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An integrator for a pulse-position-modulation analogue computer. Larsen, Raymond Sverre 1958

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AN INTEGRATOR FOR A PULSE-POSITION-MODULATION ANALOGUE COMPUTER by RAYMOND SVERRE LARSEN B . A . S c , University of B r i t i s h Columbia, 1 9 5 6 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 Engineering We accept t h i s thesis as conforming to the standards, required from candidates f o r the degree of Master of Applied Science Members of the Department of E l e c t r i c a l Engineering The University of B r i t i s h Columbia A p r i l , 1 9 5 S A b s t r a c t T h i s t h e s i s d i s c u s s e s the d e s i g n of the b a s i c c i r -c u i t s f o r an i n t e g r a t o r f o r a p u l s e - p o s i t i o n - m o d u l a t i o n analogue computer. The computer operates on a time<=sequen-t i a l p r i n c i p l e , u t i l i z i n g a magnetic drum memory. In the i n t e g r a t o r , pulse i n f o r m a t i o n from the drum i s t r a n s l a t e d i n t o a v o l t a g e by a sweep c i r c u i t . The i n f o r m a t i o n i s i n t e g r a t e d u s i n g pulse techniques and put back i n t o pulse form t o be r e -w r i t t e n on the magnetic drum. In the prototype i n t e g r a t o r , the method of i n t e g r a -t i o n i s a simple s t r a i g h t - l i n e p r o j e c t i o n of the f i r s t d e r i v a -t i v e a c c o r d i n g to the equation y = dy_At. The i n t e g r a t i o n dt w i l l t h e r e f o r e have r a t h e r poor accuracy, but t h e o r e t i c a l l y any d e s i r e d accuracy can be achieved by simply extending the c i r c u i t s developed i n t h i s t h e s i s t o i n c l u d e h i g h e r - o r d e r d e r i v a t i v e s . Recommendations f o r the c o n s t r u c t i o n of a f i n a l prototype i n t e g r a t o r are made at the end of the r e p o r t . The c i r c u i t s used are an ac-coupled sweep a m p l i f i e r , an accurate v o l t a g e comparator, and standard f l i p - f l o p s and g a t i n g c i r c u i t s . T e s t s were performed which i n d i c a t e the r e l i a b i l i t y of these c i r c u i t s f o r accurate i n t e g r a t i o n . i i In p r e s e n t i n g 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 of 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 r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f 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 o f my Department or by h i s r e p r e s e n t a t i v e . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of E l e c t r i c a l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8 , Canada. Date A p r i l 1 0 . 1 9 ^ 8 A c k n o w l e d g e m e n t T h e a u t h o r i s g r e a t l y i n d e b t e d t o D r . E 0 V 0 B o n n , s u p e r v i s o r o f t h e p r o j e c t , D r „ F 0 N o a k e s , g r a n t e e o f t h e - p r o -j e c t , a n d t o o t h e r m e m b e r s o f t h e D e p a r t m e n t o f E l e c t r i c a l E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h C o l u m b i a , f o r t h e i r g e n e r -o u s a s s i s t a n c e . T h e w o r k d e s c r i b e d i n t h i s t h e s i s w a s p e r f o r m e d u n d e r t h e s p o n s o r s h i p o f t h e D e f e n c e R e s e a r c h B o a r d , D e p a r t -m e n t o f N a t i o n a l D e f e n c e , G r a n t N u m b e r D R B C - 9 9 3 1 - 0 2 ('5'50 - G C ) . T h i s w o r k w a s m a d e p o s s i b l e b y a N a t i o n a l R e s e a r c h C o u n c i l B u r s a r y a w a r d e d t h e a u t h o r i n 1 9 5 6 , a n d b y f i n a n c i a l a s s i s t a n c e r e c e i v e d w h i l e o n e d u c a t i o n a l l e a v e f r o m t h e D e f e n c e R e s e a r c h B o a r d , C a n a d i a n A r m a m e n t R e s e a r c h a n d D e v e l o p m e n t E s t a b l i s h m e n t , V a l c a r t i e r , P „ Q o v i i i Table of Contents page AbStr£LC"t ooooooooooooooao»»ooooooooooooooooooo««o«oo 11 Acknowledgement v m OOftOOOOOOOOOOOOOOOOO • • O O Q 0 O O 0 0 © O 0 © O O 1 o l i l t Ti O d \ l C t IOJTI OOOOOOOOOOOOOOOOOOOOOQOOOQOOOOO*'©© 1 2 . General D e s c r i p t i o n of the Computer ........... 6 2 - 1 . Block Time S o l u t i o n of the Basic E C J U c i t l O I T oooooooo««oo©ooo*ooooooocooo©o 6 2 - 2 . The Magnetic Storage Drum ............. 9 2 - 3 . Pulse R e p r e s e n t a t i o n of F u n c t i o n s ..... 1 1 2 - 4 . Dual Channel R e p r e s e n t a t i o n ........... 1 1 3 o Theory of I n t e g r a t o r O p e r a t i o n ................ 14 3 - 1 . I n t e g r a t o r C i r c u i t A c t i o n ............. 14 3 - 2 . A n a l y s i s of the E r r o r ................. 1 5 4 . Review of the B a s i c C i r c u i t s Required : . . . . a . . . . 1 8 4 - 1 . Sweep or I n t e g r a t o r C i r c u i t ........... 1 8 4 — 2 o B i s t a b l e F i x p " F l o p . . . o o o o o o . o o o o . o o o o o 1 9 4 = 3 o Monostable or Delay F l i p - F l o p ......... 1 9 4 ° * 4 o A s t a b l e F l i p — F l o p oo.oooo.oo.ooooo.ooo. 2 0 4—5° Pulse Generator O o o o o o o o . o o o o o o . o o o o o o o 2 1 4 — 6 o D i v i d e r C i r c u i t s . o o o © o . 0 0 0 0 0 0 0 0 0 0 . 0 . 0 0 2 1 4 ™ * 7 o The AND Gate o o o o o o o o o o o « o . . . . . . . . . . . ° o 2 3 4 ° - $ 0 Voltage Comparators ................... 2 4 $. Block-Schematic D e s c r i p t i o n of the I n t e g r a t o r C i r c u i t s ...................................... 2 6 5 - 1 . Coarse-Channel I n t e g r a t o r s . . . . . . c o c o o . 2 6 5 - 2 . Fine-Channel I n t e g r a t o r s .............. 2 9 5 - 3 . Combined Coarse and Fine I n t e g r a t o r s „. 3 2 6 . D e s c r i p t i o n of the C o n t r o l C i r c u i t s ........... 3 5 7 . C i r c u i t D e t a i l s of the C o n t r o l System ......... 3 9 7 - 1 . The Clock A m p l i f i e r and L i m i t e r „ . 0 0 o o o 3 9 7 - 2 . The Pulse Generator .......... .... .... <> 4 0 7 - 3 . Division-by-Two and D i v i s i o n -by""Four* C i r c u i t s Oooooooooooooooooooooo A-l 7 - 4 ° Phantastron D i v i s i o n - b y - T h i r t e e n CirCU - l t oooooooooooooooooooo»o»ooooooo© A-3 111 page 7-5. The 10-Microsecond C o i n c i d e n t Gates .... 45 7=6. The 300-Microsecond Gates and T r i o d e AND Gelt G o o © o o o o o o o o o o o o o o o o o o o « o o » o o 6 » hrl 7-7. The Zero- and La t e - P u l s e S e l e c t o r Gelt 6 S 0000000000000000000000000000000.0 0 ^ 7-8. C o n t r o l F l i p - F l o p and Channel Gates ... 49 7-9. Late Pulse Triode-Pentode Gates ....... 50 7-10. The P- and PO Pulse S e l e c t o r Gates . 5 1 7- 11. The Fine-Channel Schmitt Comparators cind. AssocicitGcl GcitGS O © o o o o o o o o o o o o o o o o 5^-8, I n t e g r a t o r C i r c u i t D e t a i l s .. „...»<>°....,.. .... 