave,
voltage-doubler, and full-wave circuits are shown in Figs. 194, 195,
and 196, respectively. Fig. 197
shows curves of output ripple voltage (as a percentage of Eav) for
all three types of circuits.
The following example illustrates the use of these curves in
rectifier-current calculations. Both
exact and approximate solutions
are given. For the half-wave circuit of Fig. 188(a), the resistiveto-capacitive reactance CLlCR L is
given by

For an exact solution using Fig.
192, the ratio of R. to RL is first
calculated as follows:

WCRL= 2'11" X60X2.5 X 10-6 X 200,000

Figure 194. Relationship of applied ac
peak voltage to dc output voltage in halfwave capacitor-input circuit.

189

R 8 = ~ =0.075
RL
200,000

100.------.---,.---,..,:==--""T.o5
j..-.----t-,.5
90 ~---+----~~~~==~I

=--+---+2

I-

80 r----+----~_=~~~~4

~-f--_+6

70 ~-~--~~~~~--~8

0::

~-+---_+IO

ILl

~ 60r'["-

..J

:I:

__+--A~~:::::::::$~~12.5
15

~ _ _ _~~~~*=~~;20
50'l"
25

~
.....0
';. 30

...;JI."

35
~~~~~'30
40
60
~50

100

1000

.,CRL (C IN FARADS,R L IN OHMS)

Rectification

159

200
.I
'~_--,.25

I-

0::

180'[------+--7OSol--....,.5
_ _+_--1.75
:...-+-----11.0

'f---------t-~~~==~~~~5

z 160

(!)

::;
III

::>
0

_-""'---;3
140

r-----~~~~~4
_--+----15

(!)

~
~

Figure 195. Relationship of applied ac peak voltage to dc
output voltage in capacitorinput voltage-doubler circuit.

120

r---Jf~~~~~~

-=----+----la

0::

II.
0

L-I1W===$~IO12

w 100 ~
....

.
>

--1------+----.415

~:::j::======j:::::::::j20
10

100

.. CRL (C IN FARADS, RL IN OHMS)

IOO'r----,----,----=::::;;::;::::::====~.05.1

.5
I

4
I-

0::

6
8
10
12.5
15

<>
W

70
%RS/RL=

..J
..J

::>

II.
0::

II.

25
30
35
40

....>
w"
;;e

50
60
70
80

100

",CR L (e IN FARADS. RL IN OHMS)

Figure 196.

Relationship of applied ac peak voltage to dc output voltage in full-wave
capacitor-input circuit.

RCA Silicon Power Circuits Manual

160

CIRCUIT

PARAMETER

HALF-WAVE
VOLTAGE-DOUBLER

>
o

FUll-WAVE

~ 10~--~------~~~~~------~

(!)

>
w
-'

!l.
!l.

a::
~

:::>

I~--~------

!l.

:::>

100

1000

wCR l (C IN FARADS, Rl IN OHMS)

Figure 197.

RMS ripple voltage in capacitor-input circuits.

The values for wCR L and RsiRL
are then plotted in Fig. 194 to determine the average output voltage Eav and the average output
current lavas follows:
Eav/Epeak = 98 per cent
Eav = 0.98 X 4950 = 4850 volts
Iav = Eav/RL
Iav = 4850 volts/200,OOO ohms
= 24.2 milliamperes
This value of Iav is then substituted in the ratio of I rm8/I"v obtained from Fig. 192, and the
exact value of rms current I rms in
the rectifier is determined as follows:
Irms/lav = 4.4
I rms = 4.4 X 24.2
= 107 milliamperes.
For a simplified solution using
Fig. 193, it is assumed that the

average output current Iav is approximately equal to the peak input voltage Epeuk divided by the
load resistance R L , as follows:
lav
Iav

=
=

Epeak/RL
4950/200,000
24.7 milliamperes

This value of Iav is then substituted in the ratio of IrmsiIav obtained from Fig. 193, and the
approximate rms current is determined, as follows:
Irms/lav = 5.7
I rms = 5.7 X 24.7
= 141 milliamperes
Current-versus-temperature ratings for rectifiers are usually
given in terms of average current
for a resistive load with 60-Hz
sinusoidal input voltage. When the

161

Rectification
ratio of peak-to-average current
becomes higher (as with capacitive loads), however, junction
heating effects become more and
more dependent on rms current
rather than average current.
Therefore, capacitive-load ratings
should be obtained from a curve
of rms current as a function of
temperature. Because the ratio of
rms-to-average current for the

rated service is 1.57 (as shown by
IrmjIav at low wCR on Figs. 192

and 193), the current axis of the
average-current rating curves for
a sinusoidal source and resistive
load can be multiplied by 1.57 to
convert the curves to rms rating
curves. Fig. 198 shows an example
of this conversion for RCA stack
rectifier rating curves.
I400

CRIOI

CRI02
I I
CRI03

"'800
B-

ili

'"
~

CRI04

- - - f-

I-

a 105

~600

CRI06

CRi07 TO 110

z
e[

o
II.

I-

~400

-f.-

n:
:::>

CR201 TO 212

:l:

-- -

-1-

::E
:::>
::Ii

- - f-

x
-60

Figure 198.

-40

-20
0
20
40
60
80
AMBIENT TEMPERATURE _·C

100

n:
o
"-

- 600

I-

- 800

~ ~ ,- - ,--.
"' ~ N~ --

15200

'"
- - - I OOO~

~ ~ 1\II-

-- - -

-~ ~

'"~

E
t- - I I
l- t- - - I 200 '"
B-

f.- l- f-

'"n:n:
:::>

400 :;:
::E
n:
::E
200

::E

120

Current-temperature ratings for silicon stack rectifiers.

162

Power
Conversion
I

N many applications, the optimum value of voltage is not
available from the primary
power source. In such instances,
dc-to-dc converters or dc-to-ac
inverters may be used, with or
without regulation, to provide
the optimum voltage for a given
circuit design.
An inverter is a power-conversion device used to transform
dc power to ac power. If the ac
output is rectified and filtered
to provide dc again, the over-all
circuit is referred to as a converter. The purpose of the converter is then to change the magnitude of the available dc voltage.
Power-conversion circuits, both
inverters and converters, consist
basically of some type of "chopper," which is used to develop a
wave shape that is acceptable to
a transformer, and the transformer. The design of the transformer is an important consideration because this component
determines the size and frequency
of the converter (or inverter) ,
influences the amount of regulation required after the conversion
or inversion is completed, and
provides the transformation ratio
necessary to assure that the desired value of output voltage is

delivered to the load circuit. The
chopping or switching function in
the inverter circuit is usually performed by high-speed transistors
or SCR's connected in series with
the primary winding of the output transformer.
Inverters may be used to drive
any equipment which requires an
ac supply, such as motors, ac
radios, television receivers, or
fluorescent lighting. In addition,
an inverter can be used to drive
electromechaniGal transducers in
ultrasonic equipment, such as
ultrasonic cleaners and sonar detection devices. Similarly, converters may be used to provide the operating voltages for equipment
that requires a dc supply.
Transistor and SCR inverters
can be made very light in weight
and small in size. They are also
highly .efficient circuits and, unlike their mechanical counterparts,
have no moving components.

TRANSISTOR INVERTERS
Several types of transistor circuits may be used to convert a
steady-state dc voltage into either
an ac voltage (inversion) or another dc voltage (conversion). The
simplest converter circuit is the

163

Power Conversion
blocking-oscillator, or ringingchoke, power converter which consists of one transistor and one
transformer. More complex circuits use two transistors and one
or two transformers.

Basic Circuit Configurations
Fig. 199 shows the basic circuit
configuration for a ringing~choke
dc-to-dc converter. In this converter, a blocking oscillator (chopper circuit) is transformercoupled to a half-wave rectifier

=
Figure 199. Basic circuit configuration for
a ringing-choke dc-to-dc converter.

type of output circuit. The rectifier converts the pulsating oscillator output into a fixed-value dc
output voltage.
When the oscillator transistor
Ql conducts (as a result of either
a forward bias or external
dri ve), energy is transferred to
the collector inductance presented by the primary winding
of transformer T l ' The voltage
induced across the transformer
feedback winding connected to
the transistor base through resistor RR increases the conduction of Q 1 until the transistor is
driven into saturation. The rectifier diode CRr in series with the
secondary winding of transformer T1 is oriented so that no
power is delivered to the load

circuit during this portion of the
oscilla tor cycle.
With transistor Q1 in saturation, the collector current
through the primary inductance
of transformer T 1 rises linearly
with time (-di/dt
ElL) until
the base drive supplied by the
transformer feedback winding
can no longer maintain Q1 in
saturation. As
the current
through Q 1 decreases from the
saturation level, the voltage induced into the feedback winding _
decreases, and transistor Q 1 is
rapidly driven beyond cutoff.
The energy stored in the collector inductance (primary of transformer T 1) is released by the
collapsing magnetic field and
coupled by the secondary winding of transformer T l' through
rectifier diode CRt, to the load
resistance RL and filter capacitor Cl' The filter capacitor stores
the energy it receives from the
collector inductance. When no
current is supplied to the load
circuit from the oscillator (i.e.,
during conduction of transistor
Ql), capacitor Cl supplies current to the load resistance Rr•
to maintain the output voltage
at a relatively constant value. The
switching action of rectifier diode
CR 1 prevents any decrease of the
energy stored by capacitor Cl because of the negative pulse coupled
from the oscillator during the
periods that transistor Ql conducts.
The operating efficiency of the
ringing-choke inverter is low, and
the circuit, therefore, is used primarily in low-power applications.
In addition, because power is delivered to the output circuit for
only a small fraction of the oscillator cycle (i.e., when Ql is
not conducting), the circuit has
a relatively high ripple factor

164

RCA Silicon Power Circuits Manual

which substantially increases
output filtering requirements.
This converter, however, provides definite advantages to the
system designer in terms of design
simplicity and compactness.
The push-pull switching inverter is probably the most widely
used type of power-conversion circuit. For inverter applications,
the circuit provides a square-wave
ac output. When the inverter is
used to provide dc-to-dc conversion, the square-wave voltage is
usually applied to a full-wave
bridge rectifier and filter. Fig.
200 shows the basic configuration
for a push-pull switching converter. The single saturable transformer controls circuit switching
and provides the desired voltage
transformation for the squarewave output delivered to the
bridge rectifier. The rectifier and
filter convert the square-wave
voltage into a smooth, fixed-amplitude dc output voltage.
When the voltage Vee is applied
to the converter circuit, current
tends to flow through both switching transistors Q 1 and Q2. It is
very unlikely, however, that a perfect balance can be achieved between corresponding active and

Figure 200.

passive components of the two
transistor sections; therefore, the
initial flow of current through
one of the transistors is slightly
larger than that through the
other transistor. If transistor Q1
is assumed to conduct more heavily initially, the rise in current
through its collector inductance
causes a voltage to be induced in
the feedback windings of transformer T 1 which supply the base
drive to transistors Ql and Q2.
The base-drive voltages are in the
proper polarity to increase the
current through Ql and to decrease the current through Q2. As
a result of regenerative action,
the conduction of Q 1 is rapidly
increased, and Q2 is quickly driven
to cutoff.
The increased current through
Ql causes the core of the collector inductance to saturate. The
inductance no longer impedes the
rise in current, and the transistor
current increases sharply into the
saturation region. For this condition, the magnetic field about the
collector inductance is constant,
and no voltage is induced in the
feedback windings of transformer
T 1 • With the cutoff base voltage
removed, current is allowed to flow

Basic circuit configuration of a single-transformer push-pull switching
converter.

Power Conversion
through transistor Q2. The increase in current through the collector inductance of this transistor causes voltages to be induced
in the feedback windings in the
polarity that increases the current
through Q:! and decreases the current through Qt. This effect is
aided by the collapsing magnetic
field about the collector inductance
of Q1 that results from the decrease in current through this
transistor. The feedback voltages
produced by this collapsing field
quickly drive Q 1 beyond cutoff and
further increase the conduction of
Q~ until the core of the collector
in-ductance for this transistor
saturates to initiate a new cycle
of operation. The square wave of
voltage produced by the switching
action of transistors Qt and Q 2
is coupled by transformer T t to
the bridge rectifier and filter,
which develop a smooth, constantamplitude dc voltage across the
load resistance R L • The small
ripple produced by the square
wave greatly simplifies filter requirements.
Push-pull transformer-coupled
converters with full-wave rectification provide power to the load
continuously and are, therefore,
well suited for low-impedance,
high-power applications. Although
not as economical as the ringingchoke design, the push-pull configuration provides higher efficiency and improved -regulation.
Fig. 201 shows a four-transistor, single-transformer bridge
configuration that is often used
in inverter or converter applications. In this type of circuit,
the primary winding of the output transformer is simpler and
the breakdown-voltage requirements of the transistors are reduced to one-half those of the

165

Figure 201. Basic circuit configuration of
a four-transistor, single-transformer
bridge inverter.

transistors in the push-pull converter shown in Fig. 200.
Fig. 202 shows the schematic
diagram for a two-transistor, twotransformer converter. In this
circuit, a small saturable transformer provides the base drive
for the switching transistors, and
a nonsaturable output transformer
provides the coupling and desired
voltage transformation of the output delivered to the load circuit.
With the exception that it uses
a separate saturable transformer,
rather than feedback windings on
the output transformer, to provide
base drive for the transistors, this
converter is very similar in its
operation to the basic push-pull
converter shown in Fig. 200. The
saturable-transformer technique
may also be applied in the design of a bridge converter, as
shown in Fig. 203.

Transformer Considerations
The selection of the proper core
material in the design of a transformer to be used in an inverter
depends on the power-handling requirements, operating frequency,
and operating temperature of the

166

RCA Silicon Power Circuits Manual

~1I~~-------4~~VCC

Figure 202.

Basic circuit configuration of a two-transformer push-pull switching converter.

Figure 203. Basic configuration of a fourtransistor bridge inverter that uses a
saturable output transformer.

inverter. For high-frequency applications, the ferrite core is superior to the iron type in both
performance and economy. Even
at low frequencies, ferrite cores
may be more economical because
the iron type must be made in
thin laminations or in the form.
of a tape-wound toroid.
Power loss in ferrite is approximately a linear function of
frequency up to 40 kHz. Above
this frequency, eddy-current
losses decrease the efficiency of
most ferrites. Laminated iron
cores are normally restricted to
frequencies below 10 kHz.
The operating temperature of
the transformer is an important
consideration in the choice of the

particular ferrite core. For many
ferrite cores, the Curie temperature is low. The manufacturer's
data on ferrite material indicate
the maximum operating temperature which, together with the
variation in flux density as a
function of temperature and the
desired flux density (B), must be
considered to select the proper
core.
Another important consideration is the efficiency of the transformer. The transformer efficiency desired can be used to
obtain an approximation of allowable magnetic power, PM' dissipated by the transformer. When
PM and the core loss factor are
known, the maximum volume of
core material which can be used
is estimated. The core loss factor
at the operating frequency is obtained from the manufacturer's
data.
The remammg design considerations follow the conventional
rules of transformer design. The
size of the wire must be large
enough to ensure that copper
losses are low. The selection is
made on the basis of a 50-per-cent
duty cycle. If the wire size is too
small, copper losses will be appreciable and cause an increase
in core temperatures. In highpower, high-frequency inverters,

Power Conversion
a large number of turns in the
primary should be avoided to
minimize copper losses and maintain a low value of leakage inductance. Moreover, because of the
relatively small size of the core
and the large size of wire that
must be used, a large number of
turns may be physically impossible. Good balance and close
coupling between primaries is
normally achieved by the use of
bifilar windings.

Additional Considerations
In addition to the previous considerations for ringing-choke-type
and transformer-coupled types of
dc-to-dc converters, there are
other factors which may require
consideration in practical designs,
such as starting-bias methods, the
use of voltage-multiplication techniques, and maximum operating
temperature. Excellent starting
under heavy load conditions may
be obtained by the use of a transistor-type switch which will provide a large starting bias and
then be cut off by the buildup of
the output voltage. It is also possible to obtain satisfactory starting by the use of a fixed bias
resistance, provided the value of
this resistance is high enough so
that it does not materially affect
normal switching.
For dc output voltages higher
than those given in the particular design procedure, a voltagemultiplier-type rectifier circuit
may be used to avoid use of larger
transformer step-up ratios. Although the use of a voltagemultiplier circuit results in a
reduction in over-all efficiency,
this condition is more acceptable
than one which results in higher
copper losses, magnetic-coupling
probll~ms, and higher core losses

167
that may result from the use
of higher transformer step-up
ratios.
The transistor requirements
given later in Tables XIII through
XVI are for operation at a case
or flange temperature of 55°C. To
convert case or flange temperature to ambient temperature, it
is necessary to know the thermal
resistance between the transistor
and free air. This resistance is
a function of the contact resistance between the transistor case
or flange and the chassis; the
thermal resistance of any insulating washer used; the size, thickness, and material of the chassis;
and the method used to cool the
chassis (for example, forced-air
cooling, water cooling, or simple
convection cooling).
To assure reliable operation at
any permissible ambient temperature, care must be taken that the
collector-junction temperature of
the transistor is not greater than
that specified by the manufacturer.
The average temperature of the
junction TJ(uv) is equal to the
ambient temperature plus the
product of the average power dissipated in the transistor and the
thermal resistance between junction and case plus the case-to-air
thermal resistance as indicated by
the following equation:

The average junction temperature calculated by use of Eq.
(189) is equivalent to the effective case temperature TC(~ff)
usually given on transistor safearea-rating charts. The effects of
switching on the instantaneous
temperature must be evaluated
by use of standard safe-area
techniques, as described in the
section on Safe-Area Ratings.

RCA Silicon Power Circuits Manual

168

Design of Practical
Transistor Inverters
The design of practical inverter
(or converter) circuits involves,
essentially, selection of the
proper transistors and design of
the transformers to be used. The
particular requirements for the
transistors and transformers to
be used are specified by the individual circuit design. The following paragraphs discuss the design
of three basic inverter circuits:
the simple one-transistor, onetransformer (ringing-choke) type
and two push-pull switching converters (a two-transistor, onetransformer type and a two-transistor, two-transformer type).
The operation of each circuit is
described, design equations are
derived, and a sample design is
presented.
One-Transistor,
One-Transformer Converter-Fig. 204(a)
shows the basic configuration for

a practical circuit of a ringingchoke converter, which is basically
a one-transistor, one-transformer
circuit. Fig. 204(b) shows the
waveforms obtained during an
operating cycle.
During the "ON" or conduction
period of the transistor (ton), energy is drawn from the battery
and stored in the inductance of
the transformer. When the transistor switches OFF, this energy
is delivered to the load. At the
start of tom the transistor is
driven into saturation, and a substantially constant voltage, waveform A in Fig. 204(b), is impressed across the primary by the
battery. This primary voltage
produces a linearly increasing
current in the collector-primary
circuit, waveform B. This increasing current induces substantially constant voltages in the
base windings, shown by waveform C, and in the secondary
winding.

,
I

I L

"v,,!
o:=J.
I

+0----=.;
RECTIFIER
DIODE

(A)

-----r-I

''''-o~
I

(B)

e BASE 0----: -

i SEC

I
I

r-------t=

(D)

O~
I

o~
r--tON
-:'
tOFF""1
(E)

(b)

Figure 204. Ringing-choke converter circuit: (a) Schematic diagram; (b) Typical operating
waveforms in a ringing-choke converter-(A) primary voltage; (B) primary current;
(e) base-to-emitter voltage; (D) secondary current; (E) magnetic flux in transformer core.

169

Power Conversion
The resulting base current is
substantially constant and has a
maximum value determined by the
base-winding voltage, the external
base resistance Rn , and the input
conductance of the transistor. Because the polarity of the secondary
voltage does not permit the rectifier diode to conduct, the secondary
is open-circuited. Therefore, during the conduction period of the
transistor ton> the load is supplied
only by energy stored in the output capacitor Couto
The collector-primary current
increases until it reaches a maximum value Ip which is determined
by the maximum base current and
base voltage supplied to the transistor. At this instant, the transistor starts to move out of its
saturated condition with the result that the collector-primary
current and the voltage across the
transformer windings rapidly decrease, and "switch-ofl''' occurs.
After
the
transistor
has
switched "OFF," the circuit starts
to "ring", i.e., the energy stored
in the transformer inductance
starts to discharge into the stray
capacitance of the circuit, with the
result that the voltages across the
primary, base, and secondary
windings reverse polarity. These
reverse voltages rapidly increase
until the voltage across the secondary winding exceeds the voltage across the output capacitor.
At this instant the diode rectifier
starts to conduct and to transfer
the energy stored in the inductance of the transformer to the
output capacitor and load. Because
the output capacitor tends to hold
the secondary voltage substantially constant, the secondary current decreases at a substantially
constant rate, as shown by waveform D in Fig. 204(b). When this

current reaches zero the transistor switches "ON" again, and the
cycle of operation repeats.
DESIGN EQUATIONS: In the
following derivation of the equations used to design the onetransistor, one-transformer inverter, all references to transformer
windings, circuit components, voltages, and currents are for the circuit shown in Fig. 204(a). All
references to time periods and
waveforms apply to those shown
in Fig. 204 (b).
The average value of the current
in the primary winding of the
transformers Ip(AY) may be expressed as follows:

where lout is the load current in
amperes, V out is the dc output
voltage in volts, '1'J is the circuitefficiency factor as given in Table
XIII, and V in is the dc input voltage in volts.
The peak value tp of the triangular waveform of primary
current, waveform B in Fig.
204(b), is expressed by the following equation:

=
=

2I p (Av) (T/ton)
(2T /7] ton) (Vout/Vin) lout (191)

where T = tou + tofi' and is in
seconds.
If the saturation resistance of
the transistor (R.Rt) and the resistance of the primary winding
(R]l) are sufficiently small, essentially the full dc input voltage
ViII is impressed across the primary during ton' and the required primary inductance Lp in
henries may be determined from
the following relation:
Lp (dlp/dt)

V in

(192)

RCA Silicon Power Circuits Manual

170

For the triangular current waveform, waveform B in Fig. 204(b),
the following equation relates the
rate of change of primary curcurrent (dIp/dt) to peak current
(Ip) and the transistor conduction period ton:
dlp/dt = lp/ton

(193)

When this relationship [Eq.
(193) ] is used, Eq. (192) may be
rewritten in the following form:
Lp = (Vin/h) ton

;:::)

(;~2) (~ )

Lplp/Vin

(198)

V'out
Yin + V'out

(200)

This relationship is used in Eq.
(195) to obtain the following expression for the required primary
inductance:

(196)
(Np/Ns)2 Vout2
[ Vin2 + (Np/N S)2
+ 2 Yin Vout (Np/Ns)

]

(197)

(201)

where Is' is the secondary current
referred to the primary [I: =
Is (N./Np) J, V'out is the secondary
voltage referred to the primary
[V'out = VO\lt (No/N g ) J, Np is
the number of turns on the primary, and N. is the number of
turns on the secondary.
The derivative dI:/dt defines
the slope of the secondary cur-

The required primary inductance Lp can also be expressed in
terms of the maximum permissible
flux-density swing in the transformer core, which is given by

Lp (dIs'/dt)

Lp (lp/v' out)

The ratio of ON time to total
period of oscillation, therefore,
can be expressed as follows:

An equation for the OFF period
(tou) can be derived from the following relationship:
V' out

The total period of oscillation
(T = ton + toft), as determined
from the summation of Eqs.
(196) and (198), is given by the
following equation:

(195)

where f is the operating frequency
in hertz, and is equal to liT.
Before Eq. (195) can be evaluated, the ratio ton/T must be determined. From Eq. (194) the
conduction period of the transistor ton is given by
ton

toff

(194)

With Ip defined as indicated in
Eq. (191), the primary inductance
Lp may then be expressed as follows:

rent (referred to the primary) as
a function of time (i.e., dI:/dt =
Ip/toft ). The OFF period, therefore, may be determined as follows:

ilcp = lp (4'11" Np) [
A

1
]
li/,ui + Is/,us
(202)

Power Conversion

171

where A is the cross-sectional area
of the core in square centimeters,
Ii is the length of the magnetic
path in centimeters, la is the
length of the air gap in centimeters, /Li is the permeability of
the core material, and /La is the
permeability of air (/La = 1).
The maximum permissible fluxdensity swing may also be expressed as follows:
111/>
A

111/>

I/>(res)

p =

(207)
The required number of turns for
the base winding is given by

= (Lp tp/Np) X 108

(204)

(N p 111/> X 10-8) Itp

(205)

(411" N

(203)

Eqs. (202), (204), and (205) can
be combined to provide the following expression for the required primary inductance:

Vp = Yin - t p (Rsat + Rp + Rsupply)

NB
I/>(max) _

where cp(lllux) is the saturation flux
density for the core material and
CP(l"e.) is the residual flux density
in the core. The primary inductance can be defined in terms of
I1cp by means of the following relation:
or

cuit. The primary voltage V p at
the end of the conduction time
ton is expressed by the following
equation:

p2) [ (Ii/lLi) A 1+ (IallLa) ]

109

(206)
The length of air gap la should be
adjusted to assure operation of
the core near but not in the saturation region (Le., at a maximum
flux density slightly less than the
saturation value for the core material used). The value of the flux
density can be checked by means
of Eq. (204).
The ind1,lced voltage in the base
windings must provide a base-toemitter voltage sufficiently large
to supply the required peak primary current for any transistor
of the type to be used in the cir-

NpVB
Yin - t p (Rsat + Rp + R.upply)
(208)

VB is chosen to be twice the necessary V BE (max) for the transistor
used. One-half of the voltage VB
is dropped across R B. This voltage division helps compensate for
variations in VIlE from one transistor to another and at different
temperatures. Eq. (208) may be
rewritten to express NB in terms
of VllE as follows:
NB

2Np VBE(max)
Yin - Ip (Roat + Rp + R.upply)

(209)
The required number of turns for
the secondary N s is determined
from the relationship of input
voltage Yin, output voltage V ollb
number of turns on the primary Np, and maximum allowable
collector-to-base voltage VOB(max)
for the transistor (the value during t off ), as follows:
VOB(max)

Vin + (N piN s) Vout (210)

Np Vout
VOB(max) - Vin

or
Ns

(211)

The external base resistance RB
is necessary to compensate for individual differences in base-toemitter voltage VBE of the transistors used. The required value

RCA Silicon Power Circuits Manual

172

for this resistance may be determined from the following relationship:
RB

VBE(max)/IB

(212)

where VBE(max) is the maximum
allowable value of V BE for the
transistor type used and IB is the
typical value of base current required to provide the peak primary
current Ip at a base-to-emitter
voltage V BE' Transient losses that
occur during switch-off because of
hole-storage effects can be minimized if the value of RB is maintained as small as possible.
The peak secondary current I.
and the peak secondary voltage
V. can be expressed by the following equations:
(213)

The value of the output capacitor Cmit should be such that the
time constant Cout RL is at least
10 times larger than ton to assure
that the output voltage Vout remains essentially constant. The
capacitance value required for
this condition is determined as
follows:
RL = Vout2/Pout
CoutRL = 10 ton
Cout = (10 ton Pout) /V out2

(215)

The optimum ratio of primaryto-secondary winding space K2 for
the transformer is determined
from the following expression:
K=

1
(216)
y(Ns/Np) (Vin/Vout)+1

SAMPLE DESIGN: The application of the relationships derived in the preceding section to

the design of a practical ringingchoke inverter can best be illustrated by use of a numerical
example. In this example, a converter is designed to convert 12
volts dc to 150 volts dc with a
maximum power output of 1 watt.
The first step in the design of
any converter is the selection of
the transistor(s) to be used. For
the ringing-choke circuit, the list
of typical design parameters given
in Table XIII provides an excellent basis for this selection. For
specified values of dc output voltage Vout> output power Pout> and
dc input voltage Vln, this table indicates the maximum allowable
transistor saturation resistance
R sut and the minImum transistor
rating requirements for collector-to-base breakdown voltage
VCB(sat)' peak collector current
IC(l'k)' and maximum allowable
power dissipation P'l" The transistor selected must satisfy these
basic requirements.
For Vout
150 volts, Pout
1 watt, and Yin
12 volts, Table
XIII indicates that the transistor
used in the converter should have
a saturation resistance R.ut that
does not exceed 10 ohms, a collector-to-base breakdown voltage
VCB(max) of at least 35 volts, a
peak collector current rating Ic(,.k)
of at least 400 milliamperes, and
a dissipation rating p,l' at 55°C
of at least 80 milliwatts. The collector-to-emitter voltage of the
transistor must also be considered.
During the transistor OFF period,
the worst-case value of this voltage is equal to the product of
the base-winding-to-primary-winding turns ratio (NIl/Nl') and the
maximum collector-to-base voltage
[VCIl(muX)]' If this product exceeds the base-to-emitter breakdown voltage of the transistor, a

Power Conversion

173

Table XIII-Typical Design Parameters For Ringing-Choke-Type
DC-To-DC Converters That Have Output Ratings Up To 50 Watts.
APPLICATION
REQUIRf-MENTS
Max.
DC
Poot
Yout
VI.
(W)
(V)
(V)

Max.

250
500
750
250
500
750
300
500
750
400
600
750
500
750

5
10
20
1
2
8
0.8
1
1.2
0.5
0.8
1
0.5
0.5

6-10
10-15
15-20
6-12
12-20
20-28
6-12
12-18
18-28
10-18
18-26
26-36
12-24
24-36

TRANSISTOR
REQUIREMENTS
Min.
Min. Min.
Rut Vcn(max) Ic(pk) PD'
(n)
(V)
(A)
(W)

25
35
45
30
5
45
60
30
10
45
60
45
25
60
80
60
50
80
• Case or Flange Temperature = 55·C.

0.5
0.4
0.3
3
2
1
6
4
2
10
6
3
15
8

diode must be inserted in series
with the base.
A suitable transistor for use in
the 12-to-150-volt converter is the
RCA-2N3053. This transistor has
a peak-collector-current rating of
700 milliamperes, a maximum collector-to-base voltage rating of
60 volts, a maximum saturation
resistance of 9_5 ohms, and a
maximum dissipation rating at
25·C of 5 watts. [The maximum
saturation resistance is not given
in the published data on the transistor, but is readily determined
from the maximum rating for
the collector-to-emitter saturation
voltage VCE(sat) = 1.4 volts at a
collector current Ic of 150 milliamperes.]
Table XIII also provides data
on the required cross-sectional
area A and length of magnetic
path Ii for the transformer core
and on the expected circuit efficiency factor 71. The data in Table
XIV provide a basis for selection
of the core material for a suitable operating frequency. For the
specified converter operating con-

0.1
0.08
0.07
1.5
1
0.5
3
2
1
10
5
2
20
7.5

TRANSFORM'ER-CORE
PARAMETERS
Area
Length
A
(em)
(cm')

CIRCUIT
EFFICIENCY
Factor
'I

0.5-1.5

2.5-10

0.75

0.5-5

2.5-12

0.75

0.5-5

2.5-12

0.7

1-7.5

2.5-15

0.7

1-10

5-15

0.65

2-15

7.5-20

0.6

dition (i.e_, Vout = 150 volts, Vln
12 volts, and Pout
1 watt),
the data in these tables indicate
that a suitable transformer would
use a ferrite core that has a crosssectional area A of 1.3 square
centimeters, such as Ferroxcube
Part No. 9F520 (E type core,
type 3C material) or equivalent.
A suitable operating frequency is
8 kHz, and the expected circuit
efficiency is 75 per cent.
After a suitable transistor has
been selected and the parameters
of the magnetic core have been
determined, the following step-bystep procedure is used to complete
the design of the transformer and

Table XIV-Optimum Core
Materials For Different
Operating Frequencies.
Transformer Operating Frequency
Material
(kHz)
Ferrite
1-20
Silicon Iron
0.1-1
(Grain-Oriented)
Silicon Steel
0.1-1

174

RCA Silicon Power Circuits Manual

to determine the constants for the
output rectifier and filter:
1. The transformer secondaryto-primary turns ratio Ns/Np is
determined from Eq. (211) on the
basis of the desired dc output
voltage You!> the available dc input voltage Vim and the transistor
collector-to-base breakdown voltage rating V CB (max), as follows:
Ns
Np

Vout
VCB(ma) - Vln
150
3.1
60 - 12

[The use of the 60-volt V CB(max)
rating of the RCA-2N3053 rather
than the 35-volt value obtained
as the minimum V CB(max) rating
from Table XIII reduces the required step-up ratio.]
2. The value determined for
N./Np and Eq. (201) are used in
the following calculation of the
required primary inductance:
Lp

(0.7)(12)2
(2)(1)(8 X 103)

(150/3.1)2
]
(12)2 + (150/3.1)2
+ 2(12) + (150/3.1)
=4mH
[

3. The required number of primary turns N p is calculated, for
an air-gap length In of 0.01 cm,
from Eq. (206) as follows:
Np

~4 X 10-3
4'11"

8.1
+ 0.01) 109
1.3 X 103
1.3
= 63 turns
X

4. From Eq. (200), the ratio of
conduction time ton to the total
period of oscillation T is calculated
as follows:
ton
T

V out (Np/N.)

Yin

+ Vout (Np/N.)

150/3.1
12 + 150/3.1

0.78

5. From Eq. (191), the peak
primary current is calculated to
be

2 (1)

(0.7)(12)(0.78)

= 0.3 ampere

6. The maximum flux density in
the transformer core is determined on the basis of the relation
expressed by Eq. (204) from the
following calculation:
BM

Llcp
A

Lp Ip X 108
NpA

= (4 X 10-3)(0.3) = 600 gauss
63(1.3)
This calculation shows that the
Ferroxcube 9F520 core is acceptable as the core material because
the calculated value of flux density
does not exceed the saturation
value of this core, which is 4600
gauss. (Table XV shows typical
values of magnetic parameters for
commercial transformer-core materials.)
7. From the published data on
the RCA-2N3053 transistor, the
typical values of V BE and IB required for a peak primary current

Power Conversion

175

Table XV-Typical Values Of Magnetic Parameters For
Commercial Transformer-Core Materials.
Maximum
Permeability

Material

1000-4000

Maximum
Flux Density
(Bm)-Gauss
2000-5000

8500

10,000-15,000

30,000

15,000-20,000

70,000

15,000-20,000

(/lm)

Ferrite
Silicon Iron
(Grain-Oriented)
Silicon Steel
("Hi-Mu" Type)
Nickel-Iron Alloy

Ip of 0.3 ampere are, respectively,
1.2 volts and 4.3 milliamperes. The

maximum values for these parameters are 2.3 volts (this value includes the drop across the diode
which must be used in series with
the base, as shown below) and 11
milliamperes, respectively.
If RJl + RSI1PPiY is assumed to
be 2 ohms, which is generally the
case, the required number of turns
for the base winding is calculated
from Eq. (209), as follows:

(63) (2.3) (2)
10 - (0.3) (12)

34 turns

8. The following calculation is
used to determine the base-toemitter voltage of the transistor:
VBE

(NB/N p ) VCB(max)

(34/63) 60

VBE(max)/IB

(2.3)/(11 X 10-3)

210 ohms

10. From Eq. (211), the required number of turns for the
secondary winding is calculated
to be

Ns = N p (Vout)/[VCB(max)-Vinl
=

63(150)/(60-12)

200 turns

11. The calculation of the peak
secondary current and the peak
secondary voltage, from Eqs.
(213) and (214), respectively,
yields the following results:

t p (Np/Ns)

= 300/3.1 = 0.097 ampere

Vs =

[VCB(max) -

Yin] (Ns/N p )

= (60-12)(3.1) = 150 volts

32.5 volts

Because this value exceeds the
base-to-emitter breakdown-voltage
rating of the 2N3053, a diode must
be used in series with the base.
9. From Eq. (212), the required
value of the external base resistance is calculated to be

12. The values obtained for Is
and V. dictate that the diode selected for use in the rectifier circuit must be capable of handling
a peak current of 0.097 ampere
and must have a peak-inverse-voltage rating of more than 150 volts.
The RCA-INI763A silicon recti-

176

RCA Silicon Power Circuits Manual

fier has a maximum peak-inverse
rating of 400 volts and a maximum dc-forward-current rating
of 3.5 amperes and, therefore, fulfills these requirements.
13. The value of an output capacitor Cout capable of storing the
energy required by the load and
delivering this energy to the load
during the conduction period ton
at a substantially constant voltage
can be calculated from the following relationship [Eq. (215)]:

Secondary

= No.

32 for Is
of 0.097 ampere
Base
= No. 36 for In
of 0.011 ampere
16. From Eq. (216), the optimum ratio of primary-to-secondary winding space K is calculated
as follows:

1
V(Ns/Np)(Vin/V out)
1

-V17.(3;:=.I:=c')(7::=12;::=/~15="'OOC=)+~I =

From Step 5, the ratio of "ON"
time to total period of oscillation
was calculated as ton/T
0.78.
The period of oscillation T, however, is the reciprocal of the operating frequency (f
8 kHz).
The value of tom therefore, can be
determined as follows:

ton

(0.78/8) X 10-3 - 97 X 10-6

From the initial conditions, the
output power Pont is 1 watt and
the output voltage Vont is 150
volts. The value of the output capacitor then is calculated to be
C

> 10 (97 X 10-6)(1)
out -

22.5 X 103

0.042 F
P.

A RETMA standard value of 0.047
microfarad would be suitable.
15. From the peak currents in
the primary, secondary, and base
windings (the peak base current
In is the maximum In required
to produce the necessary value of
II,)' the wire sizes based. on the
conservative rating of 700 circular
mils per ampere are as follows:
Primary

= No. 26 for Ip of
0.300 ampere

+1
0.9

The best coupling is achieved
when the winding order with respect to the core is primary, base,
and secondary.
The design described could be
improved by use of a transformer
core having a cross-sectional area
greater than 1.3 square centimeters. Because such a core would
permit the use of fewer turns on
the primary, base, and secondary
windings, and a larger window
area or winding space, it would be
possible to use wires of larger
sizes, and thus to achieve a substantial reduction in copper loss
with only a slight increase in core
losses because of the larger core.
Two-Transistor, One-Transformer Converter-Fig. 205 shows
a push-pull, transformer-coupled,
dc-to-dc converter that uses one
transformer and two transistors.
Fig. 206 shows the waveforms
obtained from this circuit during
one complete operating cycle.
During a complete cycle, the
flux density in the transformer
core varies between the saturation
value in one direction and the
saturation value in the opposite
direction, as shown by waveform
A in Fig. 206. At the start of the

Power Conversion

177

BASE
WINDING
PRIMARY
WINDING

+
TRANSISTOR
B

BASE
WINDING

Figure 205.

Two-transistor, one-transformer push-pull switching converter.

conduction period for one transistor, the flux density in the core is
at either its maximum negative
value (-B sat ) or its maximum
positive value (+B sat ).
For example, transistor A
switches "ON" at -B sDt • During
conduction of transistor A, the
flux density changes from its initial level of - B snt and becomes
positive as energy is simultaneously stored in the inductance of
the transformer and supplied to
the load by the battery. When the
flux density reaches +B sa (, transistor A is switched "OFF" and
transistor B is switched "ON."
The transformer ensures that energy is supplied to the load at a
constant rate during the entire
period that transistor A conducts.
This energy-transformation cycle
is repeated when transistor B
conducts.
Initially, sufficient bias is applied to saturate transistor A. As
a result, a substantially constant
voltage, waveform B in Fig. 206,
is impressed across the upper half
of the primary winding by the dc
source Vln • This bias voltage can
be a temporary bias, a small fixed
bias, or even a small forward bias

B0--+--___ ~--- ---1--.
~

' --------~+BSAT

-B sAT - -

I
I
I

(B)

1
(A)
I

"::t----J ---t
I
I

"o-I--J
V

I
I
I

(e)

I
1
1

B~~-------1--------F:=
I
I

(?)
I

I
1

~
I·
I
I

III
I
I

O--t--------(EI------t-Is

I
I

(F)

O---r-----------------r-1

Figure 206. Typical operating waveforms
for a two-transIstor, one-transformer switching converter: (A) flux density in transformer core· (6) collector voltage of one
transistor; (e) collector current of one transistor; (D) base voltage of one transistor;
(E) primary current; (F) secondary current.

178

RCA Silicon Power Circuits Manual

developed across the bias winding
as a result of leakage and saturation current flowing in the transformer primary. The constant
primary voltage causes a dc component and a linearly increasing
component of current, waveform
C in Fig. 206, to flow through
transistor A. As in the ringingchoke converter, the linearly increasing primary current induces
substantially constant voltages,
waveform D in Fig. 206, in the
base winding and secondary
winding. The induced voltage
in the base winding limits the
maximum value of the base current and, therefore, of the collector current.
In the push-pull transformercoupled converter, the transition
to switch-off is initiated when the
transformer begins to saturate.
As long as the transistor is not
saturated, the product of the
transformer inductance and the
time rate of change of the collector current remains constant.
VVhen the transformer core saturates, however, the inductance decreases rapidly toward zero, with
the result that the time rate of
change of the collector current increases towards infinity. VVhen
the collector current reaches its
maximum value, transistor A
moves out of saturation and the
winding voltages decrease and
then reverse and thereby cause
transistor A to switch "OFF." The
reversal of the winding voltages
switches transistor B "ON," and
the switching operation is repeated.
DESIGN EQUATIONS: If it
is assumed that the full dc supply
voltage is impressed across onehalf of the primary winding, the
. current flowing in the collector
circuit of the conducting transis-

tor may be determined by means
of the following equation:
Lp (dlp/dt)

Vin

(217)

where LI> is the inductance of onehalf the primary winding in henries, dIp/dt is the rate of change
of primary current in amperes per
second, Ip is the magnitude of the
change in collector current during one conduction interval, and
Vln is the dc supply voltage in
volts.
For the triangular current
waveform, waveform C in Fig.
206, the instantaneous rate of
change of current can be approximated as follows:
dlp/dt

2I p/O.5T

4fh
(218)
where T is the total period of oscillation in seconds and f is the
operating frequency in hertz
(f = liT).
Eqs. (217) and (218) are combined and terms are re-arranged
to obtain the following expression
for the peak value of the current
in the collector of the conducting
transistor:
=

41p/T

Vin/4f Lp

(219)

The average value of collector
current in the conducting transistor is given by:

The maximum primary current
then can be expressed by the following equation:
IP(max) =

Ip + IAV

(Vin/4f Lp)

+ (PoutiTJ Vin)

(221)

The required inductance for
one-half of the primary is de-

Power Conversion

179

termined from the following relationship:
Lp = (NpLlI/>/Ip) X 10-8

(222)

In the push-pull transformercoupled converter, however, the
swing on the B-H saturation
curve is symmetrical about the
origin. The residual flux density
O"~R/ A, therefore, is zero, and the
maximum permissible magnetic
swing is determined as follows:

lll/> = I/>max _ I/>re.
A

I/>max
A

= Bmax
(223)

The required inductance for onehalf of the primary may, therefore, be expressed in terms of the
maximum flux density B max , as
shown in the following equation:
Lp

(Np Bmax A X 1O-8)/Ip (224)

where Bmnx is expressed in gauss.
If Eq. (219) is substituted into
Eq. (224), the following result
can be obtained:
Yin

4 Npf Bmax A X 10-8

(225)

Eq. (225) may be rewritten to obtain the following expression for
the required number of turns in
the primary:
Np

(Vin X 108)/4f Bmax A (226)

Because no air gap is required,
the required inductance for onehalf the primary is given by

To determine the required number of turns for each section of
the base winding, it is necessary
to know the maximum base-toemitter voltage V BE (max) at
which the transistors provide the

peak primary current tp. This voltage may be obtained from the published data for the transistor type
used or from the transistor manufacturer. The number of turns
for each half of the base winding
is then expressed as follows:
NB

Np [2 VBE(max)/Vinl

(228)

The required number of turns
for each half of the secondary
winding is expressed as follows:

where Rout is the resistance of
the secondary and reflected primary resistance. Because Rout is
usually very small in transformercoupled converters, it can be
neglected in the initial calculations.
The value of the external base
resistance Rn is found in the same
manner as for the ringing-choke
converter. If extreme flexibility of
operation is desired, a separate
external resistor may be used in
each base circuit.
In the push-pull transformercoupled circuit, the maximum allowable dc input voltage V ln is
limited by the coIIector-to-basevoltage rating for the transistor
type used. The maximum permissible supply voltage V ln is given
by
Vin(max) ~ [VCB(max) - VBE(wind)J/2
(230)

where VCB (max) is the maximum
collector-to-base-voltage rating for
the transistor type used and
V BE (wind) is the induced voltage
in one-half of the base winding.
Eq. (230) is based on the assumption that the leakage inductance
in the transformer is zero. In
practice, V in should not be more

180

RCA Silicon Power Circuits Manual

than about 90 per cent of the value
given in Eq. (230).
The peak secondary current is
approximately equal to the dc load
current, i.e.,

= IRL = Pout/Vout

(231)

and the peak secondary voltage is
given by
Vs = Vin (NsINp)

(232)

For good filtering of the output
voltage, the value of Cout should
be chosen so that the output time
constant is at least 10 times the
period of the oscillator; i.e.,
RL Cout

lOT = 10/f

or
C out = 10/RL f

(233)

where the load· resistance RL is
determined as follows:
RL

(V s/Is)

(234)

The starting resistor R. is
chosen so that a voltage of 0.6
volt appears at the center tap of
the feedback winding when the
supply voltage is applied, i.e.,

(Vin - 0.6) R
0.6
B

(235)

Slightly higher starting voltages
may be required for operation at
low temperatures.
SAMPLE DESIGN: The design
data shown in Table XVI can be
used as the starting point in the
design of a practical single-transformer type of push-pull converter. For specified operating conditions (application requirements),
the data in the table provide the
criteria used in the selection of
the converter transistors, give the
parameters of the transformer
core, and indicate the expected
circuit efficiency. When these de-

sign data are used as the starting
point, a practical single-transformer push-pull converter can be
designed by proper application of
the design relationships derived
in the preceding section, as shown
by the following numerical example.
In the example, it is assumed
that the converter circuit to be
designed is required to develop a
dc output voltage Vont of 110 volts
and a dc power output Pont of 100
watts from a dc input voltage of
13.6 volts. For these application
requirements, the data in Table
XVI indicate that the transistor
selected for use in the converter
should have a maximum saturation resistance R Nnt less than 0.5
ohm, a collector-to-base breakdown
voltage V OIl (max) greater than 45
volts, a minimum collector-current
rating IC(I.k) of at least 15 amperes,
and a minimum dissipation rating
of 15 watts at a temperature of
55°C. The published data on the
RCA-40251 transistor indicate
that it would be suitable for use
in the converter circuit. This
transistor has a maximum saturation resistance R,nt of 0.2 ohm
[i.e., VeR("n!)
1.5 volts at a collector current of 8 amperes], a
collector-to-base breakdown voltage Ven (max) of 50 volts, a peak
collector current rating IC(pI3.5 KHz

Figure 207. Schematic diagram of 13.6-tonO-volt transformer-coupled push-pull
converter.
150

VOLTAGE

V
./

...-40

..,.......

~IENCY

value of flux density at saturation.
These disadvantages can be overcome by the use of two transformers in various circuit arrangements, such as that shown
in Fig. 209.
In this type of circuit, a saturable base-drive transformer T 1
controls the inverter switching
operation at base-circuit power
levels. The linearly operating output transformer transfers the output power to the load. Because
the output transformer T.) is not
allowed to saturate, the peak collector current of each transistor
is determined principally by the
value of the load impedance. This
feature provides high circuit efficiency. The operation of the inverter circuit is· described as follows:
It is assumed that, because of
a small unbalance in the circuit,
one of the transistors, Qt for example, initially conducts more
heavily than the other. The resulting increase in the voltage

100

POWER OUTPUT-W

Figure 208. Output voltage and efficiency
as a function of power output for the
converter circuit shown in Fig. 207.

therefore, depends on the available
base voltage, the gain of the transistor, and the input characteristic of the transistor. Second,
because of the dependence of the
peak current on transistor characteristics, the circuit performance depends on the particular
transistor used because there is
a wide spread in transistor characteristics. Third, the transformer, which is relatively large,
must use expensive square-loop
material and must have a high

_
\!prl
+

T~I

tv.

~;:--_ _-+--II
-

~---~--.
I

Figure 209. Two-transistor, two-transformer
push-pull switching converter.

184

RCA Silicon Power Circuits Manual

across the primary of output
transformer T 2 is applied to the
primary of base-drive transformer
T 1 in series with the feedback resistor R fll • The secondary windings of transformer T 1 are arranged so that transistor Q 1 is
driven to saturation. As transformer T 1 saturates, the rapidly
increasing primary current causes
a greater voltage drop across feedback resistor R fll • This increased
voltage reduces the voltage applied to the primary of transformer T 1 ; thus, the drive input
and ultimately the collector current of transistor Ql are decreased.
In the circuit arrangement
shown in Fig. 209, the base is
driven hard compared to the expected peak collector current
(forced beta of ten, for example).
If the storage time of the transistor used is much longer than
one-tenth of the total period of
oscillation T, the transistors begin
to have an appreciable effect on
the frequency of operation. In
Fig. 209, the storage time could
conceivably be quite long because
there is no turn-off bias (the
drive voltage only decreases to
zero) for Q 1 until the collector
current of Q 1 begins to decrease.
Two methods of overcoming
this problem by decreasing the
storage time are shown in Fig.
210. In Fig. 210(a), a capacitor
is placed in paraIlel with each base
resistor R H • When V, is positive,
th'.! capacitor charges with the
polaritv shown. When V, decreases
to zero, this capacitor provides
turn-off current for the transistor. In Fig. 210 (b), a feedback
winding from the output transformer is placed in series with
each base. The base-to-emitter
voltage VIII<; is then expressed as
foIlows:

VBE

V. - Vrh - VT

(236)

If Vs decreases to zero and the

collector current does not begin
to decrease, then thebase-toemitter voltage is expressed simply by
V BE = Vrh - VT

(237)

A turn-off bias is thus provided
to decrease the collector current.
The energy stored in the output
transformer by its magnetizing
current is sufficient to assure a
smooth changeover from one transistor to the other. The release of
this stored energy allows the inverter-circuit switching to be accomplished without any possibility
of a "hang-up" in the crossover
region during the short period
when neither transistor is conducting.
The operation of the high-speed
converter is relatively insensitive
to small system variations that
may cause slight overloading of
the circuit. Under such conditions,
the base power decreases; however, this loss is so small that it
does not noticeably affect circuit
performance. At the same time,
the amount of energy stored in
the output transformer also increases. Although this increase
results in a greater transient dissipation, the inverter switching is
still effected smoothly.
A practical design of the highspeed converter should include
some means of initiaIly biasing
the transistors into conduction to
assure that the circuit will always
start. Such starting circuits, as
described later, can be added
readily to the converter, and are
much more reliable than one which
depends on circuit imbalance to
shock the converter into oscillation.

Power Conversion

185

RIb

o-~

~ !t9=!

2Vee

'..

om 0

~---------''---+-----lll

Vee

(b)
Figure 210. Two-transistor, two-transformer push-pull switching converters in which
transistor-storage times are reduced: (a) Capacitor in parallel with each base resistor
assures sharp turn-off of associated transistor; (b) Feedback winding from output transformer in series with base of each transistor assures sharp cutoff characteristics.

DESIGN EQUATIONS AND
PROCEDURE: The design of a
high-speed two-transistor, twotransformer converter is based on
the available supply voltage, the
required output voltage and
power, and the range of ambient
temperature over which the converter is required to operate.
Moreover, the converter specifications usually provide additional
preliminary design information
such as size and weight limitations, operating frequency, and

stability requirements for the operating frequency.
The first step in the design of
a practical converter is the selection of the transistors to be used
in the circuit. After suitable transistors have been chosen on the
basis of the pre-established criteria, a value for the maximum
case temperature To is determined, and the transistor parameters given in the manufacturer's
data for this value are then used
in the following step-by-step pro-

RCA Silicon Power Circuits Manual

186

cedure to design the converter
circuit:
1. The power input to the output transformer T2 (P'out) is
computed as follows:
p' out = P out/7J2

(238)

where POll I is the required output
power of the inverter circuit and
'Y]~ is the transformer efficiency (a
transformer efficiency of 90 to 95
per cent is usually assumed).
2. An estimate of the transistor
colIector current for a square wave
O'c) can then be obtained from
the ratio of P'ol1t to the supply
voltage V R, as follows:
I'e

P'out/Vs

(239)

3. From the manufacturer's
data, the transistor saturation
voltage VCE(sat) that corresponds
to the collector current I' c and
case temperature T e is determined. A second estimate of the
transistor colIector current is then
computed as follows:

Ie"

P'ont/[Vs-VeE(sat)]

(240)

4. The manufacturer's data on
the transistor is then consulted
to determine the base-to-emitter
voltage VIlE required for the collector-to-emitter saturation voltage Vcr.; (sat), as given in step 3,
at the collector current I'e and
the case temperature T e. The
common-emitter forward-transfer
ratio hr"E at this collector current
and case temperature is also obtained from the manufacturer's
data. A forced value of the ratio
h'FE that is low enough to insure
saturation (usually, h'FE is about
one-half of h FE ) is then used, together with the value determined
for V HE , to estimate the basecircuit input power Pin> as follows:

VnE (I,e")
h FE

+ (Ie,,)2Rn
hFE

(241)

The base stabilizing resistance RB
is small and is usually chosen so
that the voltage drop across it is
about one-half of VBE'
5. The input power to the basedrive transformer T 1 can be approximated on the basis of the
base-circuit input power Pin and
the transformer efficiency 'Y]l, as
follows:
P'io

Pio/7Jl

(242)

6. The collector current can
then be approximated on the basis
of the total power developed in
the converter circuit:
Ie

Pont' + Pin'
V s - VeE(sal.)

(243)

If the collector current given by
Eq. (243) is significantly higher
than that given by Eq. (240),
steps 4, 5, and 6 should be repeated with this higher value of
collector current substituted for
Ie". The collector current also includes the magnetizing current 1m
of the output transformer T? In
steps 2 through 6 it is assti'med
that 1m is less than 10 per cent of
Ie·
7. The turns ratio of the output
transformer T 2 is computed on
the basis of the specified load impedance Zr, and the reflected impedance Zr: determined as follows:

Zr,'

(Vs - Vsat)/Ie

(244)

Thus, the turns ratio N" for T"
is determined from the following
equation:
N 22

ZL/ZL'

(245)

8. The value of the feedback resistor Ro, is usually chosen so that

Power Conversion

187

approximately one-half of the
available voltage is dropped across
this resistor. Thus, the primary
voltage Vprll is equal to (Vs V,at) .and the total primary current Ipril is determined as follows:
IpriI

+ 1m! =

(Pin'IV pri!)

+ 1m!

(246)

9. The turns ratio for transformer T! is given by

where the base current IB is equal
to lc/h'FE'
10. The minimum number of
turns in the primary winding of
the output transformer T 2 is given
by
N p = (Vpri X 10 8)/4fAB

(248)

where V prl is the primary voltage
in volts, f is the operating frequency in hertz, A is the area of
the transformer core in square
centimeters, and B is the flux
density in gauss. Eq. (248) is also
used to determine the number of
turns required in the primary
winding of the base-drive transformer T! to produce the proper
frequency.
11. The magnetizing current in
the primary of T! is determined
from the following equation:
1m!

(Hs IM(1.26 N p)

(249)

where Np is the number of turns
in the primary winding, Ii is the
magnetic-path length in centimeters, and H. is the value of the
magnetizing field strength in
oersteds at the value of Bused
in Eq. (248).
This value of 1m! must be added
to 1""1 when the value of R fb is
determined (step 8). Eq. (249)
is also used in the design of the
output transformer T" to assure
that 1m2 is small compared to Ic.

If 1m2 is not small enough, the
minimum number of turns as
given by Eq. (248) should be increased.
SPECIAL TRANSISTOR REQUIREMENTS: The type of
transistor selected for use in a
high-speed converter circuit is dictated by the following conditions:
1. In a high-speed converter,
the peak value of the collector-toemitter voltage of each transistor
is equal to twice the supply voltage plus the amplitude of the voltage spikes generated by transient
elements. Therefore, the collectorto-emitter breakdown voltage V CEO
of the transistors should be
slightly greater than twice the
supply voltage (usually an additional 20 per cent is sufficient).
2. The transistors must be
capable of handling the currents
necessary to produce the required
output power at the given supply
voltage, and their saturation voltage at these currents must be low
enough so that the high efficiency
desired can be obtained.
3. The junction-to-case thermal
resistance of the transistors 6,T-0
must be low enough so that the
manufacturer's maximum ratings,
for the given ambient temperature
and the available heat sink and
cooling apparatus, are not exceeded.
The maximum collector current,
the dissipation, and the heat-sink
thermal resistance of the transistors can be approximated on the
basis of these limiting conditions
as follows:
The maximum collector current
If' is approximately given by
Ie =

Pout

7}/[Vs -

VCE(sat)]

(250)

where V s is the supply voltage,
VeElsat) is the transistor collector-

188

RCA Silicon Power Circuits Manual

to-emitter saturation voltage (for . The estimate of the required
a specific Ic), Pout is the required heat-sink thermal resistance, topower output, and 7J is the de- gether with the manufacturer's
sired efficiency of the output trans- maximum rating curve or safe
former (usually 90 to 95 per cent). operating region, completes the
The transistor dissipation can determination of transistor rebe approximated as follows (be- quirements.
cause the base dissipation is very
SECOND-BREAKDOWN CONsmall, it is neglected in this ap- SIDERATIONS: - A high-speed,
high-power inverter requires tranproximation) :
sistors that have high powerPD = (Tt/T) (VCE (S8t) Ie + 2IeEx V s) handling capabilities and very
+ [(ton+tf)/T] (V sIe/3) (251) fast saturated-switching speeds.
Reverse-bias second breakdown
(which is discussed in an earlier
where V s is the supply voltage,
V CE (sat) is the transistor satura- section of this manual) is a faction voltage (for a specific Ic) ; Ie tor that must also be considered
is the collector current, as given in the design of these circuits.
Reverse-bias second breakdown
by Eq. (250); I cEx is the collector
current with the base reverse- can be analyzed as follows: During
hiased (for V CE = 2V N) ; tOll js the the turn-off time toft, the transistransistor "turn-on" time [at Ie tor is subjected to high energy as
gjven by Eq. (250) and h'FE a result of energy stored in the
given in step 4 of the general pro- output-transformer leakage incedure] ; t f is the transistor "fall" ductance. This leakage inductance
time (at Ie given by Eq. (250) can be made small by careful windand h' E'E given in the general pro- ing of the transformer to obtain
cedure); T is the period recipro- close coupling. An approximation
cal of the operating frequency; of the value of leakage inductance
can be obtained by measuring the
and T] = %. [T- (ton + t f ) ] .
Eq. (251) is used as a guide for inductance of one-half the prithe first stages of design; the mary with the other half of the
exact dissipation is determined primary short-circuited. As is
experimentally. The transistor shown in the sample design at
saturated-switching characteris- the end of this section, the leaktics must be fast enough to pre- age-inductance value and the peak
vent the transient dissipation collector current can be used to
provide an analysis of reversefrom becoming excessive.
The required heat-sink thermal bias second breakdown.
FEEDBACK RESISTANCE:
resistance may be approximated
The value of feedback resistance
by the following equation:
Rrh is computed as the resistance
required to produce the difference
8e-A = (AT/PD) - 8J-e (252)
in voltage that should exist bewhere AT is the permissible junc- tween the collector-to-collector
tion temperature rise (AT =
voltage of the two transistors and
T.T,mux) - T A ) ; P D is the transistor dissipation; and ()e-A is the the voltage applied to the primary
case-to-air thermal resistance, in- of transformer T 1 at a given pricluding mounting, interface, any mary current IJll"il' The optimum
insulation material, and heat sink. value of the feedback resistor is

Power Conversion

189

then determined experimentally.
A decrease in the value of R fb increases the loss that results from
the circuit resistance and that in
the transformer core because the
magnetizing current increases.
The voltage across the primary of
the transformer then increases
and, as may be inferred from Eq.
(248), the operating frequency
increases. An increase in the value
of Rfh causes a greater voltage
drop across this resistance, and
less voltage is then available to
the primary of transformer T 1 ;
therefore, the frequency decreases.
Thus, Rfh can be used to control
frequency over a limited range
only.
ST ARTING CIRCUITS: The
circuits shown in Fig. 209 and
210 will not necessarily begin to
oscillate, especially under a heavy
load. As a result, a starting bias
must be applied so that the circuit has a loop gain greater than
unity and is always capable of
initiating oscillation. This bias
arrangement can be such that it
is connected only during starting,
or can be connected permanently
within the circuit. Two practical
starting circuits are described in
the following paragraphs.
Fig. 211 shows an inverter that
uses a resistive voltage-divider
network to supply the necessary
starting bias. The value of resistor Rl can be determined by use
of Eq. (235). With this circuit,
a compromise of reliable starting
and tolerable bleeder current
must be reached.
Fig. 212 shows a diode starting
circuit in which the bases of the
two inverter transistors are supplied by a resistance R 1 , which is
determined as follows:
(253)

Rfb

Figure 211. Two·transistor, two-transfC?r~er
push-pull inverter that uses a resls~lve
voltage-divider network to provide startmg
bias.

As the inverter begins to oscillate,
the base current is conducted
through the base-emitter diode
and through the forward direction
of the starting diode. Usually, additional drive is needed to compensate for the diode voltage
drop. Low-voltage silicon diodes
capable of carrying the base current continuously are normally
used.

Figure 212. Two-transistor, two~transforl!ler
push-pull inverter t~at !Jses a dIode startmg
CIrCUIt.

190

RCA Silicon Power Circuits Manual

SAMPLE DESIGN: The following paragraphs explain the use
of the design procedure given in
the preceding section to design
a practical high-speed, two-transformer, push-pull converter. The
operating requirements upon
which the design of the converter
is based are as follows:
de power output Pout = 250 watts
de supply voltage V. = +28 volts
operating frequency f = 50 kHz
load resistance RJ. = 25 ohms
ambient temperature T A = 25°C
The design of the converter circuit is performed in four basic
parts, as follows:
1. Selection of Transistors.
The first step in the selection of
the transistors for the high-speed
converter is to compute the power
input to the output transformer,
Pout'; a transformer efficiency of
95 per cent is assumed. Thus,
from Eq. (238),
p' out

= 250/0.95 = 262.5 watts

Eq. (239) is then used to make
the initial estimate of the transistor collector current necessary
to produce the required power
output:
Ic'

262.5/28

9.4 amperes

The transistors used in the inverter circuit must have a collectorto-emitter breakdown voltage V CEO
equal to at least twice the supply
voltage plus an additional 20 per
cent to allow for voltage spikes.
The value of VCEO is thus given
by
VCEO

2 (29)(1.20)

67 volts

The RCA-2N3265 power transistors selected for the converter
circuit have a VCEO(sus) of 90

volts, and a collector-to-emitter
saturation voltage VeE (sat) of
0.75 volt (given in the manufacturer's data for a collector current Ie of 15 amperes), which is
low enough to insure that the desired high operating efficiency can
be obtained. The switching times
for the 2N3265 transistor are as
follows:
Fall time tf
(at Ic
On time ton
(at Ic

=
=
=
=

500 nanoseconds
15 amperes)
500 nanoseconds
15 amperes)

These switching times are short in
comparison to the 20-microsecond
period at the 50-kHz operating
frequency.
It is now possible to recompute
the transistor collector current
to obtain a more accurate approximation of the maximum value of
this parameter in the converter
circuit. Eq. (240) is used to obtain the following result:
Ic" = 262.5/(28-0.75) = 9.62amperes
The data given for the 2N3265
transistor are used to determine
the hFE ratio and the base-toemitter voltage VBE of the transistor at this level of collector current. The hFE ratio is found to be
60 (5th percentile) at a collector
current of 10 amperes, which is
close enough to the value calculated for Ie". The forced value for
this ratio, h' FE, is chosen to be
20, which is small enough to assure that the transistor will saturate. The base-to-emitter saturation voltage VBE(sat) at the collector current of 10 amperes is
found to be 1.3 volts. The values
for the base current and base input resistance can then be computed as follows:

Power Conversion

191

IB = Ie"/hFE = 9.62/20
= 0.481 ampere
Rio = VBE(sat)/IB = 1.3/0.481
= 2.7 ohms
The total base-circuit input resistance, R'in, is the sum of the
quantity R ln and the transistor
bias resistor Rn. The value of Rn
is chosen to be 1 ohm. Thus, R'in
is equal to 3.7 ohms. The base-circuit input voltage V'ln can be readily calculated either as the product
of R'ltl and In or as follows:

= VnE(sat) + IBRB = 1.3 + 0.481

Vin'

1.781 volts

In the design of a high-speed
inverter circuit, the value of the
feedback resistor is usually chosen
so that the available voltage is divided equally across this resistor
and the primary of the base-drive
transformer. The voltage across
the primary V pl'i is determined,
therefore, as follows:
Vpri

=
=
=

(0.5)(2) [Vs - VeE(sat)]
(0.5)(2)(28 - 0.75)
27.25 volts

The base-circuit input power Pin
is determined from Eq. (241) or
from the product of V'in and In, as
follows:
Pin

(1.781)(0.581)

0.86 watt

If a transformer efficiency of 95

per cent is assumed, the power input to the base-drive transformer
is given by
Pin'

0.86/0.95

0.902 watt

The primary current is then determined as follows:
Ipri

0.902/27.25

0.0332 ampere

The value of the bias resistor R]
(a resistive voltage-divider starting circuit is used) required to

produce a starting current of 0.481
ampere is determined as follows:
R - Vee - 0.6
10.6
0.6
= 280.6
= 45.7 ohms
2. Output Transformer Calculations. It is then possible to calculate the transistor collector current on the basis of total power in
the inverter circuit, P' out + P'in.
The value obtained is given by
Ie = (262. + 0.902)/27.25
= 9.65 amperes
The impedance reflected into the
primary of the output transformer R'L, is computed on the basis of
this value of collector current as
follows:
RL' = 27.25/9.65 = 2.84 ohms
The ratio of the specified circuit
load impedance (R L = 25 ohms)
and this reflected impedance defines the transformer turns ratio
N ~ as follows:
N 22 = RL/RL' = 25/2.84 = 8.85
N2 = 2.98

On the basis of a transformer efficiency of 95 per cent, the power
magnetically dissipated in the output transformer is given by
PM = Pout (1.00- .95) = 12.5 watts
For an operating frequency f of
50 kHz, the Allen-Bradley type
WO-3 ferrite core material, or
equivalent, is acceptable. From
the manufacturer's data sheet for
this ferrite, the maximum usable
core temperature is 125°C. For
linear operation at this temperature, the flux density BM should
be 1000 gauss.

RCA Silicon Power Circuits Manual

192

The core loss factor p for BM
1000 gauss and f = 50 kHz is given
by
p = 3.2J.t W/em3 Hz

Thus, at 50 kHz the frequencydependent eore loss, p', is calculated as follows:
p'

= (3.2,u W/em3 Hz) (50X103 Hz)

0.160 W/em 3
The maximum permissible volume of the core for a transformer
efficiency of 95 per cent, therefore,
is given by
Vol = 12.5 W/(0.16 W/em 3) = 78 em3
=

For a pair of "C" cores, AllenBradley Type No. U2625C133A, or
equivalent, which have a crosssectional area A of 2.04 square
centimeters and a length Ii of 16.4
centimeters, the volume is only 40
cubic centimeters. As a resuit, the
core loss is less than 7 watts instead of 12.5 watts, and the transformer efficiency is greater than
the assumed value of 95 per cent.
The manufacturer's specifications do not include information
for estimation of the temperature
rise in the core. If the transformer
overheats, a new one which uses a
core that has a lower loss factor
must be designed.
When the two C cores mentioned
above are used, the number of
turns in the transformer primary
can be calculated by use of Eq.
(248) as follows:
N _
27.25 X 108
p (4)(5)(104)(2.04 X 1Q3)
= 6.55 turns
If Np
6 turns, then N.
(6)
(2.08) = 18 turns.
From the manufacturer's data
sheet, it is determined that for linear operation the value of H =
0.189 oersted results in a magnetizing current 1m given by

1m = (16.4)(0.189)/(1.26)(6.55)
= 0.376 ampere
This value is less than 10 per cent
of Ie.
The transformer wire size
should be large enough to prevent
excess copper losses, and the primary should be bifilar wound. The
transformer should be constructed
with a minimum amount of tape
applied to the core to reduce the
eore temperature rise.
3. Base-Drive Transformer Calculations. The Allen-Bradley
type RO-3 rectangular-loop ferrite core material, or equivalent,
is suitable for use in the basedrive transformer. The flux density Bm of the drive transformer
should be 3000 gauss and the saturation field strength Hs should
be 1 oersted.
The core-loss factor for a flux
density of 3000 gauss and an operating frequency of 50 kHz is given
by
p =

63 J.tW/em3 Hz

The core loss at 50 kHz is then
calculated as follows:
p' = 63 X 50 X 103 = 3.15 W/cm 3

On the basis of a transformer efficiency of 95 per cent, the magnetically dissipated power in the
drive transformer is given by
Pm

Pin (1.00-0.95)
0.43 watt

(0.86)(0.05)

The maximum volume is then calculated as follows:
Vol = Pm/P'

0.43/3.15 = 0.136 em 3

An Allen-Bradley Type No.
T0620H101A core, or equivalent,
is chosen. This core has an area A
of 0.119 square centimeter, a
length of 3.9 centimeters, and a
volume of 0.465 cubic centimeter.

Power Conversion

193

This volume is about three times
the maximum allowable volume
for 95-per-cent efficiency. The
magnetic losses, therefore, are
about 1.3 watts, and the transformer efficiency is low.
The number of turns in the primary is determined from Eq.
(248) as follows:
N _

(27.25) (1 08 )
(4)(5XJ04)(0.119)(3000)
37.5 turns

p -

For a junction temperature of
125°C, the maximum temperature
rise is given by

The total junction-to-air thermal
resistance, including heat sink,
mounting, and junction-to-case
thermal resistance, is determined
as follows:
8J-A =

The turns ratio Nl for the basedrive transformer T 1 is determined
as follows:
3.7 ohms
27.25/0.033 = 830 ohms
Nl2 = 830/3.7 = 224
Nl = 15

Rin'

Rpri =

Therefore, the number of secondary turns is given by
.
Ns = 37.5/15 = 2.5
The magnetizing current is determined from Eq. (249) as follows:
Iml

=
=

(3.9Xl)/(1.26X37)
0.084 ampere

The total primary current is then
0.033

Ipri =

+ 0.084 =

0.117 ampere

The feedback resistance R fb is
then calculated as follows:
Rfb

= 27.25/0.117 = 235 ohms

4. Thermal-Resistance Calculations. From Eq. (251), the average transistor dissipation is given
by
Pn

[(20-1)/(2X20)]
[(0.75X9.65) + 2 (0.020X28)]
+ (1/20) [(28X9.65)/31
8.65 watts

where I cEx , as taken from the
manufacturer's data, is equal to 1
to 20 milliamperes.

100/8.65

11.6°C/W

For the 2N3265, the junction-tocase thermal resistance (J,T-C is
given as l°C/W. The mounting
thermal resistance is about 0.25°
C/W. Thus, the heat-sink-to-air
therm_al resistance (JHS-A is 11.6 1.25 = 10.35°C/W.
EXPERIMENTAL RESULTS:
The leakage inductance of the output transformer, as measured on a
Q meter, is about 0.5 microhenry.
The peak collector current is calculated to be about 10 amperes,
and the reverse base-to-emitter
bias voltage is about -2 volts.
The 2N3265 transistor has an
assured capability to withstand
second breakdown at currents in
excess of 10 amperes for a collector inductance of 90 microhenries
and a reverse bias of 6 volts. The
published data on the 2N3265 indicate that a reduction in bias
voltage or in collector inductance
allows the transistor to handle
larger amounts of reverse-bias
energy. The operating conditions
for the output transformer are
well within the safe area. Both
transformers should be constructed with a minimum of tape
to provide as much surface area
as possible to ensure a low core
temperature.
Fig. 213 shows the schematic
diagram for the completed circuit.

194

RCA Silicon Power Circuits Manual
400

6;No.14 HFV
BIFILAR

37T
No.28
HFV

N~~J; .?----l~--~
HFV

250~F6T
No.14 HFV
BIFILAR

2,5T
No.22 HFV
BIFILAR
HEAT SINK
5°C/W

TYPE
2N3265

TRANSFORMER CORE MATERIALS:
T,-ALLEN-BRADLEY TYPE
T0620H101A, OR EQUIV.
T2-ALLEN-BRADLEY TYPE
U2625C133A, OR EQUIV.

HFV=HEAVY FORMVAR INSULATION

Figure 213.

Schematic diagram of 250·watt, 50·kHz push·pull dc-to·dc converter.

The values for the feedback resistance and the bias-starting resistance were arrived at experimentally with the calculated values
used as a beginning.
Fig. 214 shows the output characteristics of the converter as a
function of the load. The output
characteristics were measured at
the load at the output terminals of
the rectifier bridge. Thus, the effi-

ciency shown represents the total
circuit efficiency. The range of
values indicated on the efficiency
curve (i.e., 82 to 88 per cent) takes
into account the transistor dissipation, transformer losses, rectifier-bridge losses, and all other
circuit IR losses.
Fig. 215 shows the experimental transistor load line for a load
resistance of 25.6 ohms and a sup-

100

400

100

I-:2

N 40

:r:

u 80

Il::

w
a.

""I

t;30
:2
W

:::>

~20

...
Il::

...~ 40
W

320

0I--

--.:::..

I
I
~ 60 1--240

---

FREQUENCY

TOTAL CIRCUIT EFFICIENCY

DC OUTPUT

:::>

I--

:::>
0160

~ ?

Il::

:::>

0I--

6 20 !r

~~~

VOLTAGE

~
2

LOAD AMPERES

Fie:ure 214.

