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An analogue method of function generation using a magnetic drum Boulding, John David Richardson 1959

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4QGITB METHOD. OF FUNCTION .GENERATION  USING A. MAGNETIC DRUM by JOHN DAVID RICHARDSON BOULDING B^A.Sc,,, University of British Columbia, 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED .•.SCIENCE in the Department of El e c t r i c a l Engineering We accept this thesis as conforming to the standards required from candidates for the degree of Master of Applied Science Members of the Department of E l e c t r i c a l Engineering The University of Br i t i s h Columbia A p r i l , 19$9 ABSTRACT T h i s t h e s i s d i s c u s s e s an ^ a a l & g u e method o f f u n c t i o n g e n e r a t i o n u s i n g a m a g n e t i c drum* The f u n c t i o n g e n e r a t o r I s s u i t a b l e f o r u s e i n a p u l s e - p o s i t i o n - m o d u l a t i o n a n a l o g u e c o m p u t e r w h i c h b p e r a t e s on a t i m e - s e q u e n t i a l p r i n c i p l e tod i n r e a l t i m e . The f u n c t i o n s a r e a p p r o x i m a t e d b y l i n e a r and p a r a b o l i c a r c s , and t h e b r e a k p o i n t s ' ' a r e r e p r e s e n t e d by p u l s e p o s i t i o n s , T h e s e p u l s e p o s i t i o n s a r e s t o r e d on a m a g n e t i c drum. The f u n c t i o n g e n e r a t o r c o n v e r t s t h e s e p u l s e p o s i t i o n s I n t o t h e o r i g i n a l f u n c t i o n b y u s i n g p r e c i s e sweep a m p l i f i e r s and g a t i n g c i r c u i t s * , T he number o f f u n c t i o n s t h a t a r e a v a i l a b l e i s l i m i t e d o n l y b y t h e s i z e o f t h e drum. The method o f f u n c t i o n g e n e r a t i o n p r o p o s e d h e r e a l l o w s f o r v e r y s i m p l e programming o f t h e computer,, A c c u r a c i e s a p p r o a c h i n g one p e r cent were o b t a i n e d i n t e s t s u s i n g v e r y i n a d e q u a t e sweep a m p l i f i e r s . A c c u r a c i e s o f t h e o r d e r o f one-t e n t h o f one p e r c e n t a r e b e l i e v e d t o be p o s s i b l e by u s i n g t h e p r o p o s e d f u n c t i o n g e n e r a t o r t h a t i s d e s c r i b e d at t h e end o f t h i s t h e s i s * T h i s t h e s i s a l s o d e s c r i b e s t h e s y n c h r o h i z a t i o n and c o u n t i n g c i r c u i t s t h a t a r e r e q u i r e d t o c o n t r o l t h e o p e r a t i o n o f t h e c o m p u t e r , A l s o t h e c i r c u i t s r e q u i r e d t o w r i t e t h e i n f o r m a t i o n p u l s e s on t h e drum a r e d e s c r i b e d , , i i In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Electrical. Engineering The University of British Columbia, Vancouver 8, Canada. Date February 1.9, I.959  TABLE OF CONTENTS page A b s t r a c t <f e o o o » b Q V o o V W i 'W '." V « ' « » « o b o I I Acknowledgement « . o . . . . » < > . . < > < » » •«• . « «• <• * v i 1 » I n t r o d u o t i o n . °. •& • »• • » s ° ? i J » » * « • * ° « • ? 1 2. G e n e r a l D e s c r i p t i o n o f t h e F u n c t i o n G e n e r a t o r . . .• 5 2-1. F o r m i n g t h e P u l s e P o s i t i o n s f r o m t h e FtXHCt iOTl o o © o o o o o tf 0 o 6 a o o d o ^ 2-2» F o r m i n g t h e O r i g i n a l F u n c t i o n „ » * a * . . 6 2- 3. C o n v e r t i n g a V a l u e o f t h e F u n c t i o n . t o a T5 t l X 3 © P 0 S i t i O X l o a v a a v o a o a D O o o 7 3. S y n c h r o n i z a t i o n and C o u n t i n g . . . . . . . . . . . . 8 3- 1. D e s c r i p t i o n o f t h e Drum . . . . . . . . . . 8 3-2. D e s c r i p t i o n o f t h e S y n c h r o n i z a t i o n and C o u n t i n g S y s t e m . . . . . . . . . . . . . 10 3~3. B l o c k R e p r e s e n t a t i o n . . . . . . . . . . . . . 12 3-If. C i r c u i t D e t a i l s «, > . . . > . * <* .• . . . 15 if. W r i t i n g and E r a s i n g « . . . . , . . . . . . . . . . 2lf lf -1 . B l o c k R e p r e s e n t a t i o n . . . . . . . . . . . . 25 If-2. C i r c u i t D e t a i l s •'; . . . . > . . . . . v v v b 27 lf-3. W r i t e and E r a s e A m p l i f i e r s , . . . . . -« . 33 5» F u n c t i o n G e n e r a t i o n . . . . . . . . . . . . . . . . . 36 5-1. Read A m p l i f i e r v »• . <> . . » . . . . . . . . 36 5-2b F u n c t i o n G e n e r a t o r C i r c u i t s . , •;• 38 5~3. S i m p l i f i e d F u n c t i o n G e n e r a t o r >• . . . . . . if 1 5- If. T e s t i n g t h e S i m p l i f i e d F u n ct i o n G e n e r a t o r „ ijif 6. P r o p o s e d F o r m o f F u n c t i o n G e n e r a t i o n . . . . . . . 50 6- 1. New H i g h - G a i n DC A m p l i f i e r '-. . . . . . . . . 50 6- 2. P r o p o s e d F u n c t i o n G e n e r a t o r . . . . . . . . 53 7. C o n c l u s i o n s . . . . . a . . . . . . . . . ? . . . . . 59 7- 1. Recommendations f o r F u t u r e Work . 60 A p p e n d i x . . o ~« o * . . . ? . » . . . o . » . o o * . 62 B i b l i o g r a p h y . . . . . . . . . . . . . . . . . . . b . . 61f i i i L I S T OF ILLUSTRATIONS F i g u r e page 2- 1. R e p r e s e n t a t i o n o f F u n c t i o n s . . . . . . . t o f o l l o w ' $ 3- 1. The M a g n e t i c Drum . * , . . . ; . , . , « . . . . , . 9 3-2. C h a n n e l G a t i n g C i r c u i t s . * . . . .' . t o f o l l o w 9 3~3. C h a n n e l T i m i n g . . . . . . . . . . . * . • . , « . 10 3"k« B l o c k D i a g r a m o f S y n c h r o n i z a t i o n and C o u n t i n g S y s t e m * . . . * . . . . . . . t o f o l l o w 12 3-5- C l o c k Read A m p l i f i e r and A v e r a g i n g C i r c u i t s i •> w ; , , . . . . . . . . t o f o l l o w llf 3-6. C i r c u i t s o f P h a s e r - S h i f t e r and B u f f e r A m p l i f i e r s . . < * . . ; * * . . . ,• i •? t o f o l l o w 15 3-7, Count o f 100 C i r c u i t . V ; . . , . * . >• t o f o l l o w 16 3-8o C o u n t i n g C i r c u i t Waveforms and T i m i n g . . . . . . . .. v . . . . . y > . t o f o l l o w 17 3-9. C i r c u i t o f C o n t r o l F l i p - F l o p and A s s o c i a t e d A m p l i f i e r s . . , •* . . . . . t o f o l l o w 18 3-10. C i r c u i t Of S y n c h r o n i z a t i o n AND G a t e 20 3-11, C i r c u i t o f G a t e C o u n t i n g F l i p - F l o p s . . . t o f o l l o w 21 3- 12. C i r c u i t o f C o s i n e P u l s e G e n e r a t o r . * . . t o f o l l o w 21 i f - 1 . B l o c k D i a g r a m o f W r i t e and S i n g l e C h a n n e l E r a s e C o n t r o l C i r c u i t s . . . . t o f o l l o w , 2£ i}.-2. C i r c u i t o f T e n s and U n i t s S e l e c t o r S w i t c h e s ,• . i , i . :. :? % i , . w ,• , . t o f o l l o w 28 L{.-3- C i r c u i t o f WFFl . . . . . . ^ t o f o l l o w 29 C i r c u i t o f AND Gate WA1 . . . . . . . . . t o f o l l o w 29 l|.-5>. C i r c u i t o f WFF? , . , i -.• - , , * • , . . • ? . . . , . 30 I(.-6. WA2 and D r i v i n g C i r c u i t s . . . •* v . . . t o f o l l o w 30 lf - 7 . C i r c u i t o f - S i n 0 S q u a r e d G e n e r a t o r . . . t o f o l l o w 31 4- 8. C i r c u i t o f D i v i d e - b y - T w o F l i p - F l o p , WFFlf • i '' • • • > * ' 9 . . . . . t o f o l l o w 31 i v F i g u r e pag lf - 9 - C i r c u i t of AND Gate WA3 . . . . . . . . . . . . . . 3 J+-10. C i r c u i t of Write A m p l i f i e r . . . . . . . t o f o l l o w 3 i | - l l . C i r c u i t of Erase A m p l i f i e r . . . . . . . t o f o l l o w 3 5-1. C i r c u i t of Read A m p l i f i e r . . . . . . . . t o f o l l o w 3 5-2. Channel P u l s e Gating C i r c u i t . . . . . . . . . . . 3 5-3. Diode Gate and Sweet C i r c u i t . . . . . . t o f o l l o w 3 5-l+o C i r c u i t of G a t i n g F l i p - F l o p s . . . . . . t o f o l l o w 1+ 5-5. C i r c u i t of V o l t a g e Comparator t o f o l l o w I4. 5.-6. S i m p l i f i e d F u n c t i o n Generator . . . . . . t o f o l l o w I). 5-7• Output Waveform of S i m p l i f i e d F u n c t i o n Generator. . 5-8. P l o t of F u n c t i o n s Generated . . . . . . . . . . . . 5-9. R e s u l t s of T e s t s on S i m p l i f i e d F u n c t i o n Generator . . . . . . . . . . t o f o l l o w 6-1. S t a b i l i z e d High-Gain DC A m p l i f i e r . . . . t o f o l l o w 6-2. Proposed F u n c t i o n Generator t o f o l l o w A - l . The Sweep C i r c u i t ACKNOWLEDGEMENT The work d e s c r i b e d i n t h i s t h e s i s i s p a r t . o f a p r o j e c t sponsored by the Defence Research Board, Department of N a t i o n a l Defence, Canada, under Grant Number DRB C-9931-02 (550-GC). The author i s g r e a t l y Indebted t o Dr. E.V. Bohn, under whose guidance t h i s work was performed, and to Dr, P. Noakes, grantee of the p r o j e c t . A p p r e c i a t i o n i s a l s o expressed f o r the w i l l i n g a s s i s t a n c e g i v e n to t h e author on many occasions by o t h e r members of the U n i v e r s i t y F a c u l t y and S t a f f . The author i s indebted t o the Northern E l e c t r i c Company which granted him a s c h o l a r s h i p i n 1957, thus e n a b l i n g him to continue h i s s t u d i e s . v i AN: ANALOGUE METHOD OF FUNCTION. GENERATION  USING. A MAGNETIC; DRUM 1. INTRODUCTION P r o b l e m s I n s y s t e m s s i m u l a t i o n , f o r e x a m p l e ! t h e s t u d y o f c o n t r o l and g u i d a n c e s y s t e m s i n m i s s i l e s and h i g h - s p e e d a i r -c r a f t o r o f complex t r a i n i n g d e v i c e s s u c h as f l i g h t s i m u l a t o r s , i n v o l v e t h e s o l u t i o n o f s y s t e m s o f o r d i n a r y n o n - l i n e a r d i f f e r e n -t i a l e q u a t i o n s . T h i s s o l u t i o n r e q u i r e s t h e g e n e r a t i o n o f a l a r g e number o f n o n - l i n e a r f u n c t i o n s . T h e r e a r e s e v e r a l methods f o r g e n e r a t i n g t h e s e f u n c t i o n s and t h e y f a l l i n t o two main c a t e g o r i e s : e l e c t r o - m e c h a n i c a l methods o r e l e c t r o n i c methods. Of t h e e l e c t r o - m e c h a n i c a l d e v i c e s , t h e s e r v o - d r i v e n 6 p o t e n t i o m e t e r s a r e p r o b a b l y t h e b e s t known* Two common but r a t h e r i n f l e x i b l e s y s t e m s a r e t h e n o n - l i n e a r p o t e n t i o m e t e r wound t o r e p r e s e n t t h e f u n c t i o n and t h e l i n e a r p o t e n t i o m e t e r d r i v e n by a cam w h i c h i s shaped t o r e p r e s e n t t h e f u n c t i o n . O n l y m o n o t o n i c f u n c t i o n s may be g e n e r a t e d by t h e s e s y s t e m s . A more f l e x i b l e and more a c c u r a t e method i s t o u s e a l i n e a r p o t e n t i o -m e t e r w h i c h has a l a r g e number o f t a p s . W i t h a s e t o f a d j u s t -i n g n e t w o r k s f o r e a c h t a p ^ t h e t a p p e d p o t e n t i o m e t e r may.be a d j u s t e d t o r e p r e s e n t any f u n c t i o n p r o v i d i n g t h e number and p o s i t i o n o f t h e t a p s i s s u f f i c i e n t t o i n c l u d e a l l t h e b r e a k p o i n t s o f t h e f u n c t i o n as t h e r e s u l t i n g f u n c t i o n i s l i n e a r between t h e t a p s . The t a p p e d p o t e n t i o m e t e r h a s t h e g r e a t 1 2 a d d i t i o n a l a d v a n t a g e I n t h a t one s e r v o s y s t e m may be u s e d t o g e n e r a t e a number o f f u n c t i o n s . Two e l e c t r o - m e c h a n i c a l methods u s i n g p h o t o g r a p h s h a v e k,12 been d e v e l o p e d at t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . H i l d e b r a n d ' s g e n e r a t o r ^ s c a n n e d t h e a m p l i t u d e o f t h e f u n c t i o n , w h i c h was r e p r e s e n t e d on p h o t o g r a p h i c n e g a t i v e s , I n t i m e s e q u e n c e . I t p r o d u c e d , f r o m a p h o t o - c e l l , a v o l t a g e p r o p o r -t i o n a l t o t h e f u n c t i o n w i t h t i m e as i t s i n d e p e n d e n t v a r i a b l e . Sam-p l i n g o f t h e waveform at t h e d e s i r e d a b s c i s s a v a l u e s and g a t i n g o f t h e sampled o u t p u t s gave t h e r e q u i r e d s e q u e n c e o f f u n c t i o n v a l u e s . The e r r o r s were m a i n l y due t o n o n - l i n e a r i t y i n a m p l i t u d e r e s p o n s e , s a m p l i n g and f r e q u e n c y r e s p o n s e l i m i t -12 a t i o n s . S t a c e y ' s g e n e r a t o r u s e d a g a l v a n o m e t e r t o p o s i t i o n a beam o f l i g h t on p h o t o g r a p h i c n e g a t i v e s r e p r e s e n t i n g t h e f u n c t i o n , w h i c h were mounted around t h e s u r f a c e o f a r o t a t i n g drum, and p r o d u c e d t h e v a l u e o f t h e f u n c t i o n at t h e p r e -d e t e r m i n e d g a l v a n o m e t e r s e t t i n g . T h i s g e n e r a t o r e l i m i n a t e d t h e e r r o r s m e n t i o n e d above b ut I n t r o d u c e d an e r r o r due t o t h e r e l a t i v e p o s i t i o n i n g o f t h e p h o t o g r a p h i c n e g a t i v e . A c c u r a c i e s t o w i t h i n 1 p e r c e n t were b e l i e v e d t o be p o s s i b l e . The b i a s e d d i o d e and t h e p h o t o f o r m e r a r e t h e two most common e l e c t r o n i c g e n e r a t o r s . The b i a s e d d i o d e g e n e r a t o r a p p r o x i m a t e s t h e r e q u i r e d f u n c t i o n w i t h e i t h e r s t r a i g h t l i n e o r c u r v e d segments."*" The p h o t o f o r m e r ^ u s e s an opiaque mask cut t o r e p r e s e n t t h e f u n c t i o n w h i c h i s f a s t e n e d t o t h e f a c e o f a 3 cathode-ray tube. The a s s o c i a t e d c i r c u i t r y c o n t r o l s the t r a c e o f the tube so that i t f o l l o w s the o u t l i n e o f the mask. These systems have a h i g h frequency response and a c c u r a c i e s can be obtained t o w i t h i n 0,2 per cent. But they have the common disadvantage i n that a complete system must be repeated f o r each f u n c t i o n t o be generated, A magnetic drum has been used t o s t o r e f u n c t i o n s f o r 2 use i n analogue computing. T h i s system uses p u l s e - w i d t h modu-l a t i o n , but as the p o s i t i o n on the drum i s determined by compar-ing a sweep v o l t a g e (which i s synchronized t o the p e r i o d of the drum r e v o l u t i o n ) t o the f u n c t i o n v o l t a g e u s u a l l y g i v e n by a l i n e a r p o t e n t i o m e t e r , i t i s subj e c t t o sampling e r r o r s . A l s o d i f f i c u l t y a r i s e s i n d e s i g n i n g a sweep generator which would be w i t h i n the r e q u i r e d accuracy f o r the sweep times used and a l s o to design a p r e c i s i o n comparator. T h i s system has t h e great advantage i n that i t i s very f l e x i b l e . F u n c t i o n generators u s i n g d i g i t a l techniques are gener-a l l y not s u i t e d f o r use I n analogue computers as expensive d i g i t a l to-analogue c b n v e r s i o n d e v i c e s are r e q u i r e d . Some work has been done on d i g i t a l computers s u i t a b l e f o r use i n r e a l - t i m e systems s i m u l a t i o n problems but these are ve r y s p e c i a l i z e d , A s p e c i a l pur-pose d i g i t a l computer has been developed t o meet the needs of an 3 o p e r a t i o n a l f l i g h t t r a i n e r . T h i s computer i s l i m i t e d t o i t s s p e c i a l purpose and i s c o s t l y c o n s i d e r i n g i t s l i m i t e d use. The TRICE ( T r a n s i s t o r i z e d Real-Time Incremental Computer--Expansible), which Is a new p a r a l l e l e d d i g i t a l d i f f e r e n t i a l a n a l y z e r , i s k the closest yet to the ideal computer for use in systems simulation as it has a high computing speed, the ease of programming of the analogue computer, and the precision of the d i g i t a l computer. But i t is s t i l l too costly for most applications as the quoted component count is approximately 100 transistors and k5>0 diodes for each operational unit. In the function generator to be described in this thesis, one generator w i l l be able to generate up to five of the functions required with an accuracy approaching 0.1 per cent f u l l scale. The functions w i l l be stored on a magnetic drum which w i l l enable them to be available at a l l times and the number of func-tions available w i l l be limited only by the size of the drum. The programming of the computer w i l l be very simple as the func-tion pulse positions w i l l be put onto the drum manually by, adjust-ing three dials. The clock signal frequency is about 70 kcs and, as a result, this generator should be able to handle most real-time problems. Cost w i l l be kept low because of a time sharing principle. 