55 8=1. Sweep Input F l i p - F l o p s . . . . . . . . . . . . . . o . 55 8- 2. The Sweep A m p l i f i e r ................... 57 8- 3. The Zero Comparator ..............61 9. T e s t i n g the C i r c u i t s o o o o . . . . . . . . . . . . . . . . . . . . . . 63 9 "1 o l i l t X^OClXlC t 1 O i l o o o o o o o o o o e o o o o o o o o o o o o o o o 3^ 9=-2. Basic O p e r a t i o n of the Sweep C i r c u i t s .. 64 9- 3 o Dynamic Storage Te.st .................. 66 9-4. Incremental S u b t r a c t i o n From the St03T©d. PlJ-XS© o o o o e o o o o o o o o o o o o o o o 000000 9-5. Summary and Recommendations ........... 70 Appendix A. Recording Devices . . . o . » . . < > . . . . . . . . . . . . 74 Appendix B„ The Ring Counter „...„.„............... 76 Appendix C. L i s t of References o . o o o . o o o o o = . . . o o o o o 7& i v L i s t of I l l u s t r a t i o n s F i g u r e . page 2-1o S o l u t i o n of E q u a t i o n (1) i n Block-Time Operations t O f O 11OW^ o o o o o o o o o o o o o o o o o o o o o o o o o o o o S 2 - 2 0 The Magnetic Storage Drum t O i*OllOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 9 2-3o S i n g l e - a n d Dual-Channel F u n c t i o n Repre-s e n t a t i o n tO ^ * O l l OW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 9 /jj-^l o SWG 6 P C l ^ C U l t o o o o - o o o o o o o o o o o o o o o o o o o o o o o o o o o o 1^ 4C 12 o B l S t c l b l © F l i p ^ F l O p 000000000000000000000000*00 19 l\. """3 o jD©lciy FlXp^FlOp o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 19 L^^l^o Astcibl© F l i p ^ F l o p 00000000000000 000000000 00000 20 o Pil ls© G© ITSI*clt OX* o o o o o o o o o o o o o o « o o o o o o o o o o o » » o o 21 4~6(a) oMonostable D i v i s i o n C i r c u i t 0«»„ <». <>.»•>» .. 0» . <, <> 21 (b) oPhantastron D i v i s i o n C i r c u i t 0 o o . . . . 0 . » o » » » „ o <> 22 l± i:=r/o Th© AND Gcit © 000000000000*00000000000000000000 23 lif^^o Comp3,17cito x* s 0000000000000000000000000000000000 2 ^  5-1o The Three P o s s i b l e Coarse-Sweep Output V o l t a g e s tO follOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 26 5-2 0 The Three P o s s i b l e Fine-Sweep Output Voltages t O f o i l OW^  o o o o o o o o o o o o o o o o o o o o o o o o o o o o 29 5-3o Fine Channel Schmitt Comparator Arrangement t O f o i l O W o o o o o o o o o o o o o o o o o o o o o o o o o o o o 31 5- 4o Block Schematic of the Combined I n t e g r a t o r s t O f o i l OW^  o o o o o o o o o o o o o o o o o o o o o o o o o o o o 32 6- 1. Pulse Generator and D i v i d e r s t O f o i l O W o o o o o o o o o o o o o o o o o o o o o o o o o o o o 33 6 - 2 0 Ten-Microsecond C o i n c i d e n t Gates t O f O l lOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 ^ F i g u r e page 6 - 3 o Channel Pulse S e l e c t i o n 1l»0 f*OllOW « o o o o o o o o o o o o e o o o o o o o o o o o o o « 3 ^ 7 - 1 . Clock A m p l i f i e r and L i m i t e r C i r c u i t s tO f*OllOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 9 7 - 2 o Clock Pulse A m p l i f i e r tO follOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 7 - 3 o Division-by-Two C i r c u i t and Waveforms tO follOW o o o o o o o o o o o o o o o o o o o o ooooo ooo A - l 7 - 4 . Phantastron D i v i s i o n - b y - T h i r t e e n C i r c u i t t o f o l l o w 4 3 7 - 5 . C o i n c i d e n t Down-Gate Waveforms; ............... 4 5 7 - 6 . T r i o d e AND Gate and Waveforms tO follOW O O O O » O O O O » O O O O O O O O » O B » O » » O » » A " 7 7 - 7 . Pentode AND Gate and Waveforms tO follOW o o o o O O O O O O O O O O O O O O O O O O O O O O O O A * 7 7 - 8 . C o n t r o l F l i p - F l o p and Channel Gates tO follOW o o o o o o o o o o o o o o » o o o o o o o o o o o o o A " 9 7 - 9 . Late Pulse T r i ode-Pent ode S e l e c t o r Gate- ...... 5 1 7 - 1 0 . F i n e - S c a l e Schmitt Comparators and Down Gates tO follOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 2 8 - 1 a . Sweep Input F l i p - F l o p and S e l e c t o r Gates tO follOW o o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 3 8 - 2 . Diode Gate, Sweep A m p l i f i e r and Zero Comparator t o f o l l o w . o . 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 o o . o o o . o 5 7 8 - 3 o Sweep Input Diode Gate . . . . . o o o o o o . o o o . o . o o o o o 5 9 9 - 1 . Block and Waveforms f o r Coarse I n t e g r a t o r I .. 6 4 9 - 2 . Dynamic Storage System and Waveforms t O follOW . . . „ o . . . o o o . o . o o o o . . o o o „ „ o o o 6 6 9 - 3 . Stored Pulse T r i g g e r e d on P- EVEN ............ 6 8 9 - 4 . Incremental S u b t r a c t i o n by Pulse I n j e c t i o n tO f o i l OW^  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 » - o o o o o o o o « 6 £ ^ , . . ' 1 9 — 5 . Proposed Sweep C i r c u i t ....................... 7 3 v i Figure A - l o Servo Read-Out System " t O follOW o o o o o o o o o o B-l(a) 0Ring Counter Block Schematic (b).Circuit Details tO fOllOW o o o o o o o o o o v i i AN INTEGRATOR FOR A PULSE-POSITION-MODULATION ANALOGUE COMPUTER 1. I n t r o d u c t i o n The advent of s p e c i a l i z e d e l e c t r o n i c computers has produced s e v e r a l d i s t i n c t types of i n t e g r a t o r s . D i g i t a l com-puters are b a s i c a l l y p u l s e - c o u n t i n g systems, capable of h i g h -speed o p e r a t i o n and adapted t o a r e p e t i t i v e form of c a l c u l a -t i o n . I n t e g r a t i o n i n d i g i t a l computers r e q u i r e s the a p p l i c a t i o n of a converging i n t e g r a t i n g formula, such as the formula of 13 Simpson or Gauss, t o the o r d i n a r y a r i t h m e t i c c i r c u i t s . Analogue computers, on the other hand, use a number of b a s i c components t o form e i t h e r a d i r e c t or an i n d i r e c t e l e c t r i c a l analogy to the p h y s i c a l problem.