Output characteristics (i.e., frequency, efficiency, voltage, and power) of the
250-watt converter as a function of the load.

Power Conversion

195

iJ'1 loor

g~60

~o:~

RISE TIME
RL =25.6 .n

]

0 tJ

TlME-l's

Figure 216. Collector-current and voltage
waveforms for the 2N3265 transistors used
in the 250-watt converter.

FALL TIME
Rl =25.6 .n

II:

g
o
~

0.2

0.6

0.8

1.0

TlME-j£s

Figure 217.

Collector-current rise and fall
times.

SCR Inverter
Fig. 218 shows a typical highfrequency SCR switching inverter;
Fig. 219 shows the waveshapes
across the SCR and the output of
the transformer. For resistive
loads, this inverter is capable of
delivering 500 watts of output
power at an operating frequency
of 8 kHz, and is provided with regulation from a no-load condition
to full load. With proper output
derating, this circuit can also accommodate inductive and capacitive loads. Under a capacitive load
the power dissipation of the SCR's
is increased; under an inductive
load the turn-off time is decreased.
The inverter can be operated at
any optional frequency up to 8
kHz provided that a suitable output transformer is used and the
timing capacitors are changed in
the gate-trigger-pulse generator.
A change in operating frequency,
however, does not require any
change in the commutating components C1 and L 1 • The operation
of the SCR inverter is very simi-

RCA Silicon Power Circuits Manual

196
Eoo=ISOV

TO TRIGGER
PULSE GENERATOR

DC -

NS
TI

=
N4 CR2
LI
N3

N2
CRI

01, D2 = 600·volt, 6-ampere fast-recovery diode
Ll
Inductor, 95 turns of No. 16 magnet wire
wound on Arnold Engineering Type A4-17172

=
(or equiv.)
Tl = Output
of No. 18

core

transformer: Nl

magnet wire, two

Figure 218.

= 9 turns
strands; N2 =
N4.

=
=

TO TRIGGER
PULSE GENERATOR
36 turns of No. 18 magnet wire; N&
21 turns of No. 18 magnet wire; core, two

Na
NG
sets of Siemens Type 266215-AOOOO-R026 (or
equiv.) with 4-mil air gap

High-frequency (10-kHz) SCR push-pull switching inverter.

lar to that of the two-transistor
push-pull inverter except that external gate-trigger signals are required to initiate the SCR switching action.

CVrF\
Figure 219. Typical operating waveforms
for SCR inverter shown in Fig. 218.

Circuit operation-Fig. 218
shows the two thyristors SCR 1
and SCR2 connected to the output
transformer T 1 • These thyristors
are alternately triggered into conduction by the gate-trigger-pulse
generator shown in Fig. 220 to
produce an alternating current in
the primary of the power transformer.
The thyristors are commutated
by capacitor Cl , which is connected
between the anodes of SCRl and
SCR2 • The flow of current through
the circuit can be traced more
easily if it is assumed that initially
SCR 1 is conducting and SCR2 is
cut off and that the common cathode connection of the SCR's is the
reference point. For this condition,
the voltage at the anode of SCR2 is
twice the voltage of the dc power
supply, i.e., 2 Eoo- The load current

Power Conversion
flows from the dc power supply
through one-half the primary
winding of transformer T 1, inductor L;J, SCRb and inductor L 1 •
When the firing current is applied
to the gate of SCR:.!, this SCR
turns on and conducts.
During the "ON" period of
SCR:l, the capacitor C l begins to
discharge through L:" SCR:l' SCR 1 ,
and L:l' Inductors L2 and La function to limit the rate of rise of the
discharge current dijdt so that
the associated stresses are maintained within the capability of the
device during the turn-on of the
SCR. The effect of this control is
to decrease the turn-on dissipation, which becomes a significant
portion of the total device dissipation at high repetition rates.
The discharge current through
SCR 1 flows in a reverse direction,
and after the carriers are swept

197
out (and recombined) the SCR1
switch opens (i.e., SCR 1 switches
to the "OFF" state). At this time,
the voltage across the capacitor
C l , which is approximately equal
to -2 E oo , appears across SCR 1 as
reverse voltage. This voltage remains long enough to allow the
device to recover for forward
blocking. Simultaneously during
this interval, the conducting SCR2
establishes another discharge path
for capacitor C1 through transformer T 1 and inductors L1 and
L 3 • The role of inductor L1 is to
control the rate of discharge of
the capacitor to allow sufficient
time for turn-off.
After capacitor C1 is discharged
from -2 Eco to zero, it starts to
charge in the opposite direction to
+2 Eco. When C1 is charged to +2
Eco> because of the phase shift between voltage and current the flux

150VOC

O.
T1

== Zener
diode, 20-yolf, 'h-wall
transformer; center·tapped primary:
=Pulse
N2 = 150 turns of No. 36 wire; split

Figure 220.

secondaries: N3

100 tUrns of No. 36

wire; core material: I "diana General Type No.
CF902, or equiv.

Gate-trigger pulse generator for SCR inverter shown in Fig. 218.

198

RCA Silicon Power Circuits Manual

at that time in the inductor Ll is
a maximum. This reactive energy
stored in the inductor is normally
transferred to the capacitor and
causes an "overvoltage" or "overcharge", which in this particular
case is undesirable. Voltages on
the capacitor higher than 2 Eco
produce a negative voltage at the
anode of SCR2 with respect to the
negative terminal of the dc power
supply. This condition is prevented
by use of a clamping diode CR 2
connected to an extra tap on the
transformer oriented close to the
anode of SCR2 • As a result, the
amount of "overcharge" of the capacitor is considerably reduced.
The energy stored in inductor Ll
causes current to flow through diode CR 2 , the N 4 transformer winding inductor La, and SCR2 • Transformer windings N 4 and N:I act as
an autotransformer through which
the energy stored in the inductor
is fed back to the power supply.
When the firing current is applied to the gate of SCRb this
device conducts and the process
described above is repeated.
Each time the SCR's turn off
to interrupt the reverse recovery
current, a certain amount of energy remains in the inductor. This
energy is transferred to the device
capacitance, which is relatively
small, and thus a high-voltage
transient is generated. This highvoltage transient may exceed the
rating of the device, produce undesirable stresses, and increase the
switching dissipation. A transientsuppressor network consisting of
two IN547 diodes, resistors R l ,
R!!, and Ra, and capacitors C2 and
C:1 prevents this transient voltage
from exceeding the maximum rating of the SCR's.
Gate-Trigger-Pulse Generator
-The gate-trigger-pulse genera-

tor, as shown in Fig. 220, is a
conventional astable (free-running) multi vibrator, combined
with a threshold-sensitive switch
consisting of transistors Qs and
Q4 which turns the generator on
and off. The square-wave output of
the generator is differentiated and
fed to the gates of SCR l and SCR2
through the Ns and N4 windjngs
of pulse transformer T l . The
threshold-sensitive switch holds
the generator off until the required dc level is achieved in the
power supply. This minimum
level is necessary to maintain a
nominal repetition rate and to
supply sufficient current to trigger both SCR's. As dc power is
applied through resistor R 15 to
charge capacitor C5 , the gradually
increasing voltage at the emitter
of transistor Qa eventually rises
to a value above the Zener voltage
of the Zener diode D4 connected
between the emitter of transistor
Qs and the base of transistor Q4.
SO long as this voltage is not exceeded, the base current of transistor Q4 is zero. Because transistor
Q4 is cut off, transistor Q:\ also
remains cut off. As the voltage of
the power supply increases and
exceeds the Zener voltage of D4,
the Zener diode conducts current to the base of transistor Q4
and causes the transistor to conduct. The collector current of Q 4
then flows into the base of Qs
and causes this transistor to conduct. The collector current of
Qa is then applied to the astable
multivibrator. A polarity-sensitive
positive feedback loop consisting
of diode Da and resistor Rn provides regenerative feedback to
transistors Q4 and Qa when the
Zener diode D4 is conducting. In
the event that the power-supply
voltage decreases and current
ceases to flow through the Zener

Power Conversion
diode, this feedback network
maintains transistor Q3 in saturation until the voltage in the
circuit drops to a few volts.
The collector current through
transistors Q 1 and Q~ does not
maintain perfect balance as the
base currents of transistors Q 1
and Q:) increase. Any slight unbalance in collector current is
amplified through the positive
feedback loops. As a result, one
transistor is cut off and the other
is turned on at the extreme limit
of unbalance. If transistor Qt is
assumed turned on, the base of
transistor Q:) is driven negative
by capacitor C.>, which is connected to the collector of Qt. The
negative bias on the base of Q2
drives the transistor into the cutoff state. Capacitor C;] connected
to the base of Qt is then charged
through the load resistor R7 of
transistor Q.>, and the base drive
on transistol' Qt increases until
the capacitor is fully charged. Capacitor C.>, with its negatively
charged plate connected to the
base of transistor Q,> through a
resistor divider consisting of R4
and R G, is discharged through resistor R". Resistor R" is connected to a potentiometer R~
which controls the waveshape
symmetry and another potentiometer Rtf) which is connected
to the positive supply voltage
and serves as the repetition-rate
control.
When the negative bias decreases to zero and the base of Q:!
become positive, transistor Q2
turns "ON" and causes Qt to turn
"OFF". The capacitor C 4 which
was charged through load resistor
R7 starts to discharge through the

199
N~ primary windings of the pulse
transformer T 1 after Q~ is turned
on. This discharge current is fed
to the gate of the SCR, in the appropriate direction to fire the device. During the alternate haIfcycle of multi vibrator operation,
capacitor C t discharges through
the Nt primary windings of the
pulse transformer to trigger
SCRt·

Applications-Some of the applications of the SCR inverter are
as follows:
1. DC-to-dc converter. Conversion can be accomplished by the
use of small, light-weight, low-cost
transformers, inductors, and capacitors. This circuit is suitable
for use in computer power supplies, telephone equipment, radio
transmitters, battery chargers,
and similar equipment.
2. High-frequency fiuorescentlighting supply. Because of the
high frequency of the inverter circuit, the size and weight of the
inductive ballast is considerably
reduced; in addition, half of the
inductive components can be replaced with low-cost capacitors to
maintain a unity power factor in
the circuit. The over-all system
efficiency can also be improved;
for example, the 20- to 26-per-cent
power dissipation as a result of
the low-efficiency ballast at 60 Hz
can be reduced to a few per cent
by use of high-frequency, highefficiency inductors at moderate
cost. This decrease in power dissipation in a large industrial building can mean less burden on the
air-conditioning system.

200

Power
Regulation
THE performance of oscillators,

high-gain amplifiers, and other
electronic circuits that have exacting frequency, stability, or output requirements can be critically
affected by wide variations in dc
supply voltages. Large supplyvoltage variations may also result
in voltage levels that exceed acceptable circuit limits. Moreover,
laboratory tests and measurements of electronic devices and
circuits often require the use of
constant, precisely controlled dc
voltages. For these reasons, some
type of regulation is frequently
required to prevent significant
changes in the output of a dc
power supply as a result of linevoltage fluctuations or variations
in circuit loading.
The regulation of a dc power
supply is usually accomplished by
some type of feedback circuit that
senses any change in the dc output and develops a control signal
to cancel this change. As a result,
the output is maintained essentially constant. The nature of the
control exercised by the feedback
circuit (regulator) is determined
by the type of circuit arrangement (series or shunt). and the
mode of operation of the pass element (transistor or 8CR). In a

transistor regulator, the output
voltage from the dc power supply
is compared with a reference voltage, and the difference signal is
amplified and fed back to the base
of a pass transistor. In response
to the feedback signal, the conduction of the pass transistor is
varied, either linearly or as a
switch, to regulate the output
voltage. When the pass transistor
can be operated at any point between cutoff and saturation, the
regulator circuit is referred to as
a linear voltage regulator. When
the pass transistor operates only
at cutoff or at saturation, the circuit is referred to as a switching
regulator. All 8CR regulators are
by nature of 8CR operation
switching regulators.

LINEAR VOLTAGE
REGULATORS
All linear voltage regulators
can be classified as either series
or shunt types, as determined by
the arrangement of the pass element with respect to the load. In
a series regulator, as the name
implies, the pass transistor is
connected in series with the load.
Regulation is accomplished by
variation of the current through

201

Power Regulation
the series pass transistor in response to a change in the line
voltage or circuit loading. In this
way, the voltage drop across the
pass transistor is varied and that
delivered. to the load circuit is
maintained essentially constant. In
the shunt regulator, the pass
transistor is connected in parallel
with the load circuit, and a voltage-dropping resistor is connected in series with this parallel
network. If the load current tends
to fluctuate, the current through
the pass transistor is increased or
decreased as required to maintain
an essentially constant current
through the dropping resistor.

Series Regulators
Series-regulated power supplies
may be either voltage-regulating
types, voltage-regulating currentlimiting types, current-regulating
types, or voltage-regulating current-regulating types. Fig. 221
shows the response characteristics for each type of series-regulated power supply.

(al

(bl

Ub
(e)

(d)

Figure 221. Typical response characteristics for series-regulated power supplies: (a)
voltage-regulating types; (b) voltage-regulating current-limiting types; (c) currentregulating types: (d) voltage-regulating
current-regulating types.

Linear series regulators provide
an excellent means for prevention

of large variations in powersupply load current or output voltage. Fast response time provided
by the linear control circuit makes
possible close control of the output voltage. However, because the
series pass transistor is equivalent to a variable resistance in
series with the load, the transistor must dissipate a large amount
of power at low output voltages.
Another disadvantage of the series
regulator is that the total fault
current passes through the regulating transistor if the load becomes short-circuited. As a result,
overload and short-circuit protection in the form of current-limiting or drive-reduction networks
that operate rapidly must be used
to protect the transistor.
Fig. 222 shows a basic configuration for a linear series regulator
which is representative of the
type used in voltage-regulating
power supplies. In this type of
regulator, the series pass transistor is usually operated as an
emitter-follower, and the control
(error) signal used to initiate the
regulating action is applied to the
base. The base control is developed
by a dc amplifier. This amplifier,
which is included in the feedback
loop from the load circuit to the
pass transistor, senses any change
in the output voltage by comparison of this voltage with a known
reference voltage. If an error exists, the error voltage is amplified
and applied to the base of the pass
transistor. The conduction of the
pass transistor is then increased
or decreased in response to the
error signal input as required to
maintain the output voltage at the
desired value.
Voltage-regulating power supplies are required to maintain a
constant output voltage, independ-

RCA Silicon Power Circuits Manual

202

too:,;
fVSO:RCC:}-______________
Figure 222.

~------~~~J

Basic series voltage regulator.

ent of the load current, as shown
in Fig. 221 (a). The supply, therefore, usually has a very low output impedance. For this reason,
voltage-regulating supplies must
often be made current-limiting to
protect the regulator from very
high current drawn at the output
terminal, such as may be caused
by a short circuit. In voltageregulating current-limiting power
supplies, the load current is prevented from rising above some
predetermined design value by reduction of the power-supply output voltage when this current limit
is reached, as shown in Fig.
221 (b).
Fig. 223 shows the basic configuration for a linear regulator
circuit used in current-regulating
power supplies. This regulator
senses the voltage across a resistor
in series with the load, rather

than the voltage across the load
circuit as in the linear voltage
regulator. Because the voltage
across the series resistor is directly proportional to the load
current, a detected error signal
can be used to cancel any tendency
for a change in load current from
the desired value. Ideally, the
linear current regulator has an
infinite output impedance and output characteristics as shown in
Fig. 221(c).
The regulator circuit used with
voltage-regulating current-regulating power supplies is essentially a combination of the other
types of linear regulators. As
shown in Fig. 221 (d), the output
response characteristics of this
type of regulated supply exhibit a
crossover point at which the supply switches from voltage regulation to current regulation.

RSOURCE
...

-1"O:'c:rE__________I_R_EF__
Figure 223.

~----~~Ar~__{

Basic series regulator modified for current sensing.

Power Regulation

203

Fig. 224 shows a block diagram
of a voltage-regulating currentregulating power supply. The input ac power is rectified and filtered and is then applied to the
regulating circuit. When preregulators are used, as is normally
the case, switching types are preferred. The efficiency of the
switching regulator is extremely
high and a fast response time to
load or line variations is not required at this point in the circuit.
(The operation and characteristics
of switching regulators are discussed later in the section on
Switching Regulators.)
The output from the prereguIator is transferred to the series
pass element which provides the
fast response time for the entire
regulating circuit. At this point
in the circuit, a sample of the output voltage is compared with a
reference voltage and the resulting error signal, which is proportional to the difference between
these voltages, is amplified and delivered to the base of the pass
transistor to correct the output
voltage.
In this type of system, the resulting output voltage is highly
dependent upon the accuracy of
the reference supply. Such a voltage source may be a temperaturecompensated Zener diode in series
with a very constant source of

ACINPUT
VOLTAGE

RECTIFIER
AND
FILTER

current so that the diode incremental resistance has no effect on
the output voltage. The sensitivity
of the regulator is an inverse
function of the gain of the drive
amplifier. The smaller the variation to be sensed, the higher the
required gain of the amplifier. A
higher gain, however, results in
less stability.
Performance ParametersMost voltage-regulated power supplies are required to provide voltage regulation for wide variation
in load current. It is important,
therefore, to specify the output
impedance of the supply, llVoutl
llIoub over a large band of frequencies. This parameter indicates the ability of the power supply to maintain a constant output
voltage during rapid changes in
load. The output impedance of a
typical voltage-regulated supply is
normally less than 0.1 ohm at all
frequencies below 2 kHz. Above
this frequency, the impedance increases and may be as much as
several ohms.
A power supply must continue
to supply a constant voltage (or
current) regardless of variations
in line voltage. An index of its
ability to maintain a constant output voltage or current during input variation is called the line
regulation of the supply, which is

PRE-REGULATOR
(OPTIONAL)

Figure 224. Block diagram of series
voltage·regulating current-regulating
dc power supply.

REFERENCE
VOLTAGE
(OR CURRENT)

204

RCA Silicon Power Circuits Manual

defined as 100 (VO'/VO)' or as
the change in output voltage AVo,
for a specified change in input
voltage, expressed in per cent.
Typical values of line regulation
are less than 0.01 per cent.
Another important power-supply parameter is load regulation,
which specifies the amount that
the regulated output quantity
(voltage or current) changes for
a given change in the unregulated
quantity. Load regulation is
mainly a function of the stability
of the reference source and the
gain of the feedback network.
A power-supply parameter referred to as recovery time denotes the time required for the
regulated quantity (voltage or
current) to return to the specified
limits when a step change in load
is applied, as shown in Fig. 225.
Recovery time is a function of
the frequency response of the
feedback network of the power
supply. For voltage-regulated supplies, the "roll-off" of the feedback network increases the output

I
I

:-- RECOVERY TIME
I

I
I

,I
I
I
I

: _________ .t_

I
I

1------------,:
l-RECOVERY TIME

WITHIN

ti~Ga~II'g'N

Figure 225. Typical recovery·time charac·
teristics for regulated dc power supplies.

impedance at high frequencies,
and the impedance becomes inductive. As a result, the high-frequency harmonics of the step
change in the load current induce
a spike of voltage at the output.
The amount of change in the

output voltage of the regulated
power supply from an initial
value over a specified period of
time is referred to as drift. This
parameter is measured after an
initial warm-up period with a
constant input voltage and load
applied and the ambient temperature held constant.
Transistor Requirements-In
linear series regulators, the transistor parameters that affect circuit design and performance are
collector dissipation, maximum
collector current Ic (max), leakage
current (lCER in most cases) ,
current gains hFE and h re , collector-to-emitter saturation voltage VCE (sat), collector-to-emitter
breakdown voltage VCEO(sus), and
second breakdown Sib.
The collector-dissipation rating
limits the amount of power which
the series transistor can safely
dissipate when the power supply
is short-circuited. The maximum
collector current Ie (max) limits
the total current which the regulator can handle. A low value of
leakage current is required to
maintain the stability of the circuit and, possibly, to prevent
thermal runaway. This requirement makes silicon transistors
especially suitable for use as the
regulator pass element because
leakage current is generally much
lower in silicon transistors than
in germanium types. The currentgain parameters hFE and hre determine the amount of drive current needed at various collector
current levels. The ac forwardcurrent transfer ratio h re also determines the output impedance of
the supply. A high hre results in
a low output impedance. The saturation voltage VCE(sat) is one
factor that determines the required input voltage to the regu-

205

Power Regulation
lator for a specified output voltage
and current. The collector-to-emitter breakdown voltage VCEO (sus)
limits the maximum output voltage of the power supply. Secondbreakdown considerations in circuit applications of transistors
were discussed previously in the
section on Second Breakdown.
Current-Limitin,g Techniques
-One of the problems encountered in the design of series transistor voltage regulators is protection of the series control element
from excess dissipation because
of current overloads and short
circuits.
In some series voltage-regulator
circuits, overloading results in
permanent damage to the series
control transistor. For example,
when the output terminals of the
regulator circuit shown in Fig.
226 are shorted, the full input
voltage and available current are
applied to the series control transistor. This power usually is
many times greater than tlie dissipation ratings of the series
transistor.
+

vour
R2

VIN

o------+---+-------L--~D

Figure 226. Series voltage regulator
without current limiting.

A series fuse is sometimes used
in an attempt to protect the series
transistor from this excessive
dissipation. A series fuse cannot
usually provide the necessary
protection under all overload con-

ditions, however, because the
thermal time constant of the fuse
is normally much greater than
that of the transistor.
Protection for all overload conditions may be accomplished by
use of a circuit which limits the
current to a safe value, as determined from the dissipation rating
of the series regulator transistor.
An effective current-limiting circuit must respond fast enough
to protect the series transistor
and yet permit the Gircuit to return to normal regulator 'operation as soon as the overload condition is removed. It is desirable
to achieve current-overload protection with minimum degradation of regulator performance.
One method of achieving limiting is to use a resistor in series
with the regulator transistor. The
large resistance normally required, however, dissipates a
large amount of power and degrades the regulator performance.
The current-limiting section
(dashed line) of the regulator
circuit shown in Fig. 227 (a) is
designed to appear as a large
series resistance during current
overload and as a negligible resistance during normal operating
conditions. The value of resistance
R5 is designed so that, during
normal regulator operation, transistor Q4 operates in the saturated
condition. For the overload condition, R4 is adjusted so that the
maximum allowable value of overload current through this resistor
produces a voltage drop large
enough to cause silicon rectifier
CRl to conduct. Conduction of CR 1
reduces the bias to Q4, so that
the transistor appears as an increasing series resistance in the
regulator circuit.
Under short-circuit conditions,
the entire value of input voltage

206

RCA Silicon Power Circuits Manual

Yin appears across Q4 simultaneously with the limiting value of
current. Transistor Q4 must be
capable of withstanding the resulting dissipation. When the
current limit is reached, the
junction temperature of Q4 rises
to a value considerably above the
ambient temperature. This increase in junction temperature
causes the value of short-circuit
current to rise slightly because
of the inherent variation of the
base-to-emitter voltage VBE with
temperature in transistors. This
effect is minimized by mounting
silicon rectifier CRl and transis-

tor Q4 on a common heat sink so
that their respective junction temperatures may reach the same
value (the values of their respective VBE and forward-voltage-drop
temperature coefficients are comparable) .
Performance characteristics for
the transistor series voltage regulator of Fig. 227 (a) are shown in
Fig. 227 (b).
Although the series-regulator
circuit shown in Fig. 227 (a) provides adjustable current limiting
with simple circuitry and minimum power loss during normal
operation, it has the disadvantage

r--YIN

I
I
I

I
I

YOUT

COMMON
HEAT SINK

~_\._----

I
I

CRI
R3

I
(0)

>
I

Figure 227. Series voltage regulator with
transistor current-limiting circuit (inside
dashed lines) added: (a) schematic diagram;
(b) response characteristics.

oj>

0.2

0.4
IOUT-A
(b)

0.6

0.8

Power Regulation

207

of requiring a second series transistor capable of withstanding
short-circuit output current and
total input voltage simultaneously.
In many high-current highvoltage regulator circuits, it is
necessary to use parallel or series
connections of pass transistors so
that the voltage, current, and
power ratings of the series control element are not exceeded. The
method shown in Fig. 227 (a) may
not be practical in this application because of the additional
series transistor required. The
circuit shown in Fig. 228(a)

eliminates the need for an additional series transistor by use of
the series regulator transistor as
the current-limiting element. This
method is very effective when a
Darlington connection is used for
the series control transistor. A
desirable feature of this circuit
in high-current regulators is that
it functions well, even when the
value of resistor R4 is reduced to
zero.
In the circuit shown in
Fig. 228 (a), current limiting is
achieved by the combined action
of the components shown inside
+

LcOMMo;H~A:;:-S;;K -

---------,

--l
I
I
I
I
VOUT

I
I
I

(a)
20
16

Figure 228. Series voltage regulator using
pass transistor as part of current-limiting
circuit: (a) schematic diagram; (b) response
characteristics (for R. = 0).

> 12

I-

;:) 8
~
4

0.4

0.8

1.2
1.6
IOUT-A
(b)

2.0

2.4

2.8

RCA Silicon Power Circuits Manual

208

the dashed lines. The voltage developed across R4 and the baseto-emitter voltages of Q l and Q 2
are proportional to the circuit output current. During current overload, these voltages add up to a
value great enough to cause CRl
and Q4 to conduct. As CRl and
Q4 begin to conduct, Q 4 shunts a
portion of the bias available to
the series regulator transistor.
This action, in turn, increases the
series resistance of Ql. The value
of current in the circuit, under

current-limiting conditions, is adjusted by varying the value of
resistance R 4 •
Higher current ranges may be
obtained by increasing the number of rectifiers represented by
CRl. Temperature drift is minimized by mounting transistors Ql
and Q 4 on a common heat sink.
Performance characteristics for
this circuit (for R4
0) are
shown in Fig. 228 (b).
The circuit shown in Fig.
229(a) is a variation of that

r------,

lr--~--~--~~

nr~I~~~----~~--O

I
I
I
I
I

COMMON
SINK

I
IL

_ _ _ _ --,

(0)
20
16

> 12

\
\

I-

::>

-?8
4

0.4

0.8

1.2 1.6 2.0
IOUT-A
(bl

2.4

2.8 3.2

Figure 229. Series voltage regulator which
uses additional transistor-diode network and
series pass transistor to accomplish currentlimiting function: (a) schematic diagram;
(b) response characteristics.

Power Regulation

shown in Fig. 228(a). Current
limiting is adjusted by varying
R4 and by changing the number
of silicon rectifiers represented
by CR j • Temperature drift is
minimized by mounting the series
control transistor Qj and silicon
rectifier CR j on a common heat
sink. Performance characteristics
for this circuit are shown in Fig.
229 (b). The circuits shown in
Figs. 228 and 229 are both applicable to high-current highvoltage regulators because additional series power transistors
are not required.
Fig. 230(a) shows another
current-limiting circuit in which
the regulator series control transistor is used as the currentlimiting element. The series element must be capable of withstanding input voltage and shortcircuit current simultaneously.
The value of short-circuit current
is selected by adjusting the value
of resistor R 4 • Performance characteristics of this circuit are
shown in Fig. 230(b). The circuit functions equally well with
resistor R4 located in the positive output lead.
Design of a Practical Series
Regulated Power Supply

Fig. 231 shows the circuit diagram of a voltage-regulated
current-limited power supply.
The function. of the differential
amplifier is to maintain the output
voltage equal to the voltage at the
top of R ADJ , which is at point Vr'
Because the input impedance of the
differential amplifier is high, a
negligible amount of current flows
into its terminals. Therefore, essentially all of the current supplied by the reference voltage
supply VREF flows through the re-

209

1.2

Figure 230. Current-limiting series voltage
regulator in which series pass transistor
must be capable of withstanding input
voltage and short-circuit current simultaneously: (a) schematic dia~ram; (b) response characteristIcs.

sistive voltage divider consisting
of RCAL and R ADJ . Under quiescent
conditions, the ratio of the reference voltage to the output voltage
Vo is given by

As long as the reference voltage remains constant, a constant
current IREF flows through R CAL'
Essentially, this same current
(minus a negligible amount that

210

RCA Silicon Power Circuits Manual

flows into the differential amplifier) flows through R ADJ • The
output voltage can be expressed
by the following product:

RADJ

(255)

If a current of 0.01 ampere flows
through R ADJ , the output voltage
is then adjusted at the rate of
1/0.01 or 100 ohms per volt. The
resistance R ADJ may be located
at a remote point from the supply
to make the supply remotely programmable.
Eq. (254) implies that the stability of the dc output voltage of
the power supply is a direct function of the stability of the reference voltage. Stability of the ac
feedback system of the power
supply is maintained by the addition of a large value of capacitance in parallel with the output
voltage of the power supply, as
shown in Fig. 232, which illustrates the feedback mechanism
of a voltage-regulated power
supply. There are three points
in the circuit at which phase
shifts may occur: the pass tran-

sistor, the driver amplifier, and
the differential amplifier. If the
sum of these phase shifts is approximately 180 degrees, and
if there is a point in the circuit
at which the gain is greater than
unity, the entire system will become unstable. The addition of a
capacitor at the output decreases
the gain at higher frequencies
when the total phase shift (including that created by the capacitor itself) is 180 degrees or
more. In addition, because of the
inverse relationship of capacitance
reactance to frequency, this capacitor decreases the total output
impedance at higher frequencies.
Transistor Q L and resistor Rs
form the current-limiting configuration for this power supply.
VVhen the output current 10 exceeds the current-limiting value
of load current Io (max), the corresponding voltage drop across
Rs becomes large enough to
forward-bias transistor Qr,. Transistor Qr, then diverts all drive
current greater than that needed
to supply 10 (max) from the differential amplifier to reference

OUTPUT
VOLTAGE

RECTIFIED DC INPUT

RADJ

Figure 231.

Voltage·regulated current-limited. power supply.

211

Power Regulation

OUTPUT
AC COMPONENT OF
RECTIFIED AC INPUT

Figure 232.

----'"

AC feedback circuit for a voltage-regulated power supply.

ground. At the same time, the impedance of the pass transistor
increases to maintain the output
current at a value essentially
equal to Ic (max), while the differential amplifier remains temporarily in saturation.
Design Equations and Procedure-The following is a step-bystep procedure for the design of a
practical voltage-regulated current-limited power supply such as
that shown in Fig. 231:
1. The desired input and output conditions for the power supply and the expected deviations
from these values are determined.
In this determination, the following parameters must be considered:
Input Conditions
Input voltage Vi
Possible positive change in input voltage caused by line
variation, tlVi
Possible negative change in input voltage caused by line
variation and ripple, tlV n
Input voltage .source impedance
Ri
Maximum case temperature
Tc(max)

Output Conditions
Maximum output voltage
Vo(max)
Maximum output current
10 (max)

2. A value is selected for the
output voltage of the reference
supply that satisfies the following
condition:
Vo/20 < VREF < Vo /10 (256)
3. One of the following equations for a programmable power
supply is used to calculate the
value for R ADJ • (Typically, a programmable power supply will have
an R ADJ equal to 100 ohms per
volt or 1000 ohms per volt.)
RADJ

= 100 V o, or RADJ = 1000 Vo
(257)

4. The resistance value for
is calculated by use of the
following equation, which is obtained by rearrangement of terms
in Eq. (254):
RCAL

212

RCA Silicon Power Circuits Manual

5(a). Initially, the transistor
should satisfy the following requirements:
VCEO(SUS) ~ Vi + 6.Vi
Ic(max) ~ lo(max)

(259)

where Vi is the input supply voltage,AVi is the maximum variation in line voltage, Ic is the
maximum rating for collector current, and 10 (max) is the maximum output current.
(b) The maximum available
output current from the differential amplifier Id is then determined.
(c) The total current gain AI
of the cascaded driver stages and
the pass unit is given by
AI

= hFE(min)l X hFE(minh
X ..• X hFE(min)n

(260)

Therefore, the appropriate number of driver stages is selected so
that the total current gain will
satisfy the following requirement:
(261)

In addition, each driver transistor in the cascaded configuration
should have a collector-to-emitter sustaining voltage VCEO (sus)
equal to or greater than that of
the pass transistor Ql'
(d) The value of resistor Rs is
determined from the following relationship:
Rs

VBE/lo(max)

(262)

where VBE is the base-to-emitter
voltage of transistor QL'

(e) The current-limiting transistor QL is selected. The maximum collector-to-emitter voltage
rating of this transistor VCEO
should be greater than that of
the differential amplifier.
(f) To assure that the maximum output voltage Vo is obtained under maximum outputcurrent conditions, the following
quantities must be defined:

VBEI + VBE2 + ... + VB En-l
+ VCE(sat)n = Vx (263)
(264)

Under the prescribed conditions,
one of the two quantities Vx or
Vy , whichever is larger, appears
across the pass transistor Ql'
(Whether Vx or Vy is larger is
determined by the saturation
characteristics of the transistor
types used for the drive and pass
transistors.) This larger value
(the quantity Vx or Vy ) must be
less than the effective input voltage minus the output voltage, i.e.,
VXorVy < [Vi-6.Vn -Imax (Ri+Rs)]
- Vo
(265)
where the bracketed term in the
inequality defines the effective
input voltage.
(g) The selection of the proper
transistor for use as the pass element is based partly on the maximum power that can be dissipated
by the device. This maximum
power value is calculated according to the following procedure:
First, the output voltage from
the regulator is determined from
the following equation:
Vo

= Vi -

10 (R. + Ri)- Vpass+6.Vi
(266)

Power Regulation

213

This equation is rewritten to obtain an expression for the voltage
dropped across the pass transistor, as follows:
Vpass

Vi + IJ.Vi - Vo- 10 (Ri+Rs)
(267)

The power dissipated by the pass
transistor is given by
(268)
Substitution of Eq. (267) into
Eq. (268) results in the following
expression for the power dissipation in the pass transistor:
Ppass

10 (Vi+IJ.Vi) - 10 Vo
- 102 (Ri+Rs)
(269)

To determine at what value of
output current 10 the power dissipation is maximum, the partial
derivative of power with respect
to current is set equal to zero, as
follows:
dPpass/dl= (Vi+aVi) - Vo
- 210 (Ri+ Rs) = 0
(270)
The maximum power in the circuit occurs, therefore, when
10

Vo + IJ.Vi - Vo
2(Ri+Rs)

(271)

Eq. (271) shows that the absolute maximum power is dissipated
by the pass transistor when the
output voltage Vo is zero. For this
condition, the equation for the
output current 10 becomes
10 = Vi + IJ.Vi
(272)
2(Ri+R S)
Therefore, the maximum power
dissipated by the pass transistor

occurs when the output voltage is
zero (i.e., when the output terminals are short-circuited). If the
power supply is current-limited
to a value of current less than
(Vi + IJ. V;) /2 (R; + Rs), then the
maximum power dissipated by the
pass transistor can be expressed
as follows:
Ppas.(max)

10 (Vi+IJ.Vi)
- 102 (Ri+RS) (273)

where 10 is the maximum value
of current allowed by the currentlimiting circuit.
.
Consequently, if a transistor is
to be specified for safe operation
as a pass element, this maximum
power dissipation P pass must be
less than or equal to the maximum
power rating of the transistor at
the maximum case temperature.
(h) In addition, the maximum
safe operating region for the
transistor in this supply (a rectangle in which the upper righthand corner is Vi> 10) should be
within the maximum safe operating region of this device.
Sample Design-The following
example illustrates the use of the
basic design procedure and equations in the design of a practical voltage-regulating currentlimiting power supply. It is assumed that the rectified ac power
source is the output from a bridge
rectifier that has a 200-microfarad
filter capacitance, isolated from
the line by a 1:1 transformer.
1. The desired operating conditions are selected as follows:
Input Conditions
Input voltage Vi = 150 V
Possible positive change in input voltage aV i = 20 V

RCA Silicon Power Circuits Manual

214

Possible negative change in input voltage IIV n = 40 V
Input source impedance R j =
10 ohms
~aximum case temperature
Tc(max) = 75°C
Output Conditions
Output voltage Vo = 100 V
~aximum output current
10 (max) = 0.3 A

2. A value of 8.2 volts is selected for the reference voltage
on the basis of the following requirement:
Vo/20 < VREF < Vo/10

current gain of the driver stage is
determined as follows:
AI

(d) The 2N3440 is a suitable
drive transistor because it fulfills
the following requirement:

hFE(minh X hFE(minh > AI
20 X 40 = 800 > 750
(e) The 2N2102 transistor is
suitable as the current-limiting
device because it meets the following requirement:

3. From Eq. (257), the value of
R ADJ is calculated as follows:
RADJ = 1000 Vo = 100(120)
= 120,000 ohms
4. From Eq. (258), the value of
RCAL is calculated to be
RCAL

=
=
=

(VREF!Vo) RADJ
(8.2 X 100 X 103)/150
5500 ohms

10 (max) lId = 300 mA/0.4 mA
=750

VCEO (of QL) > Vo(max)
(of differential amplifier)
65 V> 8.2 V
(f) The quantities Vx and Vy
are determined as follows:

VBE1

= VBE (of TA2765

at 10 = 0.3 A) = 1 V
VcE(sath = VcE(sat) (of 2N3440
at Ic = 15mA) = 0.5 V
VBE1 + VCE(sath = 0.64 + 0.75
=

5(a). The RCA-2N5240 transis-

tor is selected for the pass transistor because it satisfies the
following conditions:
VCEO(SUS)
225
IcCmax)
5A

~
~
~
~

Vi X f1V i
150 + 20 = 170
Io(max)
0.3 A

(b) A differential amplifier
that has an available drive Id
equal to 0.4 milliampere is used.
(c) From Eq. (260), the total

1.39 V

VCE(sath (for TA2765)

2.5V
=Vy

Vy > Vx
Therefore, Vz = 2.5 V (Vz is used
to represent the larger of the two
quantities Vx and Vy ) . The quantity V z must meet the following
requirement:
V. < (Vi-f1Vn ) - Vo
- Io(max) (R i+ Rs)
2.5 < 170 - 40 - 120 - 0.3(10+2)
2.5 < 6.1

Power Regulation
(g) The maximum power point
is then determined as follows:

Io(max) < (Vi+~Vi)/2(Ri+Rs)
0.3 < (150+20)/2(10+2)
= 170/24 = 7.1
Therefore, P pass (max) is determined from Eq. (273) as follows:

215
(h) The maximum operating region for the 2N5240 in this supply is within the maximum safe
operating region of this device, as
shown in Fig. 233. Fig. 234 shows
the complete circuit diagram for
the voltage-regulated current-limited power supply; Fig. 235 shows
the schematic for the referencevolt,age power supply.
10
~~ MAX. (CONTIN~O~S)
4

'-.....

Ppass(max) = Io (Vi+~Vi)

I02 (R i +Rs)
(0.3) (170)
- (0.3)2 (10+2)
= 51 - 1.08 ~ 50 watts
-

..........
8
6

4
2

---

~!::CASE

DISSIPATION LIMITED
(SLOPE .-1)

IS/b LIMITED

-- --- --,"< (SLOPE=-3)
1\
TEMP. ·75°C

---

~--1VCEO j A x t i r - r 0,0
4

The maximum power rating of
the 2N5240 is 70 watts at 75°C;
therefore, the power-handling capability of this transistor makes it
suitable for use as the pass element.

,"I

10
2
4
6 8 100
2
4 6 81000
COLLECTOR-TO-EMITTER VOLTAGE-V

Figure 233, Safe-area curve for the RCA
2N5240 transistor. Dashed-line rectangle indicates that transistor operates within' ratings in the lOO-volt current-limiting (0-3
ampere) series-regulated power supply.

5.5 K

VOUT

UNREGULATED INPUT VOLTAGE
WITH Ri"IOO

Figure 234.

Schematic diagram of 100-volt series-regulated dc power supply in which
output current is limited to a maximum value of 0.3 ampere.

RCA Silicon Power Circuits Manual

216

TYPE

2N2102

A -......- - - - -.....--U+8.2V

:)1

910
3.3K

'---00
500~F

11.6 V /II;

~---~----~-------~~--~~~--~-~-4V

Figure 235.

Schematic diagram of reference voltage supply for regulated power supply
shown in Fig. 234.

Shunt Regulators
Although shunt regulators are
not as efficient as series regulators
for most applications, they have
the advantage of greater simplicity. The shunt regulator includes
a shunt element and a referencevoltage element. The output voltage remains constant because the
shunt-element current changes as
the load current or input voltage
changes. This current change is
reflected in a change of voltage
across the resistance Rl in series
with the load. A typical shunt regulator is shown in Fig. 236.
The shunt element contains one
or more transistors connected in
the common-emitter configuration
in parallel with the load, as shown
in Fig. 237.
Design Procedure and Equations-The following step-by-step
procedure is recommended for the
design of transistor shunt-type
voltage regulators:
1. The desired input requirements, load conditions, and output-voltage requirements are defined in terms of the following
parameters:

Input voltage V s
Input-voltage variation A V s
Source resistance Rs
Output load resistance RLo
Output voltage V 0
Output-voltage variation.A Vo
The terms V sand R Lo are designcenter values; AVsand ARL are
maximum deviations from these
values.
2. The transistor type selected
must operate within ratings for
the following values of V l (max),
11 (max), and maximum dissipation P 1 (max) across the shunt element when both line and load regulation are required:
Il(max)

h(max)

= Vo(RLo Vl(max)

~RL)

(274)

Vo
(under forward-bias
conditions)
(275)

217

Power Regulation

If a value of series resistance is
assumed for the reference R f , this
equation can be solved for hfe' It
can be shown that

IL I

I
I
I
I

Figure 236. Basic configuration for a
typical shunt regulator.

3. A value for resistance R2 to
provide a current 10 greater than
the minimum value required to
supply the reference voltage (Le.,
to break down a voltage-reference
diode, for example) is determined.
The following equation may be
used as a guide:

nllo

(277)

where n is the number of stages
in the shunt element.
4. The output resistance Ro of
the regulator is given by
(278)

where hfe = h fel h fe2 ... h feln , and
h fen and hie are the ac current
transfer ratio and the input impedance, respectively, of the Qn
stage.
5. The values of In and Vn for
the shunt element are determined
as follows:

where h FEn-l is the dc current gain
of the Qn-l stage of the shunt element measured at a collector current of In_I'
Vn=Vl+V2+ ... +Vn_l (281)
where Vn is the base-to-emitter
voltage of the Qn-l stage at a collector current of In_I'
6. A voltage reference source is
selected which has a resistance
less than the value that had been
assumed for Rr (or hfe is recomputed using a new value of R f),
a voltage Vu
Vo - Vn> a maximum current greater than 10 + In>
and a maximum dissipation rating
greater than V u (Io + In) .

Figure 237. Shunt regulator circuit using
two transistors as the shunt pass element.

7. The value of series resistance
R, including both source resistance Rs and external resistance

218

RCA Silicon Power Circuits Manual

. R I, is determined. The value of R
depends on the value of the input
voltage V s and its variation .!lVs;
R may be expressed in terms of
these quantities as follows:
Vs+AV s

= Vo+R [h(max)+Ir(max)]

(282)

For the usual case, 11 (max) is
equal to Idmax).
Sample Design-The following
example illustrates the procedure
used in the design of a practical
shunt type of voltage regulator
such as that shown in Fig. 238.
When the .step-by-step procedure
refers to components by reference
designations, Fig. 237 indicates
the component being considered.

Possible variation in output load
resistance .!lRL = ±55 ohms
Input voltage Vs = 49 volts
Possible change in input voltage
.!lVs = ±7 volts
Output voltage Vo = 28 volts
Possible change in output voltage .!lVo = ±O.OI25 volt
Maximum transistor case temperature Tc(max) = 55°C
2. A transistor for use as the
shunt pass element is then selected
on the basis of the maximum current, voltage, and power dissipation that the pass element will be
subjected to in the power-supply
circuit. These maximum values are
determined as follows:
II (max) = !t.(max)
= Vo/(RLo-ARd
= 0.5 ampere
VI (max) = Vo = 28 volts
under forward-bias conditions
P1(max)

=
=

VI (max) I 1 (max)
28 X 0.5 = 14 watts

The data on the RCA-2N1485 indicate that this transistor can
operate within ratings for these
circuit conditions and, therefore,
is suitable for use as the pass
element.

Figure 238. Schematic diagram of 28-volt
shunt regulator circuit.

1. The first step in the design
of a regulated power supply is to
establish the circuit operating conditions and requirements. For the
example chosen, the following parameter values are assumed:
Source resistance Rs = 10 ohms
Output load resistance R Lo =
110 ohms

3. A voltage-reference diode to
supply the voltage Vn is selected.
If an output current 10 of 2 milliamperes is required to supply the
reference voltage Vn (Le., to
break down the voltage-reference
diode) and if two stages are used
for the shunt pass element, the
value of the resistance R2 in series
with the voltage-reference diode
is calculated as follows:
R2

2/(2XlO- 3)

1000 ohms

Power Regulation

219

4. The output resistance of the
regulator is calculated as follows:
Ro

=
=

(2dYo/Yo) /RLo
(0.025/28)/110
0.10 ohm

5. If the series resistance Rr is
assumed to be 5 ohms and the Qn
stage is assumed to have a typical
input impedance hie of 50 ohms,
the ac current transfer ratio hre
of the pass element is determined
from the following calculation:

0.10

hfe

1000 X 50
5+50+1000
----'--~1000
1 + hfe 50 + 1000
52.9/0.095

560

Consequently, two stages are required for the shunt element, with
a product h rel X h re2 == 560. The
2N1485 selected in step (2) for the
first stage QI has the following
design-center values:
Ie =
ffel =
hFE =
VBE =

h = Vo/RLo = 250 rnA
56
50
0.8 volt

For the second stage Q2' therefore, the following values are required:
hfe2 = 560/56 = 10
Ie = Ir/hFEI = 250 rnA/50 = 5 rnA

An RCA-2N1481 transistor meets
these requirements. The following
design-center values can be obtained from published data for the
2N1481 for a collector current of
5 milliamperes:
h fe2

hFE2

20
25

hie = 50
VBE=0.7V

The value of hie == 50 is determined
from the slope of the typical basecharacteristics curve (V BE vs. I B )
at the 5-milliampere collector-current operating point, where IB ==
Ic/hFE2 == 5/25 == 0.2 milliampere.
If actual measurements indicate a
different value from that assumed
above, the new value is used and
h re is recomputed.
6. The current 12 and voltage V 2
are calculated as follows:
12

=
=

Ir/(hFEI hFE2)
0.20 rnA

250/(50X25)

As listed in step (5), the base-toemitter voltage of the 2N1485 for
the design-center collector current
of 250 milliamperes is 0.8 volt. For
the 2N1481, the base-to-emitter
voltage for the design-center collector current of 5 milliamperes is
0.7 volt. Therefore, V 2 is given by
V2 = 0.8 + 0.7

= 1.5 volts

7. A IN1781 silicon voltagereference diode is selected on the
basis of the following design
conditions:
Rf = 5 ohms
VR = Vo - V2 = 28- 1.5 = 26.5 volts
I(max) = 10 + 12 = 2 + 0.2 = 2.2 rnA
PI = 26.5 X 2.25 = 60 milliwatts

220

RCA Silicon Power Circuits Manual

8. The series resistance R,
which includes both the source resistance Rs and the external resistance Rt> is determined for the
condition 11 (max)
IL (max) as
follows:

Vs - AVs = Vo
49 - 7 = 28

+ [R I1(max)]
+ (0.5 R)

28 ohms

8. The external resistance R 1 ,
therefore, becomes
R1 = R- Rs = 28- 10

18 ohms

The circuit diagram of the shunt
voltage regulator that results from
this step-by-step procedure is
shown in Fig. 238.

SWITCHING REGULATOR
Fig. 239 shows the basic configuration for a switching type of
transistor voltage regulator. In
this circuit, the pass transistor is
connected in series with the load,
and regulation of the output voltage is accomplished by on-off
switching of the pass transistor
through a feedback circuit. The
feedback circuit samples the output voltage and compares it to a
reference voltage. The difference
(error signal) between the two
voltages is used to control the onoff duty cycle of the pass transistor. If'the output voltage tends to
decrease below the reference voltage, the duration of the ON-time
pulse increases. The pass transistor then conducts for a longer period of tiyU.e so that the output

voltage increases to the desired
level. If the output voltage tends
to rise above the reference voltage,
the duration of the ON-time pulse
decreases. The shorter conduction
period of the pass transistor then
results in a compensating decrease
in output voltage. Some type of
filter is required between the pass
transistor and the load to obtain
a smooth dc output. A commonly
used filter consists of an LC network and a commutating diode.
There is another method of
pulse-width modulation in which
the pass element is switched at the
line frequency and the conduction
angle is varied to obtain the desired pulse width. This type of
control is generally used with
SCR's because turn-on of an SCR
is simple and turn-off is accomplished automatically when the
line voltage reverses. Transistor
circuits, although not usually as
simple, can also be used. It should
be noted that a switching regulator operating in this mode requires that devices be used in
front of any filtering. This requirement does not exist for most
transistor switching regulators.
The major advantage of the
switching regulator over the linear
regulator is the higher efficiency
that results from the mode of
operation of the series pass transistor. In this mode of operation,
the transistor is operated in its
two most efficient stages, either at
cutoff or at saturation. As a result,
dissipation is considerably less
than when the transistor is operated in the linear region. The response time of the switching regulator, however, is usually slower
than that of the linear regulator,
but can be improved by operation
of this circuit at higher frequencies.

221

Power Regulation
to
I

nnn
ON--I i-I-OFF

OUTPUT
VOLTAGE

(a)

f:~
-r ':'"c~rC_E____________________

+-____

____-+__

(b)

Figure 239.

Basic configuration of switching type of transistor voltage regulator:
(a) block diagram; (b) schematic diagram.

Filter Considerations
A fundamental part of every
switching regulator is the filter.
Fig. 240 shows the various types
of filters that can be used. Selection of the optimum filter for a
power supply is based on the load
requirements of the particular circuit and consideration of the basic
disadvantages of the various types
of filters.
A capacitive filter, shown in Fig.
240(a), has two primary disadvantages: (1) because large peak
currents exist, R must be made
large enough to limit peak transistor current to a safe value; and
(2) the resistance in this circuit
introduces loss.
An inductive filter, shown in
Fig. 240(b) has three disadvantages: (1) The inductance may
produce a destructive voltage
spike when the transistor turns

off. This
be solved
tion of a
shown in

(a)

problem, however, can
effectively by the addicommutating diode, as
Fig. 241. This diode

~
I

(b)

0.....------.,0

(e)

~
I

Figure 240. Typical filter circuits for use
between pass element and load in a switching regulator: (a) capacitive filter; (b! inductive filter; (c) inductive-capacitive filter.

RCA Silicon Power Circuits Manual

222

commutates the· current flowing
through the inductor IL when the
transistor switches OFF. (2) An
abrupt change in the load resistance RL produces an abrupt
change in output voltage because
the current through the load IL
cannot change instantaneously.

Figure 241. Use of inductance and commutating diode as filter network between
pass transistor and load in switching
voltage regulator.

(3) A third disadvantage of the
inductive filter becomes evident
during light loads. The energy
stored in an inductor is given by

=! LF

(284)

As a result, the capability of the
inductor to store energy varies
with the square of the load current. Under light load conditions,
the inductor must be much larger
to provide a relatively constant
current flow when the transistor
is OFF than is required for a
heavy load.
Most of the problems associated
with either a capacitive filter or
an inductive filter can be solved
by use of a combination of the
two as shown in Fig. 240(c). Because the energy stored in an inductor varies directly as current
squared, whereas the energy output at constant voltage varies directly with current, it is not usually practical to design the inductor for continuous current at
low current outputs. The addition
of a capacitor eliminates the need

for a continuous flow of current
through the inductor. With the
addition of a commutating diode,
this filter has the following advantages.
(1) No "lossy" elements are required.
(2) The inductive element need
not be oversized for light
loads because the capacitance maintains the proper
output voltage V out if the
inductive current becomes
discontinuous.
(3) High peak currents through
the transistor are eliminated by the use of the inductive element.
In summary, the switching-regulator filter can take on various
forms depending upon the load requirements. However, if a wide
range of voltage and current is required, an LC filter is used in
combination with a commutating
diode.
A practical rule of thumb is to
design the inductor to be large
enough to dominate the performance during maximum-load conditions. The filter capacitor is chosen
to be large enough to dominate
performance at mid-range current
values and the full range of output voltages.
A primary advantage of the
transistor switching regulator is
that the switching freauency can.
be made considerably higher than
the line frequency. As a result,
the filter can be made relatively
small and light in weight.
The means by which the switching regulator removes the linefrequency ripple component is illustrated in Fig. 242. The ON
time increases under the valley
points of the unregulated supply
and decreases under the peaks.
The net result is to remove the
60-Hz component of ripple and

Power Regulation

introduce only ripple at the switching frequency which is relatively
high frequency and easily filtered
out.

I
ON

OFF

Figure 242. Effect of high-frequency switching of the switching regulator on powersupply ripple component.

Transistor Parameters

The transistor parameters affecting the performance of a
switehing regulator are the current gain hFE' the collector-toemitter saturation voltage, V("E ('lIt),
the leakage current I("EH' forwardbias second-breakdown voltage,
and switching times. The forwardcurrent transfer ratio hFE determines the amount of drive current
needed. The collector-to-emitter
saturation voltage Vn;(slIt) is important because it determines part
of the power loss in the circuit
and the dissipation of the transistor during the ON period. The
amount of leakage current is impOl'tant because the transistor essentially conducts this amount of
current during the OFF period
and thus increases dissipation. If
this leakage current is large
enough, the transistor can enter
into a condition of thermal runaway. Silicon transistors, with
their inherently lower leakagecurrent value, do not often exhibit this problem. Collectorbreakdown voltage should be
higher than the supply voltages
encountered or the maximum voltage that is to be switched by the
transistor if several units are connected in series.

223
The transistor safe-area rating
determines the maximum power
that can be handled by the transistor and by the supply. This
parameter and its implications
are explained in detail in the section on Safe-Area Ratings. It
should be noted, however, that
the peak power dissipated by the
transistor is also a function of
the switching time of the commutating diode. This fact can be
demonstrated by examination of
the circuit operation. It is assumed that the transistor is OFF
and the commutating diode is
conducting. When the transistor
turns ON, the diode requires
some finite time to turn OFF;
therefore, a power pulfle is generated during this interval. When
the transistor turns OFF, the inductive load maintains current
through the transistor or load
while the collector-to-emitter voltage V(']-; rises to the value of the
input voltage ViII' This condition
alone results in a power pulse
which is increased by the additional pulse created because the
diode does not conduct immediately when the voltage across it
reverses. As a result, both turnon and turn-off transients should
be investigated carefully when the
peak power requirement of the
transistor is determined.
Switching time is also a factor
in determination of the maximum
power that the transistor is
capable of dissipating. When the
transistor turns ON, the current
flows into the load and into the
output capacitor through the inductor. Energy is stored in the'
inductor and the capacitor so
that when the switch is open (i.e.,
the transistor is cut off) this energy is available to supply the
load. During the ON time, the
current through the indu.ctor is

RCA Silicon Power Circuits Manual

224

a linear ramp. The rate of increase of current dI/dt is determined by L and the voltage across
it (Vin - V out ), as follows:
dIjdt

(IlL) (Vin - Vout)

(285)

The peak current is, therefore,
given by

the base of Q~ cannot be tied to
a point more- positive than the
plus voltage of the power supply.
The circuit of Fig. 243 (a) can
avoid this problem if the collector of the driver unit is connected
to the positive side of the supply.
The disadvantage is that current
in the driver does not flow
through the load; the power associated with this current, therefore, is lost.

(286)

The switching times, tr (rise
time) and t f (fall time), are of
prime consideration in selection
of a transistor to be used as the
switch. For good regulation over
a wide range of input voltage and
output current, the duty cycle
must be variable from at least
10 to 90 per cent (Le., the pulse
width could be a minimum of
one-tenth of the period 1/10f).
For low switching losses, the rise
and fall times should each be less
than 10 per cent of the minimum
pulse width. These requirements
are summarized as follows:
tr :::; I/IOOf; tr :::; l/100f

lo}

(287)

where f is the frequency of the
pulse generator.
Switching Arrangement-The
transistor switching arrangement
usually takes on one of two forms
as illustrated in Fig. 243. If isolated supplies appear in the drive
circuits of Q 1 and Q2' performance
of the two circuits is basically the
same. However, if no isolated
supplies are used, then the circuit
of Fig. 243 (b) has the disadvantage that the V CE of Q 2 cannot be reduced below the VBE of
Q2. This condition results because

Figure 243. Basic transistor switching arrangements: (a) filter elements and load
impedance in collector circuit of switching
transistor; (b) filter elements and load impedance in emitter circuit of switching
transistor.

The circuit of Fig. 243 (b) is
usually preferred when the power
that results from a high VCE (sat)
can be tolerated.
Step-Down Switching Regulator

A transistor switching regulator can be used as a de stepdown transformer. This circuit is

225

Power Regulation

a very efficient means of obtaining a low dc voltage directly from
a high-voltage ac line without the
need for a step-down transformer.
Fig. 244 shows a typical stepdown transistor switching regu-

lator. This regulator utilizes the
dc voltage obtained from a rectified 117-volt line to provide a
constant 60-volt supply. Fig. 245
shows the performance characteristics for this circuit.

12VI/\

2V~
o 100200

,.5

10K

lOOK

60 V

O-IA

Figure 244.

Typical step-down transistor switching regulator.

RL=62,{l

------------..,

I
I
I
I

0.5

1,0

100

125

150

lOUT-A
Figure 245. -Performance characteristics of step-down switching regulator shown in
Fig. 244.

226

Thyristor AC Line-Voltage
Controls
use of thyristors is becomT HE
ing increasingly important
for power-control applications
ranging from low voltages to
more than 1000 volts at current
levels from less than half an ampere to more than 1000 amperes.
When power control involves conversion of ac voltages and/or
currents to dc and control of
their magnitude, SCR's are used
because of their inherent rectifying properties. SCR's are also
used in dc switching applications, such as pulse modulators
and inverters, because the currents in the switching device
are unidirectional. In addition,
SCR's are generally used whenever the desired function can be
accomplished adequately by this
type of device because of the
economics involved.
A triac provides symmetrical
bidirectional electrical characteristics. Triacs have been developed specifically for control
of ac power, and are used primarily for control of power to
a load from ac power lines.

initially assume a blocking, or
high-impedance state, and remain
in that statEl until triggered to
the ON or low-impedance state.
Once triggered, the thyristor remains ON until the supply voltage is reduced to zero for a short
time or reversed for an even
shorter time. Either operation returns the thyristor to its blocking state. Because both of these
operations are accomplished during every half-cycle in an ac supply, turn-off is guaranteed every
half-cycle. All that is necessary
for ac power control, therefore,
is a trigger circuit to control
thyristor turn-on so that whole
or partial cycles may be switched
to the load. When only complete
half-cycles or integral numbers
of half-cycles are desired for a
given load while control over the
average power is maintained, the
control is usually referred to as
an integral-cycle or zero-switching control. This type of control
is illustrated in Fig. 246.

Thyristor Phase Control
GENERAL CONSIDERATIONS
Thyristors are excellent devices for use in the control of
ac power. In general, thyristors

In most power-control applications of thyristors, partial ~ycles
of the applied ac voltage are
switched to the load. Because the

227

Thyristor AC Line-Voltage Controls

Figure 246.

Integral-cycle thyristor power control circuits.

power delivered to the load is
controlled by variation of the
phase angle at which the thyristor switching initiates current
flow, this type of operation is
usually referred to as phase control. The electrical angle of the
applied ac voltage waveform at
which thyristor current is initiated is termed the firing angle
(OF)' It is usually more important, however, to know and
to refer to the conduction angle
(Oe), which is the number of
electrical degrees of the applied
ac voltage waveform during
which the thyristor is in conduction. The conduction angle is
equal to 180' - OF for a halfwave circuit and 2 (180' - OF)
for a full-wave circuit. The voltage waveforms across the thyristor and the load for each type
of circuit are illustrated in Fig.
247.
Phase control of thyristor-and~
diode combinations may be employed to provide many different
ac and dc output waveforms to
a load circuit. Some basic combinations, together with the corresponding voltage waveforms at
the load for two complete cycles
of operation, are shown in Fig.
248. In general, triac circuits are
more economical for full-wave
power control than are circuits
that use two SCR's. For partial

range control when the load is
not sensitive to a nonsymmetrical waveform, such as resistive
loads, a control circuit that uses
a diode and an SCR is acceptable.
VOLTAGE ACROSS SCR

8~
~
Fi 8c V8~
8c V
I

JLl\

VOLTAGE ACROSS SCR LOAD

VOLTAGE ACROSS TRIAC

'" 8c
~
I! I I ::
:

8F'
8c ,I
I I

!:
I

9F.I

,I
I

I I

I
: :,
I I

:I
I

VOLTAGE "ACROSS TRIAC LOAD

Figure 247. Voltage waveforms showing
conduction angle for half-wave operation
(SeR) and full-wave operation (triac) of
thyristor phase-control circuits.

Current Relationships in
Phase-Controlled
Thyristor Circuits
In the design of thyristor
power-control circuits of. the
types shown in Fig. 248, it is

228

RCA Silicon Power Circuits Manual

CIRCUIT CONFIGURATION
VOLTAGE
ACROSS LOAD

(AI

(BI

(CI

(01

Figure 248.

Basic circuit configurations for thyristor power controls and voltage waveform across the load for two complete cycles of operation.

229

Thyristor AC Line-Voltage Controls

often necessary to determine the
specific values of peak, average,
and rms current that flow
through the thyristors. For conventional rectifiers, these values
are readily determined by use
of the current ratios shown in
Table I, given in the section on
Silicon Rectifiers. For thyristors,
however, the calculations are
more difficult because the current
ratios become functions of the
conduction angle and the firing
angle of the device.
The curves in Figs. 249, 250,
and 251 show several current
ratios as functions of conduction
or firing angles for three basic
SCR circuits. These curves can
be used in a number of ways to
calculate desired current values.
For example, they can be used to
determine the peak or rms current in an SCR when a certain
average current is to be delivered
to a load during a specific part of
the conduction period. It is also
possible to work backwards and
determine the necessary period
of conduction if, for example, a
specified peak-to-average current

ratio must be maintained in a
particular application. Another
use of the curves in Figs. 249,
250, and 251 is in the calculation
of the rms current at various
conduction angles when it is necessary to determine the power delivered to a load, or power losses
in transformers, motors, leads, or
bus bars. Although the curves are
presented in terms of device current, they are equally useful for
the calculation of load current
and voltage ratios.
The curves provide ratios that
relate average current I ayg , rms
current I rm ., peak current Ipb and
reference current 10 , The reference current is a circuit constant
0,9.-------,---...,---,-----.-------,---::.""

o.
0.7

0.6't----j---+

fi 0.5

!z 0.4l----+.~._+~_1_L...+----+-----j
bJ

~ 0.3

Figure 262. Typical gate-current waveform
for circuit shown in Fig. 258.

triggering devices.) The delay in
reaching the peak gate current is
a function of the speed at which
the triggering device is switched
from its high-impedance to its
low-impedance state. This delay
in effect indicates that there is a
dynamic or time-dependent characteristic of the trigger device,
which traces out a shape somewhat different from the static
characteristic shown in Fig. 261.
The magnitude and duration of
the gate pulse produced by the
triggering device and the capacitor must be adequate to fire the
thyristor. A curve of turn-on
time as a function of gate-pulse
magnitude, provided in the published data on the thyristor, defines the minimum requirements.
Because the thyristor is triggered to the ON state by the gate
pulse, and the voltage source for
the triggering circuit is taken
from across the thyristor, the
triggering circuit cannot go
through another charge-discharge
cycle after the first firing pulse.
The capacitor discharges from
point C through the potentiometer
and the thyristor for the remainder of the ac line-voltage cycle,
and the triggering process repeats
on the next ac line-voltage halfcycle.

237

Thyristor AC Line-Voltage Controls

The maximum voltage applied
to the load is limited by the
breakover voltage of the trigger
diode because the line voltage
must rise to that value before the
thyristor gate can be energized.
This condition is illustrated by
the voltage waveforms shown in
Fig. 260(b).
Several types of devices commonly used to trigger RCA thyristors are discussed in the following paragraphs:
Neon Bulbs-Neon bulbs can
be used as triggering devices for
RCA thyristors. The recommended
types are the GE-5AH and Signalite A057 or equivalents. The
breakover voltages for these devices range from 50 volts to 100
volts, with typical values of 80
volts. Tighter breakover voltage
spreads can be obtained by manufacturer's selections. A typical
current pulse resulting from a 0.1microfarad capacitor discharging
through a neon bulb and a thyristor gate is illustrated in Fig. 263.

120-volt-rms ac line, an rm& voltage loss as great as 10 per cent
can occur at the load. The losses
are caused by the relatively high
breakdown voltage of the neon
bulb. The neon bulb is also sensitive to radiation in that the breakdown point changes. When precise
control is required, it may be
necessary to shield the bulb or
to obtain bulbs specially treated
to minimize the effects of radiation. A major advantage of neon
triggers is that reliable and relatively long-lived triggers can be
obtained for a low price.
LOAD
10K

IV 120V
60Hz

O.OIIL F
IOOV
(0)

LOAD

1"~.
I

i::i

I-

It:

~ 20
(.)

' " 120V
60Hz

TIME -pS

Figure 263. Typical current pulse that results from the discharge of a O.l-microfarad
capacitor through a neon bulb and a thyristor gate.

Fig. 264 illustrates the use of
a neon bulb as a triggering device. The bilateral characteristic
of the neon bulb allows it to trigger both SCR's and triacs.
Use of a neon bulb as a trigger
device does have disadvantages.
For example, when this type of
device is used as a trigger on a

(Ill
Figure 264. Circuits showing application of
neon bulb as thyristor triggering device:
(a) SCR power control circuit; (b) triac
power control circuit.