2. GENERAL DESCRIPTION OP THE FUNCTION GENERATOR The c omputer u n d e r d e v e l o p m e n t In t h e E l e c t r i c a l E n g i n e e r i n g Department o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a i s t o be a s p e c i a l p u r p o s e computer s p e c i f i c a l l y s u i t e d f o r s y s t e m s s i m u l a t i o n . To c a r r y out t h e l a r g e number o f o p e r a t i o n s i n v o l v -i n g f u n c t i o n g e n e r a t i o n , m u l t i p l i c a t i o n , and i n t e g r a t i o n , t h e t i m e s h a r i n g f e a t u r e s and a c c u r a c y o f a d i g i t a l c omputer a r e d e s i r e d . To compute i n r e a l - t i m e and h a v e a v e r s a t i l e and s i m p l e programming, t h e o p e r a t i o n a l s i m p l i c i t y o f an a n a l o g u e c o m p u t e r 7 10 i s d e s i r e d . A c o mputer b a s e d on p u l s e - p o s i t i o n - m o d u l a t i o n ' combines t h e d e s i r a b l e f e a t u r e s o f d i g i t a l and o r d i n a r y a n a l o g u e computers i n i t s mode o f o p e r a t i o n . A p u l s e - p o s i t i o n - m o d u l a t i o n a n a l o g u e computer r e q u i r e s o n l y d i s c r e t e v a l u e s o f f u n c t i o n s at any p a r t i c u l a r t i m e f r o m t h e f u n c t i o n g e n e r a t o r as t h e c o m p u t a t i o n s a r e c a r r i e d out i n c r e m e n -7,10 t a l l y . To p r o d u c e t h e s e d i s c r e t e v a l u e s o f t h e f u n c t i o n , t h e g e n e r a t o r must d e m o d u l a t e t h e p u l s e t r a i n r e p r e s e n t i n g t h e f u n c t i o n , f i n d t h e v a l u e o f t h e f u n c t i o n at t h e g i v e n t i m e , and t h e n m o d u l a t e t h i s v a l u e i n t o a p u l s e p o s i t i o n . The two s u b -s e c t i o n s f o l l o w i n g w i l l d e s c r i b e t h e p r i n c i p l e s i n v o l v e d i n t h i s method. 2-1. F o r m i n g t h e P u l s e P o s i t i o n s f r o m t h e F u n c t i o n The f u n c t i o n i s a p p r o x i m a t e d by l i n e a r segments and p a r a b o l i c a r c s . T h i s method g i v e s e x c e l l e n t a p p r o x i m a t i o n t o most o f t h e f u n c t i o n s o c c u r r i n g i n p h y s i c a l s y s t e m s s i n c e i t F i g u r e 2-1. R e p r e s e n t a t i o n o f F u n c t i o n s 6 a p p r o x i m a t e s a c c u r a t e l y t h e c u r v a t u r e and s l o p e o f t h e f u n c t i o n o y e r s e l e c t e d i n t e r v a l s . T h i s a p p r o x i m a t i o n t o t h e f u n c t i o n i s d i f f e r e n t i a t e d t w i c e and t h e s e c o n d d e r i v a t i v e c o n s i s t s o f p i e c e -put e r as t i m e i n t e r v a l s between p u l s e s w h i c h a r e s t o r e d on a m a g n e t i c drum. The d e t a i l e d d e s c r i p t i o n o f t h e method by w h i c h t h e s e p u l s e s a r e r e c o r d e d , t h e methods u s e d t o d e t e r m i n e t h e s i g n , and t h e s y n c h r o n i z a t i o n o f t h e s y s t e m w i l l be d i s c u s s e d l a t e r . 2-2. F o r m i n g t h e O r i g i n a l F u n c t i o n i n g t h e second, d e r i v a t i v e and c a r r y out a d o u b l e i n t e g r a t i o n . T h r e e l i n e a r sweep c i r c u i t s a r e u s e d f o r t h i s I n t e g r a t i n g p r o c e s s . The f i r s t sweep c i r c u i t I s u s e d t o g e n e r a t e t h e s e c o n d d e r i v a t i v e u s i n g t h e p i e c e w i s e c o n s t a n t v a l u e s and t h e b r e a k p o i n t s d e t e r -m i n e d by t h e p u l s e p o s i t i o n s . The s e c o n d sweep c i r c u i t i n t r o -d u ces t h e i n i t i a l v a l u e f'(0) and i n t e g r a t e s t h e o u t p u t o f t h e f i r s t sweep c i r c u i t . Thus t h e f i r s t d e r i v a t i v e h a s b e en g e n e r a t e d . The t h i r d sweep c i r c u i t i n t r o d u c e s t h e i n i t i a l v a l u e f(0) and I n t e g r a t e s t h e o u t p u t o f t h e s e c o n d sweep c i r c u i t . T h us t h e * f u n c t i o n g e n e r a t i o n i s c o m p l e t e . T h e d e t a i l s o f t h e s y s t e m w i l l be d i s c u s s e d l a t e r . To g e n e r a t e t h e f u n c t i o n a l l t h a t i s n e c e s s a r y i s t o c o n v e r t t h e t i m e i n t e r v a l between p u l s e s t o a v o l t a g e r e p r e s e n t -7 2-3. Converting a Value of the Function to a Pulse Position To find the discrete value of the function at any given value of x, the integrating action is stopped at x. The output of the generator is then clamped at f(x) by the integrator action. This value of f(x) is converted into a pulse position by i n i t i a t -ing a down sweep from the third sweep cir c u i t . TaJhen the output reaches the reference voltage (in this case zero) a voltage comparator generates a pulse which terminates the down sweep. This pulse, Pf(x), is then stored on the drum and i t s position represents the value of the function^ f (x) , The function gener-ator is then ready to generate the next function. The details of this system w i l l be discussed later. This method of function generation places certain res-trictions on the maximum slope and curvature that a function may have. These restrictions are due to the sequential manner in which the pulses occur and to the limits in achieving a fast precision linear sweep and high-speed switching. However, nearly a l l empirical and theoretical functions occurring in physical systems meet these restrictions. 3. SYNCHRONIZATION AND COUNTING As t h e f u n c t i o n s i n t h e computer ar e r e p r e s e n t e d by ' p u l s e s w h i c h a r e s t o r e d on t h e s u r f a c e o f a m a g n e t i c drum, p r o v i s -i o n must be made f o r t h e s y n c h r o n i z a t i o n o f t h e drum t o t h e e x t e r n a l o o n t r o l c i r c u i t r y and f o r t h e t i m i n g o f t h e c o m p u t e r as a w h o l e . Thus a v e r y r e l i a b l e s y n c h r o n i z a t i o n and t i m i n g s y s t e m i s r e q u i r e d . T h i s s y s t e m w o u l d a l s o be u s e d when w r i t i n g t h e p u l s e s , on t h e drum, and f o r r e a d i n g t h e o u t p u t o f t h e c omputer. 3-1. D e s c r i p t i o n o f t h e Drum The m a g n e t i c s t o r a g e drum i s t h e memory o f t h e c omputer. I n f o r m a t i o n i s s t o r e d on t h e d r u m . s u r f a c e i n t h e f o r m o f p u l s e p o s i t i o n s . T h e p u l s e s a r e f o r m e d by r e v e r s i n g a n a r r o w band o f r e s i d u a l f l u x on t h e drum s u r f a c e . The s u r f a c e o f t h e drum i s c o a t e d w i t h an i r o n - o x i d e compound w h i c h h a s t h e p r o p e r t y o f r e t a i n i n g t h e s e r e v e r s a l s o v e r a v e r y l o n g p e r i o d o f t i m e . A p u l s e i s w r i t t e n by p a s s i n g a c u r r e n t t h r o u g h a " w r i t e h e a d " and e r a s e d by p a s s i n g a c u r r e n t o f o p p o s i t e p o l a r i t y t h r o u g h t h e same " w r i t e h e a d " . A p u l s e i s r e a d by o b s e r v i n g t h e p u l s e on t h e " r e a d h e a d " . The w r i t e and r e a d h e a d s a r e p h y s i c a l l y t h e same w i t h t h e o n l y d i f f e r e n c e b e i n g i n t h e c o n n e c t i o n o f t h e l e a d s , The s u r f a c e o f t h e drum i s d i v i d e d a x i a l l y I n t o t e n c i r c u m f e r e n t i a l t r a c k s , t h e v e r t i c a l d i s t a n c e between t h e m b e i n g d e t e r m i n e d by t h e p h y s i c a l s i z e o f t h e i r a s s o c i a t e d h e a d s ; See F i g u r e 3-1 f o r a p i c t o r i a l v i e w o f t h e drum. T h e s e t e n t r a c k s a r e u s e d f o r f u n c t i o n s t o r a g e w i t h any t r a c k b e i n g s e l e c t e d by 8 9 p o s i t i o n i n g a t e n - p o s i t i o n s e l e c t o r switch, Iron-Oxide Coated F u n c t i o n Storage Tracks Write and Read Heads Clock T r a c k one channel F i g u r e 3-1. The Magnetic Drum In a d d i t i o n t o the above t e n t r a c k s t h e r e i s a t r a c k on which i s permanently s t o r e d 15>60 e q u a l l y - s p a c e d magnetized c e l l s . T h i s t r a c k i s the c l o c k t r a c k and a s i n u s o i d a l s i g n a l of a frequency depending upon the drum speed appears at i t s read head. T h i s s i g -n a l , c a l l e d t h e c l o c k s i g n a l , i s used t o d e r i v e a l l the t i m i n g p u l s e s , and as a r e s u l t t o c o n t r o l the o p e r a t i o n of the computer. The s y n c h r o n i z a t i o n and counting c i r c u i t s work with t h i s c l o c k s i g n a l t o d e r i v e a l l the r e f e r e n c e p u l s e s . Because of drum e c c e n t r i c i t y and the v a r i a t i o n s i n the s p a c i n g of the magnetized c e l l s , the c l o c k s i g n a l must be averaged i n o r d e r t o produce a c l o c k s i g n a l w i t h a u n i f o r m p e r i o d . The c i r c u i t s r e q u i r e d f o r t h i s o p e r a t i o n w i l l be d i s c u s s e d l a t e r . C h a n n e l G a t i n g L o g i c Chg 1 i s a j _ h ^ Chg 9 i s a ^ 2 a l b 2 10 a 3 b 2 3 a l b 3 11 a 3 b 3 4 a l b 4 12 a 3 b 4 5 a 2 b l 13 a 4 b l 6 a 2 b 2 14 a 4 b 2 7 a 2 b 3 15 a 4 b 3 8 a 2 b 4 F i g u r e 3-2. C h a n n e l G a t i n g C i r c u i t s 10 3 - 2 . D e s c r i p t i o n o f t h e S y n c h r o n i z a t i o n and C o u n t i n g S y s t e m The s y n c h r o n i z a t i o n and c o u n t i n g c i r c u i t s d i v i d e t h e 15>60 p u l s e s o f t h e c l o c k s i g n a l i n t o 15> c h a n n e l s o f IOI4. p u l s e s p e r c h a n n e l . E a c h o f t h e l£ c h a n n e l s may be s e l e c t e d by p o s i t i o n i n g a l ^ - p o s i t i o n s e l e c t o r s w i t c h . I n O r d e r t o a c c o m p l i s h t h i s s e l e c t i o n a co d e d d i s c i s mounted on t h e same s h a f t as t h e drum. A beam o f l i g h t p a s s i n g t h r o u g h h o l e s i n t h e coded d i s c a c t i v a t e some p h o t o d i o d e s w h i c h d r i v e t r a n s i s t o r g a t e s , f r o m w h i c h e a c h o f t h e 15 c h a n n e l s a r e o b t a i n e d . T h e s e g a t e s a r e t h e n s e l e c t e d by t h e s e l e c t o r s w i t c h . The c i r c u i t s r e q u i r e d f o r t h i s o p e r a t i o n a r e s t r a i g h t - f o r w a r d and w i l l n o t be d i s c u s s e d i h t h i s r e p o r t but t h e y a r e shown i n F i g u r e 3 - 2 , See S u b - s e c t i o n 3 - 3 . The IOI4. p u l s e s i n e a c h c h a n n e l a r e f u r t h e r d i v i d e d i n t o a g r o u p o f if p u l s e s and t h e n a g r o u p o f 100 p u l s e s . T he g r o u p o f if p u l s e s i s u s e d t o c o n t r o l t h e o p e r a t i o n o f t h e c h a n n e l . The f i r s t p u l s e . h a s no p a r t i c u l a r s i g n i f i c a n c e . The n e x t t h r e e p u l s e s a r e d e s i g n a t e d e a r l y p u l s e (EP)", z e r o p u l s e ( O P ) , and l a t e p u l s e (LP) r e s p e c t i v e l y . The a c t u a l c o m p u t i n g o f t h e c h a n n e l i s done d u r i n g t h e i n t e r v a l o f t h e 100 p u l s e s . T h i s c y c l e i s t h e n r e p e a t e d f o r t h e n e x t c h a n n e l . See F i g u r e 3 - 3 . 99 100 1 2 3 98 9 9 100 I I I 1 2 KP OP LP EP OP LP C h a n n e l X - 1 - C h a n n e l X C h a n n e l X + 1 F i g u r e 3 - 3 , C h a n n e l T i m i n g 11 To w r i t e i n f o r m a t i o n o n t o t h e drum and t o t a k e i n f o r m -a t i o n f r o m t h e drum, i t i s n e c e s s a r y t o be a b l e t o s e l e c t any p o s i t i o n on t h e drum d u r i n g t h e count o f t h e 100 p u l s e s . As g a s - f i l l e d d e cade c o u n t i n g t u b e s a r e u s e d f o r t h i s count o f 100, a p a i r o f s e l e c t o r s w i t c h e s , one s e l e c t i n g t h e t e n s count and t h e o t h e r t h e u n i t s c o u n t , g i v e s t h e p o s i t i o n o f a p u l s e t o 1 p e r cent o f f u l l s c a l e . The a c c u r a c y i s g r e a t l y i m p r o v e d by u s i n g a p h a s e - s h i f t i n g c a p a c i t o r t o s h i f t t h e p h a s e o f t h e c l o c k s i g n a l t h r o u g h a l i t t l e more t h a n one c y c l e . The phase s h i f t i s c o n -t r o l l e d by a t e n - t u r n d i a l w h i c h may be r e a d t o one p a r t I n o n e - t h o u s a n d . T h u s , p r o v i d i n g t h e d r i v i n g c i r c u i t s f o r t h e p h a s e -s h i f t i n g c a p a c i t o r a l l o w t h e c a p a c i t o r t o f u n c t i o n p r o p e r l y , an a c c u r a c y o f 0.01 p e r cent o f f u l l s c a l e I s p o s s i b l e . The drum s p e e d i s about 2800 rpm w i t h t h e e x t e r n a l a l u m i n i u m s y n c h r o n i z a t i o n d i s c and t h e p h o t o g r a p h i c mounts f o r 12 S t a c e y T s f u n c t i o n g e n e r a t o r a l l mounted. The r e s u l t i n g p e r i o d o f t h e c l o c k s i g n a l I s about l k u s e e s . T h i s p e r i o d i s n o t c r i t i -c a l as l o n g as I t i s a b s o l u t e l y u n i f o r m . I f t h e p e r i o d i s c h a n g e d / t h e o n l y d i f f e r e n c e n o t i c e d i n t h e computer i s t h e s c a l e f a c t o r w h i c h w o u l d t e n d t o c a n c e l I t s e l f o u t i f t h e p e r i o d r e m a i n s u n i f o r m . The change i n s c a l e f a c t o r m i g h t t e n d t o o v e r -l o a d t h e c o m p u t i n g e l e m e n t s , s u c h as t h e i n t e g r a t i n g c i r c u i t s , and i t t h e r e f o r e s h o u l d be t a k e n i n t o c o n s i d e r a t i o n . The s y n c h r o n i z a t i o n and c o u n t i n g c i r c u i t s were d e s i g n e d f o r a c l o c k p e r i o d o f about Lk u s e e s b u t i t i s b e l i e v e d t h a t t h e c i r c u i t s w o u l d s t i l l o p e r a t e v e r y s a t i s f a c t o r i l y , w i t h some 12 minor adjustments, f o r clock periods i n the range of 10 to 2£ usees which w i l l coyer any changes i n the drum speed due to any minor modifications to the i n e r t i a of the rotating apparatus. The lower l i m i t on the period i s imposed by the decade counting tubes which are capable of counting at a maximum rate of 100 kcs. The upper l i m i t on the period may be very e a s i l y changed i f so required by making some sli g h t modifications to the c i r c u i t design. See the sub-section on c i r c u i t d e t a i l s . 3-3, Block Representation Referring to Figure 3-1+, "the clock signal from the read head must f i r s t be amplified and then averaged so that the phase of the clock s i g n a l which i s Used i n the counter c i r c u i t s i s absolutely constant. The method used to average the phase i s to use the clock signal to control a tuneable t r a n s i s t o r o s c i l -l a t o r which has a natural period of o s c i l l a t i o n of about U4. usees* The amplified signal from the read head i s tuned to i t s own average frequency and i s used to control the frequency of o s c i l -l a t i o n of the o s c i l l a t o r by means of a reactance tube. To provide added f i l t e r i n g and averaging the output from the o s c i l l a t o r i s fed into a tuned amplifier stage before i t i s ready f o r use. Any change in the drum speed must be compensated f o r by reradjusting the tuned c i r c u i t s . By using a frequency s t a b i l i z e d alternating current supply to drive a synchronous motor, major variations in the drum speed are eliminated f o r a l l p r a c t i c a l purposes as the i n e r t i a of the system does not change unless tampered with* Either one of these systems may be used to completely s t a b i l i z e F i g u r e 3r-4. .Block D i a g r a m o f S y n c h r o n i z a t i o n and C o u n t i n g System 13 t h e c l o c k p e r i o d , but by u s i n g a c o m b i n a t i o n o f b o t h , n e i t h e r o f t h e s y s t e m s becomes c o m p l i c a t e d and t h e c o s t may be k e p t v e r y l o w . The l i n e power s u p p l y d r i v i n g a s y n c h r o n o u s m o t o r i s s u f f i c i e n t t o k e e p t h e v a r i a t i o n s i n t h e drum s p e e d w i t h i n t h e r a n g e i n w h i c h t h e a v e r a g i n g c i r c u i t s can c o n t r o l . The o u t p u t o f t h e t u n e d a m p l i f i e r i s f e d t o a p h a s e -s h i f t e r w h i c h p r o v i d e s p l u s and minus s i n e and p l u s and minus c o s i n e s i g n a l s f o r t h e p h a s e - s h i f t i n g c a p a c i t o r . The p h a s e -s h i f t e r i s a s i m p l e phase I n v e r t e r d e s i g n e d t o g i v e v e r y a c c u r a t e p h a s e s h i f t s and u n i f o r m v o l t a g e o u t p u t s . T h e s e c o n d i t i o n s a r e n e c e s s a r y i n o r d e r t h a t t h e p h a s e - s h i f t i n g c a p a c i t o r w i l l s h i f t t h e p h a s e Of t h e c l o c k s i g n a l w i t h t h e r e q u i r e d a c c u r a c y . The p l u s s i n e and t h e p l u s c o s i n e o u t p u t s a r e a l s o f e d t o t h e c o u n t i n g c i r c u i t ; T h i s c i r c u i t i s t h e h e a r t o f t h e s y n -c h r o n i z a t i o n and c o u n t i n g s y s t e m and t h e c o s i n e s i g n a l i s t h e a c t u a l s i g n a l w h i c h i s c o u n t e d * T h i s method a l l o w s t h e r e s u l t i n g g a t e s t o open a q u a r t e r o f a p e r i o d b e f o r e t h e s i n e c l o c k s i g n a l . Two g a s - f i l l e d decade c o u n t e r t u b e s count o f f 100 c o s i n e p e r i o d s and t h e n t h e count i s s t o p p e d by t h e a c t i o n o f t h e c o n t r o l f l i p -f l o p on an i n p u t AND g a t e . The s w i t c h i n g o f t h e c o n t r o l f l i p -f l o p c l o s e s t h i s AND g a t e and t h e c o u n t i n g w a i t s f o r t h e f i r s t c h a n n e l g a t e f r o m t h e c o d e d d i s c m e n t i o n e d p r e v i o u s l y . As s o o n as t h i s g a t e a