^ I n t e g r a t i o n i s performed i n a separate i n t e g r a t o r u n i t by e l e c t r o n i c , e l e c t r o m e c h a n i c a l or mechanical means, each method having i t s s p e c i a l advantages. The main d i f f e r e n c e between analogue and d i g i t a l computers i s t h a t the analogue type uses a number of b a s i c components t o simulate the problem i n r e a l time, whereas the d i g i t a l type uses one set of a r i t h m e t i c c i r c u i t s and a storage u n i t t o perform a l l o p e r a t i o n s i n time-sequence. In recent y ears the a p p l i c a t i o n of d i g i t a l p ulse t e c h n i q u e s to analogue systems has gi v e n r i s e t o a h y b r i d - t y p e computer. One such computer, being b u i l t at the U n i v e r s i t y of B r i t i s h Columbia, i s known as a t i m e - s e q u e n t i a l , p u l s e - p o s i t i o n -modulation analogue computer. As the name i m p l i e s , t h i s d e s i g n embodies both the t i m e - s e q u e n t i a l p r i n c i p l e o f o p e r a t i o n of the p u r e l y d i g i t a l computer, and the i n d i r e c t - a n a l o g y approach of the e l e c t r o n i c analogue computer,, Although i t i s an analogue computer, t h i s u n i t may be quite- e a s i l y i n t e r c o n n e c t e d w i t h a d i g i t a l computer because the data i s a l r e a d y i n pulse form. C i r -c u i t s are r e q u i r e d which w i l l convert the pulse data of the a n a l -ogue computer t o the b i n a r y system of r e p r e s e n t a t i o n used i n d i g i t a l computers. T h i s t h e s i s d i s c u s s e s the d e s i g n o f an i n t e -g r a t o r f o r the p u l s e - p o s i t i o n modulation analogue computer. Analogue computers f e a t u r e s e v e r a l b a s i c types of i n t e g r a t o r s . The c l a s s i c example o f a mechanical i n t e g r a t o r i s 1 4 the K e l v i n wheel-and-disk type, which was used i n the f i r s t e l e c t r o m e c h a n i c a l d i f f e r e n t i a l a n a l y z e r , b u i l t by Bush at the 2 Masschussets I n s t i t u t e of Technology i n 1 9 3 1 . T h i s i n t e g r a t o r 1 2 was improved by Berry 8 i n 1 9 4 4 by the a d d i t i o n of a p o l a r i z e d -l i g h t f o l l o w - u p servo l i n k which enabled a l a r g e output torque t o be developed without l o a d i n g the d e l i c a t e i n t e g r a t o r wheel. Thus the K e l v i n i n t e g r a t o r became an e l e c t r o m e c h a n i c a l ra,ther than a p u r e l y mechanical d e v i c e . During World War I I the e l e c -t r o n i c o p e r a t i o n a l a m p l i f i e r became popular as a b a s i c u n i t of analogue computers. I t was pioneered by P h i l b r i c k and L o v e l l , and has s i n c e become almost u n i v e r s a l l y accepted i n the form of 1 2 a p l u g - i n u n i t . S i n c e the o p e r a t i o n a l a m p l i f i e r i s of s p e c i f i c i n t e r e s t here, i t w i l l now be con s i d e r e d i n more d e t a i l . The e l e c t r o n i c o p e r a t i o n a l a m p l i f i e r i s u s u a l l y a h i g h -g a i n d i r e c t - c o u p l e d a m p l i f i e r . Used as i n i n t e g r a t o r , i t r e -q u i r e s only negative c a p a c i t i v e feedback and a p r e c i s i o n input r e s i s t o r f o r accurate high-speed o p e r a t i o n . I t can a l s o be used i n - 3 -c o n j u n c t i o n w i t h s e r v o - d r i v e n p o t e n t i o m e t e r s as an i n t e g r a t o r f o r an e l e c t r o m e c h a n i c a l analogue computer, w h i c h i s t h e modern e q u i v a l e n t of t h e m e c h a n i c a l d i f f e r e n t i a l a n a l y z e r . Some o f t h e r e q u i r e m e n t s of o p e r a t i o n a l a m p l i f i e r s used i n c o n v e n t i o n a l systems a r e l i s t e d : ^ ( i ) S i n c e v a r i a b l e s a r e r e p r e s e n t e d by v o l t a g e s , t h e a m p l i f i e r must g e n e r a t e v o l t a g e s o f e i t h e r p o l a r i t y t o s i m u l a t e e i t h e r m a t h e m a t i c a l s i g n . ( i i ) I t must i n v e r t so t h a t n e g a t i v e f eedback can be u s e d 0 ( i i i ) I t must have h i g h g a i n and low phase s h i f t w i t h i n t h e f r e q u e n c y range o f problems t o be s t u d i e d , as w e l l as a good m a r g i n of s t a b i l i t y when a l a r g e amount o f n e g a t i v e feedbaqk i s used. The u s e f u l g a i n may v a r y from 50,000 t o 500,000 a t v e r y low f r e q u e n c i e s . ( i v ) I t must have a h i g h input-impedance so t h a t g r i d c u r r e n t i s n e g l i b l e compared w i t h s i g n a l c u r r e n t . (v) I t must have low z e r o - d r i f t . That i s , w i t h no f e e d -back and i n t h e absence o f s i g n a l , t h e output' must" remain a t zer o v o l t s . P r a c t i c a l f i g u r e s f o r z e r o -d r i f t range from 10's of m i l l i v o l t s p e r hour t o 100's of m i c r o v o l t s p e r month. The f o l l o w i n g problems a r i s e because o f f a c t o r s o t h e r t h a n i n a c c u r a c i e s i n t h e a m p l i f i e r i t s e l f : - ' ( v i ) E r r o r s i n i n t e g r a t i o n a r e a c c e n t u a t e d by l o n g computer r u n s . The e r r o r i n an i n p u t s i g n a l a ppears a t the output m u l t i p l i e d by the t i m e o f i n t e g r a t i o n i f t h e e r r o r i s a c o n s t a n t , o r i n t e g r a t e d o ver t h e ti m e o f i n t e g r a t i o n i f t h e e r r o r i s a f u n c t i o n o f t i m e . ( v i i ) S l o w l y - v a r y i n g o u t p u t s of i n t e g r a t o r s a r e i n v a r i a b l y a s s o c i a t e d w i t h low i n p u t v o l t a g e s and o f t e n w i t h low i n p u t p o t e n t i o m e t e r s e t t i n g s i n t h e problem. A low s e t t i n g l e a d s t o a g r e a t e r p e r c e n t a g e e r r o r t h a n a s e t t i n g near f u l l - s c a l e of t h e p o t e n t i o m e t e r . ( v i i i ) H i g h f r e q u e n c i e s c o n t r i b u t e t o phase s h i f t i n t h e a m p l i f i e r and have t h e same e f f e c t as n e g a t i v e damping. Servo d e v i c e s used f o r m u l t i p l i c a t i o n o p e r a t e s a t i s f a c -t o r i l y o n l y a t q u i t e low f r e q u e n c i e s . ( i x ) The dynamics o f r e c o r d i n g d e v i c e s must be c o n s i d e r e d so t h a t t h e r e c o r d e r r e s p o n s e does not a f f e c t t h e r e c o r d i n g . These a r e a few o f t h e major problems encountered i n the d e s i g n of an o p e r a t i o n a l - a m p l i f i e r t y p e analogue i n t e g r a t o r . The be s t a c c u r a c y o b t a i n a b l e i n p r e s e n t computers u s i n g t h e s e u n i t s i s i n the o r d e r o f 0.01% e r r o r . Because of t h e p h y s i c a l d i f f i c u l t y of o b t a i n i n g a c c u r a t e problem d a t a , t h i s f i g u r e i s p e r f e c t l y a c c e p t a b l e f o r many e n g i n e e r i n g problems. The i n t e g r a t o r t o be d i s c u s s e d uses some o f t h e t e c h n i q u e s o f both analogue and d i g i t a l systems. The s o l u t i o n of an o r d i n a r y d i f f e r e n t i a l e q u a t i o n w i t h v a r i a b l e c o e f f i c i e n t s i s c a r r i e d out i n a d i g i t a l manner; t h a t i s , a r e c u r r i n g c a l c u l a t i o n i s performed u s i n g o n l y one b a s i c i n t e g r a t o r u n i t . A t t h e same t i m e , t h e i n t e g r a t o r i s b u i l t o f o p e r a t i o n a l u n i t s common t o an analogue system, so t h a t some of t h e v e r s a t i l i t y , s i m p l i c i t y o f o p e r a t i o n and ease o f programming o f an analogue system i s p r e s e r v e d . The p r o t o t y p e i n t e g r a t o r has been g r