Trigger Diodes-A trigger
diode is the solid-state replacement for a neon bulb in phasecontrol triggering circuits. These
diodes offer the advantages of
reduced requirements for peak-

RCA Silicon Power Circuits Manual

238

voltage firing, higher pulse-current capability, and longer life.
The solid-state- diodes have
breakdown voltages in the range
of 27 to 37 volts and are designed
specifically for triggering bidirectional thyristors (triacs).
The trigger diodes, often referred to as silicon bidirectional
diacs, are three-layer symmetrical avalanche devices which
break over in the negativeresistance region whenever a
particular voltage, termed the
breakover voltage, is exceeded in
either voltage polarity. In these
devices, a maximum limit of 3
volts is usually imposed on the
symmetry between positive and
negative
breakover
voltages
(voltage symmetry). A typical
voltage-current characteristic of
a bidirectional trigger diac is
shown in Fig. 265.

v- Vieor
AV-

impedance. The interaction of
all circuit impedances and the
phase-shift capacitance can best
be represented by the curve of
peak current as a function of
the capacitance shown in Fig.
266.

< 0.8

.....
~

0_6

It:
It:

u 0.4

III
Q.

0.2

i/
1/

0.02 0.04 0.06 0.08
CAPACITANCE-fLF

0.1

- .. -- ..

I(BO)+ ---------- I(BO)"

-_._. --.----- I

Figure 266. Peak pulse trigger currents as
a function of the phase-shift capacitance.

Figure 265. Typical voltage·current characteristic of a bidirectional trigger diac.

The slight current offset in
the characteristic before the
voltage breakover point is leakage current lBo, which is usually
in the order of 50 microamperes.
The magnitude and duration of
the gate current pulse are determined by the value of the
phase-shift
capacitance,
the
change in voltage across and the
dynamic impedance of the trigger diac, and the thyristor gate

Unijunction Transistor-The
unijunction transistor is a threeterminal two-layer device formed
by an emitter and a base, as illustrated in Fig. 267. One lead is
connected to the emitter and the
other two leads are connected to
the base. Between the two base

EMITTER~SE

~SEI
Figure 267. Schematic symbol for a
unijunction transistor.

Thyristor AC Line-Voltage Controls
connections there is an "interbase
resistance." Fig. 268 illustrates
the use of this device in a pulsetriggering circuit.

At
SUPPLY

Figure

268. Pulse-triggering circuit
uses a unijunction transistor.

that

Proper choice of external biasing resistors, coupled with the
inter base resistance, normally
serves to reverse-bias the "emitter-to-base-l" diode. This condition holds the emitter-to-base-l
diode in a high-impedance state
until the emitter voltage is raised
to a value high enough to forwardbias this junction. As the forwardbias point is reached, the same
junction switches to a low-impedance state and causes capacitor.
C 1 to discharge into the load resistance R", which may be a thyristor gate. This voltage-sensitive
switching characteristic makes
unijunction transistors ideal for
triggering thyristors. When the
biasing resistors and the emitter
are connected to the same voltage
source, as shown in Fig. 268,
there is a degree of self-regulation of supply-voltage variation.
This regulation results because
the interbase forward-bias point
tracks the variation in emitter
voltage VI' as V" varies with supply voltage. Another advantage of
the use of the unijunction transistor is the way in which it automatically synchronizes to an ac

239

supply. At the end of every cycle,
any charge left on the capacitor
after firing is discharged when
the supply goes to zero. This action occurs because the point or
firing voltage is also reduced
toward zero. A third advantage is
the inherent ability of the device
to switch relatively high currents
and thus to assure positive triggering of high-gate-current thyristors.
The disadvantage of the unijunction device is that it is unilateral with regard to current
flow and requires a dc voltage.
These requirements indicate that
diodes must be used to ensure
that no reverse voltage appears
across the device when it is used
in an ac circuit. The output pulses
are positive-going and can be used
to trigger SCR's directly. For
triacs or inverse parallel SCR's,
transformer or capacitive coupling
is required, as shown in Fig. 269.
Two-Transistor Trigger Circuit-A two-transistor trigger
circuit that has characteristics
similar to those of a trigger diode
is shown in Fig. 270. The regeneI'ative action of this type of circuit when either transistor begins
to conduct causes switching comparable to avalanching in a trigger diode. Proper biasing of this
circuit yields triggering voltages
of 15 volts 01' less. The circuit
shown in Fig. 271 can deliver
trigger currents as high as 1 ampere and is more than capable of
triggering all RCA thyristors.
Fig. 272 shows an SCR circuit
that uses the two-transistor regenerative-trigger network. The
phase-shift characteristics are
still retained to provide conduction angles less than 90 degrees
through the RC network of R 1 ,
R~. and C1 • Resistor R;! provides

RCA Silicon Power Circuits Manual

240

(b)

(a)

Figure 269. Circuit showing application of unijunction-transistor circuit for pulse triggering of triacs and inverse parallel SCR's: (a) triggering pulse is capacitively coupled
to gate of triac; (b) triggering pulse is transformer-coupled to gate of SCR.

turn-on current to the base of
Q1 when the voltage across C1
becomes large enough during the
positive half-cycle. The base current in Q 1 turns on this transistor. Transistor Q1 then supplies
base current to Q2' When Q 2
turns on, it supplies more base
current to Ql' This regenerative
action leads to the rapid saturation of transistors Q 1 and Q2' Capacitor C1 discharges through the
saturated transistors into the gate
of the SCR. When the SCR fires,
the remaining portion of the posi.TYPE
2N3241

TYPE
2N406

+IN
5.6K

470

Figure 270. Two-transistor switch. Characteristics of this circuit are similar to those
of a trigger diode.

tive half-cycle of ac power is applied to the motor. Speed control
is accomplished by adjustment of

Figure 271. Circuit showing application of
two-transistor switch as thyristor triggering
device.

potentiometer R l • For the component values shown on the schematic diagram in Fig. 272, the
threshold voltage for firing the
circuit is approximately 8 volts,
and the maximum conduction
angle is approximately 170 degrees. Table XVII shows values
for operation of the circuit with
various RCA SCR's.

Thyristor AC Line-Voltage Controls
An advantage of the two-transistor trigger circuit is its low
threshold triggering voltage. For
all practical purposes, a full 180degree conduction angle can be
obtained when an SCR is used.

241

When two SCR's are to be triggered, a transformer must be
used to couple a gate signal of
the proper polarity to the SCR
with the proper anode-to-cathode
polarity. A triac, however, can be

SCR I

TYPE
2N324lA

SUPPLY

+ cl
luF

- i5v

Figure 272.

Half-wave SCR motor control circuit, without regulation.

Table XVII-Components For Circuit Shown in Fig. 272
AC

F,
SUPPLY CURRENT
120V
lA
3AG, l.5A, Quick Act
120V
3A
3AB, 3A
120V
7A
3AB, 7A
120V 25A
3AB, 25A
240V
lA
3AG, 1.5A, Quick Act
240V
3A
3AB, 3A
240V
7A
3AB, 7A
240V
25A
3AB, 25A

CR,
RCA-IN3755
RCA-IN3755
RCA-IN3755
RCA-IN3755
RCA-IN3756
RCA-IN3756
RCA-IN3756
RCA-IN3756

SCR,

R,
75K,
75K,
75K,
75K,
150K,
150K,
150K,
150K,

lhW
lhW
1f2W
1f2W
lhW
lhW
1f2W
lhW

RCA-2N3528
RCA-2N3228
RCA-2N3669
RCA-2N3897
RCA-2N3529
RCA-2N3525
RCA-2N3670
RCA-2N3898

242

RCA Silicon Power Circuits Manual

triggered in either direction with
positive-polarity gate signals. The
only requirement is that isolation
be maintained between the dc and
ac current. Application of the use
of the two-transistor switch to
trigger thyristor control circuits

is discussed further in the section
on Heater Controls.
Application Guide for Triggering Devices-Table XVIII provides a quick reference to the
prevalent types of applications for
various triggering devices.

Table XVIII-Firing-Circuit Families.
LOW COST
Manual or Simple OnOff Power Control

MEDIUM COST
Automatically Controlled or Regulated
power

HIGH COST
Power-Output Stage in
large Electronic or
EI ectro-Mecha nical
System

Typical
Applications

Light Dimmers
Tool Speed Controls
Appliance Speed
Controls
Gas Ignition
Photoelectric Controls
Static On-Off Switches

Regulated Power
Supplies
Temperature Controls
Commercial DC Motor
Drives
Flashers
Time Delays

Bulk Power Conversion for
Metal Refining and Electrochemical Processes
large Industrial Motor
Drives
Variable-Frequency Drives
Pulse Mod'ulators
Precise ProcessTemperature Controls
Logic-Arrays Power Output
eg.-Vending Machines
-Signs and
Scoreboards
-Computer Printer
Driver

Common
Characteristics
of the
Application

Frequently
Bidirectional
Small physical size an
asset
Low performance
demands

Frugal but not poor
Both dc and ac loads
Thyristor fired is
higher cost
Technically oriented
customers and
appl ications
Electrical feedback or
sensor input in addition to manual control
Long firing pulses often
required

Firing circuit small percentage of system cost
Rigid and extensive performance requirements
Firing circuit often merged
into other system circuits
Custom engineered
Primarily electrical inputs
from regulators or
sensors

1. Unijunction

1. Transistors

Function

Trigger Devices
in Approximate
Order of
Preference
or Use

1. Neon bulb

2.
3.
4.
5.

Three-layer diode
Five-layer diode
Four-layer diode
Unijunction
transistor
6. Two-transistor regenerative circuit
NOTE: For on-off control, a switch contact
or single transistor
may form the firing
circuit

transistor
2. Transistors
3. Magnetic ampl ifier
NOTE: Firing circuit
often includes several diodes, a zener,
pulse transformers,
control power transformers, and numerous passive components

Often built up from
standard logic and
waveshaping circuits

243

Thyristor AC Line-Voltage Controls
MOTOR CONTROLS
Silicon controlled rectifiers have
been widely accepted in powercontrol applications in industrial
systems where high-performance
requirements justify the economics of the application. The controls can be designed to provide
good performance, maximum efficiency, and high reliability in
compact
packaging
arrangements.

Speed Controls for
Universal Motors
Many fractional-horsepower motors are series-wound "universal"
motors, so named because of their
ability to operate directly from
either ac or dc power sources.
Fig. 273 is a schematic of this
type of motor operated from an
ac supply. In reality, the universal
motor is a special form of series

FIELD
WINDING
AC
'V SUPPLY

EXTERNAL
CONTROL
CIRCUIT

Figure 273. Schematic diagram for
series-wound universal motor.

The field winding of a universal
motor is in series with the armature and external circuit, as
shown in Fig. 273. The current through the field winding
produces a magnetic field which
cuts across the armature conductors. The action of this field on
the conductor of armature current
subjects the individual conductors
to a lateral thrust which results
in armature rotation.
The torque developed by a universal motor is a direct result of
the magnitude of magnetjc-field
flux and armature current. The
starting torque of a universal
motor is high because the armature current at starting time is
high. Similarly, at "stall" conditions, the armature current is
high and results in a large
torque. The stall torque of a
series motor can be as high as 10
times the continuous rated torque.
High starting torque, adjustable speed characteristics, and
small size are distinct advantages of a universal motor over
a comparably rated single-phase
induction motor. The speed can
be adjusted by variation of the
impressed voltage across the
motor. Typical performance characteristic curves for a universal
motor are shown in Fig. 274.

motor that has a laminated armature and field structure. Because
most domestic applications today
require 60-Hz power, universal
motors are usually designed to
have optimum performance characteristics at this frequency. Most
universal motors run faster at a
given dc voltage than at the same
60-Hz ac voltage for which they
are designed.

Figure

274. Typical performance
for a universal motor.

curves

244

RCA Silicon Power Circuits Manual

One of the simplest and most
efficient means of varying the impressed voltage and thus the
speed of a universal motor is by
control of the conduction angle
of a thyristor (SCR or triac)
placed in series with the load.
Typical curves of the variation
of motor speed with thyristor
conduction angle for both halfwave and full-wave impressed
motor voltages are shown in Fig.
275.

100

.....-

sation of the system to prevent
changes in motor speed. The
half-wave proportional controls
shown in Figs. 264(a) and 272
(described previously) are examples of nonregulating circuits
that may be used for motor speed
control.
Fig. 276 shows a fundamental
circuit of a direct-coupled SCR
control with voltage feedback that
is highly effective for speed control of universal motors. This

~¥

S' '<

/J~
20

II
'f/

120

150

180

CONDUCTION ANGLE - DEGREES

SUPPLY

VOLTAGE
Figure 275. Typical performance curves
for a universal motor with phase-angle
control.

Half-Wave Control-There are
many circuits available for halfwave control of universal motors; their attributes and limitations are described in detail below.
Such circuits may be selected
in preference to full-wave circuits for economy reasons. Motor
operation with half-wave control circuits, however, in general
is not as good as that obtained
with full-wave control circuits.
Half-wave \power-control circ ui ts
are divided into two classes:
regulating and non-regulating.
Regulation in this instance implies load sensing and compen-

MOTOR VOLTAGE

Figure 276. Half-wave SCR motor control
circuit, with regulation.

circuit makes use of the counter
emf induced in the rotating armature because of the residual magnetism in the motor on the halfcycle when the SCR is blocking.
This counter emf is a function

245

Thyristor AC Line-Voltage Controls
of speed and, therefore, can be
used as an indication of speed
changes for mechanical-load variations. The gate-firing circuit is a
resistance network consisting of
R J and R;l. During the positive
half-cycle of the source voltage, a
fraction of the voltage is developed at the center-tap of the potentiometer and compared with
the counter emf developed in the
rotating armature of the motor.
When the bias developed at the
gate of the SCR from the potentiometer exceeds the counter emf
of the motor,· the SCR fires. AC
power is then applied to the motor
for the remaining portion of the
positive half-cycle. Speed control
is accomplished by adjustment of
potentiometer R 1 • If the SCR is
fired early in the cycle, the motor
operates at high speed because
essentially the full-rated line voltage is applied to the motor. If the
SCR is fired later in the cycle, the
average value of voltage applied
to the motor is reduced, and a
corresponding reduction in motor
speed occurs. On the negative halfcycle, the SCR blocks voltage to
the motor. The voltage applied to
the gate of the SCR is a sine wave
because it is derived from the
sine-wave line voltage. The minimum conduction angle occurs at
the peak of the sine wave and is
restricted to 90 degrees. Increas-

ing conduction angles occur when
the gate bias to the SCR is increased to allow firing at voltage
values for which the phase delay
with respect to the line voltage is
less.
At no load and at the low-speed
control setting, "skip-cycling" op·
eration may occur, and motor
speed may be erratic. Because no
counter emf is induced in the
armature when the motor is
standing still, the SCR fires at
low bias settings. The motor is
then accelerated to a point at
which counter emf induced in
the rotating armature exceeds
the gate-firing bias of the SCR
and prevents the SCR from firing. The SCR is not able to fire
again until the speed of the motor
is reduced (because of friction and
winding losses) to a value for
which the induced voltage in the
rotating armature is less than the
gate bias. At this time the SCR
fires again. Because the motor deceleration occurs over a number
of cycles, there is no voltage applied to the motor (hence the
term "skip cycling").
When a load is applied to the
motor, the motor speed decreases
and thus reduces the counter emf
induced in the rotating armature.
With a reduced counter emf, the
SCR fires earlier in the cycle and
provides increased motor torque

Table XIX-Components For Circuit Shown in Fig. 276
AC
AC
F,
SUPPLY CURRENT
120V
lA
3AG, 1.5A, Quick Act
120V
3A
3AB, 3A
120V
7A
3AB, 7A
120V
25A
3AB, 25A
240V
lA
3AG, 1.5A, Quick Act
240V
3A
3AB, 3A
240V
3AB, 7A
7A
240V
25A
3AB, 25A

CR" CR.

SCR,

RCA-IN3755
RCA-IN3755
RCA-IN3755
RCA-IN3755
RCA-IN3756
RCA-IN3756
RCA-IN3756
RCA-IN3756

2.7K, 4W
5.6K,2W
5.6K,2W
2.7K,4W
10K,5W
10K; 5W
5.6K,7.5W
5.6K, 7.5W

IK,2W
lK,2W
500,2W
500, 2W
lK,2W
lK,2W
500,2W
500, 2W

RCA-2N3528
RCA-2N3228
RCA-2N3669
RCA-2N3897
RCA-2N3529
RCA-2N3525
RCA-2N3670
RCA-2N3898

246

RCA Silicon Power Circuits Manual

to the load. Fig. 276 also shows
variations of conduction angle
with changes in counter emf. The
counter emf appears as a constant
voltage at the motor terminals
when the SCR is blocking. Because the counter emf is essen-

tially a characteristic of the motor,
different potentiometer settings
are required for comparable operating conditions for different motors. Circuit values for use with
the various RCA SCR's are shown
in Table XIX.

'I'F

25V

MOTOR
VOLTAGE

MOTOR

~VOL_,
C,

\,'

VOLTAGE

....... '

GATE CURRENT
LIGHT LOAD
Figure 277.

--"----GATE CURRENT
HEAVY LOAD

Half-wave SCR motor control circuit using two-transistor regenerative
triggering, with regulation.

Table XX-Components For Circuit Shown in Fig. 277
AC
AC
F,
SUPPLY CURRENT
3AG, 1.5A, Quick Act
120V
lA
120V
3AB, 3A
3A
120V
3AB, 7A
7A
120V
25A
3AB, 25A
240V
3AG, 1.5A, Quick Act
lA
240V
3AB, 3A
3A
240V
7A
3AB, 7A
240V
25A
3AB, 7A

CH,
RCA-IN3755
RCA-IN3755
RCA-IN3755
RCA-IN3755
RCA-IN3756
RCA-IN3756
RCA-IN3756
RCA-IN3756

H,
75K, lhW
75K, 1/2W
75K, V2W
75K, 112W
150K, V2W
150K, lhW
150K, 112W
150K, 1/2W

SCH,
RCA-2N3528
RCA-2N3228
RCA-2N3669
RCA-2N3897
RCA-2N3529
RCA-2N3525
RCA-2N3670
RCA-2N3998

247

Thyristor AC Line-Voltage Controls
Fig. 277 shows a variation of
the circuit in Fig. 272. The basic
difference between the two circuits
is that the circuit in Fig. 277 provides feedback for changing load
conditions to minimize changes in
motor speed. The feedback is provided by R 7, which is in series
with the motor. A voltage proportional to the peak current through
the motor is developed across the
resistor. This voltage is stored on
capacitor C~ through diode CR~,
and is of a polarity that causes
the bias on the resistance network
of R:; and Rl to change in accordance with the load on the motor.
With an increasing motor load, the
speed tends to decrease. This decrease in motor speed causes more
current to flow through the motor
armature and field. When the current flowing through R7 increases,
the voltage stored on capacitor C~
increases in the positive direction.
This increase in capacitor voltage
causes the transistors to conduct
earlier in the cycle to fire the SCR,
and to provide a greater portion
of the power cycle to the motor.
With a decreasing load, the motor
current decreases and the voltage
stored across capacitor C~ decreases. The transistors and SCR
then conduct later in the cycle,
and the resultant reduction in the
average power supplied to the motor causes a reduced torque to the
smaller load. Because motor current is a function of the motor itself, resistor R7 has to be matched
with the motor rating to provide
optimum feedback for load compensation. Resistor R7 may range
from 0.1 ohm for larger-size universal motors to 1.0 ohm for
smaller types. Circuit values for
use with the various RCA SCR's
are shown in Table XX.

Full-Wave Control-This section discusses the application of
thyristors (SCR's and triacs) to
provide full-wave motor control.
Fig. 278 shows three thyristor
full-wave controls.

(a)

Figure 278. FUll-wave thyristor motor control circuits: (al Use of full-wave bridge
rectifier to enable full-wave motor control
by a single SCR; (bl Use of inverse parallel
SCR's to provide full-wave motor control;
(cl Use of triac to provide full-wave motor
control.

The speed of induction motors
can also be controlled by use of
full-wave thyristor power con-

248

RCA Silicon Power Circuits Manual

trol circuits. For fan motors,
which have a particularly steep
speed-torque curve, simple phasecontrol circuits can be used to
provide suitably stable operating speeds. Other induction motors may require more complex
feedback circuits to provide and
maintain a variable speed. Cooling provisions and bearings must
be suitable for reduced-speed
operation.
Figs. 258, 264, 266, and 278(c)
show full-wave thyristor circuits
suitable for use as motor-speed
controls.

Figure 279. Full-wave SCR motor control
circuit. without regulation.

A very simple SCR full-wave
proportional control is shown in
Fig. 279. Again, ac phase shifting
and neon triggering are used to
provide gate phase-angle control
with a small pulse transformer
utilized for isolation. The load
capabilities of the circuit for
various SCR's are shown in Table
XXI. Conduction angles obtained
with this circuit vary from 30
to 150 degrees; at the maximum
conduction angle, the voltage impressed upon the load (universal
motor) is approximately 95 per
cent of the input rms voltage.
Fig. 280 shows a full-wave control circuit that has increased conduction angle capability. Table
XXII shows the component chart
for use of the circuit with various
SCR's. In this circuit, the conduction angles may be varied from 5
to 170 degrees; this larger range
is more desirable when higher
power is to be controlled.
An SCR full-wave circuit designed for applications requiring
feedback for compensation of load
changes is shown in Fig. 281. Operation is similar to that of the
circuits discussed previously except that this circuit has full-wave
conduction with proportional control. Table XXIII gives a component list for use of this circuit
with various SCR's.

Table XXI-Components For Circuit Shown in Fig. 279
AC
AC
F,
SUPPLY CURRENT
1.5A
120V
3AG. 2A. Quick Act
120V
5A
3AB. 5A
3AB, lOA
120V
lOA
3AB, 25A
120V
25A
3AG, 2A, Quick Act
240V
1.5A
240V
5A
3AB. 5A
240V
lOA
3AB, lOA
240V
25A
3AB. 25A

R,
IK.lhW
IK. V2W
IK, V2W
IK, IW
IK,IW
IK,IW
IK.IW
IK. lW

R2
50K.lhW
50K, V2W
25K,2W
25K, 2W
50K,2W
50K.2W
25K,4W
25K •. 4W

C,
0.22 flF. 100V
0.22 flF, 100V
0.47 flF, 100V
0.47/LF. 100V
022 flF, 100V
0.22 flF, 100V
0.47 flF, 100V
0.47 flF. 100V

SCR I • SCR 2
RCA-2N3528
RCA·2N3228
RCA·2N3669
RCA-2N3897
RCA-2N3529
RAC-2N3525
RCA-2N3670
RCA-2N3998

249

Thyristor AC line-Voltage Controls

R3
5.6K
1I2W

TYPE

IN3754

TYPE

IN3754

TYPE

IN3754

SUPPLY
VOLTAGE

, ...
MOTOR
VOLTAGE

TRIGGER
PULSES

Figure 280.

FUll-wave SCR motor control circuit, without regulation, in which the
conduction angle can be varied from 5 to 170 degrees.

Table XXII-Components For Circuit Shown in Fig. 280

AC
SUPPLY

AC
CURRENT

120V
120V
120V
120V
240V
240V
240V
240V

1.5A
5A
lOA
25A
1.5A
5A
lOA
25A

F,
3AG,
3AB,
3AB,
3AB,
3AG,
3AB,
3AB,
3AB,

2A, Quick Act
5A
IDA
25A
2A, Quick Act
5A
IDA
25A

R.
75K,
75K,
75K,
75K,
150K,
150K,
150K,
150K,

lhW

V2W
V2W

lhW

V2W

1/2W

V2W

lhW

SCR" SCR.

RCA-2N3528
RCA-2N3228
RCA-2N3669
RCA-2N3897
RCA-2N3529
RCA-2N3525
RCA-2N3670
RCA-2N3898

250

RCA Silicon Power Circuits Manual

CR Z

SUPPLY
,VOLTAGE

SUPPLY

)~OLTAGE

MOTOR

C~
VOLTAGE
',/
_ _A

"' .....

--"

GATE CURRENT
LIGHT LOAD

Figure 281.

A"----_

GATE CURRENT
HEAVY LOAD

FUll-wave SCR motor control circuit, with regulation.

Table XXIII-Components For Circuit Shown in Fig. 281
AC
AC
SUPPLY CURRENT
l20V
l20V
l20V
240V
240V
240V

lA
3A
7A
lA
3A
7A

F,
3AG,
3AB,
3AB,
3AG,
3AB,
3AB,

1.5A, Quick Act
3A
7A
1.5A, Quick Act
3A
7A

CR" CR.,
CR., CR,
RCA-lN2860
RCA-40110
RCA-40110
RCA-IN2862
RCA-40l12
RCA-40ll2

Induction-Motor
Reversing Controls
Triacs are finding increasing
application in motor-reversing
circuits. Motor-reversing systems that use electromechanical
relays suffer from contact arcing,
which results in short life and
costly maintenance. Fig. 282

R,
50K,
50K,
5DK,
lOOK,
lOOK,
lOOK,

SCR,
1f2W

V2W
V2W

1f2W

V2W
V2W

RCA-2N3528
RCA-2N3228
RCA-2N3669
RCA-2N3529
RCA-2N3525
RCA-2N3670

shows a triac-controlled motorreversing circuit that uses a
split-phase capacitor-run motor.
When triac No.1 is in the OFF
state and triac No.2 is in the
ON state, motor direction is controlled by triac No.2. When triac
No.2 reverts to the OFF state
and triac No. 1 turns on, the direction of motor rotation is re-

Thyristor AC Line-Voltage Controls

120 VAC

60 Hz

Figure 282.

Motor-reversing circuit using
two triacs.

versed. Caution should be exercised in this type of circuit
because, if triac No.1 is turned
on while triac No.2 is on, a loop
current that results from capacitor discharge will occur and may
damage the triacs. A small resistance placed in the capacitorloop current path limits the
magnitude to tolerable levels and
provides reliable operation.
Use of triacs in motor-reversing circuits is illustrated by
electronic garage-door systems
which use the principle of motor-

reversing for garage-door direction control. The system contains
a transmitter, a receiver, and an
operator to provide remote control for door opening and closing. The block diagram in Fig.
283 shows the functions required
for a complete solid-state system.
When the garage door is
closed, the gate drive to the
DOWN triac is disabled as a result of the lower-limit closure,
and the gate drive to the UP
triac is inactive because of the
conduction state of the flip-flop.
A momentary keying of the transmitter causes the receiver to activate the time-delay monostable
multi vibrator, which changes the
state of the flip-flop so that continuous gate drive is provided
to the UP triac. The door continues to travel in the UP direction until the upper-limit closure
switch disables the gate drive to
the UP triac. A second keying of
the transmitter provides the
DOWN triac with gate drive and

UPPER-LIMIT
CLOSURE

Figure 283.

251

Block diagram of solid-state garage-door system.

RCA Silicon Power Circuits Manual

252

causes down travel until the
DOWN triac is disabled by the
lower-limit closure. The time during which the time-delay monostable multi vibrator is active
should override normal transmitter keying to eliminate er-

roneous firing. Fig. 284 shows a
circuit diagram which performs
the required logic for motor direction, and Fig. 285 is a timing
diagram that indicates the time
the time-delay monostable multivibrator must be active in order

120VAC

......

t------_~-

--~~-..__o15V

RECEIVER
POWER
SUPPLY

LOWER
LIMIT
RECEIVER
POWER
SUPPLY

15V

NUVISTOR
INPUT

+-11---'1>---+-1

Figure 284. Garage-door control.

Thyristor AC Line-Voltage Controls

TRANSMITTER SIGNAL
AUDIO PORTION

('~L

TIME DELAY

MOTOR REVERSES AT 1=0

Figure 285.

Timing diagram for reversing
system.

to override transmitter keying.
A significant feature of this
system is that, during door
travel, transmitter keying provides motor directions independent of the upper- and lower-limit
closures. Additional features
such as obstacle obstructions,
manual control, or time-delay
overhead garage lamps can be
incorporated into the system very
economically.
HEATER CONTROLS

Thyristors are easily adapted
to the control of power to electrical heaters. Manual adjustment
of the heater output may be made
over an infinite range by use of
phase-control circuits as described
in the section on General Considerations. Automatic temperature regulation may be incorporated in phase-control systems
through the use of a firing circuit
which adjusts the conduction
angle in response to feedback
from a temperature sensor, such
as a thermistor.
The circuits included in this
section accomplish temperature
regulation in a different manner.

253

Because the heater thermal-response time is generally much
slower than the period of the ac
line frequency, modulation of the
heater output may be accomplished
by switching the thyristor fully
ON for a short period and then
fully OFF for a period. Through
the sensitivity of the firing circuit, the temperature differential
between ON and OFF states may
be made extremely small. Precise
temperature control is then
achieved by rapid and frequent
switching from ON to OFF. An
advantage of this type of control
is the reduction or elimination of
radio-frequency interference generated by the thyristor switching,
which results because the switching always occurs at or near the
zero crossover point on the ac
voltage wave.
The heater control shown in
Fig. 286 may be used in any application in which the power requirements range from 25 watts
to 600 watts maximum and temperature regulation of ±0.2°C is
adequate. For full-wave power
control, the SCR is used in a rectifier bridge. The temperature. at
which the power is interrupted is
determined by the setting of the
500-ohm potentiometer. The potentiometer sets the threshold
level for the Qt-Q~ regenerativeswitch circuit, which is connected
in parallel with the Q:l - Q4· regenerative-switch circuit. The
complete circuit is supplied with
full-wave rectified voltage from
the ac line through the 3000-ohm,
10-watt resistor. The SCR is
turned on by the current through
the Ql-Q~ regenerative-switch
circuit after the threshold is exceeded and QJ and Q~ are in conduction. The threshold level of the
Q:I-Q4 regenerative-switch cir-

RCA Silicon Power Circuits Manual

254
600W
HEATER

TYPE
INI614
CRI

1I0V
AC

.3500.n AT OPERATING
TEMPERATURE

Figure 286.

Half-wave SCR heater control circuit.

cuit is temperature-dependent and
controlled by the thermistor. If
the temperature is less than the
reference temperature, the threshold level of the Q a-Q4 regenerative-switch circuit is higher than
the threshold level of the QI-Q2
circuit, and transistors Q 1 and Q 2
turn on and thus prevent the conduction threshold level required
for the QIl-Q4 circuit from being
reached. The current through the
QI-Q2 circuit into the gate of
the SCR turns on the SCR for the
rest of the half-cycle. If the temperature is higher than the set
reference, the Q:l-Q,I regenerative circuit turns on before the
Ql-Q2 circuit, and firing of the
SCR is prevented.
Fig. 287 shows a heater-control
circuit that features zero-volt
switching and full-wave thyristor
control for loads up to 850 watts.
The control circuit is the "anticipation" type that uses two

thermistors as temperature sensors. For convenience, it is assumed that the resistance of the
thermistor TH2 is constant. As
the voltage of the negative halfcycle (applied through a diode
CR 4 and a 5600-ohm 2-watt resistor) increases to a certain magnitude (V th2 ), it turns on transistors Q 1 and Q 2 which form a
regenerative-switch circuit. Another regenerative-switch circuit
composed of transistors Q4 and Q 5
is in parallel with the QI-Q2
regenerative-switch circuit. The
threshold level of the Q4 - Q5 circuit, V tlt2 , is a function of the resistance of thermistor TH l , which
senses the temperature to be regulated. If the temperature on thermistor THl increases, the resistance of the thermistor decreases
and the threshold level V tlt1 becomes higher. If the threshold
level V tlt1 is higher than the threshold level V tlt!!, the regenerative-

255

Thyristor AC Line-Voltage Controls

circuit transistors Q 1 and Q:! turn
on before the Q4-Q" regenerative circuit. The current through
diode CR 3 and the 4700-ohm, 2watt resistor during the negative
cycle charges the 20-microfarad
capacitor. During the positive
cycle, or slightly earlier, the 10microfarad capacitor starts to discharge through the 470-ohm resistor and the gate of the SCR2
thyristor. The discharge current
into the gate of SCR:! triggers the
device. As SCR., turns on, it closes
the circuit for -the 30-microfarad
capacitor connected to the anode
of SCR.,. The current through the
4700-oh-m, 2-watt resistor and diode CR j charges the capacitor.
The capacitor starts to discharge
through the 270-ohm resistor and
the gate of SCR 1 prior to the negative half-cycle. SCR 1 turns on for
the negative half-cycle to complete

a full cycle of operation.
If the regenerative circuit composed of transistors Ql and Q:!
turns on and a portion of the emitter current of Q" flows into the
base of transistoi· Q:l, transistor
Q:l also turns on. As transistor Q 3
turns on, it prevents the 20microfarad capacitor from being
charged; thus, SCR" is not fired
for the positive half-cycle. The
resistance of thermistor TH2
(mounted in proximity to the
heater element) is not constant
(as had been assumed previously) .
The threshold level V tIlZ , which
serves as the reference level to
which the V ill1 threshold level is
compared, is a function of the resistance of thermistor THry. As the
temperature increases on thermistor TH z, the threshold level V th2
decreases. When V th2 becomes
smaller than V t1l1 , the power from

5.6 K

110 V

TYPE
IN3193

4.7 K
2W
1.2KW

HEATER

TYPE
IN3193

CRI
TYPE
IN3193

270

15 V

TYPE
IN3193

5000.0. AT OPERATING
TEMPERATURE

Figure 287.

500.0. AT OPERATING
TEMPERATURE

FUll-wave zero-switching SCR heater control circuit.

256

.RCA Silicon Power Circuits Manual

the heater is turned off. This condition occurs somewhat earlier in
time than if the resistance of thermistor TH2 were constant.
INCANDESCENT
LIGHTING CONTROLS

A popular application of thyristors is in controls for incandescent lighting systems. Lampdimmer controls make use of the
basic phase-control techniques
described earlier in the section
General Considerations to vary
the effective voltage applied
across the lamp load.
Firing Controls for
Light Dimmers

The basic circuits used in dimmer controls can be grouped into
two categories: single-time-constant and double-time-constant circuits. A single-time-constant circuit is shown in Fig. 288. The
operation of the circuit was described previously in the section
on Triggering Devices.
An interesting aspect of the
operation of this circuit for light
dimming is the minimum level of
illumination that can be achieved

VI= 120V
60 Hz

j
Figure 288.

as the control is adjusted from its
full OFF position. The dimmer
control turns on the incandescent
lamp with an appreciable initial
brilliance for the following reason: The first instantaneous discharge of C1 reduces th~ voltage
across it by some amount IiV. This
voltage reduction is caused by the
instantaneous discharge of C1
through the trigger device and the
gate circuit of the triac. This discharge causes triggering at earlier
phase positions on succeeding halfcycles and, because the capacitor
charges from a lower potential of
opposite polarity, results in a
"quick-turn-on" effect which produces fairly high levels of initial
illumination. Continued rotation
of the potentiometer shaft increases the voltage across the load
until the points of maximum load
voltage and lamp illumination are
reached.
Rotation of the potentiometer
shaft in the opposite direction increases the resistive value of Rl
and causes the phase position of
the tria~ triggering to be increasingly delayed from the line-voltage
crossover point. This delayed triggering reduces the effective load
voltage gradually until a point is

R
F
I

F
I
L
T
E
R

Single-time-constant phase-control circuit for brightness control of
incandescent lamps.

257

Thyristor AC Line-Voltage Controls

reached at which a small increment of additional resistance
causes the triac to stop conducting.
At this point, all voltage is removed from the load and the lamp
is turned off. The value of resistance needed, R To , to turn off the
triac completely is greater than
the value RIC required to the triac
to conduct initially. Therefore,
R'l'o > RIC for a single-time-constant circuit configuration. This
difference in potentiometer settings for turn-on and turn-off is
commonly referred to as "hysteresis." The hysteresis effect can be

VI=120V
~O Hz

R
F
I
F
I
L
T

reduced by use of a double-timeconstant circuit configuration. It
should be noted that hysteresis
and "quick-turn-on" are characteristics of the single-time-constant circuit.
The two basic forms of the
double-time-constant circuit are
shown in Figs. 289 and 290. Both
these circuits produce less hysteresis and lower initial load
voltage V1L than the single-timeconstant circuit because the triggering capacitor C2 is recharged
by capacitor C1 after every trigger pulse. This recharge is shown

200K
2W

15K

CI
0.05p.F
200 V

Figure 289. Double-time-constant circuit for brightness control of incandescent lamps
in which triac is cut off when potentiometer is set for maximum resistance.

R
F
I
V,=120V
60 Hz

F
I

"L
T

E
R

lOOK
CI
0.05p.F
200 V

Figure 290. Double·time-constant phase-control circuit for brightness control of incandescent lamps in which a small amount of triac current flows when potentiometer
is set for maximum resistance.

RCA Silicon Power Circuits Manual

258

in Fig. 291. The recharge from C1
builds up the voltage on C2
to a value slightly less than the
breakdown voltage of the triggering device. This action results in
relatively constant positive and
negative reference voltages from
which the capacitor C2 is then subsequently charged to the next
trigger-device breakover voltage.
This voltage reduces the transient

Figure 291. Voltage waveform across triggering capacitor C. in double-time-constant
circuits shown in Figs. 289 and 290.

phase-back of triggering during
the first few half-cycles of conduction and allows the lamp load to be
initially energized with low effective voltage. The low effective voltage results in low levels of illumination. It is then necessary to
rotate the potentiometer only a

R
F
I
V, ~120V
60 Hz

1
Figure 292.

F
I
L
T
E
R

small amount for the triac to stop
conducting and the lamp to be
completely dark. Thus, the hysteresis effect is greatly reduced. A
fundamental characteristic of the
circuit of Fig. 290 is that the
component values are chosen so
that the triac is conducting a small
amount of current when Ra is at
its maximum resistance setting.
This current prevents the triac
from going completely out of conduction and thus prevents hysteresis and quick-turn-on from occurring.
In the lamp-dimmer circuit
shown in Fig. 292, a resistor R3
is connected in series with the
triggering diode to limit the magnitude of discharge current from
capacitor C2 and thus to reduce
the instantaneous voltage drop
across C2 • This technique results
in a further reduction of hysteresis and quick-turn-on.

Photocell·Operated
On·Off Lamp Controls
Photocells can be used in conjunction with light-dimmer circuits to provide light-operated
controls. These controls can be de-

200K
2W

R2
15 K

R3
100

C,
C2
0.05/LF
200 V

Double-time-constant circuit that uses a series gate resistor.

259

Thyristor AC Line-Voltage Controls

signed so that the lamp turns on
or off as the ambient light level
changes from dark to light, or
vice versa. Two photocell control
circuits are shown in Figs. 293
and 294.
The circuit shown in Fig.
293 causes the lamp load to
turn on gradually as the light impinging on the photocell increases
in intensity. As the ambient light
intensity increases, the photocell
resistance decreases to produce a
higher effective voltage across the
load.

The circuit shown in Fig.
294 causes the lamp load to
turn off as the ambient light level
increases. This behavior is caused
by a decrease in photocell resistance as the ambient light intensity increases. The decreasing
photocell resistance reduces the
voltage across capacitor C1 to
values less than the breakover
voltage of the triggering device
and prevents the triac from being
triggered. Circuits of this type are
useful as outdoor lighting controls
because they can be designed to

)

VI =120V
60Hz

I
Figure 293.

T
E
R

Photocell-operated on-off lamp control that energizes lamp load when
photocell is illuminated.

VI =120 V
50 Hz

1
Figure 294.

R
F
I
F
I
L
T
E
R

CI
0.05p.F
20CV

15K
2W

PHOTOCELL

Photocell-operated lamp control circuit that energizes lamp load when
photocell is not illuminated.

260

RCA Silicon Power Circuits Manual

turn on at dusk and turn off at
dawn automatically.

Performance Characteristics
of Light Dimmers
The performance characteristics
of light dimmers which are influenced by the circuit configuration include hysteresis;
the voltage across the load at
initial turn-on, V1L ; the maximum
voltage that can be developed
across the load, VL(max); and a
phenomenon called "flash at turnoff." All of these characteristics
were considered previously except
flash at turn-off. The flash at turnoff is produced in double-timeconstant circuits when the potentiometer is adjusted to turn off the
triac. This effect can also be
achieved by a reduction in the
magnitude of the line voltage applied to the circuit when the potentiometer is set at, or near,
maximum resistance. A lower line
voltage causes a shift in the phase
of gate-triggering voltage to a
point where the flashing condition
occurs. The fundamental cause of
this condition is a phase shift in
the triggering voltage beyond the
zero crossover point of the line
voltage into the early portion of
the next successive half-cycle, as
shown in Fig. 295. The effective
voltage on the load undergoes a
transient change that lasts for a
few cycles and results in the presence of an appreciable voltage
across the load during the transient condition. This transient
voltage causes the lamp filament to
become brightly illuminated for a
number of milliseconds· and is
manifested as a bright flash as the
illumination of the lamp is being
gradually reduced.

PRIOR TO
TURN-OFF

FLASH AT
-TURN-OFF---I
TIME

Figure 295. Waveforms duri!'g flash-atturn-off condition in a double-tlme-constant
phase-control circuit.

The double-time-constant circuit
is capable of producing a phase
shift of the triggering voltage
which is greater than 90 degrees.
If the circuit components are
chosen to produce this result and,
simultaneously, to maintain the
voltage magnitude across the triggering capacitor above the trigger-device breakover voltage, then
a flash at turn-off occurs. However if the circuit components are
sele~ted to limit the maximum
amplitude of the triggering voltage at the 90-degree phase-delay
condition below this critical value,
there is no flash at turn-off. It
should be noted that a trade-off
exists between the flash-at-turnoff phenomenon and the hysteresis
and VIL phenomena; i.e., elimination of the flash at turn-off produces slightly greater hysteresis
and larger values of V IL •

Trigger-Device
Characteristics
Other important factors that influence dimmer performance are

Thyristor AC Line-Voltage Controls
the characteristics of the trigger
device used in a given circuit configuration. In Fig. 259, the voltage-current characteristics for a
triggering device were given, and
several important parameters of
the device were shown, including
Vp , I ilL , and the negative-resistance characteristic RN • Devices
that have high values of VI' and
negative resistance produce large
hysteresis and high values of V 1L•
The value of VI) is fundamental in
determination of the value of V1L,
and the magnitude of the negative
resistance RN is the primary factor in determination of the hysteresis. The relationship of these
factors was described in the previous discussion, and the addition
of a fixed-value series gate resistor was shown to produce less
hysteresis than was obtained from
the same circuit with series gate
resistor.

Load Considerations
An important consideration in
lamp-dimmer circuits is the load
and its effect on the requirements
for the triac. Obviously, the triac
must be capable of handling the
steady-state load current. In addition, the triac should be capable
of handling the transient load requirements. One of the transient
requirements of incandescent lamp
loads is the initial or cold-lamp
inrush current, which may include
some large peak values. The magnitudes of the current peaks are a
function of the instantaneous
value of the line voltage and the
setting of the dimmer. Fig. 295
illustrates the current waveforms
for various initial values of line
voltage and dimmer settings.
These waveforms show that the

261

largest peak currents are encountered when the combination of
line voltage and dimmer settings
is such that load current commences at the peak of the linevoltage waveform. For this case,
the ratio of initial peak current to
the steady-state peak value is approximately 10 to 1, and can rise
as high as 15 to 1 for largewattage lamps. This relationship
implies that the triac chosen for
a particular lamp load should have
a subcycle surge capability sufficient to allow repeated passage of
the cold inrush current without
degradation of the device.
Another phenomenon associated
with the incandescent lamp load
is flashover. Flashover refers to
the internal arc which is developed in the lamp when it burns
out. Essentially, during burn-out,
the lamp filament opens and an
arc is initiated across the broken
ends of the filament. Subsequently,
the arc can transfer to the internal lead-in wires and remain there
until it self-extinguishes or the
circuit is opened. Because the currents associated with flashover
can be large, the lamps have internal fuses which are designed
to act quickly and open the circuit
to remove the current and extinguish the arc. Damage or degradation of the triac because of an
incandescent-lamp flashover can
usually be avoided by selection of
a triac that has a subcycle current
capability which is compatible
with, or in excess of, the Ft rating of the lamp fuse. If this condition cannot be achieved in· a
particular application, it may be
necessary to use external resistors
or other devices to prevent the
flashover current from exceeding
the current-handling capacity of
the triac.

262

High-Frequency
Power Amplifiers
T he advent of silicon rf power

transistors capable of supplying up to 20 watts of output power
at frequencies as high as 400 MHz
has resulted in the increasingly
widespread use of transistors in
many commercial, industrial, and
military transmitting applications.
During the past few years, silicon power transistors have demonstrated the ability to provide
good operating efficiency, high
power gain, and excellent temperature and frequency stability when
used in class A, B, or C rf power
amplifiers. This capability, together with the small size and
compact structure of the silicon
transistors, has led to the use of
these devices in many poweramplifier applications that previously were considered the sole
province of electron tubes.

DESIGN OF RF
POWER AMPLIFIERS
In the design of silicon-transistor rf power amplifiers for use in
transmitting systems, several fundamental factors must be considered. As with any rf power amplifier, the class of operation has an
important bearing on the power
output, linearity, and operating
efficiency. The modulation requirements of transistor rf power am-

plifiers differ slightly from those
for tube amplifiers. The matching
characteristics of input and output terminations significantly affect power output and frequency
stability and, therefore, are particularly important considerations
in the design of either transistor
or vacuum-tube power amplifiers.
In some applications, multiple connections of the silicon power transistors may be required to develop
the desired amount of output
power. The selection of the proper
transistor for a given circuit application is also a major consideration, and the circuit designer must
realize the significance of the various transistor parameters to
make a valid evaluation of different types.

Class of Operation
The class of operation of an rf
amplifier is determined by the circuit performance required in the
given applications. Class A power
amplifiers are used when extremely good linearity is required. Although power gain in this class of
service is considerably higher than
that in class B or class C service,
the operating efficiency of a class
A power amplifier is usually only
about 25 per cent. Moreover, the
standby drain and thermal dissi-

High-Frequency Power Amplifiers
pation of a class A stage are
high, and care must be exercised
to assure thermal stability.
In applications, such as singlesideband transmitters, that require good linearity, class B pushpull operation is usually employed
because the transistor dissipation
and standby drain are usually
much smaller and operating efficiency is higher. Class B operation is characterized by a collector
conduction angle of 180 degrees.
This conduction is obtained by use
of only a slight amount of forward
bias in the transistor stage. In
this class of service, care must be
taken to avoid thermal runaway.
In a class C transistor stage,
the collector conduction angle is
less than 180 degrees. The gain of
the class C stage is less than that
of a class A or class B stage, but

263
is entirely usable. In addition, in
the class C stage standby drain is
virtually zero, and circuit efficiency is the highest of the three
classes. Because of the high efficiency, low collector dissipation,
and negligible standby drain, class
C operation is the most commonly
used mode in rf power transistor
applications.
For class C operation, the baseto-emitter junction of the transistor must be reverse-biased so
that the collector quiescent current is zero during zero-signal
conditions. Fig. 296 shows four
methods that may be used to reverse-bias a transistor stage.
Fig. 296(a) shows the use of a
dc supply to establish the reverse
bias. This method, although effective, requires a separate supply,
which may not be available or may

..!£..

RFC

vcc-=-

(b)

(a)

rbb'

RFC
RFC

(e)

(d)

Figure 296. Methods for obtaining class C reverse bias: (a) by use of fixed dc supply
VBB; (bl by use of dc base current through the base spreading resistance rbb'; (cl by
use of dc base current through an external base resistance RB; (d) by use of self bias
developed across an emitter resistor RIO.

264

RCA Silicon Power Circuits Manual

be difficult to obtain in many applications. In addition, the bypass
elements required for the separate
supply increase the circuit complexity.
Figs. 296(b) and 296(c) show
methods in which reverse bias is
developed by the flow of dc base
current through a resistance. In
the case shown in Fig. 296(b),
bias is developed across the base
spreading resistance. The magnitude of this bias is small and uncontrollable because of the variation in rill,' among different transistors. A better approach, shown
in Fig. 296 (c), is to develop the
bias across an external resistor
RI\. Although the bias level is
predictable and repeatable, the
size of RII must be carefully chosen
to avoid reduction of the collectorto-emitter breakdown voltage.
The best reverse-bias method is
illustrated in Fig. 296(d). In this
method, self-bias is developed
across an emitter resistor R E. Because no external base resistance
is added, the collector-to-emitter
breakdown voltage is not affected.
An additional advantage of this
approach is that stage current may
be monitored by measurement of
the voltage drop across R E. This
technique is very helpful in balancing the shared power in paralleled stages. The bias resistor RE
must be bypassed to provide a
very-low-impedance rf path to
ground at the operating frequency
to prevent degeneration of stage
gain. In practice, emitter bypassing is difficult and frequently requires the use of a few capacitors
in parallel to reduce the series inductance in the capacitor leads
and body. Alternatively, the leadinductance problem may be solved
by formation of a self-resonant
series circuit between the capacitor and its leads at the operating

frequency. This method is extremely effective, but may restrict
stage bandwidth.

Modulation (AM, FM, SSB)
Amplitude modulation of the
collector supply of a transistor
output stage does not result in
full modulation. During downmodulation, a portion of the rf
drive feeds through the transistor.
Better modulation characteristics
can be obtained by modulation of
the supply to at least the last two
stages in the transmitter chain.
On the downward modulation
swing, drive from the preceding
modulated stages is reduced, and
less feed-through power in the
output results. Flattening of the
rf output during up-modulation is
reduced because of the increased
drive from the modulated lowerlevel stages.
The modulated stages must be
operated at half their- normal
voltage levels to avoid high collector-voltage swings that may exceed transistor collector-to-emitter
breakdown ratings. RF stability
of the modulated stages should be
checked for the entire excursion
of the modulating signal.
Amplitude modulation of transistor transmitters may also be
obtained by modulation of the
lower-level stages and operation
of the higher-level stages in a
linear mode. The lower efficiencies
and higher heat dissipation of the
linear stages override any advantages that are derived from the
reduced audio-drive requirements;
as a result, this approach is not
economically practical.
Frequency modulation involves
a shift of carrier frequency only.
Carrier deviations are usually
very small and present no problems in amplifier bandwidth. For

High-Frequency Power Amplifiers
example, maximum carrier deviations in the 50-MHz and 150-MHz
mobile bands are only 5 kHz. Because there is no amplitude variation, class C rf transistor stages
have no problems handling frequency modulation.
Single-sideband (SSE) modulation requires that all stages after
the modulator operate in a linear
mode to avoid intermodulationdistortion products near the carrier frequency. In many SSE applications, channel spacing is
close, and excessive distortion results in adjacent-channel interference. Distortion)s effectively
reduced by class E operation of
the rf stages, with close attention
to biasing the transistor base-toemitter junction in a near-linear
region.

Matching Requirements
A simplified high-frequency
equivalent circuit of an "overlay"
type of transistor is shown in
Fig. 297. This circuit is similar
to the hybrid-pi equivalent circuit
cbc

265
tance Cb'c vary nonlinearly with
the collector-to-emitter voltage.
Maximum performance in a
transistor rf amplifier can be
obtained only if the base and
collector terminals are properly
terminated. The input network
generally is required to match a
50-ohm source to the relatively
low base-to-emitter impedance,
which includes approximately 1 to
10 ohms of resistance and some
series reactance. The output network must match a resistive component and the transistor output
capacitance to a load impedance,
which is generally about 50 ohms.
In most applications, the output
network also acts as a band-rejection filter to eliminate unwanted
frequency components that may be
included in the collector waveform. The filter presents a high
impedance to these unwanted frequencies and also increases collector efficiency. The power output
and collector-voltage swing determine the resistive component to
be presented to the collector. The
design and form of the output
networks (resonant circuits for
narrow-band operation or transmission lines for broad-band operation) are discussed in a later
section.

rbb'

Multiple Connection of
Power Transistors
E

Figure 297.

Simplified high-frequency

equivalent circuit for an "overlay"

transistor.

of a transistor except for the addition of the capacitance Cbc ' This
capacitance represents the high
collector-to-base capacitance in the
overlay transistor which is created
by the large area of the collectorto-base junction together with the
active area under the emitter.
This capacitance and the capaci-

Many applications require more
rf power than a single transistor
can supply. The parallel approach
is the most widely used method
for multiple connection of power
transistors.
In parallel operation of transistors, steps must be taken to assure
equal rf and thermal load sharing.
In one approach, the transistors
are connected directly in parallel.
This approach, however, is not
very practical from an economic

266

RCA Silicon Power Circuits Manual

standpoint because it requires the
use of transistors that are exactly matched in efficiencies, power
gains, terminal impedances, and
thermal resistances. A more practical approach is to employ signal
splitting in the input matching
network. By use of adjustable
components in each leg, adequate
compensation can be made for
variations in power gains and input impedances to assure equal
load sharing between the trans is. tors. For applications in which low
supply voltages are used and high
power outputs are desired, the
output impedance of the rf amplifier is very low. For this reason,
it is beneficial, in the interest of
paralleling efficiency, to split the
collector loads. By use of separate
collector coils, the power outputs
may be combined at higher impedance levels at which the effect of
any asymmetry introduced by lead
inductances is insignificant and
resistive losses are less. The use
of separate collector coils also permits individual collector currents
to be monitored.

Transistor Parameters
In selection of a transistor and
circuit configuration for an rf
power amplifier, the designer
should be familiar with the following transistor and circuit characteristics :
(1) maximum transistor dissipation and derating,
(2) maximum collector current,
(3) maximum collector voltage,
(4) input and output impedance
characteristics,
(5) high-frequency currentgain figure of merit (fT) ,
(6) operational parameters
such as efficiency, usable
power output, power gain,
and load-pulling capability.

Proper cooling must be provided to prevent destruction of the
transistor because of overheating.
Transistor dissipation and derating information reflect how well
the heat generated within the
transistor can be removed. This
factor is determined by the junction-to-case thermal resistance of
the transistor. A good rf power
transistor is characterized by a
low junction-to-case thermal resistance .
The current gain of an rf transistor varies approximately inversely with emitter current at
high emitter-current levels. Peak
collector current may be determined by the allowable amount of
gain degradation at high frequencies. For applications in which
amplitude modulation or low supply voltages are involved, peak
current-handling capabilities are
very important criteria to good
performance.
The maximum collector voltage
rating must be high enough so
that junction breakdown does not
occur under conditions of large
collector voltage swing. The large
voltage swing is produced under
conditions of amplitude modulation or reactive loading because
of load mismatch and circuit tuning operations.
Before the proper matching networks for an rf amplifier can be
designed, transistor impedance
(or admittance) characteristics at
the expected operating conditions
of the circuit must be known. It is
important that the value and dependence of transistor impedances
on collector current, supply voltage, and operating frequency be
defined.
The term fT defines the frequency at which the current gain
of a device is unity. This parameter is essential to the determina-

High-Frequency Power Amplifiers
tion of the power-gain performance of an rf transistor at a
particular frequency. Because fT
is current-dependent, it normally
decreases at very high emitter
currents. Therefore, it should be
determined at the operating current levels of the circuit. A high
fl' at high emitter or collector
current levels characterizes a good
rf transistor.
The operational parameters of
an rf transistor can be considered
to be those measured during the
performance of a given circuit in
which this type of transistor is
used. The information displayed
by these parameters is of a direct
and practical interest. Operating
efficiencies can normally be expected to vary between 30 and 80
per cent. Whenever possible, a circuit should employ transistors
that have operational parameters
specified at or near the operating
conditions of the circuit so that
comparisons can be made.
In some rf power applications,
such as mobile radio, the transistors must withstand adverse conditions because high SWR's are
produced by faulty transmission
cables or antennas. The ability of
a transistor to survive these faults
is sometimes referred to as load
pulling or mismatch capability,
and depends on transistor breakdown characteristics as well as
circuit design. The load-pulling
effects that the transistor may be
subjected to can be determined by
replacement of the rf load with a
shorted stub and movement of the
short through a half wavelength
at the operating frequency. Dissipation capabilities of a transistor
subjected to load pulling must be
higher than normal to handle the
additional device dissipation created by the mismatch.

267
Circuit Considerations
In many instances, components
and constructional techniques used
for rf vacuum-tube equipment applications are not suitable for rf
transistor circuits. Primarily, this
incompatibility between tube and
transistor requirements results
because of the substantially lower
circuit impedances encountered in
transistor circuits.
Probably the most troublesome
area in high-frequency transistor
circuits is frequency stability.
Most instabilities occur at frequencies well below the frequency
of operation because of the increased gain at lower frequencies.
With the gain increasing at 6 dB
per octave, any parasitic low-frequency resonant loop can set the
circuit into oscillation. Such parasitic oscillations can result in possible destruction of the transistor.
These low-frequency loops can
usually be traced to inadequate
bypassing of power-supply leads,
circuit component self-resonances,
or rf choke resonances with circuit
or transistor capacitances. Supply
bypassing can be effected by use
of two capacitors, one for the
operating frequency and another
for the lower frequencies. For
amplifiers operated in the 25-to70-MHz range, sintered-electrode
tantalum capacitors can provide
excellent bypassing at all frequencies of concern. RF chokes, when
used, should be low-Q types and
should be kept as small as possible
to reduce circuit gain at lower
frequencies. Chokes of the ferrite
bead variety have been used very
successfully as base chokes. Collector rf chokes can be avoided by
use of a coil in the matching network to apply dc to the collector.
Because of the variation of tran-

268

RCA Silicon Power Circuits Manual

sistoI' parameters with changes in
collector voltage .and current, the
stability of an rf transistor stage
should be checked under all expected conditions of· supply voltage, drive level, source mismatch,
load mismatch, and, in the case of
amplitude modulation, modulation
swing.
Parametric oscillation is another form of instability that can
occur in rf circuits that use power
transistors. The transistor collector-to-base capacitance, as stated
previously, is nonlinear and can
cause oscillations that appear as
low-level spurious frequencies not
related to the carrier frequency.
Careful selection of components
is necessary to obtain good performance in an rf transistor circuit. The components should be
checked with an impedance bridge
for parasitic impedances and selfresonances. When parasitic elements are encountered, their possible detrimental effects on circuit
performance should be determined.
This procedure helps the designer
select coils and capacitances with
low losses and high self-resonances
(capacitors of the "bypass feedthrough" or "mica postage stamp"
variety can have very high selfresonances). Resistors used in rf
current paths should have low
series inductance and shunt capacitance (generally, low-wattage
carbon resistors are quite acceptable) .
Circuit layout and construction
are also important for good performance. Chassis should be of a
high-conductivity material such as
copper or aluminum. Copper is
sometimes preferable because of
its higher conductivity and the
fact that components can be soldered directly to the chassis. Another chassis approach now becoming popular is the use of

double-side laminated printed-circuit boards. The circuit, in this
approach, may be arranged so that
all the conductors are on one side
of the board. The opposite-side
foil is then employed as an additional shield. Whenever possible,
the chassis should be designed on
a single plane to reduce chassis
inductance and to minimize unwanted ground currents.
It must be remembered that, at
rf frequencies, any conductor has
an inductive and resistive impedance that can be significant when
compared to other circuit impedances in a transistor amplifier.
It follows, therefore, that wiring
should be as direct and short as
possible. It is also helpful to connect all grounds in a small area
to prevent chassis inductance from
causing common-impedance gain
degeneration in the emitter circuit. Busses or straps may be
used, but it should be remembered
that these items have some inductance and that the point at whi"ch
a component is connected to a buss
can affect the circuit.
Coils used in input and output
matching networks should be oriented to prevent unwanted coupling. In some applications, such
as high-gain stages, coil orientation alone is not enough to prevent
instability or strange tuning characteristics, and additional shielding between base and collector
circuits must be used.
In common-emitter circuits,
stage gain is very dependent on
the impedance in series with the
emitter. Even very small amounts
of inductive degeneration can
drastically reduce circuit gain at
high frequencies. Although emitter degeneration results in better
stability, it should be kept as low
as possible to provide good gain
and to reduce tuning interaction

269

High-Frequency Power Amplifiers
and feedback between output and
input circuits. The emitters of
many rf power transistors are internally connected to the case so
that the lowest possible emitterlead inductance is achieved. This
technique substantially reduces
the problems encountered when
the transistor is fastened directly
to the chassis. If a transistor with
a separate emitter lead is used,
every attempt should be made to
provide a low-inductance connection to the chassis, even to the
point of connecting the chassis directly to the lead (or pin) as close
to the transistor body as practicable. In extreme cases, emitter
tuning by series resonating of the
emitter-lead inductance is employed.
Another important area of concern involves the removal of heat
generated by the transistor. Adequate thermal-dissipation capabilities must be provided; in the case
of lower-power devices, the chassis
itself may be used. Finned heat
sinks and other means of increasing radiator area are used with
higher-power devices. Consideration must also be given to ambient
variations and mismatch conditions during tuning operations or
load pulling, when transistor dissipation can increase. Under such
conditions, the thermal resistance
of the transistor may be the limiting factor, and may dictate either
a change to another device of
lower thermal resistance or a parallel mode of operation using the
existing transistor.

MATCHING NETWORKS
Matching networks for rf amplifiers perform two important
functions. First, they transform
impedance levels as required by
the active and fixed elements (e.g.,

transistor output to antenna impedance). Second, they provide
frequency discrimination by virtue of the "quality factor" (Q) of
the resonant circuit, transform
harmonic energy into desired output-frequency energy, and prevent
the presence of undesired frequency components in the output.

Design Objectives of
Matching Circuits
The design of matching circuits
is based on the following requirements:
(1) desired or actual network
output impedance specified
by the series resistance R.
and series reactance X. or
shunt conductance GIl and
shunt susceptance Ell;
(2) desired or actual network
input impedance specified
by R" and X. or GI' and E,,;
(3) loaded circuit Q calculated
with input and output terminations connected.
The usual approach is to use L, T,
or twin-T matching pads or tunedtransformer networks. More sophisticated systems may use exponential ·lines and balun transformers.
. Input Matching-In practically
all power-transistor stages, the input circuit must provide a match
between a source impedance that
is high compared to the transistor
input irppedance and the transistor input. When several stages are
used, both the input and output
impedance of a driver stage are
usually higher than those of the
following stage.
In most good rf transistors, the
real part of the input impedance
is usually low, in the order of a
few tenths of an ohm to several
ohms. In a given transistor family,

270

RCA Silicon Power Circuits Manual

the resistive part of the commonemitter input impedance is always
inversely proportional to the area
of the transistor and, therefore,
is inversely proportional to the
power-output capability of the
transistor, if equal emitter inductances are assumed.
The reactive part of the input
impedance is a function of the
transistor package inductance, as
well as the input capacitance of
the transistor itself. When the
capacitive reactance is smaller
than the inductive reactance, lowfrequency feedback to the base
may be excessive. It is not uncommon to use an inductive input for
high-power large-area transistors
because the input reactance is a
series combination of the package
lead inductance and the input capacitance of the transistor itself.
Thus, at low frequencies the input
is capacitive, and at higher frequencies it becomes inductive. At
some single frequency, it is entirely resistive.
Output Matching - Although
maximum power gain is obtained
under matched conditions, a mismatch may be required to meet
other requirements. Under some
conditions, a mismatch may be
necessary to obtain the required
selectivity. In power amplifiers,
the load impedance presented to
the collector, R L , is not made equal
to the output resistance of the
transistor. Instead, the value of
Rr. is dictated by the required
power output and the peak dc collector voltage. The peak ac voltage
is always less than the supply
voltage because of the rf saturation voltage. The collector load resistance Rr. may be expressed as
follows:

Designs for tuned, untuned, narrow-band high-Q, and broad-band
coupling networks are considered
later under specific applications.
In some cases, particularly mobile
and aircraft transmitters, considerations for safe operation must
include variations in the load,
both in magnitude and phase.
Safe-operation considerations may
include protective circuits or actual test specifications imposed on
the transistor to assure safe operation under the worst-load conditions.
Network Design

The basic components to be considered in the design of matching
networks are shown in Fig. 298.
SOURCE
IMPEDANCE
MATCHING
NETWORK
Fi¥ure 298. Basic components considered
In the design of a matching network.

For the input matching network,
the source is assumed to be a generator that has a 50-ohm impedance. For the output matching
network, the source is the output
of the transistor, which can be
approximated as shown in Fig.
299.

TO
NETWORK

Figure 299.

Equivalent circuit for the output of a transistor.

Output-Circuit Design-When
the dc supply voltage and power
output are specified, the circuit
designer must determine the load

271

High-Frequency Power Amplifiers

for the collector circuit [R L
(VCE) 2/2P o ]' Because an rf power
amplifier is usually designed to
amplify a specific frequency or
band of frequencies, tuned circuits
are normally used as coupling networks. The choice of the output
tuned circuit must be made with
due regard to proper load matching and good tuned-circuit efficiency.
As a result of the large dynamic
voltage and current swings in a
class C rf power amplifier, the collector current contains a large
amount of harmonics. This effect
is caused primarily by the nonlinearity in the transfer characteristics of the transistor. The
tuned coupling networks selected
must offer a relatively high impedance to these harmonic currents
and a low impedance to the fundamental current.
Class C rf power amplifiers are
reverse-biased beyond collectorcurrent cutoff; harmonic currents
are generated in the collector
which are comparable in amplitude to the fundamental component. However, if the impedance
of the tuned circuit is sufficiently
high at the harmonic frequencies,
the amplitude of the harmonic
currents is reduced and the contribution of these harmonic currents to the average current flowing in the collector is minimized.
The collector power dissipation is
therefore reduced, and the collector-circui t output efficiency is increased.
Figs. 300 and 301 illustrate the
use of parallel tuned circuits
to couple the load to the collector
circuit. The collector electrode
of the transistor is tapped down
on the output coil. Capacitor C1
provides tuning for the fundamental frequency, and capacitor
C~ provides load matching of RL

FOR N:I TURN RATIO

= 2Vc:a2

(I) Rc
(2) XLI

Rc '

= QL =

(3) XC2 = RL

(FOR CLASS C)
N2R
T

N2R c
/I/
VRL"'-I

N2Rc

QL' (

(4) XCI a

\1-

I
XC2)
OLRL

Figure 300. Tuned-circuit output coupling
method and design equations in which
output is transferred to load by a series
coupling capacitor.

to the tuned circuit. The transformed RL across the entire tuned
circuit is stepped down to match
the collector by the proper turns
Rc'

FOR N: I TURN RATIO

V. 2
~~ (FOR CLASS C)

(I) Rc = 2
(2) XLI =

N2R
OLe
N2RcOL [

(3) XCI

= (OL2 + I)

RL]
1- OLXC2

'4) X
\

RL
cz- A/(QL2 +I)RL
V N2Rc -I

Figure 301. Tuned-circuit output coupling
method and design equations in which
output to the load is obtained from a
capacitive voltage divider.

272

RCA Silicon Power Circuits Manual

ratio of the coil L I . If the value
of the inductance LI is chosen
properly and the portion of the
output-coil inductance between
the collector and ground is sufficiently high, the harmonic portion of the collector current in
the tuned circuit is small. Therefore, the contribution of the harmonic current to the dc component of current in the circuit
is minimized. The use of a
tapped-down connection of the
collector to the coil maintains
the loaded Q of the circuit and
minimizes variation in the bandwidth of the output circuit with
changes in the output capacitance of the transistor.
Although the circuits shown in
Figs. 300 and 301 provide coupling of the load to the collector circuit with good harmoniccurrent suppression, the tunedcircuit networks have a serious
limitation at very high frequencies. Because of the poor coefficient
of coupling in coils at very high
frequencies, the tap position is
usually established empirically so
that proper collector loading is
achieved. Fig. 302 shows several
suitable output coupling networks
that provide the required collector
loading and also suppress the cirCUlation of collector harmonic currents. These networks are not dependent upon coupling coefficient
for load-impedance transformation.
The collector output capacitance
for the networks shown in Fig.
302 is included in the design equations. The collector output capacitance of a transistor varies considerably with the large dynamic
swing of the collector-to-emitter
voltage and is dependent upon
both the collector supply voltage
and the power output.

Input-Circuit Design-The input circuit of most transistors can
be represented by a resistor rbb'
in series with a capacitor Cin. The
input network must tune out the
capacitance Cin and provide a purely resistive load to the collector of
the driver stage. Fig. 303 shows
several networks capable of coupling the base to the output of the
driver stage and tuning out the
input capacitance Cin. In the
event that the transistor used has
an inductive input, the reactance
XCi is made equal to zero, and
the base inductance is included
as part of inductor LI for networks such as that shown in Fig.
303 (a) and is included as part
of L2 for networks of the type
shown in Fig. 303(c). In Fig.
303 (a), the input circuit is formed
by the T network consisting of
Cl> C2 , and Lt. If the value of the
inductance Ll is chosen so that its
reactance is much greater than
that of Cim series tuning of the
base-to-emitter circuit is obtained
by Ll and the parallel combination of C2 and (C 1 + Co). Capacitors C1 and Co provide the impedance matching of the resultant
input resistance rill,' to the collector of the driving stage. Fig.
303 (b) shows a T network in
which the location of Ll and C2 is
chosen so that the reactance of
the capacitor is much greater than
that of Cin ; C2 can then be used to
step up rbll' to an appropriate
value across L l . The resultant parallel resistance across Ll is transformed to the required collector
load value by capacitors CI and
Co. Parallel resonance of the circuit is obtained by Ll and the
parallel combination (CI + Co)
and C
The- circuits shown in Fig.
303(a) and 303(b) require the
9 •

High-Frequency Power Amplifiers

273

(I) XCI-QLRI

(2) XC2 =VR2 (QL2+1l
RIQL2

QLRI

(3)

XLI=[Q~: +~

RFC

.----..u.,Ar-U Vee

(b)
RFC

2L2L+-K-4-C-O"'NS>-T.-i\-NT-':-·K~·":B:-::A-:tNDf1':':"'::A~SS

Vee

FILTER

LET C2K=2 COUT IRI=R2; fl=LOW FREQ. CUTOFFlf2=HI-FREQ. CUTOFF
I
(II (f2-fl)=2.rcORL

Figure 302.

RI
(2) L2= LIK TU2-fl)

Additional transistor output-coupling networks including transistor output
capacitance.

RCA Silicon Power Circuits Manual

274

FOR 'XLI »XCI~ RI >R2='bb'
(I) XLI=QL R2=QL'bb'

(3) Xc2=

'bb' (QL2 +1l
QL

(b)

+Vce

(Il XLI =
(2) XL2

~L
R2

= QL'

[~-I]
[

]

RI
(3) XCI = QL •

- QLXco

Figure 303.