r r i v e s a c h a i n o f c o u n t i n g i s s t a r t e d by f o u r i d e n t i c a l t r a n s i s t o r f l i p - f l o p s . T h e s e f l i p - f l o p s a r e r e s e t b y t h e c o s i n e s i g n a l and t h e r e s e t a c t i o n o f one f l i p - f l o p s e t s t h e n e x t . I n t h i s way f o u r C o s i n e p e r i o d s a r e c o u n t e d o f f . The r e s e t o f 14 , t h e f o u r t h f l i p - f l o p r e s e t s t h e c o n t r o l f l i p - f l o p w h i c h r e s t a r t s t h e count o f 100 i n t h e c o u n t i n g t u b e s * When t h i s c ount o f 100 i s c o m p l e t e t h e c l o s i n g a c t i o n o f t h e c o n t r o l f l i p - f l o p s t a r t s t h e count i n t h e t r a n s i s t o r f l i p - f l o p s as t h e n e x t c h a n n e l g a t e w i l l c o i n c i d e w i t h t h e s w i t c h i n g a c t i o n o f t h e c o n t r o l f l i p - f l o p . T h i s c y c l e i s r e p e t i t i v e , r e s u l t i n g i n l£ c h a n n e l s f o r one drum r e v o l u t i o n * T he s y n c h r o n i z a t i o n r e s u l t i n g i n u s i n g t h e c h a n n e l g a t e s e n s u r e s t h a t t h e drum w i l l f a l l b a c k i n t o s y n c h r o n i z a t i o n w i t h t h e c o u n t e r c i r c u i t s when t h e computer i s s t a r t e d o r i f t h e cou n t i s l o s t f o r some o t h e r r e a s o n . The c o u n t i n g t u b e s u s e d h a v e a l l t e n c a t h o d e s a v a i l -a b l e * The o u t p u t s o f t h e s e c a t h o d e s a r e f e d t o t e n s and u n i t s s e l e c t o r s w i t c h e s . The s e l e c t e d t e n s and u n i t s p u l s e s a r e u s e d t o s e l e c t t h e p h a s e - s h i f t e d s i n e c l o c k s i g n a l ( s i n 0) w h i c h i s t o be w r i t t e n on t h e drum as t h e d e s i r e d p u l s e p o s i t i o n * A l s o t h e y a r e u s e d i n a c o i n c i d e n c e t y p e o f c i r c u i t t o d e t e r m i n e t h e p o s i t i o n o f any p u l s e on t h e drum, and t h u s t o p r o v i d e a method o f r e a d i n g t h e o u t p u t o f t h e c o m p u t e r . The c i r c u i t s r e q u i r e d f o r t h e s e o p e r a t i o n s w i l l be d i s c u s s e d l a t e r * The t r a n s i s t o r c o u n t i n g f l i p - f l o p s p r o d u c e t h e e a r l y ( E G ) , z e r o (0G) , and t h e l a t e (LG) g a t e s . The e a r l y , z e r o , and l a t e ; p u l s e s a r e a l s o d e r i v e d f r o m t h e s e f l i p - f l o p s . T h e s e f l i p -f l o p s a r e q u i t e e l a b o r a t e i n o r d e r t h a t t h e y w i l l d r i v e a l l t h e n e c e s s a r y c i r c u i t s and s t i l l o p e r a t e r e l i a b l y . By u s i n g t r a n s i s t o r s w h e r e v e r p o s s i b l e t h e c i r c u i t s h a v e been k e p t s i m p l e and i n e x p e n s i v e as t h e most c o n v e n i e n t Read A m p l i f i e r R e a c t a n c e Tub O s c i l l a t o r R e s i s t o r s - — A l l l/2 w a t t e x c e p t where n o t e d , — - A l l 10$. C a p a c i t o r s - - - Whole numbers i n p f , . D e c i m a l numbers i n u f . I n d u c t o r s : F i x e d i n mh, V a r i a b l e a b o u t lOmh. F i g u r e 3 r - 5 . C l o c k Read A m p l i f i e r and A v e r a g i n g C i r c u i t s IS t r i g g e r i n g p u l s e s a r e p o s i t i v e and a l s o t h e v o l t a g e l e v e l s a r e most c o n v e n i e n t f o r t r a n s i s t o r a p p l i c a t i o n s . S e m i c o n d u c t o r d i o d e s h a v e been u s e d e x c l u s i v e l y i n a l l t h e g a t e s and i s o l a t i n g c i r c u i t s . C i r c u i t D e t a i l s The c l o c k s i g n a l t a k e n f r o m t h e c l o c k t r a c k on t h e drum has an a m p l i t u d e o f about l / l O v o l t p e a k - t o - p e a k and a g r e a t d e a l o f j i t t e r , T h i s s i g n a l i s f e d i n t o a t u n e d p e n t o d e a m p l i f i e r and t h e n t o t h e p h a s e c o n t r o l c i r c u i t . See F i g u r e 3~5 f o r t h e c i r c u i t d i a g r a m . The phase c o n t r o l c i r c u i t u s e s two t r i o d e a m p l i f i e r s , pne as an a m p l i f i e r t o d r i v e t h e seoond w h i c h a c t s a s a r e a c t -a nce t u b e . The r e a c t a n c e t u b e c o n t r o l s t h e t r a n s i s t o r o s c i l l a t o r k e e p i n g t h e p h a s e o f I t s o u t p u t t h e same as t h e a v e r a g e p h a s e o f t h e c l o c k s i g n a l * The o s c i l l a t o r u s e s a c o n v e n t i o n a l C o l p i t t s t y p e o s c i l l a t o r c i r c u i t w i t h an o u t p u t v o l t a g e o f about 3 v o l t s p e a k - t o - p e a k . The o s c i l l a t o r o u t p u t i s a m p l i f i e d b y a t u n e d t r i o d e s t a g e t o about 1 0 v o l t s p e a k - t o - p e a k w h i c h i s s u f f i c i e n t t o d r i v e t h e c o u n t i n g c i r c u i t . T h i s new c l o c k s i g n a l i s v e r y s t a b l e and h a s a p e r i o d o f about lij. u s e e s . The r e s u l t i n g j i t t e r i s l e s s t h a n one p a r t i n t e n - t h o u s a n d w h i c h i s c o m p a r a b l e t o t h e e x p e c t e d a c c u r a c y o f t h e c o m p u t e r . The a v e r a g e d c l o c k s i g n a l i s now f e d i n t o a p h a s e -s h i f t i n g c i r c u i t . T h i s c i r c u i t u s e s a t r i o d e h a v i n g e q u a l p l a t e and c a t h o d e l o a d p r e c i s i o n r e s i s t o r s . R e f e r r i n g t o F i g u r e 3 - 6 , i f t h e i n p u t s i g n a l i s c o n s i d e r e d t o be a s i n e wave i n t i m e * t h e n at t h e C a t h o d e o f t h e p h a s e - s h i f t e r t h e same s i n e wave a p p e a r s w h i l e at t h e p l a t e t h e i n v e r s e , o r n e g a t i v e , s i n e wave a p p e a r s . +30(r +sin I n p u t i lOOK ? 2 7 K 1$ < \$> < 140 LOOK <1# - s i n v - c o s ^ S + C O S 3j l $ f + s i n | 12AT7, 12AT7 270 j f s i n , - s i n . , i c o s , ' - C O S 1 — . 1 +cos and + s i n To C o u n t i n g C i r c u i t s To P h a s e - S h i f t i n g C a p a c i t o r 47K Phase S h i f t e r B u f f e r A m p l i f i e r F o u r R e q u i r e d I s o l a t i n g CF Two R e q u i r e d R e s i s t o r s A l l . l / 2 w a t t , • 10$ t o l e r a n c e e x c e p t where n o t e d . C a p a c i t o r s •— Whole numbers i s p f , D e c i m a l numbers i n u f . -Fi g u r e 3 - 6 . . C i r c u i t o f P h a s e - S h i f t e r and B u f f e r A m p l i f i e r s / ' The c o s i n e and n e g a t i v e c o s i n e waves a r e o b t a i n e d by s h i f t i n g t h e s i n e waves by 90 d e g r e e s , w h i c h i s done by u s i n g i n v e r s e a r r a n g e m e n t s o f p r e c i s i o n r e s i s t o r s and a d j u s t a b l e c a p a c i t o r s so t h a t f i n e a d j u s t m e n t s may be made f o r t h e c o r r e c t phase r e l a t i o n s h i p . I n o r d e r t h a t a l l t h e o u t p u t waves h a v e e q u a l a m p l i t u d e i t was n e c e s s a r y t o p l a c e a t r i m m e r c a p a c i t o r a c r o s s t h e c a t h o d e l o a d r e s i s t o r . When a l l t h e c a p a c i t o r s a r e a d j u s t e d c o r r e c t l y th.e f o u r o u t p u t s h a v e t h e e x a c t p h a s e r e l a t i o n s h i p r e q u i r e d and a l l h a v e e q u a l a m p l i t u d e s . To a v o i d e r r o r r e s u l t -i n g f r o m l o a d i n g t h e p h a s e - s h i f t i n g n e twork^ t h e f o u r o u t p u t s a r e f e d i n t o c a t h o d e f o l l o w e r b u f f e r a m p l i f i e r s f r o m where t h e y a r e f e d t o t h e p h a s e - s h i f t i n g c a p a c i t o r . The s i n e and c o s i n e s i g n a l s a r e f e d i n t o i s o l a t i n g c a t h o d e f o l l o w e r s f r o m t h e i r b u f f e r a m p l i f i e r s , w h i c h a l l o w s s i m p l e d i r e c t c o u p l i n g , b e c a u s e t h e c o u n t i n g c i r c u i t u s e s AND g a t e s w h i c h w o u l d l o a d t h e b u f f e r a m p l i f i e r s and t h e r e b y i n t r o d u c e c o n s i d e r a b l e e r r o r i n t o t h e p h a s e - s h i f t e d d o c k s i g n a l * I t i s now p o s s i b l e t o d i s c u s s t h e c o u n t i n g c i r c u i t s i n d e t a i l . The c i r c u i t n e e d e d f o r t h e count o f 100 i s shown i n F i g u r e 3~7» I t i s n e c e s s a r y t ° g a t e o n l y t h e c o s i n e c l o c k s i g -n a l t o c o n t r o l t h e c o u n t i n g as b o t h t h e c o s i n e and t h e s i n e s i g -n a l s a r e r e q u i r e d t o d r i v e t h e u n i t s C o u n t i n g t u b e . B e c a u s e t h e s i n e wave i s n o t g a t e d t h e r e a p p e a r s on t h e t e n t h c a t h o d e o f t h e u n i t s c o u n t e r f o u r e x t r a p u l s e s a f t e r t h e 100th p u l s e when t h e t h e t u b e s h a v e s t o p p e d c o u n t i n g , b u t , a s i t i s t h e f i r s t p u l s e t h a t i s i m p o r t a n t t o t h e c o m p u t e r , t h e o t h e r f o u r a r e o f no +300 1 -300 A l U n i t s C o u n t e r Tens C o u n t e r A2 R e s i s t o r s A l l l / 2 w a t t , 10$, — -C a p a c i t o r s — Whole numbers i n p f , -D i o d e s A l l 1N19.1. P i l a m e n t s b i a s e d t o -300 v. 6910 Cathode r e s i s t o r s a l l 27K. — D e c i m a l numbers i n u f . F i g u r e 3-7. Count o f 100 C i r c u i t 17 significance. These pulses are shown in the waveforms diagram In Figure 3-8. The units counting circuit is an adaption of the e i r -13 cult recommended by Sylvania for their 6910 decade counter tube operating at frequencies up to 100 kcs* This circuit is cap-able of operating at frequencies up to 130 kcs. The output from each cathode is a pulse about 8 usees wide and 10 volts peak amplitude with the approximate shape of the positive half of a sine wave. There is an inherent time delay of about 10 usees in this counting tube which resulted in elaborate coupling circuits in the following stages to keep from losing a count; The tens counting circuit is an adaption of the c i r -13 cuit recommended by Sylvania J for their 6910 decade counter tube operating at frequencies up to 30 kcs. The outputs are pulses 110 Usees wide with an amplitude of about lk volts peak* with the exception of the ninth cathode which has a width of about 160 usees as this width includes the time for the transistor gate counters to complete their counts, As this circuit is a slower circuit the inherent time delay is about 16 usees which is greater than the period of the clock signal; To correct for this time delay the output of the tens counter Is taken from the ninth cathode and fed through a cathode follower to lower the output impedance in order to drive an AND gate. Also the edges of this long pulse are delayed by an inte-grating circuit to delay the t r a i l i n g edge long enough to allow i t to coincide with the output from the tenth cathode of the 14.3 usees 97 98 99 100 101 102 n_ L T L T U 03 104 1 2 3 " ~ _n T_F_J i_n 96 97 98 99 100 EP OP LP 1_TL 1 2 V Y c o s sq, - s x n sq, U n i t s 7 U n i t s 8 U n i t s 9 U n i t s 10 U n i t s 1 U n i t s 2 Tens 9 Tens 10 CFF OOFF EGFF OGFF LGFF Chg. J i t t e r F i g u r e 3-8. C o u n t i n g C i r c u i t Waveforms and T i m i n g 18 u n i t s c o u n t e r w h i c h i s a l s o f e d i n t o t h i s AND g a t e . A l l t h e s e waveforms a r e shown i n F i g u r e 3-8. The o u t p u t o f t h i s AND g a t e i s t h e 100th p u l s e and i t s e t s t h e c o n t r o l f l i p - f l o p . The c o n t r o l f l i p - f l o p (OFF) i s a h i g h - s p e e d f l i p - f l o p t o m i n i m i z e e r r o r s due t o t i m e d e l a y . T h i s h i g h s w i t c h i n g s p e e d e n s u r e s t h a t t h e g a t e s w i l l open and c l o s e between t h e c o s i n e c l o c k p u l s e s even t h o u g h t h e r e i s t h e d e l a y i n t h e u n i t s c o u n t e r o f t h e o r d e r o f 10 u s e e s . The s p e c i a l f e a t u r e s o f t h i s vacuum-tube f l i p - f l o p a r e : 1. A l a r g e common c a t h o d e r e s i s t o r i s u s e d t o k e e p t h e c u r r e n t s low and at t h e same t i m e t o a l l o w low p l a t e r e s i s t o r s . 2. The c o u p l i n g r e s i s t o r s a r e u n d e r c o m p e n s a t e d t o k e e p t h e r e c o v e r y t i m e c o n s t a n t s l o w w h i c h i n c r e a s e s t h e s w i t c h i n g s p e e d . 3. The c i r c u i t i s c o n s t r u c t e d between g r o u n d and -300 v o l t s t o a l l o w d i r e c t c o u p l i n g b a c k t o t h e i n p u t AND g a t e w h i c h e n s u r e s t h a t t h i s g a t e i s e i t h e r open o r c l o s e d d e p e n d i n g upon t h e s t a t e o f t h e c o n t r o l f l i p -f l o p . ' k. D i r e c t c o u p l e d t r i g g e r i n g a m p l i f i e r s a r e u s e d . A vacuum-tube f l i p r f l o p was n e e d e d as t h e g a t i n g v o l t -age had t o be at l e a s t 10 v o l t s and t h e b e s t t h e h i g h - s p e e d s w i t c h i n g t r a n s i s t o r s on h a n d would h a n d l e was 6 v o l t s . F o r c o n s i s t e n c y and s i m p l i c i t y vacuum-tube t r i g g e r i n g a m p l i f i e r s were u s e d as t h e p o s i t i v e p u l s e f r o m t h e u n i t s c o u n t e r was not large, enough t o d r i v e t h e f l i p - f l o p d i r e c t l y , The t r i g g e r i n g a m p l i f i e r s h a v e a v e r y l a r g e g a i n I n o r d e r t o t r i g g e r t h e c o n t r o l f l i p - f l o p as e a r l y as p o s s i b l e . Thus t h e s w i t c h i n g a c t i o n w i l l t a k e p l a c e b e f o r e t h e u n i t s p u l s e +300 V - 3 0 0 V R e s i s t o r s A l l l/2 w a t t e x c e p t where n o t e d , — - 10$ t o l e r a n c e . C a p a c i t o r s — Whole numbers i n p f , D e c i m a l numbers i n |4.f. F i l a m e n t s b i a s e d t o - 3 0 0 V . F i g u r e 3-9. C i r c u i t .of C o n t r o l F l i p - F l o p (CFF) and A s s o c i a t e d A m p l i f i e r s 19 has reached i t s maximum v o l t a g e r e s u l t i n g i n a s a v i n g of about k usees and, as a r e s u l t , c u t t i n g the a c t u a l time d e l a y down t o about 6 usees. The c o n t r o l f l i p - f l o p uses a h i g h - c u r r e n t and h i g h -a m p l i f i c a t i o n - f a c t o r t r i o d e (12AT7) i n o r d e r t o have a f a s t s w i t c h i n g time. The p l a t e swing i s low^ from -20 t o -100 v o l t s , and the s w i t c h i n g time i s of the order of 1 usee. See F i g u r e 3-9 f o r the C i r c u i t diagram. A l l t h e components have a 10 per cent t o l e r a n c e . The output i s d i r e c t Coupled, by the use of an a t t e n u a t i n g network, which Is over compensated t o keep the f a s t s w i t c h i n g a c t i o n (the r e s u l t i n g overshoot h a v i n g no s i g n i f i c a n c e ) , t o t h e input AND gate, A l ; T h i s AND gate i s opened by the r e s u l t i n g 11 v o l t g a t i n g s i g n a l ; The o t h e r output i s f e d through a cathode f o l l o w e r a m p l i f i e r t o lower the output Impedance i n o r d e r t o operate AND gate A3. T h i s output i s a l s o d i r e c t coupled, Much d i f f i c u l t y was encpuntered i n d e s i g n i n g AND gate A3 because o f the 20 usee j i t t e r and the 20 usee r i s e time o f t h e channel g a t i n g s i g n a l r e s u l t i n g from t h e output of t h e photo-diodes, As t h i s g a t i n g s i g n a l could not be used t o t r i g g e r the f i r s t gate counting f l i p - f l o p (00FF) d i r e c t l y , i t was used t o open A3 which allowed a cos 0 p u l s e t o pass. T h i s p u l s e s t a r t e d the counting a c t i o n o f t h e gate counting f l i p - f l o p s . The circuit diagram o f gate A3 i s shown i n F i g u r e 3-10, An a c t i v e gate was needed because of the numerous Inputs 6 The diode AND gate i n the input stage serves t o s e l e c t the s i n g l e 20 cos 0 pulse which is needed to trigger OOff. Only one cos 0 pulse must be allowed to pass as only one set of gates, per channel, -3.0 V Prom 00PF_ EGPF_ 0GFF_ LGF S00pf_L ~ -r- ^IN191 IN191 IN191 Cos 0 pulses From CFF IN191 H4-I N 1 9 1 -16' 10K < 10K odd IN67A Channel Gates In 2N2lfO .oUf even I N 6 7 A 2N240 to set OOFF i|70K 10K + l-.£v Figure 3-10, Circuit of Synchronization AND gate, A3 must be produced from the gate counting flip-flops* As A3 gates positive signals, it may be observed from Figure 3-8 that the only time this gate is open is immediately after CFF opens i t . The signals from the gate counting flip-flops are needed to close A3 immediately the cos 0 pulse which sets OOFF has passed. The 5>00pf capacitor serves to smooth out the transition pulses resulting when one gate counting flip-flop is reset and the next is set. After the LGFF is reset the CFF is reset which closes A3. 