e a t l y s i m p l i f i e d and i s expected t o have a p e r c e n t a g e e r r o r of no b e t t e r t h a n 1%. I f r e q u i r e d , b e t t e r a c c u r a c y p r o b a b l y can be a t t a i n e d by a s i m p l e e x t e n s i o n of t h e p r i n c i p l e of o p e r a t i o n o u t l i n e d i n t h i s t h e s i s . The p r e s e n t a m p l i f i e r d e s i g n meets t h e f o l l o w i n g s p e c i f i c a t i o n s : ( i ) S i n c e t h e output v o l t a g e does not d i r e c t l y r e p r e s e n t a v a r i a b l e i n t h e t i m e - s e q u e n t i a l system t o be o u t -l i n e d , t h e a m p l i f i e r need g e n e r a t e o n l y p o s i t i v e v o l t a g e s . T h e r e f o r e a m p l i f i e r d r i f t i s m i n i m i z e d because o r d i n a r y d i o d e clamps can be employed t o e s t a b l i s h s t a b l e q u i e s c e n t c o n d i t i o n s . ( i i ) I n v e r s i o n i s a c c o m p l i s h e d u s i n g one i n v e r t i n g s t a g e and one n o n - i n v e r t i n g s t a g e . - 5 -For 1 percent accuracy, a g a i n of approximately 3500 s u f f i c e s . S ince the i n t e g r a t i n g a c t i o n i s r e p e t i t i v e and f a i r l y f a s t , t h i s g a i n i s r e q u i r e d only near the frequency of 1000 cps, and consequently the a m p l i f i e r can be ac-coupled. Zero d r i f t i s e l i m i n a t e d so l o n g as the a m p l i f i e r r e -mains s t a b l e w i t h no s i g n a l a p p l i e d . The present design s a t i s f i e s t h i s requirement. The time of a p p l i c a t i o n of t h e i n p u t s i g n a l d e t e r -mines the a m p l i f i e r output v o l t a g e , because the i n -put s i g n a l i s s t a n d a r d i z e d . The d u r a t i o n of the input s i g n a l depends upon the pulse t r i g g e r c i r c u i t s , and these only r e q u i r e a s t a b l e power supply f o r r e l i a b l e o p e r a t i o n . The power supply used^ i s chop-per s t a b i l i z e d t o w i t h i n a few m i l l i v o l t s of ^300 v o l t s . The o v e r a l l accuracy of the i n t e g r a t o r can l i k e l y be made c o n s i s t e n t w i t h t h a t of the o t h e r a r i t h m e t i c c i r c u i t s . I t i s evident t h a t t h i s i n t e g r a t o r d e s i g n i s not an improvement on e x i s t i n g d e s i g n s , but r a t h e r a s p e c i a l s i m p l i f i e d a d a p t a t i o n of o p e r a t i o n a l a m p l i f i e r s to the h y b r i d - t y p e computer. I t i s hoped t h a t w i t h m o d i f i c a t i o n s the b a s i c u n i t s d i s c u s s e d h e r e i n w i l l perform e q u a l l y as w e l l as more c o s t l y u n i t s i n e x i s t i n g analogue computers. ( i i i ) ( i v ) (v) - 6 -2. General D e s c r i p t i o n of the Computer 2-1. Block-Time S o l u t i o n of the B a s i c Equation,, The computer d e s i g n equation i s the f o l l o w i n g ordinary-d i f f e r e n t i a l equation having v a r i a b l e c o e f f i c i e n t s : d n y + f , d n " 1 y + .».+ f n _ i dv_ + f y = g ( t ) , o r (1) d t n • x d t 1 1 " 1 cit y ( n ) + f i y ( n - l ) + o > # + f n _ x y ( l ) + f n y . g ( t ) The computer s o l v e s the e q u a t i o n by repeated i n t e g r a t i o n u s i n g the same set of b a s i c components f o r each o p e r a t i o n . Assuming t h a t a set of! i n i t i a l c o n d i t i o n s i s known at time t o , the procedure w i l l be as f o l l o w s : f i r s t , an i n t e g r a t i o n i s performed u s i n g the two h i g h e s t - o r d e r d e r i v a t i v e s a c c o r d i n g to the equation: y t 1 1 - 1 ) ^ + dt) - y ( n - X ) ( t 0 ) + y ( n ) ( t 0 ) d t (2) Time dt i s the simulated time f o r one in c r e m e n t a l i n t e g r a t i o n i n the computer. I t i s r e l a t e d t o r e a l time by the speed at which the computer s o l v e s the equation. In the next i n t e r v a l of time dt, the next-lowest d e r i v a t i v e i s found i n a s i m i l a r o p e r a t i o n : y ( n ~ 2 ) ( t 0 + dt) - y ( n - 2 ) ( t 0 ) + y ( n = 1 ) ( t Q + d t ) d t (3) N o t i c e t h a t these two equations d i f f e r s l i g h t l y i n that e q u a t i o n (2) c o n t a i n s the h i g h e s t - o r d e r d e r i v a t i v e evaluated a t r t i m e t 0 s whereas eq u a t i o n (2 ) c o n t a i n s the h i g h e s t - o r d e r d e r i v a t i v e e v a l u a -te d at time t 0 + d t . The reason f o r t h i s w i l l become apparent i n the f o l l o w i n g d e s c r i p t i o n . As i t happens, the d i f f e r e n c e i n the f i n a l r e s u l t caused by the assumption made i n equation (2) i s s l i g h t . I t should a l s o be n o t i c e d that time dt depends upon the computer time r e q u i r e d to s o l v e one in c r e m e n t a l o p e r a t i o n , and i s t h e r e f o r e the same i n each equation of types (2) and ( 3 K The o p e r a t i o n i n d i c a t e d by eq u a t i o n (3) can be repeated to i n c l u d e a l l d e r i v a t i v e s , u n t i l f i n a l l y a complete set of d e r i v a t i v e s evaluated at (simulated) time t 0 + dt i s ob t a i n e d . The only d e r i v a t i v e not so evaluated at t h i s p o i n t i s t h e h i g h e s t - o r d e r d e r i v a t i v e , y n ( t 0 ) „ As they are obtained, the d e r i v a t i v e s are s t o r e d i n the computer storage u n i t . Now the value of g'(t 0 + dt) can be obtained from the f u n c t i o n g e n e r a t o r , ^ s i n c e g ( t ) i s a known f u n c t i o n . Once g(to + dt) i s obtained, the computer s o l v e s f o r y n ( t Q + dt) as f o l l o w s : y n ( t Q + dt) = g ( t Q + dt) - g£ f k d y n ~ ^ + f n y l • (4) J t - t 0 + dt f o = 1 When the computer has found y ( t 0 + dt) and i s ready to begin a second i n c r e m e n t a l i n t e g r a t i o n of the d i f f e r e n t i a l equation, the r e a l - t i m e which has elapsed i s dT. A second i n c r e m e n t a l i n t e g r a -t i o n w i l l t h e r e f o r e y i e l d a set of v a l u e s at simulated time ( t Q + 2d t ) , or at r e a l - t i m e 2dT. The o p e r a t i o n i s repeated i n t h i s c y c l i c manner u n t i l a complete s o l u t i o n f o r y(t') i s obtained over the d e s i r e d range of the independent v a r i a b l e . T h i s g e n e r a l d i f f e r e n t i a l e q uation was chosen f o r the de s i g n equation o f the computer because i t i n t r o d u c e s f e a t u r e s ' i n t o the d e s i g n which w i l l be u s e f u l i n s o l v i n g a v a r i e t y of p r a c t i c a l ( i ) The f u n c t i o n g e n e r a t o r w i l l be d e s c r i b e d i n a subsequent t h e s i s from the Dept. of E l e c t r i c a l E n g i n e e r i n g , ' U.B.'C. - 8 -engineering problems. The modifications i n design required f o r solving more p a r t i c u l a r