6M 4089_Geometry_of_Magnetic_Memory_Elements_Jan56 4089 Geometry Of Magnetic Memory Elements Jan56

6M-4089_Geometry_of_Magnetic_Memory_Elements_Jan56 6M-4089_Geometry_of_Magnetic_Memory_Elements_Jan56

User Manual: 6M-4089_Geometry_of_Magnetic_Memory_Elements_Jan56

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Memorandum

6M=4089

Division

6 -

Lincoln

Laboratory

Massachusetts

Institute

of

Technology

Lexington

73,

Massachusetts

'SUBJECT:

GEOMETRY

OF

MAGNETIC

MEMORY

ELEMENTS

To:

Group

63

~

Staff

From: James

Do

Childress

Page

1

of

7

Abstractg

Two

possible

memory

element geometries

==

the

thin

film

and

the

toroid

==

are

considered

o

The

calculations

show

that

under

certain

conditions

the

thin

film

geometry

may

be

preferable

for

use

in

a

very

high=speed

memoryo

""

JDC/md

Distributiong

The

following

~

to

receive

~

complete

memorandum~

Best,

Ro,

B=131J)

Papian',9

WoNo

Bradspiesj)

So

Gurley.9

Bo

Brown,

Do

Ro

Childress~

JoDo

Davidson.9

Go

Ellis,

Do

Ho

Freeman.5l

Jo

Re

Goodenough9

'J

o

Be

GuditZ9

EoAo

Mitchell.9 Jo

Lo

Menyuk.9

No

Olsen,

KoHo

Pacl,

RoAo

Sarles,

F 0

Wo

Smiths

Do

O~

ZopattiJ;l

Ho

Other

staff

in

Group

63

are

to

receive

abstracts

onlyo

This

document

is

issued

for

internal

distribution

and

use

only

by

and

for

Lin-

coln

Laboratory

personnel.

It

should

not

be

given

or

shown

to

any

other

in-

dividuals

or

groups

without

express

authorization.

It

may

not

be

reproduced

in

whole

or

in

part

without

permissioD

in

writing

from

Lincoln

Laboratory.

The

research

reported

in

this

document

was

supported

jointly

by

the

Department

of

the

Army,

the

Depart-

ment

of

the

Navy,

and

the

Department

of

the

Air

Force

under

Air

Force

Contract

No.

AF

19(122)-458.

Memorandum

6M-4089

Page 2

of

1

Introduction:

The

peak

current

and

average

power which

the

memor,r-plane

drivers

must

deliver

can

be

reduced

by

decreasing

the

dimensions

of

the

magnetic

memory

elements

o

The

following

analysis

indicates

the

limits

of

size

reduction

and

the

results

which such

reductions

may

yield

0

I.

Theoretical

Ruminations

Ao

Possible

Geometries

The two

geometries

to

be

considered

and

their

dimensions

are

shown

in

Fig.

lA

-Thin

Film

and

Fig.

IB

-

Toroid.

Fig.

1A

-

Thin

Film

Fig.

IB

-

Toroid

Memorandum

6M-4089

Page 3

of

7

B 0 Primary

Limits

on

Geometry

The

primary

limits

on

geometry

are

(1)

the

peak

voltage

signal

V must be

great

enough

to

be sensed

reliably

and

(2)

the

p .

switch

time

~

must be

suitable

to

the

desired

memor,y

cycle

time

s

(certainly

less

than

half

the

cycle

time).

winding

is

Therefore

The

instantaneous

output

voltage

for

a one

turn

sense

-8

dB

v(

t)

=

10

A

Cit

•

where V

is

in

volts,~

in

seconds, A

in

square

centimeters,

and B

p s m

(the

maximum

induction

in

the

square

hysteresis

loop)

in

gauss.

We

can

express

the

requirement

on

A

in

terms

of

the

material

parameter

B

m

and

the

memor,y

limits

V and

~

as

p s

c.

Cross-Sectional

Areas

1.

Thin

Film

Let

w = C

1

t,

where Cl

is

a

constant

determined

by

the

magnitude

of

the

demagnetizing

field

tolerable

for

a square

loop;

C

l

is

in

the

order

of

1030

The

cross-sectional

area

is

thus

2

A =..!.

C

l

2.

