Analogue Comput$#^Using Magnetic Amplifiers

Β . E . D A V I S I . H . S W I F T A S S O C I A T E M E M B E R A I E E

TH I S Analogue c o m p u t i n g t e c h n i q u e uses d i r ec t c u r ­r e n t s as va r i ab l e s . T h e s e c u r r e n t s a r e s u m m e d

b y m a g n e t i c ampl i f ie rs t o pe r fo rm a d d i t i o n a n d s u b ­t r ac t i on o p e r a t i o n s . P r o d u c t s , q u o t i e n t s , roo ts , a n d p o w e r s a r e o b t a i n e d b y s u m m i n g o t h e r c u r r e n t s t h a t a r e p r o p o r t i o n a l to t h e l o g a r i t h m s of t h e va r i ab l e s . T h e s e l o g a r i t h m i c c u r r e n t s a r e o b t a i n e d b y n e t w o r k s of 5 ger ­m a n i u m or silicon d iodes a n d 11 prec is ion resis tors . As t h e i n p u t c u r r e n t increases , t h e d iodes in t h e c i r cu i t c u t in s e q u e n t i a l l y to s h a p e t h e o u t p u t c u r r e n t a c c o r d i n g to a l o g a r i t h m i c c u r v e . A vo l t age is supp l i ed to a v o l t a g e d i v i d e r in t h e n e t w o r k c o n t r o l l i n g t h e s w i t c h i n g po in t s of these d iodes .

F ig . 1 shows t h e basic n e g a t i v e f eedback c i rcu i t u sed for c o m p u t i n g . T h e l o g a r i t h m i c n e t w o r k s LN a r e a p p l i e d t o e a c h of t h e i n p u t c u r r e n t l eads , as s h o w n . T h e c ' n e g a ­t i v e " n e t w o r k for t h e o u t p u t c u r r e n t h differs f rom t h e " p o s i t i v e " n e t w o r k s on ly in reversa l of t h e d i r e c t i o n of c u r r e n t flow, t h e d i o d e connec t i ons , a n d t h e sign of t h e 10-volt b ias vo l t age r e q u i r e d . S ince t h e i n p u t c u r r e n t of t h e m a g n e t i c ampl i f ie r is v e r y smal l , t h e l o g a r i t h m of t h e o u t p u t is ve ry n e a r l y e q u a l to t h e s u m of t h e l o g a r i t h m s of t h e i n p u t s . T h u s t h e n e g a t i v e feedback accompl i shes t h e t a k i n g of t h e a n t i - l o g a r i t h m . T h e m a g n e t i c ampl i f ie r h a s sufficient c u r r e n t ga in t h a t its i n p u t c u r r e n t i causes a c o m p u t a t i o n a l e r r o r of less t h a n 1 / 3 p e r cen t . H e n c e , to a close a p p r o x i m a t i o n

γ log Ij —» γ log I t CURRENT HERE TO FEED

TO ANOTHER SUMMING AMP

η / aj\

If t h e û's a r e e q u a l , t h e i n p u t s a r e m u l t i p l i e d t o g e t h e r . If t h e y a r e n o t e q u a l , p o w e r s or roo t s of t h e i n p u t s a r e m u l t i ­p l ied . Also, a n y of t h e i n p u t s m a y b e m a d e to b e divisors b y u s ing a n e g a t i v e , ins tead of a pos i t ive n e t w o r k , for it . F u r t h e r m o r e , if a d d i t i o n a n d s u b t r a c t i o n is des i red , t h e ne t ­works a r e o m i t t e d .

A t r o o m t e m p e r a t u r e , n e t w o r k s m a d e w i t h g e r m a n i u m d i o d e s give a l o g a r i t h m i c o u t p u t w i t h a m a x i m u m e r r o r of 0.8 p e r cen t , for a n i n p u t c u r r e n t r a n g e of 2 to 30 mi l l i -a m p e r e s . T h e effect of t e m p e r a t u r e ( — 55 to + 7 0 C) is p r i m a r i l y to c h a n g e t h e l o g a r i t h m b a s e , c a u s i n g n o a d d i ­t i ona l c o m p u t i n g e r ro r . T h i s s t a t e m e n t is a p p l i c a b l e for

τ a. log I, io5oα I.o t 1 w w — ,

E L N ]