21 As t h e cos 0 p u l s e s a r e u s e d t o t r i g g e r OOFF, t h e e f f e c t o f t h e j i t t e r o f t h e c h a n n e l g a t i n g s i g n a l w i l l be e l i m i n a t e d b e c a u s e t h e c o u n t i n g s y s t e m w i l l keep l o s i n g c o u n t s u n t i l t h e cos 0 p u l s e w h i c h s e t s OOFF i s a l w a y s l y i n g i n s i d e t h e c h a n n e l g a t e . Now t h e s y s t e m w i l l count a c c u r a t e l y as t h e c h a n n e l g a t e a l w a y s a r r i v e s b e f o r e t h e g a t i n g s i g n a l f r o m CPF w h i c h opens A3. The f o u r g a t e c o u n t i n g f l i p - f l o p s a r e I d e n t i c a l h i g h -s p e e d t r a n s i s t o r f l i p - f l o p s . See F i g u r e 3-11 f o r t h e c i r c u i t d i a g r a m . To a l l o w t h e g a t i n g c i r c u i t s t o d r i v e a l a r g e number o f s u c c e e d i n g c i r c u i t s t h e o u t p u t s t a g e u s e s an e m i t t e r f o l l o w e r . T h i s a d d i t i o n a l s o e n s u r e s t h a t t h e o u t p u t i s an a l m o s t p e r f e c t r e c t a n g u l a r g a t e . P h i l c o h i g h - s p e e d germanium s u r f a c e b a r r i e r PNP t r a n s i s t o r s (2N2kO) a r e u s e d * T h e s e t r a n s i s t o r s h a v e a maximum c o l l e c t o r v o l t a g e o f -6 v o l t s and as a r e s u l t t h e s u p p l y v o l t a g e s f o r a l l t h e t r a n s i s t o r c i r -c u i t r y were ch o s e n as +1*5 and -3*0 v o l t s * The f l i p - f l o p s a r e t r i g g e r e d i n s u c h a manner as t o g i v e 2*5 v o l t n e g a t i v e g a t e s as an o u t p u t . T h e s e g a t e s were f o u n d t o be t h e most co n v e n e l e n t f o r t h e l o g i c c i r c u i t s w h i c h t h e y a r e t o d r i v e * The C i r c u i t I s v e r y r e l i a b l e and may be e a s i l y b u i l t u s i n g 10 p e r c ent c ompo n ent s. The OOFF i s r e s e t by t h e f i r s t cos 0 p u l s e a p p e a r i n g a f t e r t h e s e t t i n g p u l s e . The f o l l o w i n g g a t i n g f l i p - f l o p s ( E G F F , OGFF, and LGFF) a r e s e t b y d i f f e r e n t i a t i n g t h e o u t p u t o f t h e p r e v i o u s g a t e and u s i n g t h e p o s i t i v e p u l s e as a t r i g g e r . The -3 ..0V 1. 5K Prom R e s e t . B u s 1.5K' . 500_pf iT S e t Prom . P r o c e e d i n g S t a g e 1N191 2N24 .OOluf IL 1 S e t OOFF 1 r , .From A3 - ^ W W V W \4—-<+— 6.8K " /TA 1N191 Gate Out 10K +1.5 F i g u r e 3-11. C i r c u i t o f Gate C o u n t i n g F l i p - F l o p s IN 1.91 Cos I n .OOlUX 1N191 .-3.0 33QK>LK 1.5K 500pf 1.5K. 001 uf To R e s e t Bus and A3 F i g u r e 3-12. C i r c u i t o f C o s i n e P u l s e G e n e r a t o r 22 gating c i r c u i t s are reset by the cosine clock s i g n a l that Is used to drive the counting c i r c u i t s . After clamping f o r protective reasons, t h i s cosine signal Is amplified twice to obtain the cor-rect phase re l a t i o n s h i p and at the same time i s squared as the t r a n s i s t o r amplifiers are highly over driven* See Figure 3_12» The r e s u l t i n g square wave has an amplitude of 3 vo l t s peak-to-peak with r i s e and f a l l times of much less than h a l f a microsecond* This square wave i s d i f f e r e n t i a t e d and the po s i t i v e pulse i s used to reset a l l the gate counting f l i p - f l o p s * To review the gate Counting action, a f t e r the count of 100, the control f l i p - f l o p opens A3 which sets OOFF which i s reset by the leading edge of the Cosine wave. The resetting of OOFF sets EGFF which Is reset by the cosine s i g n a l . This cycle continues f o r the next two gating c i r c u i t s , OGFF and LGFF. In t h i s way the gating f l i p - f l o p s count four cosine periods before resetting the control f l i p - f l o p . At the same time these gating f l i p - f l o p s produce the required early* zero, and late gates d i r e c t l y . A l l these waveforms and the timing are shown i n Figure 3-8* This sub-section concludes the section on the synchron-i z a t i o n and counting c i r c u i t s . These c i r c u i t s control the oper-ation of the whole computer and a high degree of r e l i a b i l i t y i s es s e n t i a l . It i s f e l t that i t w i l l be very easy to keep these c i r c u i t s operating s a t i s f a c t o r i l y as there are no c r i t i c a l designs and a l l the sections are s i m i l a r whenever p r a c t i c a l * 23 Now that the counting circuit has been described i t is possible to describe the operation of writing and erasing information on the magnetic drum. k. WRITING; AND ERASING The o p e r a t i o n o f t h e c o m p u t e r i s C o n t r o l l e d by an o p e r a t i o n s w i t c h . T h i s s w i t c h h a s f i v e p o s i t i o n s w h i c h a r e , i n c l o c k w i s e s e q u e n c e : 1. W r i t e — p o s i t i o n u s e d when p l a c i n g i n f o r m a t i o n f r o m an e x t e r n a l s o u r c e o n t o t h e drum f o r u s e i n t h e c o m p u t e r . 2. R e a d — p o s i t i o n u s e d when r e a d i n g i n f o r m a t i o n f r o m t h e drum as ah o u t p u t . 3. Comput e — p o s i t i o n u s e d when t h e comput e r i s i n o p e r a t i o n . k. C h a n n e l E r a s e — p o s i t i o n u s e d when i t i s d e s i r e d t o e r a s e t h e I n f o r m a t i o n on any s p e c i f i e d c h a n n e l . $. T r a c k E r a s e — p o s i t i o n u s e d when i t i s d e s i r e d t o e r a s e t h e i n f o r m a t i o n on any s p e c i f i e d t r a c k . I n a d d i t i o n t o t h i s s w i t c h t h e r e i s a p u s h b u t t o n u s e d when w r i t i n g o r e r a s i n g , a c h a n n e l . The c i r c u i t s r e q u i r e d t o c o n t r o l t h e w r i t i n g o f t h e i n f o r m a t i o n p u l s e s o n t o t h e drum a l s o s u f f i c e t o c o n t r o l t h e e r a s i n g o f a s i n g l e c h a n n e l . A l l t h e c o n t r o l c i r c u i t r y i s t r a n s i s t o r i z e d w i t h t h e a c t u a l w r i t e and e r a s e a m p l i f i e r s u s i n g vacuum t u b e s b e c a u s e o f t h e h i g h v o l t a g e n e e d e d t o d r i v e t h e r e q u i r e d c u r r e n t s t h r o u g h t h e w r i t e h e a d . No c o n t r o l c i r -c u i t r y i s n e e d e d i n o r d e r t o e r a s e a c o m p l e t e t r a c k . The p u l s e s t h a t a r e w r i t t e n on t h e drum a r e d e r i v e d f r o m t h e p h a s e - s h i f t e d c l o c k s i g n a l w h i c h h a s been i n v e r t e d and s q u a r e d . The n e g a t i v e h a l f o f t h i s s q u a r e wave s e r v e s as t h e p u l s e , w h i c h I s about 7 u s e e s w i d e w i t h r i s e and f a l l t i m e s o f , 2k 2£ . l e s s t h a n 1 u s e e s , T he s i n g l e c h a n n e l e r a s e s i g n a l i s t h e o u t p u t o f a f l i p - f l o p w h i c h i s c o n t r o l l e d b y t h e g a t i n g f l i p - f l o p s o f t h e c o u n t i n g c i r c u i t , i | . - l . B l o c k R e p r e s e n t a t i o n When e r a s i n g a c h a n n e l , t h e c h a n n e l c h o s e n i s s e t b y p o s i t i o n i n g t h e t r a c k and c h a n n e l s e l e c t o r s w i t c h e s and t h e n t h e p u s h b u t t o n i s p u s h e d t o do t h e a c t u a l e r a s i n g . To w r i t e a p u l s e o n t o t h e drum, t h e t r a c k , c h a n n e l , t e n s , a n d u n i t s s e l e c t o r s w i t c h e s a r e p o s i t i o n e d , t h e p h a s e - s h i f t d i a l i s a d j u s t e d and t h e n t h e p u s h b u t t o n i s p u s h e d t o w r i t e t h e p u l s e . T he p u s h b u t t o n s e r v e s t o e l i m i n a t e p o s s i b l e w r i t i n g and e r a s i n g e r r o r s w h i c h may o c c u r d u r i n g t h e p o s i t i o n i n g o f t h e s w i t c h e s . R e f e r t o F i g u r e I4.-I. When t h e o p e r a t i o n s w i t ch i s i n t h e w r i t e p o s i t i o n , o p e r a t i n g t h e p u s h b u t t o n s e t s a t r a n s i s t o r f l i p - f l o p (WFF1) w h i c h opens a g a t e t o a l l o w t h e i n v e r t e d and s q u a r e d s i n e c l o c k s i g n a l t o p a s s when t h e s e l e c t e d c h a n n e l g a t e and t h e a s s o c i a t e d z e r o g a t e c o i n c i d e . T h i s s i n g l e p u l s e p a s s e s t h r o u g h t h e w r i t e OR g a t e a n d i s w r i t t e n on t h e drum* I t s f u n c t i o n i s t o s e r v e as a r e f e r e n c e p u l s e . The r e f e r e n c e p u l s e s e t s f l i p - f l o p WFP2 and WFF2 i s r e s e t f r o m OOFF. The r e s e t t i n g a c t i o n o f WFF2 r e s e t s WFF1. F l i p - f l o p WFF2 opens g a t e WA2 t o a l l o w t h e s e l e c t e d t e n s t o s e l e c t t h e d e s i r e d u n i t s p u l s e w h i c h s e t s WFF3. T h e phase -s h i f t e d , i n v e r t e d and s q u a r e d c l o c k s i g n a l ( - s i n j2f) d r i v e s a dlvlde-by -rtwb f l i p - f l o p (WFFlf) , t h e o u t p u t o f w h i c h i s an odd Push Button Write A m p l i f i e r For Low 0 Microswitch on C a p a c i t o r Shaft F i g u r e 4—1. Block Diagram of Write and S i n g l e Channel Erase C o n t r o l C i r c u i t s 26 o r e v e n g a t e . T h e s e g a t e s a r e s e l e c t e d automat I c f e l l y b y t h e u n i t s s e l e c t o r s w i t c h d e p e n d i n g on w h e t h e r t h e s e l e c t e d u n i t s p u l s e i s odd o r even* T h i s r e f i n e m e n t i s n e c e s s a r y b e c a u s e Of t h e h a l f c y c l e w i d t h and t h e p e r i o d i c i t y o f t h e c l o c k p u l s e and as a p h a s e - s h i f t e d r a n g e o f one f u l l c y c l e p l u s some o v e r s h o o t on e a c h end was d e s i r e d . T h i s p e r i o d i c i t y a l s o r e s u l t e d I n d i f * f i c u l t y i n s y n c h r o n i z i n g t h e d i v i d e - b y - t w o f l i p - f l o p . The s y n -c h r o n i z i n g was f i n a l l y a c c o m p l i s h e d by u s i n g two s y n c h r o n i z i n g p u l s e s , t h e a p p r o p r i a t e one b e i n g s e l e c t e d by a m i c r o s w i t c h o p e r a t e d by a cam p l a c e d on t h e s h a f t o f t h e p h a s e - s h i f t i n g c a p a c i t o r . T h i s odd o r e v e n g a t e i s f e d t o AND g a t e WA3 w h i c h was opened b y WPP3 and a l l o w s t h e odd o r eve n p u l s e s o f t h e - s i n 0 wave t o p a s s . The f i r s t - s i n 0 p u l s e r e s e t s WPP3 and t h e g a t e i s c l o s e d a f t e r t h i s p u l s e h a s p a s s e d . T h i s s i n g l e p u l s e p a s s e s t h r o u g h t h e w r i t e OR g a t e t o t h e w r i t e a m p l i f i e r . T hus t h e d e s i r e d p u i s e i s p l a c e d a t t h e p r e - d e t e r m i n e d p o s i t i o n on t h e drum. The c i r c u i t r y r e q u i r e d f o r t h e above o p e r a t i o n s i s v e r y s i m p l e and w i l l be d i s c u s s e d l a t e r . When t h e o p e r a t I o n s w i t c h I s i n t h e s i n g l e c h a n n e l e r a s e p o s i t i o n t h e a c t i o n o f t h e EGPP on WA1 a l l o w s t h e p u l s e p r e v i o u s t o t h a t u s e d as t h e r e f e r e n c e p u l s e t o p a s s t h r o u g h WA1. As a r e s u l t , WPP2 i s s e t one p e r i o d e a r l i e r t h a n when I t i s u s e d t o c o n t r o l t h e w r i t e o p e r a t i o n . As WPP2 I s s e t f o r t h e co m p l e t e l e n g t h o f a c h a n n e l , e x c e p t f o r a f e w m i c r o s e c o n d s a f t e r OOFF r e s e t s i t , t h e o u t p u t i s u s e d as t h e s i n g l e c h a n n e l e r a s e s i g n a l . T h i s o u t p u t I s f e d t o t h e e r a s e a m p l i f i e r . 27 Both the write and the erase amplifiers employ a volt-age amplifier and then a power amplifier. The outputs of these amplifiers are fed through the operation switch and the track selector Switch to the appropriate head of the magnetic drum assembly. k-2. Circuit Details Before explaining the details of the write and the single channel erase circuits, the operation of the selector switches w i l l be explained * The channel selector is a simple switch which choses one Pf the fifteen channel gates which are the put put of the transistor circuit activated by the photo-diodes. The tens and units selector switches are more compli-cated because of the periodicity of the clock signal and the inherent delay in the decade counting tubes* As mentioned in the sectipn oh synchronization and counting, there is a time delay of 10 usees in the units counter and 16 usees in the tens counter, or a total of 26 usees. But the period of the clock signal is about Uj. usees. If the units count er pulses can be used to do the actual triggering of the subsequent circuits, the only time delay would be due to the units counter* As the units counter is controlled by the cosine clock signal and the computer Uses the sine clock signal for a l l the other operations another 3.5 usees are gained resulting in a half period delay. This delay must be taken into account in numbering the pulses. 28 See F i g u r e 3-8. B e c a u s e o f t h e t i m e d e l a y i n t h e t e n s c o u n t e r t h e p u l s e f r o m t h e t e n t h c a t h o d e o f t h e u n i t s c o u n t e r does n o t t r i g g e r t h e t e n s c o u n t e r u n t i l 16 u s e e s h a v e p a s s e s . T h e r e f o r e i f any e v e n decade o f Count i s t o be S e l e c t e d t h e s e l e c t o r s w i t c h e s w i l l h a v e t o s e l e c t t h e t e n t h c a t h o d e o f t h e u n i t s c o u n t e r and t h e c a t h o d e p r e v i o u s t o t h a t e x p e c t e d o f t h e t e n s c o u n t e r . F o r example, i f t h e k O t h p u l s e I s t o be s e l e c t e d t h e t e n s s e l e c t o r w o u l d h a v e t o s e l e c t t h e t h i r d c a t h o d e and t h e u n i t s s e l e c t o r t h e t e n t h c a t h o d e . F o r a l l t h e o t h e r p o s i t i o n s o f t h e u n i t s s e l e c t o r no d i f f i c u l t y a r i s e s . To a v o i d c o n f u s i o n t h e t e n s and u n i t s s e l e c t o r s w i t c h e s were d e s i g n e d so t h a t i f t h e u n i t s s w i t c h i s p o s i t i o n e d a t t h e t e n t h p o s i t i o n , t h e t e n s s w i t c h w o u l d a u t o m a t i -c a l l y s e l e c t t h e c a t h o d e p r e v i o u s t o t h e p o s i t i o n at w h i c h t h e s w i t ch i s p o s i t i o n e d . T h i s a r rangement r e q u i r e d t w o - p o l e t e n -p o s i t i o n s w i t c h e s f o r b o t h t h e u n i t s and t h e t e n s . See F i g u r e l f - 2 . I n a d d I t I o n , b e c a u s e o f p e r i o d i c i t y , a n o t h e r p o l e was r e q u i r e d f o r t h e u n i t s s w i t c h t o s e l e c t t h e odd o r e v e n p h a s e - s h i f t e d p u l s e s r e q u i r e d i n t h e w r i t e o p e r a t i o n . The d e s i g n o f t h e f l i p - f l o p s f o r t h e w r i t e and s i n g l e c h a n n e l e r a s e c i r c u i t s does not ent a l 1 any new work. T h e y a r e t h e same as t h e f l i p - f l o p s u s e d i n t h e g a t e c o u n t i n g c i r c u i t s w i t h some m i n o r c hanges i n t h e i n t e r e s t s o f economy and b e t t e r o p e r a t i o n . From Tens C o u n t e r O O F F 1 K v o -o 2 -O" -O' o 1 - o - o - o 8 10 o OFFJ Tens S e l e c t o r S w i t c h e s Shown i n 100 P o s i t i o n F i g u r e 4-2. C i r c u i t o f Tens and U n i t s S e l e c t o r S w i t c h e s From U n i t s C o u n t e r O OFF K, K, o - o - o - o - o - o - o 8 •o 8 K 10 ^ 10 S e l e c t e d U n i t s t o WA2 .OFF O 3 | a 3 o 4 o 4 o 5 o 5 o 6 1 o 6 o 7 1 o 7 o 8 1 o 8 Oio j ' o * _ u A 9 U 1 0 S e l e c t e d Tens t o WA2 U n i t s S e l e c t o r o Odd From WFF5 _^1 0FFI S e l e c t e d Odd o r Ev e n E v e n Prom WFF5 t o WA3 29 The p u s h b u t t o n s e t s WFF1 t o s t a r t t h e a c t i o n o f w r i t -i n g o r e r a s i n g . T h i s f l i p - f l o p i s o f t h e same d e s i g n as t h e g a t e c o u n t i n g f l i p - f l o p s w i t h t h e e x c e p t i o n t h a t s l o w e r s p e e d t r a n s i s -t o r s a r e u s e d as t h e h i g h - s p e e d t r a n s i s t o r s a r e n o t n e e d e d and t h e i r c o s t i s o v e r t w i c e t h a t o f t h e s l o w - s p e e d t r a n s i s t o r s . A l s o t h e e m i t t e r f o l l o w e r i s not r e q u i r e d * See F i g u r e ij.