problems w i l l be dealt with when the computer becomes operative. The solution to the basic equation w i l l now be shown i n block-time form using the basic units of addition, m u l t i p l i c a t i o n , integration, storage, sign change and function generation. This block diagram^is designed to show the operations i n time-sequence, just as they occur i n the computer. The diagram shows the operation i n units of time known as cycles, where a c y c l e i s a s p e c i f i e d time related to the frequency of the magnetic storage drum, and to the angular displacement of one storage unit on the magnetic drum. Details of the storage drum are given l a t e r i n t h i s section. The block-time diagram i s shown i n Figure 1. The explanation of t h i s diagram w i l l be presented i n the paragraphs following. Assume that the derivatives y ^ , y^11-"1"^, y^ n" 2^, etc. evaluated at time to, are available as i n i t i a l conditions on the problem, and are placed i n the storage units, represented by the c i r c l e s . In cycle 1, the computer begins to solve the f i r s t incremental equation, y n _ 1 { t 0 + dt) = y n _ 1 ( t 0 ) + y n ( t 0 ) d t . (2) In cycle 2 , the quantity y I 1 ~ 1 ( t 0 + dt) i s obtained from t h i s i ntegration and immediately replaces the old value y n - 1 ( t 0 ) i n the storage unit . Simultaneously the integrator starts to solve the next incremental equation, y n _ 2 ( t 0 + dt) = y n ~ 2 ( t 0 ) + y 1 1 - 1 ( t 0 + dt)dt ( 3 ) . Also i n cycle 2, f i ( t Q + dt) i s obtained from the function generator, i s mu l t i p l i e d by y n _ 1 ( t 0 + d t ) , and the product put i n the accumulative r e g i s t e r . After n integrations (n = 1 , 2, . . . 1 3 , since there are a maximum of 13 channels 11 12 13 14 15 1 .2 3 4 5 Figure 2-l„ Solution of Equation (1) i n Block-Time Operations - 9 -a v a i l a b l e f o r i n t e g r a t i o n i n t h e example chosen) a complete s e t of new v a l u e s f o r t h e d e r i v a t i v e s i s a v a i l a b l e i n t h e s t o r a g e drum. The 14th c y c l e completes t h e s t o r a g e of f n y ( t 0 + d t ) , and t h e l ^ t h c y c l e i n t r o d u c e s g ( t 0 + d t ) i n o r d e r t o resume t h e e n t i r e p r o c e s s . At t h i s p o i n t , t h e magnetic s t o r a g e drum has completed one r e v o l u -t i o n , and t h e r e a l - t i m e w h i c h has e l a p s e d i s dT. The e n t i r e p r o c e s s i s a l l o w e d t o c o n t i n u e u n t i l t h e d e s i r e d range of t h e independent v a r i a b l e has been o b t a i n e d . The o p e r a t i o n i s most a c c u r a t e when dt i s kept s m a l l , and t h e computer r u n s h o r t . The s p e c i f i c e r r o r s i n v o l v e d i n t h e i n t e g r a t i o n p r o c e s s w i l l be con-s i d e r e d i n d e t a i l i n S e c t i o n 3. The s o l u t i o n t o the e q u a t i o n , o r t h e output of t h e o p e r a t i o n , y ( t ) , i s r e c o r d e d e i t h e r on an o s c i l l o g r a p h o r a pen r e c o r d e r , o r by s i m i l a r means. A s h o r t d i s c u s s i o n o f r e c o r d e r s i s g i v e n i n Appendix A. 2 - 2 . The M a g n e t i c S t o r a g e Drum The m a g n e t i c s t o r a g e drum i s t h e memory of t h e computer. I n f o r m a t i o n i s s t o r e d on i t s s u r f a c e i n t h e f o r m of p o s i t i o n -modulated p u l s e s . These p u l s e s a r e formed by r e v e r s i n g a narrow band of r e s i d u a l f l u x on the drum s u r f a c e . The s u r f a c e o f t h e drum i s c o a t e d w i t h an i r o n - o x i d e compound w h i c h has t h e p r o p e r t y o f r e t a i n i n g t h e s e r e v e r s a l s o v e r v e r y l o n g p e r i o d s o f t i m e . A p u l s e i s w r i t t e n and/or e r a s e d by what a r e c a l l e d " r e a d - w r i t e 7 head" o r " d e s t r u c t i v e - r e a d heads". A d e s t r u c t i v e - r e a d head e r a s e s t h e p u l s e w h i c h i t r e a d s , whereas'the r e a d - w r i t e head does not. The s u r f a c e o f t h e drum i s d i v i d e d a x i a l l y i n t o e l e v e n Iron-Oxide Coated Function-Storage Tracks Read-Head Clock Track Figure 1-2. The Magnetic Drum CPi PO CPi+1 (a) Coarse Channel L Fine Channel yfo -on*' -a to + a 2 2 CPi+1 104 "Discrete Positions Figure 1-3 „ Single- and Dual-Channel Function Representation - 1 0 -c i r c u m f e r e n t i a l t r a c k s , t h e v e r t i c a l d i s t a n c e between them b e i n g d e t e r m i n e d by t h e p h y s i c a l s i z e o f t h e i r a s s o c i a t e d heads (see F i g u r e 2 ) . On one of t h e t r a c k s i s p e r manently s t o r e d 156G e q u a l l y - s p a c e d f l u x r e v e r s a l s . The drum i s made t o r o t a t e a t a f r e q u e n c y of p r e c i s e l y 6 0 cps,^ so t h a t t h e permanent s i g n a l appears at i t s read-head as a s i n u s o i d a l wave of f r e q u e n c y 9 3 . 6 k c / s . T h i s s i g n a l , c a l l e d t h e c l o c k s i g n a l , i s used t o d e r i v e a l l t h e i m p o r t a n t t i m i n g p u l s e s . i The r e m a i n i n g t e n t r a c k s a r e used f o r f u n c t i o n s t o r a g e . Each t r a c k has a r e a d - w r i t e head and, i n the i n t e g r a t o r t r a c k s , a d e s t r u c t i v e - r e a d head. The t r a c k s a r e marked around t h e c i r c u m -f e r e n c e by p u l s e s at 24° i n t e r v a l s ; each of t h e f i f t e e n p a r t s so' o b t a i n e d i s c a l l e d a c h a n n e l , and t h e p u l s e s m a r k i n g t h e b e g i n n i n g of each c h a n n e l a r e c a l l e d t h e c h a n n e l p u l s e s (CP). These p u l s e s a r e d e r i v e d from t h e c l o c k s i g n a l and s t o r e d onto t h e drum. The " c y c l e " mentioned i n s e c t i o n 2 - 1 r e f e r s t o the t i m e t a k e n f o r one c h a n n e l l e n g t h t o pass a f i x e d r e f e r e n c e p o i n t as the drum r o t a t e s a t i t s p r e s c r i b e d f r e q u e n c y . I n the computer i s d e r i v e d a p u l s e t r a i n c o n t a i n i n g p u l s e s w h i c h c o r r e s p o n d t o e v e r y c y c l e o f t h e c l o c k s i g n a l . T h e r e f o r e , t h e r e a r e 1 5 6 0 p u l s e s g e n e r a t e d i n one drum r o t a t i o n , o r 104 i n t h e d u r a t i o n o f a s i n g l e c h a n n e l . These p u l s e s a r e c a l l e d t h e " s i n e c l o c k p u l s e s " (SCP). As w i l l be seen p r e s e n t l y , t h e y a r e used e x t e n s i v e l y i n t h e t i m i n g c i r c u i t r y and i n t h e i n t e g r a t i o n p r o c e s s . - 1 1 -2-3o Pulse Representation of Functions A function i s represented i n the computer by a pulse whose p o s i t i o n i s variable, stored i n a p a r t i c u l a r channel of the magnetic drum. The