Ego Fig. 1. Block d ia­g r a m of c o m p u t i n g s c h e m e to s u m logar i thmic cur ­

rents

\ log I 0 AVAILABLE HERE TO FEED TO ANOTHER SUMMING AMP

Fig. 2 . Circuit i l lustrating s o m e s c h e m e s u s e d for in t erconne c t i n g c o m p o n e n t s to m a k e u p a c o m ­puter . Also s h o w n is t h e in troduct ion of a m e c h a n i c a l i n p u t θ b y m e a n s of a p o t e n t i o m ­eter . T h e s y m ­bo l Δ ind icates a g r o u n d potent ia l po in t ( the i n p u t j u n c t i o n of a s u m ­

m i n g ampli f ier)

i n p u t s f rom 6 to 30 m i l l i a m p e r e s . A t low i n p u t c u r r e n t a n d h i g h t e m p e r a t u r e s , h o w e v e r , t h e e r r o r b e c o m e s a p p r e ­c i ab le (3 p e r c e n t a t 4 m i l l i a m p e r e s ) . T h e s e e r ro rs a r e n o t excessive for some a p p l i c a t i o n s . F o r o t h e r a p p l i c a t i o n s t h e n e t w o r k s c a n b e t e m p e r a t u r e c o m p e n s a t e d ove r t h e full c u r r e n t r a n g e to a b o u t t h e s a m e a c c u r a c y as o b t a i n e d a t r o o m t e m p e r a t u r e . T h i s is d o n e b y us ing t e m p e r a t u r e -sensi t ive resistors in t h e n e t w o r k . T h e p r o b l e m s of t e m p e r a t u r e c o m p e n s a t i o n a r e g r e a t l y simplified, h o w e v e r , w i t h t h e use of silicon j u n c t i o n d iodes .

T h e l o g a r i t h m i c n e t w o r k s a n d t h e s u m m i n g ampl i f ie rs c a n b e i n t e r c o n n e c t e d to solve systems of n o n l i n e a r e q u a ­t ions . T h e m e t h o d of i n t e r c o n n e c t i o n ut i l izes t h e fact t h a t t h e s u m m i n g , or i n p u t , j u n c t i o n of t h e m a g n e t i c a m ­plifier is a t z e r o p o t e n t i a l , see F ig . 1. H e n c e , c u r r e n t s m a y b e i n d e p e n d e n t l y fed in to , or d r a w n from, this po in t . As a n e x a m p l e , t h e o u t p u t of t h e c i rcu i t of F ig . 1 c a n b e fed t o t h e s u m m i n g j u n c t i o n of a n o t h e r s imi la r ampli f ier . F u r t h e r ­m o r e , th is c u r r e n t m a y b e spli t i n t o fixed f rac t ional a m o u n t s b y a s imp le p a r a l l e l resis tor n e t w o r k , a n d fed to severa l o t h e r c i rcui t s . S u c h c u r r e n t sp l i t t ing n e t w o r k s a r e a lso used as s h o w n in F ig . 2.

T h e c o m p u t a t i o n d o n e in F ig . 1 r e q u i r e s 7 ounces of c o m p o n e n t s , a n d is p e r f o r m e d w i t h a n a c c u r a c y of a b o u t 1 p e r cen t . T h e response t i m e is shor t (0.01 second, us ing a 400-cycle ampl i f i e r ) . T h e versat i l i ty of t h e t e c h n i q u e r e ­sults in a c o m p u t e r w i t h a h igh r a t i o of c o m p u t a t i o n s p e r u n i t v o l u m e or we igh t , us ing re l iab le c o m p o n e n t s . T h e s e de s i r ab l e charac te r i s t i cs , t oge the r w i t h expe r i ence to d a t e , i n d i c a t e t h a t c o m p u t e r s m a d e of these t w o bas ic c o m ­p o n e n t s shou ld h a v e cons ide rab l e u t i l i ty in mi l i t a ry a n d i ndus t r i a l app l i ca t i ons .

Digest of paper 54-389, " A n Analogue Computing Technique Using Magnet ic Am­plifiers," recommended by the AIEE Committee on Magnetic Amplifiers and approved by the A I E E Committee on Technical Operations for presentation at the Fall General Meeting, Chicago, 111., October 11-15, 1954. Published in A I E E Transactions, vol. 73, pt. I, 1954 (Jan. 1955 section), pp. 635-40.

Β. E. Davis and I. H. Swift a re both with the Naval Ordnance Test Station, Inyokern, China Lake, Calif.

158 Davis, Swift—Analogue Computers ELECTRICAL ENGINEERING