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A versatile digital-to-analog function generator and multiplier. Lovas, Laszlo Tamas 1964

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A VERSATILE DIGITAL-TO-ANALOG FUNCTION GENERATOR AND MULTIPLIER by LASZLO TAMAS LOVAS B.A.Sc, The U n i v e r s i t y of B r i t i s h Columbia, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l E n g i n e e r i n g Ve accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1964 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be aUxwed without my w r i t t e n permiss ion . Department of L £ AJ 6/A) ££& jAJ 4 The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date MARCH / r / 9 ^ f ABSTRACT This work d e s c r i b e s the design, c o n s t r u c t i o n , and t e s t i n g of a d i g i t a l - t o - a n a l o g f u n c t i o n generator and m u l t i p l i e r f o r analog computation and n o n - l i n e a r system s i m u l a t i o n . The u n i t c o n s i s t s of two separate channels each of which i s f e d by a punched paper tape. Functions (of time) are r e p r e -sented on the tapes i n b i n a r y code and are read i n t o the machine p h o t o e l e c t r i c a l l y . In one channel, voltage sources of constant value but of e i t h e r p o l a r i t y are switched i n t o the p a r a l l e l branches of a l a d d e r network i n accordance with the incoming d i g i t a l i n f o r m a t i o n . As a r e s u l t of the p a r t i c u l a r choice of r e s i s t o r values i n the ladder network the v o l t a g e at one end of the r e s i s t i v e network i s p r o p o r t i o n a l to the b i n a r y number s i g -n i f i e d by the p o l a r i t y combination of the v o l t a g e sources. In the other channel the f u n c t i o n represented on the tape c o n t r o l s the p o l a r i t i e s of the v o l t a g e sources, and the magnitudes of the source v o l t a g e s are changed according to a second f u n c t i o n , which r e s u l t s i n an output v o l t a g e p r o p o r t i o n a l to the product of the two f u n c t i o n s . This second f u n c t i o n may be generated independently i n the f i r s t channel, or i t may be an e x t e r n a l computer v a r i a b l e . One l e v e l on each tape i s reserved f o r the generation of c o n t r o l p u l s e s which can be used to de-energize the r e s e t r e l a y i n the computer, i . e . to i n i t i a t e the compute mode. The v a r i a b l e tape speed and g a i n c o n t r o l s g r e a t l y enhance the v e r s a t i l i t y of the device and render i t very u s e f u l i n analog computer s i m u l a t i o n s t u d i e s . E r r o r analyses of two r e s i s t i v e decoding networks are i i o u t l i n e d and t h e i r r e s u l t s are considered i n the f i n a l choice of the decoding network. Complete c i r c u i t diagrams with short e x p l a n a t i o n s of t h e i r o p e r a t i o n are presented. R e s u l t s of t e s t s on accuracy, speed and general performance are summarized and i l l u s t r a t e d . i i i TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS . . v i ACKNOWLEDGEMENT v i i i 1. INTRODUCTION 1 2. THEORETICAL BACKGROUND 8 2-1. D i g i t a l - A n a l o g Conversion 8 2-2. Decoding Networks ...................... 10 2-3. Network of Weighted R e s i s t o r s .......... 11 2-4. E r r o r A n a l y s i s of the Weighted Network . 15 2-5. Ladder Network 18 2-6. E r r o r A n a l y s i s of the Ladder Network ... 21 2- 7. Summary 29 3. CIRCUIT DESIGN 30 3- 1. Design Philosophy 30 3-2. Shaping C i r c u i t s 34 3-3. T r i g g e r C i r c u i t s 36 3-4. Decoding Network .. 37 3-5. Switching C i r c u i t f o r Channel A ........ 39 3-6. Switching C i r c u i t f o r Channel B ........ 43 3-7. Zero L e v e l Switching ; 43 3-8. Output A m p l i f i e r s . 46 3-9. Power Suppl i e s .......................... 46 3-10. C o n t r o l Panel and D r i v i n g Mechanism .... 49 3- 11. Summary 53 4. TEST RESULTS . 54 4- 1. T e s t i n g the Leve l s I n d i v i d u a l l y ........ 54 4-2. T e s t i n g the Decoding Network 58 i v Page 4-3. T e s t i n g the O v e r a l l Performance 58 4-4. Summary 60 5 . CONCLUSION 62 6. BIBLIOGRAPHY 64 APPENDIX I • Representation of Functions on the Tape .. 65 APPENDIX I I * C o n s t r u c t i o n D e t a i l s .... 74 v LIST OF ILLUSTRATIONS Fi g u r e Page D i g i t a l Representation of an Analog Quantity 9 2. Analog S i g n a l Recovered from D i g i t a l Information 10 3. Network of Weighted R e s i s t o r s ........ 12 4. E q u i v a l e n t C i r c u i t of the Network of Weighted R e s i s t o r s 12 5. Ladder Network f o r B i n a r y Decoding ... 18 6. E q u i v a l e n t C i r c u i t s of the Ladder Net-work 19 7. Ladder Network f o r B i n a r y Decoding ... 21 8. Block Diagram of the Combination F u n c t i o n Generator and M u l t i p l i e r 31 9. D e t a i l s of Tape L e v e l A l l o c a t i o n ..... 33 10. Pulse Shaping C i r c u i t 3 5 11. Generation of T r i g g e r Pulses ......... 36 12. T r i g g e r C i r c u i t 38 13. Decoding Network 39 14. Switching C i r c u i t f o r Channel A 41 15. S a t u r a t i o n C h a r a c t e r i s t i c s f o r the Type 2N398 B T r a n s i s t o r ... 42 16. Switching C i r c u i t f o r Channel B 44 17. Switching of Zero Level 45 18. Output C i r c u i t 47 19. S h o r t - C i r c u i t Proof Regulated Power Supply 48 20. S h o r t - C i r c u i t Proof Regulated Power Supply 50 21. Zener Regulated Power Supply ......... 51 v i F i g u r e Page 22* C o n t r o l Panel with the Tape Drives ..... 52 23* Oscillograms of T y p i c a l Waveforms ...... 55 24. Output Waveforms Showing O v e r a l l Performance 59 25. Example of Coding «. . 65 26. C o n t r o l Panel and Tape Drive ........... 74 27. a) T y p i c a l P r i n t e d C i r c u i t Card ....... 76 b) Wiring Layout f o r the Card i n a) Above 76 28. C o n s t r u c t i o n Phases of the Magnetic Reed Switching U n i t ......................... 77 v i i ACKNOWLEDGEMENT Acknowledgement i s g r a t e f u l l y given to Dr. A. C. Soudack, s u p e r v i s o r of the p r o j e c t , f o r h i s guidance and a s s i s t a n c e . A p p r e c i a t i o n i s expressed to those p r o f e s s o r s , s t a f f members and graduate students of the Department of E l e c t r i c a l Engineering who took p a r t i n d i s c u s s i o n s and o f f e r e d t h e i r h e l p f u l suggestions. In p a r t i c u l a r , many thanks are due to N. Pentland and C. S h e f f i e l d f o r t h e i r able a s s i s t a n c e i n the c o n s t r u c t i o n work. The author i s indebted to the N a t i o n a l Research Council of Canada f o r the a s s i s t a n c e r e c e i v e d under Grant BT—68. 1. INTRODUCTION The a n a l y s i s of complex systems by means of s i m u l a t i o n on a l a r g e s c a l e analog computer has created an ever i n c r e a s i n g demand f o r b e t t e r f u n c t i o n generators. The l a r g e number of d i f f erent generators a v a i l a b l e today i n d i c a t e s the great deal of e f f o r t put i n t o improving the performance of these d e v i c e s . The f u n c t i o n s used i n analog computation are of two b a s i c a l l y d i f f e r e n t types. Those having a monotone i n c r e a s i n g independent v a r i a b l e , such as time, as t h e i r argument represent one k i n d j while the other k i n d may depend on any a r b i t r a r y computer v a r i a b l e . Most f u n c t i o n generators lend themselves to gen e r a t i o n of both types of f u n c t i o n s , but some are l i m i t e d to the g e n e r a t i o n of only one type of f u n c t i o n , f o r example, the diode f u n c t i o n generator which generates f u n c t i o n s of a r b i t r a r y computer v a r i a b l e s , or the p h o t o e l e c t r i c f u n c t i o n generator whic generates time dependent f u n c t i o n s by r e p r e s e n t i n g them on photo graphic f i l m . The l i n e of development of f u n c t i o n generators s t a r t s back i n the days of the mechanical d i f f e r e n t i a l a n a l y z e r , since even i n the age of mechanical computation, people soon r e a l i z e d the need f o r f u n c t i o n g e n e r a t i o n . As a r e s u l t , the s o — c a l l e d (2) i n p u t t a b l e v } a p u r e l y mechanical f u n c t i o n generator, was de v i s e d . The input t a b l e c o n s i s t e d of two p e r p e n d i c u l a r s h a f t s 2 p l a c e d along adjacent edges of a t a b l e . Two p o i n t e r s , one attached to each s h a f t , moved along the s h a f t s at a rate p r o p o r t i o n a l to the r a t e of r o t a t i o n of the corresponding s h a f t . A p l o t of the d e s i r e d f u n c t i o n , say f ( t ) , was placed on the t a b l e . One of the s h a f t s was d r i v e n p r o p o r t i o n a l to the v a r i a b l e t , while the other s h a f t was d r i v e n manually i n such a manner that the i n t e r s e c t i o n of the two p o i n t e r s f o l l o w e d the p l o t of the f u n c t i o n . The p o s i t i o n of the manual s h a f t represented the f u n c t i o n f ( t ) . Since q u a n t i t i e s i n the mechanical d i f f e r e n t i a l a n a l y s e r were represented by s h a f t p o s i t i o n s , i t was an easy matter to couple the input t a b l e to the mechanical computer. The next phase of development was marked by the i n t r o -d u c t i o n of contour potentiometers and tapped potentiometers ^ \ both of which are s t i l l i n use today. The l a t t e r k i n d c o n s i s t s of a l i n e a r tapped potentiometer whose wiper i s u s u a l l y servo— ; set p r o p o r t i o n a l to the v a r i a b l e t . The tap p o i n t s are connected to v o l t a g e s p r o p o r t i o n a l to the r e q u i r e d f u n c t i o n f ( t ) . As the wiper moves along the potentiometer, the p o t e n t i a l on the wiper represents a linear-segment approximation of the f u n c t i o n f ( t ) . In the case of the contour potentiometer the wiper i s s p e c i a l l y shaped so t h a t i t makes contact with the l i n e a r potentiometer at a p o i n t where the p o t e n t i a l i s p r o p o r t i o n a l to the f u n c t i o n f ( t ) . Another v a r i a t i o n of the contour potentiometer i s made by shaping the potentiometer i t s e l f Throughout Chapter One the symbol f ( t ) w i l l mean a f u n c t i o n of t , where t i s e i t h e r an independent v a r i a b l e r e p r e s e n t i n g time, or an a r b i t r a r y computer variable.. 3 a c c o r d i n g to the d e s i r e d f u n c t i o n ( i . e . e x p o n e n t i a l , l o g a r i t h m i c , sine - cosine, e t c . ) . A major disadvantage of the contour potentiometer i s that e i t h e r a s p e c i a l l y shaped potentiometer body or a wiper has to be prepared f o r each f u n c t i o n to be generated. Consequently, the contour potentiometer i s s a t i s f a c t o r y f o r f u n c t i o n g e n e r a t i o n only when the same f u n c t i o n has to be generated r e p e a t e d l y as, f o r example, i n f l i g h t simu-l a t o r s . A s e r i o u s disadvantage of the tapped potentiometer i s the time r e q u i r e d to set up a f u n c t i o n . As the v o l t a g e at a g i v e n tap i s adjusted, i t a f f e c t s the s e t t i n g at every other tap. With experience the excessive set-up time can be reduced c o n s i d e r a b l y . A l s o , s p e c i a l c a l i b r a t i o n equipment and procedures are a v a i l a b l e which help shorten the set-up time, but d i m i n i s h the s i m p l i c i t y and economy of f u n c t i o n generation by potentiometers. Another disadvantage i s low speed, since t h i s type of generator i s semi-mgehanical. Perhaps the best-known of a l l are the diode f u n c t i o n (4) generators . . Containing no mechanical p a r t s they were the f i r s t high-speed f u n c t i o n generators developed. The diode f u n c t i o n generator approximates the d e s i r e d f u n c t i o n by s t r a i g h t -l i n e segments whose slope, and i n most models the break p o i n t s as w e l l , are a d j u s t a b l e . (The i n t e r s e c t i o n of two s t r a i g h t l i n e s i s c a l l e d a break p o i n t ) . In the more expensive models a high—frequency " d i t h e r 1 1 s i g n a l i s used to smooth the sharp break p o i n t s to y i e l d an even b e t t e r approximation to the d e s i r e d f u n c t i o n . Another group of e l e c t r o n i c f u n c t i o n generators makes use (2) of p h o t o e l e c t r i c p r i n c i p l e s . The photoformer i s probably the 4 best known among these d e v i c e s . I t c o n s i s t s of a cathode ray tube (CRT), a mask, and a p