-3. The - s i n 0 waveform i s o b t a i n e d by s q u a r i n g t h e o u t p u t f r o m t h e s i n e i s p l a t l o n g c a t h o d e f o l l o w e r w h i c h f e e d s t h e c o u n t -i n g t u b e s . T h i s s i g n a l i s clamped t o a v o i d t r a n s i e n t s f r o m damaging t h e t r a n s i s t o r s and i t o v e r d r i v e s a t r a n s i s t o r a m p l i -f i e r . T h i s c i r c u i t i s s i m i l a r t o t h a t shown i n F i g u r e k-7 e x c e p t t h a t t h e c a t h o d e f o l l o w e r i s n o t n e e d e d . T h i s a m p l i f i e r I n v e r t s t h e s i g n a l and t h e o u t p u t i s a s q u a r e wave w i t h r i s e and f a l l t i m e s o f much l e s s t h a n h a l f a m i c r o s e c o n d . The out put o f WFF1 opens AND g a t e WA1 w h i c h I s a c o i n -c i d e n c e g a t e f o r n e g a t i v e p u l s e s . T h i s g a t e i s shown i n F i g u r e k-k. As t h e r e i s no c l a m p i n g a c t i o n i n t h i s g a t e, t h e r e i s a s l i g h t p e d e s t a l b u t i t i s n o t l a r g e enough t o h a v e any e f f e c t on t h e s u c c e e d i n g c i r c u i t s . T he out put o f t h i s g a t e i s t h e s e l e c t e d - s i n 0 p u l s e w h i c h i s f e d t o t h e w r i t e OR g a t e and t h e n t o t h e w r i t e a m p l i f i e r . T h i s p u l s e i s a l s o d i f f e r e n t i a t e d and t h e p o s i t i v e t r a i l i n g edge p u l s e s e t s WFF2. F l i p - f l o p WFF2 i s s i m i l a r t o t h e o t h e r f l i p - f l o p s but t h e e m i t t e r l e a d s a r e c o n n e c t e d t h r o u g h a common r e s i s t o r t o t h e p o s i t i v e s u p p l y , and no e m i t t e r f o l l o w e r i s r e q u i r e d . See F i g u r e k-f? f o r t h e c i r c u i t d i a g r a m . T h i s m o d i f i c a t i o n i s n e e d e d F i g u r e 4-3. C i r c u i t o f WFF1 From, O p e r a t i o n S w i t c h 1N191 » w— E i t h e r f r o m OGFF o r EGFF F i g u r e 4-4. C i r c u i t o f AND Gate WA1 30 as t h e f o l l o w i n g AND g a t e (WA2) i s g a t i n g p o s i t i v e p u l s e s so t h e o u t p u t o f WFF2 must be p o s i t i v e when WFF 2 i s s e t * T h i s i n c r e a s e d -3.0V s e t F r o m WA1 5ft IN191 l . ^ K S 2.2K< .OOluf To WA2 Sbbpf ,001 J _ To E r a s e u f — - A m p l i f i e r 10* To R e s e t WFF1 F i g u r e lf-S. C i r c u i t o f WFF2 o u t p u t a l s o s a v e s some a m p l i f i c a t i o n i n t h e e r a s e a m p l i f i e r . T h i s f l i p - f l o p i s r e s e t f r o m t h e t r a i l i n g edge o f t h e OOFF and i t s o u t p u t i s d i f f e r e n t i a t e d and t h e t r a i l i n g edge i s u s e d t o r e s e t WFF1. The s e l e c t e d t e n s p u l s e i s p a s s e d t h r o u g h a c a t h o d e f o l l o w e r i n o r d e r t o d r i v e AND g a t e WA2. The Output o f t h i s c a t h o d e f o l l o w e r i s p a r t i a l l y i n t e g r a t e d i n O r d e r t o d e l a y t h e t r a i l i n g edge t o a l l o w t h e o u t p u t f r o m t h e t e n t h c a t h o d e o f t h e S e l e c t e d Tens + 1.5 . 470K 002 uf 100K< - L-.002uf 1N191 -3.0' -300' S e l e c t e d U n i t s ^\^ ~ - ) 12AX7 1N191 1N191 H I H 002 uf 1.5K 1001 •100K -3.0 From WFF2 1N191 1N191 lOOK L N 1 9 1 ± 1N191 -3.0 2N240 470K hit u f To S e t WFF3 on C o l l e c t o r 1 . 5K< F i l a m e n t s B i a s e d t o - 3 0 0 V - 3 . o; F i g u r e 4-6. WA2 and D r i v i n g C i r c u i t s \ u n i t s counter t o coincide -. See F i g u r e k-6 f o r t h e c i r c u i t o f gate WA2. As e x p l a i n e d above, t h i s act i o n was ne c e s s a r y because of the d e l a y In t h e tens counter* The s e l e c t e d u n i t s pulse Is a l s o passed through a Cathode f o l l o w e r and the Output i s passed through a c a p a c i t o r and b i a s e d t o -3 v o l t s . T h i s b i a s i n g method e l i m i n a t e s t h e r i p p l e t h a t Is present on the cathodes o f t h e u n i t s counter, when t h e r e i s no pul s e p r e s e n t , from p a s s i n g through t h e AND gate as more than 3 v o l t s of t h i s p u l s e are neces-s a r y t o pass through the g a t e . The g a t i n g S i g n a l from WFF2 i s coupled i n t o t h i s AND gate In the u s u a l manner. A diode i s pl a c e d across t h e loa d r e s i s t o r t o clamp the output of t h e gate from going above 1.5 v o l t s p o s i t i v e and thus t o prevent damaging t h e t r a n s i s t o r . A t r a n s i s t o r e m i t t e r f o l l o w e r Is nece s s a r y t o provide t h e current t o t r i g g e r WFF3. WFF3 i s I d e n t i c a l t o t h e f l i p - f l o p s used In t h e gate counting c i r c u i t s except t h a t the e m i t t e r f o l l o w e r i s not needed. The p h a s e - s h i f t e d s i g n a l from the p h a s e - s h i f t i n g c a p a c i -t o r i s i n v e r t e d and squared f i r s t by i s o l a t i n g t h e a m p l i f i e r c i r c u i t from the p h a s e - s h i f t i n g c a p a c i t o r , t o av o i d l o a d i n g the c a p a c i t o r , and then o v e r d r i v i n g a t r a n s i s t o r a m p l i f i e r . See F i g u r e k~7 f o r t h i s c i r c u i t . T h i s square wave (-sin0) i s d i f -f e r e n t i a t e d and the p o s i t i v e p u l s e s are used t o set and reset the divide-by-two f l i p - f l o p WFFij.. T h i s f l i p - f l o p i s i d e n t i c a l t o the counting f l i p - f l o p s exoept f o r the method of t r i g g e r i n g used and no e m i t t e r f o l l o w e r i s r e q u i r e d * F i g u r e k-8 shows t h i s c i r c u i t . As t h i s f l i p - f l o p p r o v i d e s a gate t o s e l e c t t he +300 S i n 0 Prom P h a s e - S h i f t i n J C a p a c i t o r 1M - , 12AT7 ~* . O l u f 1N191 270 -3.0 1.5KS 470 IK u w w w 3.3K iNi9rf To WFP4 I 001 ~J~[if - s i n 0 S q u a r e d t o WA3 2N240 F i g u r e 4-7. C i r c u i t o f - s i n 0 S q u a r e d . G e n e r a t o r F i g u r e 4-8. C i r c u i t o f D i v i d e - b y - T w o P l i p - P l o p , WPP4 32 a l t e r n a t e - s l n 0 p u l s e s i t must be s y n c h r o n i z e d t o t h e c l o c k s i g -n a l . B e c a u s e o f t h e h a l f c y c l e w i d t h o f t h e - s i n 0 p u l s e and t h e p e r i o d i c i t y p f t h i s wave t h e s y n c h r o n i z a t i o n must be c o n -t r o l l e d b y t h e p o s i t i o n o f t h e d i a l on t h e s h a f t o f t h e p h a s e -s h i f t i n g c a p a c i t o r . A cam i s p l a c e d on t h i s s h a f t w i t h s u c h a shape as t o o p e r a t e a m i c r o s w i t c h when t h e s y n c h r o n i z a t i o n p u l s e s h a v e t o be c h a n g e d . The most c o n v e n i e n t s y n c h r o n i z a t i o n s i g n a l s were f o u n d t o be t h e - s i n 0 c l o c k s i g n a l f o r low s e t t i n g s o f t h e p h a s e -s h i f t i n g d i a l and t h e t r a i l i n g edge o f one p f t h e g a t e c o u n t i n g f l i p - f l o p s ( t h e EGPF t a k e n as t h e most c o n v e n i e n t ) f o r t h e h i g h s e t t i n g s o f t h e d i a l , By a c t u a l e x p e r i m e n t a t i o n , i t was f o u n d t h a t t h e b e s t p o s i t i o n f o r t h e cam t o o p e r a t e t h e m i c r o s w i t c h was at a d i a l r e a d i n g o f about 190, At t h i s s e t t i n g t h e c l o c k s i g n a l c o u l d be p h a s e - s h i f t e d n e g a t i v e l y t o a r e a d i n g o f £ 2 6 on t h e d i a l , o r a l m o s t h a l f a c y c l e . A l s o t h e s i g n a l c o u l d be p h a s e - s h i f t e d p o s i t i v e l y t o a r e a d i n g o f 726 on t h e d i a l , o r al m o s t t h r e e - q u a r t e r s p f a c y c l e . T hus t h e t o t a l p h a s e - s h i f t a v a i l a b l e was 1.2 c y c l e s . T h e d i s a d v a n t a g e o f t h i s s y s t e m i s t h a t a p h a s e - s h i f t o f one c y c l e p o s i t i v e i s n o t p o s s i b l e , b u t b e c a u s e o f t h e method o f s e l e c t i n g t h e p u l s e t o be s h i f t e d , t h i s d i s a d v a n t a g e i s not t o p g r e a t as t h e n e x t p u l s e c o u l d be c h o s e n and t h e p h a s e - s h i f t d i a l s e t f o r a n e g a t i v e s h i f t i f a l a r g e p o s i t i v e s h i f t was d e s i r e d * The odd o r ev e n o u t p u t o f WFFij. i s c h o s e n by t h e u n i t s s e l e c t o r s w i t c h t o s e l e c t e i t h e r t h e odd o r ev e n p u l s e s o f t h e 33 - S i n 0 s i g n a l . T h e a c t u a l s e l e c t i o n o f t h e o d d o r e v e n p u l s e s t o g e t h e r w i t h t h e s e l e c t i o n o f t h e p u l s e d e s i r e d i s d o n e b y A N D g a t e WA3, w h i c h I s s h o w n I n F i g u r e k-9. T h e s e l e c t e d - s i n 0 o u t p u t I s d i f f e r e n t i a t e d a n d t h e p o s i t i v e p u l s e f r o m t h e t r a i l i n g e d g e r e s e t s W F F k . T h e - s i n 0 p u l s e i s p a s s e d t h r o u g h t h e w r i t e O R g a t e t o t h e w r i t e a m p l i f i e r . - 3 . 0 V 3.3 K 2.2 K F r o m WFF3 - Sln0 O d d o r E v e n f r o m U n i t s S e l e c t o r IN191 -w— IN191 -w— IN191 -w— T o R e s e t W F F 3 200pf X T o OR F i g u r e k-9. C i r c u i t o f A N D g a t e WA3 k - 3 . W r i t e a n d E r a s e A m p l i f i e r s T h e o u t p u t s o f WA1 a n d WA3 ( t h e r e f e r e n c e p u l s e , - s i n 0, a n d t h e p o s i t i o n e d p u l s e , - s i n 0) a r e p a s s e d t h r o u g h t h e w r i t e OR g a t e t o a v a c u u m - t u b e v o l t a g e a m p l i f i e r w h i c h I s c o u p l e d t o a b e a m p o w e r a m p l i f i e r . T h e C i r c u i t i s s h o w n i n F i g u r e k-10. T h i s a m p l i f i e r a m p l i f i e s t h e 3 v o l t n e g a t i v e p u l s e I n p u t t o a n 80 m a n e g a t i v e C u r r e n t p u l s e w h i c h i s p a s s e d t h r o u g h t h e w r i t e h e a d , w h i c h h a s a n I n d u c t a n c e o f 8 m h a n d a r e s i s t a n c e O f If? o h m s . T h i s 80 m a p u l s e I s s u f f i c i e n t t o s a t u r a t e t h e i r o n - o x i d e S u r f a c e o f t h e d r u m . T h e c a t h o d e o f t h e - v o l t a g e ' . From WA1 1N191 From WA3 To O p e r a t i o n S w i t c h t h e n W r i t e Head ~ZT .Write A m p l i f i e r F i g u r e 4-10. C i r c u i t o f W r i t e A m p l i f i e r From WFF2 22K +300^ lQOpf A A A A A A A / 56.0K 12AX7 + 1.5 1. 5M To O p e r a t i o n S w i t c h t h e n W r i t e Head 50pf -300 F i g u r e 4-11. C i r c u i t o f E r a s e A m p l i f i e r 3k amplifier is biased positively to eliminate grid current when there is no signal on the grid* A diode is placed across the write head to eliminate any positive voltage from being applied to the head as a result of oscillations i n the circuit* This current is a well-defined pulse with rise and f a l l times that are just a l i t t l e slower than those of the original pulse. The negative erase gate from WF2 drives a vacuum-tube voltage amplifier whose output drives a cathode follower type of beam power amplifier- See Figure I4.-II for the circuit diagram. This amplifier takes the ij. volt negative erase gate and amplifies i t to an 80 ma positive current pulse* This current pulse is sufficient to saturate the iron-oxide sur-face of the drum In the reverse direction compared to the direction of saturation used when writing. The cathode of the voltage amplifier is biased positively to l.f? volts to elimin-ate grid current when the gate is off (resting at about 1 volt positive) , The amplifier Is direct coupled to ensure that the power amplifier is cut-off when there is no input signal. This action ensures that there is no current passing through the write head except when there is an input signal* As with the write amplifier, this circuit results in a sharply defined current pulse with no overshoot. When the operation switch is in the track erase position the write head is connected to the 1.5> volt positive supply through a 12 Ohm resistor. This resistance, together with the 7.5 ohm resistance of the write head, allows an 80 ma p o s i t i v e c u r r e n t t o p a s s t h r o u g h t h e w r i t e h e a d * T h i s c u r r e n t s a t u r a t e s t h e I r o n - o x i d e s u r f a c e o f t h e c o m p l e t e t r a c k r e s u l t -i n g i n a c o m p l e t e t r a c k e r a s u r e . As t h e t r a c k i s s e l e c t e d by t h e t r a c k s e l e c t o r s w i t c h , no o t h e r c o n t r o l i s r e q u i r e d f o r t h e t r a c k e r a s e o p e r a t i o n . T h i s s u b - s e c t i o n o o m p l e t e s t h e d i s c u s s i o n on t h e w r i t e and e r a s e c i r c u i t s . C o n s i d e r i n g t h e o p e r a t i o n s p e r f o r m e d by t h e s e c i r c u i t s , t h e y a r e v e r y s i m p l e a n d , as a r e s u l t , a r e v e r y r e l i a b l e . Now t h a t t h e i n f o r m a t i o n i s a b l e t o be w r i t t e n on t h e drum, i t i s now p o s s i b l e t o d i s c u s s t h e o p e r a t i o n s o f r e a d i n g t h e i n f o r m a t i o n f r o m the drum and o f f u n c t i o n g e n e r a t i o n . 5. FUNCTION GENERATION I n S e c t i o n 2 t h e ope r a t i o n of* t h e f u n c t i o n g e n e r a t o r waa summarized. T h i s s e c t i o n w i l l d e s c r i b e t h e r e a d a m p l i f i e r , t h e v a r i o u s p a r t s o f t h e f u n c t i o n g e n e r a t o r , and a s i m p l i f i e d v e r s i o n o f t h e f u n c t i o n g e n e r a t o r t h a t was b u i l t t o t e s t t h e t h e o r y o f t h e g e n e r a t o r . The p r o p o s e d f i n a l f o r m p f t h e f u n c t i o n g e n e r a t o r w i l l be d i s c u s s e d i n S e c t i o n 6. 5-1. Read A m p l i f i e r The r e a d a m p l i f i e r i s a t r a n s i s t o r i z e d h i g h g a i n a m p l i -f i e r t h a t p r o d u c e s a v e r y s h a r p p o s i t i v e p u l s e w h enever a s i g n a l a p p e a r s at t h e r e a d h e a d o f t h e m a g n e t i c drum. The a m p l i f i e r was d e s i g n e d so t h a t t h e t i m e p o s i t i o n s o f t h e o u t p u t p u l s e s was p r e s e r v e d as t h e s e p u l s e s a r e t o be u s e d i n c o n t r o l l i n g t h e o p e r a t i o n o f t h e f u n c t i o n g e n e r a t o r . R e f e r r i n g t o F i g u r e 5>-l, t h e low l e v e l s i g n a l f r o m t h e r e a d h e a d i s a m p l i f i e d b y a c o n v e n t i o n a l t r a n s i s t o r a m p l i f i e r and t h e n a m p l i f i e d by a C l a s s B s t a g e w h i c h u s e s a cl a m p e d t u n e d c i r c u i t as t h e c o l -l e c t o r l o a d . T h i s t u n e d c i r c u i t , h a s a n a t u r a l f r e q u e n c y Of o s c i l l a t i o n o f about 70 k c s w h i c h i s t h e same as t h e c l o c k f r e q u e n c y . The p o s i t i o n o f t h e p u l s e i s t a k e n t o be t h e p o i n t where t h e v o l t a g e a c r o s s t h i s t u n e d c i r c u i t makes i t s f i r s t p a s s a g e t h r o u g h -3.0 v o l t s f r o m p o s i t i v e t o n e g a t i v e . T h i s p o i n t i s n o t dependent upon t h e a m p l i t u d e o f t h e p u l s e and, as a r e s u l t , i s v e r y w e l l d e f i n e d . The p a r t o f t h i s waveform h e a r t h e c r o s s - o y e r i s a m p l i f i e d by an a m p l i f i e r s t a g e w h i c h 36 10 OK From Read Head A ( — V W W ..Olu-f IK 470*> 470 K O u t p u t P u l s e , N240 +1.5 I n p u t From'Read Head Clamped Wave a t A O u t p u t P u l s e 2usec -3.0 -3.0 F i g u r e , 5-1. C i r c u i t o f Read A m p l i f i e r 37 i s b i a s e d a l m o s t t o c u t - o f f . T h i s a m p l i f i e r h a s a v e r y low c o l l e c t o r l o a d r e s i s t a n c e t o d e c r e a s e t h e O u t put impedance i n o r d e r t h a t t h e o u t p u t t r a i n o f p u l s e s may be u s e d d i r e c t l y t o d r i v e t h e f l i p - f l o p s i n t h e i n t e g r a t i n g c i r c u i t s o f t h e f u n c t i o n g e n e r a t o r . The o u t p u t i s a if v o l t 2 u s e e w i d e p o s i -t i v e p u l s e w i t h t h e l e a d i n g edge d e t e r m i n i n g t h e e x a c t p u l s e p o s i t i b n . Chg K I n -3.0' K 3.3 I N 6 7 A •11 1 H .lHf IN191 —-—w— Prom Read Amp, 2N2ifO .01M? 22 K C P K Out 100 i K +1.5 V F i g u r e 5-2, C h a n n e l P u l s e G a t i n g C i r c u i t T h i s p u l s e t r a i n i s f e d i n t o f i f t e e n c h a n n e l p u l s e g a t i n g c i r c u i t s i n o r d e r t o s e l e c t t h e r e f e r e n c e p u l s e s i n t h e t r a i n . T h e s e p u l s e s a r e c a l l e d c h a n n e l p u l s e s and a r e d e s i g -n a t e d CP^, C P 2 , C P 3 , ... , CP-j_£. The g a t i n g c i r c u i t r e q u i r e d i s shown i n F i g u r e 5-2, I t i s a s i m p l e ANj> g a t e which, d e t e r -mines t h e c o i n c i d e n c e o f a c h a n n e l g a t e (same g a t e s t h a t a r e 38 m e n t i o n e d i n S u b - s e c t i o n 3-2) and i t s c o r r e s p o n d i n g r e f e r e n c e p u l s e , f o l l o w e d b y an e m i t t e r f o l l o w e r s t a g e t o d r i v e t h e g a t i n g f l i p - f l o p s o f t h e f u n c t i o n g e n e r a t o r . 5-2. F u n c t i o n G e n e r a t o r C i r c u i t s B e f o r e e x p l a i n i n g t h e o p e r a t i o n o f t h e f u n c t i o n g e n e r a t o r , t h e b a s i c c i r c u i t s t h a t make up t h e g e n e r a t o r w i l l be d e s c r i b e d . The most I m p o r t a n t c i r c u i t o f t h e f u n c t i o n g e n e r a t o r i s t h e i n t e g r a t i n g o r sweep c i r c u i t . T h r e e o f t h e s e c i r c u i t s a r e r e q u i r e d and i f t h e r e i s an e r r o r i n t h e o u t p u t o f t h e s e sweep c i r c u i t s , t h e e r r o r a c c u m u l a t e s . I n o r d e r t o k e e p t h i s e r r o r as low as p o s s i b l e , h i g h - g a i n a m p l i f i e r s and a c c u r a t e t i m i n g and s w i t c h i n g c i r c u i t s a r e r e q u i r e d . The o u t p u t o f an I n t e g r a t I n g c i r c u i t i s v Q = -1/RC j v j d t , where v Q I s t h e o u t p u t f o r an i n p u t v j , t h e t i m e f o r i n t e g r a t i o n b e i n g f r o m t ^ t o i^. T h i s e x p r e s s i o n i s , I n i t s e l f , I n d e p e n d e n t o f t h e g a i n o f t h e a m p l i f i e r b u t t h e A p p e n d i x shows t h a t t h e r e i s an e r r o r t e r m w h i c h i s dependent upon t h e g a i n . I f t h e g a i n o f t h e a m p l i f i e r I s s u f f i c i e n t l y l a r g e t h i s t e r m may be n e g l e c t e d . 