p o s i t i o n of the pulse about the centre of the channel determines the value of the function (see Figure 3 ( a ) ) . The length of a channel i s a r b i t r a r i l y taken as 2 a , so that the function can assume maximum values of ±a. The p r a c t i c a l l i m i t i s somewhat les s than t h i s amount because of possible interference between channels. Since the drum i s frequency-controlled, the quantity 2a i s exactly the same for a l l channels. The p o s i t i o n of the function-pulse i n a channel i s translated into a voltage f o r use i n the c i r c u i t r y . A f t e r the operation the voltage i s changed back into pulse form and the function re-stored i n i t s channel. C i r c u i t s which accomplish t h i s action are discussed i n d e t a i l i n subsequent sections. The above system of function representation i s used extensively i n the arithmetic c i r c u i t r y of the computer. For the integrator, however, a d i f f e r e n t system i s employed. It i s c a l l e d , "dual-channel representation". 2 - 4 . Dual-Channel Function Representation. Since the integrator employs operational amplifiers, i t i s subject to the e f f e c t s of voltage d r i f t . There are additional d r i f t e f f e c t s inherent i n the magnetic storage drum. In order to maintain d r i f t at a very low l e v e l , a dual-channel function representation i s employed (see Figure 3(b)). This representation - 12 -uses two t r a c k s of t h e drum, r e f e r r e d t o as t h e " c o a r s e " and " f i n e " t r a c k s , w h i c h c o n t a i n " c o a r s e " and " f i n e " c h a n n e l s , r e s p e c t i v e l y . The f u n c t i o n under c o n s i d e r a t i o n i s stoned i n two p a r t s i n c o r r e s p o n d i n g c h a n n e l s of t h e two t r a c k s , so t h a t two p u l s e s a r e r e q u i r e d t o f u l l y r e p r e s e n t a f u n c t i o n , P ( x ) . The c o a r s e c h a n n e l c o n t a i n s o n l y t h e d i s c r e t e p a r t o f th e f u n c t i o n . That i s , d i s c r e t e p o s i t i o n s a r e d e f i n e d on t h i s t r a c k by t h e p o s s i b l e p o s i t i o n s o f t h e s i n e - c l o c k p u l s e s , o f whic h t h e r e a r e 104 p e r c h a n n e l . The p a r t o f t h e f u n c t i o n s t o r e d i n t h e c o a r s e c h a n n e l v a r i e s by i n c r e m e n t s o f ±1/104 o f the t o t a l c h a n n e l l e n g t h . T h i s i s a s s u r e d by s e l e c t i n g a c e r t a i n one o f t h e s i n e - c l o c k p u l s e s t o r e p r e s e n t t h e f u n c t i o n w h i l e i t i s s t o r e d . The f i n e c h a n n e l c o n t a i n s t h e f r a c t i o n a l p a r t of the f u n c t i o n . Only h a l f t h e a v a i l a b l e l e n g t h of t h i s c h a n n e l i s used (t h e p a r t about t h e c e n t r e ) and t h i s l e n g t h r e p r e s e n t s two (*!) d i s c r e t e p o s i t i o n s i n t h e c o a r s e c h a n n e l , o r 1/52 o f t h e t o t a l c o a r s e c h a n n e l . The f u n c t i o n - p u l s e i n t h e f i n e c h a n n e l v a r i e s i n an analogue f a s h i o n ; t h a t i s , i t can e x i s t anywhere w i t h i n t h e c o n f i n e s of t h e c h a n n e l . The i n t e g r a t i o n p r o c e s s , i t w i l l be seen, i s c a r r i e d out e n t i r e l y i n t h e f i n e c h a n n e l / a n d the c o a r s e c h a n n e l m e r e l y r e c o r d s t h e number o f t i m e s t h a t t h e f i n e c h a n n e l o v e r f l o w s i n e i t h e r a p o s i t i v e o r a n e g a t i v e d i r e c t i o n . As an example, i f the v a l u e o f a f u n c t i o n y ( t ) ( p r o p e r l y s c a l e d ) a t ti m e to were y ( t o ) = +35.85, t h e n y c o = +35 i s w r i t t e n i n t h e c o a r s e c h a n n e l , and y^o = +0 .85 i s p l a c e d i n t h e f i n e c h a n n e l . Thus y 0 = y c o + y f o = 35 + 0 . 8 5 = 3 5 . 8 5 . I f now t h e - 13 -f u n c t i o n r e c e i v e s an increment of +0,65, a count of +1 i s t r a n s -f e r r e d t o the coarse s c a l e and +0.50 remains i n the f i n e channel. The new value then i s y^ = y c l + y f l = 36 + 0 . 5 0 . The method by which t h i s t r a n s f e r i s accomplished i s l e f t t o s e c t i o n s 3 and 5 . - 14 -3 . Theory of I n t e g r a t o r O p e r a t i o n 3-1. I n t e g r a t o r C i r c u i t A c t i o n I t has been s t a t e d t h a t t h e i n t e g r a t i o n i s performed i n t h e f i n e c h a n n e l o f t h e i n t e g r a t o r . The b a s i c e q u a t i o n f o r th e f i n e c h a n n e l o p e r a t i o n i s as f o l l o w s : In-1) (n-1) ( h ) , + y f l + * * y f 0 + a + y G Q dt + a - a 2 I n t h i s e q u a t i o n , y-f}11"""1"^ i s t h e i n t e g r a t e d v a l u e of y f Q 1 1 - 1 ^ a f t e r t i me d t , and y ^ n - 1 ^ is t h e c o a r s e - s c a l e v a l u e of t h e n e x t - h i g h e s t co d e r i v a t i v e . T h i s l a t t e r term a c c o u n t s e n t i r e l y f o r t h e i n c r e -m e n t a l change i n t h e term y c o n ~ ^ + y^^'^K so t h a t t h e e q u a t i o n r e p r e s e n t s i n t e g r a t i o n by s t r a i g h t - l i n e p r o j e c t i o n o f t h e d e r i v a -t i v e a t a known p o i n t . The a's are a p p r o p r i a t e l y p l a c e d t o r e p r e s e n t t h e v a r i a b l e s as t h e d i s t a n c e , from a c h a n n e l p u l s e , s i n c e i t i s t h i s d i s t a n c e , o r t i m e - l e n g t h , w h i c h i s t r a n s l a t e d i n t o a v o l t a g e i n t h e i n t e g r a t i o n p r o c e s s . The v a r i o u s f r a c t i o n s appear because t h e maximum f i n e - c h a n n e l v a r i a t i o n i s i a^, whereas t h e maximum c o a r s e - c h a n n e l v a r i a t i o n i s ±a. The e q u a t i o n as w r i t t e n i n d i c a t e s t h e v a r i o u s o p e r a -t i o n s n e c e s s a r y t o s o l v e one i n c r e m e n t a l i n t e g r a t i o n . F i r s t t h e v a r i a b l e y ^ d t + a i s s e a l e d by 1/2 as i t i s added i n t o t h e co f i n e c h a n n e l c o n t a i n i n g t h e v a r i a b l e p u l s e , yf^'^^ + a. The o p e r a t i o n t e r m i n a t e s when t h e q u a n t i t y y ^ | n - X ) + a . i s o b t a i n e d a t t h e c o m p l e t i o n o f t h e O p e r a t i o n . I n o r d e r t h a t t h e e q u a t i o n b a l a n c e , must be s u b t r a c t e d d u r i n g t h e o p e r a t i o n . Now i f t h e new f i n e - c h a n n e l v a l u e y f { n ~ " ^ + a exceeds "3a/2 i n t h e p o s i t i v e - I n -d i r e c t i o n , or a/2 i n the negative d i r e c t i o n , then a count of +1 or -1 must be transferred into the coarse channel which (n 1) contains y | ~ + a, and the fine-channel must be reset at the " f r a c t i o n a l value which remains a f t e r the t r a n s f e r . This process represents one complete incremental integration. The c i r c u i t s which have been devised to carry out t h i s basic operation w i l l be described i n block-schematic form i n section 5 . Before t h i s , a b r i e f summary of the errors i n the integration i s given i n section 3 - 2 , and a b r i e f resume of the basic c i r c u i t s i n section 4. 