h o t o c e l l . The h o r i z o n t a l sweep of the tube i s made p r o p o r t i o n a l to the v a r i a b l e t . The mask i s a p l o t of the d e s i r e d f u n c t i o n f ( t ) with the area below the curve made opaque and the upper p o r t i o n of the mask made tr a n s p a r e n t . The p h o t o c e l l i s pl a c e d i n the path of the beam and the mask i s placed between the tube and the p h o t o c e l l . With the p h o t o c e l l disconnected the b i a s on the v e r t i c a l a m p l i f i e r i s adjusted u n t i l the beam i s d e f l e c t e d to the upper edge of the CRT. The p h o t o c e l l i s then connected i n the b i a s c i r c u i t of the v e r t i c a l a m p l i f i e r i n such a way, that i t s output opposes the b i a s p r e v i o u s l y a p p l i e d , and hence, d e f l e c t s the beam downwards. As the beam reaches the opaque r e g i o n on the mask, the p h o t o c e l l i s cut o f f , and ceases to d e f l e c t the beam any f u r t h e r . Hence the beam w i l l stay at the boundary between the opaque and t r a n s -parent r e g i o n s . Since t h i s boundary i s p l o t t e d as the f u n c t i o n f ( t ) , the volt a g e across the v e r t i c a l d e f l e c t i o n p l a t e s i s p r o p o r t i o n a l to the d e s i r e d f u n c t i o n . The photoformer i s a very high—speed but low—accuracy d e v i c e . In other p h o t o e l e c t r i c f u n c t i o n generators the r e q u i r e d f u n c t i o n f ( t ) i s represented on photographic f i l m by e i t h e r (8) v a r i a b l e d e n s i t y of v a r i a b l e area . The f i l m i s used to i n t e r c e p t the passage of a beam of l i g h t to a p h o t o c e l l . Since the t r a n s m i t t e d l i g h t i s p r o p o r t i o n a l to the f u n c t i o n , the out-put of the p h o t o c e l l represents the d e s i r e d f u n c t i o n f ( t ) , p r o v i d e d the f i l m i s moved according to the v a r i a b l e t . The x-y p l o t t e r type of f u n c t i o n generator i s b a s i c a l l y a mixture of the potentiometer generator and the e a r l y input 5 t a b l e . Here the p l o t of the f u n c t i o n i s t r a c e d by a p h o t o e l e c t r i c pick-up head whose output c o n t r o l s a servomotor which p o s i t i o n s the head above the p l o t . The servomotor also d r i v e s a potentiometer wiper which s u p p l i e s an output vol t a g e p r o p o r t i o n a l to the d e s i r e d f u n c t i o n . In a m o d i f i e d v e r s i o n of the x-y p l o t t e r generator the p l o t i s r e p l a c e d by a c u r r e n t c a r r y i n g conductor, and the p h o t o e l e c t r i c c u r v e - f o l l o w e r i s r e p l a c e d by a magnetic pick-up s t y l u s which senses the magnetic f i e l d set up by the current i n the conductor. The s i g n a l from the pick-up s t y l u s c o n t r o l s a servomotor which, i n t u r n , d r i v e s a p o t e n t i o -meter as i n the p h o t o e l e c t r i c x-y p l o t t e r generator. The most r e c e n t l y developed f u n c t i o n generators i n c o r p o r a t e many d i g i t a l t echniques. Most of the devices d e s c r i b e d i n the l i t e r a t u r e store the d e s i r e d f u n c t i o n f ( t ) i n d i g i t a l form and use a s u i t a b l e method to convert the d i g i t a l . (5) i n f o r m a t i o n i n t o analog form at the output. In one scheme d i s c r e t e values of the f u n c t i o n f ( t ) are s t o r e d on a r o t a t i n g magnetic drum. The values are read from the drum i n the c o r r e c t sequence, and are converted to analog form, the intermediate v a l u e s being produced by l i n e a r i n t e r p o l a t i o n . Another method ( 7 ) i s to store the i n i t i a l value of the f u n c t i o n along with a l a r g e number of subsequent increments. The generation, here, i s done by adding up the increments, i n other words by simple i n t e g r a t i o n . In both methods the argument of the f u n c t i o n i s represented by the r o t a t i o n of the drum. The drum i s u s u a l l y d r i v e n at a constant rate i n which case the o p e r a t i o n i s l i m i t e d to the g e n e r a t i o n of time-dependent f u n c t i o n s only. 6 In the f u n c t i o n generator d e s c r i b e d i n t h i s t h e s i s , d i s c r e t e values of the f u n c t i o n are s t o r e d i n b i i l e r y code on a punched paper tape, which i s read p h o t o e l e c t r i c a l l y . The d i g i t a l output of the tape reader i s converted to analog form by a r e s i s t i v e decoding network s u p p l i e d with a constant b i a s v o l t a g e . The analog output i s h e l d constant u n t i l the next conv e r s i o n o c c u r s . Hence the output i s a s t e p - v o l t a g e approximation of the d e s i r e d f u n c t i o n whose degree of accuracy depends on the i n t e r v a l between conversions and the step s i z e . The l a t t e r i s determined by the number of d i g i t s used i n the b i n a r y code. The device can a l s o be used as a m u l t i p l i e r . I f one f u n c t i o n , say f ^ ( t ) , i s generated i n the manner d e s c r i b e d above and the b i a s v o l t a g e on the decoding network i s v a r i e d a c c o r d i n g to another f u n c t i o n f 2 \ t ) , then the output v o l t a g e i s p r o p o r t i o n a l to f ^ { t ) f£(t), the product of the two f u n c t i o n s . The device c o n s i s t s of two channels. Channel A, which i s coun-p l e t e l y t r a n s i s t o r i z e d , i s f o r f u n c t i o n g e n e r a t i o n , and Channel B, c o n t a i n i n g high-speed magnetic reed switches, serves f o r m u l t i p l i c a t i o n . Tjjie p o s s i b l e modes of o p e r a t i o n of the deviee are as f o l l o w s : a) both channels generate f u n c t i o n s independently a c c o r d -i n g to t h e i r tape i n p u t s , b) channel A generates a f u n c t i o n , say f ^ ( t ) , channel B generates another f u n c t i o n , say f g ( t ) , and m u l t i p l i e s f B ( t ) by f A ( t ) , c) channel A generates a f u n c t i o n , f ^ ( t ) , channel B generates a f u n c t i o n , f g ( t ) , and m u l t i p l i e s f g ( t ) by an a r b i t r a r y e x t e r n a l f u n c t i o n . The ensuing chapters d e s c r i b e the theory, design, c o n s t r u c t i o n , and t e s t i n g of the d e v i c e . 8 •2. THEORETICAL BACKGROUND This chapter i s intended to form the t h e o r e t i c a l ground-work f o r the design procedure d i s c u s s e d i n Chapter 3. Reference w i l l be made to the v a r i o u s s e c t i o n s of t h i s chapter whenever a c e r t a i n step i n the design needs j u s t i f i c a t i o n . For more d e t a i l s i n regard to t o p i c s d i s c u s s e d i n t h i s chapter the reader (9) i s r e f e r r e d to the re f e r e n c e s . . l i s t e d m the b i b l i o g r a p h y . 2-1. D i g i t a l - Analog Conversion In today's e f f o r t to combine the advantages of analog and d i g i t a l techniques, an important l i n k between the two domains i s the process of d i g i t a l — t o — a n a l o g (D/A) and analog-to— d i g i t a l (A/D) conversion. In analog systems, q u a n t i t i e s are represented c o n t i n u o u s l y , while the d i g i t a l r e p r e s e n t a t i o n i n v o l v e s q u a n t i z a t i o n . Consequently, the converted analog s i g n a l can o n l y be an approximation i n the d i g i t a l domain. Consider the analog q u a n t i t y f ( t ) i n F i g . 1* In the d i g i t a l r e p r e s e n t -a t i o n of t h i s q u a n t i t y , two kinds of approximation are i n v o l v e d . Instead of continuous o b s e r v a t i o n , the analog q u a n t i t y i s measured at d i s c r e t e time i n t e r v a l s , a technique which i s c a l l e d sampling. The second k i n d of approximation occurs when the observed value d u r i n g each sampling i s approximated by the ne a r e s t a v a i l a b l e number. This i s c a l l e d q u a n t i z a t i o n . Analog-t o — d i g i t a l c onversion, then, i s nothing e l s e than the process of sampling and q u a n t i z i n g of the analog q u a n t i t y , or, i n more f a m i l i a r terms i t i s a k i n d of pulse modulation as shown by the arrows i n F i g . 1. D i g i t a l — t o - a n a l o g conversion, as the 9 1 1 1 1 1 1 1 1 ! 1 1 1 1 1—1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F i g . 1, D i g i t a l R epresentation of an Analog Quantity name suggests, i s the i n v e r s e p r o c e s s . Here the d i g i t a l i n f o r -mation i s decoded and the analog output i s assumed to have the same value u n t i l the next modulated pulse a r r i v e s . Hence, h o l d -i n g of some s o r t i s r e q u i r e d because the analog world i s continuous,and the value of a sample must be maintained u n t i l the next sample a r r i v e s . F i g . 2 shows the analog s i g n a l obtained from a pulse modulated s i g n a l . The q u e s t i o n a r i s e s : How w e l l can an analog s i g n a l be recovered a f t e r a complete c y c l e of d i g i t a l - a n a l o g conversion? The answer to t h i s q u e s t i o n i s given i n the Sampling and D i g i t a l - t o - a n a l o g conversion i s o f t e n c a l l e d decoding, while coding r e f e r s to a n a l o g - t o - d i g i t a l c onversion. RECOVERED A N A L O 6 S I G N A L DIGITAL REPRESENTATION". F i g . 2. Analog S i g n a l Recovered from D i g i t a l Information Q u a n t i z i n g Theorems which set out the c o n d i t i o n s of complete recovery i n terms of the frequency spectrum of the s i g n a l , the sampling r a t e , and the q u a n t i z a t i o n e r r o r . 2-2. Decoding Networks The b a s i c f u n c t i o n of a decoder i s to produce a v o l t a g e p r o p o r t i o n a l to a number. I f t h i s number i s b i n a r y then we t a l k about a b i n a r y decoder. There are two main groups of decoders. The f i r s t group c o n s i s t s of decoders i n which c o n v e r s i o n i n v o l v e s an intermediate step, u s u a l l y the g e n e r a t i o n of a pulse of some k i n d whose d u r a t i o n i s p r o p o r t i o n a l to the number being decoded. These devices are r e l a t i v e l y slow and complex, but i f a number of conversions have to be done r simultaneously, most of the equipment can be time shared by the v a r i o u s channels. Storage f o r h o l d i n g i n f o r m a t i o n between 11 conversions i s u s u a l l y not needed. The second group, formed by decoders which c a r r y out conversion i n a s i n g l e step, i s c h a r a c t e r -i z e d by s h o r t conversion time and extreme s i m p l i c i t y , but time s h a r i n g i s d i f f i c u l t and storage f o r h o l d i n g i s i n a l l cases r e q u i r e d . Two decoders of the second group w i l l be i l l u s t r a t e d i n the f o l l o w i n g s e c t i o n s . For d e t a i l s on the other types of decoders the reader i s r e f e r r e d to r e f e r e n c e ( 9 ) . 2—3. Network of Weighted R e s i s t o r s Perhaps the simplest method of decoding c o n s i s t s of the s w i t c h i n g of c u r r e n t or v o l t a g e sources i n t o a r e s i s t i v e network i n accordance with the number to be decoded. This method i s i l l u s t r a t e d i n both examples given here. The network of F i g . 3. i s a b i n a r y decoder. Suppose the numbers to be decoded are ( n + l ) - d i g i t b i n a r y numbers of the form P = b b n n-1 Conversion i s performed by s w i t c h i n g the v o l t a g e sources E k (k=0, 1... n) i n such a way t h a t F^ = + E i f b k = 1, and E, = - E i f b, = 0. k k To show t h a t by choosing the r e s i s t o r s r, according to the formula r k ~ ~k" (1) ft •n-l © © © © F i g . 3. Network of Weighted R e s i s t o r s the network i s capable of b i n a r y decoding, consider the e q u i v a l e n t c i r c u i t shown i n F i g . 4, where the voltage sources are assumed i d e a l . Grounding the -E and +E ter m i n a l s i n t u r n and a p p l y i n g the s u p e r p o s i t i o n theorem we can w r i t e : ? ALL 13 • ALL r. F i g . 