7 L a r s e n d e v e l o p e d a sweep c i r c u i t w h i c h was s a t i s f a c t o r y ' b u t , as i t was a c - c o u p l e d , d i f f i c u l t y a r o s e i n r e s e t t i n g t h e 39 sweep as a l l t h e c o u p l i n g c a p a c i t o r s h a d t o be r e c h a r g e d . L a r s e n recommended t h a t a t w o - s t a g e b a l a n c e d a m p l i f i e r w i t h d i r e c t C o u p l i n g between s t a g e s and a c - c o u p l i n g at t h e o u t p u t be t r i e d * A c i r c u i t o f t h i s t y p e was d e s i g n e d and I t i s shown i n F i g u r e 5-3* T h i s c i r c u i t seemed t o o p e r a t e v e r y s a t i s f a c t o r i l y b u t I t h a d a low o v e r a l l g a i n , w h i c h was about 500, and t h e r e was a s l i g h t d r i f t . B e c a u s e t h i s sweep c i r c u i t h a d a p o s i t i v e and a n e g a t i v e o u t p u t ( needed t o d r i v e t h e d i o d e g a t e s d e s c r i b e d below) i t was d e c i d e d t o u s e i t i n t h e s i m p l i f i e d v e r s i o n o f t h e f u n c t i o n g e n -e r a t o r as i t made t h i s g e n e r a t o r v e r y e a s i l y b u i l t . More w i l l be s a i d a b o u t t h i s a m p l i f i e r when d i s c u s s i n g t h e f u n c t i o n g e n e r -a t o r as a w h o l e . The d i o d e g a t e u s e d i n s w i t c h i n g and c o n t r o l l i n g t h e a c t i o n o f t h e sweep c i r c u i t s i s a l s o shown i n F i g u r e 5 -3. Two e q u a l b ut r e v e r s e d p o l a r i t y v o l t a g e s a r e a p p l i e d t o ends A and B r e s u l t i n g i n a c u r r e n t f l o w t h r o u g h P1-R1-D1-D2HR1-P2. I f a n e g a t i v e v o l t a g e i s a p p l i e d t o i n p u t C, d i o d e D3 c o n d u c t s , b l o c k i n g d i o d e D l . T h e r e f o r e t h e i n p u t t o t h e sweep a m p l i f i e r ( p i n E) i s c o n n e c t e d t h r o u g h D2-R1-P2 t o t h e n e g a t i v e s o u r c e . The o u t p u t o f t h e a m p l i f i e r i s a p o s i t i v e v o l t a g e w h i c h i s t h e i n t e g r a l o f t h e n e g a t i v e v o l t a g e on B, w i t h t h e c o n s t a n t o f i n t e g r a t i o n b e i n g ( R l + P 2 ) C 1 , By t h e same r e a s o n i n g , i f a p o s i t i v e v o l t a g e Is a p p l i e d t o D, t h e o u t p u t o f t h e sweep a m p l i -f i e r w i l l be a n e g a t i v e v o l t a g e w h i c h i s t h e i n t e g r a l o f t h e p o s i t i v e v o l t a g e on A, w i t h t h e c o n s t a n t o f i n t e g r a t i o n b e i n g ( P l + R1)G1. As t h e v o l t a g e l e v e l at p o i n t E i s h e l d v e r y c l o s e +_ D - Out r z . o i u f RI 27QK ww l / 2 $ CI . O l u f 1$ D ' s 1N461 F i g u r e 5-3. D i o d e Gate and Sweep C i r c u i t ko to zero volts by the Operational nature of the amplifier, the gat-ing voltages that are applied to the inputs C and D may be of the order of one volt. This feature leads to the use of simple transis-tor flip-flops tP provide the input gating voltages. Calibration of the two time-constants is performed on an RC bridge designed specifically for this purpose* Potentiometers PI and P2 are required to compensate for the variations in the capacitor CI in the different circuits, since this element Is the least exact of the sweep circuit, elements. In addition, the resis-tance of each half of the individual gates must be the same to ensure that the positive find the negative outputs are the same* The flip-flops used In the function generator are similar to that shown in Figure \\.-$. Figure $-\\. shows this flip-flop together with the system of triggering that is required for Use in the function generator* By Using a Common emitter resistor which allows the collector to swing positively and negatively, the same flip-flop circuit may be used to provide both the positive and negative gat es for the diode gat ing circuit s. The collector voltage swing depends upon the particular application of the flip-flop as the gated current is either absorbed or supplied by the flip-flop. The switching time Of these flip-flops is of the order of l/lO usee which ensures high-speed swit ching of the Input to the sweep amplifiers. These flip-flops are triggered by the positive pulses from the read amplifier except when negative reset pulses from the voltage comparators are used to reset these flip-flops. 1N191 w R e s e t From C o m p a r a t o r F i g u r e 5-4. C i r c u i t o f G a t i n g . . F l i p — F l o p s -3,0 1M S 10K" >50K S 4.7K 1N191 H4-H4-470pf From + Out o f Sweep C i r c u i t >15K To R e s e t F l i p - F l o p s 2N240 1,5K 15K + 1.5 1 F i g u r e 5-5. C i r c u i t o f V o l t a g e C o m p a r a t o r The y p l t a g e c o m p a r a t o r s a r e u s e d t o r e s e t t h e Sweep a m p l i f i e r s a f t e r t h e y h a v e b e e n u s e d t o g e n e r a t e a f u n c t i o n 1 . As o n l y PNP t r a n s i s t o r s were a v a i l a b l e , t h e most a c c u r a t e com-p a r a t o r w h i c h c o u l d be d e s i g n e d was one w h i c h d e t e c t e d a n e g a t i v e g o i n g v o l t a g e . The d e s i g n o f t h e a s t a b l e c i r c u i t u s e d as t h e v o l t a g e c o m p a r a t o r i s shown i n F i g u r e 5-5. The 50K p o t e n t i o m e t e r i s a d j u s t e d sq t h a t t h e b a s e o f t h e i n p u t t r a n s i s t o r I s v e r y s l i g h t l y p o s i t i v e . As t h e o u t p u t v o l t a g e o f t h e i n t e g r a t o r p a s s e s t h r o u g h z e r o v o l t s f r o m p o s i t i v e t o n e g a t i v e , t h e i n p u t d i o d e s s t a r t t o c o n d u c t . T h i s a c t i o n s t a r t s t h e r e g e n e r a t i v e a c t i o n o f t h e c i r c u i t and i t c h a n g es s t at e, The n e g a t i v e s t e p v o l t a g e a p p e a r i n g at t h e f r e e c o l l e c t o r i s d i f f e r e n t i a t e d and t h e n e g a t i v e p u l s e i s U s e d t o r e s e t t h e f l i p - f l o p s w h i c h c o n -t r o l t h e r e s e t t i n g o f t h e f u n c t i o n g e n e r a t o r . The c o m p a r a t o r r e s e t s i t s e l f i n about 10 u s e e s . Two d i o d e s a r e n e e d e d i n t h e i n p u t c i r c u i t as p o s i t i v e v o l t a g e s i n e x c e s s o f 100 v o l t s a p p e a r at t h e o u t p u t o f t h e i n t e g r a t o r s and t h e h i g h - s p e e d d i o d e s u s e d h a v e a b a c k v o l t a g e r a t I n g o f 90 v o l t s . By a d j u s t -i n g t h e i n p u t o f t h e c o m p a r a t o r t o be s l i g h t l y p o s i t i v e t h e e f f e c t o f t h e f o r w a r d r e s i s t a n c e o f t h e d i o d e s may be e l i m i n a t e d . 5-3 • S i m p l i f i e d F u n c t i o n G e n e r a t o r I n o r d e r t o t e s t t h e t h e o r y o f t h e f u n c t i o n g e n e r a t o r , a s i m p l e g e n e r a t o r w h i c h would g e n e r a t e p a r a b o l i c f u n c t i o n s w i t h no i n i t i a l c o n d i t i o n s was b u i l t and - t e s t e d . T h i s g e n e r a t o r t e s t e d t h e o p e r a t i o n o f t h e t h r e e sweep c i r c u i t s , t h e d i o d e g a t e s , t h e g a t i n g f l i p - f l o p s , and t h e v o l t a g e c o m p a r a t o r s . T h i s f u n c t i o n g e n e r a t o r I s shown I n F i g u r e 5-6 t o g e t h e r w i t h t h e I n p u t p u l s e t r a i n r e q u i r e d t o g e n e r a t e a p a r a b o l a and i d e a l i z e d waveforms a s s o c i a t e d w i t h t h e v a r i o u s s e c t i o n s o f t h e g e n e r a t o r . The o p e r a t i o n o f t h e f u n c t i o n g e n e r a t o r I s as f o l l o w s . C h a n n e l p u l s e CP^ s e t s f l i p - f l o p F F 1 whose n e g a t i v e o u t p u t , by t h e a c t i o n o f d i o d e g a t e DG1, s w i t c h e s t h e -300 v o l t s o u r c e t h r o u g h an I n t e g r a t i n g r e s i s t o r t o t h e i n p u t o f t h e f i r s t sweep a m p l i f i e r . The sweep a m p l i f i e r s t a r t s I t s sweep at t h e r a t e o f 100 v o l t s / r a s e c as t h e t i m e c o n s t a n t I s 3 msecs and t h e s u p p l y v o l t a g e i s -300 v o l t s. The n e x t p u l s e f r o m t h e r e a d a m p l i f i e r , P r , r e s e t s F F 1 w h i c h s t o p s t h e sweep. The out put o f t h e f i r s t i n t e g r a t o r i s t h e n clamped b y t h e i n t e g r a t i n g a c t i o n o f t h e a m p l i f i e r at t h e a m p l i t u d e c o r r e s p o n d i n g t o t h e s e c o n d d e r i v a -t i v e o f t h e d e s i r e d f u n c t i o n . The p o s i t i v e and n e g a t i v e o u t p u t s a r e f e d t o p i n s A and B r e s p e c t I v e l y o f a n o t h e r d i o d e g a t e , DG2. F o r t h i s s i m p l i f i e d g e n e r a t o r t h e o r i g i n o f t h e f u n c -t i o n i s t a k e n t o be at t h e p o s i t i o n o f C P 2 . Thus t h e i n t e r v a l b e tween CP^ and C P 2 i s u s e d o n l y t o g e n e r a t e t h e a m p l i t u d e o f t h e s e c o n d d e r i v a t i v e . C h a n n e l p u l s e C P 2 s e t s F F ^ w h i c h s w i t c h e s t h e p o s i t i v e o u t p u t o f t h e f i r s t sweep c i r c u i t t o t h e I n p u t o f t h e s e c o n d . As t h i s i n p u t i s a c o n s t a n t , t h e out put o f t h e s e c o n d a m p l i f i e r i s a n o t h e r sweep v o l t a g e , b ut t h i s v o l t age i s t h e f i r s t d e r i v a -t i v e o f t h e d e s i r e d f u n c t i o n . As t h e d i s c r e t e v a l u e o f t h e •k—L ci ix — 1 2 3Pf(x) P u l s e T r a i n +300 A A o — W W I I A A A A "300 P — W V V — o O u t p u t o f I f " ( x ) I n p u t t o I I Output o f I I Outp u t o f I I I +300 o — W W 2 -300 A W W — o * x (x) • — • +300 . o — W W f\ -300 W W — o F i g u r e 5-r6. S i m p l i f i e d F u n c t i o n G e n e r a t o r function at point x Is desired, the sweep of this circuit Is stopped by resetting FF3 by Px, which corresponds to the point x and the sweep is clamped at this value* The second sweep amplifier is the same as the f i r s t amplifier with the exception that, the input of the second Is considered to be positive while the outputs are negative and positive, The Only changes this action makes In the amplifier is that the comparator and the diode clamps must be Inter-changed, This action allows the more accurate positive output of the f i r s t amplifier to be used as the input to the second amplifier, and the more accurate negative output of the second amplifier to be used as the Input to the third amplifier. These outputs are more accurate because they are the outputs that are Controlled by the feedback capacitor* Channel pulse CP 2 also sets FF$ whose negative output switches diode gate " D G I 4 . allowing the output of the second ampli-f i e r to be integrated by the third sweep ci r c u i t . The Integrat-ing action of this circuit is also stopped by resetting FF5> with Px. The output of this circuit is the desired function, which for this generator Is a parabola, This output is also clamped at f(x) by the integrator action, Channel pulse CP^ starts the resetting action for the three sweep circuits. A l l three sweep circuits are reset by returning the output to zero volts at the rate of 100 volts/msec CP.3 sets FF2 and FF6 and their positive outputs, through the act;ion o f DG-l arid DGj? r e s p e c t i v e l y , s t a r t t h e r e t u r n sweep by s w i t c h i n g t h e I n p u t s o f t h e f i r s t and t h i r d sweep a m p l i f i e r s r e s p e c t i v e l y t o t h e +300 v o l t s u p p l y * S i m i l a r l y , CP^ a l s o s e t s F F k whose n e g a t i v e o u t p u t , t h r o u g h t h e a c t i o n o f DG3, s t a r t s t h e r e t u r n sweep b y s w i t c h i n g t h e I n p u t o f t h e s e c o n d sweep a m p l i -f i e r t o t h e -300 v o l t s u p p l y . As t h e o u t p u t o f e a c h o f t h e a m p l i f i e r s r e a c h e s z e r o v o l t s , t h e i r a s s o c i a t e d v o l t a g e compar-a t o r p r o v i d e s t h e n e g a t i v e r e s e t t i n g p u l s e , The f u n c t i o n g e n -e r a t o r i s now r e a d y t o g e n e r a t e t h e n e x t f u n c t i o n . As t h e O u t p u t o f t h e t h i r d sweep c i r c u i t i s f ( x ) , and t h e r e t u r n sweep r a t e i s f i x e d , t h e t i m e t a k e n t o r e s e t t h i s a m p l i f i e r c o r r e s p o n d s t o f ( x ) . T h u s t h e p u l s e g e n e r a t e d by t h e v o l t a g e c o m p a r a t O r C3 i s t h e p u l s e whose p o s i t i o n c o r r e s p o n d s t o t h e v a l u e o f t h e f u n c t i o n a t x. T h i s p u l s e I s d e s i g n a t e d P f ( x ) , and may be w r i t t e n on t h e drum f o r u s e when I t I s r e q u i r e d b y t h e com p u t e r . T h i s w r i t i n g o p e r a t i o n was not a t t e m p t e d i n t h i s work. 5>-k, T e s t i n g t h e S i m p l i f i e d F u n c t i o n G e n e r a t o r D u r i n g t h e i n i t i a l t e s t i n g o f t h e f u n c t i o n g e n e r a t o r , i t was d i s c o v e r e d t h a t t h e a m p l i f i e r s were not s a t i s f a c t o r y I n t h a t i t was v e r y d i f f i c u l t t o keep t h e m i n b a l a n c e . As a r e s u l t t h e g a i n o f t h e a m p l i f i e r was n o t t h e same f o r b o t h t h e p o s i t i v e and t h e n e g a t i v e o u t p u t s , Thus when t h e s e O u t p u t s i g n a l s were added b y t h e d i o d e g a t e f o l l o w i n g t h e a m p l i f i e r , t h e v o l t a g e at t h e i n p u t o f t h e n e x t s t a g e was n o t z e r o , As a r e s u l t , when t h i s s t a g e s h o u l d h a v e been i n clamp, i t was a c t u a l l y I n t e g r a t -i n g t h i s e r r o r v o l t a g e . So, i n s t e a d o f t h e i n t e g r a t o r h o l d i n g i t s o u t p u t s t e a d y , t h e o u t p u t would e i t h e r r i s e o r f a l l d e p e n d -i n g upon t h e r e l a t i v e g a i n s o f t h e two c h a n n e l s o f t h e p r e c e d -i n g s t a g e . T h e r e was no e r r o r o f t h i s t y p e d u r i n g t h e a c t u a l t i m e o f i n t e g r a t i o n as t h e I n p u t s o f one s t a g e were t i e d d i r e c t l y t o t h e o u t p u t s o f t h e p r e c e d i n g s t a g e by t h e a c t i o n p f t h e d i o d e g a t e s , I n an a t t e m p t t o c o n t r o l t h e d r i f t o f t h e sweep a m p l i f i e r s i t was d e c i d e d t o i n v e s t i g a t e a new t y p e o f a m p l i f i e r and t h i s work w i l l be d i s c u s s e d i n S e c t i o n 6. As t h e r e was no l a r g e e r r o r i n v o l v e d d u r i n g t h e a c t u a l t i m e t h e i n t e g r a t i n g a c t i o n was t a k i n g p l a c e , t h e e r r o r m e n t i o n e d above c o u l d be v e r y e a s i l y c a l c u l a t e d by o b s e r v i n g t h e f u n c t i o n a p p e a r i n g at t h e out put o f t h e t h i r d sweep c i r c u i t * T h e r e f o r e i t was d e c i d e d t o r u n t h e t e s t s on t h i s g e n e r a t o r as t h e e r r o r c o u l d be e a s i l y t a k e n i n t o c o n s i d e r a t i o n and c o r r e c t e d . f(x) C P 2 P x CP-C o r r e c t e d P f (x) ^ O b s e r v e d f P f (x). » x F i g u r e 5~7, O u t p u t p f S i m p l i f i e d F u n c t i o n G-eneratdr A t y p i c a l o u t p u t o f t h e f u n c t i o n g e n e r a t o r i s shown i n F i g u r e £-7, The f u n c t i o n i s g e n e r a t e d I n t h e I n t e r v a l between CP2 and Px, and I n t h i s e a s e I s a p a r a b o l a w i t h no I n i t i a l c o n -d i t i o n s * The g r e a t e s t e r r o r o b s e r v e d i n t h i s w a v e f o r m i s t h e p o s i t i v e s l o p e between Px and CP^, where t h e i n t e g r a t o r s h o u l d h a v e been I n clamp w h i c h w o u l d r e s u l t i n a l i n e w i t h z e r o s l o p e * The i n t e r v a l b etween CP^ and P f ( x ) r e p r e s e n t s t h e v a l u e o f t h e f u n c t i o n at x. The o u t p u t o f t h e g e n e r a t o r was r e s e t t o z e r o v o l t s at t h e r a t e p f -100 v o l t s / m s e c d u r i n g t h i s p e r i o d . 