Transistor input-circuit coupling networks.

[ I-

QLXco

]

High-Frequency Power Amplifiers

275

(a)

•• R,

(b)
R,< R2

(d)

(e)

(f )

(2) XC2

= QL R2

(3) XL,'

R2(QL2 +11
QL

.~*J
~+
QLR,

Figure 304.

Other suitable rf-amplifier coupling networks for maximum power transfer.

276

RCA Silicon Power Circuits Manual

collector of the driving transistor
to be shunt-fed by a high-impedance rf choke. Fig. 303(c) shows
a coupling network that eliminates
the need for a choke. In this circuit, the collector of the driving
transistor is parallel tuned, and
the base-to-emitter junction of the
output transistor is series tuned.
Fig. 304 shows several other
forms of coupling networks that
can be used in rf power-amplifier
designs.

The Impedance-Admittance
Chart
One of the most useful tools for
designing matching networks is
the impedance-admittance chart.
This chart can be described simply
as the plane of reflection coefficient for admittances, and provides an easier and faster method
of circuit analysis than that offered by rectangular admittance
or impedance charts. The chart
displays graphically all laddertype matching networks, and
shows the applicable tuning ranges
for variable components. Lumpedcomponent values for a given frequency may be determined directly
from the chart in normalized
values. The chart can be used for
idealized equivalent circuits, as
well as for circuits that employ
transformers or tapped coils.
Fig. 305 shows the basic layout
of the chart. Shunt elements in a
ladder follow the admittance circles (shown dotted). Values of
shunt elements correspond to values on the intersection arcs. Series
elements follow the impedance
circles; corresponding values are
read from corresponding intersection arcs.
Rules for Plotting Networks
and Components-When a single

component L, C, or R is added to
a known impedance, one of the
following parameters does not
change: resistance (R), reactance
(X), conductance (G), or susceptance (B). (Non-ideal components
must be divided into two separate
ideal components; e.g., a lossy
inductor into separate Land R
components.) Therefore, the component follows that constant-parameter curve. For example, an
inductor added in series with the
circuit does not change the series
resistance curve. The procedure
for each type of component is
listed in Table XXIV, which, together with Fig. 306, indicates
the direction of travel along the
curve and makes it unnecessary to
determine the plus or minus sign
on the reactances and susceptances.
Quality Factor, Q-The operating Q must be specified, together with the input and output
impedances, in the design of a
matching network. The magnitude
of the operating Q is a compromise between efficiency and harmonic rejection.
Unfortunately, the exact operating Q of a complex circuit cannot always be determined by calculations at a single frequency.
When circuit design equations are
used, this problem is circumvented
by defining an operating Q which
is easily calculated and which approximates the actual Q. The
graphical technique uses the same
type of approximation, but more
simply and more visibly. The Q of
each node of the circuit plot is determined by the constant-Q curves
shown in Fig. 307. The node that
has the highest Q dominates; this
Q is then defined as the operating
Q of the circuit.

High-Frequency Power Amplifiers

277

B=I=X

---G.B
COORDINATES
(ADMITTANCE)
-RX
COORDiNATES
(ADMITTANCE)

B=I=X

Figure 305.

Impedance-admittance chart.

Table XXIV-Procedure for Plotting Component Values on
Impedance-Admittance Chart

ra Add
Series L
Series C
Series R
Shunt + L
Shunt + C
Shunt + R

Use
Chart

Z
Z
Z

Y
y
Y

Follow a Curve of
Series R
Series R
X
Parallel R (G)
Parallel R (G)
B

Constant
Constant
Constant
Constant
Constant
Constant

Component Valae
Xr.
X. Xc
X. Rs
R. BL
B. Bo
B. l/Rp
G. -

Direction

=
=
=
=
=
=

CW
CCW
toward open
CCW
CW
toward short

Xl
Xl
RI
BI
Bl
Gl

Calculate the change in X. B. G and R by disregarding the
and - signs of the points on the
chart. However. be sure to measure the entire change in X. R. B. or G. For example. a series
capacitor which changes Xl
0.4 inductive (above pure R line) to Xl
0.3 capacitive (below
pure R line) has a value of 0.7.
Note: Shunt refers to components with one terminal grounded and in parallel with the rest of the
network.

278

RCA Silicon Power Circuits Manual

---SHUNT OR

PARALLEL
-SERIES

Figure 306.

Method used to trace constant-parameter curves for matching-network
components.

Normalized Values-Impedance
charts use normalized values. This
graphical technique requires that
normalized impedance and admittance values be consistent. The examples use 10 lu
[500] (for
impedances)
[(1/50u] (for
admittances). (Note: Brackets
are used here, and in succeeding
text and illustrations, to indicate the actual impedances or
admittances represented by the
normalized values.) The ohm
(n) and mho (u) symbols are retained on the chart to distinguish
between. impedance and suscep-

= =

tance. A 50-ohm impedance is
used as the normalizing factor
because this value represents a
common rf-amplifier load impedance.
Map'ping Technique The
matching network can be designed
or analyzed by use of a network
map, which is prepared by plotting each component (including
input and output impedances) on
the impedance chart. Dual impedance-admittance charts, such as
that shown in Fig. 305, are available for this purpose, but the

279

High-Frequency Power Amplifiers
many curves required make these
charts difficult to read. A more
practical network map is prepared
on tracing paper. The tracing paper is placed over either an impedance or an admittance chart to
trace curves, read values, and compare impedances. Figs. 308 and
309 show simplified versions of a
standard impedance chart and a
standard admittance chart, respectively. The admittance coordinates have the same shape as the
impedance coordinates except
that they have been rotated 180
degrees around the chart. This
statement can be easily verified
by superposition of Fig. 308 on
Fig. 309 with the short and open

points of one chart aligned with
the open and short points, respectively, of the other chart.
The first step in the preparation
of a network map is to trace the
perimeter of the impedance chart
(line of pure R) and those standard R, G, X, and B curves which
are absolutely necessary. The
"open" and the "short" points (or
the pure R line) should also be
marked to assist in accurate realignment of the tracing paper.
The values of components may
be determined with sufficient accuracy from curves that are
traced from impedance or admittance charts placed under the
tracing paper.

--........

4571020 ...

OFFS~T ~!
Figure 307.

Chart of constant-Q curves.

~~NTER

RCA Silicon Power Circuits Manual

280

Figure 308.

Impedance chart

The following numerical examples illustrate the use of the mapping technique in the determination of the parameters of various
types of matching networks.
DETERMINATION OF INPUT IMPEDANCE: Fig. 310
shows a typical output matching
network, together with the network map used to determine the
required input impedance for this
network. The reactance of each
component in the matching network is known (from component
values and operating frequency)
and the input impedance is to be
determined. The component reactions are plotted by use of curves
traced from the Z, Y, and Q charts
as follows: The output load imped-

ance, 50 ohms normalized t() 1
ohm, is located on the Z chart.
Next, the series C2 curve is plotted
on a constant-R curve through 1
ohm, as indicated in Fig. 310. The
series C2 curve must change the
reactance by its given value, 100
ohms normalized to 2 ohms, and
the required normalized constant
X
2 ohms curve is traced from
the Z chart. The C2 curve ends at
point A, where B = 0.04 mho, and
the shunt L curve begins at this
point. The shunt inductor has a
normalized susceptance of 1 mho.
The curve of this inductor follows the constant Rp admittance
coordinate, passes through point
A, and ends at Bf
BL - Bi
1 - 0.4
0.6 mho. (Table XXIV
summarizes this procedure. It

High-Frequency Power Amplifiers
should be remembered that, in
this case, the curve crosses the
pure R axis.) This point is labeled
point B on the network map
shown in Fig. 310. Similarly, the
series C1 curve is plotted along
the constant Rs coordinate, passes
through point B, and ends at
Xf = Xc - Xi = 1.5 - 1.5 = 0
ohms. The normalized value of
input impedance is read on the
Z chart as 0.5 ohm. The Q of
the matching network is read
from the Q curves at both points
A and B. The Q is 2 at point A
and 3 at point B. The higher value
3 is taken as most representative
of the network Q.
DETERMINATION OF NETWORK COMPONENTS: In the
following examples, the graphical

Figure 309.

281
procedures used in the design of
four different types of matching
network are given. For the first
type, a detailed explanation of the
graphical procedure is given. For
the other types, a tabular list of
the steps required is considered
sufficient because of the basic
similarity of the graphical processes. The network maps for
these examples show only the
curves that are required to determine network parameters; all
other curves are omitted for clarity. (In the examples, component
curves are plotted as described in
Table XXIV.)
1. Design of tapped-C network.
Fig. 311 shows the circuit configuration and the network map

Admittance chart.

282

Figure 310.

RCA Silicon Power Circuits Manual

Typical output matching network and network map used to determine
required input impedance for this network.

used to dtltermine the component
values for a tapped-C matching
network that is required to transform 50 ohms to 20 ohms with a
Q of 6. The procedures used to
prepare the network map are as
follows:
(a) The normalized input and
output points (Le., points
1 + jOn and point 0.4 +
jOn are located on the impedance-chart coordinates.
(b) The Q = 6 curve is traced
from the Q chart, Fig. 307.
(c) The curve for the shunt L
is traced along the con-

stant Rp
1.0u curve
(from the
admittance
chart) from the termination point 1 + jOn to the
intersection of this curve
with the Q 6 curve. This
intersection is labeled A
for further reference.
(d) A constant Rs curve for
the series C1 is traced from
the impedance chart. The
starting point for this
curve is point A.
(e) The curve for the shunt
C2 is then traced between
the termination point 0.4
+ jOn and the intersection

High-Frequency Power Amplifiers
of this curve with that for
the seriesC 1 • The intersection of the C1 and C2 curves
is labeled point B. (Although the intersection B
is determined after the
curve for the shunt C2 is
traced, this intersection is
considered as the starting
point for the shunt C2
curve.)
(f) As a routine matter, the
reactance X and the susceptance B values for the
intersection points A and
B are determined by means
of series and parallel
charts.

283
For point A, X = 0.16 ohm
and B
6 mho.
For point B, X = 0.10 ohm
and B = 9 mho.
(g) As indicated in Table
XXIV, normalized reactance values for the shunt
inductor L, the series capacitor C1, and the shunt
capacitor C2 are determined by subtraction of
the values at the starting
point of the curves for
these components from the
values at the end point of
these curves. The following values are obtained:

SHORT~----------~~~~--~~~~------------~~

Figure 311.

Circuit configuration and network map used to determine the component
values for a tapped·C matching network.

RCA Silicon Power Circuits Manual

284

XL = 50/AB L = 50/6
= 8.3 ohms
XCl = 50 (AX Cl ) = 50(0.06)
=3 ohms
X C2 = 50/ABc2 = 50/9
= 5.5 ohms
(i) The component values for
the filter can then be calculated on the basis of the
reactances and the operating frequency.

An intuitive analysis of the
tapped-C network indicates that
the shunt inductor L reduces the
50-ohm output impedance to the
value represented by point A on
the network map and that the
shunt capacitor C2 reduces the
impedance of the 20-ohm input to
a nearly equal value, as represented by point B. The series capacitance C 1 makes up the difference in the reactance of the two
impedance points A and Band
provides resonance. The values of
both capacitors Cl and C2 must
be changed together to maintain
resonance when the input impedance is changed. The Q is determined by inductor L and the
50-ohm load impedance. At the input side, the transformation ratio
is smaller, and the Q must be
smaller.

The detailed step-by-step procedure given above is summarized
in Table XXV. For one familiar
with the basic graphical processes,
this table provides sufficient information for the design of the
filter network.

2. Design of pi network. Fig.
312 shows the circuit configuration and the network map for a
pi-type matching network required to transform 50 ohms to
20 ohms with a Q of 5. The network-mapping procedures used to

Ll.BL = B CatA) -BCatl+l00)
=6u-0=6mhos
Ll.Xel = X CatB) - X CatA)
= 0.10 - 0.16 = 0.06 ohm
Ll.Bo2 = B Cat 0,4+ iOn) - B Cat B)
=0-9u =9 mhos
(h) The actual reactance values
for L, C, and C2 can then
be determined as follows:

Table XXV-Procedure for Determining Component Values for
Tapped-C Matching Network
Step
No.

Component Curves
COMPONENT

1
2
3
4

Q
6
Shunt l
Series C.
Shunt C.

FINAL POINT
AND HOW IT IS DETERMINED

INITIAL
POINT
(1

+ jO)n
A

A, determined by intersection of land Q 6 curves
11. determi~ed by intersection of C. and C. curves

O.4n

+ jOn

= [20nl

Intersection Parameter Valuestrom X and Y Charts
INTERSECTION
REACTANCE X

5
6

0.16n
0.10n

SUSCEPTANCE B

6u
9u

Computing Component Values
INITIAL
FINAL
PARAMETER CHANGE
COMPONENT
COMPONENT POINT
POINT
(NORMALIZED VALUES)
VALUE
7
Shunt l (1
jO)n
A
Ll.B = 6 - 0 6u
XL = 501Ll.B = 8.33n
8
Series C.
A
B
Ll.X = 0.1 - 0.16 = 0.06n XQ1 = Ll.X(50) = 3n
9
Shunt Co
B (0.4 jo)n Ll.B = 0 - 9 = 9u
Xo. = 501Ll.B = 5.5n

285

High-Frequency Power Amplifiers

Figure 312.

Circuit configuration and the network map used to determine the component
value for a pi matching network.

Table XXVI-Procedure for Determining Component Values for
Pi Matching Network
Step
No.
1

3
4

5
6

Component Curves

FINAL POINT
INITIAL
AND HOW IT IS DETERMINED
POINT
COMPONENT
Q
5
A, intersection of C1 and Q
5
(1 + jO)n
Shunt C1
B, intersection of Cl and C. (step 4)
Series L
A
(0.4 + jO)n
Shunt C.
B
Intersection Parameter Values
REACTANCE X
INTERSECTION
SUSCEPTANCE B

0.19n

O.l1n
B
Uu
Compute Component Values
INITIAL
FINAL
PARAMETER CHANGE
COMPONENT
COMPONENT
POINT
POINT
(NORMALIZED VALUES)
VALUE
7
Shunt C1 (1
jO)n
A
~B = 5 - 0
5u
XCl 50/~B
8
Series L A B
~X
0.11
0.19 = 0.3n XL
50(~X)
9
Shunt C.
B
(0.4 jO)n ~B = 0 - 8.33
8.33u Xc. 501~B

=
=
=

=
==IOn
15n
6n

286

RCA Silicon Power Circuits Manual

determine the component values
for the pi network are given in
Table XXVI.
In the pi matching network,
the shunt C across the 50-ohm output reduces the output impedance
to the value represented by point
A on the network map. The shunt
capacitor across the 20-ohm input
reduces the input impedance to
the nearly equal value represented
by point B. The Q at the input
is smaller because the change in
impedance is less. The series inductor connects the input and output and cancels the reactances of
the two capacitors. The impedance

Figure 313.

transformation is determined by
the difference in the input and
output Q.
3. Design of lossy-L network.
Fig. 313 shows the circuit configuration and network map for
a lossy-L matching network required to transform 50 ohms to
10 ohms with a Q of 5. Table
XXVII gives the graphical procedure used to determine the
component values for this network.
In the lossy-L network, the
series inductor increases the impedance of the 10-ohm input and

Circuit configuration and the network map used to determine the component
values for a "Iossy"-L matching network.

287

High-Frequency Power Amplifiers

Table XXVII-Procedure for Determining Component Values for
Lossy-L Matching Network
Step

No.
1

Component Curves

COMPONENT
Q
5

2
Series L
Shunt C,
3
4
Series C.
Determine Component Values

COMPONENT
L
C,
C.

INITIAL
POINT
0.212
A,B = 0.96
B,X
2.0

FINAL POINT
AND HOW IT IS DETERMINED

INITIAL
POINT
O.W
A
B

A, intersection of Land Q = 5 curves
B, intersection of C, and C. curves

LOn

FINAL
POINT
X
1.0
B, B 0.395
1.0

=
=

determines the operating Q of the
network. The series capacitor increases the impedance of the 50ohm output, and the shunt capacitor tunes out the surplus reactance.
In spite of the large impedance
transformation (10 to 50 ohms),
all component values have nearly
equal impedances (56, 90, and 100
ohms). These relatively large values make the components quite
practical, and are particularly advantageous for matching into the
base of a transistor in which the
impedance is only a few ohms.
4. Design of network containing four unspecified components.
Fig. 314 shows the circuit configuration and network map for a
matching section required to
transform a 50-ohm load impedance to 12.5 ohms for the collector load impedance of a transistor
amplifier that has a Q of 5. The
transistor collector has a parallel
output capacitive reactance of
250 ohms. This network has four
unspecified components (L I , L 2 ,
Cl> and C2 ) and three required
conditions. The values for only
three of the components can be
determined by the graphical techniques; the value of the fourth
component must be arbitrarily assigned. The value of Ll is nor-

PARAMETER CHANGE
(NORMALIZED VALUES)
AX
1.0 - 0
1.012
AB = 0.395 - 0.96
0.56u
AX
0 - 2.0
2.012

=
=

= =
=

COMPONENT
VALUE
XL
5012
XcL
89.512
Xc.
10012

=
=
=

mally selected so that this component is nearly resonant with Cin
at the operating frequency. In this
example, however, the value selected for Ll is purposely small to
demonstrate the flexibility in the
choice.
The first step in the preparation
of the map is to plot all known
and assigned values. The three remaining components are then plotted and calculated as in examples
1, 2, and 3. The graphical procedures are outlined in Table

XXVIII.
This network provides the best
separation of impedance transformation, resonance adjustment, and
operating Q. The components Ll
and Cin nearly resonate; however,
perfect resonance is not required.
The circuit tunes well even for
large errors in Cin or L j • The
capacitor C2 reduces the 50-ohm
output impedance to the series resistance required at the input. The
capacitor C2 , therefore, is the
principal loading adjustment for
the amplifier. The components L2
and C1 form a series resonant circuit which compensates for the
differences in input and output
reactances. Inductor Ll and the
12.5-ohm input determine the operating Q relatively independent
of resonance. The Q, therefore, is

288

RCA Silicon Power Circuits Manual

tiDr-oJ

12.

. CIN
250.0

LI 2

' C:ll..C2

0-5

50.0
~----

Figure 314. Circuit configuration and network map used to determine component values
for matching network that includes four unspecified components.

Table XXVIII-Procedure for Determining Component Values for
Matching Network in Which Four Unspecified Components Are Used
Step
. ND.
1
2
3
4
5
6

COMPONENT
Shunt C,,,
Shunt It
Q
5
Series l.
Series C1
Shunt C.

COMPONENT
C'n
It
l.
Cl
C.

A,B
B,X
C,X
D,B

INITIAL
POINT
(0.25 + JOIn
A

INITIAL
POINT
0.25n
= 0.2u
= 0.04n
= 1.8n
= 1.77u

FINAL POINT
AND HOW IT IS DETERMINED
A, determined by given value for XC,,,
B, determined' by' assigned value for XL1

C, determined by intersection of l. and Q = 5
D, determined by intersection of C1 and C. (step 6)

B
C
D

FINAL
POINT
A,B = 0.2u
B,B = 0.6u
C,X = 1.8n
D,X
0.43n
LOn

+ JOIn

REACTANCE
PARAMETER CHANGE
(NORMALIZED VALUES)
VALUE
Xc,,, = 250n
AB = 0.20 = 0.2u
XLI = 62.5n
AB = 0.6 + 0.2 = 0.8u
AX = 1.8 - 0.04 = l.76n XLI = 88n
AX
0.43 - 1.8
1.37n Xci = 68.5n
Xc. = 28.2n
AB = 0 - 1.77 = 1.77u

High-Frequency Power Amplifiers

289

rather tightly controlled. Capacitor C1 compensates for the additional inductor L2 needed to provide the proper Q but not needed
to match the input to the output.
Therefore, C1 is the resonance adjustment, and C2 is the loading
adjustment.

for an input impedance of 20
ohms, but it may be changed by
means of variable components.
Two components must be varied
to (1) change the impedance, and
(2) maintain resonance. For this
pi network, XCI is increased in
steps and L is kept constant, as
shown in Fig. 315. Also shown
is the X C2 required to produce
resonance, and the resulting Q
and input impedance.
It should be noted that the first
step increase in XCI (35 %)
changes the Q and RiD greatly, but
requires little change in X C2 • The

Effect of Component Changes
in Graphical Design-A particular advantage of graphical network design is that changes in
component values can be easily
evaluated. The pi network in example 2 (Fig. 312) was designed

L
15.5£1

IN~ 1~50D

lOt!'
I

I
,,
I

,-,,/'

... " "
OPEN

O.OI£1F=1=l=~~~!..!.....!c---l......----~~:!!:....--------=:"::::!..--1

O.04DI--I-T-"-';'

RESULTS
POINT Q
XC2
SQ
0
5
13.5Q
C
3.8 9Q
16.6£1
8
3 50£1

XcI

RIN
20Q
6£1
5.5Q

Figure 315. Circuit configuration for pi matching network and network map showing
tuning range for variable components used in this type of matching network.

RCA Silicon Power Circuits Manual

290

second step increase in XC! (23%)
changes the Q slightly, changes
the input very little (8%), but requires a large change in X C2 ' Any
further change in X C2 makes resonance impossible.

Transm ission-Line
Matching Techniques
The network-design techniques
discussed in the previous sections
apply largely to lumped-constant
circuits operated in the vhf and
uhf ranges. In the uhf and microwave-frequency ranges it may be
more desirable to use short sections of transmission lines to
provide the reactive elements
needed in the previous discussions. The Smith Chart is generally used in these determinations
also. There are many special-case
conditions which the circuit designer can use without resorting
to the general transmission-line
equation .or the graphical method
of the Smith Chart. A few of the
more useful expressions are presented in this section.
Half-Wave Line Sections-Sections of uniform transmission
lines which are electrically an
integral number of half-wavelengths (Ai2) in length are useful in transferring an impedance
from one point to another, i.e.,
the terminating impedances on
the line are equal, or ZI'l = Zr..
Quarter-Wave Line SectionsSections of uniform transmission lines which are electrically
a quarter of a wavelength (Ai 4)
in length have a number of interesting and useful properties.
A quarter-wave line which is
short-circuited at one end provides a very high impedance at
the open end. This property can

be used to provide high resistance
stub supports for rf structures
as well as to provide rf-choke
action for dc bias circuits.
The quarter-wave lines are
also useful as an impedance
transformer between real impedances. The characteristic impedance can be determined as
follows:
Zo = (Rs X RL)1/2

(289)

where Rs is the source or input
impedance and RL is the load or
output impedance.
Eighth-Wave Line SectionsEighth-wave (Ai8) sections of
uniform line have additional useful properties. If the eighth-wave
section of line is terminated in
a pure resistance, the input impedance will have a magnitude
equal to the characteristic impedance Zo of the line. Conversely,
an eighth-wave section of line
which is terminated in an impedance whose magnitude is
equal to Zo must have a real input
impedance. Therefore, for an
eighth-wave line section, ZL is
real if the following relationship
is valid:

Zo = I Z.I

= (RS2 + XS2) 1/2

(290)

The real impedance ZL can be
determined from the Smith Chart
or by use of the following equation:
R
X

1 -

(291)

IZsl

where R and X are the real and
imaginary parts, respectively, of
the complex impedance Zs.
Tapered Line Section-Quarter-wave or eighth-wave line sections in which the impedance

291

High-Frequency Power Amplifiers

changes exponentially (or hyperbolically) have additional properties useful to the circuit designer. These line sections can
be tapered directly to a desired
real impedance rather than a
predetermined impedance as was
the case for a uniform line. In
addition, because of the nature
of the TEM mode of propagation
in these tapered lines, substantial reductions in effective line
lengths and increased transformation bandwidths are possible.
The design of an amplifier circuit
at a frequency of 2 GHz is described as an example. The dynamic input impedance Zin and
collector load impedance ZCL of
the transistor to be used are as
follows:

Zin
ZCL

= 7.5 + j 8.0 ohms

= 6.5 + j 33 ohms

(291)
(292)

The amplifier uses an air-line input circuit and an air-line output circuit similar to that shown
in Fig. 316.

Figure 316.

Capacitive-probe-coupled output cavity.

For the design of the output
circuit, the optimum characteristic impedance Z" of the output
line is calculated from Eq. (290)
to be 31 ohms. The collector load
impedance ZCL is normalized as
follows:

ZCL' = ZcdZo = 0.18 + jO.915

(293)

Point ZCL' is then located on the
Smith Chart shown in Fig. 317
and rotated about the constantVSWR circle toward the load. The
intersection of the VSWR circle
and the 1.39 constant-resistance
circle is denoted as point ZL' (the
load resistance is assumed to be
50 ohms and the normalized load
resistance is, therefore, 1.39
ohms). At point ZL', the normalized impedance is given by

ZL'

= 1.39

- j 3.3

(294)

The load impedance ZL is then
equal to

ZL = ZoZL' = 36 (1.39 - j 3.3)
= 50 - j 119 ohms
(295)
The line length required to transform the transistor collector load
impedance from· 0.5 ohm to a
load impedance of 50 ohms
is determined from Fig. 317 to
be equal to 0.33 A (where A is
the wavelength in air). At 2
GHz, A is equal to 5.9 inches, and
the length of output line is calculated to be 1.95 inches. A capacitive reactance component with
a value equal to 119 ohms is
needed to complete the output circuit, as shown in Fig. 318(a).
For the design of the input
circuit, a characteristic impedance
Zo of 11 ohms is calculated from
Eq. (290). The input impedance
Zin is normalized as follows:

Zin' = (Zin/Zo) = 0.68 + 0.725
(296)
Point Zin' is then located on the
Smith Chart shown in Fig. 319
and rotated about the constantVSWR circle toward the generator to locate the intersection between the VSWR circle and
the 4.55-ohm constant-resistance
circle. (The driving-source impedance is assumed to be 50 ohms

292

RCA Silicon Power Circuifs Manual

Figure 317.

Smith-chart admittance I?lot for design of output transmission-line
matching section.

(a)

A/4

Figure 318. Input and output transmission
lines with transmission-line matching sections added to provide required impedance
transformation: (al output line; (bl Input
line using series matching section; (cl input line using series matching section
foreshortened by reactive elements.
(b)

High-Frequency Power Amplifiers
and the normalized source impedance is, therefore, 4.55 ohms.)
However, Fig. 319 shows that
such an intersection is not possible and that a more sophisticated
input circuit is needed. One
possible circuit employs another
section of line. For minimum
VSWR in the added section of
line, the line length for the 11ohm line must be A/8 or 0.75 inch,
as discussed previously. This
point, denoted as ZI' in Fig. 319,
is equal to 2.5 ohms; the impedance ZI is then 27.4 ohms. The
characteristic impedance of the
added line section required to

Figure 319.

293
transform a resistance of 27.4
ohms to a 50-ohm source is calculated from Eq. (289) to be 37
ohms. Such an input circuit is
shown in Fig. 318 (b). Another
possible input circuit uses added
reactive elements, as shown in
Fig. 318(c), to foreshorten the
additional line section.
The design of microstripline
circuits is the same as that described for air-line circuits, except that the wavelength of the
line must be modified by a factor
of livE, where E is the dielectric
constant of the insulator material
of the stripline.

Smith-chart admittance plot used for design of input transmission-line
matching sections.

294

RCA Silicon Power Circuits Manual
MARINE RADIO

Marine radios are used primarily for ship-board communications involving the safety or
navigation of the carrying vehicle; citizens-band radios used
aboard boats are covered in a
separate section. The term
"radio", as used here, refers to
a receiver-transmitter combination. Telegraphy, disaster and
emergency radios, public ship communications, or navigation-only
radios are not discussed. The type
of radio considered is the type
normally used on small private
power boats, which features simple operation and requires no
technical operator training. Radios of this type add to· safety of
the boat because of their ability
to transmit on distress and calling
frequencies (2.182 MHz, 156.3
MHz, and 156.8 MHz) constantly
monitored by other boats and by
the Coast Guard.
Ship-to-ship and ship-to-shore
communications are permitted
over certain frequencies assigned
by the Federal Communications
Commission and shared by all
boats; all marine-radio operation
is regulated by the FCC. These

regulations concern the granting
of licenses, assignment of frequencies, technical specifications
of radio equipment, and allowable
usage for each frequency. The
exact regulations depend upon the
geographic location of the boat,
its use, and its size. A condensed
listing of the FCC regulations for
marine radio, as they affect transmitter design, is given in Table
XXIX.
Marine radios are designed to
operate in either the hf or the vhf
band. The transmitter for the hf
band (1.605 to 27.5 MHz) usually
covers from 2 to 3 MHz in four
channels with dc input of 25 watts
(rf output of 12 to 15 watts).
Higher-power transmitters usually cover the frequency range
from 2 to 5 MHz and feature
more channels. The rest of the
hf band is covered by specialpurpose transceivers not usually
found on private boats. The vhf
band is not as popular as the hf
band in marine radio. Because
of overcrowding on the hf band,
however, the vhf band is becoming increasingly popular. VHF
transmitters usually cover the entire vhf band, from 156 to 174
MHz, and feature frequency-modulated output.

Table XXIX-Marine-Radio Transmitter Regulations*
BandFrequency Modula- width
Band
tion
kHz

Deviation
kHz

Frequency
Accuracy
%
Hz

:I~~; i~ t!

I:;

3500 kHz
4000 kHz27.5 MHz
156 MHz-

0.005

SSB

3.5
8.0
3.5

Required
Power Output·· FreMin. Max. quency

l1 ~5~0

50
50

1000
40
100

Min.
No. of
Channels

1
1
3

2182

156.3

174 MHz
FM
40.0
15
0.002
156.8
• These are not complete specifications and are intended only as a general guide for transmitter
design. See FCC Rules and Regulations, Part 83.
•• Value depends upon location, ship weight, and ship type.

High-Frequency Power Amplifiers
Transistorized equipment offers the advantages of small
size, ruggedness, and improved
reliability. In addition, the inverter power supply may be
eliminated because the transmitter can operate directly from the
13.6 volts available from the
boat battery.

Design Problems
Amplitude modulation in a transistorized marine-radio transmitter is an important design consideration. The transistor used must
deliver the peak power required
for upward modulation. The theoretical requirement is for a peak
envelope power (PEP) of four
times the cw power at 100-percent modulation. This requirement
is seldom met, however, for the
following reasons: the gain of a
transistor decreases at high peak
currents, the VCE(sat) increases at
high peak current, and modulator
losses rise during upward modulation. A minimum performance
requirement is set by the FCC at
75 per cent upward and 100 per
cent downward for an equivalent
total modulation specification of
(100 + 75)/2 = 87.5 per cent.
This specification corresponds to
a PEP requirement of 3.1 times
the cw power.
Marine-radio owners want reliable, foolproof radio equipment,
particularly because it is used in
times of emergency. The owners/
operators, however, generally lack
technical knowledge and have inadequate concern for maintenance.
Unfortunately, maintenance of the
vulnerable antenna and transmission line has a direct effect on the
performance of the radio. Optimum performance occurs only

295
when the transmitter is properly
loaded. A mismatch causes low
power output and may cause spurious outputs or oscillation. Even
more important, antenna and
transmission-line faults place a
stress on the transmitter output
stage and could destroy the transistor. The best transistors for
marine-radio transmitters, therefore, are those that can withstand
such load faults without damage.
The hf-band radio must operate over a wide frequency range,
as mentioned previously, usually
2 to 3 MHz. Because of this relatively low operating frequency
and broad range, tuning capacitors capable of operating through~
out the range must be large in
value and, therefore in size. Unfortunately, capacitors (and variable inductors) of large value are
not commercially available, and
changes in operating frequency
require the switching of entire
tuned circuits or the changing of
taps on coils with simultaneous
switching to separate sets of capacitors. The low, wide frequency
band also complicates antenna design. Because the antenna only approximates a constant impedance,
the load presented to the transmitter may range from 5 to 50
ohms with a parallel capacitance
in the ±200-picofarad range.
The impedance varies with operating. frequency, length of transmiSSIOn line, and installation.
Whatever the impedance, the
tuned circuits in the transmitter
output stages must match this
value properly and transform it
to the optimum load impedance
for the output transistor. Because
of this requirement, the tunedcircuit components must be capable of operating over very wide
frequency ranges.

296

RCA Silicon Power Circuits Manual
VHF FM Transmitter

New FCC regulations indicate
that marine-radio communications will be gradually shifted
from the 2-to-3-MHz AM band
into the 156-to-174-MHz FM
band. These new rulings have
stimulated an interest in the design of all-solid-state vhf FM
transmitters. Although the new
FCC regulations are not entirely
firm, they indicate that the maximum allowable power output for
such marine-radio transmitters
shall not exceed 25 watts with
the provision that a maximum
power output of 1 watt shall be
imposed for harbor communications.
The new interest in vhf
FM marine-radio communications systems has led to the design of multiplier-amplifier and

power-amplifier sections of a vhf
FM transmitter, such as that represented by the block diagram
shown in Fig. 320. The circuits
operate at any frequency in the
156-to-157.4-MHz marine band
without necessity of retuning.
Only a change in the crystal frequency of the exciter section is
required to change the output
frequency of the transmitter.
Multiplier-Amplifier-Fig. 321
shows a schematic diagram for
the multiplier-amplifier section
of the transmitter. This section,
which consists of three frequency-multiplier stages and a
power-amplifier stage, can deliver a power output of 1 watt
over the frequency range of 156
to 157.4 MHz. With the output of
the power-amplifier stage connected to the antenna (through

o~~Ir:~ 1 - - - - - . \

PHASE
MODULATOR

13 MHz

r-----i CMffE~_
AMPLIFIER

!5mW
13MMz

MULTIPLIER-AMPLIFIER

~
13 MHz

TRIPLER
40637

DOUBLER
39MHz . 40637

78MHz

DOUBLER
40637

100mW
156MHz

AMPLIFIER
40280

~
156M Hz

POWER AMPLIFIER

LOW
156MHz

AMPLIFIER
40281

Figure 320.

LP.
FILTER

lOW
156 MHz

Block diagram of a typical vhf FM marine-band transmitter.

297

High-Frequency Power Amplifiers
1.2

0.82

'--------------------Q+12V

POUT=IW
ATI56mH
-50pF

ALL CAPACITOR VALUES ARE
IN PICOFARAOS UNLESS
OTHERWISE SPECifiED
ALL RESISTORS 1/4 W

'------------*--~-O+12V

11, L2 = 10Y2 turns No. 22 enamel wire, closewound, 10/32" slug tuned coil forms 15/64"
OD, shield can 1f2" x 1/2" x 1"; slug
carbonyl S.F. or equiv.
La, L4. = 4112 turns No. 22 enamel wire, closewound! 10/32" slug tuned coil forms 15/64"
00, Shield can '/2" x V2" x l"i slug
carbonyl S.F. or equiv.
ls, L.
11/2 turns No. 20 B.T., 1.4" long, closewound, 10/32" slug tuned coil forms 15/64"

Figure 321.

00, shield can V2" x V2" X l"i slug-carbonyl
S.F. or equiv.
= 2Y2 turns No. 20 B.T., %" long, closewound, 10/32" slug tuned coil forms 15/64"
00, shield can '/2" x 1/2" x l"i slug
carbonyl S.F. or equiv.

= 2 turns No. 20 B.T., 3/16" D, 3/16"· long

RFC
4 turns No. 30 enamel wire, ferrite bead,
Ferroxcube No. 56-590-65/4B or equiv.

VHF marine-band multiplier-amplifier.

a low-pass filter), this section
may be used to provide the
maximum power output of 1 watt
specified for harbor communications.
Each frequency-m u It i p lie r
stage uses an RCA-40637 transistor, and the power-output
stage uses an RCA-40280 transistor. The 5-milliwatt I3-MHz
input signal applied to the first
multiplier stage (tripler) from
the exciter section of the transmitter is sufficient to saturate
the multiplier stages; as a re-

sult, any amplitude modulation
generated in the frequencymultiplier stages is eliminated.
The second and third multiplier
stages operate as frequency
doublers.
Emitter-bias resistors are used
in the multiplier stages to reduce
current drain and dissipation in
the multiplier transistors. The
coupling between·· stages is accomplished by double-tuned coils
to achieve maximum rejection of
unwanted frequencies. The impedance transformation from the

RCA Silicon Power Circuits Manual

298

preceding collector to the following base is made possible
through the use of a capacitive
divider, which also forms a part
of the resonant circuits. Heat
sinks are not required for the
first two multiplier transistors.
The third multiplier and the amplifier transistors require fin
radiators. The output from the
second doubler is 100 milliwatts
at 156 MHz. With 100 milliwatts
into the power-amplifier stage,
either the ouput to the antenna
or the input to the power-amplifier section of the transmitter is
1 watt.
Power
Amplifier-When
a
power output greater than 1
watt is required, the poweramplifier section of the transmitter provides two additional
stages of power amplification.
Fg. 322 shows a schematic diagram for the power amplifier.
This circuit uses an RCA-40281
transistor in the driver stage
and an RCA-40282 transistor in
the output stage. With the 1-

watt, 156-MHz output from the
multiplier-amplifier applied to
the driver stage, the power amplifier provides more than 10
watts of power output.

CITIZENS-BAND
TRANSMITTERS
The Federal Communications
Commission established the citizens band (CB) with 23 channels
near 27 MHz and 48 channels near
465 MHz for business and personal use. Although many restrictions exist on transmitters for
these bands and on the operating
procedures, there are few restrictions and no technical requirements imposed upon the operators.
As a result, the citizens band has
become very popular.
Some of the equipment restrictions are listed in Table XXX.
Most notable of the restrictions is
the maximum dc input power to
the final transmitter stage. Many
restrictions on production qualification, on harmonic interference,
and on operation are detailed by

Vcc+

~.o
PO=II.5W
Z=50n

156 MHz

e4, C5, C6, Areo 404 or equiv.
CT, C. = 0.022 p.F, 25 V
C8, C1. = 1000 pF, ceramic standoff
Lt, L. = 1 turn No. 20 wire, 1/.1" 10, 3/32" long

Cl, C2, C3,

Figure 322.

h, L. = 1112 turns No. 20 wire, 1/4" 10, 3/32"
long
L. = 2 turns No. 18 wire, 1/.1" 10,5/16" long
RFC = 4 turns No. 30 wire, ferrite beod Ferroxcube No. 56-590-65/48 or equiv.

iS6-MHz marine-band power amplifier.

299

High-Frequency Power Amplifiers

Table XXX-FCC Specifications for Citizens-Band Transmitters
Use
Signaling
Communications

Classification
Class C"
Class D"
Class A"

Handy-Talky
Control Model
Aircraft
Communications

Restricted ""
Radiation
Device
Class C"
Class B"

Frequency
5 channels
26.955-27.255 MHz
27.255 MHz
23 channels
near 27 MHz
48 channels
462.55-466.45 MHz
Same band as
Class D, but
not channels
5 channels
72.08-75.64 MHz
All Class A
frequencies plus
465.00 MHz

Max DC
Input
Power

Formal
License

Other
Restrictions

5W
30 W
5W

Yes 1
Yes 1
Yes 1

60 W

Yes 1

No Voice
No. Voice
AM or SSB Modulation,
crystal-controlled

0.1 W

AM or SSB
modulation

5W
5W

Yes 1

1 Type Approval Re~uired.
" Current FCC restrictions detailed in Vol. VI, Part 97 of FCC Regulations.
"" Current FCC restrictions detailed in FCC Regulations.
(These units are not, in fact, CB sets, but share the same frequency band with CB.)

the FCC in the publications listed.
Canada also established a citizens
band with channels common to
FCC specifications. Other Canadian specifications are different;
licensing is not reciprocal.
There are three popular types of
citizens-band transmitters. The
most popular type is the 100-milliwatt hand-held transceiver, which
usually incorporates small-signal
transistors. The second type in
popularity is the "full-5-watt" set
designed for maximum operating
range with from 5 to 23 channels.
The dc voltage supply used in the
full-5-watt set is 13.6 volts for
both fixed and mobile locations.
The third type of set is hand-held
and operates on batteries, but has
a transmitter power capability of
1 or 2 watts and provides more
range than the 100-milliwatt sets.
Extra features are added to
each type to interest hobbyists.
For business use, for example, extra quality is built in. In every
design, however, cost is very im-

portant because the citizens-band
market is highly competitive.
Design Problems
Amplitude modulation in a
transistorized citizens-band transmitter is an important design
consideration. The peak upwardmodulation power requirement
must be met by the transistors.
The theoretical requirement is for
a PEP of 4 times the cw power.
This requirement is seldom met
because of both technical and economic reasons. Unfortunately,
there is no standard for the quality of the modulation. It has been
referred to as "talk power", although there is no definition for
this term. The quality of modulation directly influences the range
and performance of the transmitter. However, good modulation is
difficult to achieve and is expensive. Because no specification exists, it is often compromised.
. The citizens-band equipment appeals to non-technical persons who

300

RCA Silicon Power Circuits Manual

generally assume the equipment
to be foolproof. A particularly
dangerous type of mistreatment is
operation into a mismatched antenna/transmission-line combination. This type of operation may
cause low power output and spurious outputs and oscillations, or
may destroy transmitter transistors. A mismatched transmitter
load condition must be evaluated
carefully. Some transistor manufacturers recommend only certain
transistor types for citizens-band
AM service. The best transistors
for citizens-band transmitters can
withstand any antenna or transmission-line faults without damage.
The 23 channels available for
citizens-band operation at 27
MHz have close frequency spacing; consequently, transmitter circuits that have a moderate loaded
Q cannot operate at any channel
without retuning. Harmonic-output specifications are strictly enforced by the FCC and require
extra care in circuit design. Additional harmonic filtering is required at the output of the transmitter and usually takes the form
of a pi-network, low-pass filter.
Because fundamental-frequency
oscillators are normally used,
there is no output below the operating frequency and no filtering is
needed below this frequency.

12 V SUPPLY

Design Example and
Transistor Requirements
The most popular circuit for 5watt (input) transmitters is one
that employs three stages. An oscillator stage employing a thirdovertone crystal rated at a dissipation of 2 milliwatts is used to
establish the frequency. This stage
drives a class C intermediate amplifier which, in turn, drives an
output stage. The last two stages
are collector-modulated. A block
diagram of this arrangement is
shown in Fig. 323.
This circuit is popular because
it uses an economic combination
of available transistors. The 12volt supply is readily available in
automobiles and easily generated
in a base station and, when amplitude-modulated, rises to 24-volt
peaks. The 12-volt supply is almost
universally accepted in transistorized citizens-band set designs.
The modulator portion of the
5-watt transmitter can be operated in either the class A or the
class B push-pull mode. The
class A output type requires continuous dissipation of approximately 7 watts in either "receive"
or "transmit" operating modes.
The push-pull class B output
type draws little power during
"receive" and "transmit" operating modes, and almost no power
12V MOD.

124 V PEAK)

EXTRA HARMONIC
FILTERING

Figure 323.

Block diagram of a 5·watt (dc input power to final amplifier) citizens-band
transmitter.

High-Frequency Power Amplifiers
during standby. This advantage
is particularly important in battery-operated transceivers. The
class B modulator requires
smaller heat sinks, but larger
transformers, than the class A
type. Each circuit has been used
in 5-watt CB transmitters.
The requirements for the transistors in the circuit of Fig. 323
were considered when the circuits were selected; the selection of the best circuit and the
selection of the best transistor for
that circuit are in no way independent. The best guide for selection of a circuit is a comparison
of the circuits and transistors recommended by the transistor manufacturer. The cost of the transistors greatly affects the cost of the
circuit; therefore, the transistors
must be carefully selected.
The oscillator stage operates at
the output frequency determined
by the crystal (Le., at the third
harmonic of the crystal). This output frequency must be held constant to within ±0.005 per cent to
meet FCC requirements. The crystals employed usually have a dissipation limit of 2 milliwatts. The
dissipation limit is based on economic considerations and on the
loss of frequency accuracy caused
by increases in dissipation. The
dissipation limit restricts the
available 27-MHz power output of
the oscillator stage. The power
level is low, and the stage is usually designed for class A bias to
assure starting without introduction of a dissipation problem in
the transistor. A gain of 17 dB
can be obtained from low-cost silicon transistors. This gain provides a minimum rf output of 100
milliwatts from the oscillator.
The output stage is designed
for maximum cw power output

301
within the FCC limit of 5 watts
of dc input power. RF output of
more than 3 watts is typical. The
output stage must also withstand
operation into mismatched loads.
The output stage is required to
deliver more than 3 watts of output when modulated; a theoretical
peak envelope power (PEP) of
four times the 3-watt cw output
can be obtained at 100-per-cent
modulation. The four-times capability is not usually achieved because of the increase in rf V.at
of transistors at high current, the
decrease in transistor gain at high
currents, and modulator losses (as
explained in the general section on
AM). Although no standards exist, a PEP of 9 watts, or three
times the 3-watt cw power (Le.,
85-per-cent modulation) is considered good modulation. This
power is obtained by modulating
the collector supply voltage of the
output transistor from a nominal
value of 12 volts to a peak value
of 24 volts. Therefore, the output
transistor must deliver 9 watts at
27 MHz with a 24-volt supply. The
requirements for the output transistor are listed in Table XXXI.
The
intermediate amplifier
(driver) must make up the difference between the rf drive required by the output stage and
the rf power supplied by the oscillator. For the circuit discussed,
the driver stage must increase the
oscillator output of 100 milliwatts
to 1 watt at the modulation peaks;
this increase corresponds to a
gain of 10 dB. Unmodulated, the
required gain is 100 to 400 milliwatts, or 6 dB.
Again, the modulation peaks
dominate transistor requirements.
It is best to take advantage of the
high supply voltage available from
the modulated supply, rather than

302

RCA Silicon Power Circuits Manual

Table XXXI-CB Transmitter Transistor Requirements
Output Am8lifier
Modulated
nmodulated
Oscillator
Operation
Crysta I-Control Ied
Modulated RF Amplifier
Oscillator
Designed for
Min. Crystal Diss.
Maximum Efficiency
(gain "")
Max. P.O. (gain)
Operating Mode
Class A required
Class C
for starting
Supply Voltage
12 V"
24 V"
12 V"
Typical Performance 17 d'S min. gain
9 W out·· min. 3 W out
2 mW crystal diss.
max. 5 W in
Operating Current
35 rnA Typical
415 rnA max.
Breakdown Voltage
24 V·
24 V·
48 V·
Reverse bias •••
Mode
Open base
Max. Dissipation
420 mW
See Text
Typ. Dissipation
250 mW
2W
• High line and transients must be added .
•• Parameter is compromised to achieve other requirements .
••• Supplied by rf drive.

to use the straight 12-volt supply,
to obtain the required 6-dB gain.
Thus, modulation of the driver
reduces the required performance
of the driver transistor and, in
addition, reduces circuit cost and
improves modulation linearity.
The distortion caused by power
feedthrough in the output transistor on the downward-modulation
peaks is severe when a constant
1-watt drive is used. Modulation
of the drive to the final amplifier
causes the output transistor to
operate at nearly constant gain,
rather than at constant drive, and
reduces the feedthrough effect.
The intermediate amplifier, therefore, is modulated and supplies a
PEP of 1 watt with a 24-volt supply and a constant 100-milliwatt
drive. The intermediate amplifier
is usually operated with reverse
bias to improve efficiency, primarily because the use of this bias
mode reduces the dissipation requirements of the transistor and
the power-output requirements of
the modulator. The requirements
for a transistor for the intermediate amplifier are also listed in

Intermediate Amplifier
Modulated Unmodulated
Modulated RF Amplifier
Efficiency"" and Gain
Class C
24 V·
1W

12 V·
0.4 W

75 rnA
24 V·
48 V·
Reverse bias •••
0.5 W

Table XXXI.
The modulator circuit must
supply audio power to the transmitter equal to one-half the dc
input power. For the transmitter
circuit described, the dc input
power is the sum of the input
power to the output stage (5
watts) and the input power to the
intermediate amplifier (12 V X 75
mA = 90 mW). The audio power
must be nearly 3· watts to modulate the transmitter fully. The
audio input originates at a microphone. A large amount of audio
amplification is necessary in the
small-signal class A stage (microphone amplifier). The microphone
amplifier is followed by an audio
power amplifier which must deliver audio power of 3 watts.
Either a class A or a class B
push-pull audio power amplifier
may be used.
The efficiency of a class A output stage approaches 50 per cent
at full output power. If allowance
is made for some change in bias
current and some transformer
losses, the nominal dissipation is
approximately 7 watts. The tran-

High-Frequency Power Amplifiers
sistor must be capable of withstanding this dissipation at high
ambient temperatures (approaching 75°C). The results of calculations of required thermal resistance for the modulator output
transistor are given in Table
XXXII.
Table XXXII-Modulator OutputTransistor Requirements

Designed for

No. of Transistors
Audio Input Power
Supply Voltage
Operating Current:
Peak
Average
Breakdown Voltage
Mode

Class A
Type
Class A
Amplifier
3 W Audio
Output
1

Class B
Push-Pull
Type
Class B
3 W Audio
Output
2

12 V·

1.0 A
0.5 A
24 V·
Low

0.5 A
0.2 A
24 V·
Reverse
Bias •••
0

Dissipation: Con7W
tinuous
Talk Time
1.5 W each
7W
Max. Thermal Resistance (Transistor and
125°C/W
Heat Sink for 75°C 17°C/W
Ambient)
• High Iine voltage and transients must be
added.
•• This parameter is compromised to achieve
other requirements .
••• Supplied by audio drive power.

The peak operating current for
the output transistor can be calculated as 1 ampere. The gain of
the circuit may be calculated from
the characteristics of the transistor selected at a peak current of
1 ampere and the operating junction temperature.
A class B push-pull modulator
requires two power transistors
and two transformers, but reduces
idling current. The idling current
is only that required to reduce
cross-over distortion, approximately 20 milliamperes in each

303
transistor. This idling current results in a dissipation of 13.6 V X
0.020 A = 0.272 watt in each transistor. When a signal is present,
the transistor dissipation rises.
The peak dissipation occurs at 40
per cent of the rated output power
and is equal to 20 per cent of the
rated output power. For the example, the worst-case transistor
dissipation is 0.272 W + (0.2 X
3) W, or less than 0.9 watt. It is
possible, therefore, to use simple
finned heat sinks and to wire the
transistors on the printed-circuit
board. Heat sinks are supplied
with certain RCA transistors. The
transistors must handle a peak
current of 0.5 ampere; gain may
be calculated on the basis of the
highest junction temperature expected with the heat sinks used.
This gain is usually higher than
that for the class A circuit.
In selection of the output transformer for the modulator, many
factors must be considered, not
the least of which are cost and
size. The transformer is required
to match the output impedance of
the modulator to the speaker used
for public address and receiver
service. It must have a winding
to modulate the transmitter supply voltage with an impedance of
VCC/IDC' The unbalanced direct
current through this winding cannot be allowed to saturate the
transformer. The winding must
have a low dc resistance to reduce
the voltage for the rf transistors
and decrease the upward modulation. The windings driven by the
modulator transistors must have
a low dc resistance. An unbalanced direct current may also flow
through this winding.
A complete circuit design for
a CB transmitter and modulator
is shown in Fig. 324. This circuit uses straight-forward design

RCA~ilicon

304

Power Circuits Manual

+IITOI5V
C:t
Lt

Arco No. 429 or equiv.
= 14:3 turns No. 22 wire, 1/4" crc
coil form with "green dot" core,
0.75-1.2 pH, Q
100
L.2
1.4:2 3/4 turns No. 22 wire, 114"
eTC coil form with "green dott' core,
0.75-1.2 pH, Q ::::: 100

=
=

11 turns No. 22 wire, 'I." CTC
coil form with .. green dot" core,
0.5-0.9 pH, Q
120
L.
7 turns No. 22 wire, '14" CTC
coil form with "green dot" core,
0.21-0.34 /LH, Q = 140
RFCl, RFCs
15 /LH, Miller No. 4624
La

or equiv.

Figure 324. 27-MHz citizens-band transmitter.

methods and has the following
features:
(1) It can be economically produced.
(2) The number of tuning components is minimized. The rf
transformers, Ll and L2 , have
only on~ adjustment, which varies
both coupling and inductance.
However, one adjustment cannot
optimize both resonance and impedance matching. Therefore, the
transformer turns ratio may have
to be varied if any other characteristics are changed. Transformer
L2 may be optimized by changing the values of the 47- and 51picofarad capacitors.
(3) The output stage is coupled
to the transmission line and antenna through a double-pi network. This network reduces the
harmonic output below the 50-dB
reduction required by the FCC.
One section of the double-pi network should always be peaked for
maximum output; the other sec-

tion is adjusted to a limit of 5
watts dc input to the final amplifier as required by the FCC.

MOBILE RADIO
In the United States, three frequency bands have been assigned
to two-way mobile radio communications by the Federal Communications Commission. These fre~
quency bands are 25 to 50 MHz,
148 to 174 MHz, and 450 to 470
MHz. The low-frequency band for
overseas mobile communications
is 66 to 88 MHz.
Frequency modulation (FM) is
practiced in mobile radio communications in the United States
and most overseas countries. The
modulation is achieved by phasemodulation of the oscillator frequencies (usually the 12th or 18th
submultiple of the operating frequency). In vhf bands, the frequency deviation is ±5 kHz and
channel spacing is 25 kHz. In uhf

305

High-Frequency Power Amplifiers
bands, at present, the modulation
deviation is ±15 kHz and channel
spacing is 50 kHz. In the United
Kingdom, AM as well as FM is
used in mobile communications.
The minimum mobile-transmitter power-output levels in the
United States are 50 watts in the
50-MHz band, 30 watts in the 174MHz band, and 15 watts in the
470-MHz band. Some of the transmitters used in the United States
have power-output ratings as high
as 100 watts. Overseas, poweroutput requirements are much
more moderate; the most common
power-output levels are in the 10watt range.

Cost Considerations
Today, all-solid-state mobile radios still cost more than vacuumtube radios that have equivalent
power-output ratings. However,
all-solid··state mobile radios permit
lower operating costs because they
. are relatively maintenance-free. In
many mobile-radio applications
(such as in ambulances, police patrol cars, and fire-fighting equipment) where failures cannot be
evaluated in terms of money, solidstate radio equipment is the only
logical choice. Even in less critical
services (such as taxicab or truck
dispatching), down-time on communications equipment is difficult
to tolerate and is usually costly.

Transistor Requirements
The transistors in the rf power
stages are the heart of every solidstate transmitter. In fact, the
present frequency and power capabilities of these transistors constitute one of the major limitations
to the advance of new mobiletransmitter design. For example,

one of the basic requirements for
a good rf power transistor is high
fT (appreciable current gains at
high radio frequencies). Other requirements are high power dissipation and current-handling capability. However, these requirements
are conflicting. Good current-handling capability requires a large
emitter periphery, while high
gains at high frequencies require
that capacitances, and thus emitter area, be minimized. Some
overlay transistors have emitter
periphery-to-area ratios of 10 to
20 mils of emitter edge per square
mil of emitter area, and 1 to 2
mils of emitter edge per square
mil of base area; these transistors
satisfy the requirements for rf
power stages very well.

DC Operating VOltages
All-solid-state mobile transmitters can be divided into two basic
types: transmitters that operate
from 24- to 28-volt collector supply
voltages, obtained from dc-to-dc
converters, and transmitters that
operate directly from the 12-volt
electrical system of a vehicle.
Both types have advantages and
disadvantages. The advantages of
24- to 28-volt operation include
higher power gains per stage,
good transient suppression, and
fairly simple current and voltage
limiting. The disadvantages are
the additional cost of dc-to-dc converters and the somewhat higher
power consumption and increased
size of the radio. Direct operation
from a 12-volt system permits savings in cost and size, as well as
higher efficiency. Because 12-volt
operation produces less gain per
stage, however, additional rf
stages are often needed. Transient
suppression and voltage and cur-

306

RCA Silicon Power Circuits Manual

rent limiting are also somewhat
more difficult.
Because of the two discrete
voltage ranges used for mobile
radios, the transistor must be designed specifically for either 24- to
28-volt operation or 12~volt operation. Devices designed for 24- to
28-volt operation have substantially higher collector-breakdown
voltages. In addition, all elements
are usually isolated from the case
to permit access to the emitter.
The use of an emitter-biasing resistor is of great importance at
these operating voltages because it
contributes to good reliability under mismatched load conditions.
Transistors intended for 12-volt
operation have very high peakcurrent capability to realize substantial amounts of rf power at
low voltage. The emitter electrode
is usually connected to the case
internally so that inductance in
the emitter path and, consequently, gain degeneration are kept to
a minimum. If reverse biasing is
desired in grounded-emitter amplifiers, it can be obtained by use
of a resistor in the base circuit.
Matching Networks

The design of high-power, highfrequency transistor amplifiers
presents unique problems. Low operating voltages and relatively
high power levels result in impedances that become very small and
circulating rf currents that become very large. For example, if
an rf power output of 60 watts is
required from an amplifier operating directly from a 12-volt supply,
the collector load impedance to the
final amplifier must be approximately 1 ohm. Under these conditions, the peak current can be

as high as 20 amperes. In view
of these factors, the well-proven
vacuum-tube techniques become
practically useless. Because the
collector-to-base capac'itance of the
transistor is voltage-dependent,
the neutralization of large-signal
transistor amplifiers is impractical.
It has been observed that
large-signal transistor amplifiers
perform best when the output
matching circuit presents a high
impedance to the harmonic currents generated at the collector.
The design of such networks was
discussed previously in the section on Network Design.
Parallel Operation of
Output Transistors

In applications that require
more rf power output than one
transistor can deliver, two or more
transistors must be operated in
parallel. Parallel operation in transistor circuits is somewhat more
complex than in vacuum-tube circuits. The main problem is to
assure that the load and collector
currents are shared equally by all
transistors in the parallel array.
For this reason, the bases of the
transistors should not be tied together directly, but rather should
be connected through individual
base-input coils which allow adjustment of drive to the individual
transistors. The collectors of the
paralleled transistors can be tied
together directly, as is the usual
practice in lower-power amplifiers
operating from 24- to 28-volt supplies, in which collector load impedances are relatively high. For
best parallel-operation efficiency in
amplifiers operating from 12-volt
supplies, where low collector load
impedances are encountered, the

307

High-Frequency Power Amplifiers

collectors of the transistors should
be connected through individual
collector coils. This technique permits parallel operation at higher
impedance levels. Fig. 325 shows
a circuit diagram of a 50-MHz
power amplifier that delivers 60
watts with 12-volt collector supply
voltage; this circuit demonstrates
the techniques described.
Instabilities in VHF
Transistor Amplifiers

In transistor vhf power amplifiers. the most common instabiIi-

ties occur at frequencies far below
operating frequency because the
gain of the transistor increases at
a rate of approximately 6 dB per
octave as the frequency decreases.
For example, a device that has a
power gain of 5 dB at 174 MHz
may have a gain of as much as 30
dB at 10 MHz. With such high
gain, any kind of stray low-frequency resonant circuits can set
the circuit into violent oscillation
and even cause destruction of the
transistor.
These low-frequency oscillations
can be prevented by means of the

C1, Ca

= 65
=

Ca, C.
100
Co, Y, c. =
Co, Y, YO =
ell 0.2 pF

340 pF
- 560 pF
1000 pF, feedlhru
1800 pF ceramic
ceramic

b''1.L,~, I~~g=

2·'12
Lo, 4, L. = 3·'12

tis;1 long
L'I", La, b
'12"~~

"::"

lurns No. 16 wire,

%2" 10,

lurns No. 18 wire,

'14" 10,

turns

No.

1.4 wire,

3/."

10,

bo = ferrile choke, Z
450 ohms
Note: For coils It-La, use General Ceramics Co.
Q. malerial 1'1." - 28 x 3fs") or equiv.

Figure 325.

ell

Vee +

12 V
50·MHz parallel·transistor power amplifier that delivers 50 watts of output
power from a 12·volt de supply.

RCA Silicon Power Circuits Manual

308

following simple precautions, as
indicated in Fig. 326:
(1) Because the base-emitter
junction is highly capacitive at
low frequencies, a resonant circuit can be easily formed with this
capacitance and the choke RFC.

Figure 326. Circuit indicating areas where
simple precautions prevent low-frequency
osci liations.

This low-frequency resonant circuit can be avoided by the replacement of RFC with a low-Q, ferritetype choke or even a wire-wound
resistor.
(2) The emitter bypassing
should be effective not only at
operating frequencies, but also at
low frequencies; thus, two bypassing capacitors should be used. One
of these capacitors should be effective at operating frequency, and
the other at low frequencies.
(3) DC-power wiring should
have adequate bypassing both at
operating and low frequencies to
shunt out stray inductances in the
wiring.
(4) Output-matching networks
should make use of a coil as an
integral part of matching for feeding dc to the collector. As a rule,
the inductance of these coils is
much smaller than that of selfresonant rf chokes, and thu.s the
reactances are lower at low frequencies.

17S-MHz Power Amplifier
Fig. 327 shows a 175-MHz amplifier-chain design that incorpo-

rates the techniques discussed for
calculating matching networks and
avoiding low-frequency oscillations. The amplifier operates from
a 12-volt collector supply and delivers 35 watts at 175 MHz with
an input of 125 milliwatts. The
over-all efficiency of the amplifier
chain is 60 per cent. The first part
of the amplifier, Fig. 327(a), consists of three stages that provide
output powers of 1, 4, and 12
watts from each consecutive stage.
The second part of the amplifier,
Fig. 327 (b), has only one stage
consisting of three transistors in
parallel. This stage delivers 35
watts of power with a 12-watt rf
input.

Reliability
Mobile-radio application places
a severe requirement on transistors. The devices must withstand
the no-load conditions created by
objects near the transmitting antenna, or a break in the transmission line anywhere between zero
and half wave length. Under these
conditions, the transistors must
handle not only increased dissipation, but also sudden energy
surges that can destroy them in a
matter of microseconds.
The development of transmitters immune to these failures is a
result of a joint effort between
semiconductor-device and mobileradio manufacturers. To avoid excessive junction temperatures, the
equipment manufacturer must select transistors of sufficiently low
thermal resistance. If a transistor
lacks enough dissipation capability, two should be used, even
though one could deliver the required rf output power. To protect
the devices under high-ambienttemperature operating conditions,
it is necessary to use adequately

309

High-Frequency Power Amplifiers

12V

(a)

u =

3.35 pF

Co, Co, uo, c..
8.60 pF
Ca, C., Cll
0.01 p.F
c., Ca, Cu 1500 pF
Co, ClO, Cu, u., c.a
7 Co = 14 - 150 pF
C", = 1.5 - 20 pF
u., C1o, C10
0.2 pF
Coo, em, c.. = 1500 pF

=
=

100 pF

12 V

=
h

1/.."