4» E q u i v a l e n t C i r c u i t of the Network of Weighted R e s i s t o r s 13 - i E out -1 -E (2) where summations are c a r r i e d out over a l l i and j such that = 0 and b. = 1 . Equation (2) can be s i m p l i f i e d to give E out n Rn + Y, r, 0 Q k Combining ( l ) and (3) we o b t a i n 1 ^ E out 1_ 9 n + l R 0 (3) (4) Observe t h a t i f p i s the b i n a r y number corresponding to the s t a t e of the voltage sources, then L, r , L 0 R o (5) since r . stands f o r each of those r e s i s t o r s whose corresponding 14 b i n a r y d i g i t i s 1. Consequently, n y L_ = y i _ _ y L. r ± r k Z_, r , i 1 0 .1 J a, o 2n+l _ 1 - R~ P or 1_ r 0 ~n+l , 2 - p - ,1 (6) Using (4), (5) and (6) we o b t a i n out E 2p + 1 ;n+l - 1 (7) ( 9 ) E q u a t i o n (7) which was d e r i v e d by Susskind , i s a l i n e a r r e l a t i o n between v'^^, the analog output v o l t a g e , and p, the b i n a r y number to be decoded. Note t h a t i f p i s changed by 1, E the output v o l t a g e v . ' o u - j . changes by — e r r o r i s given by A v E out j hence the q u a n t i z a t i o n (8) E q u a t i o n (8) a l s o f o l l o w s from the f a c t , that with n + 1 b i n a r y d i g i t s , a t o t a l of 2 d i f f e r e n t b i n a r y numbers can be formed. A simple examination of equation (7) w i l l show that no b i n a r y i n t e g e r e x i s t s f o r which v ^ = 0. I f E / 0, f o r ^ Q U^. to be zero 2p+l = 2n+^, i . e . p = 2 n -• \ must h o l d . However, since p i s an i n t e g e r the l a s t r e l a t i o n cannot hol d , and hence V Q U ^ . cannot be zero. Hence, a s p e c i a l p r o v i s i o n must be made f o r v , = 0. out 15 Since the r e l a t i o n s h i p between component t o l e r a n c e s and conversion accuracy f o r decoders i s of considerable i n t e r e s t , we w i l l consider the f o l l o w i n g e r r o r a n a l y s i s . 2-4. E r r o r A n a l y s i s of the Weighted Network For the network of weighted r e s i s t o r s , the output v o l t a g e v , i n terms of component values was given by equation (3) out which i s repeated here f o r convenience: E out (9) n R, 0 y -^ r k 0 K D i f f e r e n t i a t i o n of (9) with r e s p e c t to r ^ , r^ and RQ i n t u r n w i l l i n d i c a t e the r e l a t i o n between small changes i n r e s i s t o r values and the r e s u l t i n g changes i n the output v o l t a g e . Thus, n 1 d_ E dr. out I .o 1 -i 1 n 0 0 k which combined with ( l ) , (5) and (6) reduces to d v out E = K . ( p ) dr. r. I (10) where the f a c t o r of p r o p o r t i o n a l i t y K^(p) i s a f u n c t i o n of p 16 and i s giv e n by Equation (10) r e l a t e s the percent e r r o r i n r e s i s t o r r ^ to the corresponding f u l l s c a l e e r r o r i n the output voltage i n terms of the b i n a r y number p f o r the cases when b^ = 0. D i f f e r e n t i a t i o n of (9) with respect to r . y i e l d s a 3 s i m i l a r r e l a t i o n f o r the cases when b. = 1: J d v , dr. - g 2 ^ = K.(p) (12) J where K.(p) i s given by 2 p - 2 n + 2 + 1 K ( p ) . = .... (13) J ^ ( n + l ^ - j F i n a l l y i f (9) i s d i f f e r e n t i a t e d with respect to RQ the f o l l o w i n g r e s u l t i s obtained d v , dR n out = K ( p ) 0 ( 1 4 ) where E - — R Q 2p - 2 n + 1 •+ 1 K ( P ) = 2 2 ( n + l ) ' < 1 5> Equations ( l O ) , (12) and (14) can be s i m p l i f i e d i f tjie c o e f f i c i e n t s Ki(p)> K (p> and K(p) are r e p l a c e d by t h e i r maximum values over the range d e f i n e d by 0 < p < 2n+'1' -1. ¥ith the assumption that 2 » 1 we may s i m p l i f y and combine (10) and (12.) to o b t a i n d v , dr, — 2 S i < —L— (16a) E 2 n - k r k and r e w r i t e (14) as d V o u t s _ ^ E 2 n + 1 R 0 (16b) The i n e q u a l i t i e s given by (16) d e f i n e an upper bound f o r the f u l l s c a l e r e l a t i v e c o n v e r s i o n accuracy i n terms of component t o l e r - . ances. I f equations (10), (12) and (14) are m u l t i p l i e d by E / V q u ^ . , the f o l l o w i n g r e l a t i o n s are obtained;-d v , , dr. out «= ~k k / T T \ - 2 - j - , (17a) V o u t ^ d V o u t = 1 _ ^ 0 v o u t 2 n + 1 R ° (17b) The i n e q u a l i t i e s given by (17) i n d i c a t e an upper bound f o r the r e l a t i v e c onversion accuracy i n terms of component t o l e r a n c e s . The weighting f a c t o r s (powers of two) appearing i n (17) are c l o s e l y r e l a t e d to the place values of the b i n a r y d i g i t s , and t h e r e f o r e i n d i c a t e t h a t the r e s i s t o r a s s o c i a t e d with the most s i g n i f i c a n t b i n a r y d i g i t must be the most accurate. 18 2-5. Ladder Network Our second example of b i n a r y decoders i s shown i n P i g . 5. The process of decoding i s e x a c t l y the same as i n the f i r s t example, i . e . the v o l t a g e sources are switched according to rHWvVfiA/vw riMM t-wwHr '1R 2^R © @ © © © >2R <2R F i g . 5. Ladder Network f o r Bi n a r y Decoding the b i n a r y number to be decoded. To derive the b i n a r y con-v e r s i o n formula, use w i l l be made of the e q u i v a l e n t c i r c u i t s i n F i g . 6, and the v o l t a g e sources w i l l be assumed i d e a l . From F i g . 6, the v o l t a g e at the k^1*1 node due to the k**1 source i s giv e n by E k k,k f o r k = 0, 1, 2 ...n-1 (18a) and E n f o r k - n. (18b) n.n 19 I t f o l l o w s from equation (l8a) that k+l,k 1 2 E k+2,k 1 4 E n - l , k 0 n - l - k a) k = 0,-1. ...n-1 b) k = n F i g . 6. E q u i v a l e n t C i r c u i t s of the Ladder Network R e f e r r i n g to F i g . 6b we may wr i t e the output v o l t a g e due to the i t h -k source alone as E, n,k 2R n - l r k 4 0 n - l - k 20 or - ^ n, k 0n-k+l (19) Comparing (19) with (l8b) we f i n d t h a t (19) holds f o r a l l values of k = 0, l . . . . . . n . . I t remains, then, to f i n d the output v o l t a g e due to a l l sources. This can be found by superimposing the output v o l t a g e s due to the i n d i v i d u a l sources, thus n n out k+1 k=0 k=0 or E out ,n+l \ -i -i / (20) where i and i are such that b. = 0 and b. = 1 . Since I * = and n £v = Y, 2 k - Z 2J = 211+1 • 1 _ p k=0 where p i s the b i n a r y number to be decoded, we have E out ,n+l p - ( 2n + 1 - 1 - p) 21 or v , = E out 2p+l ,n+l - 1 (21) which i s the d e s i r e d r e l a t i o n . Equations (21) and (7) are i d e n t i c a l , and hence, the ladder network,too, i s capable of b i n a r y c o n v e r s i o n . 2-6. E r r o r A n a l y s i s of the Ladder Network In order to c a r r y out the e r r o r a n a l y s i s f o r the ladder network i t i s again necessary to express the output voltage i n terms of the decoding r e s i s t o r s . The network i s redrawn i n -f—MW-ii — R k ' )< * k - i \ ^" o -MY*—I—t—(—MAA f-\AAAA—f I © I +• + fe) r — T Q — r ^ — •..... = r , = 2R, n-1 ' n 2 R Q =-B1 = = R ~ — R, R = — R n-2 ' n-1 2 F i g . 7. Ladder Network f o r Binary Decoding F i g . 7 wi t h the r e s i s t o r s i d e n t i f i e d i n a more convenient way f o r the a n a l y s i s . A^ and are the e q u i v a l e n t r e s i s t a n c e s of the two s e c t i o n s of the ladder as i n d i c a t e d , where t h e i r v a l u e s are giv e n by the c o n t i n u e d - f r a c t i o n expansions k + 1 \ + l + • (22) + r k + 2 B k + 2 + 22 r , B , + r n-1 n-1 n and " k - 1 ^ - 2 + k-2 R k_ 3 + . r l + 0 1_ , 1 * r 0 r The v o l t a g e at the k^1*1 node due to the k^*1 source,E,, i s given by E, I I - + -k 1 B k *k E, k,k r k + >-l r, r. ! + _k + _k A B A k c k 23 and 1 •+ 1 -1 V k + l , k ~ v k , k r k + l Ak+1 E, •k+1 -1 r k r k l + — + — A, + B, k k '1 + r k + l Ak+1 E. k n,k 1 + B kM i + k+l Ak+1 R , R , ! + _£zl + _n=l n n (24) The t o t a l output v o l t a g e i s the sum of the c o n t r i b u t i o n s of the i n d i v i d u a l sources. Hence, n = I V * ( 2 5 ) out k=0 where the v . are given by (24). The e r r o r a n a l y s i s can now be c a r r i e d out by d i f f e r e n t i a t i n g equation (25) with r e s p e c t to r , R and r i n t u r n . Consider the d i f f e r e n t i a t i o n of (25) K i t h s s r e s p e c t to r g f i r s t . We can w r i t e n dr out = 1 k=0 dr n.k' s ' (26) The d e r i v a t i v e s on the r i g h t hand side of equation (26) are obtained from r e l a t i o n (24). I t i s convenient to consider the 24 f o l l o w i n g three cases: case a) s -e k, where -j-j— A-^  : 0, s (27a) case b) s = k, where ^ - j — - B dr k s 0, and (27b) case c s k, where ^ B^ = 0. s (27c) The d i f f e r e n t i a t i o n of equation (24) i s c a r r i e d out u s i n g the general formula d dx abc Case a) -1 abc ,1 da 1 db a dx b dx * (28) dr n i k s * where s«= k t=k R t + R t r t + l At+1 k d Bf^ dr c k k s  ! + JL + JL A B A k B k (29) dr k s B, B, = n 2 dr k-1 Bk-1 s B "k-1 c k - l B 1 + k-1 •k-1 dr Bk-1 s B. 1 + k-1 "k-1 B 1 + k-2 "k-2 dr Bk-2 s . ; 1 i + H 2 ( i + ^ f •••• i + H 2 l i + H r k - l | 1 r k - 2 / I r s + l | I B s / 25 or dr ~k s B,_ = k-1 (30) 1 + r ,2 s B 1 + V 2 t=s+l Equations (30) and (29) can now be combined and s i m p l i f i e d to dr n.k / s s -c k=n E n 3 r s 2 2 ( n - s ) (31a) and dr n.k s ' J s < k«= n E, 3r s 2n+3c - 2s+l (31b) Case b) D i f f e r e n t i a t i o n of (24) wit h r e s p e c t to r g f o r the case s•= k gives E, dr n.k s ' J s=k n-1 t=k 1 + + t r t + l At+1 fk M fk Ak Bk r, r, 1 + + A B A k c k which a f t e r much s i m p l i f i c a t i o n reduces to E _ _ n 4r dr n.k s T J s=k=n and (32a) dr n.k s ' s=k«=n E, 3r 0n-k s 2 (32b) Case c) For the t h i r d case w i t h s =» k the d i f f e r e n t i a t i o n of e q u a t i o n (24) r e s u l t s i n t h e f o l l o w i n g : d r n , k E k_ ' r k d . .2 d r A k A k s r, r , 1 J s ^ k ! + k + J * I A k B k l n-1 t = k + f R + R + i + _ L _ + _ L . r t + i A t f + i 1 + ! k f k A k B k R s-2 d .2 d r ~ k + l A k+1 s \ -k+l Ak+1 ' + . . . . + .2 d r s-1 A , s s—1 Rs _ 2 R s-2' » r s - l s-11 R s-1 R_ .-, R i A 3 ' w h e r e ( 3 3 ) 1 d ^ — A d r A k A, k+1 d r A k+1 s k+1 ~ k + l 1 + ••k+1 : k + l - — A d r A k+1 s 1 + * k + l •k+1 1 + 0 d r A k+2 .2 s +2 k+2 1 + v k + l 'k+1 1 + *k+2 "k+2 1 + k s - l 's-1 1 + r s 27 or dr A k = s 2 s-1 (34) 1 s I IT t=k+l 1 + t A f t e r combining and s i m p l i f y i n g equations (33) and (34) ve o b t a i n dr n.k s ' S - e k s—n E k 1 r _n-k+l s 2 - 1 - + 2. s-k + 4 s-k-1 i = i > (35a) and dr n.k s ' s*k s<n s-k _ i i / i i . + y (I - r g 2n-k+l \3 A s - k • Z, U : lVtl (35b) f =1 I f s u b s t i t u t i o n of equations ( 3 l ) , (32) and (35) i n t o r e l a t i o n (26) i s c a r r i e d out, a f t e r s i m p l i f i c a t i o n the r e s u l t i s d v , , dr, o u t ^ 1 ^ k ( 3 6 a ) E 2 n ~ k + 1 r k D i f f e r e n t i a t i o n of equation (26) w i t h respect to R^ and r produces the f o l l o w i n g r e s u l t s : d v , 1 dR, — ^ S - S I + I r - ( 3 6 b ) E 2 k and d v out 1 dr ( 3 6 c ) E 2 n + 2 r The r e l a t i o n s given by (36) i n d i c a t e the dependence of the f u l l s c a l e conversion accuracy on component t o l e r a n c e s f o r the l a d d e r network. Comparison of r e l a t i o n s (.36) with r e l a t i o n s (16) r e v e a l s that the output voltage of the ladder network i s l e s s s e n s i t i v e to changes i n component values than t h a t of the network of weighted r e s i s t o r s , and t h e r e f o r e , f o r the same degree of conversion accuracy the ladder network r e q u i r e s r e s i s t o r s h a l f as accurate as those i n the weighted network. Consequently the conversion accuracy f o r the ladder network can be d e r i v e d from the r e l a t i o n s i n (17) by making the appr o p r i a t e adjustment by a f a c t o r of two. Thus, d v , -i -i dr, _ _ o u t s 2 k - l _ k ( 3 7 a ) out k and then, comparing (36a) with (36b) and (36c) one obtains d v...x -, dRj^ v — ~ 2 K " 1 ~R7 ( 3 7 B ) o u t K and 1 dr 4 r ' (37c) 29 2-7. Summary In summary, then, both networks are capable of b i n a r y decoding, the accuracy of which depends on the number of decoding r e s i s t o r s and on the t o l e r a n c e s of t h e i r v a l u e s . Furthermore, these t o l e r a n c e s should be weighted by f r a c t i o n s of two as i n d i c a t e d i n (16) and (18) f o r the weighted network and i n (36) and (37) f o r the ladder network. I t was al s o shown t h a t f o r the same t o l e r a n c e s the ladder network i s twice as accurate as the network of weighted r e s i s t o r s . 30 3. CIRCUIT DESIGN 3-1. Design Philosophy The o b j e c t of t h i s work was 1) to i n v e s t i g a t e the use of a d i g i t a l - t o - a n a l o g conversion device as a combination f u n c t i o n generator and m u l t i p l i e r , and 2) to b u i l d and t e s t such a device i f f e a s i b l e . The double-input f u n c t i o n generator was to provide a r b i t r a r y d r i v i n g f u n c t i o n s f o r purposes of analog r e a l - t i m e computation and s i m u l a t i o n . One of the two channels (one corresponding to each input) was to be capable of m u l t i p l i c a t i o n as w e l l as f u n c t i o n g e n e r a t i o n . In order f o r the device to be compatible with analog computer f a c i l i t i e s the standard output range of + 100 v o l t s , with o v e r a l l accuracy of lfo or b e t t e r , was sought. The f i r s t attempt r e s u l t e d i n the b l o c k diagram of the device as shown i n P i g . 