2 The f u n c t i o n g e n e r a t e d was o f t h e f o r m f ( x ) = ex . The v a l u e o f c i s d e t e r m i n e d b y t h e p o s i t i o n o f p u l s e P r as f " ( x ) = 2 c , To t e s t t h e g e n e r a t o r , t h r e e d i f f e r e n t p o s i t i o n s o f P r were t a k e n and t h e c o r r e s p o n d i n g c u r v e s o f t h e i n t e r v a l CP-j t o P f ( x ) v e r s u s t h e i n t e r v a l CP2 '£0 Px measured i n p e r i o d s p f t h e c l o c k s i g n a l were p l o t t e d . The p o s i t i o n p f P r was known as i t s p o s i t i o n was n o t e d when i t was w r i t t e n on t h e drum u s i n g t h e w r i t e o p e r a t i o n d e s c r i b e d i n S e c t i o n The i n t e r v a l CP2 t o Px was a l s o known b y n o t i n g t h e p o s i t i o n p f Px when i t was w r i t t e n on t h e drum. The i n t e r v a l CP3 t o P f ( x ) was m e a s u r e d by m e a s u r i n g t h e c o r r e s p o n d i n g t i m e i n t e r v a l u s i n g t h e d e l a y i n g sweep a c t i o n o f a T e k t r o n i x $\\$ O s c i l l o s c o p e , T he e r r o r was c a l c u l a t e d b y o b s e r v i n g t h e a m p l i t u d e o f t h e f u n c t i o n at Px and at CP^, t a k i n g t h e i r d i f f e r e n c e and m u l t i -p l y i n g i t by ~'^Qo U Y p i t ' & s t i x G d 0 W 1 s w e e P r a t e i s -100 v o l t s / msec, and a d d i n g t h i s r e s u l t t o t h e t i m e i n t e r v a l CP3 t o P f (x) . T h i s c o r r e c t i o n o p e r a t i o n may be o b s e r v e d I n F i g u r e $-7v As an 47 example. I f t h e f u n c t i o n i n c r e a s e s b y 1 v o l t between Px and CP-j, 10 u s e e s w o u l d be s u b t r a c t e d f r o m t h e t i m e i n t e r v a l CP^ t o P f (x) . I n t h i s manner any e r r o r o c c u r r i n g a f t e r t h e p u l s e P x would be e l i m i n a t e d . T h i s c o r r e c t e d t i m e i n t e r v a l was d i v i d e d by 14.3 u s e c s / p e r i o d as t h e e x a c t c l o c k p e r i o d i s 14.3 u s e e s . T h u s t h e c o r r e c t e d p o s i t i o n o f P f (x) was c o n v e r t e d i n t o a number o f c l o c k p e r i o d s . P f (x) in 6 P e r i o d s P r = 68 CP, 20 40 60 80 P x i n - P e r i o d s o f C l o c k S i g n a l r = 48 100 CP-F i g u r e 5-8. P l o t o f F u n c t i o n s G e n e r a t e d k8 A f t e r t h e c u r v e s were p l o t t e d as i s shown i n F i g u r e £-8, t h e i r e q u a t i o n s were c a l c u l a t e d . T h e s e e q u a t i o n s were c h e c k e d by c o m p a r i n g t h e c a l c u l a t e d and t h e o b s e r v e d v a l u e s o f F f ( x ) at v a r i o u s a b s c i s s a and t h e s e r e s u l t s a r e tabulated I n F i g u r e £-9, F o r t h e c u r v e s w i t h P r s e t at 68 and k8 ( c o r r e s p o n d i n g t o 70 and £0 c l o c k p e r i o d s r e s p e c t i v e l y as 2 p e r i o d s a r e l o s t i n t h e g a t e c o u n t i n g a c t i o n — s e e F i g u r e 3-8) v e r y good agreement b e t w e e n t h e c a l c u l a t e d and o b s e r v e d p o i n t s was o b t a i n e d . F o r t h e t h i r d c u r v e , w i t h P r at 28, an e q u a t i o n was n o t f o u n d as i t i s o b v i o u s t h a t t h e r e was a l a r g e e r r o r i n v o l v e d . T h i s l a r g e e r r o r was t h e r e s u l t o f t h e low o u t p u t v o l t ages o f t h e v a r i o u s sweep . c l r c u l t . 3 . The b e t t e r a c c u r a c i e s o b t a i n e d f o r t h e l a r g e r v a l u e s o f P r c a n be e x p l a i n e d b y n o t i n g t h a t t h e s e c o n d d e r i v a t i v e was l a r g e r r e s u l t i n g i n a l a r g e r v o l t a g e o u t p u t , and t h e r e f o r e t h e p e r c e n t -age e r r o r w o u l d be l e s s , as t h e a b s o l u t e e r r o r o f t h e o u t p u t i s q u i t e c o n s t a n t . T h i s r e a s o n i n g a l s o e x p l a i n s t h e s l i g h t e r r o r n o t i c e d f o r t h e l o w e r v a l u e s o f Px, B e c a u s e o f t h e d r i f t i n t h e a m p l i f i e r s , t h e o u t p u t s o f t h e I n t e g r a t o r s were, n o t a l l at z e r o v o l t s b e f o r e t h e p r o c e s s o f f u n c t i o n g e n e r a t i o n was »started. T h i s e r r o r a c c o u n t s f o r t h e s m a l l i n i t i a l c o n d i t i o n s that a r e p r e s e n t i n t h e f i r s t two . c u r v e s . The r e s u l t s o f t h e s e t e s t s were v e r y e n c o u r a g i n g and i t was f e l t t h a t i f a good o p e r a t i o n a l a m p l i f i e r was d e s i g n e d a l m o s t a l l t h e d i f f i c u l t i e s t h a t a r o s e I n t h e s i m p l i f i e d f u n c t i o n g e n e r a t o r c o u l d be o v e r c o m e . A new a m p l i f i e r was d e s i g n e d f o r p o s i t i v e o u t p u t s o n l y , b u t as an o p e r a t i o n a l a m p l i f i e r was n e e d e d k9 as an i n v e r t i n g s t a g e , i t was d e c i d e d t o w a i t u n t i l t h e f i n a l f o r m o f t h e f u n c t i o n g e n e r a t o r was d e s i g n e d b e f o r e t h i s a m p l i f i e r w o u l d be u s e d . T h i s a m p l i f i e r , t o g e t h e r w i t h t h e g e n e r a l p l a n Of t h e p r o p o s e d final f o r m o f t h e f u n c t i o n g e n e r a t o r , w i l l be d e s c r i b e d i n S e c t i o n 6. F o r P r = 68 f ( x ) = 0.28 + 6.54(10~^)x2 b y c a l c u l a t i o n P x P f ( x ) C a l c . P f ( x ) O b s e r v e d % D e v i a t i o n 10 0.35 o.35„ 0.k6" 0 20 - 0.55 24 30 " 0,87 . 0,86 1 kO 1.33 1.33 0 50 1.92 2.06 7 60 2.6k 2.73 3 70 }M 343 1 80 k,k6 447 0*2 90 5.58 5.53 1' 95 6.18 5.95 3 * T h i s r e s u l t was n e g l e c t e d as o b v i o u s l y i t was i n e r r o r , F o r P r = 48 -4 2 f ( x ) - 0.22 + 4.67(10 ) x b y c a l c u l a t i o n Px P f ( x ) C a l c , P f ( x ) O b s e r v e d % D e v i a t i o n 10 0.27 0.25 8 20 O.41 O.42 2 30 0.64 0.66 3 40 0.97 0.98 0.94** 1 50 1.39 -60 1.90 1.89 1 70 2.51 2.55 2 80 3.21 3.15 2 90 4^01 3.99 0.5 95 4-44 441 0.7 T h i s r e s u l t was n e g l e c t e d as i t i s i n e r r o r as may be o b s e r v e d f r o m t h e c u r v e s i n F i g u r e 5~8. F i g u r e 5-9, R e s u l t s O f T e s t s on S i m p l i f i e d F u n c t i o n G e n e r a t o r 6. PROPOSED F O R M OF F U N C T I O N G E N E R A T I O N T h e f i n a l f o r m p f t h e f u n c t i o n g e n e r a t o r m u s t b e a s t a b l e s y s t e m made u p p f t h r e e h i g h - g a i n d c a m p l i f i e r s s e r v i n g a s s w e e p g e n e r a t o r s . T h i s f u n c t i o n g e n e r a t o r m u s t a l s o b e c a p a b l e o f h a n d l i n g p o s i t i v e a n d n e g a t i v e f u n c t i o n s w i t h i n i t i a l v a l u e s . T h i s S e c t i o n w i l l d e s c r i b e a g e n e r a t o r w h i c h w i l l b e a b l e t o s a t i s f y t h e s e r e q u i r e m e n t s . B e f o r e d i s c u s s i n g t h e p r o p o s e d g e n -e r a t o r a s a w h o l e t h e new d e s i g n o f t h e a m p l i f i e r w i l l b e d i s -c u s s e d . 6-1. New H i g h - G a i n DC A m p l i f i e r A s was s e e n i n S u b - s e c t i o n £-1}. t h e a c c u r a c y o f t h e f u n c t i o n g e n e r a t o r d e p e n d s u p o n t h e a c c u r a c y o f t h e i n t e g r a t i n g c i r c u i t s . T h e p r o p e r t i e s r e q u i r e d o f t h e o p e r a t i o n a l a m p l i f i e r s a r e : 1. T h e a m p l i f i e r m u s t b e d i r e c t c o u p l e d t o a v o i d t h e u s e o f c o u p l i n g c a p a c i t o r s w h i c h m u s t b e r e c h a r g e d a f t e r e a c h c y c l e o f t h e g e n e r a t o r . * 2. T h e a m p l i f i e r m u s t h a v e a h i g h g a i n i n o r d e r t o k e e p t h e e r r o r o f t h e s w e e p s a s l o w a s p o s s i b l e * T h i s e r r o r m u s t b e l e s s t h a n 0.01 p e r c e n t t o be c o n s i s -t e n t w i t h t h e a c c u r a c y p o s s i b l e i n t h e c o u n t i n g c i r c u i t s . 3* T h e a m p l i f i e r m u s t b e v e r y s t a b l e , 1|* O u t p u t v o l t a g e s o f b e t t e r t h a n p l u s a n d m i n u s 100 v o l t s w o u l d b e d e s i r e d . A t f i r s t g l a n c e t h e o p e r a t i o n a l a m p l i f i e r s , e s p e c i a l l y t h e K2-X, p r o d u c e d b y G . A , P h i l b r i c k R e s e a r c h e s I n c . s e e m e d t o f u l f i l t h e s e r e q u i r e m e n t s b u t t h e i r g a i n I s l o w a n d t h e y a r e n o t 50 +300 V - 3 0 0 V A l l r e s i s t o r s l / 2 w a t t e x c e p t where n o t e d . DC g a i n a b o u t 1800. F i g u r e 6-1. S t a b i l i z e d H i g h - G a i n DC A m p l i f i e r 51 v e r y s t a b l e . C o n s e q u e n t l y , a new a m p l i f i e r was d e s i g n e d w i t h an a u t o m a t i c b i a s i n g c i r c u i t , As a p o s i t i v e o u t p u t was r e q u i r e d an PNP t y p e t r a n s i s t o r was n e e d e d t o d e t e c t when t h e o u t p u t went b e l o w g r o u n d p o t e n t i a l , . T h i s t y p e o f t r a n s i s t o r r e q u i r e s a n e g a t i v e s u p p l y and t h e r e f o r e i t s o u t p u t would be a n e g a t i v e b i a s i n g v o l t a g e . The f i n a l d e s i g n o f t h i s a m p l i f i e r i s shown i n F i g u r e 6-1. I n o r d e r t o a l l o w n e g a t i v e b i a s i n g on t h e p o s i t i v e i n p u t g r i d , t h e p l a t e s u p p l y v o l t a g e o f t h e n e g a t i v e i n p u t t u b e h a d t o be d e c r e a s e d t o about 100 v o l t s . To p r o v i d e t h i s s u p p l y a t r i o d e was u s e d as a c a t h o d e f o l l o w e r w i t h i t s g r i d l e v e l s e t at about 100 v o l t s . The c a t h o d e o f t h i s t r i o d e w o u l d t h e n be k e p t s l i g h t l y p o s i t i v e w i t h r e s p e c t t o i t s g r i d and would be i n d e p e n d e n t o f t h e c u r r e n t drawn f r o m t h e t u b e p r o v i d e d t h a t t h e c u r r e n t was k e p t w i t h i n t h e r a t i n g o f t h e t u b e . The r e m a i n d e r o f t h e a m p l i f i e r i s c o n v e n t i o n a l . The o v e r a l l dc g a i n was m e a s u r e d t o be 1800 w i t h t h e a m p l i f i e r c o n -n e c t e d as an ope r a t i o n a l a m p l i f i e r , Some d i f f i c u l t y was e n c o u n -t e r e d w i t h h i g h - f r e q u e n c y , p a c i l l - a t i o n s b u t t h e s e were e l i m i n a t e d b y t h e u s e o f h i g h - f r e q u e n c y a t t e n u a t i n g n e t w o r k s i n t h e p l a t e s o f t h e two a m p l i f i e r s t a g e s . F r o m t h e "Appendix i t w i l l be s e e n t h a t f o r an I n t e -g r a t i n g t i m e c o n s t a n t o f 3 msecs and a s u p p l y o f 300 v o l t s , t h e e r r o r i n a l i n e a r sweep may be e x p r e s s e d as :>.:;r:t,; ••• , where t i s 6(1+A) t h e t i m e I n m i l l i s e c o n d s a n d A i s t h e g a i n o f t h e a m p l i f i e r . 52 T h e r e f o r e , f o r a g a i n o f 1800 and a "sweep t i m e o f 1 msec, t h e e r r o r i s •...-•.j;... , w h i c h i s e q u i v a l e n t t o 0*0092 p e r c e n t f u l l s c a l e * 10800 H F o r t h i s g a i n t h e d i f f e r e n c e i n t h e s l o p e o f t h e sweep i s about 0.056 p e r c e n t o f t h e f i x e d r a t e o f 100 v o l t s / m s e c * T h e b i a s i n g of t h i s a m p l i f i e r i s as f o l l o w s ; As s o o n as t h e out put t r i e s t o go n e g a t i v e t h e d i o d e s s t a r t t o c o n d u c t w h i c h draws c u r r e n t t h r o u g h t h e t r a n s i s t o r . T h i s c u r r e n t i s a m p l i f i e d about t w e n t y t i m e s d e v e l o p i n g a p o s i t i v e v o l t a g e change a c r o s s t h e 10K c o l l e c t o r r e s i s t o r . T h i s v o l t a g e i s i m m e d i a t e l y p a s s e d t h r o u g h t h e d i o d e t o t h e 0.22uf c a p a c i t o r w h i c h I n c r e a s e s t h e v o l t a g e p o s i t i v e l y on t h e p o s i t i v e i n p u t g r i d . T h i s s m a l l change i s a m p l i f i e d b y t h e a m p l i f y i n g a c t i o n o f t h e a m p l i f i e r and t h e o u t p u t t r i e s t o go p o s i t i v e , w h i c h c u t s o f f t h e t r a n s i s -t o r , l o w e r i n g t h e c o l l e c t o r v o l t a g e . B e c a u s e o f t h e h i g h g a i n s i n v o l v e d t h e s e changes a r e v e r y s m a l l . T h i s d e c r e a s e o f t h e c o l l e c t o r v o l t a g e i s t r a n s f e r r e d t o t h e p o s i t i v e g r i d w i t h a t i m e c o n s t a n t o f t h e o r d e r o f 220 msecs as t h e d i o d e i s b i a s e d i n r e v e r s e . As t h i s d e c r e a s i n g v o l t a g e i s b e i n g t r a n s f e r r e d t o t h e g r i d , t h e o u t p u t v o l t a g e o f t h e a m p l i f i e r d r o p s and when i t r e a c h e s z e r o v o l t s t h e s y s t e m becomes s t a b l e . B e c a u s e o f t h e l o n g t i m e r e q u i r e d f o r t h e b i a s i n g n e t w o r k t o o p e r a t e a f t e r t h e o u t p u t h a s gone p o s i t i v e , t h e o u t p u t i s n o t a f f e c t e d b y t h i s a u t o m a t i c b i a s i n g u n l e s s i t i s h e l d at a p o s i t i v e v o l t age f o r d u r a t i o n s o f more t h a n 5 m s e c s , T h i s t i m e l i m i t i s s a t i s -f a c t o r y as t h e d u r a t i o n o f one c h a n n e l i s o f t h e o r d e r o f 1.5 m secs. 53 T h i s a m p l i f i e r was t e s t e d v e r y t h o r o u g h l y and i t was f o u n d t o be v e r y s t a b l e * A f t e r t h e Output was d r i v e n h i g h l y p o s i t i v e , t h e a m p l i f i e r w o u l d r e c o v e r i n about one s e c o n d . The a m p l i f i e r was n o t t e s t e d u n d e r t h e a c t u a l O p e r a t i n g c o n d i -t i o n s as t h e work r e q u i r e d t o s e t up t h e f u n c t i o n g e n e r a t o r was q u i t e i n v o l v e d . Prom t h e t e s t s c o m p l e t e d , i t was f e l t t h a t t h i s a m p l i f i e r w o u l d f u l f i l a l l t h e n e c e s s a r y c o n d i t i o n s o f t h e a m p l i -f i e r s r e q u i r e d i n t h e f u n c t i o n g e n e r a t o r . T h i s a m p l i f i e r does n o t h a v e a n e g a t i v e o u t p u t . I n o r d e r t o g e t t h e n e g a t i v e o u t p u t , an a m p l i f i e r may e a s i l y be d e s i g n e d u s i n g t h e above t h e o r y and u s i n g an NPN t y p e t r a n s i s t o r as t h e b i a s i n g c o n t r o l . As t h e c o l l e c t o r o f an NPN t r a n s i s t o r i s p o s i t i v e w i t h r e s p e c t t o t h e e m i t t e r , t h e b i a s i n g v o l t a g e a p p l i e d t o t h e g r i d w o u l d be p o s i t i v e . T h e r e f o r e , t h e K2-X, o r s i m i l a r , a m p l i f i e r c o u l d be u s e d . T h i s c i r c u i t was n o t d e s i g n e d as i t was f e l t t h a t t h e r e was no p a r t i c u l a r p r o b l e m p r e s e n t . 6-2, P r o p o s e d F u n c t i o n G e n e r a t o r I n t h e p r o p o s e d f u n c t i o n g e n e r a t o r t h e sweep a m p l i -f i e r s ; a r e a l w a y s b i a s e d i n one. d i r e c t i o n r e s u l t i n g i n a p o s i -t i v e o u t p u t , The o u t p u t o f t h e g e n e r a t o r i s e q u a l t o a + f ( x ) where » a 1 i s a c o n s t a n t v a l u e s e t at about m i d s c a l e o f t h e o u t p u t v o l t a g e , T h i s method g r e a t l y s i m p l i f i e s t h e g e n e r a t o r as p o s i t i v e and n e g a t i v e f u n c t i o n s may be g e n e r a t e d and s t i l l t h e sweep a m p l i f i e r s a r e not r e q u i r e d t o h a v e p o s i t i v e and n e g a t i v e o u t p u t s . The p r o p o s e d f u n c t i o n g e n e r a t o r i s p a t t e r n e d s i f t e r t h e g e n e r a t o r d i s c u s s e d i n S e c t i o n 5>. O u t s i d e o f t h e c i r c u i t s r e q u i r e d f o r t h e i n s e r t i o n o f t h e i n i t i a l c o n d i t i o n s and t h e s i g n s f o r t h e n e g a t i v e d e r i v a t i v e , t h e o n l y change'^in t h e g e n -e r a t o r i s i n t h e c o n n e c t i o n o f t h e o p e r a t i o n a l a m p l i f i e r s . The new h i g h ^ g a i n dc a m p l i f i e r s a r e u s e d w i t h a d d i t i o n a l a m p l i f i e r s u s e d i n e x a c t p h a s e i n v e r t i n g c i r c u i t s t o p r o v i d e t h e o p p o s i t e p o l a r i t y s i g n a l s f o r t h e d i o d e g a t e s . The c o m p l e t e b l o c k s c h e m a t i c , t o g e t h e r w i t h t h e c o n t r o l l i n g p u l s e t r a i n , f o r t h e p r o p o s e d f u n c t i o n g e n e r a t o r i s shown i n F i g u r e 6-2. The o p e r a t i o n i s s t a r t e d by h a y i n g t h e f i r s t c h a n n e l p u l s e CP-^ s e t F F l w h i c h c l o s e s GI b l o c k i n g t h e p u l s e s i n t h e p u l s e t r a i n f r o m t h e r e a d a m p l i f i e r f r o m t h e I n p u t t o t h e f i r s t sweep a m p l i f i e r . CP^ a l s o . S e t s FF10 w h i c h i s r e s e t by t h e n e x t p u l s e P f ( 0 ) . The o u t p u t o f sweep a m p l i f i e r I I I would t h e n r e p r e s e n t a+f (0) and i s clamped at t h i s v a l u e b y t h e i n t e g r a t o r a c t i o n . The r e s e t p u l s e g e n e r a t e d by FF10 s e t s FF8 w h i c h I s r e s e t by t h e n e x t p u l s e P f ' ( 0 ) . T h e o u t p u t o f t h e s e c o n d sweep a m p l i f i e r , I I , i s t h e n - ( a + f ' ( 0 ) ) , T h i s c o n s t a n t »a» i s l e f t i n t h e o u t p u t i n o r d e r t o g i v e i t a b i a s v o l t a g e . The c o n s t a n t i s s u b t r a c t e d d u r i n g t h e i n t e g r a t i n g p r o c e s s by a method w h i c h w i l l b e d i s c u s s e d l a t e r . The I n i t i a l v a l u e s a r e now i n t h e f u n c t i o n g e n e r a t o r . The r e s e t a c t i o n o f FF8 r e s e t s F F l w h i c h opens G I a l l o w i n g t h e n e x t two p u l s e s , P r ^ and Px-j_, t o pas3. As t h e s i g n f l i p - f l o p , FF3, i n t h e r e s e t s t a t e , a l l o w s p u l s e s J L J L t . •Sign P u l s e i i L C P X P f (0.) P f ' ( 0 ) P r x C P 2 P x x P y x Pr. 2 P x 2 P y 2 CPg P f ( x ) >- * I -300' r , W W — O DG1 P u l s e W v \ 1 DG2 -300 1 W V \ — o DG3 DG4 DG5 F i g u r e 6-2. P r o p o s e d F u n c t i o n G e n e r a t o r r e p r e s e n t i n g a p o s i t i v e s e c o n d d e r i v a t i v e t o p a s s t h r o u g h Gk, P r ^ and P x ^ s e t and r e s e t FPlj.. The o u t p u t of sweep a m p l i f i e r I t h e n r e p r e s e n t s t h e s e c o n d d e r i v a t i v e p l u s t h e c o n s t a n t 'a* O v e r t h e i n t e r v a l ( x j _ , y^) . The r e s e t p u l s e f r o m F F k s e t s F F 2 w h i c h c l o s e s GI and opens G2 a l l o w i n g t h e n e x t p u l s e P y ^ t o p a s s . T h i s p u l s e r e s e t s F F 2 , T hus P F 2 i s s e t f o r t h e I n t e r v a l ( x 1 ? j^). The s e t t i n g and r e s e t t i n g a c t i o n o f F F 2 s e t s and r e s e t s F F 6 and F F 7 . The a c t i o n o f F F 6 On d i o d e g a t e DG2 g a t e s t h e o u t p u t f r o m t h e f i r s t sweep c i r c u i t so t h a t t h e s e c o n d d e r i v a t i v e p l u s t h e c o n s t a n t f o r t h e whole i n t e r v a l a p p e a r s at t h e i n p u t o f I I . The c o n s t a n t «a» i s s u b t r a c t e d b y t h e action o f F F 7 on DG3 l e a v i n g t h e s e c o n d d e r i v a t i v e , f " ( x ) . T h i s v o l t a g e I s i n t e g r a t e d b y sweep a m p l i f i e r I I , whose o u t p u t I s t h e n - ( a + f ( x ) ) . The s e t t i n g a c t i o n o f F F 2 a l s o s e t s F F 9 and F F 1 1 . The s e t t i n g o f F F 9 a l l o w s t h e o u t p u t o f I T t o p a s s t h r o u g h DGk t o DG5 where t h e s e t t i n g o f F F 1 1 s u b t r a c t s t h e c o n s t a n t ' a ' . Thus t h e I n p u t t o a m p l i f i e r I I I i s t h e f i r s t d e r i v a t i v e , f » ( x ) . The o u t p u t o f I I I I s a c o n s t a n t p l u s t h e r e q u i r e d f u n c t i o n , t h a t i s , a + f ( x ) . The above argument i s v a l i d f o r p o s i t i v e s e c o n d d e r i v a -t i v e s o n l y . I f t h e s e c o n d d e r i v a t i v e i s n e g a t i v e t h e o p e r a t i o n i s t h e same e x c e p t f o r a m i n o r change i n t h e i n p u t t o I . F o r e xample, i f t h e s e c o n d d e r i v a t i v e f o r t h e i n t e r v a l ( x 2 , y 2 ) is n e g a t i v e an e x t r a p u l s e i s p l a c e d on t h e drum one c l o c k p e r i o d a f t e r p u l s e P y ^ i T h i s p u l s e may be s e e n I n t h e p u l s e c h a i n shpwn I n F i g u r e 6-2. The o p e r a t i o n i s as f o l l o w s . A l o n g w i t h resetting FF2, Py^ sets the delay multivibrator, DM, which has a delay of about 20 usees, or slightly more than one clock period. Setting DM opens G3 which allows the sign pulse to pass i f i t is present. This sign pulse sets FF3 which closes Gi| and opens Gf? allowing P r 2 and Vx^ to set and reset FFj?. This action initiates a negative sweep at the output of I, resulting in the negative second derivative.