~6"

2 turns No. 16 wire,
long

= ferrite rf choke, Z
Lll = rf choke, I p.H

L., h, L.
ohms

La, L.,
L4, L-z
ID,

3 turns No. 16 wire,

= 1/,,"11/2longturns
ID, 3/." long

Lto

No. 16

wire,

2 turns No. 16 wire,

~6" long

Lu, Lu, Ll4,

= 3 12
1

10,

12 V

= 450
~6"

'/.. "

V,," ID,

turns No. 16 wire,

'14" 10, 3'8" long (slug tuned)

= 2 turns
V," ID, Va" long
Lts, Ln, L20 = 2 turns

L15, be, It'2'

1/./' 10, '/.. " long

No. 18 wire,

(bl

Figure 327. 175-MHz power-amplifier chain
that delivers 35 watts of power output for
an input of 125 milliwatts: (a) three-stage
input section (Pin
125 mW; Po
12 W);
12 W; Po
35 W).
(b) output stage (Pin

=
=

12 V

310

RCA Silicon Power Circuits Manual

sized heat sinks, as well as current
limiting to prevent excessive junction temperature rise under mismatched load conditions. As an
added precaution, a thermostat
can be mounted on the heat sink
to reduce the transmitter power
in the event that the temperature
becomes excessive.
The protection of transistors
from instantaneous failure is more
difficult because the time response
of current or voltage limiters is
not fast enough. Biasing the emitters of transistors operating from
24- to 28-volt supplies helps to prevent this type of failure. Fig. 328
shows a circuit which is sufficiently fast in response time to protect
the devices from instantaneous
energy surges that result from
mismatched load conditions. This
circuit operates on the principle
of reflected power. Under matched
load conditions, there is no output
from the VSWR detector. The control amplifier is saturated, and the
gain-controlled rf amplifier operates at maximum gain. For this
condition, maximum power output
is obtained from the power amplifier. If a mismatch occurs, a nega-

tive voltage from the VSWR
bridge brings the control amplifier
out of saturation and thus reduces
the gain in the gain-controlled rf
amplifier. Gain is reduced because
the base of therf amplifier becomes more negative with respect
to the emitter, and because the
unsaturated control amplifier has
a degenerative effect on the rf
amplifier. Because the gain of the
gain-controlled rf amplifier is reduced, the drive to the power
amplifier is decreased to safe
levels. Once the load mismatch is
removed, the system returns instantaneously to normal operating
conditions.
SINGLE·SIDEBAND
TRANSMITTERS

The increase in communication
traffic, especially in the hf and vhf
ranges, necessitates more effective
use of the frequency spectrum so
that more channels can be assigned to a given spectrum. It has
been shown that one of the more
efficient methods of communication is through the use of singlesideband (SSB) techniques. In the
VSWR DETECTOR

r----l

I
I

INPUT

I
I

~~~______~I~

I OUTPUT
I

I
I

l _____ J

Figure 328.

Load·mismatch protection
circuit.

311

High-Frequency Power Amplifiers
past, the power-amplifier stages of
an SSB transmitter invariably employed tubes because of the lack
of suitable high-frequency power
transistors. Recent transistor developments, however, have made
it feasible and practical to design and construct all-solid-state
single-sideband equipment for
both portable and vehicular applications.
Unlike most commercially available rf power transistors, which
are normally designed primarily
for class C operation, an SSB transistor is designed for linear applications and should have a fiat
beta curve for low distortion, and
emitter ballast resistance for
stability and degeneration. In
high-power amplifiers, transistor
junctions experience wide excursions in temperature and a
means must be provided to sense
the collector-junction temperature so that an external circuit
can be used to provide bias compensation to prevent an excessive shift in operating point and
to avoid catastrophic device failure as a result of thermal runaway.

Advantages of SSB Transmission
Single-sideband communication
systems have many advantages
over AM and FM systems. In
areas where reliability of transmission as well as power conservation are of prime concern, SSB
transmitters are usually employed.
The main advantages of SSB operation include reduced power consumption for effective transmission, reduced channel width to
permit more transmitters to be
operated within a given frequency
range, and improved signal-tonoise ratio.

In a conventional lOO-per-cent
modulated AM transmitter, twothirds of the total power delivered
by the power amplifier is at the
carrier frequency, and contributes
nothing to the transmission of
intelligence. The remaining third
of the total radiated power is distributed equally between the two
sidebands. Because both sidebands
are identical in intelligence content, the transmission of one sideband would be sufficient. In AM,
therefore, only one-sixth of the
total rf power is fully utilized. In
an SSB system, no power is transmitted in the suppressed sideband,
and power in the carrier is greatly
reduced or eliminated; as a result,
the dc power requirement is substantially reduced. In other words,
for the same dc input power, the
peak useful output power of an
SSB transmitter, in which the
carrier is completely suppressed,
is theoretically six times that of
a conventional AM transmitter.
Another advantage of SSB
transmission is that elimination
of one sideband reduces the channel width required for transmission to one-half that required for
AM transmission. Theoretically,
therefore, two SSB transmitters
can be operated within a frequency spectrum that is normally
required for one AM transmitter..
In a single-sideband system, the
signal-to-noise power ratio is eight
times as great as that of a fully
modulated double-sideband system
for the same peak power.

Analysis of SSB Signal
A single-sideband signal is usually generated at low level and
then amplified through a chain of
linear amplifiers to the desired
power. The two most commonly

312

RCA Silicon Power Circuits Manuar

used
band
type
type

methods of generating sidesignals are with the filtergenerator and the phasinggenerator.
It can be shown mathematically
that a single-sideband signal is
derived from an amplitude-modulated wave. If an rf carrier frequency is modulated by an audio
frequency, the resulting AM wave
can be expressed by the following
equation:
e

Eo (l+m cos 271" fm t) sin 271" fe t

Eo sin 271" fe t
+ m Eo cos 271" fm t sin 271" fe t
(297)

in which fm is the audio modulating frequency, fe is the carrier
frequency, and m is the per-centmodulation factor. Expansion of
the last term of this equation into
functions of sum and difference
angles by the usual trigonometric
formulas results in the following
expression:
e = Eo sin 271" fe t
+ (m Eo/2) sin 271" (fc+fm ) t
+ (m Eo/2) sin 271" (fe-fm) t
(298)

This equation contains three
components, each of which represents a wave. The first wave, represented by the term Eosin27Tfet,
is called the carrier. It is present
with or without modulation and
maintains a constant average amplitude at a frequency f e. The
other two components of the equation represent waves that have
equal amplitude, but frequencies
above and below the carrier frequency by the amount of the modulating frequency. These components contain identical intelligence

and are called sideband frequencies. The amplitude of the sideband frequencies depends on the
degree of modulation (m). The
higher the m factor, the greater
the "talk power." Because only the
sidebands transmit intelligence
and because each sideband is a
mirror image of the other, it is
reasonable to assume that if the
carrier and one sideband are eliminated, the remaining sideband is
adequate for transmission of intelligence. This technique is applied in single-sideband transmission.
As mentioned previously, the
elimination of one sideband reduces the bandwidth" required by
one half. This advantage is not
fully realized unless the transmitter has the capability to amplify
a signal linearly without introducing distortion products. Excessive distortion nullifies the advantage of reduced bandwidth in SSB
transmission by generating unwanted frequencies which occupy
segments of the spectrum that are
allocated for other transmitters.
The main objection to this distortion is not that it seriously affects
intelligibility of the signal in the
passband, but that it radiates rf
energy on both sides of the passband and interferes with adjacent
channels.

Linearity Test
For an amplifier to be linear, a
relationship must exist such that
the output voltage is directly proportional to the input voltage for
all signal amplitudes. Because a
single-frequency signal in a perfectly linear single-sideband system remains unchanged at all
points in the signal path, the signal cann'ot be distinguished from
a cw signal or from an unmodu-

313

High-Frequency Power Amplifiers

lated carrier of an AM transmitter. To measure the linearity of
an amplifier, it is necessary to use
a signal that varies in amplitude.
In the method commonly used to
measure nonlinear distortion, two
sine-wave voltages of different
frequencies are applied to the amplifier input simultaneously, and
the sum, difference, and various
combination frequencies that are
produced by nonlinearities of
the amplifier are observed. A frequency difference of 1 to 2 kHz is
used widely for this purpose. A
typical two-tone signal without
distortion, as displayed on a spectrum analyzer, is shown in Fig.
329. The resultant signal envelope

'2.

FREQUENCY

Figure 329. Frequency spectrum for a
tY,Jlcal two-tone signal without distortion.

varies continuously between zero
and maximum at an audio-frequency rate. When the signals are
in phase, the peak of the twofrequency envelope is limited by
the voltage and current ratings of
the transistor to the same power
rating as that for the single-frequency case. Because the amplitude of each two-tone frequency
is equal to one-half the cw amplitude under peak power condition,
the average power of one tone of
a two-tone signal is one-fourth the
single-frequency power. For two
tones, conversely, the PEP rating
of a single-sideband system is two
times the average power rating.
Intermodulation Distortion
Nonlinearities in an amplifier
generate intermodulation (1M)

distortion. The important 1M
products are those close to the
desired output frequency, which
occur within the pass band and
cannot be filtered out by normal
tuned circuits. If fl and f2 are the
two desired output signals, thirdorder 1M products take the form
2fl - f;! and 2f2 - fl. The matching third-order terms are 2fl + f2
and 2f2 + fl' but these matching
terms correspond to frequencies
near the third harmonic output of
the amplifier and are greatly attenuated by tuned circuits. It is
important to note that only oddorder distortion products appear
near the fundamental frequency.
The frequency spectrum shown in
Fig. 330 illustrates the frequency
relationship of some distortion
products to the test signals fl and
f 2 • All such products are either in
the difference-frequency region or
in the harmonic regions of the
original frequencies. Tuned circuits or filters following the nonlinear elements can effectively remove all products generated by the
even-order components of curvature. Therefore, the second-order
component that produces the second harmonic does not produce
any distortion in a narrow-band
SSB linear amplifier. This factor
~

::>

FIFTH-ORDER

~ L-_L-IL-J......J.......l---t::..-.DI STORTION
NN-N--

N
N7--'7
.: _
_N.!..N
",

t\I

,.,

FREQUENCY

Figure 330. Frequency spectrum showing
the frequency relationship of some distortion products to two test signals " and f2.

explains why class AB and class
B rf amplifiers can be used as
linear amplifiers in SSB equipment even through the collector-

RCA Silicon Power Circuits Manual

314

current pulses contain large
amounts of second-harmonic current. In a wide band linear application, however, it is possible
for harmonics of the operating
frequency to occur within the pass
band of the output circuit. Biasing
the output transistor further into
class AB can greatly reduce the
undesired harmonics. Operation of
two transistors in the push-pull
configuration can also result in
cancellation of even harmonics in
the output.
The signal-to-distortion ratio
(in dB) is the ratio of the amplitude of one test frequency to the
amplitude of the strongest distortion product. A signal-to-distortion specification of -30 dB
means that no distortion product
will exceed this value for a twotone signal level up to the PEP
rating of the amplifier. A typical
presentation of IM distortion for
an RCA developmental transistor at various output-power
levels is shown in Fig. 331.
I
Z

~
::;;l

U1Z

-'"

COLLECTOR BIAS CURRENT- 20 .. A

~; 30

fi~
5 111
~ ~ 400

100

PEAK ENVELOPE POWER OUTPUT-W

1!E

Figure 331. Typical intermodulation distortion in an RCA developmental transistor at various output power levels.

Transistor Requirements
Most high-frequency power
transistors are designed for class
C operation. Forward biasing of
such devices for class AB oper~
ation places them in a region
where second breakdown may oc-

cur. The susceptibility of a transistor to second breakdown is
frequency-dependent. Experimental results indicate that the higher
the frequency response of a transistor, the more severe the secondbreakdown limitation becomes.
For an rf power transistor, the
second-breakdown energy level at
high voltage (greater than 20
volts) becomes a small fraction of
its rated maximum power dissipation. This behavior is one of the
reasons that vacuum tubes have
traditionally been used in singlesideband applications.
A power transistor designed
especially for use as a linear amplifier is required to perform
satisfactorily when forwardbiased for class AB operation,
as well as to exhibit the desired
high-frequency response. The
ability of the transistor to withstand second breakdown is improved by subdividing the emitter into many small sites and resistively ballasting the individual
sites. An RCA developmental
transistor designed specifically
for linear-amplifier service in
SSB applications has an overlay
structure with 540 parallel emitter sites, interconnected with
metal fingers. Current-limiting resistors are placed in series with
each emitter site between the metalizing and the emitter-to-base
junction. The SSB developmental
transistor has a high emitterperiphery-to-collector-area and
-to-emitter-area ratio and thereby
combines good high-current performance with low capacitance.
Physically, second breakdown is
a local thermal-runaway effect induced by severe current concentrations. The evidence of the random distribution of hot spots over
the surface of the unit indicates

315

High-Frequency Power Amplifiers
that second breakdown may occur
anywhere in the transistor. When
a ballast resistor is used in each
emitter site, current concentration
is minimized. Fig. 332 is a schematic representation of the transistor showing the separate emitters with resistors in series with

fect on the device performance.
However, if a large number of
sites are connected in parallel,
high-value individual resistors
(re) can be sustained while a
small total resistance (R t ) is
still maintained at the input of
the transistor, as indicated by the
following relationship:
(I!R t )

Figure 332. Schematic representation of
the separate emitter sites in an "overlay"
transistor with a resistor connected in
series with each site.

each site. The voltage drop across
each site is expressed by the following equation:

VBE

+ ie re

(299)

Changes in VBE have an exponential effect on the emitter current
ie, as follows:
ie

1]
(V - ie re) -1]

= is [e(q/kT) Vn -

[e(q/kT)

(300)
This equation indicates that
when a constant voltage V is applied across the emitter-to-base
junction and resistor network, an
increase in ie at anyone site
causes a rise in the iere voltage
drop which, in turn, results in a
decrease in the current to that
site, Le., the exponential term of
the equation diminishes as the
quantity (V - iere) decreases.
This condition effectively stabilizes that region. The addition of
resistance to the emitters of the
transistor has a degenerative ef-

(I!rel) + (1!re2) + (I!rea)
+ ... + (J!ren)
(301)

A relatively large value of
ballast resistance is desirable for
prevention of second breakdown
and for improvement of thermal
stability and linearity of transfer
characteristics. However, because ballast resistors are in
series with the load, excessive
ballasting can seriously degrade the rf performance of the
transistor. Therefore, in a highfrequency power amplifier with
low supply voltage, the impedance of the emitter resistance can become an appreciable
portion of the reflected load presented to the collector and, as a
result, can limit the power output.
In determining the proper emitterresistance' value, a compromise
must be made empirically so that
sufficient second-breakdown protection is provided without serious effects on rf performance.
The adverse effect of high ballast resistance, besides reduced rf
output power, is the increase in
saturation voltage. Viewed externally, the total saturation voltage
also includes the voltage drop
across the ballast resistance. This
additional voltage makes the
"soft" output characteristics of a
transistor at high-current even
softer. As a result, the available
linear region through which the
signal can swing is limited.

316

RCA Silicon Power Circuits Manual

Examination of the relationship
of 1M distortion to power output
reveals that third-order distortion
increases at both high and low
output levels, as shown in Fig.
331. The inherent decrease in
beta at high current, which causes
variation in gain over a large portion of the collector dynamic characteristics, introduces additional
distortion. The additional distortion is indicated by flattening of
the peak of the sinusoidal swing.
The operation of a transistor
near the saturation region has a
pronounced effect on third-order
distortion. All higher odd-order
distortion products do not seem
to be affected greatly by· transistor operating conditions. The increase in distortion below 20 watts
PEP can be attributed to lack of
sufficient collector quiescent current. Nonlinearity caused by the
voltage-current characteristic of
the base-to-emitter junction affects distortion at low power
levels. Third-order distortion is
improved by use of a higher bias
current, as shown in Fig. 333.

duced. As a result, distortion because of saturation occurs much
sooner. The controlling factor in
determining the proper bias-current level is usually the maximum
distortion that can be tolerated
at a given power output. For a
given transistor type, the bias
point that yields the best compromise between linear performance
and good collector efficiency must
be determined experimentally. A
collector bias current of from 2 to
20 milliamperes for the RCA
SSB developmental transistor is
adequate to deliver 100 watts
PEP. Fig. 334 shows a curve
of power output as a function of
supply voltage with distortion
maintained at -30 dB.

•

~ 100

INTERMODULATION DISTORTION7
-30 dB
/"
COLLECTOR BIAS
o 80 CURRENT. 20 .. A

i...

II:

g
~ 40

III

I
Z

II:..J

~c 20 PEAK ENVELOPE POWER
m· Z
-ell
OUTPUT-IO W
Qm

~~30
-0

!c..J
..Jill

2012

16
20
24
28
32
COLLECTOR SUPPLY VOLTAGE-V

Figure 334. Peak envelope power as a
function of cOllector sUflply vOltaJe for
the RCA SSB developmental transistor.
~

:)111

i!ll40 1

ffi

...~

6 810

Bias Control

COLLECTOR BIAS CURRENT-lOA

Figure 333. Intermodulation distortion as
a function of collector bias current for the
RCA SSB developmental transistor.

If collector bias current is set
too high initially, in an attempt to
improve linearity at low poweroutput levels, the linear region of
the collector characteristic is re-

Operation of the transistor in a
class AB amplifier to improve
linearity requires the use of a
positive base voltage for an n-p-n
silicon transistor. The magnitude
of the positive voltage must be
large enough to bias the transistor
to a point slightly beyond the
threshold of collector-current conduction. The class AB bias condi-

High-Frequency Power Amplifiers
tion must be maintained over a
wide temperature range to prevent an increase in idling current
to the level at which the transistor can be destroyed as a result of
thermal runaway and to minimize
distortion that results from a shift
in the quiescent point.
It is particularly difficult to
maintain the bias current of a
transistor high-power class AB
amplifier at a constant level. As
the drive increases, the dissipation increases and the junction
temperature rises. If the conventional biasing technique is employed (an ac-bypassed emitter
resistor and a constant voltage
supply to the base), the varying
emitter current that results from
the varying drive changes the
voltage drop across the emitter
resistor and causes the bias to
shift with drive. If a constantcurrent base-bias supply is used,
the drive power is rectified and
the bias point is changed.
The problem of maintaining a
stable quiescent current is caused
by a reduction in the VBE of the
transistor when the temperature
rises. The base-to-emitter voltage
decreases at a rate of approximately 2 millivolts per ·C rise in
. temperature. Unless this condition
is compensated for (i.e., bias voltage made to vary according to the
V BE decrease), the transistor is
destroyed by the thermal effects.
Bias-point control for the 88B
developmental transistor is accomplished by use of a diode
placed next to the transistor pellet in the same package. The
cathode of the diode is connected
internally to the emitter lead. The
anode of the diode is connected
to a fourth terminal, as shown in
Fig. 335. The diode is forwardbiased between 1 to 5 milliamperes
to provide a forward-voltage drop

317

Figure 335. Package outline for the RCA
sse developmental transistor showinl{ internal-package diode used for transistor
bias-point control.

that is temperature-sensitive. At
such a low current the diode operates in the low-conductance region
where it does not provide the stiff
voltage necessary for the transistor bias. In this case, the diode
acts merely as a thermometer; an
external amplifier must be used
for current amplification. Compensation is achieved because the
diode has approximately the same
temperature coefficient for its
forward-voltage drop as does the
base-emitter junction of the
transistor. Good tracking is obtained by mounting the diode
and transistor pellets in the
same case in very close proximity to minimize any thermal
time lag. Temperature coefficient
depends, to a large extent, upon
the operating current. If the diode
current can be adjusted so that
it is approximately equal to the
base current, good compensation
can be achieved. The block diagram of a current amplifier that
uses a low-conductance diode is
shown in Fig. 336.

RCA Silicon Power Circuits Manual

318

RBIAS
OUTPUT
OUTPUT
MATCHING
NETWORK
INPUT
INPUT
MATCHING
NETWORK
RFC

BIAS
CONTROL
AMPLIFIER

RFC

I'- _ _ _ _ _ _ JI
LOW-CONOUCTANCE
COMPENSATING DIODE

Figure 336.

Block diagram of 3O-MHz amplifier that uses a low-conductance diode for
temperature compensation.

The schematic diagram of the
current amplifier is shown in Fig.
337. The current amplifier employs a dc differential amplifier.
The output voltage is the bias
source for the power transistor.
The use of a differential amplifier makes the entire amplifier

relatively insensitive to temperature variations. Two additional
stages are used for current amplification with negative feedback for stability.
Transistor collector-bias current
can be adjusted by varying the
lOO-ohm potentiometer connected
+28V

2000
IpF

2000

12K

(3V)

RBIAS

RFC
'---I~--TO

TRANSISTOR BASE

100

RFC

Figure 337.

TO ANODE OF DIOOE

Linear 3O-MHz amplifier with temperature-compensating circuit.

319

High-Frequency Power Amplifiers
in series with the temperaturecompensating diode. The diode
current established by R bias determines the degree of compensation. Overcompensation occurs
when diode current is greater than
base current. Fig. 338(a) shows
collector quiescent current, initially biased at 10 milliamperes,
as a function of case temperature. With compensation, the
transistor is thermally stable
even for case temperature as high
as 150·C. Without compensation,
however, the transistor tends
toward thermal runaway at a
case temperature of approximately 75"C.
Because both input and output
C
E

ffiloo
II::

II::

a 80

I
I

II::

~ 60

::140

WITHOUT

r--

I
L~r--

ffi
~ ~~

COMPEN~ATION-

!i3

I-

COLLECTOR SUPPLY
VOLTAGlE = 28 V-

COMPENSATION

00 ~ ~ IW I~
CASE TEMPERATURE _·C

(a)

iI
I

~90

ffi

POWER

~
g60

....

1
~ISTOIRTlO~

~ 5020 40 60 80 100 120
~
III
Go

CASE TEMPERATURE _DC

are isolated through rf chokes, the
external circuit provides compensation without degrading the rf
performance of the power amplifier. Fig. 338(b) shows that no
appreciable decrease in output
power nor much increase in the
third-order 1M distortion occurs
with increasing case temperatures up to To
120·C. The
slight decrease in output power
and the increase in distortion, together with a decrease in collector efficiency, can be attributed
to a rise in rf saturation voltage
and a decrease in transistor beta
at high temperature.
Despite the extra circuit needed
to achieve temperature stabilization, the approach provides a
practical solution for achievement of reliable operation of a
class AB amplifier over a wide
temperature range. The use of
a small diode as a temperaturesensing element offers the following advantages:

(a) Diode and transistor pellets need not be matched
for forward-voltage drop.
(b) Transistor quiescent current can be either overcompensated or undercompensated against changes in
temperature by variation
Of the diode current.
(c) A diode idling current as
low as 1 to 5 milliamperes
can be used.
(d) Current of less than 50
milliamperes at 28 volts is
needed to operate the external compensating circuit.

(b)

Figure 338. Performance characteristics for
the 30·MHz amplifier: (a) collector current
as a function of case temperature with and
without temperature compensation; (b) output power and intermodulation distortion as
a function of case temperature.

Typical Linear Amplifier
The common-emitter configuration should be used for the power

RCA Silicon Power Circuits Manual

320

amplifier because of its stability
and high power gain. Tuning is
less critical, and the amplifier is
less sensitive to variations in
parameters among transistors.
The class AB mode is used to obtain low intermodulation distortion. Neither resistive loading nor
neutralization is used to improve
linearity because of the resulting
drastic reduction in power gain;
furthermore, neutralization is difficult for large signals because
parameters such as output capacitance and output and input impedances vary nonlinearly over
the limits of signal swing.
Fig. 339 shows a schematic diagram of a narrow-band, highpower, 30-MHz amplifier. The amplifier provides an output power
in excess of 100 watts PEP from
a 28-volt power supply. The impedance of the base-to-emitter
junction of the RCA SSB developmental transistor in this circuit
is transformed to 50 ohms to
match the impedance of the drive
source. The input circuit to the
transistor can be represented as
·28V

TO OUTPUT OF
COMPENSATING
CIRCUIT

2-TONE

TEST SIGNA
INPUT
I nl~,""",""-4I
(SO,Q)

Cl
C2

= Areo 426 or equiv.
= Areo 427 or equiv.

=
<=. =
Lt =
b =

80-480 pF, Areo 469 or equi •.
140-680 pF, Areo 466 or equi •.
3 turns No. 14 wire, 1/4" 10, '12" long
3 turns No. 10 wire, '12" 10, 3/s" long
3-'12 turns No. 10 wire, 5/8" 10, '12" long

Figure 339.

Narrow-band, high-power 30MHz amplifier.

a resistance (rl>l>') in series with
a capacitance Cj • The input net-

work must tune out the capacitance Ct and must present a pure
resistive load to the driver. The
input network is formed by the
T-network consisting of capacitors C] and C2 and inductor L I •
The value of L1 is chosen so that
the inductive reactance is much
greater than the reactance of Ci'
Series tuning of the base-to-emitter circuit is obtained by L] and
the parallel combination of C2
and C1 , together with the capacitance of the driver stage.
Inductor L2 in the output circuit is selected to resonate with
the transistor output capacitance.
Capacitors Cs and C4 and inductor La provide the proper impedance transformation from 50
ohms to 3.13 ohms at the resonant
frequency. Base-bias voltage is
obtained from the output of the
compensating circuit. If the bias
voltage is not temperature-compensated, both linearity and collecter efficiency can be affected.
When an rf signal is applied to
the amplifier under high-power
conditions, the rectifying property
of the base-to-emitter junction
charges any capacitance present
in the base circuit and transistor.
This charge can alter the bias
point and reduce the angle of conduction; the amplifier then operates more toward class C, and
distortion and efficiency are both
increased.
In low-power linear amplifiers,
the use of temperature-compensating circuits is sometimes not
necessary provided that the transistor output power is less than
50 per cent of its maximum cw
power rating. The RCA-2N5070
transistor is useful in such application. This transistor is specified for SSB applications without
temperature compensation as follows:

321

High-Frequency Power Amplifiers
Frequency = 30 MHz
Po (PEP) at 28 V = 25 W
Power Gain = 13 dB (min.)
Collector Efficiency
40 % (min.)

Fig. 340 shows a 2-to-30-MHz
wideband linear amplifier that
uses other types of RCA rf transistors. At 5 watts (PEP) output,
1M distortion products are more
than 40 dB below one tone of a
two-tone signal. Power gain is
greater than 40 dB.

The SSB Developmental
Transistor
The RCA SSB developmental
transistor is mounted in a
plastic stud package. A diagram of the electrical connections for this transistor is shown

in Fig. 336. Typical SSB performance of the transistor for
-30 dB distortion is tabulated
below for 30-MHz operation with
the transistor biased at a quiescent collector current of 10 milliamperes:
Po (PEP) at 28V = 90 W
Power Gain = 13 dB
Collector Efficiency = 50%
The effect of forward bias on
the performance of the transistor
is illustrated in Fig. 333. The figure shows an improvement in
linearity when the transistor bias
is increased from the threshold
of collector conduction (class B)
to a collector quiescent current
of 25 milliamperes. Biasing the
transistor further into class AB
under high output power improves distortion performance

0.0033

,.F

'h, T2

18 turns twisted pair. No. 28 enamel

wire on Ql CF 102 form

Figure 340.

50 turns No. 30 enamel wire on CF 102

Ql form

2-to-30·MHz .linear power amplifier.

RCA Silicon Power Circuits Manual

322

very slightly. Even though the
transistor has ballast resistance
and a temperature-compensating
diode, care must be used to prevent transistor damage by selecting the minimum quiescent
collector current to obtain the
desired low level of distortion at
the maximum output-power level.
AIRCRAFT RADIO
The aircraft radios discussed in
this section are of the type used
for communication between the
pilot and the airport tower. The
transmitter operates in an AM
mode on specific channels between
118 and 136 MHz. Radios of this
type are regulated by both the
FCC and the FAA (Federal Aeronautics Administration). The
FCC assigns frequencies to airports and places some requirements on the transmitters, particularly as regards spurious
radiation and interference. The
FAA sets minimum requirements
on radio performance which are
based on the maximum authorized
altitudes for the plane, whether

paying passengers are carried,
and on the authorization for instrument flying. The FAA gives
a desirable TSO certification to
radio equipment that satisfies
their standards of airworthiness.
The FCC checks aircraft-radio
transmitter designs for interference and other electrical characteristics (as it does all transmitters). Additional requirements are
specified for radios intended for
use by scheduled airlines by a
corporation supported by the airlines themselves. The name of this
corporation is ARINC (Aeronautical Radio, Inc., 2551 Riva Road,
Annapolis, Maryland 21401.
All these specifications combine
to generate radio-transmitter requirements for different types of
aircraft, as indicated in Table
XXXIII.
Desirable Features
Because multiple channel use is
necessary, it is desirable that aircraft radios have all 360 channels.
These channels are spaced every
50 kHz from 118 to 136 MHz, and

Table XXXIII-Four Popular Aircraft-Radio Transmitters
(Designs by Aircraft Type*)

TYPICAL OWNER

NO. OF
FAU
ENGINES IN ARINC
AIRCRAFT CLASS

VOLTAGE
AVAIL·
ABLE

TRANS·
MITTTER
POWER
(MIN.)

TYPICAL
POWER
RANGE

TRANSMITTER
FEATURES

>1.5 W Type Low cost, few
#1 channels, may be
portable
Type
Panel mounted,
4W
13 V
>6.0 W
Owner/Pilot
#2 90 or 360 chan·
nels.
4W 6 to > 20 W Type
28 V
Private/Business
2
II
#2
>20 W Type Remote Opera·
28 V
16 W
Chartered &
III
2·4
#3 tion, 360 chanCargo
nels.
28 V
25 W
30 W Type Maximum reliaScheduled
2-4
111&
#4 bility
Air Lines
ARINC
Jets
* This chart is not complete or exact and is not intended to show actual requirements, but merely
what is typical. Consult FAA for complete requirements.
Private Planes

13 V

High-Frequency Power Ampilfiers

are assigned to specific airports.
Each must be crystal-controlled.
Synthesizer techniques are used
to reduce the number of crystals
required.
Simple, foolproof operation is
necessary because the pilot has
little time to spare and little interest in adjustments to the radio
equipment. The frequency settings
are made by switches that provide
a digital read-out. "Squelch,"
volume, and on/off controls are
added.
Size is important because the
instrument panel is crowded. On
large aircraft, the transmitter is
operated by remote control by
means of a set of switches on the
panel. Weight and power drain
are secondary considerations.
A primary consideration in all
aircraft equipment is reliability.
Spare radios are common in private aircraft, and are universal
in aircraft equipped for instrument flying. The inherent reliability of transistorized equipment is a major advantage in
aircraft radios.
Design Problems

Amplitude modulation is an important design consideration for
all transistor power amplifiers (as
explained in the general section
on AM). Amplitude-modulation
requirements are set by the TSO
at a minimum of 85 per cent,
which corresponds to a PEP of
3 times the carrier power. Careful
design is required to meet this
specification because many factors
tend to limit the PEP, including
the decrease in transistor gain at
high currents, transistor rf
V (JI'l (sat), and modulator losses.
The owners and pilots of aircraft require reliable, foolproof

323
operation of their radio equipment. Unfortunately, they are not
often technically trained and do
not appreciate the importance of
proper maintenance of the antenna and the transmission line.
These vulnerable items directly
affect the performance of the
radio because optimum performance is achieved only when the
transmission line VSWR is unity.
With a mismatch (i.e., VSWR
greater than 1), the power output
may be low and there may be
spurious or distorted output. Even
more important is the fact that
antenna and transmission-line
faults stress the transmitter output stage with high voltage-current products and/or high power
dissipation. These characteristics
can overstress and destroy a weak
transistor. The likelihood and the
drastic effects of a load mismatch
make the transmitter output transistor a primary influence on
equipment reliability and make
mandatory the selection of a transistor rugged enough to withstand
the possible stresses.
Aircraft radios must cover the
entire frequency range from 118
to 136 MHz. The more expensive
radios cover all 360 channels. This
18-MHz bandwidth is a major design challenge which may be met
by use of either a narrow-band
step-tuned transmitter or a broadband transmitter.
A narrow-band transmitter is
mechanically tuned in each stage
in 18 steps (or more if necessary),
each covering 1 MHz. A particular
problem arises in assuring that
each component is varied in accordance with its own tuningversus-frequency curve. This technique requires special cams and
mechanical linkage. Remote operation of the transmitter requires expensive and complex

324

RCA Silicon Power Circuits Manual

servo mechanisms. The inherently
high Q of vacuum-tube circuits
has forced the development and
refinement of these techniques to
produce good aircraft radios.
Transistors may be used in place
of tubes in narrow-band transmitter designs that use conventional circuits.
A broad-band transceiver design is possible with transistors.
In a power transistor, the input
may be considered to consist of
the base-lead inductance Lb in
series with rbb'. If Lb is minimized,
the Q is reduced, and broad-band
operation is possible. The outputcircuit Q is less of a problem than
that of the input. The Q is formed
by Cob in parallel with the load
impedance presented to the collector by the tuned circuit. Broadband matching circuits between
amplifier stages commonly use
ferrite-core transformers of the
transmission-line type (balun).
The use of broad-band amplifiers permits the largest portion
of the transmitter to be remotely
located without the need for expensive and complex servo tuning
mechanisms. This feature is a
great advantage in larger aircraft.
One problem encountered with
a broad-band amplifier is reduction of harmonic output. Harmonics originate in the class C
operating mode because of the
nonlinear characteristics of transistors. These nonlinear characteristics, particularly the voltage
sensitivity of Cbc , cause subharmonic-frequency generation as
well as harmonic-frequency generation. The wide-band gain also
increases the possibility of oscillation if any feedback exists. This
condition is further intensified by
the use of high-gain transistors or

by excessive over-all gain.
The amount of harmonic output
and transmitted interference permitted is rigidly specified by the
FCC. A broad-band, band-pass filter should be added, therefore,
after the transmitter.

Design Example
The design considerations for
an aircraft-radio transmitter are
illustrated by an example. The example is a popular transmitter
which meets the requirements for
privately owned single-engine aircraft. This transmitter is designed to provide a minimum
output of 6 watts at a modulation
of 85 per cent and to operate
from the 12-volt airplane battery
without converters. It is small
enough to be mounted on the instrument panel.
Transmitters smaller than the
one in the example are readily
designed by removal of the highpower stage. Transmitters larger
than the example have a much
higher cost factor (rf-watt-output
per dollar), and have smaller
markets. However, they can be designed by use of the same techniques as those set forth in the
example.
The design begins with the output stage and moves toward the
crystal oscillators. The oscillators
are not discussed in this section
because they are low-power types
and are not limited by the performance of available transistors.
A block diagram of the transmitter is shown in Fig. 341.
The output stage of the transmitter is critical. It handles the
most power, costs the most, and
must be capable of accepting a
load mismatch. The output power

325

High-Frequency Power Amplifiers

FREQUENCY 0.1 W PRE-DRIVER
STAGE
SYNTHESIZER

PEP-18W
MIN
PEP .. O.7W
PEP-S W '---"'CW"6 W
CW-O.S W DRIVER CW=2 W OUTPUT MIN
STAGE
STAGE

12 V SUPPLY
(UP MOD)

1---.

12 V SUPPLY
(MOD)

Figure 341. Block diagram of transmitter designed to deliver a minimum of 6 watts of
rf power at 85-per-cent modulation for operation from a 12-volt airplane battery without
converters.

for the transmitter is a minimum
of 6 watts cw with a 12-volt supply (13.6 volts minus modulator
and other voltage drops). The
most important requirement is
for upward modulation to a
theoretical limit of 4 times the
carrier power output, which corresponds to 24 watts PEP. FAA
specifies 85 per cent minimum
modulation, which is equivalent to
18 watts PEP. The limit of 24
watts is not achieved, however, because of the reduction in transistor gain at high currents, transistor rf VCE (sat), and modulator
losses.
The output transistor must deliver the required PEP; it must
also withstand a mismatched load
(transmission lines and antenna).
The severity of the load mismatch
is increased with any increases in

Operation
Drive
Designed for

PEP, supply voltage, and/or ambient temperature. The severity
of the mismatch is limited by any
transmission-line and harmonicfilter losses (at high VSWR), by
power-supply limiting, and by the
energy stored in the modulation
transformer. Therefore, a true
test of the ability of the transistor to withstand load mismatch
can be made only in a completed
transmitter. The completed transmitter must also be tested for
stability and interference output
with a mismatched load. Before
the transmitter is completed, the
best guide to load-mismatch capability of transistors is the transistor manufacturer.
The requirements for the output transistor used in the transmitter are given in Table XXXIV.
It should be noted that gain is

Table XXXIV-RF Transistor Requirements
OUTPUT STAGE
DRIVER STAGE
PREDRIVER STAGE

Modulated RF Amp.
Modulated RF Amp.
Antenna
Output Stage
Max P.O. From Transistor P.O.
At 24 V
Gain Linearity
(Gain")
Load-Mismatch Capability
Supply Voltage
12 V'
24 V'
12 V'
24 V'
Typical Performance
6 WMin.
18 W Min. PEP 2 W
7W
24 WTyp.
8 W Typ.
Operating Current
0.7 A
0.25 A
Breakdown Voltage
24 V'
48 V'
24 V'
48 V'
Mode
Reverse Bias'"
Reverse Bias'"
Dissipation
See Text 1 W
1.5 W
• High supply-voltage limit and transients must be added .
•• This parameter is sacrificed to achieve other requirements .
••• Supplied by rf drive

Modulated RF Amp.
Driver Stage
Gain
Pre·Distortion

12 V'
0.5 W

24 V'
1 WPEP

0.lA
24 V'
48 V'
Reverse Bias'-'

326

RCA Silicon Power Circuits Manual

of secondary importance as compared to power output and loadmismatch capability. The gain
achieved in this example is only
about 2.6 times the carrier power
output, or 4.1 dB. As a result,
drive power of 7 watts peak must
be delivered by a modulated driver
transistor.
The driver transistor must deliver a PEP of 7 watts with a peak
supply voltage of 24 volts, and
a cw power of 2 watts at 12 volts.
These values yield a PEP-to-cw
power ratio for the driver transistor of 7 :2, which is greater than
that for the output transistor
(8:6) and requires the use of
smaller peak currents relative to
the maximum rating. Modulation
of this stage has three important
advantages: (1) it reduces the
over-all modulation distortion;
(2) it reduces the dissipation requirement of the driver transistor; and (3) it reduces rf drive
to the output transistor on the
downward modulation and thus
reduces the feedthrough power
which tends to distort downwardmodulation peaks.
The pre driver stage is a class
C power stage which must generate cw power of 0.5 watt and a
PEP of 1 watt. This stage is also
modulated and has a constant
drive power. Modulation of this
stage reduces the dissipation requirement, but can cause distortion problems. Modulation of more
than two stages distorts downward modulation because transistors exhibit a threshold effect. At
low supply voltages, the gain and
power output decrease very
rapidly. This decrease causes a
"notching" in the audio waveform and zero rf power output if
more than two stages are modulated. If only two stages are modu-

lated, the feedthrough power
prevents complete cutoff of the
transistors.
Both improved upward modulation and un degraded downward
modulation may be achieved simultaneously if only up-modulation is used in the pre-driver
stages. This purposeful distortion
partially compensates for the
nonlinear (gain-current) characteristic of the transistor, and is
swamped out and undetectable if
two fully modulated stages follow
the distorted stages.
The gain of the pre-driver stage
is usually high because the operating currents are small. A constant
drive power of 100 milliwatts is
needed. This power level is available from the frequency synthesizer (channel selector).
The actual circuit design for a
narrow-band transmitter follows
conventional techniques, as described above. The completed design for the example is shown in
Fig. 342. The transmitter requires
a good-size modulator capable of
delivering an audio power equal
to half the total dc input power to
the transmitter. For a 6-watt
transmitter, the dc power input
is approximately 12 watts, and a
full 6 watts of audio power is required.
Four combinations of modulators and power supplies are listed
in Table XXXV, together with
the advantages and disadvantages
of each. For aircraft radios, each
combination should be considered
along with the other features
planned for the radio (e.g., multiple voltages, remote operation,
size, and weight). Only two modulator designs are included in the
table.
The series modulator uses one
transistor to reduce an input sup-

327

High-Frequency Power Amplifiers

C" C3, C5, C7 = 3-35 pF
G, C" Co, Co = 8-60 pF
CD, CU, C'3 = 0.03 pF
C1O, C12, C14 = 1000 pF
h, to
3 turns No. 16 wire, 1/4" 10, 114" long
b, L5
ferrite choke, Z - 450 ohms
L3 = rf choke, 1.5 JLH
L4, l7 == .4 turns No. 16 wire, 1/4" 10, 3/8" long
L. = rf choke, 1.0 JLH

==
==

wire~wound

resistor, R

Figure 342.

= 2.4

ohms

bo == 5 turns No. 16 wire, 3/e " 10, V2" long
Rl = 220 ohms
R3 = 180 ohms
SR = IN2858A

35-MHz, 6-watt, narrow-band amplitude-modulated transmitter.

ply voltage of 28 volts to 12 volts,
and to modulate this voltage. The
input voltage must exceed the
peak modulated supply voltage for
the transmitter. The dissipation
of the modulator transistor is
maximum when there is no modulation. The dissipation then is
equal to the transmitter operating current times the difference
between the input voltage and the
unmodulated output voltage. This
dissipation must exceed the unmodulated de power input to the

transmitter. For the example, the
peak dissipation would be (1 ampere) (28-12) = 16 watts_ The
worst-case dissipation occurs with
maximum input voltage.
The size and weight of the heat
sink for the modulator transistor
is balanced by the elimination of
the modulator transformer. Elimination of this transformer allows
the use of simple feedback to reduce distortion.
The elimination of supply-voltage transients from the 13-volt

Table XXXV-Modulator and Power-Supply Combinations for
Aircraft Radio
Type of
Power Supply
Min. Input Voltage
Output Voltage
Type of Modulator
Main Advantage

Inverter

None
12 V
25 V
30 V Transients
25 V Transients'
Series-Type Class A

Excellent Transient
Limit

Other Advantages

Excellent Transient
Limit,
low Cost
light-Weight TransLight Weight
formers (High Freq.) No Transformers
Convertible To Any
Supply Voltage
low Distortion
low Distortion

Disadvantages

Expensive, large
Heat Sinks

large Heat Sinks

Active
Limiter

13.6 V
13 V

Passive
Transient
Limiter

13.6 V
13.5 V

Transformer-Type
Push-Pull Class B
low loss
Simplicity
No Inverter
No Inverter
Noise or
Hash
Small Heat
Sinks
large Transformers
(Audio)

No Inverter
No Inverter
Noise or
Hash
Small Heat
Sinks
Large Transformers
(Audio)

328

RCA Silicon Power Circuits Manual

internal supply results directly
from the feedback used to reduce
modulator distortion. It is necessary only that the series transistor have a breakdown voltage
greater than any expected transient, and a pulsed-power capability to absorb the transient.
The transformer type of modulator usually employs a push-pull
class B circuit. This type of operation requires two transistors, but
produces an efficient modulator
that has low transistor dissipation. The total transistor dissipation is a maximum of 40 per cent
of the designed output power,
or 2.4 watts for the example. This
dissipation occurs when the modulator output is 40 per cent of the
maximum.
The modulation transformer
must be rather large to meet all
its requirements. The resistance
of the windings must be low, or
the modulated performance of the
transmitter is degraded. The output winding matches an impedance of VcciIDC = 12/1 = 12
ohms for this example. An unbalanced dc current equal to IDe (the
transmitter operating current)
flows through this winding. This
current may rise if there is a
mismatch in the output of the
transmitter; there should be a
·25-per cent power-output margin
designed into the transformer.
Fig. 343 shows a block diagram
and Fig. 344 shows the circuit
schematic of another aircraft
transmitter. This transmitter

operates over the frequency
range from 118 to 136 MHz and
requires no retuning to cover
the entire band. The push-pull
output stage in this broadband
transmitter delivers 40 watts of
peak envelope power. The first
stage of the four-stage chain is
operated as a class A amplifier
to produce a maximum amount
of amplification of the relatively
low output from the frequency
synthesizer and to provide isolation between synthesizer and
modulated stages. The remaining three stages of the transmitter operate class C, and all are
amplitude-modulated. The nominal supply voltage for the transmitter is 12.5 volts.
COMMUNITY-ANTENNA
TELEVISION

Comm uni ty -an tenna television
systems (CATV) have experienced rapid growth in the last
decade. These systems serve areas
in which conventional antennas do
not provide adequate television reception. The basic equipment consists of a "head-end" that picks
up the off-air signals, and the distribution system that delivers the
signals to the subscriber's television receiver. The central antenna is erected at the most advantageous site for best reception;
in remote locations, program reception is usually accomplished by
means of microwave relays.

40291
DRIVER

FREQUENCY
SYNTHESIZER

12.5V

Figure 343.

12.5V
(UP MOD)

I2.5V
(MOD)

Block diagram of broadband 118·to·136·MHz Aircraft Transmitter.

329

High-Frequency Power Amplifiers

C'9 Z=50.n

F=IIS TO 136 MHz
P=5mW
Z=50.n TYPE
2N3866

+Vcc
12.5V

+MOD.VCC
12.5V

C,
330 pF, Area S.M. or equiv.
C. = 0.005 p.F, ceramic
Ca, C" Cs, C., Cn, C17 = 1000 pF, feedthru
C6, C9, C12, C18 = 0.05 .uF, ceramic
C. = 50 pF, 5%, Area S.M., or equiv.
CI0, C13, C15
82 pF, 50/0, Areo S.M., or equiv.
Cu, C,., C,.
150 pF, 5%, Area S.M., or equiv.
c.o = Variable capacitor, 8-to-60 pF, Area 404

=
=

or equiv.

= 7 turns No. 22 wire, 13/64" 10, 9/16" long,
tapped at 1.5 turns
Figure 344.

5 112 turns No. 22 wire, 13/64" 10, close
wound, tapped at 2 turns

= 6 turns No. 22 wire, 13/64" 10, interwind
with L. on IRN-9 core material

= 4 turns No. 22 wire, 13/S4" 10, interwind
with La on IRN-9 core material
= 5 turns No. 22 wire, 13/64" 10, centertapped, interwind with L.
L. = 5 turns No. 22 wire, 13/64" 10, interwind
with L5
RFC
1 turn No. 28 wire, ferrite bead, Ferroxcube No. 56-590-65/48 or equiv.
L.1,

118-to-136-MHz broadband amplifier for aircraft radio.

The distribution system has
two major parts: the main transmission or "trunk" line, and the
distribution or "feeder" line. The
main trunk line consists of lowloss coaxial cable with main trunk
amplifiers spaced along the cable.
Bridger amplifiers are used to
provide several outputs to the
feeder lines from which signals
are tapped off to individual subscribers. The backbone of the distribution system is the wide-band
amplifier.

System Operation
Fig. 345 shows a simplified
block diagram of a CATV system in which the TV signals are
received directly off the air (no
microwave relay). Elaborate arrays of stacked antenna elements

in conjunction with narrow-band
preamplifiers are used to receive
signals in each channel; the signals are then fed into a combining
network. The combined multichannel signal is then fed into the
main trunk line, which brings the
signal from the antenna into the
community. The trunk line consists
of wide-band amplifiers spaced
along a 75-ohm coaxial cable. The
gain of each amplifier is adjusted
to compensate for cable losses and
attenuation characteristics. Typical trunk-line amplifier spacing is
of the order of 2500 feet. At various points along the trunk line,
signals are supplied to the feeder
lines by bridger amplifiers. A
bridger amplifier provides several
outputs to the feeder lines from
which signals are tapped off to individual subscribers. One or more
line-extender amplifiers may be

RCA Silicon Power Circuits Manual

330
SINGLE-CHANNEL
ANTENNA-AMPLIFIER

LINE-EXTENDER
AMPLIFIERS

Figure 345.

Simplified community-antenna Television (CATV) system.

placed along each feeder line, depending upon its length and the
number of subscribers.

Amplifier Requirements

presently used between trunk amplifiers is 25-dB cable length at
channel 13. The gain of the trunk

...o
o

The first requirement for CATV
wide-band amplifiers is large
bandwidth. The amplifiers should
be able to cover the entire television band, from 54 to 216 MHz.
The next major consideration
for a CATV wide-band amplifier
is the required gain. The attenuation characteristic of a coaxial
cable is a function of frequency;
the cable losses increase logarithmically, as shown in Fig. 346.
Typical loss is 0.4 dB per 100 feet
at channel 2, and 1 dB per 100
feet at channel 13. The spacing

.,:

III

0.8

0.6

0.4

/CHANNEL 13

J./

'"i;:(

/iHAITEi21
4

8 100

FREOUENCY-MHz

Figure 346. Attenuation characteristics of
a coaxial cable as a function of frequency.

amplifier operating at this spacing, therefore, should be 25 dB
at 216 MHz. In addition, such an
amplifier must be compensated for

331

High-Frequency Power Amplifiers

cable-attenuation differences at
each channel by controllable "slop"
or "tilt." The amplifier gain must
be higher at the high end of the
band than at the low end. The
gain of a bridger amplifier is
somewhat lower than that of the
wide-band amplifier (about 18
dB). These amplifiers usually contain 2 to 4 stages of individual
amplification, depending on the
gain requirement.
The final requirement is for
output power or voltage, which is
determined by the distortion and
signal-to-noise-ratio requirements.
If the level of power or voltage is
too high, overloading and interference between channels occur;
if the level is too low, the signalto-noise ratio decreases. The most
serious distortion is cross-modulation, which is also referred to as
"windshield-wiper" effect. Crossmodulation results when several
channels are passing through a
wide-band amplifier. The modulation of undesired interfering signals appears as modulation of the
desired signal. The permissible
cross-modulation level is 57 dB
below the operating output-voltage
level in an all-band CATV amplifier.
"Snowy"
pictures
can
be
avoided if the signal at any point
in a system is made strong enough
to over-ride the noise. This relation is expressed by the signal-tonoise-ratio. The required ratios
for various grades of picture quality have been determined as follows: 45 dB for excellent picture
(no perceptible snow), 36 dB for
fine picture (snow just perceptible), and 29 dB for passable picture (snow definitely perceptible
but not objectionable). The signal-to-noise ratio always decreases
when a signal passes through an
amplifier. The difference between

the input signal-to-noise ratio in
dB and the output signal-to-noise
ratio in dB is defined as the noise
figure in dB. Noise figure, therefore, is the measure of degradation of signal-to-noise ratio in an
amplifier. The noise figure in a
CA TV cascaded system increases
3 dB each time the length of the
system is doubled; the signal-tonoise ratio decreases 3 dB under
the same condition.
Some current, typical requirements for trunk-line amplifiers to
be used in a CATV cascaded system are as follows:
Bandwidth_
= 54 to 216 MHz
Input Operating Level
= 10 dBmV
Output Operating Level
35 dBmV
Maximum Output Capability
50 to 55 dBmV
Gain
25 dB
Response
± 1 dB over the band
Noise Figure
12 dB at channel 13
8 dB at channel 2
Tilt
12 dB over the
frequency range
Voltage Available
= 30 V (+ 15Vand -15V)

These performance specifications
must be met in outdoor temperatures ranging from -40 to 140°F.

Transistor Wide-band
Amplifier

The gain-bandwidth product of
a transistor connected in a common-emitter configuration is equal
to fTo Thus, the bandwidths of an

332

RCA Silicon Power Circuits Manual

uncompensated common-emitter
amplifier stage may be expressed
as follows:

BW = h/hfe = fT (l-a o )/ao (302)
where hfe is the low-frequency
common-emitter current gain of
the transistor and a o is the lowfrequency common-base current
gain. Eq. (302) dictates the
bandwidth of a transistor amplifier stage if the source impedance
is large and if the load impedance
is small compared to the output
impedance of the transistor. In
practice, the load and source impedance are such that the bandwidth of the actual amplifier is
smaller than the value determined from Eq. (302). Fig. 347
shows a common-emitter transistor amplifier in which RL is the
load resistance and Rg the source
resistance. The transistor can be
represented by its hybrid-pi
equivalent circuit, shown in Fig.
348(a), in which parasitics are
not included. One difficulty with
the circuit of Fig. 348(a) is the
capacitance Ce, which prevents
'b'

1
Figure 347.

Common-emitter transistor
amplifier.

the circuit from being unilateral.
The effect of Ce may be approximated by connecting a "Millereffect" capacitance Ceq equal in
value to Ce (1 + a o Rdre') from
point b' to ground and omitting
the capacitance Ce entirely. The
resulting equivalent circuit is
shown in Fig. 348(b). Because, in
general, l/wTre' »
Ce and
a o = 1, the value for Ceq is conveniently approximated by
Ceq~(l/W t

r e') (1 +W t Cc R L ) (303)

With the aid of the simplified circuit of Fig. 348(b), the following
equations for the gain and band-

'rf
I-ao
Vg

Cal
'Ii

Ceq

=<:ewfre. (I T WI Cc RL l

(b)

Figure 348.

Equivalent circuits for common-emitter amplifier shown in Fig. 347: (a) without parasitic elements; (b) simplified equivalent circuit.

333

High-Frequency Power Amplifiers
width of the amplifier are derived:

(1-a o ) (Rg+rb') + re'

(Rg+rb') re' Ceq

+ W t Co R

[ 1 - ao

+ (Rg~fb,J

(305)

Eq. (305) shows that the bandwidth is decreased by an increase
in the load resistance RL and increased by a reduction in the
source resistance Rg • For a given
Rg and R L , the bandwidth is also
increased by an increase in WT
and by a decrease in rb' and Ce •
Thus, a transistor suitable for
wideband operation should have
high fT (or WT), a low collector
capacitance Ce , and a low base resistance rb'. If a transistor which
has an f'l' of 1.5 GHz and a Ce of
1.5 picofarads is used, the bandwidth calculated from Eq. (304)
is 8 MHz for Rg
75 ohms, R r•
300 ohms, and Ie = 50 milliamperes. The corresponding voltage gain is 140. To obtain the
bandwidth required in CATV, it
is necessary to use compensation
techniques that permit the trade
of gain for increased bandwidth.
Transistor amplifiers cannot be
designed to permit a gain-forbandwidth trade in a 1:1 ratio.
The voltage gain of a common-

emitter amplifier stage, as can be
determnied from Eqs. (304) and
(305), is not inversely proportional to the bandwidth. One of
the important criteria of a wideband transistor amplifier, therefore, is its ability to trade gain
for bandwidth. Another way of
stating this criterion is that
degradation in gain-bandwidth
should be small.
Collector-to-Base Shunt Feedback-One common method for
trading gain for bandwidth in a
common-emitter amplifier is by
use of shunt resistance-inductance
feedback, as shown in Fig. 349.
Simple feedback is provided from
collector to base for trading gain
and bandwidth. The current gain
at low frequencies is approximately equal to the ratio of R t
to Rv The feedback resistance
R f should be in the range
RL R e •
The effect of the capacitance Ce in
shunt with the emitter resistance
Re is to decrease the degeneration
at high frequencies~ The required
value of capacitance Ce is approximately equal to 1/ (15fT Re).

Two-Stage Wide-band
Amplifier
Degenerative feedback around
two stages offers large bandwidth
increase with minimum loss of
gain-bandwidth product. Two such
feedback methods are shown in
Fig. 351. The circuit shown in
Fig. 351 (a) uses a combination
of voltage and current feedback.
The resistance Re2 provides emitter degeneration in the second
stage, while the resistance Rf2
provides a form of current feedback to the first stage. The current gain is approximately equal
to the ratio R f2 /R e2 • Because the
feedback is obtained from a lowimpedance point and is returned
to a point of somewhat higher
impedance around the current
amplification of both transistors,
substantial increases in bandwidth
(up to 0.5 f T ) can be obtained
for a constant gain-bandwidth
product.

335

High-Frequency Power Amplifiers

(al

(b)

Figure 351. Two-stage wide-band rf amplifiers that use a combination of voltage and
current feedback to increase circuit bandwidth: (a) Feedback is coupled from emitter
of output transistor (low-impedance point) to base of input transistor (higher impedance
point); (b) feedback is coupled from collector of output transistor (high-impedance point)
to emitter of input transistor (low-impedance point).

The circuit shown in Fig.
351 (b) is satisfactory when moderate bandwidth (up to 0.1 f T )
is desired. This circuit differs
from that of Fig. 351 (a) in that
the feedback is obtained from a
high-impedance point and is applied only around the current amplification of the second stage.

The shunt peaking method
shown in Fig. 352(b) employs an
inductance in series with the input shunting resistance. The inductance is adjusted so that the

Series and Shunt Peaking

Series peaking or shunt peaking
schemes can also be used to extend
the bandwidth of an amplifier.
Fig. 352(a) shows a series interstage inductance that connects
the base of the second stage and
the collector of the preceding
transistor. This inductance increases the bandwidth by forming a resonant impedance-matching network with transistor input
and output capacitances at frequencies near the amplifier cutoff frequency. The value of L can
be determined from the following
equation:

(al
SERIES PEAKING

(bl
SHUNT PEAKING

Figure 352. Circuits showing use of peaking coils to increase bandWIdth: (a) series
peaking; (b) shunt peaking.

load is reduced in the frequency
range in which the transistor
gain begins to decrease. The required inductance L is equal to
Rr/15 fT'

336

RCA Silicon Power Circuits Manual
Wideband Transformer

The choice of dc bias for a wideband transistor amplifier to be
used in CATV depends on such
factors as power-output requirements, power dissipation, crossmodulation, noise figure, gain, and
bandwidth. In general, the transistor should be biased at a point
that provides the maximum gainbandwidth product fT' In addition, the stage that requires highlevel output should be biased at
a point at which good linearity or
minimum distortion can be obtained. The first stage should be
biased at a point for which a
minimum noise figure can be
achieved. The operating conditions
at a given voltage of 15 to 30
volts (available in a CATV system) are determined by the collector load resistance RL in the
circuits shown in Figs. 348
through 352. Because the inputsource and output-load resistances
in a CATV wideband amplifier are
75 ohms, wideband transformers
must be used to provide the proper
operating conditions of the transistor.
The
wideband transformer
shown in Fig. 353 consists of a
ferrite toroid around which a
twisted pair of wires are wound.
This transformer is of the transmission-line type and has excellent
bandwidth ratios. The transmission lines take the form of twisted
pairs. In this transformer, the
coils are so arranged that the
interwinding capacitance is a
component of the characteristic
impedance of the line, and forms
no resonances which seriously
limit the bandwidth, as in the
case of a conventional transformer. For this reason, the windings can be spaced closely to-

E
.-----+----2--~

Figure 353. Wideband transformer. This
transformer may be used to provide a 4:1
impedance ratio, as indicated in top dia·
gram. The transformer is basically a
twisted-pair transmission line wound about
a ferrite torroid, as shown in lower diagram.

gether to assure good coupling.
Transformers of this type can
provide good high-frequency respons(~ (this response is determined by the length of the windings) .
The low-frequency response, on
the other hand, is determined by
the permeability of the core. The
greater the core permeability, the
fewer the turns required for a
given low-frequency response and
the larger the bandwidths. Thus,
a good core material is desirable.
Ferrite toroids have been found
very satsfactory. The permeability of some ferrites is very high
at low frequencies and decreases
at higher frequencies. Large reactance, therefore, can be obtained
with few turns at low frequencies.
When the permeability decreases,
the reactance is maintained by
the increase in frequency, and

High-Frequency Power Amplifiers
good response is obtained over a
large frequency range. It is impOl'tant that coupling be high at
all frequencies, or the transformer
action fails.
The transformer shown in Fig.
353 has an impedance ratio of 4:1.
The high-frequency response of
this transformer may be calculated by use of the following equation:
Power Available
Power Output
(1 +3 cos 13 1)2 + 4 sin 2 13 I (310)
4 (1 +cos 13 1)2
where B is the phase constant of
the line and I is the length of the
line. The response is down 1 dB
when the line length is AI 4; the
response is zero at A/2. For wideband response, therefore, this
transformer must be made small.

337
inversely related to the dc emitter current (1': = 26/1.); therefore, there is a value of Ie that
corresponds to a minimum noise
figure. At higher frequencies, the
(f/f']') ~ term in the noise-figure
equation becomes predominant,
with the result that the noise figure asymptotically approaches a
6-dB-per-octave slope. From the
viewpoint of noise considerations,
the 1'1>' and leo of the transistor
should be low, and f,1' should be
high. Eq. (311) shows that the
noise figure is also a function of
the source resistance Rg and,
therefore, can be minimized by
proper selection of R g • The optimum source resistance can be determined if Eq. (311) is differentiated and the result is set equal
to zero and solved for R g • The following equation for Rg is then
obtained:

Transistor Noise-Figure
Considerations
The noise figure, defined as the
ratio of the input signal-to-noise
ratio to the output signal-to-noise
ratio, of a single-stage transistor
amplifier is a function of frequency and transistor parameters,
as shown by the following equation:

At frequencies below approximately 0.1 f'1" the noise figure is
constant with frequency and is
primarily determined by R g , rb',
r., and ao. The resistance r e' is

At low frequencies, where (f/fT)2
is small, a transistor that has high
dc current gain requires a high
source resistance Rg for best noise
performance. As the frequency approaches fT' the second term of
Eq. (312) becomes small, and the
optimum source resistance approaches (rb ' + r e'). The typical
noise figure for a high-frequency
silicon transistor at 216 MHz is in
the order of 2.5 to 3 dB. Such a
noise figure cannot be obtained in
a CATV amplifier because the
source resistance for such an amplifier (75 ohms) is not the optimum source resistance required
for minimum noise figure.

RCA Silicon Power Circuits Manual

338
Cross-Modulation
Distortion

Cross-modulation results when
several channels are passing
through a wideband amplifier. The
modulation of undesired, interfering signals appears as modulation
of the desired signal. Cross-modulation in a transistor amplifier is
produced mainly by nonlinear
characteristics of the emitter-tobase diode and by transfer characteristics that are not linear.
The voltage-current relations
for the emitter-to-base diode of a
transistor can be expressed as follows:
Ie

= 10 [e(q-V)/kT -

(313)

Expansion of Eq. (313) shows
that the emitter current contains
fundamental as well as harmonic
components. The relative magnitude of the harmonics is proportional to the applied voltage.
Therefore, when two or more signal voltages are applied, crossmodulation products are generated.
Transfer characteristics that
are not linear, such as the current gain of a common-emitter
stage, are another source of crossmodulation. If the output collector
current is proportional to the input base current, no cross-modulation exists. However, because the

common-emitter current gain
(h fe ) is not constant with current
levels, the output current is not
proportional to the input current.
When two or more signals are
present, the amplitude of the first
signal is dependent on the amplitudes of the other signals, and
cross-modulation results.
Because cross-modulation is a
transfer of modulation from one
channel to another, it can be
measured by determining the degree of modulation produced on
an unmodulated carrier by various
combinations of interfering signals. The basic test for crossmodulation is shown in Fig. 354.
A number of clean TV (modulated) signals at the various channel frequencies are combined and
fed through the amplifier under
test. The output signal is viewed
on a good television receiver, and
the output levels are increased
until "windshield-wiper" (crossmodulation) effects are just visible in the picture. The level at
which this condition occurs is
called the maximum usable output of the amplifier.
This test is not really conclusive,
however, because TV "windshieldwiper" effects can be seen much
more readily on some pictures
than on others. The accuracy of
the test is greatly increased if an
unmodulated signal is substituted
for the picture signal on the view-

VIDEO
SIGNAL
SOURCE

Figure 354.

Block diagram of basic test setup used for cross-modulation measurements.

High-Frequency Power Amplifiers
ing channel. This technique provides a white screen which does
not change during the test, and
allows more consistent and critical
observations.
A test for cross-modulation can
also be made by use of a fieldstrength meter in an arrangement
such as that shown in Fig. 355.
Two channel frequencies are used
in the test. The measurement procedure is as follows:
1. The equipment is set up as
shown in Fig. 355.
2. Generator No.1 is set to 150
MHz modulated 30 per cent
by 1000 hertz and the fieldstrength meter is tuned to
150 MHz.
3. The output of generator No.
1 is adjusted to the rated output of the amplifier.
4. The potentiometer is adjusted and the voltmeter is
calibrated for a convenient
level. This level then corresponds to 100-per-cent crossmodulation.
5. The modulation is then removed from the input signal.
6. Generator No.2 is set to 210
MHz modulated 30 per cent

Figure 355.

339
by 1000 hertz and the fieldstrength meter is tuned to
210 MHz.
7. The output of generator No.
2 is adjusted to provide the
rated output of the amplifier.
(If the amplifier has a flat
response, the output of the
two signal generators will be
equal.)
8. The field-strength meter is
tuned to 150 MHz.
9. The voltmeter is set to proper
scale for reading, and is
read. The percentage of
cross-modulation is then calculated based upon the lOOper cent level set in step 4.
This method is good enough to
determine the cross-modulation of
an amplifier on a relative basis.
For accurate cross-modulation
measurement, multi-channel frequencies must be used.

The 2N5109 Overlay Transistor
The RCA-2N5109 transistor,
packaged in a TO-39 case, is
designed to provide large dynamic range, low distortion, and
low noise, and is well suited for
use in a wideband amplifier in
CATV applications. The 2N5109

Block diagram of cross-modulation test setup in which a field-strength meter
is used.

RCA Silicon Power Circuits Manual

340

is an epitaxial silicon overlay transistor that features low rb' and Co
and high and relatively flat fT
with current level. Fig. 356 shows
the fT of a typical 2N5109 as a
function of collector current at a

20 per cent of its maximum value
from 25 to 100 milliamperes. Fig.
357 shows the fT of a typical
2N5109 as a function of VCE at
N

:I:

:e 1800

CO~LECTOR

l:;

:I:

:e
I 1800

...UI600

f1400

-r-

:1:1200 ~ r-COLLECTOR-TO-EMITTER -

jlOOO

VOLTAGE-15V I

g1600
0::
A.

IleOmA

:I:

25mA

1;1400

~12005

CURRENT (I c l=50 mA

8
C!I

:::3
o

......

100

COLLECTOR CURRENT - mA
Figure 358. Noise figure as a function of
collecter current for a typical RCA-2N5109
transistor.

2N5109 operating as a narrowband 200-MHz amplifier at a VCE
of 15 volts. The best noise figure
occurs at a collector current of
less than 10 milliamperes.
Choice of Operating Conditions
for 2N5109

The most important parameter
in the input stage of a CATV system is the noise figure. Distortion
is not usually important in the
input stage because the voltage
and current swings of the transistor are small. The dc bias of the
transistor should be chosen for
mimimum noise figure. An RCA2N5109 used in the first stage
should be biased at a collector
current Ic of 10 milliamperes
and a collector-to-emitter voltage VCE of 10 to 15 volts. The
noise figure of a typical 2N5109
measured in a CATV amplifier is
8 dB at channel 13.
The final stage, on the other
hand, should be biased so that
maximum power output can be
obtained with minimum crossmodulation distortion. In addition,
the bias condition should be within
the dissipation capability of the

341
transistor. For example, if it is
assumed that 1 volt rms (60
dBmV) is required across a load
of 75 ohms, the peak-to-peak voltage swing across the 75-ohm load
is 2.83 volts, and the corresponding current swing is 36.4 milliamperes. The 75-ohm load must
be transformed into the collector
load with the use of a wideband
transformer. If a 1:1 impedance
transformer is used, the collector
voltage and current swings are
the same as those of the 75-ohm
load. The collector bias current
Ic can then be selected from Fig.
356 for minimum change in fT
within the 36.4-milliampere current swing. The value of Ic that
satisfies this condition is approximately 60 milliamperes. The
VCE corresponding to a collector
load of 75 ohms is therefore 4.5
volts. Figs. 356 and 357 show
that large current swings (rather
than voltage swings) result in a
change in fT and, therefore, in
large distortion.
If a 4:1 impedance transformer
is used, the collector load becomes
300 ohms and the collector voltage
and current swings become 4.66
volts and 18.2 milliamperes, respectively. From Fig. 356, the
value of Ic can be chosen as 55
milliamperes for a minimum
change of fT within this current
swing. The VCE value corresponding to the collector load of 300
ohms is 16.5 volts. Fig. 357 shows
that the fT is substantially constant within the 4.66-volt swing
around 16.5 volts. The power dissipation is 0.9 watt, which is within
the limit of the 2N5109. The
power output for a typical
2N5109 operated at 16.5 volts and
55 milliamperes in a 12-channel
system is 52 dBm with -57 dB
cross modulation.

342

RCA Silicon Power Circuits Manual
A Wideband Amplifier
Using the 2N5109

A typical single-stage wideband
amplifier circuit is shown in Fig.
359. This common-emitter class A
amplifier uses the RCA-2N5109
transistor and is designed for

LOAD

SOURCE
(75£1)

(75£1)

-VE

el, Co, e. == 0.002
Co == 8·60 pF, Areo
e. == 0.03 JLF
es, e. == 1500 pF

consistent with present CATV
systems, which have both positive
and negative 15-volt supplies.
The amplifier of Fig. 359 uses
a 2N5109 operated at an Ie of 55
milliamperes and a VCE of 16.5
volts, and can provide a minimum
gain of 12 dB within the band of
54 to 216 MHz.
Fig. 360 shows the use of the
2N5109 in a more sophisticated
wideband amplifier. This amplifier
also employs a 4 : I-impedance
wideband transformer and emitter
peaking and degeneration. Output
impedance matching at the upper
cutoff frequency is provided by
L 2 , C9 and ClO • This method results
in a small increase in gain at the
upper cutoff frequency. The same

+vcc

JLF

404 or equiv.

Rl == 390 ohm., '/, walt
R. == 330 ohm., 1 walt
Re == 6.8 ohm., '/, walt
Rt == 200 ohm., '/, walt
T = 4~turn bifilar winding, ~6" ID, No. 30 wire;
Core: G.I. material Q,. or equiv.
.

Figure 359. Single-stage wideband ampli·
fier using the RCA·2N5109 transistor to provide a gain of 12 dB in the frequency
band from 54 to 216 MHz.

75-ohm source and load resistances; it is suitable for the CATV
application. A ferrite-toroid wideband transformer that has an impedance ratio of 4:1 is used in the
output to transform a 75-ohm load
into a 300-ohm collector load. Both
shunt feedback and emitter degeneration are employed through
Rf and Re, respectively. Emitter
peaking is accomplished by the
use of Ca. Two dc power supplies
are used; one supply provides the
collector reverse bias, and the
other supply provides the emitterto-base forward bias through resistances RI and R 2 • The dualdc-power-supply arrangement is

VCC=15V

el == 1.5 - 20 pF
e. == 0.002 pF
Cd == 55 - 300 pF
C., Co == 0.02 pF
es, e. == 1000 pF
e. == 32 - 250 pF
e. == 7 - 100 pF
elO

8 - 60 pF
11 = 7 turns, ~,"
diameter, No. 26 wire

3 turns, ti,"
diameter. No. 26 wire
== 30 ohm.
R. == 390 ohm.
Ra == 220 ohm.
l:.!

4-turn bifilor winding, ¥t," ID; Core:
G.I. material Ql or
equiv.

Figure 360. Single-stage wideband amnlifier using the RCA·2N5109 transistor which
employs various matching, pe.aking, and
feedback techniques to increase the gambandwidth product.

technique is used in the input
through LI and CI . The combination of Ca and RI tends to reduce
the gain of the amplifier at low
frequencies through the effect of
R I. At high frequency, full gain

High-Frequency Power Amplifiers
is obtained through the shunting
effect of C:1• As compared to the
amplifier circuit of Fig. 359, this
amplifier can provide 1 to 2 dB
more gain under the same operating conditions. However, the amplifier circuit of Fig. 360 is more
complicated, particularly its tuning procedure.
Trunk line and bridger amplifiers usually contain 2 to 4 stages.
The single-stage circuits of Figs.
359 and 360 provide the basic
building blocks for such an amplifier. The first stage must have a
low noise figure and, for that reason, "tilt" control is usually not
used in this stage. Because it increases the low-frequency noise
figure, tilt control is usually incorporated only in the second
stage.

VHF AND UHF MILITARY
RADIO
Military radios, which operate in the vhf and uhf ranges,
vary greatly in requirements.
Telemetering devices may operate with as little output as
0.25 watt, while communication
systems may require outputs of
50 watts and more. Modulation
may be AM, FM, PM (pulse modulation), or PCM (pulse-code
modulation). Equipment may be
designed for fixed, mobile, airborne, or even space applications.
Although the circuits described
in this section apply only to specific military applications, they
are representative of the general
design techniques used in all
military vhf and uhf radio
equipment.

Sonobuoy Transmitters
A sonobuoy is a floating submarine-detecting device that in-

343
corporates an underwater sound
detector
(hydrophone).
The
audio signals received are converted to a frequency-modulated
rf signal which is transmitted to
patrolling aircraft or surface
vessels. The buoy is batteryoperated and is designed to have
a very limited active life.
Typical requirements for the rftransmitter section of the sonobuoy are as follows:

=
=
=

Frequency 165 MHz
Supply Voltage
8 to 15 volts
CW Output
0.25 to 1.5 watts
Over-all Efficiency = 50 per cent
Harmonic Output 40 dB down
from carrier

Figure 361 shows a diagram of
an experimental sonobuoy transmitter designed to produce a power
output of 2 watts at 160 MHz.
Only three stages, including the
crystal-controlled oscillator section, are required. Efficiency is
great,er than 50 per cent (overall) with a battery supply of 12
to 15 volts.
The 2N3866 or 2N4427 transistor can be used in a class A osciIlator-quadrupler circuit which is
capable of delivering 40 miIIiwatts of rf power at 80 MHz.
Narrow-band frequency modulation is accomplished by "pulling" of the crystal oscillator. The
crystal is operated in its fundamental mode at 20 MHz. The
oscillator is broadly tuned to
20 MHz in the emitter circuit and
is sharply tuned to 80 MHz in
the collector circuit. The supply
voltage to the oscillator section
is regulated at 12 volts by means
of a Zener diode. Spectrumanalyzer tests indicate that this
stage is highly stable even
though rather high operating
levels are used.

344

RCA Silicon Power Circuits Manual
OSCILLATOR-QUADRUPLER

OUTPUT
(50 n)

c. =

0.05 p.F
'" = 75 pF
Ca = 32·250 pF
C•• C.O. C.6. C.. = 3·35 pF
C. = 2200 pF. feedthru
Ce, C12, CUi
0.01 JLF
C7
14·150 pF
C. = 50 pF
Co
500 pF
Cll. C.. = 1500 pF. feedthru
C.3
8·60 pF
L. = 22 p.H
La == 5.5 JLH

=
=
=

= 35 turns
turns

VCC'15V

turns No. 18 wire, ¥32" ID (close

=
=
=

1/... " 10 x

1/2" long

No. 22 wire, Y1," 10 (close wound)
2.'/4 turns No. 16 wire. 'I." ID x 3fa" long

Figure 361.

=2.1,4

wound)
L7. L. =. 1.0 p.H
Le
5 turns No. 16 wire, 1/4" 10 x 3/a" long
R.
1000 ohms
R. = 1200 ohms
Ra
47 ohm.
R. = 10 ohms
R5
100 ohms
R6 = 51 ohms

No .. 16 wire,

FINAL

DOUBLER

R'1
potentiometer, 50 ohms
RH ::::::: 100 ohms

Var

varactor

Ref. Diode = 12·Yolt zener diode
I.S-watt (rf power output) sonobuoy transmitter.

The oscillator-quadrupler section is followed by a 2N3553 class
C doubler stage. This stage delivers a power output of 250 milliwatts at 160 MHz from a 12- to
15-volt supply. The over-all output
of the sonobuoy can be adjusted
by varying the emitter resistance
of this stage.
The final power output is developed by an RCA developmental transistor which operates
as a straight-through class C amplifier at 160 MHz. A pi network
matches this output to the 50-ohm
line. The spurious output (measured directly at the output port)
is more than 35 dB down from
the carrier. This suppression is
achieved by means of series resonant trap circuits between stages
and the use of the pi network in
the output.

Many sonobuoy systems require power outputs in the range
of only 0.25 to 0.5 watt, preferably with a supply voltage of 8
to 12 volts. The 2N4427 transistor
is suitable for use as the doubler
and also the final output device
in such low-power applications.
Fig. 362 shows a diagram of an
output stage which uses the
2N4427 as a straight-through
175-MHz class C amplifier. This
circuit can deliver output power
of more than 500 milliwatts with
a supply voltage of 10 volts and
a drive power of 60 milliwatts.
For the lower power-output
requirement at low supply voltages, the oscillator-quadrupler
stage should use lower-power
transistors such as the 2N1491
or 2N914. Only 10 to 15 mill iwatts of fourth harmonic power

345

High-Frequency Power Amplifiers

is required in this case. The
bias-network resistors (R 2 and
R 3 ) should be adjusted for reliable oscillator starting conditions at these lower supply
voltages.
Sonobuoy circuits, in general,
must be reliable, simple, and low
in cost. The three-stage transmitter circuit shown in Fig. 361
is intended to be representative
of the general design techniques
used in these systems. However,
four-stage sonobuoy transmitter
systems are also in common use
at the present time. Typically,
a four-stage arrangement consists of an oscillator-tripler
stage, a second tripler stage, a
buffer stage, and a final amplifier stage. Most present-day sonobuoy applications require CW
power output between 0.25 and
0.5 watt.

C" Co, C<, C. = 7-10-100 pF Areo 423 or equiv.
C. = 14-10·150 pF, Areo 424, or equiv.
Co = 0.01 p,F, 50 V
C. = 1000 pF, feedlhru
h
0.75 p,H
Lo
1 lurn No. 18 wire, %.2" ID

=
=
=

La = 11/2 turns No. 18 wire, 1f,," 10
l'
11/4 turns No. 18 wire, ¥16" 10
RFC = 450 ohm., ferri1e

Figure 362.

O.S-watt-17S-MHz sonobuoy rf
power output stage.

Air-Rescue Beacon

The air-rescue beacon is intended to aid rescue teams in locating airplane crew members
forced down on land or at sea.
The beacons are amplitude-modulated or continuous-tone line-ofsight transmitters. They are battery-operated and small enough to
be included in survival gear.
Typical requirements for rescue
beacons are as follows:
Frequency = 243 MHz (fixed)
Power Output 300 milliwatts
(carrier)
Efficiency = greater than 50 per
cent
Supply Voltage
6 to 12 volts
Modulation
AM, up to ±100
per cent

The 2N 4427 transistor is especially suited for this service.
A general circuit for the driver
and output stages is shown in
Fig. 363. Collector modulation, as
well as some driver modulation,
is used to achieve good downmodulation of the final ampHfier. Conventional transformercoupled modulation is used;
however, a separate power supply and resistor network in the
driver circuit are provided to
adjust the modulation level of
this stage independently of the
output stage.
The rf-amplifier design is conventional; pi- and T-matching
networks are used; simpler circuits
(e.g.,
device-resonated
tapped coils), however, could be
used. The T-matching network at
the driver input is used to match
the amplifier to a 50-ohm source
for test purposes. A 10-to-20milliwatt input signal is needed
to develop a 300-to-400-milliwatt
carrier output level.

RCA Silicon Power Circuits Manual

346

AUDIO INPUT

U
RFC

RFC

+BV

POUT=300 mW
(CARRIER)
LOAD (50 !l)

PIN"IOmW
SOURCE (50 III

=
Figure 363.

Driver and output stage for a 243-MHz beacon transmitter.

Miniaturized Low·Power
Oscillators
Low-power transistor oscillators
are used as transmitters for telemetering or signal use in such devices as radiosondes, military
fuses, beacons, and other remote
sensing devices. Many of these
units currently operate in the uhf
range at output levels of about
0.25 to 1 watt. Battery supplies
are normally used.
The 2N3866 and 2N4427 transistors are ideally suited for
low-power oscillator service. Fig.
364 shows a simple microstripIine circuit in which these
transistors can provide power
outputs of up to 1 watt in the frequency range of 400 to 600 MHz.
The frequency of oscillation is
primarily determined by capacitor C and the parasitic emitterlead inductance. The microstripline output circuit can be

matched to a wide range of loads
by use of taps along the line
length.
VCC =20V

+
1200

1500 pF

t--r---i

RFC
0.22 Jl-H

.l. -

1500 pF

RFC
0.22 Jl-H

Figure 364. I-watt, 500·MHz microstripline
oscillator using the RCA 2N3866 or 2N4427
tranSistor.

Fig. 365 shows a very simple lumped-constant oscillator
circuit for operation in the 700to-lOOO-MHz frequency range.

High-Frequency Power Amplifiers

500 to 1000 milliwatts into a
50-ohm load can be developed by
this simple circuit.

VCC'2e v

1000

........--l)l 1500 pF
1500 PFTI(--l
RFC
0.15p.H

347

RFC

O.l5}1-H

HOpF

Figure 36S. O.s·watt, lOOO·MHz lumpedconstant oscillator using the RCA 2N3866
transistor.

The parasitic emitter- and baselead inductances are tuned directly with high-Q air dielectric
capacitors, and no other external
inductances are required for this
frequency range. The collector is
grounded directly to the ground
plane for best dissipation of transistor heat. Capacitor C primarily
determines the oscillator frequency, and the output capacitors are used primarily for
impedance matching. The 2N3866
is used for operation at supply
voltages of 20 to 28 volts, and
the 2N4427 is preferred for supply voltages of 15 to 20 volts.
Power outputs in the order of

Military Communications
The frequency range from 225
to 400 MHz is used in a large
variety of relatively-high-power
military communication syste.ms.
Equipments are usually amplitudemodulated and used for voicecommunication purposes. The circuits discussed in this section
are limited to class B and class
C amplifiers for use in driver
or final output stages that provide power outputs in the range
from 5 to 40 watts.
Fig. 366 shows the use of the
2N3733 transistor in a 5-watt
power-amplifier circuit of microstripline construction. A commonemitter configuration is used. The
transmission-line elements are
constructed from 1/32-inch Teflon fiberglass microstrip board.
The 750-ohm ferrite choke in the
base return provides low-frequency stability for this circuit.
Fig. 367 shows the schematic
diagram and components required
for 225-MHz and 400-MHz lumpedconstant circuits using the RCA2N5016 transistor. This transistor can provide a power output

5eA
MICROSTRIP

1114" LONG

Pour=SW

LOAD
e-60pF (5041

MICROSTRIP

I 114" LONG
1-30pF

1-30

+
Figure 366.

5-watt, 375-MHz stripline amplifier.

348

RCA Silicon Power Circuits Manual

Vee=2ev
fOR 225-MHz OPERATION
C1 = 4-40 pF
Co
7-100 pf
Co
3-35 pF
C.
8-60 pF
C.
1500 pF, feedlhru
Co'
0.01 ILf, disc ceramic
h = 1.3 turns No. 16 wire, '14" 10, ~," long
Lo
ferrile choke, Z
750 ohms
La
rf choke, 0.44 pH
L4
4. turns No. 16 wire, '14" ID, 0.3" long
Rl
0.68 ohms, wire wound, 1 waH

=
=
=
=
=

==
=
=

Figure 367.

FOR 400·MHz OPERATION
C1, C3 = 1 .5-20 pF
Co, C.
3-35 pF
C.
1000 pF, feedlhru
C&
0.01 p.f, disc ceramic
b = 1.3 turns No. 16 wire,
ID, '14" long
L. = ferrite choke, 2
750 ohms (or 0.12-pH
choke)
La = rf choke, 0.13 pH
L,
3 turns Y32" x Va" copper ribbon, ~6" ID,

=
=
=

lh"

v.."

long

= 0.68

ohms, wire wound, 1 watt

Lumped-constant power amplifier circuit for operation at 225 MHz or 400 MHz.

of more than 20 watts at 225
MHz and more than 15 watts
at 400 MHz when operated from
a 28-volt supply. A T-network is
used to match the relatively low
impedance of the input (1 to 3
ohms) of this device to a 50-ohm
source impedance. A pi network is
used to match the output to a 50ohm load. Self-bias is provided
by the base resistance R 1•
Figure 368 shows the use of
a 2N5016 transistor in a microstrip amplifier circuit that provides an ouput of 15 watts at
400 MHz when operated from a
28-volt collector supply. The
transmission lines are constructed on 1/16-inch Teflon
fiberglass circuit board with the
foil on one side acting as a
ground plane. The side lines are
used to tune out the transistor
input and output reactances. The
main lines, together with capaci-

tors C1 and C7 are used to provide real-to-real impedance transformations_ Base self-biasing is
accomplished through resistor
R 1 • Even though no dc blocking
is employed on the 50-ohm input,
proper biasing is obtained, provided that the 50-ohm source impedance has a dc impedance of
50 ohms or more.
Fig. 369 shows a microstripline amplifier circuit designed
for broadband operation over the
frequency range of 225 to 400
MHz. This circuit is constructed
on a 1/32-inch Teflon fiberglass
circuit board with the foil on one
side acting as a ground plane
for the micros trip elements. This
amplifier employs a broadband
step-transformer output network
which transforms the 50-ohm
load down to about 20 ohms for
the collector load and provides
the best mateh in the center of

349

High-Frequency Power Amplifiers

C1, c" C. = trimmer capacitor, 2 to 18 pF,
Amperex HTIOA/218 or equiv.
Co
0.03 p.F, cerClmic disc
C.
470 pF, feedthru, Allen Bradley FA5C or
equiv ..
Co, C. = 0.005 p.F, cerClmic disc

Figure 368.

R1 = 5.1 ohms, 0.5 watt, cdrbon
Notes:
1. BroCld = 11,..' Teflon board (e = 2.6), Budd
Co. Polychem Diy., GrClde 10BT, 1 OZ, doubleclad copper, or equiv.

2. Dimensions in inches.

400-MHz microstripline amplifier using the RCA-2N5016 transistor.

DIMENSIONS IN INCHES
EXPONENTIAL
TAPER

VCC"28 VOLTS
PSOURCE -4.5 VOLTS

~30

1---

~20
II.

a: 10

---'

~!'c~'ll=ffl~E!!.C!. --

POWER1OUTPJ

INPUT REFLECTED POWER

200

R
L

220

240

260

== 0.27-ohm
I-watt wire wound
O.l-p.H rf choke

Figure

369.

Schematic and

280
300 320
FREQU£NCY-MHz
Notes:
BOClrd
ltU" Teflon (e
2.6), Budd Co.
Polychem Div. grClde 108T, 1 OZ, double
clad copper, or equiv.
Dimensions in inches.

performance curves of a
broadband rf amplifier.

200-to-400-MHz microstripline

350

RCA Silicon Power Circuits Manual

the band. The fact that only an
approximate match of the transistor output capacitance is provided at midband does not result
in serious performance degradation. The input network consists
of an exponentially tapered impedance
transformer
which
matches the complex input impedance of the transistor at 400
MHz. At frequencies below 400
MHz, the input network matches
the real part of the base impedance, but not the reactive
part. The resultant mismatch
offsets the increasing gain of
the 2N5016 transistor as lower
operating frequ.encies are ap-

proached and results in a relatively constant power output
over the band. With 5 watts of
drive, this circuit develops about
15 watts of output power across
the 225-to-400-MHz band with a
total output variation of 1.5 dB.
The lumped-constant circuit
shown in Fig. 370 uses low-pass,
LC ladder networks for impedance transformation. (The values
given for the various components
in the circuit diagram are measured at 400 MHz and include
parasitic elements.) The output
network transforms the 50-ohm
load down to 20 ohms for the collector load. The dynamic output

. - - -....-

... +VCC=28V

RFC

C.
C..

=c. 2000
pF
= = 7.5 pF

C2
10 pF
C. = 1.5 to 30 pF (Johonson type or equiv.)
C. = 26.5 pF
C. = 17.5 pF
C. = 26.5 pF
11
4.5 nH
L.
14 nH (includes inductance of input cou·
piing capacitor Ce)

=
=

Figure 370.

=
8.5 nH
=
5.6 nH
=
10 nH
l6 = 19.5 nH (includes inductance of output

La
L.
Ls

cou~

piing capacitor ee)

Note:
All fixed components measured at 400 MHz

Lumped-constant 22S-to-400-MHz power amplifier.

351

High-Frequency Power Amplifiers

capacitance of the transistor provides the first shunt capacitor
in the output network, and capacitor Cc provides dc blocking.
Similarly, the base input inductance of the 2N5016 transistor
provides the last series inductor
of the input network, and capacitor Cc is again used for dc blocking. As in the microstripline circuit, shown in Fig. 369, the input
match of the lumped-constant
circuit is optimized at 400 MHz.
The m-derived end section (LI
and C1 ) helps to provide the
proper amount of mismatch at
frequencies below 400 MHz to
compensate for the gain characteristic of the transistor. With
6 watts of drive, this circuit provides approximately 17 watts of
output power across the 225-to400-MHz frequency band with a
total output variation of 0.5 dB,
as shown in Fig. 371.
The new RCA hermetic stripline package makes possible the
design of broadband power amplifiers without compromise of
hermetic reliability. This new
radial lead package, shown in
Fig. 372, uses ceramic-to-metal
seals and is superior to uhf plastic packages in two respects: it
has lower parasitic inductances
and is hermetically sealed. For
example, the first transistor in
a series of hermetic radial-lead
packages, had a dynamic input
impedance of 1.5 + j1.2 ohms at
400 MHz as compared to 2 + j2
ohms for a plastic 2N5017. Fig.
373 shows the power output and
efficiency of this developmental
transistor as a function of input
power, measured at a frequency
of 400 MHz and a collector-toemitter voltage of 28 volts. This
transistor can deliver 19 to 20
watts of power output with a
gain of 6.5 dB and a collector

VCE" 28 VOLTS

Pin" 6 WATTS
18t-----i1-::;oo-..:--+--_+--.;

16
14t-----li--....,.I,-___-t----t

12.I----:JI'''"'''-i'---=~=,.,c.._I_--_I,60ffic.>
~

IIOI----+--+-----f------l5O

6~-_lc__-_+--_+--.;30~

2~-_l--_+-~:+---lIO

o~-~--~--~-~~

200

250

350

400

FREQUENCY- MHz

Figure 371. RF power output, input reflected power, and collector efficiency of
the RCA 2N5016 transistor as functions of
frequency.

efficiency of approximately 70
per cent at 400 MHz. An important feature of this transistor

Figure 372. Hermetic Strip-Line Type
Ceramic·to-Metal transistor Package (Isolated Electrodes)

352

RCA Silicon Power Circuits Manual
MICROWAVE AMPLIFIERS
AND OSCILLATORS

ffi

~ lO\-..L--+
0..
IL

0::

RF POWER INPUT-W

Figure 373. Typical power output or collector efficiency as a functIon of power
input at 400 MHz.

is that the power gain is linear
within 0.6 dB at power outputs
in the range from 3 to 18 watts.
The transistor can also supply
20 watts of output with a gain
of more than 10 dB at 225 MHz.
Fig. 374 shows the power output
as a function of frequency for
the developmental radial-lead
transistor. Fig. 375 shows the
circuit configuration for a 400MHz amplifier that uses this
transistor.

Continued development of rf
power transistors has extended
their high-power capability into
the microwave region. Commercial
microwave transistors capable of
cw power outputs up to 1 watt are
now available for use at frequencies up to 2.3 GHz. CW power outputs of 10 watts at 1 GHz and
5 watts at 2 GHz have been obtained with laboratory developmental transistors, and future
prospects are even more promising.
This section describes the use
and capabilities of overlay transistors in such applications as
microwave straight-through amplifiers
and
fundamental-frequency oscillators. The use of
overlay transistors as amplifiermultipliers and oscillator-multipliers .also provides important
building blocks in microwave
equipment are discussed separately in the section on Frequency Multipliers.

Circuit-Design Considerations
CASE TEMPERATURE (TC1=25-C
COLLECTOR SUPPLY VOLTS (VCcl=28
~20~--~~~----~---r--~

l=>

~ 15~--~~-4~~~~-+--~

i3
ffi

~ ~~--~~-+~~~~~~~

l::
~~~3~OO~~400~--~~~--~~~--~~
FREOUENCY- MHz