8. Channels A and B form the generating channel and m u l t i p l y i n g channel, r e s p e c t i v e l y . Two t w e l v e - l e v e l punched paper tapes provide the d i g i t a l i n put f o r the two channels. The t r i g g e r c i r c u i t s d r i v e n by the incoming d i g i t a l i n f o r m a t i o n a c t i v a t e the s w i t c h i n g and decoding networks which i n t u r n produce analog v o l t a g e s corresponding to the hole and no-hole combinations read by the p h o t o e l e c t r i c r e a d e r s . The two channels d i f f e r from each other i n the method of sw i t c h i n g and the b i a s v o l t a g e across the decoding network. In Channel A t r a n s i s t o r switches are used to connect the proper b i a s v o l t a g e s to the decoding network. For -Jl LU < O CQ S P E E D CONTROL ~J \ Ul T A P E D R I V E < l * X fl(t) T A P E DRIVE f.(t) PHOTO-ELECTRIC READER PHOTO-ELECTRIC READER TRIGGER CIRCUITS g(t) HIGH-SPEED RELAY SWITCHING A N D DECODING NETWORK -Sf(t) + E TRIGGER CIRCUITS ! So L i b "STATE • V SWITCHING AND DECODING NETWORK SPEED CONTROL - E GAIN CONTROL OUTPUT A M P L I F I E R S OUTPUT AMPLIFIERS J GAIN CONTROL — > Figo 8. Block Diagram of the Combination Function Generator and Mu l t i p l i e r f u n c t i o n g e n e r a t i o n the b i a s i s + E v o l t s , where E i s a constant. In the case of m u l t i p l i c a t i o n the b i a s across the decoding network has to vary a c c o r d i n g to the m u l t i p l i c a n d which i n t u r n may change s i g n . In t h i s case high—speed r e l a y s , which are i n s e n s i t i v e to changes i n p o l a r i t y , have to be used instead; of t r a n s i s t o r switches. Channel B can a l s o be used to generate f u n c t i o n s p r o v i d e d the b i a s across the decoding network i s h e l d constant ( i . e * g ( t ) = c o n s t a n t ) . The speed and gain c o n t r o l s add a great deal of v e r s a t i l i t y to the device because they provide means of v a r y i n g the time s c a l e and magnitude of the generated f u n c t i o n . The dotted l i n e connecting the two blocks l a b e l l e d TAPE DRIVE i n P i g . 8 i n d i c a t e s p r o v i s i o n f o r s y n c h r o n i z a t i o n between the two independent channels. At t h i s p o i n t , with the general o u t l i n e of the f u n c t i o n generator and m u l t i p l i e r i n the background, we are ready f o r the f i r s t step towards the r e a l i z a t i o n of our b l o c k diagram. F i g . 9 shows the middle b l o c k of the channels i n F i g . 8 i n somewhat more d e t a i l . The diagram shows how the twelve a v a i l a b l e l e v e l s of the tape are assigned. One l e v e l (No. 12) i s used to generate c l o c k pulses f o r the purpose of s y n c h r o n i z a t i o n between the v a r i o u s l e v e l s . Nine l e v e l s (Nos. 1 to 9 ) , each corresponding to a b i n a r y d i g i t , are reserved f o r the p o i n t value r e p r e s e n t a t i o n of the d e s i r e d f u n c t i o n . One of the remaining two l e v e l s (No. 10) p r o v i d e s zero output, s i n c e , as i t was shown i n Chapter 2, no q u a n t i z a t i o n l e v e l c o i n c i d e s w i t h zero, and hence, an e x t r a l e v e l i s r e q u i r e d to ground the output d i r e c t l y whenever zero output i s c a l l e d f o r . F i n a l l y the l a s t l e v e l (No. l l ) generates c o n t r o l p u l s e s which provide communication between the generator and the SHAPING CIRCUITS TRIGGER CIRCUITS SWITCH IMG CIRCUITS F R O M T A P E P H O T O -E L E C T R I C R £ A D S.R LEVEL I LEVEL 2 LEVEL 9 LEVEL 10 L E V E L L E V E L 12 ( C L O C K ) B I T O B I T I BIT e Z E R O CONTROL B I T 0 BIT I BIT 8 ZERO DECODING NETWORK T O OUTPUT A M P L 1 F I E R S >• TO C O M P U T E R >-' F i g . 9. D e t a i l s of Tape L e v e l A l l o c a t i o n 34 computer. The b i n a r y code f o r r e p r e s e n t i n g f u n c t i o n s i s given i n Table 1 i n Appendix I where the use of the t a b l e i s i l l u s t r a t e d by an example. The f u n c t i o n s of the v a r i o u s blocks i n F i g ^ 9 are as f o l l o w s . When the reader senses a hole i n a p a r t i c u l a r l e v e l on the tape i t sends a pulse to the corresponding shaping c i r c u i t which produces a square pulse with short r i s e and f a l l times. The c o n t r o l pulse de-energizes the h o l d and r e s e t r e l a y s i n the computer, and hence i n i t i a t e s the compute mode. The nine b i t pulses and the z e r o - l e v e l pulse are combined with the c l o c k pulses i n the t r i g g e r c i r c u i t s which produce nine t r i g g e r pulse t r a i n s of evenly spaced sharp pulses synchronous with the l e a d i n g edges of the square c l o c k p u l s e s . The p o l a r i t y of the p u l s e s changes according to the i n f o r m a t i o n r e c e i v e d from the tape. I f a hole i s observed i n a l e v e l the corresponding t r i g g e r c i r c u i t sends a p o s i t i v e p u l s e , and i n the absence of a hole i t generates a negative p u l s e . S i n g l e - s i d e d t r i g g e r i n g of the f l i p - f l o p s i n the s w i t c h i n g c i r c u i t s then r e s u l t s i n a one-to-one correspondence between the presence or absence of holes and the s t a t e of the f l i p — f l o p s . The f i n a l step: i n o b t a i n i n g the analog output i s to switch the v o l t a g e sources i n accordance with the s t a t e of the f l i p - f l o p s . The f o l l o w i n g s e c t i o n s deal with c i r c u i t s designed to . perform f u n c t i o n s c a l l e d f o r i n the b l o c k diagram r e p r e s e n t a t i o n . 3-2. Shaping C i r c u i t s The shape of the pulses generated by the l i g h t sensors depends a great d e a l on the speed of the paper tape. As the hole approaches the l i g h t sensor the amount of t r a n s m i t t e d l i g h t 35 i n c r e a s e s g r a d u a l l y , a t t a i n s a maximum, and then again f a l l s down te a minimum. Consequently, the p h o t o e l e c t r i c response has s i m i l a r r a t h e r poor r i s e and f a l l time c h a r a c t e r i s t i c s which have to be improved by pulse shaping. The shaping c i r c u i t (see F i g , 10) c o n s i s t s of a Schmidt t r i g g e r (formed by T 2 and T^) and an input t r a n s i s t o r (T^) which i s turned on when only the dark c u r r e n t i s f l o w i n g , and i s turned o f f by the l i g h t c urrent due to a h o l e . The d e c i s i o n l e v e l of the Schmidt t r i g g e r i s set LS = Type LS222 L i g h t Sensor R 2 = 4*7K R 6 = 47K T 1 , T 2 * T 3 = Type 2N1304 R 3 = 10K R 7 = 100K C = 0.01 |if R 4 = 47K R g .= 4.7K R l = 50K R 5 = 4.7K V cc = +6 v o l t s F i g . 10. Pulse Shaping C i r c u i t 36 between the two extreme valu e s of the c o l l e c t o r v o l t a g e of , and hence, the output of the shaping c i r c u i t i s a f a s t r i s i n g and f a l l i n g square pulse c o i n c i d e n t with, but somewhat narrower than, the input p u l s e . The pulse width at the output can be a d j u s t e d by R^, since the degree of s a t u r a t i o n of T^, depends on the b i a s set by R^  and R^r which a l s o determines the amount of l i g h t r e q u i r e d to b r i n g T^, out of s a t u r a t i o n . 3—3« T r i g g e r C i r c u i t s The g e n e r a t i o n of t r i g g e r pulse t r a i n s can best be understood from the b l o c k diagram i n P i g . 11 where the method of combining the c l o c k pulses w i t h the b i t pulses from a p a r t i c u l a r l e v e l i s shown. By means of the pulse width adjustment d e s c r i b e d i n the previous s e c t i o n the b i t pulses are made to overlap the JUUIMJL CLOCK PULSES BIT PULSES N A N O DIFFERENTIATE AND CLIP 1 INHIBIT A DIFFERENTIATE AND CLIP 11 J l F i g . 11. Generation of T r i g g e r Pulses c l o c k pulses i n d u r a t i o n so that the output pulses of a l l the NAND and INHIBIT c i r c u i t s are synchronized to the l e a d i n g edges of the c l o c k p u l s e s . The waveforms shown at key-points i n F i g . 11 make any f u r t h e r e x p l a n a t i o n unnecessary. In the c i r c u i t diagram of the t r i g g e r pulse generator ( F i g . 12) the diodes D^ and along with t r a n s i s t o r T^ perform the NAND f u n c t i o n , while T 2, D,-, and D^ make up the INHIBIT c i r c u i t . The pulses are d i f f e r e n t i a t e d by C^R^ and C ^ ^ l l ' c l i p P e ( l by and D^Dg, then added by R^ and R- 2^* a n c ^ f i n a l l y a m p l i f i e d by T-j. 3—4, Decoding Network Although the p a r t immediately f o l l o w i n g the t r i g g e r c i r c u i t i s the switching c i r c u i t , i t i s more convenient to di s c u s s the decoding network f i r s t and then f i l l i n the gap between the t r i g g e r c i r c u i t and the decoding network. We have alr e a d y s t a r t e d comparing the two b i n a r y decoders i n t r o d u c e d i n the previous chapter, where i t was found that the ladder network was more accurate than the network of weighted r e s i s t o r s . From the c i r c u i t designer's p o i n t of view the ladder network has a d d i t i o n a l d e s i r a b l e p r o p e r t i e s f o r which i t was chosen over the other network* One such advantage i s that each of the sources, E^, sees the same e q u i v a l e n t r e s i s t a n c e , which i s not t r u e f o r the weighted network* Another u s e f u l property of the ladder network i s that i t s component values are of the same order of magnitude. P r e c i s i o n r e s i s t o r s w i t h a wide range of values as r e q u i r e d f o r the weighted network would be: very expensive and troublesome to o b t a i n * The network i s redrawn i n F i g , 13 with a l l component and t o l e r a n c e values shown. The 38 F i g . 12. T r i g g e r C i r c u i t = 12K R g = 8.2K R15 = 27K R 2 = 100K R 9 = 18K CV°2 = 0.002 (if R 3 = 18K R 1 0 = 12K D1 to D8 = T y P e 1N34A diodes R 4 = 8.2K R l l = 47K T1!T2 = Type 2N1304 t r a n s i s t o r s R 5 = 47K R 1 2 = 22K T3 = Type 2N1381 t r a n s i s t o r R 6 = 22K R l 3= 470K ^ c c l = +6 v o l t s R 7 = 100K R 1 4 = 1.5K V c c 2 = -40 v o l t s 39 t o l e r a n c e values are commercially a v a i l a b l e values nearest to those obtained from i n e q u a l i t i e s (37) i n which a r e l a t i v e accuracy of 0,5$ i n the output v o l t a g e was assumed. - v w - v v — >k-l 0 = 10K, 1$ r = 10K T 2% = 10K, R Q = 5K, 1$ 2 •= 10K, .25$ R l - 5K, .5$ 3 = 10K, • 196 *2 = 5K, .25$ 4 = 10K, .05$ R 3 = 5K, .1% 5 = 10K, .02$ R4 = 5K, .05$ 6 - 10K, .01$ R5 = 5K, .02$ 7 = 10K, .005$ :R6 = 5K, .01$ 8 = 7*5K, .005% :B7 = 2.5K, .005$ F i g . 13. Decoding Network 3—5. Switching C i r c u i t f o r Channel A To provide the source v o l t a g e s y E^, i n F i g . 13 we requi r e a c i r c u i t a c t i v a t e d by the t r i g g e r pulses that w i l l give at i t s 40 output e i t h e r + E or - E v o l t s depending on the s i g n of the t r i g g e r p u l s e s . In a d d i t i o n to t h i s , the c i r c u i t should ho l d i t s output constant u n t i l the next change i n the s i g n of the t r i g g e r pulses occurs. The c i r c u i t of F i g . 14 f u l f i l s both of these requirements. The b i s t a b l e m u l t i v i b r a t o r ( f l i p - f l o p ) c o n s i s t i n g of T-^  and i s t r i g g e r e d at the base on one s i d e , and hence changes i t s s t a t e only when the s i g n of the t r i g g e r pulses changes. The c o l l e c t o r voltage of the opposite side i s coupled to the t r a n s i s t o r p a i r T-j, T^ which provide turn-on and t u r n - o f f currents f o r the sw i t c h i n g t r a n s i s t o r s Tj- and T^. Depending on the state of the f l i p - f l o p , T,_ and T^ can be e i t h e r i n the ON or OFF s t a t e s , but not i n the same state .?' simultaneously. I d e a l l y , the output voltage i s + E v o l t s when T i - i s on, and - E v o l t s when T^ i s on. In p r a c t i c e , however, due to the non-zero s a t u r a t i o n v o l t a g e of the t r a n s i s t o r s the output volt a g e w i l l only approximate the supply v o l t a g e s + E , The e r r o r can be made r e l a t i v e l y small by choosing as la r g e a value f o r E as the maximum V^-g, and V^g r a t i n g s of t r a n s i s t o r s T,- and T^ all o w . The s a t u r a t i o n v o l t a g e , or i n other words, the e r r o r i t s e l f can be decreased by d r i v i n g the t r a n s i s t o r s w e l l i n t o s a t u r a t i o n , and a l s o by op e r a t i n g them i n the i n v e r t e d mode. In Fig» 15 average s a t u r a t i o n c h a r a c t e r i s t i c s f o r the type 2N398B t r a n s i s t o r (Tj- and T^) are shown. According to the curves, f o r the same loa d and base currents the s a t u r a t i o n voltage f o r small load currents i n the i n v e r t e d mode i s c o n s i d e r a b l y l e s s than that i n the normal mode. Design va l u e s f o r the base d r i v e c u r r e n t s were obtained from the s a t u r a t i o n c h a r a c t e r i s t i c s as f o l l o w s . Vhen T,. i s on, the output current f l o w i n g i n t o the * ~ " ~~ ' In the i n v e r t e d mode the r o l e s of the emitter and c o l l e c t o r are i n t e r changed. F i g . 