Toroid

(I)

(2)

Because about

four

mutually

perpendicular

wires

of

a~sumed

diameter

d must

pass

through

the

toroidal

memory

element,

the

w

inner

diameter

d.

has

a lower

limit,

d.>

2d

;

also

geometry

dictates

that

1 I W

Memorandum

6M-4089

Page 4

of

7

the

following

assumptions be

made:

(a)

do = C2di; C2> 1

(b)

h = C

3di; C

3

/1

The

area

is

given

as

C

-1

2

k=C

3

Ld

41

2 i

Do

H-I

Relationships:

10 Thin

Film

In

the

calculation

of

the

field

between two

sheets

of

current,

the

following

approximations

are

made:

(a)

The

field

inside

a

rectangular

coil

of

length

w

centimeters

and

of

N

turns

is

the

same

as

for

a

similar

solenoid.

(3)

(b)

The

current

sheets

above and below

the

thin

film

can be

created

by

overlapping

the

rectangular

coil

as

shown

in

Fig.

20

Figo 2 - Approximation

of

Current

Sheets

Memorandum

6M-4089

Page 5

of

7

From

this

crude

analysis

we

get

4nN. 4 I

H

~

---2:. = n

law

lOw

(4)

where I

is

the

total

current

in

amperes

flowing

in

both

sheets

(split

equally

between

the

two) and H

is

in

oersteds.

2.

Toroid

The

field

in

a

toroid

is

H

~

8I

~

--IO---l(-d-+~d-

.....

)

o

~

E.

Geometry

Factor

We

define

a geometry

factor

F

as

g

H

F = - •

g I

(5)

(6)

SUbstituting

the

cross-sectional

area

limit

of

Eq.

(1)

into

Eqs.

(2)

and

(3)

and

these

into

Eqs.

(4)

and (5),

respectively,

gives

and

F

(thin

film)

~

8n

x

10-

51 v

Bm

\

g

'fCi

p't

s

F

(toroid)

g

F.

Order-of

-Magnitude

Calculations

For

purposes

of

comparison,

the

geometry

factor

of

the

F397

toroid

(d.=

54

mills,

d =

80

mills,

h =

22

mills)

is

2.4.

~

0

We

make

the

following

general

assumptions

for

both

geometries:

(1)

V

~

10-

2

volt

(in

present

memory

V

~

10-

1

volt)

p p

(2)

't

~

10-

7 second

(present

't

is

10-6

second).

s s

(8)

Memorandum 6M-4089 Page 6

of

7

With

these

assumptions,

we

get

for

thin

films

F

(thin

film)

~

16

oersted

g ampere

where 01= 2 x

10

3;

Bm=

8 x 103

gauss,

typical

for

square

loop

metalso

For

a

toroid

where 02=

1;

03=

2;

Bm=

1~5

x.l0

3

gauss,

typical

for

ferrites,

. F

(toroid)

~

50

oersted

g ampere

The

next

section

indicates

the

relative

difficulty

of

obtaining

the

above

geometry

factors

o

IIo

Discussions

and

Conclusions:

The

ease

of

fabrication

is

one

factor

governing

the

practica:Lity

of

a

given

memory-element

geometry.

In

the

Fg

.factors

'.

.

-2,:1

..

;

above,

the

thin

film

would

have

the

dimensions

w =

7x

lO'em

by

t = 305 x

10

....

5 cm;

the

toroid,

d.

:;:::

3 x

10';"3

em, d = 6 x

lO-3

cm

, h =3xlO-3

cm

o

~

. 0

The

thin

film

could

be

made

by

evaporation

techniques

with

relative

ease;

but

the

ultra-small

toroid

would .be

almost·~

impossi'ble

to

make.

A

toroid

a

scale

magnitude

larger

would

be

possible;

this

gives

F

-:=.50

. g

Also

it

must

be

remembered

that

a miniDllm

of'

three

conductors

each

capable

of

carrying

milliampere

currents

must

pass

through

the

toroid

0

Thus

fabrication

difficulties

seem

to

make

the

thin

film

geometry

more

feasible

o

other

geometries

may

offer

mo~e

~han.the

thin

film

so

that

a

further

study

of

geometry

is

worthwhile.

Changing

geometry

alone

is

not

the

answer

to

the

very-fast-

memory.

problem.

In

the

preceding

calculations

it

has

been

assumed

that

magnetic

materials

and

memory scheme

exist

such

that

a memory

cycle

time

of

about

2 x 10 -7

second

is

possible

and

the

V

~

10-

2

volts

can

be

p

sensed

reliably.

In

conclusion,

a memory

element

can

be

reduoedin

size

(1)

yielding

an

improvement

in

the

peak

current-average

power

requirement

of

the

memory

(2)

at

the

expense

of

the

peak

signal

voltage

if

and

only

if

Memorandum

6M=4089

Page 7

of

7

(3)

a

material

and

memory scheme

exist

such

that

't'

~

10-

7

second

is

s

possible

e

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