Figure 374. Typical power output as a
function of frequency.

The important performance criteria in microwave power-amplifier circuits are power output,
power gain, efficiency, and bandwidth. Transistors suitable for
power amplification must be capable of delivering power efficiently with sufficient gain in the
frequency range of interest.
The power output that can be
obtained from a transistor is determined by the current- and voltage-handling capabilities of the
device in the frequency range of
interest. Because high-voltage
operation of high-frequency transistors is usually not prac-

353

High-Frequency Power Amplifiers

=
=

0.1:

INPUT STRIP
OUTPUT STRIP

1----1.~1-------O..

ooJl

0·125

---10---1-- 0.32

METAL
GROUND PLANE

-....e.=-====
DETAIL OF FEED THROUGH
CAPACITOR MOUNTING

DIMENSIONS IN INCHES

Ibl

Cs, C. = 0.005 /LF, disc type
C" Co, C7
2 to 18 pF, Amperex HTJOMA/218,
h
0.22 /LH, rf choke
or equiv.
Rl = .5.1 ohm., '/2 W, cmbon
C. = 0.03 /LF, disc type
X" X. = Details given in (bl
C. = 470 pF, feedthru, Allen-Bradley FA.5C, or
equiv.
Figure 375.400-MHz stripline rf amplifier test circuit for measurement of power output:
(al circuit diagram; (bl details of striplines.

RCA Silicon Power Circuits Manual

354

tical, high power output requires a transistor which has a
high current capability. The overlay transistor is suitable for highpower operation at ultrahigh and
microwave frequencies because its
construction provides a substantial increase in the ratio of emitter periphery to emitter area
which results in a high currenthandling capability.
A proper collector load impedance that provides the necessary voltage and current swings
over the entire frequency range
must be maintained to obtain
maximum power output from the
transistor. The real part of this
load impedance should be a function of the collector supply voltage Vco and the power output
Po. For class B operation, in
which the collector rf voltage is
sinusoidal, the real part of the
load impedance can be expressed
as follows:
R
L

_ [V cc - V CE( . . t)]2
2P o

(313)

The dynamic output capacitance
Co of the transistor is very nearly
equal to the open-circuit output
capacitance COl> at the supply
voltage used. For class C operation, in which the collector rf
voltage waveform resembles the
waveform of a half-wave rectifier, the real part of the load
impedance is modified as follows:

=
L

K [V cc

VCE (sat)]'

2P o

(314)

where the constant K is less than
unity and is equal to 0.8 when
the collector voltage waveform
approaches that of a half-wave
rectifier. In class C operation,
the dynamic collector output capacitance Co depends upon the
conduction angle and is gener-

ally substantially higher than the
capacitance COb. The imaginary
parts of the load and transistor
impedances are made part of the
output circuit (where they are
generally tuned out).
The power gain PG of a transistor power amplifier may be expressed in many forms; one of
the simplest is as follows:
PG = (I h2112 R L )/[4 Re (Zin)] (315)
where h21 is the dynamic currenttransfer ratio (current gain) of
the transistor, RL is the real part
of the collector load impedance
determined from the required
power output, and Re(Zin) is the
real part dynamic input impedance (when the collector is
loaded by a complex load impedance ZL).
Eq. (315) shows that, for highgain operation, large-signal power
transistors should have (a) high
current gain, which is also required for small-signal operation; (b) constant current gain
with current-level variations for
large-signal operation; and (c)
low dynamic input impedance.
This type of performance can
usually be obtained with overlay
transistors.
For good efficiency, transistors
are usually operated under the
signal-bias condition at which the
collector-to-base junction is reverse-biased and the emitter-tobase junction is partially forwardbiased by the input-drive signal.
The collector efficiency of a transistor amplifier is defined as the
ratio of the rf power output at
the frequency of interest to the
dc power input. Therefore, high
efficiency implies that circuit
losses should be minimal, that
the ratio of the real part of the
dynamic output admittance of the
transistor to its collector load

High-Frequency Power Amplifiers
conductance should be maximum
at the frequency of interest, and
that the circulation of harmonic
current in the circuit should be
minimized. For efficient operation, a transistor that has a small
dynamic
output conductance
should be used in a low-loss circuit that can block the flow of
all harmonic currents. Because
transistor output conductance increases very rapidly with frequency, a high ratio of output
conductance to collector-load
conductance is essential for efficient operation.
The bandwidth of a transistor
power amplifier is limited by
three factors: (1) the intrinsic
transistor structure, (2) transistor parasitic elements, and (3)
the external circuitry, i.e., the
input and output matching networks. For a given collector load
resistance and frequency, the inherent bandwidth of a transistor
power amplifier increases with
the gain-bandwidth figure of
merit f1' and is inversely proportional to the collector-to-base
capacitance Cob. Transistors suitable for wideband operation,
therefore, should have a high
f1' and a low COb.
Parasitic elements contributed
by the transistor package impose limitations on bandwidth.
The most critical parasitic elements are base and emitter inductances. Either type of inductance can be reduced greatly by
grounding the corresponding
terminal directly to the package.
These inductances, in series with
the intrinsic transistor structure,
increase the input Q and thus reduce the bandwidth. Additional
parasitic inductances also increase the variation in transistor
input and output impedances
with frequency.

355
A suitable package for transistors required to provide stable
operation over large bandwidths in microwave-frequency
applications should have low
common-lead inductance, low
shunt and feedthrough capacitances, and good thermal-resistance properties. Such requirements are readily obtainable by
use of coaxial or stripline transistor circuit structures designed
for use at microwave frequencies. Best high-frequency performance is provided by commonbase configurations in coaxial
packages of the type shown in
Fig. 376. The lower section of
.497
.503

DIA.

.162

DIA.

(bl

Figure 376. RCA-2N5470 coaxial transistor
(a) outline; (b) external view.

356

RCA Silicon Power Circuits Manual

the coaxial package, which concains the emitter coaxial lead, is
insulated from the flange, which
serves as the base lead, by an
aluminum oxide disc. Another
disc separates the base flange
from the copper collector lead.
The use of this package in a coaxial circuit requires a proper
heat sink. Fig. 377 shows a coaxial transistor package that
uses a standard beryllium oxide
ring to facilitate heat conduction
from the center conductor to the
outside conductor of an air-dielectric line section. This type of
arrangement is useful for power
dissipation of 5 watts or less.
A more efficient heat sink is obtained by use of a boron nitride
cylinder that makes intimate contact between the coaxial line
conductors over the entire length
of the cavity. This arrangement
results in much improved heat
conduction and, therefore, is
more suitable for high-power
microwave transistors. In addition, the boron nitride, which
has electrical and thermal properties similar to those of beryllium oxide, is readily machineable and is nontoxic. Coaxial line
lengths are also substantially
reduced.
N-TYPE CONNECTIONS
(BOTH ENDS)

Figure 377.

The coaxial line package is
useful well into the S-band frequency range. The JEDEC TO60 and TO-39 packages are useful in amplifier circuits to 1 GHz
and in oscillator circuits to 2
GHz. The hermetic construction
of these packages leads to increased device reliability under
stringent environmental operating conditions.
The choice of transistor configurations at uhf and microwave
frequencies is dependent upon
both performance and stability
requirements. Common-base amplifiers provide higher gains than
common-emitter amplifiers at frequencies above the fT of the
transistor. Collector efficiency for
common-base and common-emitter circuits is about the same.
It is generally acknowledged,
however, that a common-emitter
configuration provides a more
stable circuit at frequencies below the fT of the transistor. This
assumption arises from the linear
analysis of transistors in which
parasitic elements are not included. For high-power operation at uhf and microwave frequencies, transistor parasitics
contributed by the package must
be treated with the intrinsic
TYPE
2N5470

Heat sink for use with coaxial transistor package.

High-Frequency Power Amplifiers

transistor. Stable operation can
also be obtained in common-base
configurations provided parasitic
elements can be controlled.
Because transistor parameters
change with the power level, certain forms of instabilities (e.g.,
hysterisis, parametric oscillations, and low- and high-frequency oscillations) can be incurred in both common-emitter
and common-base circuits. Usually, most of these instabilities
can be eliminated or minimized
by careful design of the bias
circuit, by proper location of the
transistor ground connections,
and by use of packages in which
parasitic inductance and capacitance are held to a minimum.
Stable operation has been obtained at 2 GHz with both common-base and common-emitter
configurations. However, common-base coaxial packages have
been empirically found to be
more stable at the higher frequencies.

Circuit-Design Approach

The design of transistor microwave power circuits involves two
steps: (1) the determination of
load and input impedances under
dynamic operating conditions, and
(2) the design of properly distributed filtering and matching
networks required for optimum
circuit performance. For design
of the input circuit, the input
impedance at the emitter-to-base
terminals of the packaged transistor at the drive-power frequency under operating conditions must be known. For design
of the output circuit, the load
impedance presented to the collector terminal at the fundamen-

357
tal frequency must be known.
These dynamic impedances are
difficult to calculate at microwave
frequencies because transistor
parameters, such as h21 in Eq.
(315), vary considerably under
large-signal operation from smallsignal values, and also change
with power level. Small-signal
equations that might serve as
useful guides for transistor design cannot be applied rigorously to large-signal circuits,
although it has been determined
empirically that some small-signal parameters at the 10-volt
level correspond rather closely
with the large-signal values at
28 volts. Because large-signal
representation of microwave
transistors has not yet been developed, transistor dynamic impedances are best determined experimentally by use of slotted-line
or vector-voltmeter measurement
techniques.
The system required to determine transistor impedances under
operating conditions is shown in
Fig. 378. The system consists of
a well-padded power signal generator, a directional coupler (or
reflectometer) for monitoring the
input reflected power, an input
triple-stub tuner, an input lowimpedance line section, the transistor holder (or test jig), an
output line section, a bias tee, an
output triple-stub tuner, another
directional coupler for monitoring
the output waveform or frequency,
and an output power meter. At a
given frequency and input-power
level, the input and output tuners
are adjusted for maximum power
output and minimum input reflection power. When the system has
been tuned properly, the impedance across terminals 1-1, without
the transistor in the system, is
measured at the same frequency

358

Figure 378.

RCA Silicon Power Circuits Manual

Block diagram of test setup used to determine input and output impedances
of transistors.

in a slotted-line set-up or with
a vector voltmeter. The conjugate of this impedance equals
the dynamic impedance of the
transistor. Similarly, the impedance across terminals 2-2, without
the transistor in the system, is
the load impedance presented to
the collector of the transistor.
Such measurements are performed at each frequency and
power level.
In addition to determining dynamic input impedance and load
impedance, the system shown in
Fig. 378 is also useful for determination of the performance
capability of the transistor.
Power output, power gain, and
efficiency are readily determined.
For optimum performance of the
test system, careful consideration must be given to the selection of the line length and the
characteristic impedance Zo of
the input and output line sections (11 and 12 , respectively).
Eighth-wavelength (X/8) line
sections are preferred for 11 and
12 because, as pointed out in the

discussion of Matching Net·
works, such sections exhibit the
lowest VSWR and the smallest
line losses.
An alternative method of determining the dynamic input impedance is shown in Fig. 379.
This method uses a well-padded,
high-power signal generator connected in series with a slottedline setup.

Figure 379. Block diagram of dynamicimpedance test setup that may also be
used to test transistor performance
capability.

The setup beyond terminals 1-1 is
identical to that of Fig. 378. The
high-power generator is adjusted
until a desired power output is
obtained. The input impedance under this condition can be measured simultaneously in a slottedline setup. In this case, the test
fixture must contain a short line
section (a X/8 section is preferred for smallest line losses)

359

High-Frequency Power Amplifiers

to provide a connection to the
transistor.
Circuit-Design Techniques

When the dynamic input impedance and the load impedance
of a packaged transistor have been
established, either by direct measurement (as described in the
preceding paragraph) or from
the manufacturers published
data, the input and output circuits can be designed. The network design methods described
in the section Matching Networks may be used. For most
microwave-circuit applications,
INPUT CIRCUITS

however, either air-line or strip-

line arrangements are generally
used.
This section discusses only
some simple designs of the types
shown in Fig. 380. Although
coaxial-line configurations are
shown, the design procedures are
similar for the other forms of
TEM-mode distributed line sections. For the circuit shown in
Fig. 380 (a), the line section I
transforms the small input impedance of the transistor to a
value closer to that of the driving-source resistance (such as a
50-ohm generator). If line section I is made an eighth-waveOUTPUT CIRCUITS

(a)

(b)

(e)

(f)

Figure 380. Transistor input and output coupling circuits suitable for use at microwave
frequencies: (a) direct·coupled input network usinfl series tuning capacitor; (b) directcoupled input network using shunt tuning capacitor· (c) resonant·line input circuit;
(d) capacitlve-probe-coupled output cavity; (e) inductive-probe-coupled coaxial output
cavity; (f) resonant-line output circuit.

360

RCA Silicon Power Circuits Manual

length long and its characteristic impedance Zo is determined
by use of Eq. (290), then the
complex input impedance is
transformed to a real value at
the other end of this line, and
the VSWR on the line section is
a minimum. Capacitors C1 and
C2 , together with some lead inductance, are used as reactive
dividers to step up or step down
the impedance depending on the
value of the real impedance to
the 50-ohm source. Transformation directly to 50 ohms or some
other desired real impedance is
also possible with this configuration. The length of the line section 1 is less than a quarterwavelength when the dynamic
input impedance is inductive and
greater than a quarter-wavelength for capacitive inputs. In
this type of application, capacitors C1 and C~ serve to tune out
imaginary components, modify
imaginary components, or adjust
the values of real components,
depending on the frequency and
the characteristics of the line
sedion 1.
The input circuit shown in Fig.
380 (b) can be used effectively
when the dynamic input impedance of the transistor is inductive. Capacitor C2 is used to tune
out the inductive component of
the input impedance. A quarterwave line of the proper characteristic impedance is then used
for the impedance transformation between the small input resistance of the transistor and
the driving-source resistance.
The characteristic impedance of
this line can be determined from
Eq. (289). Capacitor C1 may be
used to adjust for minor differences between transistors.
The output circuit shown in

Fig. 380 (d) is a capacitiveloaded, foreshortened quarterwave coaxial-line cavity. A capacitive probe is used to match
the output to the desired real
load impedance. The location of
this probe is best determined empirically because a mathematical
relation for such a case has not
been developed. In the design of
the circuit, the line section 1,
the capacitance Ca, and the dynamic output capacitance of the
transistor must be resonant at
the desired frequency.
The ouput circuit shown in
Fig. 380(e) is similar to that
shown in Fig. 380 (d) except that
inductive loop coupling is used.
Again, the design of the coupling
loop is empirical. In general, the
inductive loop is placed near the
ground (high-current) end of the
line; in fact, it may be tapped
directly to the center conductor.
Conversely, capacitive probes are
generally located near the highvoltage end of the line.
The coupling networks shown
in Fig. 380 (a) through Fig.
380 (e) can apply to either input
or output circuits, and the specific illustrations are used for
discussion only. The circuits
shown in Figs. 380 (c) and 380
(d) make use of inductive coupling and are particularly suitable for stripline circuits. This
technique enables additional circuit isolation as well as additional filtering action. The technique can also be extended to
provide pass-band filtering.

Microwave Amplifier Circuits
The RCA 2N5108 transistor
can be used in the common-emitter amplifier mode at L-band frequencies. A typical circuit con-

High-Frequency Power Amplifiers

figuration for operation at the
1.0-to-1.5-GHz range is shown in
Fig. 381. This circuit can provide an output power of 1 watt
at 1 GHz when operated from a

+Vcc
Cl, C!!, C3, C1

= Variable

capacitor. 0.3 to 3.5

pF, Johanson piston type or equiv.

C, = 420 pF, feedthru
1== As described in text
RB = 2.7 ohms, 1,4 W
RFC

0.1 .uH

Figure 381. l-GHz. l-watt amnlifier using
the RCA-2N5108 transistor.

28-volt power supply. The emitter of the transistor is directly
connected to the ground plane of
the stripline circuit board. The
input circuit consists of the capacitors C1 and C2 and the parasitic lead inductance of the
2N5108 transistor. The output
circuit uses a capacitively loaded
50-ohm section of strip line which
is resonant at the operating frequency. Power output is taken
from this line at the proper impedance level. Amplifier power
gain is in the order of 6 dB and
collector efficiency is about 35
per cent.
For operation at high L-band
or low S-band frequencies, the
RCA-2N5470 coaxial transistor
can provide greater stable power

361
outputs. Fig. 382 shows a coaxial-line amplifier circuit which
can provide 1.2 watts of output
power at 2 GHz with a 28-volt
power supply. The coaxial transistor is placed in series with the
center conductors of the coaxial
air lines, and the base is properly grounded to separate the input and output cavities, as shown
in Fig. 380. The input line Ll
has a characteristic impedance
Z" of 20 ohms and a length of
about 0.80 inch. This line directly transforms the input impedance of the 2N5470 (at 2
GHz) to an impedance of about
50 ohms at the input. The output line L2 has a characteristic
impedance of 36 ohms and a
length of about 1.8 inch. Power
output is taken from the capacitor network loading this output
line. The two rf chokes isolate
the rf lines from the bias supply.
The 2N5470 coaxial-line amplifier can supply a cw power output of 1.2 watts at a gain of 5
dB and has a collector efficiency
greater than 35 per cent. Fig.
383 shows the variation in power
output of the 2N5470 transistor
as a function of frequency at the
0.2-watt and 0.3-watt drive levels,
and Fig. 384 shows the transistor power output and collector
current as a function of drive
power at the 2-GHz operating
point. Because of the excellent
input- and output-circuit isolation (within the 2N5470 transistor as well as in this coaxialcircuit design), the common-base
circuit configuration shown in
Fig. 382 is extremely stable. Improved efficiencies and power
outputs can be expected by use
of boron nitride dielectric-loaded
"heat sink" lines, as discussed
previously.

362

RCA Silicon Power Circuits Manual
TYPE

2N5470

= 0.8 10 10 pF, Johnason 4355, or equiv.
= 1000 pF, feedthru, Allen·Bradley FB2B,
or equiv.
C. = 0.3 10 3.5 pF, Johnason 4701, or equiv.
C,
C.

C.
0.35 10 3.5 pF, Johnason 4702, or equiv.
11, L2 = RF choke, 3 turns No. 30 wire, Yt6"
10, y,," long
X" X. = Details given in (b)
(b)

COAXIAL
OUTPUT
CONNECTOR

X2
COAXIAL INPUT
CONNECTOR

0.453

TYPE

DIA.

2N5470

BERYLLIUM
OXIDE WASHER

DIMENSIONS IN INCHES
(b)

Figure 382.

2-GHz power amplifier using the RCA-2N5470 coaxial transistor: (a) circuit
schematic; (b) construction details.

I!II

COLLECTOR SUPPLY VOLTS-28V
CASE TEMPERATURE-25-c

COLLECTOR-TO-BASE VOLTAGEFREQUENcy=r GHZ
28V

1.2
~

i
l-

1.5

S
II:

["':.:

0.5

1.5

)

/ ..

I:-o.r

FREQUENCY-GHz

Figure 383. Power output as a function of
frequency for the RCA-2N5470 transistor.

014

I400(

o~Jt/

~ i'...

I60

I20~

t.'

Il!
II::
IOQG

""COLLECTOR
CURRENT

II"
JI

0.1

II::

80
60

().3

0.4

frl

40
0.l5

POWER INPUT-W

Figure 384. Power output as a function of
input for the 2-GHz amplifier shown in
Figure 382.

363

High-Frequency Power Amplifiers

FUNDAMENTAL-FREQUENCY
OSCILLATORS
Transistors capable of power
amplification are also suitable for
power oscillation. The most important part of every oscillator is
an element of amplification. It is
then necessary only to provide a
path that feeds back a part of the
power output to the input in the
proper phase, together with a
source of dc power. The maximum
frequency of oscillation, which is
related to f max in a small-signal
transistor, is usually difficult to
define in a uhf or microwave
power transistor because of the
added parasitic elements. The circuit-design approach for an oscillator circuit is similar to that
discussed previously for amplifier circuits.

Basic Microwave
Oscillator Circuits
The parasitic elements of a
transistor package can sometimes
be used to form an economical
microwave oscillator circuit. The
high-frequency oscillations discussed previously usually occur at
a frequency close to the output
frequency of the amplifier when
the input power is removed. This
form of instability can be attributed to the parasitic elements
of the package which set up the
frequency of oscillation with the
intrinsic transistor. Such parasitic elements can be used to form
a transistor oscillator operated at
microwave frequencies, provided
the frequency of oscillation can
be controlled.
Fig. 385 (a) shows a Colpitts
transistor oscillator suitable for
microwave applications. The inductance L and the capacitances

C 1 and C~ can be considered as the
parasitic elements of the package.
Although the transistor configuration is not too well defined in this
oscillator circuit, the device can be
grounded in high-frequency operation at the collector, the base,
or the emitter without effect on
its performance. For example, a
useful oscillator circuit can be derived from the basic Colpitts oscillator by the use of a TO-39
transistor. In Fig. 385 (b), the
collector of such a transistor is
returned to ground through the
collector parasitic inductance L.
This connection is a convenient
method of applying a heat sink to
the collector, which is connected
to the case in a TO-39 package.
Output power is obtained from
the base through capacitances C3
and C4 • Fig. 385 (c) shows another method of coupling power
output from the oscillator.

(a)

r-41- -.,

:~cz~
~---)

r--~
:l::c,

I ____ _
L

fYY"'l

OUTPUT
(e)

Figure 385. Colpitts oscillator for use at
microwave frequencies: (a) basic ac circuit
configuration; (b) basic ac circuit with
collector returned to ground through parasitic inductance L and the output taken
from base through capacitive voltage divider; (c) basic ac circuit with transformer
coupled output.

364

RCA Silicon Power Circuits Manual
L-Band Oscillators

Fig. 386 shows the complete
circuit diagram of a 1.68-GHz
fundamental-frequency oscillator which makes use of the RCA2N5108 transistor. The collector

400

!300

ffi

~200

Ion

c. =

1200n

Variable capacitor, 0.35 to 3.5 pF,

piston type

Ca, C. = 470 pF, feedthru
b = Described in text
RFC = 5 turns No. 28 wire, Va" 10 x '/2" long
Figure
quency

20 22

24 26

SUPPLY VOLTAGE-V

28 30

Figure 387. Power output as a function of
supply voltage for the 1.68-GHz oscillator
shown in Fig. 386.

RFC

-Vee

i--

100
12

51n

o=>
II.

RFC

386. 1.68-GHz
fundamental-freoscillator using the RCA-2N5108
transistor.

of this transistor, which is packaged in a TO-39 case, is grounded
to the ground plane of a 1/16inch Teflon fiberglass microstripline board. Power output is taken
from the base through a 0.75-inch
section of 50-ohm microstripline
and the capacitor network C1 and
C2 • This oscillator can supply
more than 0.3 watt of power output at 1.68 GHz and has an efficiency of 20 per cent when operated from a supply voltage of
25 volts. Fig. 387 shows the oscillator output power as a function of supply voltage.
This basic oscillator circuit is
useful at frequencies from 1 to
2 GHz; only slight modifications
in the length of the transmissionline Ll are required to cover this

range. For example, the line
length is increased to 0.8 inch
to obtain optimum circuit operation at 1.5 GHz. An output power
of 400 miIIiwatts (with a 24-volt
supply) can be expected at this
frequency. Another modification
of interest (with the O.8-inch
line) is that optimum operation
at 1.25 GHz is achieved simply
by movement of capacitor Cz to
the position indicated by the
dotted lines. Movement of this
capacitor results in an improved
output transformation network
which can develop more than 800
miIIiwatts of output power at 1.25
GHz for operation from a 24volt supply.
The inductive element introduced by the line section Ll
(Fig. 386) can be supplied by
a high-Q varactor diode, as
shown in Fig. 388. The bias supplied to this varactor, in effect,
electrically varies this inductive
component so that broadband oscillator tuning is possible. The
output capacitor network, C1
and C z, which is used to transform a relatively small load-line
impedance to the 50 ohms of the
output port, could be replaced

365

High-Frequency Power Amplifiers

simplify circuit requirements,
e.g., essentially lumped-constant
S-band circuits can be designed
around this unit. However, because of the low feedback capacitances of this transistor, external
feedback loops are generally
needed for stable oscillation at
S-band frequencies.
Fig. 389 shows a simple
lumped-constant circuit that
uses the 2N5470 transistor. The
circuit is tunable over the frequency range of 1.8 to 2.3 GHz.
+Vcc
RFC

Cl, C2

0.1 /LH

1 to 7 pF, piston capacitors

C" C" C, = 470 pF, feedthru
Var. = Described in text

Figure 388. Wideband Varactor-tuned L-Band
Oscillator using the RCA-2N5108 transistor.

with an inductive-reactive divider-network, such as a tapped
transmission line or helical coaxial line. Tests, in which a
cartridge-type silicon microwave
varactor is used in this circuit,
show a relatively constant power
output of 600 miIliwatts over the
range of 1.0 to 1.5 GHz. The bias
on this particular varactor
ranges between 0 and 22 volts
for the specified tuning range,
and a transistor collector supply
of 28 volts is used.

S-Band Oscillators
The RCA-2N5470 coaxial transistor, although designed for
stable operation at 2.3 GHz in
the common-base amplifier mode,
can also deliver a power output
of 0.3 watt at 2.3 GHz in an oscillator. In oscillator applications of the 2N5470, advantage
is taken of the very low parasitic
elements in this transistor to

TYPE

2N5470

C1 = 0.82 pF, "gimmick" capacitor (manufactured by Quality Components, Inc. St. Mary's,
Pa.)

=
=

C2, C.
100 pF, Allen-Bradley FASC or equiv.
C. = 0.01 pF, disc ceramic
C5, C.
Trimmer capacitor 0.35 to 3.5 pf,
Johanson Type 4702 ar equiv.
h
0.05" length of No. 22 wire

L2, La

Rl
R2
R.

4 turns 7-mil wire, .062" 10 x ~6" long

= 51 ohms, V2 watt
= 1200 ohms, 1/2 walt
= 5 to 10 ohms, V2 watt

Figure 389. Lumoed-constant 2-GHz oscillator circuit using the RCA-2N5470 transistor.

Power output at 2 GHz is typically 0.3 watt with a 24-volt supply, and circuit efficiency is in
the order of 16 per cent at this
frequency. The collector is
grounded, and power output is
taken from the base circuit. All
leads must be kept short for
best high-frequency response.
The "gimmick" capacitor C1

366

RCA Silicon Power Circuits Manual

forms a necessary part of the
feedback loop of the circuit. The
circuit is basically a Hartley
type of oscillator in that inductor Ll and the parasitic inductance of C1 make up a tapped
inductor in this feedback loop.
Tuning is achieved largely by
adjustment of capacitor C6 , and
capacitor C5 is adjusted to maintain the output match over the
tuning range.
Figure 390 shows the use of
the 2N5470 transistor in a Colpitts type of microstripline oscillator circuit that operates

phase-resonant loop provided by
line section L 4and capacitor C1 •
The output line section L2 makes
use of standard micros trip line
techniques to provide the necessary reactance to tune out the
output capacitance; line section
Ll is a quarter-wave transformer
which transforms the real part
of the collector load impedance
to about 50 ohms. This circuit
can also provide about 0.3 watt
of output power at 2 GHz when
operated from a 24-volt supply.

FREQUENCY MULTIPLIERS

C" c. = 0.35 to 3.S pF, Johanson Type 4702 or
equiv.
Ca, C.
100 pF, Allen-Bradley Type SASC or
equiv.
h
microstrip line; :::=; 0.70" long x 0.30" wide

strip;

mounted on

V32"

Teflon fiberglass board

microstrip line;
0.43" long x 0.080" wide
strip; mounted on Y32" teflon fiberglass board
La
5 turns 7-mil wire, 0.062" ID x Y16" long
L4 = 50-ohm miniature coaxial line, 1.5" long

Figure 390. Microstrioline 2-GHz oscillator
circuit using the RCA-2N5470 transistor.

over the frequency range of 1.8
to 2.2 GHz. In this circuit, the
base of the transistor is directly
grounded to the ground plane of
the strip line board, and collector
heat is dissipated to this board
through a beryllium oxide insulating washer. The necessary
feedback is provided by the

Operation of the overlay transistor in the harmonic-frequency
mode can extend the upper limit
of the frequency range far beyond
that possible from the same transistor operating in the fundamental-frequency mode. A further
advantage of the harmonic mode
of operation is that frequency
multiplication and power amplification can be realized simultaneously. An overlay transistor operating in this mode provides power
amplification at the fundamental
frequency of the input-drive
power, and the nonlinear capacitance of the collector-to-base junction, acting as a varactor, generates harmonics of the input-drive
frequency. It is possible, therefore, to use a single transistor to
replace a transistor power amplifier and a varactor-diode frequency multiplier. In comparison
with varactor frequency-multiplier
circuits, the transistor multiplier
is simpler, less costly, and equally
efficient. It is anticipated that this
mode of operation permits extension of the available frequency
spectrum for overlay transistors
by a factor of two.

High-Frequency Power Amplifiers
Transistor Considerations
An overlay transistor used in a
frequency-multiplier circuit operates simultaneously as a power
amplifier to provide gain at the
fundamental frequency of the input driving power and as a varactor diode to generate harmonics
of the driving power frequency.
Thus, two mechanisms provide
amplification and frequency multiplication in overlay transistors:
one capable of gain at the fundamental frequency, and the other in
which the collector-base capacitance serves as a varactor capable
of frequency multiplication. Transistors suitable for multiplier applications must be capable of delivering power with gain at the
fundamental frequency and of
converting the power from the
fundamental frequency to a harmonic frequency. A good multiplier transistor, therefore, must
first be a good uhf transistor capable of high power output, gain,
and efficiency. In addition, its varactor section should have minimum losses to provide maximum
conversion efficiency.
The figure of merit for the
amplifier portion of the transistor
in which parasitic elements are
not included is given by the maximum frequency of oscillation
f max as follows:
f max = (PG)! f
= [(1/871") (1/lbb' C e

Tee))

(316)

where PG is the power gain, f is
the fundamental frequency of operation, rbb' is the intrinsic basespreading resistance, Cc is the collector capacitance, and Tee is the
emitter-to-collector transit or signal-delay time.

367
The efficiency of the varactor
portion formed by the collectorbase junction is determined by the
cutoff frequency f VCB as follows:
fVCB = 1/[271" Croin (rb'+r.)]

(317)

where Cmin is the minimum collector-to-base capacitance and r.
is the collector series resistance.
Fig. 391 shows a cross-sectional
view of an overlay transistor that
indicates the capacitance and loss
distributions. Fig. 392 shows how
the varactor portion separates
from the intrinsic transistor portion. The collector-to-base capacitance consists of two parts. The
major part, which comprises the

Figure 391. Cross-sectional view of an
overlay transistor ind,catmjil the capacitance and loss distrobutions.

active portion of the varactor, consists of the capacitance formed by
the part of the collector-to-base
junction that is not opposite emitter sites. This part of the capacitance is called the outer collector
capacitance Cbc ' The second part
consists of the part of the collector-to-base junction that is opposite the emitter-to-base junction.
This part is called the inner collector capacitance Cb'c' The outer
capacitance Cbc is a much more
efficient varactor than the inner
capacitance Cb'c because Cb'c has
to charge and discharge through
both the intrinsic and the extrin-

368

RCA Silicon Power Circuits Manual

sic base-spreading resistance rbb'
and rb" as well as through the
series resistance rsb while Cbc can
charge and discharge through only
rb' and rso. Because the intrinsic
base-spreading resistance rbb' is
much greater than the extrinsic
base-spreading resistance rb" the
cutoff frequency f YCB is much
larger in the active varactor portion represented by Cbc than in
the Cb'c portions. The difference
in rb' and rbb' results from the
use of different sheet resistances
in the two areas. Another unique
feature of the overlay transistor is
that the emitter area is much
smaller than the base area. As a
result, the inefficient portion of
the varactor formed by the collector-to-base junction opposite
. the emitter sites is almost negligible because of the reduced emitterarea.
The varactor cutoff frequency
f YCR is also maximized by use of
minimum collector series resistance roo. This resistance is kept
to a minimum by the n-n+ epitaxial structure used for the collector region. The n-type epitaxial
.layer forms the dominant part of
the·collector series resistance. The
thIckness of this layer is kept to
the minimum value that provides
the
required
collector-to-base
breakdown voltage.
Because of the features described above, varactor loss is
minimized in overlay transistors
and, therefore, high conversion
efficiency can be achieved. The inherent varactor frequency-multiplication ability of the collector-tobase junction capacitance, added
to the excellent frequency capability of these transistors, has
made possible the use of overlay
devices as efficient frequency multipliers.

Operation
The outer collector capacitance
Cbc shown in Fig. 392 varies nonlinearly with the transistor collector voltage in much the same
way as the capacitance of a varactor diode varies with the voltage
across the diode junction. This
rso

c
Cbc

Figure 392. Circuit showing the nonlinear
im"edance factors that maKe possible fre·
quency multiplication with overlay
transistors.

variable
junction capacitance
makes possible harmonic generation in overlay transistor circuits.
The nonlinear relationship between the collector-to-base capacitance CbC and the collector bias
voltage in overlay transistors may
be expressed as follows:
Cbc = K (- V)-n

(318)

where K is a constant determined
by the area and doping of the
junction, () is the contact potential, V is the magnitude of the
collector reverse-bias voltage, and
the exponent n is a constant determined by the impurity distribution on both sides of the junction.
Figure 393 shows the variation
in the collector-to-base capacitance
CbC as a function of the collector
bias voltage V bc. However, this
form of capacitance-voltage curve
is difficult to apply directly in the
analysis of high-frequency, highpower transistor circuits. Because

High-Frequency Power Amplifiers

VOLTAGE (Vbc)

Figure 393. Collector-to-base capacitance
Cb,· as a function of collector bias in
overlay transistors.

power is the product of current
and voltage swings in the transistor. The transistor current can be
related to the collector-to-base capacitance if the charge Q across
the junction is known. Because
dQ/dV = C (V), the charge Q can
be determined as follows:
Q=

J Cbc dV

369
waveform, shown in Fig. 395(b),
contains components of the fundamental frequency and of harmonic
frequencies. Power output at the
desired harmonic is obtained when
suitable selective circuits are coupled to the collector of the transistor. In an actual circuit, the
driving voltage developed by the
transistor contains both fundamental-frequency and harmonicfrequency components.
-v

i\'ir--I\.
I

(319)

If the capacitance CllC is defined

as in Eq. (317), the integration
indicated in Eq. (318) can be
performed with respect to the
voltage V to obtain the charge.
The result of this integration,
shown in Fig. 394, shows the
variation in the charge Q as a
function of the voltage VBO'
If a sinusoidal voltage such as
that shown in Fig. 395(a) is developed by the amplifier section of
the overlay transistor to drive the

VOLTAGE (Vbc)

Figure 394. The charge Q in the collectorIO-oase Junction as a function of collectorto-base voltage in an overlay transistor.

nonlinear capacitance Cllc , a highly
distorted charge (or current)
waveform is produced because of
the nonlinear charge-voltage characteristics of the capacitance. This

t
(al

(bl

Figure 395. (a) Sinusoidal voltage developed by the amplifier section of an
overlay transistor to drive the nonlinear
collector-to-base capacitance; (b) distorted
charge, or current, waveform produced by
the nonlinear collector-to-base capacitance
of an overlay transistor in the generation
of harmonic power.

Basic Transistor FrequencyMultiplier Circuits
Overlay transistors used in frequency multipliers may be connected in either common-base or
common-emitter circuit configurations. In the common-base transistor frequency multiplier, harmonic
generation is accomplished in essentially the same way as in a
shunt-type varactor frequency
multiplier because the nonlinear
collector-to-base capacitance of the
transistor is connected in shunt
with the input circuit. In the
common-emitter transistor frequency multiplier, the nonlinear
capacitance is connected in series
with the input; the operation of
the transistor circuit is then simi-

370

RCA Silicon Power Circuits Manual

lar to that of the series-type varactor frequency multiplier.
Fig. 396 shows the basic circuit
configuration for the use of an
overlay transistor in a commonbase frequency doubler. A T
matching network, or other type
of matching section, must be used
in the input of the doubler to set
up a conjugate match across the
emitter-to-base terminals of the
transistor at the fundamental frequency of the input driving power.
This conjugate match is required
to obtain a maximum transfer of

transistor in the common-base
frequency tripler and quadrupler, respectively. These circuits are very similar to the
common-base doubler, except that
an additional second-harmonic
idler loop is connected in shunt
with the transistor collector.
The second-harmonic components
produced by this idler loop beat
with the fundamental-frequency
components to generate addi-

BiG
(01 TRIPLER

Figure 396. Basic configuration for use of
an overlay transIstor on a common-base
frequency doubler.

power from the driving source to
the transistor. Because gain at the
fundamental frequency is of primary importance, an idler circuit
must be connected between the
collector and base of the transistor. The idler loop, which consists of a simple series LC circuit,
resonates with the transistor collector-to-base capacitance at the
fundamental frequency and thus
enhances the flow of fundamental
current through the transistor.
The idler circuit also develops the
driving voltage required by the
nonlinear collector-to-base capacitance for the generation of harmonic power. A suitable output
circuit, which is series-tuned to
select output power at the second
harmonic of the input frequency,
completes the basic doubler circuit. In some circuits, an output
trap must be added to restrict the
flow of fundamental-frequency
current in the output loop.
Fig. 397 shows the basic circuits for the use of an overlay

:rJfr~
(bl QUADRUPLER

Figure 397. Basic configurations for use
of an overlay transistor on a common-base
frequency tripler (a) and frequency
quadrupler (b).

tional harmonic outputs. In this
way, the second-harmonic idler
loop enhances the conversion
efficiency. When an overlay-transistor frequency multiplier is used
in a common-emitter circuit, an
additional series resonant circuit
must be incorporated in the input.
Otherwise, the input, output, and
idler circuits of common-emitter
multipliers follow the considerations already described for the
common-base multipliers.
Design of Transistor
Frequency Multipliers

The design of transistor frequency-multiplier circuits generally consists of the selection of a
suitable transistor and the design
of proper filtering and matching

High-Frequency Power Amplifiers
networks for optimum circuit performance.
Transistors suitable for this
application must provide the desired output power and gain at
the fundamental frequency and
must be able to convert the power
from the fundamental frequency
into power at the desired harmonic
frequency. If a lossless circuit
were coupled to a lossless nonlinear capacitance Cbc, power at
the fundamental frequency could
be converted into power at any
harmonic frequency with lOO-percent conversion efficiency. In practice, however, efficiency is limited
by the series resistance associated
with the nonlinear capacitance and
the circuit losses. It can be considered that the harmonic output
power of a transistor multiplier
circuit, at a given input power
level, is equal to the product of the
power gain of the transistor at
the drive frequency and the conversion efficiency that results from
the varactor action of the collector-to-base capacitance Cbc • Conversion gain can be obtained only
if the power gain of the transistor
under consideration at the fundamental frequency is larger than
the conversion loss.
In the design of such circuits,
the input impedance at the fundamental frequency that exists at the
emitter-to-base junction of the
transistor as well as the load impedance presented to the collector
at both the fundamental and harmonic frequencies must be known.
Knowledge of the collector load
impedance at the harmonic frequency is required for design of
the output circuit. Knowledge of
the collector impedance at the fundamental frequency is needed to
determine the input impedance of
the transistor at that frequency so
that matching networks can be

371
designed between the driving
source and the transistor. The
three impedances, of course, are
interrelated and are functions of
operating power level (i.e., are
determined by voltage and current
swings). These dynamic impedances can be determined experimentally as described in the section on Microwave Amplifiers and
Oscillators. Once the impedances
are established, the design of the
matching networks is straightforward. For the input circuit, a
matching section having low-pass
characteristics is preferred; for
the output circuit, a matching section having high-pass or band-pass
characteristics is preferred. Such
arrangements assure good isolation between input and output circuits. As the frequency of operation increases above 800 MHz, the
design of transistor multiplier circuits requires the use of distributed circuit techniques.

Stability and Biasing
Considerations
In general, the major problem
of nonlinear devices is stability.
Various types of instabilities can
be incurred in transistor frequency-multiplier circuits, including
hysterisis, low-frequency oscillations, parametric oscillations, and
high-frequency oscillations. These
difficulties can be eliminated or
minimized by careful design of
the bias circuit, by proper location of transistor ground connections, and by the use of packages
that have minimum parasitic elements.
Hysteresis refers to discontinuous mode jumps in output power
that occur when the input power
or frequency is increased or de-

372

RCA Silicon Power Circuits Manual

creased. This effect is caused by
the dynamic detuning which results from variation in the average value of the nonlinear capacitance with rf voltage. The tuned
circuit has a different resonant
frequency for a strong drive input
than for a weak drive input. It
has been found experimentally
that hysteresis effects can be minimized, or sometimes eliminated,
when the transistor is used in a
common-emitter configuration.
Low-frequency oscillations occur because the gain of the transistor at low frequency is much
higher than that at the operating
frequency. This effect can be eliminated by use of a small resistance
in series with the rf chokes used
for the biasing circuit, as shown
in Fig. 398.
Parametric oscillations result
because spurious low-frequency
modulation is added to the harmonic output. This effect can be
eliminated by careful selection of
the bypass capacitance C:l in Fig.
398 to provide a low impedance to
the spurious component in addition to that provided by the rf
bypass capacitance C1 •

High-frequency oscillation is indicated by oscillations that occur
at a frequency very close to the
output frequency when the input
drive power is removed. With a
TO-60 package transistor, common-emitter circuits are found to
be less critical in this respect than
common-base circuits. The highfrequency oscillations are also
found to be strongly related to the
input drive frequency. This type
of instability can be eliminated if
the input frequency is kept below
certain values. The input frequency at which stable operation
can be obtained seems to depend
upon the method of grounding
the emitter of the transistor. The
highest frequency of operation
can be obtained when the emitter
has the shortest path to ground.
In practice, stable and reliable
operation of transistors in frequency multipliers has been successfully obtained. The circuits
discussed in this section are all
stable frequency-multiplier circuits.

The 2N4012 Transistor

RFC

SMALL
R

-=Figure 398. Circuit showing biasing techniques and bypassing capacitances used
to eliminate instabilities in common·emitter
frequency multipliers.

The 2N4012 power transistor is
characterized for frequency-multiplication applications and can provide a minimum power output of
2.5 watts as a frequency tripler at
an output frequency of 1 GHz and
a collector efficiency of 25 per
cent. This overlay transistor is
designed to operate in military and
industrial communications equipment as a frequency multiplier in
the uhf or L-band range. It can
be operated as a doubler, tripIer,
or quadrupler to supply a power
output of several watts at frequencies in the low gigahertz
range.

373

High-Frequency Power Amplifiers

Fig. 399 shows the power-output capabilities as a function of
output frequency for a typical
2N4012 transistor used in common-emitter circuit configurations
for frequency doubling, tripling,
and quadrupling. In a commonemitter doubler circuit, the transistor delivers power output of 3.3
watts at 800 MHz with a conversion gain of 5 dB. In a commonemitter tripler circuit, it can
supply power output of 2.8 watts
at 1 GHz with a conversion gain
3.4

3
~

~2.6

'"1\"
...

~g2.2

'"~'" I.B

=I W

\..

+YPE
2N4012

\\ ~

1.4

I
O.B

CURVE (J) DOUBLER,
COMMON EMITTER
~ CURVE (2) TRIPLER,
,\
COMMON EMITTER
CURVE (3) QUADRUPLER,
\
COMMON EMITTER

0.9

'\ \

I
1.1
1.2
1.3
OUTPUT FREQUENCY-GHz

1.4

1.5

Figure 399. Power output of the RCA2N4012 overlay transistor as a function of
frequency when operated in commonemitter doubler, tropler and quadrupler
circuits.

of 4.5 dB. In a common-emitter
quadrupler circuit, it can provide
power output of 1.7 watts at 1.2
GHz with a conversion gain of
2.3 dB.
It is of interest that the transistor frequency multipliers provide greater power outputs at
higher output frequencies than
the unity-gain output obtained
from the transistor power amplifier at 700 MHz. When the frequency of operation is low enough
so that the transistor can supply
rf power with substantial gain,
the output capabilities of the
transistor frequency multipliers

are essentially the same as those
of the transistor power amplifier.
For operation at the same output
frequency and with the same input driving power, approximately
equal amounts of power output can
be obtained.
Fig. 399 shows that the amount
of power output that can be supplied by a transistor frequency
multiplier depends upon the order of multiplication. For a given
multiplier circuit, the highest
output power is obtained at the
frequency for which the product
of power gain and conversion
efficiency has the largest value.
When a 2N4012 overlay transistor is used, maximum power output is obtained at 800 MHz from
a doubler circuit, at 1 GHz from
a tripler circuit, and at 1.3 GHz
from a quadrupler circuit.
The circuit arrangements and
performance data shown in this
section illustrate several practical
frequency-multiplier circuits that
use the 2N4012 and other RCA
overlay transistors. These circuits
include a 400-to-800-MHz doubler,
a 150-to-450-MHz tripIer, a 367to-lIOO-MHz tripIer, and a 420-to1680-MHz quadrupler. As mentioned previously, the design of
multiplier circuits that have an
output frequency of 800 MHz or
higher requires the use of distributed-circuit techniques. All
such high-frequency circuits described use coaxial-cavity output
circuits. These circuits are discussed first. The low-frequency
circuits, which use lumped-element
output circuits, are then described.
400-To-800-MHz Doubler

Fig. 400 shows the complete circuit diagram of a 400-to-800-MHz
doubler that uses the 2N 4012 tran-

RCA Silicon Power Circuits Manual

374

sistor. This circuit uses lumpedelement input and idler circuits
and a coaxial-cavity output circuit.

The curve is nearly linear at a
power output level between 0.9
and 2.7 watts. The power output

3.8

...13.0
•

1/ /

It:

800 MHz
Figure 400. 400-to-800-MHz common-emitter
transistor frequency multiplier.

The transistor is placed inside the
cavity with its emitter properly
grounded to the chassis. A pi section (C 1 , C2 , L 1 , L 2 , and Cg ) is
used in the input to match the
impedances, at 400 MHz, of the
driving source and the base-emitter junction of the transistor. L2
and Ca provide the necessary
ground return for the nonlinear
capacitance of the transistor. La
and C4 form the idler loop for the
collector at 400 MHz. The output
circuit consists of an open-ended
11,4-inch-square coaxial cavity. A
lumped capacitance C5 is added in
series with a 1,4-inch hollow-center
conductor of the cavity near the
open end to provide adjustment
for the electrical length. Power
output at 800 MHz is obtained by
direct coupling from a point near
the shorted end of the cavity. The
bias arrangement is the same as
that used in the circuit shown in
Fig. 400.
Fig. 401 shows the power output at 800 MHz as a function of
the power input at 400 MHz for
the doubler circuit, which uses a
typical 2N4012 operated at a collector supply voltage of 28 volts.

'"~2.2

1.8

1.4

...~ 2 6
5

/:T~PE
2N4012

/0 If

3.4

OUTPUT

Vo'28V

+28 V

III

0.4

0.8
1.2
1.6
POWER INPUT-W

I4
2.0

Figure 401. .output power and collector
efr,ciency as a function of input power for
the 400-to-800-MHz frequency doubler.

is 3.3 watts at 800 MHz for an
input drive of 1 watt at 400 MHz,
and rises to 3.9 watts as the input
drive increases to 1.7 watts. The
collector efficiency, which is defined as the ratio of the rf power
output to the dc power input at
a supply voltage of 28 volts. is
also shown in Fig. 401. The efficiency is 43 per cent measured at
an input power of 1 watt. The 3dB bandwidth of this circuit measured at power output of 3.3 watts
is 2.5 per cent. The fundamentalfrequency component measured at
a power-output level of 3.3 watts
is 22 dB down from the output
carrier. Higher attenuations of
spurious components can be
achieved if more filtering sections
are used.
The variation of power output
with collector supply voltage at an
input drive level of 1 watt is

375

High-Frequency Power Amplifiers
shown in Fig. 402. This curve is
obtained with the circuit tuned at
28 volts. The curves of Figs. 401
and 402 indicate that the transistor amplifier-multiplier circuit is
capable of amplitude modulation.
3.

4 INPUT POWER-I W

3.0

/
V

TYPE 2N4012

OUTPUT
1.1 GHz

Figure 403. 367-MHz-to·1.1-GHz commonemitter transistor frequency tripler.

1.4

1.0
10

COLLECTOR SUPPLY VOLTAGE-V

Figure 402. Power output as a function of
supply voltage for the 400-to·800·MHz fre·
quency doubler.

curve shows the power output obtained with the circuit tuned at
the 2.9-watt output level. A power
output of 2.9 watts at 1.1 GHz is
obtained with drive of 1 watt at
367 MHz. The 3-dB bandwidth
measured at this power level is
2.3 per cent. The spurious-frequency components measured at

367-To-ll00-MHz Tripier
3. 2

The 367-to-llOO-MHz tripler
shown in Fig. 403 is essentially
the same as the doubler shown in
Fig. 400 except that an additional
idler loop, (L 4 , C6 ) is added in
shunt with the collector of the
transistor. This idler loop is resonant with the transistor junction
capacitance at the second harmonic frequency (734 MHz) of
the input drive.
Fig. 404 shows the power output of the tripler at 1.1 GHz as a
function of the power input at
367 MHz. This circuit also uses a
typical 2N 4012 transistor operated at a collector supply voltage
of 28 volts. The solid-line curve
shows the power output obtained
when the circuit is retuned at each
power-input level. The dashed-line

2.B

367 MHz TO 1.1 GHz
TRIPLER
VC=2BV

2.4

II
/

O.B

0.4

VI' -

V/
I

0.2

I. POWER OUTPUT OBTAINED
BY RE-TUNING AT EACH
IN~UT POWER LEVEL
2.POWER OUTPUT OBTAINED
WITH TUNED AT IW
INPUT POWER LEVEL

0.4

0.6
O.B
POWER INPUT-W

1.2

Figure 404. Power output as a function
of power input for the 367-MHz-to-1.1-GHz
frequency tripler.

376

RCA Silicon Power Circuits Manual

the output are as follows: -22dB
at 340 MHz, -30dB at 680 MHz,
-35dB at 1360 MHz.
The variation of power output
with collector supply voltage at an
input drive level of 1 watt is
shown in Fig. 405. The variation
of collector efficiency is also
shown. These curves were obtained with the circuit tuned at
28 volts.

input level (1 watt) . The efficiency
varies between 60 to 75 per cent,
and has an average value of 65
per cent; this performance is comparable to that of a good varactor
multiplier in this frequency range.
A similar tripler circuit that
uses a selected 2N3866 and that
is operated from 500 MHz to 1.5
GHz can deliver a power output
of 0.5 watt at 1.5 GHz with an
input drive of 0.25 watt at 500
MHz.

3.2 367MHz TO 1.IGHz TRIPLER
PIN=IW

150-To-450-MHz Tripier Circuit

2.61-----+---+---t-F---+34I-

<>
a:

2.41----1~---+-+--++--___!30~

Fig. 406 illustrates the use of
the 2N 4012 transistor in a 150-to450-MHz frequency tripler. The
input coupling network is designed

I~
~
z
:: 2.01---j--~-__j'-+--___!26 UJ
~

fo '

450 MHz

~ 1.6

22:=

CIRCUIT TUNED AT
:.l
2.95 W OUTPUT
...J
POWER LEVEL
1.2f---jL..f----i4---+--___!16 <>

COLLECTOR VOLTAGE-V

Figure 405. Power output as a function of
cOllector supply vOltage for the 367·MHzto-1.1-GHz frequency tripler.

A 367-MHz amplifier that used
the same circuit configuration and
components as those of the tripler
circuit shown in Fig. 403 was.
constructed to compare the performance between amplifier and
tripler. The conversion efficiency
for a large number of tripler units
was then measured. The conversion efficiency of the tripler is defined as the 1.1-GHz power obtained from the tripler divided by
the 367-MHz power obtained from
the amplifier at the same power-

+VCE'
+28 V

Figure 406. 150-to-450-MHz common-emitter
transistor frequency tripler.

to match the driving generator to
the base-to-emitter circuit of the
transistor. The network formed by
C~ and L2 provides a ground return for harmonic output current
at 450 MHz. The idler network in
the collector circuit (La, L 4 , and
C 4 ) is designed to circulate fundamental and second-harmonic components of current through the
voltage-variable collector-to-base
capacitance, Cue. The network

High-Frequency Power Amplifiers
formed by Cr., C n, C7 , L:;, and La
provides the required collector
loading for 450-MHz power output. Fig. 407 shows the 450-MHz
power output of the tripler as a
function of the 150-MHz power

377
4

TYPE 2N4012

::c
=-3

oIt)
v

I-

VCE -28VDC

TYPE 2N4012

o
0.4
0.8
1.2
1.6
2.0
RF POWER INPUT AT 150 MH;rt-W
Figure 407. Power output as a function of
power input for the 150-to-450-MHz frequency tripler.

input. For driving power of one
watt, power output of 2.8 watts
is obtained at 450 MHz. The rejection of fundamental, second,
and fourth harmonics was measured as 30 dB below the 2.8-watt,
450-MHz level. The variation of
power output with supply voltage
is shown in Fig. 408.

Common-Emitter and
Common-Base Circuits
The performance data in this
section are given for amplifiermultipliers in which the transistor
is connected in a common-emitter
configuration. When transistors
are used in common-base circuit
configurations, different results

"'
"
f
f

I-

~'q"

::>

II:

'"o I
~

q,.;'
I

II:

o
12
16
20
24
28
32
36
DC COLLECTOR-TO-EMITTER VOLTS-V

Figure 408. Power output as a function of
cOllector supply voltage for the 150-to-450MHz frequency tripler.

are obtained. Fig. 409 shows
curves of power output and efficiency for a common-base and a
common-emitter tripler circuit using a 2N4012 transistor. At low
power levels, the common-base
tripler provides higher gain and
collector efficiency; at high power
levels, higher gain and collector
efficiency are provided by the
common-emitter circuit. At a
power input of 1 watt at 367 MHz,
the common-emitter tripler delivers a power output of 2.9 watts
at 1.1 GHz and the common-base
circuit an output of 2.4 watts.
The collector efficiencies for both
circuits are approximately the
same and are better than 30 per
cent. The 3-dB bandwidth measured in the common-emitter tripler is 2.3 per cent, as compared
to 2.5 per cent in a common-base
tripler. The major difference between the two circuits is that the
power output of the common-emitter tripler saturates at a much
higher power-input level than that
of the common-base circuit. This

378

RCA Silicon Power Circuits Manual

3.0

COMMON BASE ."

~2.2
Go
~

5 1•8

is
c.>

0::

...