14. Switching C i r c u i t f o r Channel A B l = 150K R g = 82K C c = 0.1 pf R 2 = 560K R 9 = 27K C1' C2 = 0.001 fif R 3 = 33K R10= 12K T1' T2 = Type 2N1304 t r a n s i s t o r s E 4 = 22K R l l = 180K T3 = Type 2N1381 t r a n s i s t o r B 5 = 8.2K R 1 2 = 6.8K = Type 2N398B t r a n s i s t o r s B 6 = 150K B l 3 = IK ^ c c l = -40 v o l t s R 7 = 560K R 1 4 = IK cc2 = +40 v o l t s E = 25 v o l t s Fig« 15« S a t u r a t i o n C h a r a c t e r i s t i c s f o r the Type 2N398B T r a n s i s t o r ro decoding network, which has an e q u i v a l e n t input impedance of 15K, i s 25v/l5K or 1.67 ma. From the curves i n F i g . 15 a base d r i v e of 2 ma with a load c u r r e n t of 1.67 ma r e s u l t s i n l e s s than 25mv s a t u r a t i o n v o l t a g e which represents an e r r o r of approximately 0.1$ of the output value of 25 v o l t s . When i s on, the output c u r r e n t i s again 1.67 ma fl o w i n g i n t o the c o l l e c t o r of T^, but the loa d c u r r e n t i s only 1.67 ma l e s s the base d r i v e c u r r e n t . By t r i a l and e r r o r one f i n d s that a base d r i v e of 0.8 ma ( i . e . a l o a d c u r r e n t of 0.87 ma) y i e l d s an e r r o r comparable to that i n t r o d u c e d across T^ .. 3-6. Switching C i r c u i t f o r Channel B Ve already know th a t i n the m u l t i p l y i n g channel the r o l e of the constant sources of + 25 v o l t s i s taken by v a r i a b l e v o l t a g e s , say + g ( t ) . I t i s immediately apparent that the t r a n s i s t o r switch of F i g . 13 cannot work i n t h i s case since the c o l l e c t o r supply, g ( t ) , changes i n both magnitude and s i g n . In F i g . 16 t r a n s i s t o r s T,. and are r e p l a c e d by high—speed magnetic read switches, which e l i m i n a t e the need f o r t r a n s i s t o r s and as w e l l . The f l i p - f l o p (T-^  and T^) i s s t i l l present,, and holds the i n f o r m a t i o n between conversions^ as b e f o r e . The f i e l d c o i l s of the reed switches appear d i r e c t l y i n the c o l l e c t o r c i r c u i t s , and hence, the switches are a l t e r n a t i v e l y c l o s e d or open according to the st a t e of the f l i p - f l o p . D e t a i l s about the c h a r a c t e r i s t i c s and p r e p a r a t i o n of the f i e l d c o i l s are given i n Appendix I I . 3—7. Zero-Level Swtiching Ve have seen that a weakness of the r e s i s t i v e decoding 44 FROM TRIGGER CIRCUIT { '1 TO D E C O D I N G N E T W O R K R l = 3.3K R 5 = 820 FC 1 , F C 2 R 2 .= 820 R 6 = 3.9K T l > T2 = R 3 = 3.9K C l = 1 |if V cc R 4 = 3 3 c 2 , c 3 = 0.02 (if = F i e l d c o i l of reed switch Type 2N1381 t r a n s i stor F i g , 16. Switching C i r c u i t f o r Channel B networks i s the i n a b i l i t y to give a zero l e v e l output when used as a dual p o l a r i t y decoder (range of +E v o l t s ) . In cases when the f u n c t i o n to be generated only crosses the zero l e v e l t h i s i s not a.disadvantage because the conversion time, i n general, w i l l not c o i n c i d e w i t h the time of c r o s s i n g . However, when the f u n c t i o n takes on the zero value over a number of conversion i n t e r v a l s i t may be d e s i r a b l e to have p r o v i s i o n f o r zero l e v e l decoding. The use of an e x t r a l e v e l on the tape serves t h i s purpose ( F i g * 17). T r i g g e r pulses are generated the same way as 45 FROM SWITCHING C I R C U I T S A A A / 1[ "FROM ZERO TRIGGER DE-CODING NETWORK O U T P U T A M P L I F I E R OUT R l = 3.3K R 5 = 820 C 2 ' C 3 = 0.02 [if B. = 820K = 3*9K FC = F i e l d c o i l of reed switch = 3.9K R 7 = 82 T1' T2 = Type 2N1381 t r a n s -i s t o r s R 4 = 33 C l = 1 ixf V cc = -6 v o l t s F i g . 17. Switching of Zero L e v e l f o r the other b i t l e v e l s . Vhen a hole appears i n the zero l e v e l on the tape a p o s i t i v e going pulse from the zero t r i g g e r turns t r a n s i s t o r T^ o f f and on* and hence the reed switch c l o s e s and grounds the output a m p l i f i e r * As soon as the holes i n the zero l e v e l are absent the t r i g g e r pulses change s i g n , turns o f f and the ground i s removed from the output a m p l i f i e r . The c i r c u i t of F i g . 17 a p p l i e s f o r both channels A and B. 46 3-8. Output A m p l i f i e r s The requirements imposed on the output a m p l i f i e r s are t h r e e - f o l d . They should: ( i ) convert the r e l a t i v e l y high: output impedance o f f e r e d by the decoding networks to a low v a l u e , ( i i ) have a v a r i a b l e gain i n order to enhance the v e r s a t i l i t y of the device, ( i i i ) have c a l i b r a t e d f i x e d gains to y i e l d an output range of e x a c t l y + 100 v o l t s . F i g . 18 i l l u s t r a t e s the i n t e r c o n n e c t i o n of Channels A and B w i t h the three s t a b i l i z e d D.C. a m p l i f i e r s G^, G^, G^, o f t e n known as computing a m p l i f i e r s . Besides meeting the above requirements, these a m p l i f i e r s (except G 2 ) must a l s o be capable of d e l i v e r i n g a c u r r e n t of at l e a s t 8.5 ma which i s the r e q u i r e d d r i v e f o r the decoding network of channel B. Switches a, b, c, d and e are s e c t i o n s of a r o t a r y s e l e c t o r switch ( F i g . 22) which s e l e c t s the mode of o p e r a t i o n f o r the d e v i c e . The output range of + 100 v o l t s f o r both channels A and B i s adjusted by R^Q and R^, r e s p e c t i v e l y , with the SELECT switch i n p o s i t i o n 1 and the potentiometers R^ and Rj- set at 0.25. The SELECT switch i s then moved to p o s i t i o n 3 and Rj i s adjusted u n t i l the output range of channel A i s + 25 v o l t s . 3-9. Power Supp l i e s Except f o r the high-voltage sources f o r the a m p l i f i e r s which are s u p p l i e d by an e x t e r n a l power source, a l l v o l t a g e s are provided by i n t e r n a l power s u p p l i e s . The f i r s t of these ( F i g . 19) 47 -+25" FROM TAPS vWW- OUT EXTERNAL MULTIPLICAND ±25 /OttS MAX, + 25" C H A N N E L A R6 V -25 OUT B^,B^ = 100K, 1 0 - t u r n potentiometer R 2 , R 3 , R 6 , R G , R 9 = 10M, 1 $ r e s i s t o r R^JR^.,R^Q= 500K, v a r i a b l e r e s i s t o r B 1 1 , R 1 2 = 1 0 M ' ^ r e s i s t o r ^1*^2'^3 = High g a i n D.C. a m p l i f i e r s a,b fc fd,e = Sections of r o t a r y switch F i g . 18. Output C i r c u i t - 4 0 V O L T S (APPROX.) F i g . 19. S h o r t - C i r c u i t Proof Regulated Power Supply Type 1N2484 r e c t i f i e r diodes Type 1N1366A Zener diode Type 1N936 Zener diode Type BZT66 Zener diode Type 2N144 t r a n s i s t o r Type 2N13G4 t r a n s i s t o r Type 2N1381 t r a n s i s t o r Hammond 167U transformer 5 b , 2 watt D 1,D 2,D 3,D 4 390 ZD r 10K ZD 2 5.6K ZD 3 IK v a r i a b l e T l 10K v a r i a b l e T, 2 4 1000 | i f 5 0 WDC TX 1.8K T 3 , T 4 49 p r o v i d e s -40 v o l t s and -25 v o l t s . The full-wave r e c t i f i e r b r idge with c a p a c i t i v e output provides approximately -52 v o l t s d.c. which i s stepped down to approximately -40 v o l t s by the Zener diode r e g u l a t o r (ZD^). The r e s t of the c i r c u i t i s a feedback r e g u l a t o r p r o v i d i n g e x a c t l y -25 v o l t s f o r the decoding network b i a s . The low temperature c o e f f i c i e n t Zener diode ZD 2 i s the r e f e r e n c e element. The output v o l t a g e i s compared with the r e f e r e n c e by the d i v i d i n g r e s i s t o r s R^f Rj, and by the d i f f e r e n t i a l a m p l i f i e r T^, T^, Any unbalance i s f e d back to the s e r i e s r e g u l a t o r t r a n s i s t o r s T 2» T-^  which c o r r e c t the output v o l t a g e i n the d i r e c t i o n to r e s t o r e the balance. The output v o l t a g e i s a d j u s t a b l e by r e s i s t o r s and R^ ,. For low output c u r r e n t s good r e g u l a t i o n i s assured by the "keep a l i v e " c u r r e n t s through r e s i s t o r s R^ and R^. The value of R^ determines the c u r r e n t l i m i t a t i o n which i s an i n h e r e n t f e a t u r e of the c i r c u i t . The low output impedance at the —25 v o l t t e r m i n a l s ( l e s s than 0,1 ohm) which appears e f f e c t i v e l y i n s e r i e s with the decoding r e s i s t o r s i s low enough to have n e g l i g i b l e e f f e c t on the accuracy of conversion. The c i r c u i t of F i g . 20 which provides +40 v o l t s and +25 v o l t s i s i d e n t i c a l to i t s counterpart i n F i g . 19 except that p o l a r i t i e s and diodes are r e v e r s e d and type PNP t r a n s i s t o r s are r e p l a c e d by type NPN. One of the two i d e n t i c a l power s u p p l i e s p r o v i d i n g +6 and -6 v o l t s i s shown i n F i g . 21. 3-10* C o n t r o l Panel and D r i v i n g Mechanism With the a i d of the schematic diagram of the c o n t r o l panel See r e f e r e n c e (3), pp. 215-218. VOLTS (APPROX.) F i g . 20. S h o r t - C i r c u i t Proof Regulated Power Supply R 56 , 2 watt D 1 ' D 2 ' D 3 ' D 4 = Type 1N2484 r e c t i f i e r diodes R 2 = 390 : 1N1366AR Zener diode B 3 t B 4 10K ZD 2 Type 1N936 Zener diode R 5 = 5.6K ZD 3 - Type BZY66 Zener diode R 6 = IK, v a r i a b l e T l = Type 2N143 t r a n s i s t o r R 7 10K v a r i a b l e T2 • = Type 2N1381 t r a n s i s t o r R 8 1.8K T 3 , T 4 = Type 2N1304 t r a n s i s t o r C 1000 u.f, 50 WDC TX = Hammond 167U transformer 51 R = C = T l -T„ = 560 2000 [if, 50 WVDC Type 2N1073 t r a n s i s t o r Type 2N600 t r a n s i s t o r D ,D ,D ,D = Type 1N1218 ^ r e c t i f i e r diodes ZD = Type BZI66 Zener diode TX = Hammond Z10E Transformer F i g . 21. Zener Regulated Power Supply ( F i g , 22) we s h a l l now d i s c u s s the v a r i o u s modes of o p e r a t i o n of the d e v i c e . The two b l o c k s marked A and B are the reading heads f o r channels A and B, r e s p e c t i v e l y , and c o n t a i n the l i g h t sensors (lower h a l f ) and the l i g h t source (upper h a l f ) . The sprocket wheels A-^ , A 2 and B^ are d r i v e n by two 2-phase servo, motors with tachometer feedback to ensure constant, s l i p — f r e e motion of the tapes, A-^  and B^ are mech a n i c a l l y coupled and are d r i v e n by one motor (synchronous operation) while the other motor d r i v e s k^. G E N INT MULT CHANNEL A EXT MULT ON A M P L I T U D E 'COARSE SPEED OFF FINE CHANNEL B -B-( § ) 9 OFF A M P L I T U D E COARSE OUT CONT CONT OUT o o SPEED FINE o o o E X T IN o o i i — < - - \ B / p \ \ F i g . 2 2 . Control Panel with Tape D r i v e r s U l t o 53 The input tape of channel B i s always d r i v e n by sprocket B_^ , while the other tape may be engaged i n e i t h e r A-^  ( f o r synchronous operation) or i n A 2 ( i f independent speeds are d e s i r e d ) . The modes of o p e r a t i o n s e l e c t e d by the t h r e e - p o s i t i o n SELECT switch are the f o l l o w i n g . GEN. Both channels generate f u n c t i o n s according to t h e i r tape input ( f ^ ( t ) , f g ( t ) ) . INT. MULT. Channel A generates f ^ ( t ) ; Channel B generates f g ( t ) and m u l t i p l i e s the two f u n c t i o n s together. EXT. MULT. Channel A generates f ^ ( t ) ; Channel B generates f-g(t) and m u l t i p l i e s f g ( t ) by the e x t e r n a l f u n c t i o n i n t r o d u c e d at EXT, IN. The output of each channel and the control, p u l s e s f o r de-energ-i z i n g the r e s e t r e l a y i n the computer are brought out at the upper r i g h t corner of the pan e l * 3—11. Summary A general o u t l i n e of the device was presented i n the form of a block diagram. C i r c u i t s to perform according to i n i t i a l s p e c i f i c a t i o n s were designed, and were i n t e r c o n n e c t e d according to s e c t i o n 3-1, ( F i g . 9 ) . The r e s u l t s of v a r i o u s t e s t s conducted on the i n d i v i d u a l l e v e l s and on the complete device as a whole are di s c u s s e d and i l l u s t r a t e d i n the f o l l o w i n g chapter. 