3 - 2 . Analysis of the Error To understand the mathematical errors involved i n the integration process, consider the simple d i f f e r e n t i a l equation dy = k = k c + kf • The solution to t h i s equation i s of the form y = k Q t + k^t. The increment i n y obtained i n one drum revolution i s y = k cdT. This increment accumulates i n the f i n e channel u n t i l an overflow occurs, causing the coarse-scale count to increase by 1. I f n i s the number of drum revolutions required f o r the coarse-scale count to increase by 1, and the t o t a l number of revolutions i s N, the the count transferred to the coarse scale i s y e = N. But the n t o t a l time involved f o r N revolutions i s T = NdT, and i n n revolutions we have k cdTn = 1. Substituting these expressions i n the previous expression f o r y c y i e l d s y c = NkcdT = k cT . - 16 It i s apparent that the only error involved i s due to neglecting the fine-scale increment y j ; since the value of yf can always he kept at 1/2 unit or l e s s , t h i s error i s i n the order of l f o or l e s s . In a r e p e t i t i v e chain of integrations, truncation errors are introduced (from neglecting higher-order derivatives i n the integration), but these are second-order errors. The truncation error i s derived i n the following paragraph. For t h i s simple ease, the exact increment per drum revolution Ay = y(dT) - y(o). The computer increment i s y^ 1^ (t^)dT, o < tj_ < dT.' Therefore the error made by the compu-ter i s E » y(dT) - y(o) - y ^ U i ) dT Expanding y(o) i n a Taylor series i n terms of i t s value at time dT y i e l d s E -^y^Ho) -jM (•*!)^ dT + y< 2) (o)JdTj. 2 + ... Substituting ,, , /, * , . y U , ( o ) = y c 1 J ( o ) + ^ ' ( o ) gives E - ( y ^ h o ) - y c ( 1 l t 1 ) ] dT + y | U ( d T ) + y ( 2 ) ( o ) ( d T ) + ... 2 1 This expression shows that a l l terms are of the second order, since dT i s the time f o r one drum revolution, and i s quite small, Hence the truncation error i s of the second order. The f i r s t error considered, that due to the act i o n of the integrator, can t h e o r e t i c a l l y be eliminated by extending the c i r c u i t r y to take into account the f i n e - s c a l e portion of the derivative, y ^ ^ ( o ) , since t h i s quantity i s avail a b l e i n the storage drum. Then the increment i n y would become Ay - Y(to) + y^^T + y ^ d T The truncation error can be minimized by decreasing dT (increasing drum speed) and by taking into account higher-order derivatives. For the type of problems which the pulse-position-modulation analogue computer i s designed to solve, however, these refinements are not j u s t i f i e d . For example, i n systems simulation, the system i s usually stable and integration errors are not cumulative; therefore a 1% integrator error i s p e r f e c t l y acceptable. On the other hand, the degree of accuracy required i n the adders, m u l t i p l i e r s and function generators must usually be considerably better than t h i s because of the p o s s i b i l i t y of appreciable cumulative errors. This error analysis has been fo r a very simple equation. The analysis becomes increasingly d i f f i c u l t for more compli-cated equations, and a complete analysis i s p r a c t i c a l l y impossi-ble. It i s f e l t that f o r a l l p r a c t i c a l purposes, the foregoing i n d i c a t i o n of the magnitude of error i s s u f f i c i e n t . 0 4. Review of the Basic C i r c u i t s Required, - 18 -Before embarking on a discussion of the integrator c i r c u i t s i t i s f i r s t desirable to b r i e f l y review the basic c i r c u i t s which w i l l be encountered. A block-schematic w i l l be given f o r each c i r c u i t . 4-1. Sweep or Integrator C i r c u i t The sweep c i r c u i t (Figure 4-1) consists of a high-gain ac-coupled a m p l i f i e r having a series r e s i s t o r input and negative capacitive feed-back. It i s shown i n subsequent sections that f o r the gain A very large, the arrangement acts as an integrator and the output i s e s s e n t i a l l y independent of the amplifier c h a r a c t e r i s t i c s . The output e Q f o r an input e^ i s given by Figure 4-1. Sweep C i r c u i t to obtain an output ramp from a step input given by a bistable f l i p - f l o p . It^ i s i n t e r e s t i n g to note that the output depends only upon the time-constant RC f o r A s u f f i c i e n t l y large, and not upon R and C i n d i v i d u a l l y . Therefore i n order to build several i d e n t i c a l sweep c i r c u i t s , i t i s necessary only to assure that the time-constants are i d e n t i c a l . This i s accomplished by using a bridge c a l i b r a t o r . 4-2. Bistable F l i p - F l o p The bistable f l i p - f l o p i s a double-tube c i r c u i t which has two stable states, either of which may be achieved by applying a t r i g g e r pulse to the grid of the conducting tube. The units used i n the integrator supply an output voltage, taken from a grid, of ±15 v o l t s . This signal i s used to actuate the sweep c i r c u i t s and to supply c e r t a i n gating signals to the pulse control c i r c u i t s . The two possible states of the f l i p - f l o p are referred to as the "set" and "reset" conditions. The set condition refers to the state when a usable signal i s being supplied the integrator, and the reset condition to the state when the signal i s blocked. The figure i n brackets i n the schematic i s the slope of the normalized sweep caused by these f l i p - f l o p s being applied to t h e i r respective diode gates. 