1.0

22
0.2

0t4

0.6

o.e

1.0

1.2

c.>

~ 28
I::i
~ 26

l;l

0.6

COMMON BASE

~30

COMMON EMITTER_

0::

0.2

TYPE 2N4012

~34

2.6

~
o

36 V ·28V DC
C

TYPE 2N4012

VC· 2 8VDC

0.2

0.4

COMMON EMITTER

0.6

0.8

1.0

1.2

P'()WER INPUT-W

POWER INPUT-W

(b)

(a)

Figure 409. Comparison of performance characteristics of common-base and commonemitter tripler circuits using the RCA-2N4012 transistor: (a) Power output as a function
of power input; (b) collector efficiency as a function of power input.

effect has also been observed in a
straight-through amplifier. In addition, the common-emitter circuit
is less sensitive to hysteresis and
high-frequency oscillations, as discussed previously.
A 420-MHz-To-l.68-GHz

Oscillator-Quadrupler
The inherent varactor frequency-multiplication ability in overlay
transistors also permits use of
these devices as oscillator-multipliers. Fig. 410 shows an oscillator-quadrupler circuit that uses a
selected 2N3866 transistor. This
circuit can deliver a power output
of more than 300 milliwatts at
1.68 GHz. The first two rf chokes
and the resistors Rl and R2 form
the bias circuit. The fundamental

frequency of the oscillator is 420
MHz, as determined by Co, Lv and
C1 • L2 and C2 form the secondharmonic idler. The second-harmonic component produced by this
idler circuit beats with the fundamental-frequency component to
generate additional fourth-harmonic components. A series-tuned
circuit consisting of Ls and Cs
completes the output circuit.

-v
Figure 410.

Oscillator-quadrupler circuit.

379

Control and Low-Frequency
Power Amplifiers

ILICON power transistors offer
many advantages when used
in the power-output and driver
stages of high-power audio amplifiers and in applications such as
ultrasonic generators, servomechanism control systems, inverters,
and automobile ignition systems.
In these applications, silicon transistors can be used, over a wide
range of ambient temperatures, to
develop power output of tens of
watts to drive loudspeakers, ultrasonic transducers, or servo motors. Alternatively, silicon-transistor amplifiers may be required to
increase the output of some type
of transducer to a level at which
it may be used to control some
process or indicator.

GENERAL CONSIDERATIONS
Transistor power amplifiers may
be designed for operation in
either linear or pulsed (switching) service. In pulsed service,
the transistors are switched, usually in response to a control signal,
between cutoff and saturation to
develop a rectangular-wave output. This switching may be symmetrical to provide equal ON and
OFF times, or may be asymmetrical for increased or decreased
ratios of ON time to OFF time as
determined by the control function desired. In linear service, the

circuit designer can select any
one of three basic classes of operation for the transistors. This
selection is dictated by a combination of such factors as required
power output, dissipation capability, efficiency, gain, and distortion characteristics.

Classes of Operation for
Linear Amplifiers
The three basic classes of operation (class A, class B, and class
C) for linear transistor amplifiers
are defined by the operating point
of the transistor. In class A operation, the active element conducts
for the entire input cycle. In
class B operation, the active element conducts for 180 degrees of
an input cycle and is cut off during the remainder of the time. In
class C operation, the active element conducts for some amount
less than 180 degrees of an input
cycle. The following paragraphs
discuss the distinguishing features of class A and class B operation. In general, because of the
high harmonic distortion introduced as a result of the short con'duction angle, class C operation is
used primarily in rf-amplifier applications in which it is practical
to use tuned output circuits to
eliminate the harmonic components. For this reason, class C
operation is not discussed further.

RCA Silicon Power Circuits Manual

380

Class A Operation-Class A
amplifiers are used for linear
service at low power levels. When
power amplifiers are used in this
class of operation, the amplifier
output is usually transformercoupled to the load circuit, as
shown in Fig. 411. At low power
levels, the class A amplifier can
also be coupled to the load by resistor, capacitor, or direct coupling techniques.

Figure 412. Basic class B, push-pull transformer-coupled amplifier.

If conduction in each device oc-

. - - -......---.()+vcc

""""---+----0 COMMON
Figure

411.

Basic class A, transformercoupled amplifier.

There is some distortion in a
class A stage because of the nonlinearity of the active device and
circuit components. The maximum
efficiency of a class A amplifier is
50 per cent; in practice, however,
this efficiency is not realized. The
class A transistor amplifier is usually biased so that the quiescent
collector current is midway between the maximum and minimum
values of the output-current
swing. Collector current, therefore, flows at all times and imposes
a constant drain on the power
supply. The consistent drain is a
distinct disadvantage when higher
power levels are required or operation from a battery is desired.
Class B Operation-Class B
power amplifiers are usually used
in pairs in a push-pull circuit because conduction is not maintained
over the complete cycle. A circuit
of this type is shown in Fig. 412.

curs during approximately 180
degrees of a cycle and the driving
wave is split in phase, the class
B stage can be used as a linear
power amplifier. The maximum
efficiency of the class B stage at
full power output is 78.5 per cent
when two transistors are used. In
a class B amplifier, the maximum
power dissipation is 0.203 times
the maximum power output and
occurs at 42 per cent of the maximum output.
Transistors are not usually used
in true class B operation because
of an inherent nonlinearity, called
cross-over distortion, that produces a high degree of distortion
at low power levels. The distortion results from the nonlinearities in the transistor characteristics at very low current levels. For
this reason, most power stages
operate in a biased condition somewhat between class A and class B.
This intermediate class is defined
as class AB. Class AB transistor
amplifiers operate with a small
forward bias on the transistor to
minimize the nonlinearity. The
quiescent current level, however, is
still low enough so that class AB
amplifiers provide good efficiency.
This advantage makes class AB
amplifiers an almost universal'
choice for high-power linear amplification, especially in batteryoperated equipment.

Control and Low-Frequency Power Amplifiers
Drive Requirements for
Linear Amplifiers
In class A amplifiers, the output stage is usually connected in
a common-emitter configuration.
The relatively low input impedance that generally characterizes
this type of configuration may result in a severe mismatch with the
output impedance of the driver
transistor. Usually, at low power
levels, RC coupling is used and the
loss is accepted. It may be advantageous in some circuits, however,
to use an emitter-follower between the driver and the output
stage to obtain an improved impedance match.
Class AB amplifiers have many
types of output connections. One
form is the transformer-coupled
output stage illustrated in Fig.
413. Again, the common-emitter
circuit is usually employed because it provides the highest power
gain. The load circuit is never
matched to the output impedance

Figure

413. Basic class AB, push-pull,
transformer-coupled amplifIer.

of the transistor, but rather is
fixed by the available voltage
swing and the required power output. The transformer is designed
to reflect the proper impedance to
the output transistors so that the
desired power output can be
achieved with a specific supply
voltage.

381

The use of transformer coupling
from the driver to the input of
the power transistor assures that
the phase split required for pushpull operation of the output stages
and any necessary impedance
transformation can be readily
achieved. Output transformer coupling provides an easy method for
matching several values of load
impedance, including those encountered in sound-distribution
systems. For paging service, servo
motor drive, or other applications
requiring a limited bandwidth, the
transformer-coupled output stage
is very useful. However, there are
disadvantages to the use of transformer coupling. One disadvantage is the phase shift encountered
at low- and high-frequency extremes, which may lead to unstable operation. In addition, the
output transistors must be capable
of handling twice the supply voltage because of the transformer
requirements.
Another type of transistor output circuit is the series-connected
output stage. With this type of
circuit, the transistors are connected in series across the supply
and the load circuit is coupled to
the midpoint through a capacitor.
There must be a l80-degree phase
shift between the driving signals
for the upper and lower transistors. A transformer can be used
in this application provided that
the secondary consists of two separate windings, as shown in Fig.
414. Other forms of phase splitting can be used; all have problems such as insufficient swing or
poor impedance matching. Capacitor output coupling also has disadvantages. A low-frequency phase
shift is usually associated with the
capacitor, and it is difficult to obtain a capacitor that is large
enough to produce an acceptable

RCA Silicon Power Circuits Manual

382
+Vcc

COMMON

Figure 414. Class AB, push-pull amplifier
with series output connection.

low-frequency output. These disadvantages can be alleviated by
use of a split supply and by connection of the load between the
transistor midpoint and the supply
midpoint with the return path
through the power-supply capacitors. The power-supply capacitors
must be large enough to prevent
excessive ripple.
Complementary amplifiers are
produced when p-n-p and n-p-n
transistors are used in series. A
capacitor can be used to couple
the amplifier output when a single
supply is used, or direct coupling
can be employed when a split
power supply is used, as shown in
Fig. 415. Because no phase inversion is needed in the driving circuit for this output configuration,
there are definite advantages in
the simplicity of the design. One
SINGLE SUPPLY VOLTAGE

+Vcc

disadvantage of this type of amplifier is that the driver must be a
class A stage which may have a
high dissipation. This dissipation
can be reduced, however, by use of
a Darlington compound connection
for the output stage. This compound connection reduces the driving-stage requirement. A method
of overcoming this disadvantage
completely is to use a quasi-complementary configuration. In this
configuration, the output transistors are a pair of p-n-p or n-p-n
transistors driven by a complementary pair in the driver. In this
manner the n-p-n/p-n-p drivers
provide the necessary phase inversion. The availability of both
n-p-n and p-n-p silicon driving
transistors that have the same
electrical characteristics is good.
The driving transistors are connected directly to the bases of
the output transistors, as illustrated in Fig. 416.
Adequate drive may be a problem with the transistor pair shown
in the upper part of the quasicomplementary amplifier unless
suitable techniques are used to assure that this pair saturates. Care
must also be taken when split supplies are used to assure that any
ripple on the lower supply is not
introduced into the predriving
stages by this technique. The adSPLIT SUPPLY VOLTAGE

+Vcc

EOUT~ COMMON

C}------~~----~~-COMMON

-..--------{.] -Vcc

Figure 415. Circuit arrangements for operation of complementary output stages (al from
single de supply; (b) from symmetrical dual (positive and negative) supplies.

Control and Low-Frequency Power Amplifiers

383

.-.s:.:------1I>----{) + vee

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

__---()COMMON

UPPER TRANSISTOR

LOWER TRANSISTOR

Figure 416. Compound output stage in which output transistors are driven by complementary driver transistors: (a) over-all circuit; (b) upper transistor pair; (c) lower
transistor pair.

vantage of a split supply is that
it makes possible direct connection to the load and thus improves
low-frequency response_
To this point, phase inversion
has been mentioned but not discussed. Phase inversion may be
accomplished in many ways. The
simplest electronic phase inverter
is the single-stage configuration.

This configuration can be used at
low power levels or with high-gain
devices when the limited drive
capability is not a drawback. At
higher power levels, some impedance transformation and gain may
be required to supply the drive
needed. There are several complex
phase-splitting circuits; a few of
them are shown in Fig. 417.

+VCC

I------oEoUTI

+----t---+c::>EOUTI
,=--+0IEOUT2

EIN

1------0 EOUT2
COMMON

EIN

o--+--.......---~"-4-o

(a)

COMMON

(b)

+vCC

t------=f-OEOUTI
EOUT2

0 - - + - - - - - - - - - + - 0 COMMON
(e)

0-......-

.......------<1>0 COMMON
(d)

Figure 417. Basic phase-inverter circuits: (a) single stage phase-splitter type (b) twostage emitter coupled type; (c) two-stage low impedance type; (d) two-stage
similar-amplifier type.

384

RCA Silicon Power Circuits Manual

Other Design Considerations
Some additional design problems involve the consideration of
thermal stability, high line voltage, line-voltage transients, excessive drive, ambient temperature,
load impedance,and other factors
that may subject the transistors
to abnormal high-stress conditions. A prime consideration is the
maximum power dissipation at
high supply voltage. Thermal stability is another problem that is
often difficult to control. The problem is complex because the base-toemitter voltage VBE of a transistor
decreases with an increase in
junction temperature at a constant level of collector current.
Therefore, if the V BE of the transistor is held constant, the collector current Ie increases as the
junction temperature rises. This
process is regenerative because
the dissipation increases with an
increase in the value of Ie. One
solution is to place a resistor in
series with the emitter lead. This
approach is not the best solution
to the problem, however, because
the use of the resistor increases
circuit losses. A decrease in the
loss may be obtained if the resistor is bypassed. Another approach
is to use a thermistor or similar
device which, when properly connected, reduces the base drive at
high temperatures. This approach
improves the stability without increasing the circuit loss.
The collector-to-base leakage
current I cllo can also be a problem because a fraction of this current is multiplied by the transistor
h r,. and appears as a component of
the collector-to-emitter current.
In general, the value of I clIo is in
the order of microamperes in silicon devices and milliamperes in

germanium devices. This leakage
current is composed of two components. One component is caused
by surface leakage and is unpredictable in its variations with temperature. It increases with voltage
and may even decrease with' increasing temperature. The other
component is a function of the device material and geometry. This
component approximately doubles
with every 7°e temperature rise
in silicon devices, and approximately doubles for every Iooe
temperature increase in germanium devices. This component may
also be voltage-dependent.
The total leakage is of interest
to the circuit designer because it
can be the mechanism for thermalrunaway problems. An increase
in this leakage increases the total
base current and thus causes an
increase in collector current and
dissipation. The increase in collector current and dissipation
causes a rise in temperature which
possibly may produce a regenerative cycle that leads to thermal
runaway. If an external resistor
is connected between the base and
emitter, some of this leakage current is shunted from the base, and
the thermal-stability problem is
reduced.
Another potential source of
trouble in amplifiers is the feedback loop. Feedback is used to reduce distortion and extend the
frequency range of the amplifier.
The feedback loop usually encloses several if not all of the amplifier stages and can cause several
problems. When transformer coupling is used, phase shifts may occur at the high- or low-frequency
extremes; a positive voltage may
then be fed back and cause oscillation. High-signal-level transients
may cause the value of the trans-

Control and Low-Frequency Power Amplifiers
former inductances and other components to change and become unstable so that they initiate oscillation. A similar condition can occur
at low frequencies when capacitorcoupled transformerless designs
are used.
Excessive drive levels at high
frequencies can cause dissipation
problems. An excessive drive level
forces the output stages to saturate before the peak of the input
signal is reached. This additional
drive lengthens the storage time
which, at high frequencies, may
approach the period of the drive
signal. Under this condition, two
results occur: First, feedback does
not increase after the point where
the output stage saturates. This
condition permits the drive signal
to increase. Second, one transistor
may not turn off until the second
has been turned on. In series-type
output stages, the second transistor is turned on with the full supply voltage present. This condition can lead to forward-bias
second-breakdown problems. In
germanium units, the excessive
dissipation caused by excessive
drive levels at high frequencies
also contributes to the thermal"';unaway problem.
Another potential source of difficulty with amplifiers occurs when
the output is open- or short-circuited. Transformer-coupled output stages are particularly susceptible to operational problems
with no load. Without a load, the
transistors operate into a purely
inductive load line and the probability of reverse-bias second breakdown must be considered. In
series-type output stages, the
major problem arises under shortcircuit load conditions. As a result of the short circuit, feedback
is removed and an open-loop gain
condition exists together with the

385

excessive-drive-condition problems
previously mentioned. It is advisable to use some form of
fast-acting overload protection for
the power transistor; a fuse is
usually not fast enough.
Some frequency exists at which
the gain of any transistor begins
to decrease. This decrease in gain
can be corrected over the required
frequency range by use of feedback or a higher-frequency device.
Roll-off of the frequency response
of the preamplifier stages at some
point prior to the limiting value
of the frequency characteristics
of the transistor is necessary.
This technique assures that the
drive is limited to a safe value by
the input stage so that even the
drivers are not affected by the
high dissipation mentioned previously,
Several other factors that should
be considered in the design of amplifiers for audio-frequency service
include the frequency response
desired, gain, optimum load, noise,
and power output needed.
Linear single-phase servo amplifiers are usually audio power
amplifiers that operate at a single
frequency. The servo. amplifier is
usually designed and biased for
class AB or class B operation.
Greater distortion can be tolerated
than would be acceptable in a
high-fidelity audio amplifier. Hum
and noise may still be problems
if they are near the operating frequency used in the servo application. Servo amplifiers often use
transformer-coupled driver and
output stages because the operation is generally at a single frequency.
The amplifiers described can be
used with any ultrasonic equipment requiring a sine-wave drive.
The previous discussion of lowfrequency amplifiers is applicable

386

RCA Silicon Power Circuits Manual

to ultrasonic equipment except
that consideration must be given
to the frequency involved; ultrasonic equipment usually operates
in the frequency range between
20 kHz and 100 kHz. The oscillator power amplifier already described is best used at low frequencies; however, special attention must be given to the selection
of transistors to assure that they
will operate efficiently at the frequency chosen.
The power oscillator may also
be used as an ultrasonic generator; it supplies sufficient energy
for the load without the need for
any additional amplification. This
amplifier type is particularly useful at lower power levels.
A dc-to-ac inverter may be used
as a source of power for an ultrasonic transducer. The design of
such circuits is covered in the
section on Power Conversion.

configuration for an audio power
amplifier is dictated by the particular requirements of the intended application. The selection
of the basic circuit configuration
that provides the desired performance most efficiently and economically is based primarily upon the
following factors: power output to
be supplied, required sensitivity
and frequency-response characteristics, maximum allowable distortion, and capabilities of available
devices.
Class A Transformer-Coupled
Amplifiers-Fig. 418 shows a
three-stage class A transformercoupled audio amplifier that uses
dc feedback (coupled by R I , R z,
R a, R., and CI ) from the emitter
of the output transistor to the
base of the input transistor to
obtain a stable operating point.

AUDIO-FREQUENCY POWER
AMPLIFIERS
The quality of an audio power
amplifier is measured by its ability to provide high-fidelity reproduction of audio program material
over the full range of audible frequencies. The amplifier is required
to increase the power level of the
input to a satisfactory output level
with little distortion, and the sensitivity of its response to the input
signals must remain essentially
constant throughout the audiofrequency spectrum. Moreover, the
input-impedance characteristics of
the amplifier must be such that
the unit does not load excessively
and thus adversely affect the characteristics of the input-signal
sources.

Basic Circuit Configurations
The selection of the basic circuit

Figure 418. Three-stage, transformercoupled, class A amplifier.

An output capability of 5 watts
with a total harmonic distortion
of 3 per cent is typical for this
type of circuit. In general, this
output level is the upper limit for
class A amplifiers because the
power dissipated by the output
transistor in such circuits is more
than twice the output power. For
this reason, it is economically impractical to use class A audio amplifiers to develop higher levels of

Control and Low-Frequency Power Amplifiers
output power. A circuit such as
the one shown in Fig. 418 usually
requires no over-all feedback unless extremely low distortion is
required. Local feedback in each
stage is adequate; amplifiers of
this type, therefore, are usually
very stable.
Class AB Push-Pull Transformer-Coupled Amplifiers-At
power-output levels above 5 watts,
the operating efficiency of the circuit becomes an important factor
in the design of audio power amplifiers. The circuit designer may
then consider a class AB push-pull
amplifier for use as the audiooutput stage.
Fig. 419 shows a class AB pushpull transformer-coupled audiooutput stage. Resistors R 1 , R 2 , and
Ra form a voltage divider that
provides the small amount of
transistor forward bias required
for class AB operation. The transformer type of output coupling
used in the circuit is advantageous

+Vcc
R2

Figure 419. Class AB, push-pull, transformer-coupled audIo output stage.

387

in that a suitable output transformer can be selected" to match
the audio system to any desired
load impedance. This feature assures maximum transfer of the
audio-output power to the load circuit, which is especially important
in sound-distribution systems that
use high-impedance transmission
lines to reduce losses. A major
disadvantage of transformer output coupling is that it tends to
limit the amplifier frequency response, particularly at the lowfrequency end. Variations in
transformer impedance with frequency may produce significant
phase shifts in the signal at both
frequency extremes of the amplifier response. Such phase shifts
are potential causes of amplifier
instability if they occur within
the feedback loop. Open-circuit
stability is always a problem in
designs that use output transformers because the gain increases
sharply when the load is removed.
If too much over-all feedback is
employed, the amplifier may oscillate. The local feedback caused by
the bias arrangement of R2 and
Ra helps to eliminate this problem.
Push-pull output stages, which
use identical output transistors,
require some form of phase inversion in the driver stage. In the
circuit shown in Fig. 419, a center-tapped driver transformer is
used for this purpose. The requirements of this transformer
depend upon the power levels involved, the bandwidth required,
and the distortion that can be
tolerated. This transformer also
introduces phase-shift problems
that tend to cause instabilities in
the circuit when high levels of
feedback are employed. Phaseshift problems are substantially
reduced when the output stage is

388

RCA Silicon Power Circuits Manual

designed to operate at low drive
requirements. The reduced drive
requirements can be achieved by
use of the Darlington circuit
shown in Fig. 420. Resistors R1
and R2 shunt the leakage of the
driver and also permit the output
transistors to turn off more
rapidly. Impedance levels between
the class A driver and the output
stage can be easily matched by the
use of an appropriate transformer
turns ratio.
+Vee

+ Vee

input of the output transistor
causes a dc voltage to be produced
across the capacitor under high
signal levels. An alternate solution is to use a Darlington pair
to increase the input impedance
of the output stage.
Class AB Series-Output Amplifiers-For applications in which
low distortion and wide frequency response are major requirements, a transformerless approach is usually employed in the
design of audio power amplifiers.
With this approach, the common
type of circuit configuration used
is the series-output amplifier.
PUSH-PULL DRIVEN CIRCUlTS: The class-AB-operated
n-p-n transistors used in the
series-output circuits shown in
Fig. 421 require some form of
phase inversion of the drive signal for push-pUll operation. A
common approach is to use a
driver transformer that has split

Figure 420. Class AB, push-pull, trans·
former-coupled audio output stage in
which Darlington pairs are used to reduce
drive requirements of output transistors.

An alternative method of phase
inversion is to use a transistor in
a phase-splitter circuit, such as
those shown in Fig. 417. U nUke
the center-tapped transformer
method, impedance matching may
be a problem because the collector
of the driver, which has a relatively high impedance, operates
into the low input impedance of
the output stage. One solution is
to reduce the output impedance
of the driver stage by the use of
smaller resistors. The resultant
increase in collector current, however, also increases the dissipation. Moreover, very large coupling capacitors are necessary for
the achievement of good low-frequency performance. The nonlinear impedance exhibited by the

+Vcc

+Vee

e
LOAD

LOAD

+Vee
(0)

(b)

Figure 421. Circuit arranj!ements for operation of series output circuit from (a) a
single dc supply and (b) symmetrical
dual supplies.

secondary windings, as shown
in Fig. 422. The split secondary
windings are required because of

Control and Low-Frequency Power Amplifiers
the mode in which each of the
series output transistors operates.
If ground were used as the drive
reference for both secondary
windings of the circuit shown in
Fig. 422, transistor Q r would operate as an emitter-follower and
would provide gain of somewhat
less than unity. Transistor Q~,

+Vcc

+VBB

+Vcc

Figure 422. Circuit using a driver transformer that has split secondary windings
to provide phase inversion for push-pull
operation of a series·output circuit.

however, is connected in a common-emitter configuration which
can provide substantial voltage
gain. For equal output-voltage
swings in both directions, the
drive input to transistor Q 1 is
applied directly across the base
and emitter terminals. Transistor
Q 1 is then effectively operated in
a common-emitter configuration
(although there is no phase reversal from input to output) and
has a voltage gain equal to that
of transistor Q~.
The disadva~tages of a driver
transformer discussed previously
also apply to the circuit shown in

389

Fig. 422. In addition, coupling
through interwinding capacitances
can adversely affect the performance of the circuit. Such coupling is particularly serious because at both ends of the upper
secondary (terminals 1 and 2) the
ac voltage with respect to ground
is approximately equal to the output voltage. During signal conditions, when output transistor Q 1
is turned on, this coupling provides an unwanted drive to Q1.
The forward transistor bias required to maintain class AB circuit operation is provided by
the resistive voltage divider R 1 ,
R~, R 3 , and R 4 • These resistors
also assure that the output point
between the two transistors (point
A) is maintained at one-half the
dc supply voltage V cc.
As in the case of the transformer-coupled output, phase inversion can be accomplished by
use of an additional transistor.
Fig. 423 shows a circuit in which
the transistor phase inverter is
used, together with a Darlington
output stage to minimize loading

1
Figure 423. Push-pull series-output amplIfier in which driver and output transistors are connected as Darlington pairs and
drive-signal phase inversion is provided by
phase-splitter stage Ql.

390

RCA Silicon Power Circuits Manual

on the phase inverter. It should
be noted that capacitor C provides
a drive reference back to the
emitter of the upper output transistor. In effect, this arrangement
duplicates the drive conditions of
the split-winding transformer approach. A disadvantage of this
circuit is the high quiescent dissipation of the phase inverter Q1
which is necessary to obtain adequate drive at full power output.
An unbypassed emitter resistor R
is necessary because a signal is
derived from this point to drive
the lower output transistor. When
transistor Ql is driven into saturation, the minimum collector-toground voltage that can be obtained is limited primarily by the
peak emitter voltage under these
conditions. To obtain the necessary voltage swing at this collector
(a voltage swing that is also approximately equal to the output
voltage swing), it is necessary to
use a quiescent collector-to-emitter
voltage higher than that required
in a stage that uses a bypassed
emitter resistor.

Figure 424.

COMPLEMENTARY AMPLIFIERS: When a complementary
pair of output transistors (n-p-n
and p-n-p) is used, it is possible
to design a series-output type of
audio power amplifier which does
not require push-pull drive. Because phase inversion is unnecessary with this type of configuration, the drive circuit for the
amplifier is simplified substantially. Fig. 424 shows a basic complementary type of series-output
circuit together with a simple
class A driver stage. The voltage
drop across resistor R provides the
small amount of forward bias required for class AB operation of
the complementary pair of output
transistors.

thermally connected to one of the
output transistors and tracks with
the VBE of the output transistors.
The complementary circuit is by
far the most thermally stable output circuit. It places the output
transistors in a VCES mode because both transistors are operated with a low impedance between base and emitter. Therefore,
the I CBO leakage is the only component of concern in the stability
criteria. At power-output levels
from 3 to 20 watts, a complementary-symmetry amplifier offers advantages in terms of circuit simplicity. At higher power levels,
however, the class A driver transistor is required to dissipate
considerable heat, the quiescent

In practice, a diode is employed
in place of resistor R. The purpose of the diode is to maintain
the quiescent current at a reasonable value with variations in junction temperatures. It is usually
"Vaa

+ vee

e
R

Basic complementary type of
series-output circuit.

Control and Low-Frequency Power Amplifiers
power-supply current drain becomes significant, and excessively
large filter capacitors are required
to maintain a low hum level. For
these reasons, the maximum practical output for a true complementary-symmetry amplifier is considered to be about 20 watts; at
higher power levels, this type of
amplifier is usually replaced by the
quasi-complementary circuit.
QUA S I-COMPLEMENTARY
AMPLIFIERS: In the quasi-complementary amplifier, shown in
Fig. 425, the driver transistors
provide the necessary phase inversion. A simple but descriptive way

391
"EFFECTIVE" COLLECTOR

r--------·- -

I
I

I
IL _ _ _ _ _ _

Figure 426. Connection of p-n-p driver
transistor to n-p-n output transistor.

without inversion. If the emitter
of the n-p-n transistor is considered as the "effective" collector of
the composite circuit, it becomes
apparent that the circuit is equivalent to a high-gain, high-power
p-n-p transistor. The output characteristics of the p-n-p circuit
shown in Fig. 426 and of a highgain, high-power n-p-n circuit
formed by the connection of the
same type of n-p-n output transistor and an n-p-n driver transistor
in a Darlington configuration, such
as shown in Fig. 427, are compared in Fig. 428.

r---------, c
Figure 425. Basic quasi-complementary
type of series-output circuit.

to analyze the operation of a quasicomplementary amplifier is to consider the result of connecting a
p-n-p transistor to a high-power
n-p-n output transistor, as shown
in Fig. 426. The collector current
of the p-n-p transistor becomes the
base current of the n-p-n transistor. The n-p-n transistor, which is
operated as an emitter-follower,
provides additional current gain

I
1

I ____ _
L

I
1

I
I
I

_.J

Figure 427. Darlington connection of n-p-n
driver transistor to n-p-n output transistor.

392

RCA Silicon Power Circuits Manual
5 r-

__ r-

-~5

VOLTAGE-V

p-n-p
(a)

'"""

-~5

VOLTAGE-V

as stable as that of the complementary amplifier, but presents no
problem for silicon transistors.
A typical quasi-complementary
amplifier is shown in Fig. 429.
Capacitor C performs two functions essential to the successful
operation of the circuit. First, it
acts as a bypass to decouple any
power-supply ripple from the
driver and predriver stages. Second, it is connected as a "bootstrap" capacitor to provide the
drive necessary to pull the upper
Darlington pair of transistors into
saturation. This latter function
results from the fact that the
stored voltage of the capacitor,
with reference to the output point
A, provides a higher voltage than
the normal collector-supply voltage to drive transistor Q2' This

n-p-n
(b)

Figure 428. Output characteristics for
(a) p-n-p I n-p-n driver-output transistor
pair shown in Fig. 426 and for (b) Darlington pair of n-p-n transistors shown in
Fig. 427.
POINT A

The saturation characteristics
of the over-all circuit in both cases
is the combination of the base-toemitter voltage VIlE of the output
transistor and the collector saturation voltage of the driver transistor. Moreover, in both cases the
current gain is the product of the
individual betas of the transistors
used. A quasi-complementary amplifier, therefore, is effectively the
same as a simple complementary
output circuit such as that shown
in Fig_ 424, and is formed by the
use of high-gain, high-power n-p-n
and p-n-p equivalent transistors.
In both cases, the resistor R between the emitter and base of the
output transistor places the device
in a VCEll mode. This mode is not

Figure 429. Quasi-complementary audio
power amplifieT that operates from a single
dc supply.

higher voltage is necessary during
the signal conditions that exist
when the upper transistors are
being turned on because the emitter voltage of transistor Q 2 then
approaches the normal supply voltage. An increase in the base voltage to a point above this level is

Control and Low-Frequency Power Amplifiers
required to drive the transistor
into saturation. Resistor Rl provides the necessary dc feedback to
maintain point A at approximately
one-half the nominal supply voltage. Over-all ac feedback from
output to input is coupled by resistor R2 to reduce distortion and
to improve low-frequency performance.
As indicated in Fig. 421 (b),
series-output circuits can be employed with separate positive and
negative supplies; no series output capacitor is then required. The
elimination of this capacitor may
result in an economic advantage,
even though an additional power
supply is used, because of the size
of the series output capacitor necessary in the single-supply case
to obtain good low-frequency performance (e.g., a 2000-microfarad
capacitor is required to provide a
3-dB point at 20 Hz for a 4-ohm
load impedance). Split supplies,
however, pose certain problems
which do not exist in the singlesupply case. The output of the
amplifier must be maintained at
zero potential under quiescent conditions for all environmental conditions and device parameter variations. Also, the input ground
reference can no longer be at the
same point as that indicated in
Fig. 429, because this point is at
the negative supply potential in a
split-supply system.
If the ground-point reference
for the input signal were a common point between the split supplies, any ripple present on the
negative supply would effectively
drive the amplifier through transistor Qr, with the result that this
stage would operate as a common-base amplifier with its base
grounded through the effective impedance of the input signal source.

393

To avoid this condition, the amplifier must include an additional
p-n-p transistor as shown in Fig.
430. This transistor (Q6) reeluces
the drive effects of the negative
supply ripple because of the high
collector impedance (1 megohm or
more) that it presents to the base
of transistor Ql, and effectively

Figure 430. Quasi-complementary audio
power amplifier that operates from symmetrical dual dc power supplies. The p-n-p
transistor input stage is required to prevent ripple component from driving
amplifier.

isolates the input source impedance from transistor Ql. In practice, transistor Q 1 may be replaced
by a Darlington pair to reduce the
loading effects on the p-n-p predriver.
Negative dc feedback is applied
from the output to the input stage
by R 1 , R 2, and C1 so that the output is maintained at about zero
potential. Actually, the output is
maintained at approximately the
forward-biased base-emitter voltage of transistor Q6' which may
be objectionable in a few cases,
but which can be eliminated by a
method discussed later. Capacitor
C1 effectively bypasses the negative dc feedback at all signal frequencies. Resistor R3 provides ac

394

RCA Silicon Power Circuits Manual

feedback to reduce distortion in
the amplifier.

Power Output in Class B
Audio Amplifiers
For all cases of practical interest, the power output (Po) of an
audio amplifier is given by the following equation:
Po

=
=

I(rms) X E(rms) = (Ip Ep)/2
(Ip2 R L)/2 = Ep2/2RL

where Ip and Ep are the peak load
current and voltage, respectively,
and RL is the load impedance presented to the transistor. Fig. 431
shows the relationship among

these various factors in graphic
form. Obviously, the peak load
current is the peak transistor current, and the transistor breakdown-voltage rating must be at
least twice the peak load voltage.
The vertical lines that denote 4ohm, 8-ohm, and I6-ohm resistances are particularly useful for
transformerless designs in which
the transistor operates directly
into the loudspeaker.
Audio-Power-Amplifier Rating
Methods--The Institute of High
Fidelity (IHF) and the Electronic
Industries Association (EIA)
have attempted to standardize

I03~--~----~~__~~__~~-r--~~~~-r--~~~~~
8~--~~--~~-+~~~Pr~-+--~+-~~~~~~~~~

.!.::>==
~
::>

4~--~~~~~-+~~~~~~~~~~~~~~

III

2~--~----~~~~~~~?--+~+-~~~-P~~~~~~

IO~--~--+-.J.L*~~¥
8~--~~~~~~~~~
6.~--~~~~~~~~~~

810

LOAD RESISTANCE-.Q

Figure 431.

Peak transistor currents and load voltages for various output powers and
load resistances.

Control and Low-Frequency Power Amplifiers
power-output ratings to establish
a common reference of comparison
and to provide a solid definition of
the capabilities of audio power amplifiers. Obviously, an audio power
amplifier using an unregulated
supply can deliver more output
power under transient conditions
than under steady-state conditions.
The rating methods which have
been standardized for this type of
operation are the IHF Dynamic
Output Rating (lHF-A-201) and
the EIA Music Power Rating
(EIA RS-234-A).
Both of these measurement
methods allow the use of regulated
supply voltage to simulate transient conditions. Because the regulated supply has no source impedance or ripple, the results do
not completely represent the transient conditions, as will be explained later.
MEASUREMENT METHODS:
The EIA standard is used primarily by manufacturers of packaged equipment, such as portable
phonographs, packaged stereo
hi-fi consoles, and packaged
home-entertainment consoles. The
EIA music power output is defined as the power obtained at
a total harmonic distortion of 5
per cent or less, measured after
the "sudden application of a signal during a time interval so
short that supply voltages have
not changed from their no-signal
values." The supply voltages are
bypassed voltages. These definitions mean that the internal
supply may be replaced with a
regulated supply equal in voltage to the no-signal voltage of
the internal supply. For a stereo
amplifier, the music power rating is the sum of both channels,
or twice the single-channel rating.

395

The IHF standard provides two
methods to measure dynamic output. One is the constant-supply
method. This method assumes
that under music conditions the
amplifier supply voltages undergo only insignificant changes.
Unlike the EIA method, this
measurement is made at a reference distortion. The constantsupply method is used by most
high-fidelity component manufacturers. The reference distortion chosen is normally less than
one per cent, or considerably
lower than the EIA value of 5
per cent used by packagedequipment manufacturers.
A second IHF method is calJed
the ''transient distortion" test.
This method requires a complex
setup including a low-distortion
modulator with a prescribed output rise time and other equipment. The modulator output is
required to have a rise time of
10 to 20 milliseconds to simulate
the envelope rise time of music
and speech. This measurement is
made using the internal supply
of the amplifier and, consequently, includes distortion
caused by voltage decay, powersupply transients, and ripple.
This method tends to be more
realistic and to yield lower
power-output ratings than the
constant-supply method. Actually, both IHF methods should
be used, and the lowest power
rating obtained at reference distortion with both channels operating, both in and out of phase,
should be used as the power rating. (There is some question
concerning unanimity among
high-fidelity manufacturers on
actually performing both IHF
tests.)
Because music is not a continuous sine wave, and has av-

396

RCA Silicon Power Circuits Manual

erage power levels much below
peak power levels, it would appear that the music power or
dynamic power ratings are true
indications of a power amplifier's ability to reproduce music
program material. The problem
is that all three methods described have a common flaw.
Even the transient-distortion
method fails to account for the
ability of the audio amplifier to
reproduce power peaks while it
is already delivering some average power. The amplifier is almost never delivering zero output
when it is called on to deliver
a transient. For every transient
that occurs after an extremely
quiet passage or zero signal,
there are hundreds that are imposed on top of some low but
non-zero average power level.
This condition can best be
clarified by consideration of the
power supply. Many amplifiers
have regulated supplies for the
front-end or low-level stages, but
almost none provides a regulated
supply for the power-output
stages because regulation requires extra transistors or other
devices; it becomes costly, especially at high power levels. The
power supply for the output
stages of power ampliers is commonly a nonregulated rectifier
supply having a capacitive input
filter. The output voltage of such
a supply is a function of the output current and, consequently,
of the power output of the amplifier.
EFFECT OF POWER-SUPPLY REGULATION: Power-supply regulation is dependent on
the amount of effective internal
series resistance present in the
power supply. The effective series
resistance includes such things

as the dc resistance of the transformer windings, the amount and
type of iron used in the transformer, the amount of surge resistance present, the resistance
of the rectifiers, and the amount
of filtering. The internal series
resistance causes the supply
voltage to drop as current is
drawn from the supply.
Fig. 432 shows a typical regu'::
lation curve for a rectifier power
supply that has a capacitive input filter. The voltage is a linear

MAGNITUDE OF THE
CONSTANT SLOPE
BETWEEN THESE TWO
POINTS- EFFECTIVE
SERIES RESISTANCE

Figure 432. Regulation curve for capacitive
rectifier power supply.

function of the average supply
current over most of the useful
range of the supply. However,
a rapid change in slope occurs
in the regions of both very small
and very large currents. In class
B amplifiers, the no-signal supply current normally occurs beyond the low-current knee, and
the current required for the amplifier at the clipping level occurs before the high-current
knee. The slope between these
points is nearly linear and may
be used· as an approximation of
the equivalent series resistance
of the supply.
The a:rnount of power lost depends on the quality of the power

397

Control and Low-Frequency Power Amplifiers
supply used in the amplifier. Accordingly, rating amplifier power
output with a superb external
power supply (that is, not using
the built-in amplifier power supply) provides false music power
outputs. Under actual usage the
output is lower, as illustrated by
the following example.
Figs. 433 and 434 show equivalent circuits for capacitive-input

_,,,V', __

:JII

~+Es/2

Figure 434. Equivalent circuit for split capacitive-input rectifier supply.

Figure 433. Equivalent circuit for singleended capacitive-input rectifier supply.

rectifier supplies. In these circuits, Ide is the average supply
current, RH is the effective
equivalent series resistance of
the power supply, Eo is the nosignal voltage, and Es is the
steady-state supply voltage. The
steady-state voltage, Es, is related to the no-signal voltage,
Eo, as follows:

power supply delivers current on
alternate half-cycles, and each
half of a split supply delivers
current on alternate half-cycles.
Therefore, in each case the supply current, Ide' is related to the
peak output current, as follows:

(321)
The power output is related to
the peak output current, as follows:

(320)
Eq. (320) shows that the supply voltage, E .. is equal to the nosignal supply voltage, Eo, only
when there is no current other
than the no-signal current being
drawn from the supply. As soon
as the amplifier begins to deliver
some power to the load, the power
supply is called upon to deliver
some current. A single-ended

(322)

where RL is the speaker load resistance. Consequently, the supply current is related to the
power output by

Ide

(~)V.
71"' RL

(323)

Combining Eqs. (320) and (323),

398

RCA Silicon Power Circuits Manual
2P
E, = Eo - R. ( 7r'RoL

)%(324)

In relating average current
and power output, it is assumed
that sine-wave signals are included and that no parasitic
losses exist.
This relationship can be simplified if it is assumed that RL
is 8 ohms and 71"2 is 10. Eq. (324)
then becomes
E.

Eo - 0.158 R, (Po) %

(325)

To illustrate the inability of
the no-signal supply voltage to
indicate the transient power capability of an amplifier, it is assumed that an amplifier power
supply has the regulation characteristics shown in Fig. 432. Using the values for voltage and
current from Fig. 432, the music
power rating, based on the nosignal voltage (44.8) and an 8ohm load, is given by
P

Eo'
8R I.
= 31.5 watts/channel

mUSlC=--

If no parasitic losses are assumed, therefore, the stereo
music power would be 63 watts.
[The factor, 8, in Eq. (326) is
derived in converting peak-topeak volts to rms volts.]
The effective series resistance,
according to Fig. 432, is approximately 6 ohms. If the amplifier is
delivering an average power of
2 watts per channel, or a total
of 4 watts, the supply voltage
decreases from 44.8 volts to a
smaller value, determined from
the following equation.

= 44.8 -

0.158 (6) (2)

55r---~----~----~-----,

~
a..
~35~-+--~----+-----4-~~~
II>
I-NO SIGNAL CURRENT
u
I
C
I
250L--L--L-----L-----~--~2

(326)

The music power rating is then
given by Es2/8RL = 28.7 watts
per channel, or 57.4 watts for
stereo. The difference in these
ratings represents a 10-per cent
decrease in the actual transient
power capability.
,
The preceding calculations
prove that an amplifier with
a 31.5-watt-per-channel music
power rating may, in fact, have
an actual power-output capability of only 28.7 watts per channel.
This decrease of 10 per cent
in measured transient capability
may be as much as 20 per cent
in some cases. One such case is
where the no-signal load is less
than that shown in Fig. 435. The

= 42.9

0.5

1.5

DC OUTPUT CURRENTIIdc1

Figure 435. Typical power-supply
regulation curve.

no-signal load includes the class
AB bias current of the output
stages and all of the current
drawn by the preceding stages
and their associated bias networks. When this total current
is below the 250-milliampere
value shown, the no-signal voltage is located on the steep portion of the regulation curve. As
a result, there is a greater decline in supply voltage when the
amplifier is called on to deliver
2 watts or more of average power.

Control and Low-Frequency Power Amplifiers
It should be emphasized that,
while there is a discrepancy between the actual power available and the power measured
under the EIA Music Power or
the IHF Dynamic Power methods, these methods are not without merit. The IHF dynamic
power rating, in conjunction with
the continuous power rating, produces an excellent indication of
how the amplifier will perform.
The EIA music power rating
which is measured at a total harmonic distortion of 5 per cent
with a regulated power supply,
provides a less adequate indication of amplifier performance because there is no indication of
how the amplifier power-supply
voltage reacts to power output.
Some important factors considered by packaged-equipment
manufacturers,
the
primary
users of the EIA music power
rating, are mostly economic in
nature and affect many aspects
of the amplier performance. Because there is no continuous
power output rating required,
two amplifiers may receive the
same EIA music power rating but
have different continuous power
ratings. The ratio of music
power to continuous power is,
of course, a function of the regulation and effective series resistance of the supply.
One reason for the difference
between ratings used by the console
or
packaged-equipment
manufacturer and those used by
the hi-fi component manufacturer
is that the latter does not always
know just what will be required
of the amplifier. The console
manufacturer always designs an
amplifier as part of a system,
and consequently knows the
speaker impedances and the

399

power required for adequate
sound output. The console mailUfacturer may use high-effciency
speakers requiring only a fraction of the power needed to drive
many component-type acousticsuspension systems. The difference may be such that the console may produce the same sound
pressure level with an amplifier
having one-tenth of the power
output. High ratios of musicpower to continuous-power capability are common in these consoles. A typical ratio of IHF
music power to continuous power
may be 1.2 to 1 in component
amplifiers, whereas a typical
ratio of EIA music power to continuous power in a console system may be 2 to 1. Console manufacturers use the EIA music
power rating to economic advantage as a result of the reduced
regulation requirement of the
power supply. A high ratio of
music power to continuous power
means higher effective series resistance in the power supply.
This resistance, in turn, means
less continuous dissipation on
the output transistors, smaller
heat sinks, and a lower-cost
power supply.
Basic Power-Dissipation Relationships-Under ideal conditions (i.e., with a perfectly regulated dc power supply), maximum
transistor power dissipation in a
class B audio output stage is approximately 20 per cent of the
maximum un clipped sine-wave
power output and occurs when
the output stage is delivering approximately 40 per cent of the
maximum output power to the
load. In the following paragraphs, this statement is verified
by analysis of a typical complementary-symmetry amplifier,

RCA Silicon Power Circuits Manual

400

such as those shown in Fig. 436.
The effect of a nonregulated
power supply on transistor dissipation is then examined.

The dissipation P T for each transistor is equal to half the difference between the supply power
delivered p. and the power dissipated in the load Po, as follows:
P T = (P, - Po) /2
(331)
If Eq. (331) is differentiated and

(a)

(b)

Figure 436. Typical complementarysymmetry circuits.

REGULATED SUPPLY: When
the amplifier circuit shown in
Fig. 436(a) is operated from a
regulated supply, the capacitor
C, under no-signal conditions, is
charged to a voltage equal to
one-half the supply voltage (i.e.,
Ee = E./2) at the clipping level.
The maximum peak load current
Ipk(max) is given by
I pk (max)

E,/2 RL

(327)

Because the supply delivers current on alternate half-cycles, the
average supply current Ide is
given by
Ide = I pk /1I"

(328)

The power Po delivered by the
supply can then be expressed as
follows:
P = (I pk E.) /11"
8

(329)

The power delivered to the load
Po is given by
Po

(I pk' R L ) /2

(330)

solved for the peak load current
Ipk at maximum average transistor dissipation, the following expression is obtained:
I pk = E,/ (11" R L )
(332)
When this value is substituted
in Eq. (331), the ratio of maximum average transistor dissipation PT(max) to power delivered
to the load at full power output
Po (max) can be expressed as
follows:
P T (max)
2
(333)
Po (max)
11"2
Eq. (333) indicates that maximum
transistor dissipation is approximately 20 per .cent of full power
output. At the point of maximum
dissipation, the power output is
given by
E s 'Po (max diss.) - - 211"2 RI,

(334)

The ratio of the power output
at maximum dissipation Po (max
diss.) to maximum power output
Po (max) is then given by
Po (max diss.)
Po (max)

4
11"'

(335)

NONREGULATED SUPPLY:
In the case of a nonregulated
supply that has an internal resistance R.. the supply vol.tage
E. is expressed by Eq. (320). If
this value for E. is substituted
in Eq. (331), the following result
is obtained:

401

Control and Low-Frequency Power Amplifiers
PT

(I pk ) ' RL
4
(336)
The partial derivative of Eq.
(336) with respect to Ipk is set
equal to zero, tested for a maximum value, and solved for Ipk.
This value of Ipk is then used
in Eq. (336) to determine the
maximum transistor dissipation
P T (max), as follows:
=

I pk Eo _ R, (I pk )2
2".
2".'

dP,.r = Eo _ I pk 2 Rs + ".'R L
dI1)k
2".
2 ".'
(337)
Eo'"
(338)
Eo'
8 Rs + 4,..' RL
(339)
Clipping begins at the point
where the peak collector current
Ipk is given by

P T (max)

I
pk =

Eo'"

+ 2 7r RL

(340)
Power output at clipping can
then be expressed as follows:
Po (clipping)

2 (R s

+ 2 7r RL)2

(341)
If Rs = 0 is substituted in Eq.
(341), the power output may be
expressed as follows:
Po = Eo2 / 8 RL
(342)
This value is equivalent to the
power output just prior to clipping with a fully regulated
supply and, for the remainder of
this discussion, is referred to as
the music power output [This
definition of music power output, i.e., as the maximum unclipped sine-wave power output,
differs from the EIA standard
(RS-234-A), which defines the

music power output as the point
at which the total harmonic distortion is 5 per cent when a
regulated supply is used. The
EIA value is about 10 per cent
greater.]
Maximum average transistor
dissipation is related to the music
power output by the following
expression:
P T (max)
Po (music)

[7r 2+ Rs]-1
2
RL (343)

The power output at which
maximum average transistor dissipation occurs Po (max diss) is
related to the music power output as follows:
Po (max diss.)
Po (music)
[

7r2
Rs
RS2] -1
-+-+-4
RL 7r'RL2
(344)

The continuous power output
at the clipping level, Po (clipping) is related to the music
power output by the following
expression:
Po (clipping)
Po (music)
[1

RS
,.. RL

R s' ] -1
4,..2 R L'
(345)

Eq. (343), (344), and (345)
are plotted in Fig. 437. Power
levels are normalized with respect to the music power output
and are plotted as a function of
Rs/RL·
The equations plotted in Fig.
437 suggest some interesting
possibilities. Transistor power
dissipation is only a small fraction of the clipping power output
for higher ratios of Rs/RL. For
example, a 100-watt amplifier

402

RCA Silicon Power Circuits Manual

....~

40r---+-~~---r---+--~

....

~ 20i.1~~;:~~~~~t:::J
I~AXIMUM
Q:

....

a..

TRANSISTOR

Rs/RL

Figure 437. Power output and dissipation
as functions of Rs and RL.

could be built using transistors
and associated heat sinks capable of only about 7 watts of
maximum dissipation each.
The equations presented, however, do not consider high line
voltage or effects of ripple voltage. Calculations for average
transistor dissipation should also
include no-signal bias dissipation and the increase in bias
dissipation with increasing ambient and junction temperatures
in class AB circuits. Storage effects, phase shift, and thermal

tracking should also be considered.
Of the above factors, bias dissipation probably contributes the
greatest percentage of average
worst-case transistor dissipation.
The output stage is usually
biased ON slightly (class AB) to
reduce cross-over distortion .
It is possible, however, to design amplifiers for which bias
dissipation is not a problem. One
such amplifier is shown in Fig.
438. The bias dissipation in this
amplifier is negligible at all
practical temperatures. One side
is cut off and the other conducts less than one milliampere.
Thermal runaway cannot be initiated in the output stage at any
junction temperature below its
maximum rating. Consequently,
thermal tracking may also be
neglected so long as the ambient
temperature plus the product of
the instantaneous dissipation
times the junction-to-ambient
thermal resistance is less than
the maximum junction temperature rating.

8--0HM
SPEAKER

Figure 438.

Class B complementary-symmetry power amplifier.

Control and Low-Frequency Power Amplifiers
Storage effects are also reduced as a result of the reverse
bias provided for the OFF-transistor by the ON-transistor in
complementary symmetry. This
circuit, then, is one practical example of an amplifier capable of
achieving the characteristics
shown in Fig. 437.
Maximum Ratio of Music
Power to Continuous Power Output-Some advantages of high
values of the ratio Rs/RL and
corresPQndingly high ratios of
music power output to transistor dissipation are as follows:
1. Reduced heat sink or tran-

sistor cost: Because the
volt-ampere capacity of the
transistor is determined by
the music power output, it
is not likely that reduced
thermal-resistance requirements will produce significant cost reductions. Alternatively, the heat-sink
requirements may be reduced.
2. Reduced
power
supply
costs: Transformer and/or
fi It e r-capacitor specifications may be relaxed.
3. Reduced
speaker
cost:
Continuous power-handling
capability may be relaxed.
These cost reductions may be
passed along to the consumer
in the form of more music power
per dollar.
The question arises as to how
high the ratio Rs/RL and the
corresponding ratio of music
power output to continuous
power output may go before the
capability of the amplifier to reproduce program material is impaired.
The objective is to provide the

403

listener with a close approximation of an original live performance. Achievement of this objective requires the subjective
equivalents of sound pressure
levels that approach those of a
concert hall. Although the peak
sound pressure level of a live
performance is about 100 dB, the
average listener prefers to operate an audio system at a peak
sound pressure level of about 80
dB. The amplifier, however,
should also accommodate listeners who desire higher-than-average levels, perhaps to peaks of
100 dB.
A sound pressure level of 100
dB corresponds to about 0.4 watt
of acoustic power for an average
room of about 3,000 cubic feet.
If speaker efficiencies are considered to be in the order of 1
per cent, a stereophonic amplifier must be capable of delivering
about 20 watts per channel.
Higher power outputs are required for lower-efficiency speakers. The peak-to-average level
for most program material is between 20 and 23 dB. A system
capable of providing a continuous level of 77 dB and peaks of
100 dB would satisfy the power
requirements of nearly all listeners. For this performance to be
attained, the power-supply voltage cannot drop below the voltage required for 100 dB of
acoustic power while delivering
the average current required for
77 dB. Moreover, because sustained passages that are as much
as 10 dB above the average may
occur, the power-supply voltage
cannot drop below the value required for 100 dB of acoustic
power while delivering 87 dB
of acoustic power (87 dB of
acoustic power corresponds to
about 1 watt per channel). This

RCA Silicon Power Circuits Manual

404

performance means that for 8ohm loads, with output-circuit
losses neglected, the power-supply voltage must not decrease to
a value less than 36 volts, while
delivering the average current
required for 1 watt per channel
(0.225 ampere dc).
It should be noted that the
power-output
capability
for
peaks while the amplifier is delivering a total of 2 watts is not
the music power rating of the
amplifier because the powersupply voltage is below its nosignal value by an amount depending on its effective series
resistance.
Maximum Effective Series Resistance-There is a relationship
between the maximum effective
series resistance of the power
supply and the music power rating of the amplifier if it is to
perform to the standards as outlined above.
The power-supply series resistance Rs may be expressed as
a function of music-power output, as follows:

power value that will allow the
amplifier to deliver a minimum
of 100 dB of acoustical power
output as described above.
Use of Fig. 440 in conjunction
with Fig. 437 shows that very
high ratios of music power output to continuous power output
may be employed without sacrifice of the subjective ability of
C;'I

1200
w
o

f'!

iii

160

0::

ii1120

§>

....
....
w

Rs = [( 8R d Plo, (mUSiC)] 1/2
E s (min)

Figure 439.

~ DC OUTPUT CURRENT
I
Power-supply regulation curve.

::IE
::>
::IE

(346)

where Es(min) is the minimum
voltage required for 100 dB of
acoustical power output and I
is the current required for 87
dB of acoustical power output,
less the idle current. [Es (min)
should, in practice, be increased
by peak output-circuit voltage
losses.]
Eq. (346) is plotted in Fig.
439. The value of Rs is the absolute maximum value of effective
supply resistance for each music-

/
eo

100

MUSIC-POWER OUTPUT PER CHANNEL-W

Figure 440. Maximum effective s If

POWER OUTPUT-W
(a)

POUT=20W

(50

THO

0.1

32
ii...J

....
0::

10 2

103

FREQUENCY-Hz
(b)

Figure 450. Performance characteristics for the 20-watt complementary-symmetry amplifier: (a) distortion as a function of power output; (b) relative response as a function
universal complementary-symmetry design.)

TYPE

IN3754

Note:

POUT

(W)

40
70

Vs
(±V)

19
26

(SEE NOTE)

All resistances are in ohms and are '/2-watt
types unless otherwise specified.
All capacitance values are in microfarads unless otherwise specified.

Figure 451. Universal quasi-complementary-symmetry audio-amplifier circuit. This circuit
configuration may be used for four separate audio amplifiers capable of power outputs of
12 to 70 watts (rms).

417

Control and Low-Frequency Power Amplifiers

manufacturers of high-fidelity
amplifiers. This basic circuit can
be used for four separate audio
amplifier circuits that provide
continuous sine-wave power out-'
puts of 12, 25, 40, and 70 watts
(rms) with just minor changes
in component values, supply
voltage, and transistors. Values
of some components (shown on
the circuit schematic) and the
input, predriver, and protection
circuit transistors remain the
same for all output-power levels.
Table XXXIX lists the other
component requirements for the
four circuits. The voltage chart
shown with the circuit schematic
indicates the supply voltage required for each output-power
level.
The universal quasi-complementary-symmetry amplifiers feature rugged hometaxial-base silicon n-p-n output transistors.
These transistors and the complementary driver transistors are
operated class AB in an arrangement that ensures a small zero-

signal current drain. Other features of the circuit include
direct-coupled preamplifier and
predriver stages and short-circuit protection or safe-area limiting.
The preamplifier stage consists
of a balanced-bridge circuit (Ql
and Q2) that maintains quiescent
zero dc voltage at the output.
Feedback is coupled through resistor R 6 , and ground reference
is provided through resistor R2
and capacitor C2 • The common
emitters are returned to the positive supply through resistor Ra,
diode D 1 , and resistor R5 • Diode
Dl and capacitor C4 minimize
turn-off transients and provide
power-supply decoupling. The
bridge circuit is direct-coupled to
a class A predriver stage (Qa),
which is coupled to the complementary drivers (Q4 and Q5)
through R 12 • The dissipationlimiting protection circuit is also
connected at this point. The purpose of this circuit, as previously
indicated, is to prevent the out-

Table XXXIX-Transistor Requirements and Component Values for
Universal Quasi-Complementary-Symmetry Audio-amplifier
Design Packages
POWER OUTPUT
watts (rms)
TRANSISTOR
COMPLEMENT

12
All
Silicon

25
All
Silicon

40
All
Silicon

70
All
Silicon

Transistor types for driver and output stage:
Q. (n-p-n driver)
Q5 (p-n-p driver)
06, Q7 (output)

2N3568
2N3638
40631

2N3568
2N3638
40632

40635
40633
40633

Resistance values (aI/ resistors are Y2-watt unless otherwise specified)
R. (kilohms)
10
12
15
R7 (ohms)

R. (ohms)
RlO (ohms)

Rll (ohms)
RllI (ohms)
Roo, R.. (ohms)

750
1000
1800
40
180
0.47/5W

680
1800
2200
47
270
O.43/5W

560
2200
2700
47
390
0.39/5W

40594
40595
40636

18
470
2700
3300
47
470
O.33/5W

418

RCA Silicon Power Circuits Manual

put stage from being driven into diode Ds. Current is sampled
conduction if abnormally high across resistor R22 for negativedissipation occurs. The dissipa- cycle limiting and coupled to
tion-limiting circuit provides a transistor Q9 through resistor
shunt path for the drive current R1S ' Voltage sampling by resisfrom the associated driver and tors RIO and R16 and diode D7
output devices. Resistor R12 pro- causes a change in the slope of
vides some limiting of the cur- the limiting characteristics. Rerent that transistor Q9 must sup- sistors R24 and R25 , capacitors
port during overload conditions. CIS and C15 , and inductor Ll
Capacitor C9 bypasses R12 to im- provide high-frequency roll-off
prove transient response. Diodes (above 50 kHz) so that a good
D2, D3, and D4 and resistor Rll margin of stability can be mainprovide a controlled forward tained under any loading condibias on the drivers and output tions; capacitors CIO' Cl l , and
devices so that class AB opera- C12 provide additional stability
tion is maintained. The "boot- during limiting. Diodes D5 and
strap" capacitor Cs supplies the Ds prevent forward-biasing of
extra voltage swing necessary to the collector-base junctions of
saturate the upper output pair transistors Qs and Q7 during al(Q4 and Q6) through resistors ternate half-cycle signal swings.
Rs and RIO' Capacitor C7 supplies Capacitors C14 and C16 provide
a controlled voltage swing parasitic suppression. Diode D9
through R9 and Ria to overcome and resistor R IS ensure a transthe normal losses introduced by conductance match between the
resistor RI2~ Resistor Ria and ca- upper and lower Darlington pairs
pacitor Cs provide high~fre to minimize low-level distortion.
quency decoupling for the negaTable XXX X summarizes the
tive dc supply line. Resistors R20 performance characteristics of
and R 2I , with R22 and R 23 , provide the four amplifiers that can
the necessary stabilization for be designed from the univerthe output transistors (Qs and sal quasi-complementary-symmeQ7)' Current is sampled across try design package. Each ampliresistor R 2a for positive-cycle fier provides the full rated power
sensing and coupled to transis- output to frequencies well betor Qs through resistor RI7 . Si- yond 20 kHz at a total harmonic
multaneous voltage sampling is . distortion of 1 per cent. The
provided by resistor R14 and curves of distortion as a function

Table XXXX-Typical Performance Data for Quasi-ComplementarySymmetry Circuits (12 to 70 Watts)
(Measured at a line voltage of 120V, TA

Circuit
Description
12-W (All Si)
25-W (All Si)
40-W (All Si)
70-W (All Si)

= 25°C, and a frequency of 1 kHz, unless otherwise specified.)

Power Output (W) (So load)
Continuous Music
Dynamic
(1 % THD,
(5% THD, (1 % THD,
unregulated regulated regulated
supply)
supply)
supply)
12
18
16.5
25
38
33
40
55
50
70
lOO
88

Hum and
Noise (dB)
(Below con·
tinuous POUT
Input Input
Shorted Open
75
70
80
75
80
75
85
80

Sensi·
tivity

10 dB below
continuous POUT

Input
(For con- Resist· IMD (%)
(60 Hz and
tinuous ance
(ko)
7 kHz, 4:1)
POUT
500
20
0.2
600
20
0.1

(mV)

600

700

20
20

0.1
0.1

Control and Low-Frequency Power Amplifiers
of power output and of output
response as a function of frequency for the 60-watt amplifier,
shown in Fig. 452, are indicative
of the performance capabilities
of these amplifiers.
5

....tz..,

1=1 kHz

~I 0.5

0.2

o.I

REGULATED
SUPPLY ' j

It:

r-- IM

THe

~O.o~)J2512510

40
70
POWER OUTPUT-W

100

(a)

...mI

2
I
60 WATTS

~ 0
It:

....>

II'"

i= -2

419

voltage-breakdown capabilities
required of conventional circuits.
This performance is possible because the load can swing the full
supply voltage on each halfcycle. The load is direct-coupled
between the center point of
two series-connected push-pull
stages. This bridge type of arrangement eliminates the need
for expensive coupling capacitors or transformers. These features are very attractive in
applications for which the supply voltage is fixed, such as automotive or aircraft supplies.
The bridge-amplifier configuration consists essentially of two
complementary-symmetry amplifiers with the load direct-coupled
between the two center points.

ii1-3
It:

FREQUENCY-Hz
(b)

Figure 452. Performance curves for the 70watt quasi-complementary-symmetry audio
amplifier: (a) distortion as a function of
power output; (b) relative response as a
function of frequency. (These curves are
representative of the performance provided
by the universal quasi-complementarysymmetry design.)

Bridge-Am plifier
Design Approach

Figure 453. Block diagram of bridge type
of audio-amplifier circuit.

Fig. 453 shows the block diagram of an audio-amplifier configuration that, for a given dc
supply voltage, transistor voltage-breakdown capability, and
load, can provide four times the
power output obtainable from a
conventional push-pull audiooutput stage. Alternatively, given
power-output and load requirements may be achieved from this
circuit configuration with half
the supply voltage and transistor

Each amplifier section is driven
by a class A driver stage that
uses a transistor Darlington
pair. The amplifiers must be
driven 180 degrees out of phase.
This dual-phase drive is provided by a differential-amplifier
type of input stage, which also
provides the advantage of a high
input impedance.
Fig. 454 shows the basic configuration of an experimental
breadboard circuit designed to

420

RCA Silicon Power Circuits Manual

Figure 454.

Basic circuit configuration for a bridge type of audio amplifier.

evaluate the bridge-amplifier approach to audio-amplifier design.
The major difference between
this type of circuit and the conventional complementary-symmetry circuit, besides the increased
output power, is the higher current requirement of the class A
driver stages. This current is
twice the value normally required because the peak value of
the output current is doubled.
The feedback network from each
tomplementary-symmetry output
section back to the base of the

corresponding class A driver
stage, which establishes the center-point voltage in the output
stage, also provides a minimum
of 22 dB of ac feedback.
The differential-amplifier input stage operates at ten times
the required value of peak input
current to ensure linear operation. Balanced feedback is taken
from each side of the load and
coupled back to the separate
bases of the differential-amplifier transistors. Fig. 455 shows
curves of total harmonic distor-

Control and Low-Frequency Power Amplifiers
12

CURVE I FEEDBACK I SENSITIVITY
A
B
C

OdB
20dB
28dB

1I00mv FOR 6W
IVFOR6W
3V FOR 6W

r--

i)/
..J

j!!

I-

V v
l-

J
B/''(f

I,..- t;{

complementary-symmetry output
stages. The dc dissipation in the
load circuit is, of course, proportional to the square of the offset
voltage. In this breadboard circuit, two potentiometers are used
to balance the center-point voltage of the two output-stage sections.

2345678
POWER OUTPUT-W

3
III

Figure 455. Total harmonic distortion (at
1 kHz) of the bridge audio amplifier as a
function of power output for different values
of balanced loop feedback. (Distortion performance is comparable to that of a singleended amplifier that provides one-quarter
of the power output for the same dc
supply voltage.)

421

::>

~
o

r'\.

~ -I ..... ""

...a:

..J _

tion as a function of power output for operation of the bridge
amplifier with 0 dB, 20 dB, and
28 dB of balanced feedback. Figs.
456 and 457 show total harmonic
distortion and relative response
as functions of frequency for the
bridge amplifier operated with
20 dB of balanced feedback.
One problem encountered in
the bridge amplifier is the
achievement of a zero centerpoint (offset) voltage. The load
circuit conducts a direct current
proportional to the difference
(offset) between the voltage at
the center points of the two

III I

_l OP

~Eb!!ACJ'20Id~

-i II

~JJT.Jw

·ilt~~

'"2.

I
I--

1/
V

POUPO.5W

4 681022

4681032

468 104 2-

FREQUENCY-Hz

Figure 456. Total harmonic distortion of
the bridge audio amplifier as a function
of freq uency.

2
~ 6 e103 2.
FREOUENCY-Hz

68 10 2 2

Figure 457.

4 68104 2.

Relative response of the bridge
audio amplifier.

ULTRASONIC POWER SOURCES
Ultrasonics is a term applied to
the relatively new field of engineering in which high-frequency
acoustical energy is used to effect
an ultimate improvement in a
product or process. The improvement may take place in cleaning,
soldering, welding, drilling, defoaming, and degassing, or in control, measurement, detection, and
medical diagnostics.
The frequency range used in
ultrasonics is typically between 15
kHz and 10 MHz. A few applications employ lower frequencies to
achieve maximum particle displacement; at these lower frequenCies, however, the power level
must be kept low to avoid painful
discomfort to those working in
the vicinity. In testing applications, higher frequencies are required because the smaller the

422

RCA Silicon Power Circuits Manual

wavelength, the smaller the ':!law
that can be detected.
The power level used in ultrasonic engineering depends upon
the application. Large-scale indus-,
trial-cleaning operations may require many kilowatts, while measuring and testing applications
may require only a few microwatts. Table XXXXI lists some of
the general industrial applications
of ultrasonics, together with a
brief description of the various
applications and the typical power
level and frequency required for
each.
Many devices can be used to
produce ultrasonic energy; these
devices are called transducers. All
transducers can be classified in one

of three groups: mechanical, magnetostrictive, or electrostrictive.
Mechanical transducers are applied for the most part to the production of acoustic and ultrasonic
oscillations in air or other gaseous
media. Mechanical transducers
used as sources of ultrasonic
waves in air include whistles, gasjet generators, and sirens. The
power sources used in these devices usually incorporate a type of
pressurized gas or fluid. The gas
and liquid transducers convert a
steady mechanical force into a
vibratory mechanical force.
In solids, however, the same effect is not possible. In this case
a source of electrical energy at
the required operating frequency

Table XXXXI-Ultrasonic Applications
APPLICATION
Ultrasonic cleaning
and degreasing.

DESCRIPTION
Cavitated cleaning solution scrubs parts
immersed in solution.

Drilling, cutting, and
polishing of hard
and brittle materials.

Abrasive slurry between
vibrating tool and
work piece cuts
into material.
Ultrasonically vibrating solder removes
oxide film eliminating the need for flux.
Vibrating tool generates high temperature at interface of
the two materials.
Mixing and homogenizing of liquids, slurries and creams.
Interruption or deflection of beam, damping of transducer.
Determination of size
and location of flaws
in solids by the
pulse-echo technique.
Ultrasonic surgical
knife cuts through
tissue. Locating tumors and other
flaws using the
pulse-echo technique.

Soldering and
brazing.
Welding metals
and plastics.
Emulsification, dispersion,
and homogenization.
Control and measurement, alarm systems,
counting.
Flaw detection.

Medical: surgery
and diagnostics.

POWER RANGE
(Watts)
50 to 25,000
(Typically 100 watts
per gallon of
solution).
50 to 2,000

FREQUENCY RANGE
(kHz)
20 to 40

16 to 30

0.5 to 250

16 to 30

10 to 1,000

16 to 30

100 to 2,000

16 to 1,000

0.1 to 50

16 to 45

0.5 to 20

1,000 to 10,000

1 to 1,000

100 to 10,000

Control and Low-Frequency Power Amplifiers
is converted into a vibrating mechanical force. This conversion is
accomplished through the use of
special materials which have magnetostrictive or electrostrictive
properties.
Magnetostriction is the name
applied to the change in length of
a magnetic material under the influence of an external magnetic
field. Whether a magnetic material
(such as iron, nickel, cobalt, or a
magnetic alloy) lengthens or
shortens depends on a property of
the material and is not dependent
on the direction of the magnetic
field. Fig. 458 shows the strain
(change in length per unit length)
as a function of magnetic field
60
'" 40
'0
;c

(

.r-

0
-20

-40

,...

CAST
C~~LI_

IRON
--.."

\'---

.".

----

tNNEALED
COBALT

"'-.... ~
o

r,
I
I
I

dL:
:

:
: EQUILIBRIUM
POSITION
(j-O)

,,,I r( {\

+I~
f

. 0

'-I

CLAMPED

Figure 459. Reaction of a bar of material
that has a positive strain coefficient to an
alternating magnetic field when no static
biasing field is used. Waveforms show
change in length of bar (top) and alternat·
ing current (bottom) used to produce the
magnetic field .

PERMENDUM

;a1..J20
I

423

200

400

600

800

MAGNETIC FIELD STRENGTH-G

Figure 458. Strain as a function of mag·
netic field strength for several magneto·
strictive materials.

strength for several magnetostrictive materials. It can be seen that
nickel gets shorter as the magnetic
field is increased, while Permendum gets longer. Fig. 459 shows
how a bar of material that has a
positive strain coefficient (lengthens with increased magnetic field)
would react to an alternating magnetic field with no static biasing
field. It can be seen that the bar
vibrates at twice the generator
frequency and that the amplitude
is ~L peak to peak.