54 4. TEST RESULTS 4-1* T e s t i n g the L e v e l s I n d i v i d u a l l y In order to s i m p l i f y the t e s t i n g procedure, each l e v e l was i s o l a t e d and t e s t e d s e p a r a t e l y * The f i r s t step was to ad j u s t the shaping c i r c u i t of each l e v e l i n c l u d i n g the c l o c k pulse l e v e l (No* 12), as e x p l a i n e d i n s e c t i o n 3-2. The purpose of these adjustments was to make the s i g n a l pulses s l i g h t l y wider than the c l o c k p u l s e s * This i s r e q u i r e d f o r proper s y n c h r o n i -z a t i o n of the t r i g g e r pulses of the v a r i o u s l e v e l s . The o s c i l l o g r a m s i n F i g . 23 show t y p i c a l waveforms observed d u r i n g the p r e l i m i n a r y t e s t s on the s i g n a l l e v e l s . In F i g . 23a the reshaped c l o c k pulses ( l e v e l 12) and s i g n a l pulses of l e v e l 2 are d i s p l a y e d . In t h i s p a r t i c u l a r case the hole p a t t e r n i n l e v e l 2 on the tape was p e r i o d i c * ***110011001100.••• where the numbers 1 and 0 s i g n i f y the presence and absence of h o l e s , r e s p e c t i v e l y . The s i g n a l p u l s e s i n F i g . 23a are indeed wider than the c l o c k pulses and they f o l l o w the same p a t t e r n as the holes on the tape. F i g . 23b shows the s i g n a l pulses of l e v e l 2 with the output of the a s s o c i a t e d s w i t c h i n g c i r c u i t i n channel A« This output i s the, source v o l t a g e (see F i g . 13). I t i s seen i n F i g * 23b t h a t the p o l a r i t y of the source v o l t a g e changes i n accordance with the presence or absence of h o l e s . The corresponding waveform f o r channel B i s shown i n F i g . 23c. The small dots at the d i s c o n t i n u i t i e s manifest the r e l a t i v e l y long s w i t c h i n g time of the magnetic reed c o n t a c t s . In r e a l i t y , at any d i s c o n t i n u i t y there i s onl y one dot, but, since a single—sweep Clock pulses ( l e v e l 12) a f t e r shaping (approx* 200 pulses per second) S i g n a l pulses ( l e v e l 2) a f t e r shaping Output of the switching c i r c u i t A s s o c i a t e d s i g n a l pulses Channel A (Level 2) Output of the switching c i r c u i t A s s o c i a t e d s i g n a l pulses Channel B (Level 2) 56 t r a c e d i d not leave an adequate impression on the photographic f i l m , m u l t i p l e exposure had to be used which r e s u l t e d i n the c o l l e c t i o n of dots at each of these places on the f i l m . The waveforms of F i g . 23 were recorded at a tape speed of approximately 200 cha r a c t e r s per second (ch/sec) but s i m i l a r o b s e r v a t i o n s were made over the range from 50 ch/sec to 500 ch/sec. F u r t h e r i n c r e a s e i n tape speed was l i m i t e d by the d r i v i n g mechanism. The next"step was to make measurements on the speed and accuracy of the i n d i v i d u a l l e v e l s : a) Channel A Even at a tape speed of 500 ch/sec, which i s the upper l i m i t set by the d r i v i n g mechanism, the sw i t c h i n g time of the t r a n s i s t o r s (a few u.sec) i s at l e a s t two orders of magnitude sma l l e r than the con v e r s i o n i n t e r v a l of 2 msec, corresponding to t h i s maximum tape speed. Consequently, the switching tiijie can be assumed n e g l i g i b l e . In Channel A i t i s the s a t u r a t i o n v o l t a g e across the s w i t c h i n g t r a n s i s t o r s t h at may l i m i t the q u a l i t y of the o v e r a l l performance. Measured values of s a t u r a t i o n v o l t a g e s ranged from 5mv to 20mv i n the o f f st a t e (—25 v o l t output) and from 15mv.to 25mv i n the on st a t e (+25 v o l t output), which agreed v e r y w e l l with design v a l u e s . b) Channel B Again, only one measurement i s important, but t h i s time i t i s the o b s e r v a t i o n of the sw i t c h i n g speed. The t r a n s i t i o n from one st a t e to the other was observed to take place i n l e s s than 300 u.sec ( i n c l u d i n g bounce) w i t h a maximum time delay of 200 (xsec. Both the t r a n s i t i o n time and the delay time have un— 57 d e s i r a b l e consequences, namely j. they introduce sharp spikes i n the generated f u n c t i o n . For an i d e a l r e p r o d u c t i o n of the f u n c t i o n the switches have to change t h e i r s t a t e i n s t a n t a n e o u s l y and with no time delay* I f each switch i s delayed by the same amoTj^rj;, but acts i n s t a n t a n e o u s l y * the f u n c t i o n w i l l s t i l l be t r u l y reproduced but with a time delay equal to t h a t of the s w i t c h e s . The time delays f o r the read switches are not n e c e s s a r i l y the same f o r each u n i t * and t h e r e f o r e , i n a d d i t i o n to the s l i g h t d e l a y , the reeds w i l l not switch i n synchronism, and hence, the f u n c t i o n being generated may take on any indeterminate value d u r i n g the s w i t c h i n g i n t e r v a l . This indeterminate value shows up as a sharp s p i k e . The non-zero t r a n s i t i o n times cause sharp s p i k e s , too* since d u r i n g the t r a n s i t i o n i n t e r v a l s the source v o l t a g e s (E^.) themselves are indeterminate, and hence t h e i r weighted sum, i . e . the value of the f u n c t i o n being generated i s a l s o indeterminate* I t i s impossible to e s t a b l i s h a c r i t e r i o n f o r the maximum acceptable switching time* Zero d e l a y and zero t r a n s i t i o n time are i d e a l * and delay and t r a n s i t i o n times comparable to the conversion i n t e r v a l are d e f i n i t e l y not a c c e p t a b l e . Hence, the maximum l i m i t i s somewhere between the two extremes and i t s exact place depends on the q u a l i t y of r e p r o d u c t i o n sought. I t must be emphasized t h a t u s u a l l y a. f a i r number of spikes can be t o l e r a t e d * s i n c e , having a l i m i t e d frequency response, most of the analog computing and r e c o r d i n g equipment w i l l tend to smooth the spikes out, or may not even "see" them at a l l . Both the time delays and t r a n s i t i o n times of 200 [xsec and 300 u.sec* r e s p e c t i v e l y , are only small f r a c t i o n s of the conversion i n t e r v a l 58 at low and moderate tape speeds* As the tape approaches the speed of 500 ch/sec, however, they become comparable to the conversion i n t e r v a l , and consequently, f o r channel B, the con-v e r s i o n speed i s not l i m i t e d by the t a p e - d r i v e mechanism only, but by the s w i t c h i n g time of the reed contacts as w e l l . In channel B the switching accuracy i s determined by the contact r e s i s t a n c e of the reeds which were found to be l e s s than 0*5 ohms. With a c u r r e n t of l e s s than 2 ma f l o w i n g through them* the r e s u l t i n g v o l t a g e drop of l e s s than 1 mv across the reed switches can be assumed n e g l i g i b l e compared to the f u l l s c a l e v alue of 25 v o l t s , 4—2* T e s t i n g the Decoding Network Bias v o l t a g e s of + 25 v o l t s were a p p l i e d to the nine decoding r e s i s t o r s d i r e c t l y from the power s u p p l i e s . Output v o l t a g e s i n v a r i o u s regions over the f u l l output range were measured with a high accuracy d i f f e r e n t i a l voltmeter, and were found to be very accurate i n the v i c i n i t y of f u l l s c a l e output. The degree of accuracy decreased w i t h lower output v o l t a g e s , but remained l e s s than ifo even around the zero l e v e l output. 4—3* T e s t i n g the O v e r a l l Performance When the i n d i v i d u a l l e v e l s had been checked s e p a r a t e l y , the device as a whole was t e s t e d f o r f u n c t i o n g e n e r a t i o n and m u l t i p l i c a t i o n . F i g . 24a shows the t e s t f u n c t i o n as generated by channel A, while the same f u n c t i o n generated by channel B appears i n F i g . 24b. The two waveforms appear to be the same, however? the sp i k e s d i s c u s s e d i n s e c t i o n 4-1 were v i s i b l e on the 59 a) Test f u n c t i o n as generated by Channel A b) Test f u n c t i o n as generated by Channel B c) Product of the t e s t f u n c t i o n and an e x t e r n a l f u n c t i o n (sinu-Fig» 24. Output Vaveforms Shoving O v e r a l l Performance 60 o s c i l l o s c o p e but d i d not r e g i s t e r i n the photographic f i l m i n F i g . 24b, f o r they were very narrow and f a i n t . I t i s i n t e r e s t i n g to note that the l a r g e s t spike occurred at the mid-p o i n t of the ramp p o r t i o n , i * e * when the switch a s s o c i a t e d with the most s i g n i f i c a n t b i n a r y d i g i t changed i t s s t a t e . The next l a r g e s t spikes (two of approximately equal magnitudes) appeared 1 3 at p o i n t s ^ and -r of the di s t a n c e along the ramp. These p o i n t s corresponded to the second most s i g n i f i c a n t b i n a r y d i g i t . A few more spikes were observed but t h e i r magnitudes were very s m a l l . The next step c o n s i s t e d of the t e s t i n g of the EXTERNAL MULTIPLY mode of o p e r a t i o n . The t e s t f u n c t i o n was generated on channel B and an e x t e r n a l sine f u n c t i o n was a p p l i e d as the b i a s on the decoding network of channel B. The product of the two f u n c t i o n s i s shown i n F i g , 24c* as i t appeared at the output of channel B. The frequency of the sine wave was a few times l a r g e r than t h a t of the t e s t f u n c t i o n . The INTERNAL MULTIPLY mode of o p e r a t i o n was not t e s t e d , because two of the l i g h t sensors i n one of the reader heads were a c c i d e n t a l l y damaged, and replacements d i d not a r r i v e i n time f o r t e s t r e s u l t s to be i n c l u d e d i n t h i s p u b l i c a t i o n . Both channels were t e s t e d s e p a r a t e l y and the r e s u l t s i n d i c a t e t hat the device can be expected to work s a t i s f a c t o r i l y i n t h i s t h i r d mode of o p e r a t i o n as w e l l . 4—4, Summary The v a r i o u s t e s t s on the i n d i v i d u a l l e v e l s and on the i n t e g r a t e d device i t s e l f , were conducted mainly to e s t a b l i s h 61 speed and accuracy measurements and to check the general performance of the device* The r e s u l t s can be summarized as f o l l o w s t Channel As Switching speeds are n e g l i g i b l e over the speed range determined by the t a p e — d r i v e mechanism. Switching accuracy i s adequate, measured o f f s e t v o l t a g e s being the same as, or l e s s than,the design v a l u e s * Channel B? O f f s e t v o l t a g e s (across reed contacts) are n e g l i g i b l e . Switching speeds are adquate at low and medium speeds but become unacceptable at speeds approaching 500 ch/sec. The device was t e s t e d f o r m u l t i p l i c a t i o n i n the EXTERNAL MULTIPLY mode onl y , and was found to f u n c t i o n s a t i s f a c t o r i l y . 62 5. CONCLUSION A double input device c o n s i s t i n g of two channels and operated by punched tape vas developed. In i t s three modes of op e r a t i o n the u n i t cans a) generate two f u n c t i o n s independently, b) generate two f u n c t i o n s and m u l t i p l y them together, and c) generate two f u n c t i o n s and m u l t i p l y one of them by an e x t e r n a l computer v a r i a b l e . In both channels the simplest and f a s t e s t method of d i g i t a l - t o -analog conversion*, namely, the decoding by a r e s i s t i v e network, i s used* The p r e c i s i o n r e s i s t o r s used i n the decoding networks and* i n channel A, the t r a n s i s t o r i z e d switching c i r c u i t s ensure high-speed and high-accuracy ( b e t t e r than Vfo) f u n c t i o n generation* The a p p l i c a t i o n of magnetic reed switches i n channel B allows f o r high-accuracy four—quadrant m u l t i p l i c a t i o n , but the r e l a t i v e l y slow s w i t c h i n g speeds of the reed contacts prevent the m u l t i p l i e r channel from being used at tape speeds higher than 400 ch/sec. The speed and g a i n c o n t r o l s provide convenient time and amplitude s c a l i n g of the output of both channels, and hence g r e a t l y i n c r e a s e the v e r s a t i l i t y of the device i n analog computer a p p l i c a t i o n s , e s p e c i a l l y where the r e l a t i o n between system performance and changes i n d r i v i n g f u n c t i o n amplitude and/or frequency i s i n v e s t i g a t e d * In l i g h t of the experimental r e s u l t s the f o l l o w i n g comments on the p o s s i b l e improvement of the device are i n ord e r . In i t s present form the device i s operated by a 12-1evel tape, which 63 has to be punched manually p r i o r to the use of the device* A major improvement would be to change the tape to a 7 - l e v e l tape used i n the r e c e n t l y a c q u i r e d d i g i t a l computer i n s t a l l a t i o n of the Department of E l e c t r i c a l E n g i n e e r i n g , This change would make the use of the high-speed punch p o s s i b l e and would g r e a t l y shorten the time of tape p r e p a r a t i o n * The m o d i f i c a t i o n s on the device r e q u i r e d by the use of t h i s new tape would be J i ) to change the sprocket wheels to f i t the dimensions of the new tape* and i i ) to c o n s t r u c t new r e a d i n g heads, which would read two l i n e s at a time (block reader) so that a l l twelve b i t s of a c h a r a c t e r can be read simultaneously. The proposed m o d i f i c a t i o n suggests a new f i e l d of a p p l i c a t i o n of the d e v i c e , namely h y b r i d computation and s i m u l a t i o n , where analog f u n c t i o n s have to be generated d i r e c t l y from the output of a d i g i t a l computer* In view of the experience gained d u r i n g h i s a s s o c i a t i o n with t h i s p r o j e c t , the author b e l i e v e s that the device developed could be improved by the proposed m o d i f i c a t i o n , but i s none-t h e l e s s a worth—while and v e r s a t i l e a d d i t i o n to the f i e l d of analog computation* 64 6. BIBLIOGRAPHY 1. Johnson, C L . , Analog Computer Techniques, New York, McGraw-Hill, 1956. 