* Setting DM also closes Gl to block the sign pulse as i t is not a direct function pulse. The resetting of FF£ resets FF3 and sets PF2. FF3 is now ready for the next second derivative pulse which may be either positive or negative depending on whether the sign pulse is absent or present. The action of the remainder of the function generator does not change. When Px, which represents the independent variable at x, occurs i t sets FF1 which blocks the pulse train stopping the integrating act ion. Also Px resets FF9 and FPU which clamps the output of amplifier III at f(x). Assuming that the pulses for the function are contained in Channels 1 and 2, channel pulse CP-j starts the resetting action of the generator by sett-ing FF5, FF7, and FF11. These f l i p - f l o p s are reset by pulses from their respective voltage comparators CI, C2, and C3. The pulse obtained from C3 is Pf(x) and represents the value of the function at x. As the constant 'a' is not subtracted from the output of I ' l l , Pf(x) also includes this constant. This Is the most convenient form of Pf (x) for use in the arithmetic and integrating circuits of the computer. 57 Now t o summarize t h e o p e r a t i o n o f t h i s g e n e r a t o r . The o u t p u t o f a m p l i f i e r I r e p r e s e n t s t h e s e c o n d d e r i v a t i v e o v e r t h e i n t e r v a l s ( x ^ , y^) o n l y . As FF6 and FF7 a r e c o n t r o l l e d by FF2 w h i c h i s s e t and r e s e t by P x ^ and P y ^ , t h e i n p u t t o a m p l i f i e r I I I s t h e s e c o n d d e r i v a t i v e f o r t h e whole f u n c t i o n I n t e r v a l . As t h e I n t e r v a l b e f o r e P x ^ was u s e d t o g e n e r a t e t h e i n i t i a l v a l u e s , t h e o u t p u t o f a m p l i f i e r I I does not. r e p r e s e n t t h e f i r s t d e r i v a t i v e u n t i l P x ^ o c c u r s . The f i r s t s e t t i n g o f F F 2 , w h i c h r e p r e s e n t s P x l f s e t s FF9 and FF11 a l l o w i n g I I I t o i n t e g r a t e t h e ^ output o f I I . T he i n t e g r a t i o n c o n t i n u e s u n t i l s t o p p e d b y Px. The f l i p - f l o p s and t h e v o l t a g e c o m p a r a t o r s t h a t would be u s e d I n t h i s p r o p o s e d f u n c t i o n g e n e r a t o r a r e t h e same as t h o s e shown i n F i g u r e s 5~5 and 5 - 6 . The a m p l i f i e r s h a v e a l r e a d y b e e n d e s c r i b e d i n S u b - s e c t i o n 6 - 1 . The o n l y d e s i g n t h a t has not b e e n done f o r t h i s g e n e r a t o r i s t h a t o f t h e 20 u s e e d e l a y m u l t i v i b r a t o r , b u t no d i f f i c u l t y i s e x p e c t e d i n t h i s d e s i g n * Some comments S h o u l d be made about t h e .diode g a t e s . By r e f e r r i n g a g a i n t o F i g u r e 5~9 i t w i l l be o b s e r v e d t h a t t h e a m p l i t u d e o f t h e o u t p u t o f t h e s i m p l i f i e d f u n c t i o n g e n e r a t o r was v e r y low. To i n c r e a s e t h i s a m p l i t u d e , w h i c h w o u l d a l s o g r e a t l y I n c r e a s e t h e o v e r a l l a c c u r a c y p f t h e g e n e r a t o r , t h e i n t e g r a t i n g t i m e c o n s t a n t s a s s o c i a t e d w i t h d i o d e g a t e s DG2 and DGij. s h o u l d be d e c r e a s e d . A l s o a f i n e a d j u s t m e n t P f t h e t i m e c o n s t a n t s a s s o c i a t e d w i t h g a t e s DG3 and DG5 would have t o be made as t h e s e g a t e s a r e u s e d t o s u b t r a c t t h e c o n s t a n t ' a ' f r o m t h e o u t p u t s o f sweep a m p l i f i e r s I I and I I I r e s p e c t i v e l y . 58 P r o b a b l y t h e most s i m p l e method o f a d j u s t i n g t h e s e v a r i o u s t i m e c o n s t a n t s would be b y c h o o s i n g a p p r o p r i a t e s i z e s o f t h e I n t e -g r a t i n g r e s i s t o r s i n t h e g a t e s t o g e t h e r w i t h a f i n e a d j u s t m e n t c o n t r o l f o r e a c h r e s i s t o r . The i n v e r t i n g a m p l i f i e r s l a and I l a a r e r e q u i r e d t o p r o v i d e t h e r e v e r s e d p o l a r i t y o u t p u t s n e e d e d t o o p e r a t e t h e d i o d e g a t e s . A l s o I l a p r o v i d e s t h e p o s i t i v e o u t p u t o f t h e v o l t -age r e p r e s e n t i n g t h e f i r s t d e r i v a t i v e and is*, t h e r e f o r e u s e d t o O p e r a t e t h e v o l t a g e C o m p a r a t o r C2 i n t h e r e s e t t i n g o p e r a t i o n , A new v o l t a g e C o m p a r a t o r w h i c h w o u l d be C a p a b l e o f d e t e c t i n g p o s i t i v e g o i n g v o l t a g e s c o u l d be d e s i g n e d and u s e d a t t h e o u t p u t o f I I , but by u s i n g t h e method shown i n F i g u r e 6-2, a l l t h e c o m p a r a t o r s a r e i d e n t i c a l . 7. CONCLUSIONS The r e s u l t s o f t h e t e s t s on t h e s i m p l i f i e d v e r s i o n o f t h e f u n c t i o n g e n e r a t o r were v e r y e n c o u r a g i n g * A f t e r t a k i n g i n t o c o n s i d e r a t i o n t h e e r r o r due t o t h e d r i f t o f t h e sweep a m p l i f i e r s u s e d , i t was f o u n d t h a t f u n c t i o n s c o u l d be g e n e r a t e d w i t h an a c c u r a c y a p p r o a c h i n g 1 p e r c e n t . I t i s f e l t t h a t i t w i l l be p o s s i b l e t o g e n e r a t e f u n c -t i o n s w i t h a c c u r a c i e s /bett'.er^than 0.1 p e r oent w i t h t h e p r o p o s e d f o r m o f t h e f u n c t i o n g e n e r a t o r , as t h e m a j o r s o u r c e o f e r r o r p f t h e s i m p l i f i e d v e r s i o n was i n t h e sweep a m p l i f i e r s . The new a m p l i f i e r s h a v e a much h i g h e r g a i n and t h e y a r e c o m p l e t e l y f r e e f r o m d r i f t * A l s o by p r o p e r a d j u s t m e n t o f t h e i n t e g r a t i n g t i m e c o n s t a n t s a s s o c i a t e d w i t h t h e d i o d e g a t e s , f u l l u s e may be made o f t h e a v a i l a b l e o u t p u t v o l t a g e o f t h e sweep a m p l i f i e r s * The p e r c e n t a g e e r r o r i s g r e a t l y d e c r e a s e d i f t h e o u t p u t l e v e l s a r e l a r g e as t h e e r r o r p r e s e n t * due t o s l i g h t v a r i a t i o n s i n t h e p u l s e p o s i t i o n s and i n t h e a m p l i f i e r g a i n s , i s i n d e p e n d e n t o f t h e a m p l i t u d e o f t h e o u t p u t , The p r o p o s e d f o r m o f t h e g e n e r a t o r w i l l be v e r y e a s y t o programme as t h e p u l s e s may be w r i t t e n on a n y c h a n n e l o f • a n y t r a c k o f t h e drum v e r y e a s i l y b y s e l e c t i n g t h e t e n s , u n i t s , and p h a s e o f t h e s i n e c l o c k s i g n a l * A l l t h e s e l e c t i n g i s done b y p o s i t i o n i n g s e l e c t o r s w i t c h e s w i t h t h e e x c e p t i o n o f t h e p h a s e a n g l e o f t h e c l o c k s i g n a l w h i c h i s done by p o s i t i o n i n g a t e n -t u r n d i a l w h i c h may be r e a d t o one p a r t I n o n e - t h o u s a n d * The 59 60 p u l s e s must be w r i t t e n on t h e drum i n d i v i d u a l l y , but t h i s o p e r -a t i o n i s much s i m p l e r t h a n programming a d i g i t a l computer* The most I m p o r t a n t p a r t o f t h e work on t h e f u n c t i o n g e n e r a t o r was t h e d e s i g n i n g and t h e b u i l d i n g o f t h e s y n c h r o n i z -i n g and c o u n t i n g c i r c u i t s . T h e s e c i r c u i t s c o n t r o l t h e o p e r a t i o n Of t h e computer and t h e i r r e l i a b i l i t y was e s s e n t i a l . A f t e r t h e s e c i r c u i t s were put I n t o o p e r a t i o n , t h e y o p e r a t e d w i t h o u t f a i l u r e f o r w e l l o v e r 100 h o u r s , and t h e r e were no I n d i c a t i o n s t h a t any f a i l u r e s h o u l d o c c u r . 7-1. Recommendations f o r F u t u r e Work C o n c e n t r a t e d e f f o r t i n t h e f u t u r e s h o u l d be s p e n t on t h e d e v e l o p m e n t o f t h e p r o p o s e d f o r m o f t h e f u n c t i o n g e n e r a t o r . A l t h o u g h i t i s f e l t t h a t no p a r t i c u l a r p r o b l e m s a r e p r e s e n t i n t h i s d e v e l o p m e n t , some d i f f i c u l t i e s c o n c e r n e d w i t h d e t a i l s might a r i s e . The o u t l i n e o f t h i s g e n e r a t o r i s p r e s e n t e d I n t h e s e c t i o n o f t h e p r o p o s e d f u n c t i o n g e n e r a t o r . See S u b - s e c t i o n 6-2, T h i s t h e s i s does n o t c o v e r any c i r c u i t s t o be d e v e l o p e d f o r t h e o p e r a t i o n o f o b t a i n i n g t h e o u t p u t f r o m t h e m a g n e t i c drum, The out put o f t h e drum w i l l be i n t h e f o r m o f p u l s e p o s i t i o n s , and t h e t i m e i n t e r v a l between t h e r e f e r e n c e p u l s e and t h e o u t p u t I n f o r m a t i o n p u l s e w i l l n o t be known. The s i m p l e s t method o f d e t e r m i n i n g t h i s t i m e I n t e r v a l would be t o compare i t t o a s i m i l a r i n t e r v a l whose l e n g t h may be a d j u s t e d b y p o s i t i o n i n g t h e t e n s , u n i t s , and p h a s e - s h i f t i n g c a p a c i t o r d i a l s . I f b o t h o f t h e s e i n t e r v a l s were c o n v e r t e d t o p u l s e s o f c o r r e s p o n d i n g w i d t h s , 61 their difference taken, and the result integrated, a difference in the length of the time interval could be detected by using a simple detection c i r c u i t . The three dials could then be adjusted u n t i l no signal appears at the detector. The two time intervals would then be identical and the interval may be read off the tens, units, and phase-shifting capacitor dials. Outside of the above recommendations it is f e l t that no additional work or improvements are needed for the system, The synchronization and counting Circuits may be used as at present to time the operations of the whole computer. APPENDIX. RESPONSE OF SWEEP CIRCUITS Th e sweep, o r i n t e g r a t i n g , c i r c u i t i s shown I n F i g u r e A - l , - A / W W W F i g u r e A - l . The Sweep C i r c u i t 62 F o r a v e r y h i g h I n p u t impedance o f t h e a m p l i f i e r I]_ = ±2 w h i c h e q u a l s I T h e r e f o r e v ^ - V g = i R And u s i n g L a p l a c e T r a n s f o r m s A l s o y g " v ° = ic V o = -Av, 0 * " g S u b s t i t u t e (3) i n t o (1) v , + -JJSL = i R 1 A S i m i l a r l y s u b s t i t u t e (3) I n t o (2) • j f > - v 0 = - ^ ( 1 + A) E l i m i n a t e i by c o m b i n i n g (k) and (j?) = (1 + A) _sCR 1 v 0 = ~ A v i s C R ( l + A + _ L J sCR = - A v i s C R ( l ' + A) + 1 F o r a s t e p I n p u t v o l t a g e o f a m p l i t u d e b Y i ( s ) = b / s Now v 0 ( s) = , .... ..• -Ab . ....... s ( sCR [1"+' A ] + I) (1) (2) (3) (4) (5) ,-Ab : . Rearranging v 0(s) = CRM + A) s + C R ( 1 + A ) J Take inverse Laplace Transform ,. Prom the tables on page 217 in Thomson"^ " inverse transform #8 is of the form of the above equation. Substitute in v 0(t) = -Ab f CR(1 + A) (1 - e CR(l +-A)} CR( 1 + A) [_ Expand the exponent i a l v 0(t) = -Ab(l - 1 + t - VA-., -1 r t ~) C R (1 + A) 2 | _ C R ( L + A)_J + is - 1 3 . . . . ) 3! 1CR(1 + A)J -Abt . . P 1 : i + A ) |_ t;. •.. .  • . + . t 2 CR(1   2CR(1 + A) 6[CR(L + A) ] Por the sweep circuits in the function generator C = 0.01 uf. and R = 300k Therefore CR = 3 msecs And the step input voltage is b = 300 volts Assume that the gain A is greater than 100 Then t p is less than 1 for t less than 6[CR(1 + A) ]. 540000 1 msec. Therefore this and a l l succeeding terms may be omitted. Therefore the output sweep voltage may be expressed as v Q(t) = -lOQAt f 1 - t.. , ~1 where t is in msecs. 1'+ A L 6(1 + A)J The error at any time in a linear sweep would then be t ,. . for t in msecs. 6(1 + A) These expressions are valid only for a 3 msec time constant and a step input of 300 volts. -But as a time constant of this order will be used to generate the second derivative in the function generator, these expressions will serve satis factorily to estimate the error of the generator. 6k BIBLIOGRAPHY 1. Chance, B., Hughes, V., M a c N l c h o l , E . F . , S a y r e , D., and W i l l i a m s , F.C., Waveforms. New Y o r k , M c G r a w - H i l l , 19k9. ( R i d e n o u r , L.N., ed., M.I.T. R a d i a t i o n L a b o r a t o r y S e r i e s . v o l . 19.) .< -2. D o u c e , J . L . , and West, J.C . , "A M a g n e t i c - D r u m S t o r e f o r A n a l o g u e Comput i n g " , The P r o c e e d i n g s o f The I n s t i t u t i o n o f E l e c t r i c a l E n g i n e e r s . v o l . 105, no. 2k, p a r t B, November 1958, P P . 577-580. 3. Dunn, W.H., E l d e r t , C , and L e v o n i a n , P.V., "A D i g i t a l Computer f o r Use I n an O p e r a t i o n a l F l i g h t T r a i n e r " , I.R.E. T r a n s a c -t i o n s on E l e c t r o n i c C o m p u t e r s , v o l . EC-k, no. 2, June 1955, P P . 55-63, k. H i l d e b r a n d , B.P., "A S a m p l i n g - T y p e F u n c t i o n G e n e r a t o r and F o u r - Q u a d r a n t A n a l o g u e M u l t i p l i e r " , M.A.Sc. T h e s i s . U n i v e r s i t y Of B r i t i s h C o l u m b i a , 1956. " '' 5. J o h n s o n , C.L., A n a l o g Computer T e c h n i q u e s . New Y o r k , McGraw-H i l l , 1956. ' 6. K o r n , G.A. and K o r n , T.M., E l e c t r o n i c A n a l o g C o m p u t e r s . New Y o r k , M c G r a w - H i l l , 1952. " " '' " ' ' ' ' " 7. L a r s e n , R.S., "An I n t e g r a t o r f o r a P u i s e - P o s i t i o n - M o d u l a t i o n A n a l o g u e Computer", M.A.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b I a , 1958. " ' ' ' ' " 8. M i l l m a n , J . and Taub, H., P u l s e and D i g i t a l C i r c u i t s . New Y o r k , M c G r a w - H i l l , 1 9 i ? 6 . ' ' " " : , ' ' ' ' ' ' ' X . _ • 9. Mitche11, J.M. and Ruhraan, S., "The T R I C E — A H i g h S p e e d I n c r e m e n t a l C ompute r r t , I.R.E. N a t i o n a l C o n v e n t i o n R e c o r d , p a r t k, 1958, pp. 206-209. " '"' 10. P a r k , W.J., " A r i t h m e t i c C i r c u i t s f o r a T i m e - S e q u e n t i a l P u l s e -P o s i t I o n M o d u l a t i o n A n a l o g u e Computer", M.A.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b i a . 11. R u b i n o f f , M., " A n a l o g u e v s . D i g i t a l Computers - A C o m p a r i s o n " , P r o c e e d i n g s o f t h e I.R.E.. v o l . Ij.1, no. 10, O c t o b e r 19!?3, 12. S t a c e y , J . S . , "A F u n c t i o n G e n e r a t o r f o r a Time S e q u e n t i a l A n a l o g u e Computer", M.A.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l u m b i a . 1 3 . S y l v a n i a , E n g i n e e r i n g D a t a S e r v i c e on 6910 T u b e . Woburn, Mass., 1956. I k . Thomson, W.T., L a p l a c e • T r a n s f o r m a t i o n ^ N e w Y o r k , P r e n t i c e -H a l l , I n c . , 1950. 

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