Fig. 460 shows the effect of
adding a static biasing magnetic
field. This bias could also be supplied by a permanent magnet. The
dc bias field yields an initial displacement ~L. Under these condi-

-T
+dL'
I

'I I,
"

+dL~

EQUILIBRIUM
POSITION
DC BIAS-I
0
AC CU~RENTi=O -dL

~~~

1-_ _---'

~ 11---...,.---

Figure 460. Reaction of bar of material
that has a positive strain coefficient to an
alternating magnetic field when static
biasing is employed. Waveforms show
change in length of bar (top). alternating
current used to produce alternating field
(center), and direct current (bottom) used
to produce the bias field.

RCA Silicon Power Circuits Manual

424

tions, the bar oscillates about its
equilibrium position at the frequency of the generator with a
peak-to-peak amplitude of 2AL.
The piezoelectric effect is a
phenomenon that occurs in certain crystals; the crystals are
deformed when subjected to an
electric field. The converse is
also true; i.e., if the crystal
(quartz, Rochelle salt, barium
titanate) is strained, an electric
charge appears at its edges.
The piezoelectric effect in the
first mode is used in the generation of high-frequency sound
waves. This effect is accomplished
by application of an alternating
voltage of the desired frequency
to the crystal. Fig. 461 shows an
example of this method.

CRYSTAL OF PIEZOELECTRIC
MATERIAL (2"/SIDE)

Figure 461. Application of an alternating
voltage to a piezoelectric crystal to produce high-frequency sound waves.

In the design of equipment that
uses
electromechanical transducers, a useful equivalent circuit
for the transducer must be available. Fig. 462 (a) shows the equivalent of a magnetostrictive transducer in which ZA' ZB, and N
depend upon the magnetic and
physical properties of the core material. Fig. 462 (b) is an approximate equivalent circuit for the
transducer. The reactive component of the input impedance is
attributed primarily to the inductance of the winding. This induc-

::r
a£~= L.l:
INPUT

LOAD

(a)

(b)

Figure 462. (a) Actual equivalent circuit
and (b) simplified approximation of a
magnetostrictive transducer.

tance is a function of the number
of turns and the transducer core
material. The resistance R represents the mechanical load. To obtain mechanical energy, it is necessary to provide electrical power
to this resistance. Because magnetostrictive transducers usually
operate with a static bias field, a
dc component of current must be
supplied to the transducer. Fig.
463 shows a typical circuit.
C

TRANSDUCER

1--""1

~--~~--~~I~

I
I

~_ _ _ _ _ _~~~II

_ _ -1

Figure 463. Circuit showing application of
electrical power to a magnetostrictive
transducer.

In the circuit, the choke is used
to prevent the high-frequency signal from shorting through the lowimpedance dc supply. The capacitor C is required to prevent dc
from flowing through the generator. In addition, the value of C

Control and Low-Frequency Power Amplifiers
can be chosen so that the inductive reactance of the transducer
is cancelled.
Fig. 464 (a) is the equivalent
circuit for a piezoelectric crystal;
ZA' Zn, and N are functions of the
electrical and physical properties
of the crystal. Fig. 464 (b) shows
the approximate equivalent circuit
used to represent a piezoelectric
transducer for the purpose of

o-~-r

~a:
ELECTRICAL
INPUT

MECHANICAL
LOAD

(0)

(b)

Figure 464. (al Actual equivalent circuit
and (b) simplified approximation of a
piezoelectric crystal.

making calculations. The capacitance is usually tuned out by use
of either a parallel or series inductor in the matching circuit
between the generator and transducer.
The majority of ultrasonic applications employ a continuously
oscillating power source. In fact,
the only application listed in Table
XXXXI that does not make use of
a continuous wave is flaw detection by the pulse-echo technique.
For this reason, the following
discussion of ultrasonic power
sources is limited to the continuous-wave type. Table XXXXI
shows that most of the frequencies and power levels required are
such that transistors can be used
in the power generators. Therefore, the power sources discussed
below are of the solid-state type.

425

The waveform delivered to the
transducer can be of the square
or sinusoidal type. As a result,
there are four basic methods of
power generation:
1. a low-power square-wave
inverter followed by a class
B push-pull power amplifier,
2. a square-wave power inverter that drives the load directly,
3. a low-power sine-wave oscillator followed by a class
B push-pull amplifier,
4. a self-oscillating power amplifier that drives the load
directly.
The detailed explanation of circuit operation and design procedures for each of these circuits is
given in other parts of this manual.
If the transducer used can operate with a square-wave power
source, then an inverter should be
used because it affords very high
efficiency. However, if the electromechanical transducer is required
to deliver sinusoidal power to its
load (cleaning solution, abrasive
sl urry, and the like), sinusoidal
electrical power must be delivered
to the resistor representing the
load in the equivalent circuit of
the transducer.
Fig. 465 shows one method of
obtaining a voltage sine wav~

_ _ _ _ _ _ ..J

MATCHING
NETWORK

Figure 465. Use of a transducer and
resonant matching network to convert
a square-wave input to a sinusoidal output.
Reactive component of transducer is used
as the shunt inductor or capacitor of the
matching network depending upon whether
a magnetostrictive or electrostrictive type
of transducer is used.

426

RCA Silicon Power Circuits Manual

across RL • In this circuit, the generator supplies a square-wave
voltage; the matching network
filters out the harmonics so that
only the fundamental component
remains. The matching network
includes the reactive component of
the transducer as a shunt inductor
or capacitor, depending upon
whether the transducer is of the
magnetostrictive or electrostrictive type. In other words, the reactive component of the transducer is used as part of the filter.
With this type of network a transistorized inverter can be used to
drive the transducer. The Q of the
series tuned matching circuit
should be at least 5.
The simplicity of this type of
system is shown in Fig. 466. In
the push-pull inverter with a series tuned load, each transistor
provides current half of the time.
The current flows only during the
time that the transistor collectorto-emitter voltage is near zero
[Vem (sat) ]. During the half-cycle
when the voltage across the transistor is equal to 2Vee, there is no
current flow. During both halfcycles, the dissipation in the device is essentially zero. Theoretically, then, the efficiency could

approach 100 per cent. A thorough
analysis and detailed design procedure for inverters is given in
the section on Power Conversion.
One disadvantage of the inverter approach is that the fundamental frequency is determined by
the feedback network. Any time
there is a change in the reactance
of the load, its resonant frequency
changes and the operating frequency of the inverter must be
adjusted to the new resonant frequency. If the frequency is not
adjusted, the power delivered to
the load decreases and the power
dissipated in the transistor increases. With most practical transducers, the reactive component is
continually changing.
One method used to overcome
this problem is to let the load determine the frequency by use of a
tuned-load class C oscillator, such
as that shown in Fig. 467. With
this arrangement, the operating
frequency is always the resonant
frequency of the load.
Fig. 468 shows that the class C
oscillator provides a pulse of current to the load. The load is parallel tuned; the voltage across the
load, therefore, is sinusoidal. The
period (T) of the current pulse is

'
1
oJl

1::~orL
LJ

'CI

j:~

o-.f\

IC 20

Figure 466.

A-

Vcc

5]~'~v=

TUNED
LOAD

Use of a push-pull switching inverter to drive a transducer that forms part
of a series-tuned load circuit.

Control and Low-Frequency Power Amplifiers

Figure 467. Class C oscillator that operates
into a tuned load circuit.

equal to the reciprocal of the resonant frequency fr of the load.
Therefore, if fr changes, there is

Iff

T=...L
fr
Figure 468. Simplified equivalent circuit
for the class C oscillator shown in
Fig. 467.

a corresponding change in T. Fig.
469 shows the collector voltage
and collector current for the class
C oscillator.

Vee

2Vee
Vee

427

tion time of ic is made smaller,
the efficiency increases; however,
ic must also increase to maintain
the same power output. In the
limit, an infinite pulse of zero
width would yield 100-per-cent
efficiency. However, this limit
would require an infinite circuit
Q. It can easily be shown that, for
a fixed VCC' the power output is
proportional to the area under the
current pulse shown in Fig. 469,
where the area is determined by
the magnitude and conduction
angle of the current pulse. The
maximum value of ic is limited by
the maximum current rating of
the transistor used. The maximum
power output [for a given Vcc
and IC(max)], therefore, is proportional to the conduction angle.
However, because the efficiency is
inversely proportional to the conduction angle, it is obvious that
some sort of compromise must be
made. The following examples
should help to determine the best
compromise:
Example No.1: In class C oscillators, the maximum collector voltage rises to a value equal to twice
the supply voltage [Le., VCE(max)
2Vcd, as indicated in Fig. 470.
This condition occurs when the

ol-~£-_---

I:II--H-n_

I~NDUCTION
ANGLE

Figure 469. Collector voltage and current
waveforms for the Class C oscillator shown
in Fig. 467.

The magnitude of the collectorcurrent pulse is determined by the
load power. The current peak occurs at V CE (sat), which is approximately zero. As the conduc-

1 f\

ve:vcc

Vce~

iC1h
o

2Tr

Figure 470. Collector voltage and current
waveforms for an oscillator circuit that has
a conduction angle of 180 degrees.

transistor is reverse-biased. The
VCEV(sus) rating of the transistor used, therefore, should be

RCA Silicon Power Circuits Manual

428

equal to, or greater than, 2Vee .
The relationship between dc input
power p", power delivered to the
load P L , transistor dissipation P d,
and circuit efficiency 'YJ can be calculated for a typical transistor
operated in a circuit of this type.
The parameters assumed for the
transistor are as follows:
VeEv(Sus) = 100 volts
Ie(max) = 20 amperes
Td(max) = 200°C
TRJ-C (includes heat sink) = 3°C/W
TA = 80°C (ambient)
For these parameters, P d should
not exceed (200 - 80) /3, or 40
watts. For Vee 100/2 50 volts,
Ip
Ie (max)
20 amperes, and
conduction angle () = 1T (maximum
power output), the quantities p.,
P L , P d , and 'YJ are calculated as follows:

=
=

.l1
1"
2
..

211"
=

Vee ie dO

Vee

Ip sin 0 dO

211"

= Vee Ip
211"

0)]"
0

+ 1).

= VeeIp
- - = 0.317 Vee Ip
11"

=.l Jr"
211" o

_ Vee Ip

---

211"

320 watts

Vee sin 0 Ip sin 0 dO

f" .

SIn

Example No.2: If the conditions Vee
50 volts and ()
1T
are maintained, then the efficiency
YJ is. still 78 per cent. The peak
current I,,, therefore, must be reduced so that the transistor dissipation P d does not exceed 40 watts.
(The same heat sink and thermal
temperature used in example No.
1 are assumed.) The new value of
II> is calculated as follows:

P d = 0.067 Vee Ip
Ip

40 watts

40/(0.067 X 50) = 11.5 amperes

PL = (0.25)(50)(11.5)

[Vee Ip (-cos

The power delivered to the load
PI, then becomes

211"

watts) exceeds the maximum allowable value (40 watts). This
condition indicates the value calculated for the maximum power
output (PL
250 watts) cannot
be obtained because of thermal
limitations.

0 dO =
Vee
Ip
-0

0.25 Vee Ip = 250 watts
Pd = p. - PL = 0.067 Vee Ip
= 70 watts
1] = PdP. = 78%
=

The calculated value for the
transistor dissipation (P d
70

142 watts

Although the transistor current
is only slightly more than onehalf the maximum current rating,
the dissipation is equal to the
maximum allowable value under
the given conditions. In other
words, the junction temperature
is at its maximum rating.
Example No.3: If the conduction angle is decreased to Y3 of
the cycle (i.e., () = 21T/3 = 120°),
the transistor dissipation is substantially reduced. Fig. 471 shows
the collector current and voltage
waveforms for this condition. If
all other conditions are assumed
to be the same as for example No.
1, the dc input power, load power,
transistor dissipation, and efficiency are calculated as follows:

Control and Low-Frequency Power Amplifiers

429

51/"16

Ps = ~
Vee Ip sin! 0 dO
271" "16
2

v
f\
Ve~~

2 ee \
vee

Ip (_ -cos2
3 O)J 51r 16
-_ [Vee
-271"
3
2
,,16
-_ - Vee Ip [ cos -3 (571")
371"
2 6
- cos

t (~) ]
Figure 471. Collector voltage and current
waveforms for an oscillator circuit that has
a conduction angle of 120 degrees.

= Vee J p (2) (_ 1 )
371"
V2
= 0.15 Vee Ip = 150 watts

1
1
5,,16

PL = ~
Vee sin 0 Ip sin! 0 dO
271" 1/"16
2
= Vee Ip 51r16 sin 0 sin l 0 dO
271"
1/"16
2
sin (~- 1)
Vee1p [ _.,.-::-2_....,.."=271"
2 2- 1

(3 )

)151r16
3
+ 1.
= Vee Ip
sin ( 2

2 (~+ 1)
2

271"

rz . J
l
.1

SIl1

"/6

5 l51/"16
20
0- - 5
SIl1

9/JL

= Vee Ip (0.966-0.05-0.26+0.193)
271"
= 0.85 Vee Ip =0.135 Vee1p=35 watts
271"
Pd=p.-PL=0.015 Vee Ip=15 watts
1/ = PLiP. = 90 per cent
For a conduction angle of onethird of a cycle, therefore, the
transistor is not limited by power
dissipation under the conditions
stated. The transistor can operate
at full voltage and current ratings.
If the heat sink used in examples

Nos. 1 and 2 is employed, the junction temperature is maintained
well below the rated level.
Example No.4: The design of
a practical class C oscillator which
has a conduction angle () of 120·
and an over-all circuit efficiency 'YJ
of about 80 per cent is illustrated
by the following example;
The design conditions are as
follows;
Vee = 50 volts; PL = 125 watts
RL = 1000 ohms in parallel with a
0.D05-microfarad capacitor
f
= 25kHz
TRHs = 2°C/W
TA = 80°C
e = 271"/3
For these conditions, the following values are calculated:
PL =
125=
Ip =
Pd =

(0.135) (Vee) (Ip)
(0.135) (50) (Ip)
18.5 amperes
(0.015)(50)(18.5) = 14 watts

The Q of the load circuit, which
is equivalent to Rd27TfL for a
parallel tuned network, is 2.5. The
value of the load-circuit· induc-

430

RCA Silicon Power Circuits Manual

tance L, therefore; may be calculated as follows:
L = 1000/(211")(25)(103)(2.5)
= 2.5 millihenries
The load-circuit capacitance then
is determined as follows:

mary. The remainder of the circuit design procedure is covered
under the design of class C oscillators in the section on High-Frequency Power AmpUfiers. Fig.
472 shows the schematic diagram
of the completed circuit, and Fig.
473 shows the circuit waveforms.

211"f= l/(LC)i
C = 0.01 microfarad

50V

Because the load resistance RL
is shunted by a capacitance of
0.005 microfarad, the actual value
of the capacitor used in the output
tuned circuit is 0.015 - 0.005, or
0.01 microfarad.
The transistor requirements are
as follows:
VeEV(Sus) ~ 2 Vee = 100 volts
Ic(max) ~ 18.5 amperes
Pd(max) ~ 14 watts at Te = 108°C
[80°C ambient + (14)(2°C/W)]
Therefore, the thermal resistance
from junction to case TR J _c :::; 7°/
watt.
Information on the selection of
core size and material is given in
the section on inverters. For this
design, a toroid of linear material (Arnold Engineering No.
A438381-2 or equivalent) is used.
Use of 100 turns of No. 24 wire
for the secondary winding provides 2.7 millihenries of open-circuit inductance. This secondary
provides the inductance of the
matching network.
The power output P L is equal to
125 watts and the load resistance
RL is equal to 1000 ohms. The
peak voltage across the load, therefore, is 500 volts. The transformer
turns ratio then becomes
N = 500/50

1.2K

0.1

5W
40K

50V

Figure 472.

IS 0

125-watt, 25-kHz, class C
oscillator.

~ 27 P. S -I10l-

l'3A

Ie 0

~25 p.S --\12

0------------------

-4V

-22V

Vee

10:1

Ten turns of No. 22 wire, therefore, are required for the pri-

Figure 473. Current and voltage waveforms
for the class C asci lIator shown in Fig. 472.

Control and Low-Frequency Power Amplifiers
SERVO AMPLIFIERS
A servomechanism system is a
feedback control system in which
the difference between a reference
input and some function of a controlled variable is used to supply
an error signal to the control elements. The error-signal amplifier
is used to drive the control element to reduce the difference between the two functions to zero.
The amplifiers used for such functions may be operated in either
linear or switching service depending upon the type of control
system desired.

Linear Servo Amplifiers
The design of a linear electronic
servo amplifier depends on the nature of the input error signal and
the output requirements. Selection
of transistors and detailed circuit
design are accomplished by normal
design procedures as discussed in
the section on Audio-Frequency
Power Amplifiers. The types of
amplifiers that are used may be
classified according to input and
output requirements as follows:
(1) dc-input, dc-output
(2) dc-input, ac-output
(3) ac-input, dc-output
(4) ac-input, ac-output
Special circuit design is usually
necessary in all classes to control
phase shift over the range of frequencies involved. Normally, the
ac signal is of constant frequency
(60 or 400 Hz) ; the design problems, therefore, are not too difficult.
Servo amplifiers in classes (2),
(3), and (4) are essentially
normal amplifiers except that class
(2) types may include a "chopper"

431

and in class (3) types the output
stage includes rectification and,
possibly, filtering.
In class (1), the usual stability
and drift problems common to dc
amplifiers must be solved. If
necessary, a direct-coupled amplifier may be used; when possible,
however, the more desirable
"chopper-stabilized" dc amplifiers
should be used. A chopper-stabilized dc amplifier consists of two
switches, sometimes built into the
same package and driven synchronously. The input switch
chops the dc signal and thus converts it into a series of pulses
that can be amplified by a normal
ac amplifier. The second sVvitch is
connected to the amplifier output,
and synchronously rectifies the ac
output signal. With this technique,
the dc drift of the amplifier is not
a factor in the dc output signal.
For the case of the directcoupled amplifier, the output
stages follow conventional class A
or class B designs except for special techniques used to assure
thermal stability and drift-free
operation when the amplifier is
operated over the entire expected
temperature range.
For applications in which the
circuit arrangement must drive an
amplifier with a dc input and produce a reversible-phase ac output
(class 2), special techniques must
be employed in the output stage.
This type of servo amplifier,
which is similar to the balanced
modulator with suppressed carrier, is the most common, and is
found in many X-Y plotters.
Fig. 474 shows a simple control
system with direct feedback. In
this circuit the reference input
and the feedback are passed to a
comparator in which an error signal is produced and amplified to
produce the controlled variable.

432

RCA Silicon Power Circuits Manual

;:ev I?>
REFERENCE

E:ROR

CONTROLLED
VARIABLE

t~EEDBACK
Figure 474. Block diagram of a simple
control system that uses direct feedback.

Fig. 475 shows a phase-sensitive amplifier which takes a dc input and produces an ac output.
The collectors of both transistors
are fed from the ac supply, which
must be in phase with the servosystem supply so that a phase reference is provided. Both collectors
go positive at the same half-cycle,
and when there is no input both
carry the same amount of current. Under these conditions, the
output transformer produces zero
voltage. If terminal A becomes
more positive, Q 1 conducts more
heavily than Q~; thus, there is a
net field, and a resultant net
voltage, coupled through the

OUTPUT

,1;,,'

T
r-,..AAA.r-_

r;gufcl 475. Fhase-sensnive linear servo
amplifier that develops an ac output for a
dc input.
transformer windings. If terminal B becomes positive with respect to terminal A, the phase of
the ac output voltage reverses.
This type of amplifier can easily

be adapted to the case of ac input
to ac output with the addition of
an input transformer. An application of an amplifier similar
to that of Fig. 412 has been previously identified as an X-Y
plotter. In this application, a
servo motor is supplied with
a voltage from the servo supply system to one winding; the
output voltage of this amplifier
is applied to another winding.
This motor drives the mechanical
pen in one of the axes. A position
voltage is obtained from a potentiometer setup connected to the
mechanical assembly. This voltage
is compared to the input voltage
of the instrument, and the resulting error voltage is applied to the
amplifier. The servo motor drives
the assembly in the direction that
tends to cancel the error voltage.
A similar arrangement is used for
the other axis.
The basic principle of feedback
control tends to produce accurate
performance because the control
system endeavors continually to
correct for any error. This corrective action, however, can give rise
to a condition of unstable action
when the control elements exhibit
large amounts of amplification and
phase shift. An unstable system
may produce large sustained oscillation or erratic control, either
of which makes the entire system
useless.
In an effort to increase the accuracy of a system, the usual approach is to increase the gain of
the servo amplifier. This approach
always reduces the stability of the
system because undesirable effects of the amplifier become more
pronounced. Obviously, the requirements for stability are incompatible with those of accuracy;
there is always a trade-off between
these factors.

Control and Low-Frequency Power Amplifiers
The requirements of the servo
amplifier are easily described, but
are usually difficult to obtain. As
discussed in the section on AudioFrequency Power Amplifiers,
negative feedback is usually employed to maintain the over-all
gain of the amplifier. In an audio
system, if the gain varies with
aging components, or if the output
dc drifts with changes in ambient
temperature, nothing disastrous
occurs to the over-all operation of
the system. In a servo system,
however, steps must be taken to
assure a constant gain under all
operating conditions. Therefore,
large amounts of feedback are employed in applications of this nature. Because of the large variation of parameters that can be
expected from transistors, designs
tend to be ultra-conservative, with
more devices employed to provide
a given amount of gain than in
a conventional audio amplifier. In
practically every stage, some form
of temperature compensation is
employed to maintain the operating point and the gain of the
stage. It is not uncommon to employ 60 dB of over-all feedback
in such an amplifier. In such applications, steps must be taken to
assure that the amplifier itself is
stable. Careful analysis using the
Nyquist stability criterion is the
only way to assure not only good
amplifier performance but good
over-all system stability. The Nyquist stability criterion places on
a firm mathematical basis the
physical fact that instability results when the feedback signal is
equal in magnitude and in phase
with the actuating signal. Thus,
this criterion indicates the necessary conditions for stability in
terms of the ratio between the input signal and the feedback signal.
For applications in which a

433

high-power dc amplifier is required, a circuit similar to the
70 - w a t t quasi-complementarysymmetry amplifier shown in Fig.
116 or to the universal quasicomplementary amplifier shown
in Fig. 451 may be employed. The
input circuit must be modified
to provide a dc capability.

Switching-Mode Servo Control
Switching-mode servo controls
afford an efficient means for amplification of directional information. As an alternative to the use
of cascaded linear stages to drive
a class B push-pull output stage,
this switching mode of control allows the active elements of the
amplifier to operate in either saturation or cutoff. Because a relatively small length of time is spent
in the active region of the devices,
where power dissipation is high,
the average power .dissipation is
lower. The efficiency of the overall system, therefore, is higher.
Switching servos are used in
stable platforms for guidance and
navigational systems, control of
memory access devices in compu- ,
tel' and data-processing systems,
and other applications in which
efficiency is a prime factor. Fig.
476 shows the circuit diagram of
a pulse-width-modulated output
stage for a servo-motor-drive
system.

General Circuit DescriptionFig. 477 shows the block diagram
of a pulse-duration-modulated
switching-servo control system.
The directional error signal (commonly a 400-Hz sine wave) is used
to modulate the pulse width of a
square-wave pulse having a con-

434

RCA Silicon Power Circuits Manual
48V

-z~""""~\r--- + IV

.::zz:
. . . ~~

:::~:::::::::::\~

f=400 Hz
+40V

Figure 476.

Pulse-width-modulated servo-motor-driver output stage.

stant repetition rate. The waveforms at the input and output of
the pulse-duration modulator are
shown in Fig. 478.
The error signal has a frequency
fo' and the ramp-generator waveform has a fundamental frequency
f1 which is much greater than
f o • The resulting pulse-duration~
modulated (PDM) signal has
three components. One is a dc or
average component, the second is
the error component having a

frequency spectrum equal to the
error signal (fo ), and the third
is a summation of components of
the upper harmonics of f o •
The pulse is amplified in the
switching driver and power switch
amplifier. It is then sent through
a band-pass filter that has a cutoff frequency equal to that of the
error signal. The band-pass filter
appears as a large impedance to
the collectors of the power switching transistors at harmonics of

o
Figure 477.

ROTOR

Block diagram of a pulse-duration-modulated switching-servo control system.

Control and Low-Frequency Power Amplifiers
DIRECTIONAL
ERROR SIGNAL

RAMP
GENERATOR

PDM ERROR
SIGNAL

00000

Figure 478. Input and output waveforms
for the pulse-duration-modulated servo control system.

f o • Thus, only the fundamental
component of collector current
flows in the servo-control winding.
The original sinusoidal error signal is then almost completely
recovered. The quality of the recovered signal is an inverse function of harmonics introduced into
the system by the switching characteristics of the amplifiers and
a direct function of the sharpness
of cutoff of the band-pass filter.
The error-phase flux and the
recovered-phase flux form a resulting control flux that directs
the servo rotor.

435

Practical Circuit-Fig. 479 is
the circuit diagram of a switching-servo-control amplifier that
uses a pulse-width modulator. The
pulse width is modulated by adjustment of the trigger level of
the OR gate. A constant-amplitude
ramp function appears at point
(a). The linearity of the ramp is
enhanced by the constant-current
source which charges capacitor
C1 •

Whenever the voltage at point
(a) is greater than the threshold
voltage VT , Q 1 turns on. At this
time, Q~ turns off because its baseemitter-junction is reverse-biased.
The threshold trigger voltage is
continuously varying as a function
of the modulating input voltage
at the input of the transformer.
When the input signal is at its
greatest value, the threshold is
greatest. As a result, the OR gate
switches later in the ramp period.
The pulse duration then varies
with the instantaneous magnitude
of the modulating signal. Fig. 480
shows the waveforms and the timVee

RAMP GENERATOR
MODULATOR
SERVO SWITCH
AMPLIFIER
REFERENCE PHASE

Figure 479.

'--~.r--'

ERROR PHASE

Switching-servo control amplifier with a pulse-width modulator.

436

RCA Silicon Power Circuits Manual
./

I--

.,."

I-

r--

./
,/

r--

THRESHOLD

VOLTAGE AT
COLLECTOR
OF QI
VOLTAGE AT
COLLECTOR
OF QZ

b.t=t
,

- THRESHOLD

i rtrl~r

TS
,

, (0)

hi
~
~l-r

Figure 480. Waveforms showing the threshold switching control for the control amplifier shown in Fig. 479.

(b)

____________ ",

, ,
'---',--VCE(SAT)
,
"

1 "'-

ing relationships between the
threshold voltage and the collector
voltages of Q 1 and Q2'
The pulses at the collectors of
Q1 and Q2 provide an alternating
current through the load which
consists of the error field winding
and the filter. This filter should be
designed as a low-pass filter with
a cutoff at 400 Hz. The flux in
this winding then becomes a
function of the fundamental frequency of the error signal only.
Efficiency Consideration-Fig.
481 shows the approximate voltage and current switching waveforms of the power output transistors of the switching servo amplifier shown in Fig. 479. It can
be shown that the switching configuration is much more efficient
than a class B push-pull system.
The latter system has a maximum
ideal efficiency of 78 per cent. An
approximate expression for ideal
efficiency for the switching servo
amplifier can be derived if the
following simplifying assumptions
are made:
1. A perfectly loss-free filter
with a cutoff frequency of
400 Hz is used.
2. The current waveform
through the load is purely

(e)

Figure 481. Approximate switching waveforms of the output transistors in the control amplifier shows in Fig. 479.

sinusoidal, and a perfect
reproduction of the input
signal.
3. The current has a peak
val ue of V CC/RL
Ip ,
where RL represents the
dissipation of real power
in the servo.
4. The current and
VCE
switching waveforms are
linear, as shown in Fig. 481.
5. The leakage current Ico is
negligible.
First, an expression for power
dissipated in transistor pair Qa-Q 4
or Q5 -Q 6 during the turn-off (or
turn-on) is defined.
Total VCE(t)

2 CCE(sat)

+ [Vcc-2 VCE(sat)] (tiT)
Ic(t)

Ip - Ip (tiT)

(347)
(348)

The average power dissipated can
be approximated as follows:

Control and Low-Frequency Power Amplifiers

Pd > (l/T)

437

[2 VCE(sat)

+ {VCE - 2 VCE(sat) I (t/T)]
[Ip - Ip (t/T)] dt

Then, the efficiency 'Y} is approximately equal to (Pin - PI) /P im
that is,

= (Ip/6) [4 VcE(sat) + Vcel (T /T)
=

(349)

During each sampling interval,
both transistor pairs are switching; therefore, 2P s is dissipated.
During this interval, switching
takes place twice; therefore, a
total of 4P s is dissipated during
switching. If there are N sampling
intervals in an error-signal cycle
that lasts for T seconds, then
4NP s is dissipated where T =
NT •.
Next, the approximate power
dissipated during all time other
than the switching time is calculated. The current is sinusoidal
and throughout the cycle one set
of transistors is on.

P avg

~ (l/T)

2 VCE(sat)

Ip sin (27rt/T) dt

The following typical values are
used in an example to show how
the ideal efficiency is calculated:

N = 20
VCE(sat) = 2.5 volts
Ip = 2 amperes
Vcc= 200 volts
T
= 2 X 10- 6 second
t = 1/400 = 2.5 X 10-3 second

With these values, the following
results are obtained:

p. = (Ip/6) [4 VCE(sat)+Vcel (T/t)
= (2/6) [4X2.5+200]
[(2 X 10-6 ) / (2.5 X 10-3)]
= 0.56

= [2 VcE(sat) Ip/7r]
Then, the power dissipated in the
devices during this time is less
than a value PI' expressed by the
following equation:

PI = 0.056 + [2 VCE(sat) Ip/7r]
= [(2X2.5X2)/3.14]+0.056=a.25

The power supplied by the Vee
source is given by

TJ =
=

(2 Vc cI p )/7r
= (2X200X2)/3.14 = 255

(Pin- PNPin) = 1 - (3.25/255)
1 - 0.012 = 99 per cent

438

Bibliography
Aronson, H. L., "Applying Power
Transistors to Control", Control
Engineering, October 1956.
Beaufoy, R., and Sparkes, J. J., "The
Junction Transistor as a Charge
Control Device", ATE Journal, Vol.
B, pp. 310-327, October, 1957.
Birman, P., "An Analysis of Cooling
Methods for Reliable Operation of
Components", Electronics, June 22,
1962.
Breece, H. T., "High Speed Inverters
Using Silicon Power Transistors",
R9A Application Note, SMA-37.
Brown, Morgan, and Stephenson,
"The Design of Transistor Push-Pull
DC Converters", Electronic Engineering, October, 1959.
Carley, D. R., P. L. McGeough, and
J. F. O'Brien; "The Overlay Transistor, Part 1: New Geometry Boosts
Power", Electronics, August 23, 1965.
Caulton, M., H. Sobol, and R. Ernst;
"Generation of Microwave Power by
Parametric Frequency Multiplication
in a Single Transistor", RCA Review, June, 1965.
Chang, Z. F., and Turner, C. R.,
"Characterization of Second Breakdown in Silicon Power Transistors",
RCA Application Note, SMA-21.
Chipp, R. D., "Community Antenna
Television Systems", XEEE Spectrum, July, 1966.
Dewitt and Rossofl', Transistor Electronics, McGraw-Hill, New York,
1957.
Donahue, D. J., and A. Jacoby, "Part
II: Putting the Overlay to Work at
High
Frequencies",
Electronics,
August 23, 1965.
Ebers, J. J., and J. L. Moll, "LargeSignal Behavior of Junction Transistors", Proc. IRE, Vol. 42, Dec. 1954.
Eimbinder, J., and C. R. Turner,
"Determining Permissible Dissipa-

tion for Silicon Power Transistors",
Electronic Design, August 16, 1961.
Elementary Circuit Properties of
Transistor, SEEC Vol. 3, J. Wiley
& Sons, 1964.
Frederick, J. R., Ultrasonic Engineering, J. Wiley & Sons, 1965.
Gartner, W., Transistors: Principles, Design and Applications, D.
Van Nostrand Co., 1960.
Gold, R. D., and Sondermeyer, J. C.,
"Designing Silicon Transistor HighFidelity Amplifiers", Electronics
World, Sept., Oct., and Nov., 1966.
Goldman, W. E., "9 Ways to Improve
Heat Sink Performance", Electronic
Products, Oct. 1966.
Greiner, R. A., Semiconductor Devices and Applications, McGraw-Hill
Book Company Inc., New York, 1961.
Pages 274-299.
Grinich and Noyce, "Switching Time
Calculations for Difl'used Base Transistors", IRE WESCON Convention
Record, Part 3., Electron Devices,
August, 1958.
Gutzwiller, F. W., and T. D. Sylvan,
"Power Semiconductor Ratings Under Transient and Intermittent
Loads", Communication and Electronics, Jan. 1961.
Hartz, R. S., and F. S. Kamp,
"Power Output and Power Dissipation in Class B Transistor Amplifiers," preprint No. 545, Audio
Engineering Society 33rd Convention, Oct. 16 - Oct. 19, 1967.
Hartz, R. S., and F. S. Kamp,
"Stereo Amplifier Power Ratings,"
Audio, April 1968.
Hunter, L. P., Handbook of Semiconductor Electronics, McGraw Hill
Book Co., Inc., 1958.
Jensen, J. L., "An Improved SquareWave Oscillator Circuit", IRE

Bibliography
Transactions on Circuit Theory, September 1957.
Kolody, O. A., and R. R. Langendorfer, "Measure Transistor Y -Pa"rameters", Electronic Design, August 30, 1966.
Kuhn, N., "Simplified Flow-Graph
Analysis", The Microwave Journal,
November 1963, pp. 59-66.
Lee, H. C., "Microwave Power Generator Using Overlay Transistors",
RCA Review, June 1966.
Lee, H. C., "Microwave Power Transistors", WESCON Record, 1966.
Lee, H. C., and G. J. Gilbert, "Overlay Transistors Move into Microwave Region", Electronics, March
21,1966.
Lee, H. C., and R. Minton, "Designing Transistor Multipliers", Microwaves, November 1965.
Light, L. H., and M. Hooker, "Transistor DC Converters", The Institute
of Electrical' Engineers, Paper
#1862R, April 1955.
Light, L. H., "The Design and Operation of Transistor DC Converters",
Mullard Technical Communications,
Vol. 2, 17, Feb. 1956.
Matyckas, S. J., "RF Power Transistors In Vehicular Radio Communications Equipment", WESCON Record, 1966.
Millman, Taub: Pulse, Digital, and
Switching Waveforms, McGraw-Hill
Book Co., Inc., New York, N.Y.,
1965.
Minton, R., "Semiconductor HighFrequency Power Amplifier Design",
WESCON Record, 1966.
Minton, R., "Design of Large Signal
VHF Transistor Power Amplifiers",
RCA Application Note, SMA-36.
Moll, J. L., "Large Signal Transient
Response of Junction Transistors",
Proc. IRE, Vol. 42, pp. 1773-1784,
December, 1954.
Morin, F. J., and J. P. Maita, Physical Review, Volume 96, 1954.
Nielson, E. G., "Behavior of Noise
Figure in Junction Transistors",
Proc. IRE, June 1951.
Nowicki, J. R., "New High-Power
LC Converter Circuits", Mullard
Technical Communications, April,
1960.
Nyquist, H., "Regeneration Theory",
Bell System Technical Journal, Volume II, January 1932.

439
Pappenjus, E. W., W. B. Bruene, and
E. O. Schoen ike, Single-Sideband
Principles and Circuits, McGrawHill Book Co., Inc., N.Y.
Pettit and McWhorter, Electronic
Amplifier Circuits, McGraw-Hill
Book Co., Inc., N.Y., 1961.
Phillips, A. B., T1'ansistor Engineer,
McGraw-Hill Book Co., Inc., New
York, N.Y., 1962.
Physical Electronics and Circuit
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Chap. 8.
Roddam, T., Transistor Inverters
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N. 4, p. 166.
Ruthroff, C. L., Some Broad-Band
T1'ansformers, Proc. IRE, Aug. 1959.
Schiff, P., "Second Breakdown in
Transistors Under Conditions of
Cutoff", RCA Application Note,
SMA-30.
Schlicke, H. E., Essentials of Dielectromagnetic Engineering, 1961, John
Wiley, New York.
Searle, C. L., Boothroyd, A. R., Angelo, Jr., E. J., Gray, P. E., and
Pederson, D.O., Elementary Circuit
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Vol. 3, John Wiley & Sons, Inc., New
York, New York, 1964.
Sears, F. W., and M. W. Zemansky,
College Physics, Addison-Wesley,
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Simmons, C. D., "Transistor Heat
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Sorensen, A. A., "Semiconductor
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Steinberg, "Ultrasonics in Industry",
Proc. IEEE, Vol. 53, No. 10, Oct.
1965.
Tatum, J., "RF Large Signal Transistor Amplifiers, 'Part I-Theoretical Considerations", Electrical Design News, May, June, and July,
1965.
Turner, C. R., "Design of Transistorized DC-to-DC Converters", Electronic Design, Sept. 16 and 30, 1959.
Uchrin, G. C., and Taylor, W., "A
New
Self-Excited
Square-Wave
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Wolf, H., "Recent Advances in HighFrequency Power Transistors", Solid
State Design, June 1963, pp. 21-28.

440

Index

Acceptor .................... .
AC Line-Voltage Controls .... .
Aircraft Radio ................. .
Alloy-junction transistor ............. .
Anode .......................... .
Audio-frequency power amplifiers ... .
Basic circuit configuration ....... .
Bridge amplifier design approach ..
Maximum effective series resistance
Music power ratings ........... .
Thermal stability requirements ... .
Universal amplifier design approach
Avalanche voltage ................... .
Average current ...................... .
Base
........................ .
Base-width modulation
Biasing (reverse and forward) ....... .
Blocking voltage .................... .
Breakdown voltage
................ .
Breakover voltage ................... .
Bridger amplifier ................... .

Page
12
226
322
65
9
386
386
419
404
394
404
408
18
20

111
13
12
18
33
329

Capacitive load circuits .............. .
155
Capacitive filter ..................... . 221
Carrier flow analysis ................. .
12
Cathode
.............. .
9
Center gate ......................... .
39
Characteristics and ratings (silicon rec.................. .
tifiers)
15
Forward voltage drop ........... .
17
Important characteristics ........ .
16
Reverse current ................. .
17
Reverse recovery time ........... .
18
Thermal impedance ............. .
16
Characteristics and ratings (thyristors)
40
Maximum average ON-state current 46
Surge ON-state current ......... .
46
Charge-carrier interactions ........... .
32
Circuit configurations, basic (power conversion) ....................... . 163
Citizens-band transmitters ........... . 298

Page
Chopper ................. ~ . . . . . . . . .
162
Collector ............................
10
Collector catcher .................... 135
Community-antenna TV .............. 328
Amplifier requirements
330
Cross-modulation distortion
338
Commutated turn-off time .......
53
Complementary amplifier ........ 382, 390
Conduction angle .................... 227
Control
and
low-frequency
power
amplifier ....................... 379
Conventional current flow ............
9
Converter
162
Current
F l o w . . .....................
7
Forward
.... . .. ................
19
Holding
. . . . . . . . . . . . . . . . . . . .. 32, 48
Latching . . . . . . . . . . . . . . . . . . . . . . . .
48
On-state .......................
45
30
Reverse blocking ................
Reverse ..........................
17
Reverse-recovery ..............
18
Surge " ...... ,.... . . . . . . . . . .
21
Current-limiting techniques ............ 205

DC-to-dc converter (ringing-choke) ....
Delay time
. . . . . . . . .. SO,
Depletion layer ..................... .
Depletiqn region
Diac
......................... ,
Diffused junction transistor ......... .
Diffusion current ........... .
Diode ............................ ..
Diodes, tunnel ............ .
Donor .............................. .
Drift
............................ .
Drift current
Drift-field transistor
Dynamic resistance

10
12
204
6
65
20

EIA music power rating ............. .
Emitter .....
.. .............. ..

394
10

163

131
6
13

238
66
6
9

441

Index
Energy barrier
Epitaxial structure
Equivalent circuits
Common base "
Common collector
Common emitter
Input

Page
7
67
105

118
118
109
116

132
Fall time
21
Fault current
Feedback circuit
200
Fermi energy level ......... .
14, 33
Filtering
153, 221
Firing angle
227
Flashover ...
261
14, 34
Forbidden-energy region
Carrier concentration
15
Doping level ............ .
15
Forward bias .................. 8, 13, 15
Forward-bias capacitance-discharge test
91
Forward-bias Is/b test ............. .
90
Forward-blocking state
30, 35
Forward-breakover voltage
31
Forward conducting state ............. .
36
Forward ON-state voltage
31
Forward-voltage drop .. .
17
Frequency multipliers .... .
366
Basic transistor circuits
369
Design
............ . 370
Operation ....................... . 368
Stability and biasing considerations 371
Full-wave control
........... .
246
Fundamental-frequency oscillator
363
L-Band ..................... .
364
S-Band
365
Transistor considerations
367
Fuses ........................ .
21, 205
Gain-bandwidth product
Gate characteristics (thyristors)
Gate nontrigger voltage ...... .
Gate-recovery time
Grown-junction transistor ..
Half-wave control
Heat sinks ............. .
Dissipation capability .
Insulators ......... .
Performance
Types
.......... .
Heater controls
High-voltage rectifier assemblies
Holding current .....
Hole
Hole current .....
Hometaxial transistor ....... .
h-parameter equations ... .
Hybrid-circuit parameters
IHF dynamic output rating
Impedance-admittance chart
Impurities

70
54

S5
52
65
244
79

84
82

81
80
253
25
31, 48
5
9
66

106
106
394

276
4

Page

Incandescent lighting controls
Basic circuit configurations
Light-dimmer circuits
Photocell control ............... .
Inductive filter
Inductive-load switching
Inrush current
Inverter .....
Large signal:
Analysis of power transistors in
linear service ................. .
Characteristics
Equivalent circuits ............. .
L-band oscillators ................... .
Light-dimmer circuits ............... .
Line regulation
......... .
Linear voltage regulators ........... .
Load-line analysis
Load regulation

256
256
256
258
221
141
261
162

124
128
126
364
2S6
203
200
139

204

Magnetostriction
Marine radio ....................... .
Matching networks
Designs of lossy-L network ..... .
Design of pi network ........... .
Designs of tapped-C network ... .
Impedance-admittance chart ..... .
Input-circuit design .. .
Input matching ................. .
Mapping technique
.......... .
Output-circuit design
Output matching ................ .
Quality factor (Q)
Rules for plotting networks and
components
Transmission·1ine techniques ..... .
Mesa
........ ..
Microwave amplifiers and oscillators ..
Circuit design approach ......... .
Circuit design techniques ..
Device considerations ...
Fundamental-frequency oscillators
Power amplifier (lGHz, 1 watt)
Power amplifier (2GHz, 1 watt)
Mobile radio
Cost considerations ............. .
DC operating voltage
......... .
Instabilities in vhf transistor amplifiers
Matching networks
Parallel operation of output transistors
Reliability
Transistor requirements ......... .
Power amplifier (175 MHz) ..... .
Motor controls ...

423
294
269
286
284
281
276
272
269
278
270
270
276

Network properties ..................
Nonrepetitive peak reverse voltage ....
N-P-N structures ....................
N-type material ......................

119
43
8

276
290

66
352
357
358
356
362
361
362
304
305
305
307
306

306
308
305
308
243

442

RCA Silicon Power Circuits Manual

Page
OFF-state voltage .............
42
ON-state voltage .................. 42, 43
One-transistor,
one-transformer
converter ......................... . 168
Open-circuit impJldance parameters
106
Overlay transistor .............. . 68, 265
Packaging (rectifiers) ............... .
Parallel arrangements (rectifiers) ... .
Peaking .......................... .
Peak OFF-state voltage ..... .
Peak reverse voltage ............... .
Phase control ............... .
Photocell control circuits
Piezoelectric effect ............. .
Planar transistor ..."................ .
P-N junctions ......
. ........... .
P-N-P structures ................... .
P-N-P-N structures
Point-contact transistor
Potential-hill analysis ......... " .. .
Power amplifier
Audio-frequency ..................
Control .........
. . . . . . . . . ..
High-frequency ... " . . . . . . . . . . .
Low-frequency ...................
Power conversion ....................
Power dissipation
..............
Power supplies ......................
Voltage regulating .... . . . . . . . . ..
Voltage-regulating current limiting
Voltage-regulating current regulating
Power regulation ................ 200,
Power switching ..................
P-type material .................
Pulse generator (gate trigger) ......
Pulse triggering (thyristor) ..........
Pulse width modulation .....
Push-pull switching inverter ...

27
24
335
43
19
227
258
424
67
6
8
29
65
14

Quasi-complementary amplifiers ..

391

Rate

386
379
262
379
162
137
201
201
202
202
396
130
6
198
55
220
164

of rise of OFF-state voltage
critical, dv /dt .............. 48, 62
Rate of rise on ON-state current,
critical, di/dt .......... . . .. 47, 62
Ratings (silicon rectifiers) .......... 15, 18
Amperes squared-seconds (1"1) ..
23
Forward current .................
19
Peak reverse voltage
19
Surge current ....................
21
Ratings (thyristor) ...... . . . . . .
41
Current .........................
44
Thermal resistance ............. .
44
Voltage and temperature ..... .
42
RC-compensated assemblies .. .
25
Recovery time .............. .
204
149
Rectification ................ .
Rectifiers:
Silicon ....................
10, 12
Silicon controlled ................
10
Repetitive peak reverse voltage ......
43

Page
Resistance (thermal)
.............
44
Resistivity .".........................
3
Reverse bias .................... 7, 13, 15
Reverse bias capacitance discharge test
94
Reverse bias ES /b test ..........
92
Reverse blocking current ........
30
Reverse blocking thermal runaway
18
Reverse blocking voltage ............
42
17
Reverse current ......................
Reverse-recovery current .............
18
Reverse-recovery time ............. 18, 52
RF Power Amplifiers .........
262
Circuit considerations ............ 267
Class of operation .............. 262
Matching requirements ............ 265
Modulation (AM, FM, SSB) ...... 264
Multiple connection of power transistors ......................... 265
Transistor parameters ............ 266
Ringing choke (dc-to-dc) converter 163, 168
Reverse voltage (for reverse-blocking
thyristors) .....................
43
. . . . . . . . . . . . . . . .. 50, 131
Rise time ...
Rms current ...................... . .
20
94
Safe-area ratings
94
Forward-bias
Reverse-bias
.............. . 102
S-band oscillators ................... . 365
Scattering parameters ............... . 107
SCR inverter:
Applications ..................... . 199
Circuit operation ............... . 196
Gate-trigger-pulse generator ..... . 198
87
Second Breakdown ................. .
87
Forward-bias
Reverse-bias ..................... .
89
90
Tests for ....................... .
Semiconductor materials, junctions and
devices ........................
.3
Series-connected output stage .......... 381
Series regulators ..................... 201
Servo amplifiers ................ 385, 431
Linear servo amplifier ........ 385, 431
433
Switching mode servo control
Short-circuit admittance parameters
106
Shorted emitter ............... 39, 48, 55
Shunt regulators ..................... 216
Silicon controlled rectifier (SCR) .. 10, 29
65
Silicon power transistors ............
Basic transistor parameter
69
Current ratings ..................
72
Design and fabrication ............
65
Effect of thermal factors on dissipation capability ................
84
Heat removal ....................
79
Maximum ratings ................
71
Power ratings ....................
72
Selection and use of external heat
sinks .................
79
Selection and use of insulators ...
82
Small-signal analysis ............. 105

Index

443
Page

Switching service
130
Thermal considerations
73
Thermal resistance ....
73
Silicon rectifiers
10, 12
SmaIl signal
Analysis of power transistors in
linear service .................. 105
Equivalent circuits ....... . . . . . .. 105
Parameters, variation of .........
121
Snubber network ....................
62
Sonobuoy tninsmitters .........
343
Space-charge region ...........
13
SSB transmitters .................... 310
Bias control .................... 316
Intermodulation distortion ........ 313
Linearity test .................... 312
Transistor requirements .......... 314
Typical linear amplifier .......... 319
Storage time ...................
132
Surge current ........................
21
Switching characteristics (thyristor) ...
49
Switching inverter (push-pull) .......... 164
Switching regulator .............. 220, 224
Switching speed ...................... 130
Temperature derating factor ..........
85
Thermal impedance:
External to transistor ............
77
lunction-to-case ..................
74
Thermal runaway ....................
73
Thyristors ......................... 10, 29
Charge-carrier interactions ........
33
Commutating dv/dt ..............
63
Construction .....................
38
Current ratings ..................
44
Gate characteristics ..............
54
Line-voltage control .............. 226
Phase control .................... 226
Pulse triggering .................
55
Pulse width .....................
59
Ra! .ngs and characteristics ........
41
S~ties and paraIlel operation ....
60
Switching characteristics ..........
49
Theory of operation ...........
29
Thermal resistance ............ 44, 73
Transient protection ............
61
Trigger circuit requirements ...... 232
Trigger devices .................. 234

Page

Trigger level
Turn-off time
Turn-on time .................. ..
Voltage and temperature ratings ..
Voltage-current characteristics .. .
Transformer considerations ........... .
Transformer-coupled output stage ... .
Transient reverse voltage ........... .
Transistor inverters ................. .
Transistor parameters ............... .
Transition region ................... .
Triac . . . . . . . . . . . . . . . . . . . . . . .. 10, 29,
Triac triggering modes ............. .
Trigger diode ....................... .
Triggering devices .................. .
Tunnel diodes ...................... .
Turn-off
one-transformer
conTwo-transistor,
verter .................... .
two-transformer
conTwo-transistor,
verter .................... . 165,

54.
52
SO
42
29
16S
381
19
162
69

6
226
31
237
234
10
37
176
182

UHF military radio ................ ..
Air-rescue beacon ............. ..
Military communications ........ .
Miniaturized low-power oscillator .
Sonobuoy transmitters ........... .
Ultrasonic power sources ........... .
Uncompensated rectifier assembly
Unijunction transistor ........... .
Universal motors ............... .

343
345
347
346
343
421
26
238
243

Vacancy ............................ .
VHF and UHF military radio ..... .
Voltage:
Avalanche
Breakdown .................... ..
Gate nontrigger ................ ..
OFF-state ....................... .
ON-state ........................ .
Peak reverse .................... .
Reverse
Voltage regulators ...

5
343
18
18
S5
42
42
19
43
200

V-Parameter

106

equations

Z-Parameter equations ............... .
Zener voltage ....................... .

106
18

444

RCA Technical Publications
on Electron Tubes, Semiconductor Products,
and Batteries

OPIES of the publications listed
below may be obtained from your
RCA distributor or from Commercial
Engineering, Radio Corporation of
America, Harrison, N. J.

Electron Tubes
• RCA INTERCHANGEABILITY DIRECTORY OF INDUSTRIAL-TYPE ELECTRON
TUBE5-ID-I020-H (lOW' x 8%")-12
pages. Lists more than 2300 basic type
designations for 22 classes of industrial
tube types; shows the RCA Direct Replacement Type or the RCA Similar
Type, when available. Single copy free
on request.
• RCA INDUSTRIAL RECEIVING-TYPE
TUBE5-RIT 104F (lOW' x 8%")-24
pages. Concise technical data on over
200 types used in military, industrial,
and commercial equipment. Includes
application guide, chart of prototype
versus similar RCA industrial types, interchangeability list of domestic versus
RCA replacements, terminal diagrams,
and socket and connector information.
Price 25 cents. *
• RCA RECEIVING TUBES AND PICTURE TUBE5-ERT-1275M (lOYS" x
8%")-56 pages. Contains classification
chart, application guide, characteristics
chart, and base and envelope connection
diagrams on more than 1300 entertainment receiving tubes and picture tubes.
Price 40 cents. * t
• RCA INTERCHANGEABILITY DIRECTORY OF FOREIGN vs. U.S.A. RECEIVING-TYPE ELECTRON TUBE5-ERT197E (8%" x 10Ys")-8 pages. Covers
approximately 800 foreign tube types
used principally in AM and FM radios,
TV receivers, and audio amplifiers. Indicates U.S.A. direct replacement type

or similar type if available. Price 10
cents.·
• RCA NUVISTORS-INDUSTRIAL AND
MILITARY-NIT-140-28 pages. A guide
for communication equipment designers,
researchers and experimenters. Describes design features and performance
characteristics. Contains characteristic
charts, curves, socket information, dimensional outlines, and terminal diagrams. Price 35 cents. *
• RCA
PERIODICALLY
FOCUSED
TRAVELING-WAVE TUBE5-ICE-204-56 pages. Contains theory of operation,
design features, and performance characteristics of RCA periodically focused
traveling-wave tubes. Prince 50 cents. *
• RCA RECEIVING TUBE AND PICTURE TUBE SUBSTITUTION GUIDEERT-198-Price 25 cents.*
• RCA PHOTOMULTIPLIER AND IMAGE
TUBES-PIT-700 (lOW' x 8%")-36
pages. Includes concise data on RCA
photomultiplier tubes, gas and vacuum
photodiodes, sockets and shields for
phototubes, and dimensional outlines
for photo and image tubes. Price 60
cents. *
.,RCA PHOTOMULTIPLIER TUBES FOR
NEW-EQUIPMENT DESIGN-PIT-70316 pages. Reviews some of the applications of photomultiplier tubes. RCA's
wide selection is demonstrated by a
composite graph of spectral responses;
a matrix of spectral response designations versus configuration further assists
in preliminary selection of tube types.
Additional characteristics are tabulated
to help narrow the choice. Price 35
cents. *
• RCA PICTURE TUBE PRODUCT
GUIDE-COLOR AND BLACK & WHITE
-PIX-300B-24 pages. Includes inter-

RCA Technical Publications
changeability chart and characteristics
chart on all industry types where RCA
has a replacement for both black-andwhite and color picture tubes. Basing
diagrams and illustrations depicting
safety features are also included. Price
30 cents."
• PRODUCT GUIDE FOR RCA POWER
TUBES-PWR-506B-40 pages. Contains tabulated data on all RCA power
tubes in order of type designation within
each general class of service. Includes
maximum ratings, temperature ratings,
heater or filament requirements, outline
drawings, and basing diagrams. Price 30
cents ...
• RCA INDUSTRIAL TUBES PRODUCT
GUIDE-TPG-200C (lOYS" x 8%")-28
pages. Covers all RCA industrial-tube
product lines. Gives a brief description
of each product line together with quickselection data. Single copy free on request.
• RCA STORAGE TUBES AND CATHODERAY TUBES-STC-900B-l6 pages.
Contains technical information :m RCA
storage tubes, special-purpose kinescopes and oscillograph-type cathoderay tubes including display-storage tubes,
radechons, scan-conversion tubes, flyingspot tubes, monitor, projection, transcriber, and view-finder kinescopes; as
well as data on fluorescent screens.
Price 20 cents."
• RCA TRAVELING-WAVE TUBE CLASSIFICATION
CHARTS-MWD-IOIC-4
pages. Contains catalog-type data. Single copy free on request.
• RCA PENCIL TUBE CLASSIFICATION
CHARTS-MWD-I02B-4 pages. Contains catalog-type data. Single copy free
on request.
• RCA CAMERA TUBES-CAM-600A26 pages. Contains classification charts,
defining data and typical characteristic
curves for RCA image orthicons and
vidicons. Camera tubes recommended
for new equipment design are highlighted. Price 50 cents."
• VIDICONS-CAM-700-16 pages.
Supplies tube selection guidance and

445
data on RCA vidicons for commercial,
educational, industrial, and military
service. Also included are tube replacement information and typical vidicon
characteristic curves. The information
contained in this pUblication supersedes
the vidicon section of the booklet CAM600A. Price 30 cents.*
• TECHNICAL BULLETINS-Authorized
information on RCA receiving tubes,
transmitting tubes, and other tubes for
communications and industry. Be sure
to mention tube-type bulletin desired.
Single-copy on any type free on request.

Semiconductor Products
• RCA SEMICONDUCTOR PRODUCTS
DATABOOK-SPD-I00. Two loose-leaf
binders for standard 81;2" x 11" data
booklets with more than 900 pages of
data and curves on RCA semiconductor
devices such as transistors, silicon rectifiers, and semiconductor diodes. Available on a SUbscription basis. Price
$15.00* including service for first year.
Also available with RCA Electron Tube
Handbook HB-3 at special combination price of $30.00. *
• RCA SEMICONDUCTOR PRODUCTS
GUIDE-SPG-20lD (lOYS" x 8%")
-44 pages. Contains classification
chart, index, and ratings and characteristics on RCA's line of transistors,
silicon rectifiers, semiconductor diodes,
and photocells. Price 75 cents. *
• RCA DIFFUSED-JUNCTION SILICON
RECTIFIER STACKS AND BRIDGES-SRS300-10 pages. Contains technical data
on RCA's diffused-junction silicon rectifier stacks and bridges. Characteristics
of basic rectifier circuits are also given
to assist in selection of proper RCA
rectifier device. Price 20 cents."
• RCA SMALL-SIGNAL SILICON N-P-N
TRANSISTORS-SST-210-8 pages. Contains technical data on 2N2102 family
of silicon transistors including highvoltage types, very-high voltage types,
linear-beta types, and general types.
Also includes quick-reference guide.
Price 20 cents."

446

RCA Silicon Power Circuits Manual

• DESIGN OF TRANSISTOR SWITCHING CIRCUITS FOR DATA-PROCESSING EQUIPMENT-CTG-161-42pages.
Gives design considerations for a variety of transistor switching circuits for
data-processing e~uipment such as logic
gates, flip-flops, and memory drivers. It
includes a review of switching theory,
design procedures, methods of specifying characteristics and ratings for computer switching transistors; examples of
design procedures; typical circuits using
RCA transistors; and a complete listing
of RCA Computer Transistors with
ratings, characteristics, and performance
data. Price 75 cents.*
• RCA MOS FIELD-EFFECT TRANSISTORS PRODUCT GUIDE-MOS-160-20
pages. Includes comprehensive data on
RCA dual insulated-gate and single
insulated-gate MOS FET's in easy-tofind format plus background information on MOS construction and application. Price· 20 cents. *
• HEAT-SINK GUIDANCE FOR RCA
THYRISTORS USING TO-5 AND "MODIFlED TO-5" PACKAGES-SCR-501-6
pages. Application guide on heat-sink
methods for RCA thyristors. Single copy
free on request.
• RCA HOMETAXIAL BASE SILICON
POWER TRANSISTORS-HBT-400A18 pages. Contains data, dimensional
outlines and theoretical information on
hometaxial-base silicon power transistors. Price 30 cents. *
• RCA lOW-NOISE COMMUNICATION-TYPE TRANSISTORS-CTG-165Contains quick-selection graphs' and
charts and capsule data for RCA Bipolar Transistors and MOS Field-Effect
Transistors for Low-Noise VHF and
UHF Communication and Industrial instrumentation Applications. Includes
special characteristics curves showing
quick-selection chart containing curves,
G p (dB) and NF (db) vs. f (30 to 1000
MHz) for each listed transistor type.
Single copy free on request.
• MOUNTING HARDWARE FOR RCA
INDUSTRIAL SEMICONDUCTOR DEVICES-MHI-300-4 pages. Contains

mounting information for RCA industrial transistors, thyristors, and rectifiers.
Single copy free on request.
• RCA RF POWER TRANSISTORSRFT-700B-6 pages. Contains data,
selection guide, and a quick-selection
graph on RCA "overlay" transistors.
Single copy free on request.
• RCA
PHOTOCELLS-SOLID-STATE
PHOTOSENSITIVE DEVICES-CSS-800A
-32 pages. Contains detailed and updated information on RCA cadmiumsulfide and cadmium-sulfo-selenide
photoconductive-cell characteristics, an
extended section on photoelectric measurements, a new section describing design, new circuits, and an extension
replacement guide. Price 35 cents. *
• RCA PHOTOCONDUCTIVE CELLSFile No. 312-8 pages. Contains descriptive material, characteristic curves,
and classification charts on RCA
cadmium-sulfide and cadmium-sulfoselenide brood-area photoconductive
cells. Single copy free on request.
• RCA SILICON POWER TRANSISTOR
APPLICATION
GUIDE-ICE-215-28
pages. For designers of industrial and
military equipment. Discusses ratings,
stability conditions, parameters and
equivalent circuits. Includes design procedures and specific design equations for
several transistor circuits. Price 50
cents. *
• SILICON VHF TRANSISTORS APPLICATION GUIDE-ICE-228-20 pages.
For designers of industrial and military
equipment. This guide describes the
capabilities of RCA silicon vhf transistors for application at frequencies up to
300 MHz. Includes typical circuits for
the 2NF1491 family of silicon vhf transistors. Maximum ratings and characteristics are included. Price 50 cents. *
• RCA THYRISTORS (SCR's AND
TRIACSl-SCR-500A-,.22 pages. Contains tabulated data, classification charts
and dimensional outlines for all-diffused
silicon thyristors. Price 40 cents. *
• RCA TOP-OF-THE-L1NE SOLID-STATE
REPLACEMENT GUIDE-SPG-202-E--:-48

447

RCA Technical Publications
pages. Lists 31 RCA "Top-of-the-Line"
SK-Series replacement semiconductor
devices which can replace more than
9600 types of transistors, integrated circuits, and rectifiers used in entertainment electronic equipment, including
U.S.A. industry-standard (EIA) types,
foreign types, and types identified only
by device-manufacturers' part numbers.
Price 15 cents. *
• TRANSISTORIZED VOLTAGE REGULATOR APPLICATION
GUIDE-ICE-

254-12 pages. Discusses transistorized
voltage regulators of the series and
shunt types. Includes design considerations, step-by-step design procedures,
and the solutions to sample design problems. Price 20 cents. *

Batteries
•

RCA BATTERY MANUAL-BOG-Ill

(lOYs" x 8%")-68 pages. Contains information on dry cells and batteries
carbon zinc, mercury, and alkaline
types. Includes battery theory and applications, detailed electrical and mechanical characteristics, a classification
chart, dimensional outlines, and terminal connections on each battery type.
Price 50 cents.*t
• RCA BATTERIES-BAT-134H (lOYS"
x 8%")-36 pages. Technical data on
146 carbon-zinc, alkaline, and mercury batteries for consumer and industrial applications. Includes replacement information for 4000 portable
radios, and cross-references 860 domesticbattery types to their RCA replacements. Price 35 cents. *t

Test and Measuring
Equipment
• INSTRUCTION BOOKLETS Illustrated instruction booklets are available
for all RCA test instruments at the
prices indicated below.

WA-44A (Audio Signal
Generator) ......... $0.50*
WA-44C (Audio Signal
Generator) .......... 1.00·
WO-33A (Super Portable
Oscilloscope) ......•. 1.00*

WO-88A
WO-91A
WO-91B
WR-36A
WR-46A

(5-in. Oscilloscope) ••• 0.75*
(5-in. Oscilloscope) ••• 1.00*
(5-in. Oscilloscope) ... 1.00*
(Dot-Bar Generator) .0.50*
(Video Dot/Crosshatch
Generator) .......... 1.00*
WR-49A (RF Signal
Generator) .......... 0.50*
WR-49B (RF Signal
Generator) .......... 1.00*
WR-50A (RF Signal
Generator) .......... 1.00*
WR-51A (Stereo FM Signal
Simulator) .......... 1.00*
WR-52A (Stereo FM Signal
Simulator) ........•. 1.00*
WR-61B (Color-Bar
Generator) .......... 1.00*
WR-64A (Color Bar/Dot/Crosshatch Generator) ..... 1.00*
WR-64B (Color/Bar/Dot/Crosshatch Generator) ..... 1.00*
WR-67A (Test-Oscillator) ..... 0.25*
WR-69A (Television/FM Sweep
Generator) .......... 1.00*
WR-70A (RF-IF-VF Marker
Adder) ............. 0.75*
WR-86A (UHF Sweep
Generator) .......... 0.50*
WR-99A (Marker Calibrator) .. 1.00*
WT-IOOA (Electron-Tube Micro
Mho Meter) ......... 1.75*
WT-lOOA (Electron-Tube Micro
Mho Meter, Ser. No.
1001 and over) ...... 2.00*
WT-JOOA (Tube Chart
JCE-163) ............ 3.00*
WT-l lOA (Automatic ElectronTube Tester) ........ 0.75*
WT-llOA (lCE-174 Card Punch
Data) .............. 0.25*
WT-llOA (lCE-234 Card Punch
Data) .............. 1.00*
Wf-1l5A (Color Picture Tube
Tester) ............. 0.50*
WV-37A (Radio Battery
Tester) ............. 0.25*
WV-37B (Radio Battery
Tester) ............. 0.25*
WV-38A (Volt-OhmMilliammeter) ...•... 0.50*

448

RCA Silicon Power Circuits Manual

WV-65A (VoltOhmystt) ••.... 0.25*
WV-74A (High Sensitivity
AC VTVM) ...•.••.. 0.75*
WV-75A (VoltOhmystt) •••••. 0.25*
WV-76A (High Sensitivity
AC VTVM) ....••.•. 0.75*
WV-77A (VoltOhmystt) •..... 0.25*
WV-77B (VoltOhmystt) .•.... 0.25*
WV-77E (VoltOhmystt) ....•. 1.00*
WV-84C (Ultra-Sensitive DC
Microammeter) •.•••. 0.75*
WV-95A (Master
VoltOhmystt) •••••.. 0.25*

WV-97A (Senior
VoltOhmystt) ••••••• 0.75*
WV-98A (Senior
VoltOhmystt) ....••• 1.00*
WV-98B (Senior
VoltOhmystt) ••••••. 1.00*
WV-98C (Senior
VoltOhmystt) •••••.. 0.50*
195-A (VoltOhmystt) ...•••••. 0.25*
• Trade Mark Reg. U.S. Pat. Off.
• Prices shown apply in U.S.A. and are
subject to change without notice.
t Suggested price.

Other RCA Technical Manuals
• RCA TRANSISTOR MANUAL-SC-13
(8%" x 5%")-544 pages. Contains up-todate definitive data on over 770 semiconductor devices including tunnel diodes,
silicon controlled rectifiers, varactor diodes,
conventional rectifiers, and many classes
of transistors. Features easy-to-understand
text chapters, as well as tabular data on
RCA discontinued transistors. Contains
over 40 practical circuits, complete with
parts lists, highlighting semiconductordevice applications. Price $2.00. *t

.v(. RCA

LINEAR INTEGRATED CIRCUITS-IC-41 (8W' x 5%")-352 pages.
Contains basic principals involved in design and application of linear integrated
circuits-includes description of silicon
monolithic fabrication process-derivation
of design equations and performance criteria-schematic diagrams, operating characteristics, and performance data for RCA
multiple-function silicon integrated circuits
for a variety of linear applications. Price
$2.00.*t
• RCA SOLID·STATE HOBBY CIR·
CUlTS MANUAL-HM-90 (8%" x 5%")
-224 pages. Contains complete construction information on 35 circuits of general
interest to all experimenters. Circuits use
diodes, transistors, SCR's, triacs, MOS
transistors, integrated circuits, and light
and heat detectors. Circuit operation is
described in detail; construction layouts,
photographs, schematic diagrams, and
parts lists are given; and full-size drilling
templates are included for most circuits
to simplify construction. Price $1.75.*t

• RCA TUNNEL DIODE MANUALTD-30 (8%" x 5%")-160 pages. Describes
the microwave and switching capabilities
of tunnel diodes. Contains information on
theory and characteristics, and on tunneldiode applications in switching circuits and
in microwave oscillator, converter, and
amplifier circuits. Includes data for over
40 RCA germanium and gallium arsenide
tunnel diodes and. tunnel rectifiers. Price
$1.50.*t
• RCA SILICON CONTROLLED REC·
TIFIER EXPERIMENTER'S MANUAL
-KM-71 (8%" x 5%")-136 pages. Contains 24 practical and interesting control
circuits that can be built with a complement
of active devices available in kit form.
Includes photographs, schematic diagrams,
and descriptive writeups. Also includes
brief descriptions of solid-state components

used (rectifiers, transistors, SCR's) and
short section on trouble-shooting. Price
95 cents.*t
• RCA RECEIVING TUBE MANUALRC-26 (8" x 51/.4")-656 pages. Contains
technical data on more than 1400 receiving tubes for home-entertainment use. Includes six easy-to-read text chapters that
provide basic information on electron·
tube operation, ratings and characteristics,
and applications. Also features a detailed
application guide for receiving tubes;
quick-reference charts for replacement and
discontinued RCA receiving tubes, blackand-white and color picture tubes, and
voltage-regulator and voltage-reference
tubes; and a Circuits section that includes
schematic diagrams, descriptive writeups,
and complete parts lists for 36 practical
electron-tube circuits for a wide variety of
applications. Price $1.75.*t
• RCA TRANSMITTING TUBES-TT-

5 (8W' x 5%")-320 pages. Gives data

on over 180 power tubes having plateinput ratings up to 4 kw and on'associated
rectifier tubes. Provides basic information
on generic types, parts and materials, installation and application, and interpretation of data. Contains circuit diagrams for
transmitting and industrial applications.
Features lie-flat binding. Price $1.00.*t
• RCA PHOTOTUBE AND PHOTO·
CELL MANUAL-PT-60 (8W' x 5%")192 pages. Well-illustrated informative
manual covering fundamentals and operating considerations for vacuum and gas
phototubes, multiplier phototubes, and
photocells. Also describes basic applications for these devices. Features easy-touse selection chart for multiplier phototubes. Data and performance curves given
for over 90 photo-sensitive devices. Price
$1.50.*t
• RADIOTRON° DESIGNER'S HAND·
BOOK-4th Edition (8%" x 5W')-1500
pages. Comprehensive reference covering
the design of radio and audio circuits and
equipment. Written for the design engineer, student, and experimenters. Contains
1000 illustrations, 2500 references, and
cross-referenced index of 7000 entries.
Edited by F. Langford-Smith. Price
$7.00.*t
° Trade Mark Reg. U.S. Pat. Off.
• Prices shown apply in U.S.A. and are
subject to change without notice.
t Suggested price.

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