2. Joyce, M.V., and C l a r k e , K.K., T r a n s i s t o r C i r c u i t A n a l y s i s , Reading, Massachusetts, Addison-Wesley P u b l i s h i n g Co., 1961. 3. Korn, G.A., and Korn, T.M., E l e c t r o n i c Analog Computers, New York, McGraw-Hill, 1952. 4. Lee, R.C., and Cox, F.B.,"A High-Speed A n a l o g - D i g i t a l Computer f o r Si m u l a t i o n " , I.R.E. Transactions on  E l e c t r o n i c Computers, v o l . EC - 4, no. 2, June 1959, pp. 186-196. 5. Millman, J . , and Taub, H., Pulse and D i g i t a l C i r c u i t s , New York, McGraw-Hill, 1956. 6. Nordstraud, R.B., A Method of F u n c t i o n Generation For Sim-u l a t i o n Computers Using Combined Analogue and D i g i t a l Techniques, M.A.Sc. T h e s i s . The U n i v e r s i t y of B r i t i s h Columbia, 1958. 7. DeMatteiSj W.M., A L i n e a r 4 - b i t D i g i t a l - t o - A n a l o g Converter, P h i l c o A p p l i c a t i o n Lab Report 743, 1961. 8. Ross, H. McG., Equipment of Instrumental Accuracy f o r Re-cording and Reproduction of E l e c t r i c S i g n a l s Using Cinematographic F i l m , The Proceedings of the  I n s t i t u t i o n of E l e c t r i c a l E n g i n e e r s ^ v o l . 102, no* 3, p a r t B, May, 1955, pp. 323-342. 9. Susskind, A.K. , Notes on A n a l o g - D i g i t a l Conversion Techniques, Technology Press of Massachusetss I n s t i t u t e of Technology and John Wiley and Sons Inc., New York, 1957. 1 APPENDIX I Representation of Functions on the Tape Functions of time to be generated are s t o r e d on the tape by p o i n t - v a l u e r e p r e s e n t a t i o n . The values of the f u n c t i o n at equal i n t e r v a l s are coded i n t o b i n a r y numbers by means of Table 1, i n which the numbers 0 and 1 mean the absence and presence of a h o l e , r e s p e c t i v e l y , (Level 1 i s the one c l o s e s t to the panel when the tape i s i n p o s i t i o n ) . L e v e l 12 generates the c l o c k pulses and should have h o l e s punched i n every p o s i t i o n along i t . L e v e l 11 i s reserved f o r the generation of c o n t r o l +81.55 -82.35 TAPE M O T I O N I -L. 1 J / V —\ i L_ _i / w >—c \ n S ! / 7 1 \ T T LEVEL I SPROCKET HOLES LEVEL 12 INCREASING TIME F i g . 25. Example of Coding pulses and should have one hole to mark the beginning of the f u n c t i o n . The pulse due to t h i s hole de-energizes the r e s e t r e l a y i n the computer and i n i t i a t e s the compute mode. EXAMPLE: Suppose the f u n c t i o n to be generated changes from +82.35 v o l t s to T82.35 v o l t s . The two consecutive c h a r a c t e r s r e p r e s e n t i n g t h i s d i s c o n t i n u i t y are punched as shovn i n F i g . 25. The f i r s t c h a r a c t e r i s found by l o c a t i n g the range i n the "MAGNITUDE" column t h a t i n c l u d e s the absolute value of the f u n c t i o n , i . e . 82,35, and then by choosing the hole combinatio i n the "POSITIVE" column,since the value of the f u n c t i o n i s p o s i t i v e . The second c h a r a c t e r i s found i n the same l i n e but i n the "NEGATIVE" column, since the value of the f u n c t i o n i s n e g a t i v e . 67 Table 1. Binary Code f o r Representing Functions on the Tape MAGNITUDE SIGN + LEVEL LEVEL From-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 0.000 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0.001 - 0.391 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0.392 ;- 0.781 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0.782 :- 1.17 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1.18 -1.56 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1.57 - 1.95 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1.96 -2.34 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 2.35 - 2.73 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 2.74 - 3.16 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 3.17 - 3.52 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 3.53 - 3.91 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 3.92 - 4.30 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 4.31 - 4.69 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 4.70 - 5.08 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 5.09 -5.47 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 5.48 - 5.86 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 5.87 - 6.25 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 6.26 -6.64 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 6.65 - 7.03 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 7.04 - 7.42 0 1 0 0 0 1 0 0 1 0 0 6 1 1 1 0 1 1 0 1 7.43 - 7.81 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 7.82 -8 . 2 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 8.21 - 8 . 5 9 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 8.60 -8.98 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 8.99 -9 . 3 6 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 9.37 - 9 . 7 7 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 9.78 -10.2 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 10.3 -10.5 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 10.6 -10.9 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 11.0 -11.3 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 11.4 -11.7 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 11.8 -12.1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 12.2 -12.5 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 12.6 -12.9 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 13.0 -13.3 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 13.4 -13.7 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 13.8 -14.1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 14.2 -14.5 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 14.6 -14.8 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 14.9 -15.2 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 Table 1 (Contd.) MAGNITUDE SIGN + LEVEL LEVEL From-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 15.3 -15.6 0 1 O t 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 15.7 -16.0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 16.1 -16.4 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 16.5 -16.8 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 16.9 -17.2 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 17.3 -17.6 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 17.7 -18.0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 18.1 -18.4 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 18.5 -18.8 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 18.9 -19.1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 19.2 -19.5 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 19.6 -19,9 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 20.0 -20.3 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 20.4 -20.7 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 20.8 -21.1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 21.2 -21*5 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 21.6 -21.9 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 22.0 -22.3 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 22.4 -22.7 0 1 0 0 1 ll 1 0 0 1 0 0 1 •1 0 0 0 1 1 0 22.8 -23.1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 23.2 -23.4 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 23.5 -23.8 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 23.9 -24.2 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 24.3 -24.6 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 24.7 -25.0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 .0 0 0 0 0 25.1 -25.4 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 25.5 -25.8 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 25.9 -26.2 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 26.3 -26.6 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 26.7 -27.0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 27.1 -27.3 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 0 27.4 -27.7 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 27.8 -28.1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 28.2 -28. 5 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 28.6 -28.9 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 29.0 -29.3 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 29.4 -29.7 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 29.8 -30.1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 30.2 -30.5 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 30.6 -30.9 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 Table 1 (Contd.) MAGNITUDE SIGN LEVEL LEVEL From-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 31.0 -31.3 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 0 31.4 -31.6 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 31.7 -32.0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 32.1 -32.4 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 32.5 -32.8 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 •1 0 0 32.9 -33.2 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 33.3 -33.6 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 33.7 -34.0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 34.1 -34.4 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 34.5 -34.8 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 34.9 -35.2 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 35.3 -35. 5 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 35.6 -35.9 0 •1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 36.0 -36.3 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 36.4 -36.7 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 36.8 -37.1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 37.2 -37.5 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 37.6 -37.9 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 38.0 -38.3 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 38.4 -38.7 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 38.8 -39.1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 39.2 -39.5 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 39.6 -39.8 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 39.9 -40.2 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 40.3 -40.6 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 40.7 -41.0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 41.1 -41.4 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 41.5 -41.8 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 41.9 -42.2 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 42.3 -42.6 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 42.7 -43.0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 43.1 -43.4 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 43.5 -43.8 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 43.9 -44.1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 44.2 -44.5 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 44.6 -44.9 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 45.0 -45.3 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 45.4 -45.7 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 45.8 -46.1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 46.2 -46.5 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 70 Table 1 fContd.) MAGNITUDE SIGN LEVEL LEVEL Prom-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 46.6 -46.9 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 47.0 -47.3 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 47.4 -47.7 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 47.8 -48.0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 48.1 -48.4 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 48.5 -48.8 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 48.9 -49.2 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 49.3 -49.6 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 49.7 -50.0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 50.1 -50.4 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 50.5 -50.8 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 50.9 -51.2 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 51.3 -51.6 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 51.7 -52.0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 52.1 -52.3 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 52.4 -52.7 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 52.8 -53.1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 53.2 -53.5 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 53.6 -53.9 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 54.0 -54.3 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 54.4 -54.7 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 54.8 -55.1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 55.2 -55.5 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 55.6 -55.9 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 56.0 -56.3 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 56.4 -56.6 0 1 1 0 0 1 0 0 0 0 0 0 0 1 i 0 1 1. 1 1 56.7 -57.0 0 -1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 57,1 -57 ."4 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 57.5 -57.8 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 57.9 -58.2 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 58.3 -58.6 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 58.7 -59.0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 59.1 -59.4 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 59.5 -59.8 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 59.9 -60.2 0 1 1 0 0 1 1 .0 0 1 0 0 0 1 1 0 0 1 1 0 60.3 -60.5 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 60.6 -60,9 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 61.0 -61.3 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 61.4 -61.7 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 61.8 -62.1 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0/ 1 Table 1 (Contd 0) MAGNITUDE SIGN LEVEL LEVEL From-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 62.2 -62.5 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 62,6 -62. 9 0 1 1 0 1 0 0 0 0 0 o1 0 0 1 0 1 1 1 1 1 63.0 -63.3 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 63.4 -63.7 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 63.8 -64.1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 64.2 -64. 5 X) 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 64.6 -64.8 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 64.9 -65.2 • 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 65.3 -65.6 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 65.7 -66.0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 66.1 -66.4 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 66. 5 -66.8 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 66.9 -67.2 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 6?.3 -67.6 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 67; 7 -68.0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 68.1 -68.4 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 68.5 -68.8 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 68.9 -69.1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 69.2 -69.5 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 69,6 -69.9 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 70.0 -70.3 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 70.4 -70.7 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 70.8 -71.1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 71.2 -71.5 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 71.6 -71.9 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 72.0 -72.3 0 1 1 0 1 1 1 0 0 0 0 Q 0 1 0 0 0 1 1 1 72.4 -72.7 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 72.8 -73.0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 73.1 -73.4 0 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 73. 5 -73.8 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 73.9 -74.2 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 74.3 -74.6 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 74.7 -75.0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 75.1 -75.4 0 1 1 i 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 75.5 -75.8 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 I 1 1 1 0 75.9 -76,2 0 I 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 76.3 -76.6 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 76,7 -77.0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 77.1 -77.3 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 Oi 1 0 77.4 -77.7 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 Table 1 (Contd.) MAGNITUDE SIGN LEVEL LEVEL From-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 77.8 -78.1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 78.2 -78.5 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 78.6 -78.9 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 79.0 -79.3 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 79.4 -79.7 0 1 1 1 0 0 •1 0 1 1 0 0 0 0 1 1 0 1 0 0 79.8 -80.1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 80.2 -80. 5 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 80.6 -80,9 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 81.0 -81.3 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 81.4 -81.6 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 81.7 -82.0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 82.1 -82.4 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 82.5 -82.8 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 82.9 -83.2 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 83.3 -83.6 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 83.7 -84.0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 84.1 -84.4 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 84.5 -84.8 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 84.9 -85.2 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 85.3 -85.5 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 85.6 -85.9 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 86.0 -86.3 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 86.4 -86.7 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 86.8 -87.1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 87.2 -87.5 0 1 1 1 0 1 1 1 1 1 p 0 0 0 1 0 0 0 0 0 87.6 -87.9 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 88.0 -88.3 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 88.4 -88.7 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 88.8 -89.1 0 1 1 1 1 0 0 ,0 1 1 0 0 0 0 0 1 1 1 0 0 89.2 -89.5 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 89.6 -89.8 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 89.9 -90.2 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 90.3 -90.6 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 90.7 -91.0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 91.1 -91.4 0 1 I 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 91.5 -91.8 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 91.9 -92.2 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 92.3 -92.6 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 92.7 -93.0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 93.1 -93.4 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 Table 1 (Contd.) MAGNITUDE SIGN + LEVEL LEVEL Prom-To 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 93.5 -93.8 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 93.9 -94.1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 94.2 -94.5 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 94.6 -94.9 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 95.0 -95.3 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 95.4 -95.7 •0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 95.8 -96.1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 96.2 -96.5 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 96.6 -96.9 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 97.0 -97.3 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 .0 0 1 1 1 97.4 -97.7 0 1 1 1 1 1 1 0 0 1 .0 0 0 0 0 0 0 1 1 0 97.8 -98.0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 88.1 -98.4 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 98.5 -98.8 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 98.9 -99.2 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 99.3 -99.6 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 000 0 1 99.7 -100 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 74 APPENDIX II C o n s t r u c t i o n D e t a i l s The combination f u n c t i o n generator and m u l t i p l i e r made up of three p a r t s i s mounted on a standard 19 inch rack ( F i g . 26). The lower p a r t consists of the sprocket wheels and reader heads i n f r o n t of the panel and the d r i v i n g motors and the transformers behind the p a n e l . The middle part i s the con-F i g . 26. C o n t r o l Panel and Tape Drive t r o l panel and supports a l l the switches and knobs used dur i n g the o p e r a t i o n of the d e v i c e . The top p a r t covered by an empty panel houses the e l e c t r o n i c p a r t s on p r i n t e d c i r c u i t cards. Removal of the empty panel allows the cards to be p u l l e d out 7 5 towards the f r o n t f o r easy s e r v i c i n g . Extension cards were s p e c i a l l y made i n order to keep the cards " i n the c i r c u i t " while they are i n the p u l l e d — o u t p o s i t i o n . One of the A\ by 14^ i n c h cards accommovlj, t i n g nine shaping and t r i g g e r c i r c u i t s i s shown i n F i g . 27a,and the corresponding sketch f o r the w i r i n g l a y o u t i s d i s p l a y e d i n F i g . 27b. A t o t a l of nine cards were needed to mount the c i r c u i t r y i n c l u d i n g power s u p p l i e s and output a m p l i f i e r s . Two high-power t r a n s i s t o r s (+ 6 v o l t power supply) and two Zener diodes (+ 40 v o l t nominalj + 25 v o l t power supply) are l o c a t e d on heat sinks at the r e a r of the lower p a r t . The t o t a l power d i s s i p a t e d by these components averages approximately 28 watts with a p o s s i b l e maximum of 36 watts. The p r e p a r a t i o n of the f i e l d c o i l s f o r the magnetic reed switches^ was;a s i z e a b l e p r o j e c t i t s e l f . According to the manufacturer's s p e c i f i c a t i o n s the re e d switches have a nominal p u l l — i n s e n s i t i v i t y of 40 ampere—turns (AT) and are able to cl o s e and open 500 times a second* A 1500-turn f i e l d c o i l e x c i t e d by a cur r e n t of 40 ma provides the r e q u i r e d p u l l - i n f o r c e , with adequate o v e r — d r i v e to account f o r v a r i a t i o n s i n p u l l - i n s e n s i t i v i t y of the swit c h e s . The r e l a t i v e l y low number of t u rns i s chosen to a v o i d excessive delay i n sw i t c h i n g due to c o i l i n ductance. The diameter of the bobbin ( F i g . 28) i s also minimized to keep the c o i l inductance at a low v a l u e . The switch and c o i l t e r m i n a l s are brought out to the heavy wires f i x e d i n the bobbin (see F i g . 28) which a f t e r p l a s t i c e n c a p s u l a t i o n serve as sturdy supports f o r mounting on the p r i n t e d c i r c u i t cards. a) T y p i c a l P r i n t e d C i r c u i t Card b) Wiring Layout f o r the Card i n a) above P i g . 27. 77 F i g . 28. C o n s t r u c t i o n Phases of the Magnetic Reed Switching U n i t Measurements made a f t e r the e n c a p s u l a t i o n r e v e a l e d t h a t some of the switches changed t h e i r p u l l - i n s e n s i t i v i t i e s d u r i n g e n c a p s u l a t i o n . The changes were very l i k e l y caused by s t r e s s e s due to shrinkage of the p l a s t i c . Those switches that demonstrated p u l l - i n s e n s i t i v i t i e s much d i f f e r e n t (+ 5$) from the nominal value were d i s c a r d e d . 

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