4 - 3 . Monostable or Delay F l i p - F l o p . one of which i s stable. It may be triggered into i t s unstable e = ±15 v o l t s Figure 4-2. Bistable F l i p - F l o p The monostable f l i p - f l o p has two possible states, only state by applying a negative pulse to the g r i d of the conducting tube. The time spent i n the unstable state i s determined by an e^ = t r i g g e r pulse e 0 = 10 microsecond gating pulse Figure 4 - 3 . Delay F l i p - F l o p - 20 -RC timing network placed i n the grid of the normally-conducting tube, and also by the amplitude and shape of the t r i g g e r pulse. This time i s c a l l e d the "delay time'1. The delay time i s not always accurately calcuable because of the several factors which influence i t s length. The monostable c i r c u i t used i n the integrator serves c h i e f l y to supply gating waveforms of from 10 to 500 micro-seconds duration. The same basic c i r c u i t with d i f f e r e n t timing combinations i s used over t h i s entire range. The pulse generator reviewed i n t h i s section i s merely a monostable f l i p - f l o p having an extremely short delay time. 4-4. Astable F l i p - F l o p The astable f l i p - f l o p i s another double-tube c i r c u i t , and has two unstable states. The time-duration of each state (in the free-running condition) depends upon the timing networks i n the grids. However, as i s done i n the p a r t i c u l a r a p p l i c a t i o n here, the f l i p - f l o p can be synchronized by a pulse t r a i n . o f frequency higher than the natural frequency. m 1000 kc/s synch pulse = channel-gating pulse Figure 4-4. Astable F l i p - F l o p No.l The astable f l i p - f l o p i s used i n a device separate from the integrator c a l l e d a ring-counter. This device consists of 15 f l i p - f l o p s connected i n a r i n g so that the signal from one f l i p - f l o p t r i g g e r s i t s following neighbour. The device i s - 2 1 -synchronized such that a signal obtained from each f l i p - f l o p i s used to select a p a r t i c u l a r channel pulse. These pulses, f i f t e e n i n a l l , must be selected i n d i v i d u a l l y f o r use i n the general programming of the computer„( see Appendix B) . 4-5, Pulse Generator. As mentioned e a r l i e r , the pulse generator i s a mono-stable f l i p - f l o p having a very short delay time. It i s used to generate the sine-clock pulses from the clock signal of the magnetic drum. The sinusoidal clock signal i s amplified and Pulse Gen. Figure 4-5. Pulse Generator e-j_ = clock signal e Q f 3 microsecond clock pulses clipped to supply the signal f o r the pulse generator. Two pulse generators are employed, one to generate sine-clock pulses and the other to generate cosine-clock pulses, which are displaced i n phase by 180° from the sine pulses. 4-6. Divider C i r c u i t s . (a) Monostable F l i p - F l o p Divider. The monostable f l i p - f l o p i s used as a frequency d i v i d e r f o r pulse t r a i n s by making the delay time l a s t over one or more of the input t r i g g e r pulses. A f t e r the f l i p - f l o p i s ®i \ m M -5-2 ) e± = 93.6 kc/s PRF e 0 a 46.8 ke/s PRF Figure 4-6(a). Monostable Division-by-Two C i r c u i t - 22 -triggered into i t s unstable state, the input i s disconnected by a diode, so that only a f t e r the f l i p - f l o p returns to i t s stable state, which may be several pulses l a t e r , can the tri g g e r be ef f e c t i v e . The output i s obtained from the plate of the normally-off tube. The d i v i s i o n r a t i o i s a direct function of the timing network, i n i t i a l voltage l e v e l s , and the size and shape of the input t r i g g e r . This type of divider i s used once as a d i v i s i o n -by-two c i r c u i t to divide the clock signal from 93.6 kc/sec to 46.8 sec, and then a f t e r an intermediate stage as a d i v i s i o n by four c i r c u i t to divide the PRF (pulse recurrence frequency) of 3.6 kc/sec to 0.9 kc/sec. The dividers are b a s i c a l l y the same c i r c u i t but with d i f f e r e n t time constants. (b) Phantastron Divider The phantastron d i v i d e r consists of a pentode with independent grids which has an RC timing c i r c u i t connected between i t s plate and i t s control g r i d . This type of d i v i d e r Is more stable over long d i v i s i o n times than the monostable type. Normally the tube i s not conducting plate current. When a = 4 6 . 8 ke/s PRF = 3 . 6 kc/s PRF Figure 4 - 6(b). Phantastron Division-by-Thirteen C i r c u i t . t r i g g e r pulse i s received from the input, the tube begins to conduct plate current, and the source i s disconnected. The timing c i r c u i t action causes the plate current to increase l i n e a r l y u n t i l f i n a l l y the tube bottoms. Shortly thereafter the - 23 -condenser of the timing network re-charges very rapidly, causing the tube to return to i t s non-conducting state. Then the next t r i g g e r i s accepted and the process repeated. The cathode supplies a low-impedance output f o r t r i g g e r i n g the next d i v i d e r . The phantastron divides the clock PRF from 4 6 . 8 kc/sec by 13 to give a 3 . 6 kc/sec,output. A potentiometer i s used i n the timing c i r c u i t to adjust the d i v i s i o n r a t i o to the exact value. 4 - 7 . The AND gate The AND gate i s a c i r e u i t which selects one waveform i f i t occurs i n conjunction with a c e r t a i n part of a second wave-form. For example, the ring counter mentioned, e a r l i e r supplies a signal which i s used i n conjunction with a . t r a i n of 10-microsecond channel-gate pulses to select a p a r t i c u l a r channel-gate pulse. Two types of AND gate are used i n the integrator. e^ = pulse gate &2 = pulse t r a i n e = selected pulse o (a) Triode AND Gate In the triode AND gate the g r i d of the tube i s biased to cutoff so that conduction occurs only when the two input wave-forms add so as to bring the g r i d above cuto f f . The addition of the two waveforms i s accomplished with r e s i s t o r s , r e s i s t o r s and condensers, or with r e s i s t o r s and diodes. The objection to t h i s type of gate i s that there i s always i n t e r a c t i o n at the sources Figure 4 - 7 . The AND Gate - 24 -of the waveforms, which i n some cases i s i n t o l e r a b l e . In such cases, the pentode AND gate i s used. (b) Pentode AND Gate The pentode AND gate i s used extensively f o r gating t r i g g e r pulses f o r the integrator f l i p - f l o p s . With the posit i v e gating pulse applied to the suppressor, and with the pos i t i v e t r i g g e r pulse t r a i n applied to the control g r i d (both grids are biased to c u t o f f ) , the tube selects one pulse from the t r a i n and delivers a very large, sharp negative t r i g g e r pulse. The tube has a very large gain which makes the c i r c u i t i d e a l l y suited to t h i s p a r t i c u l a r a p p l i c a t i o n . 4 - 8 . Voltage Comparators The voltage comparator i s a device which de l i v e r s an output pulse when the input signal reaches equality with a cer t a i n reference voltage l e v e l . Comparators are used i n the integrator to d e l i v e r a pulse when the output waveform from the sweep c i r c u i t reaches, and to perform c e r t a i n l o g i c a l - d e c i s i o n operations i n pulse s e l e c t i o n . The Schmitt comparator i s e s s e n t i a l l y a dc-coupled multivibrator with the input g r i d biased to cutoff. In one application, the input i s a pos i t i v e ramp, and the c i r c u i t t r i g g e r s when the grid comes out of clamp f a r enough to star t regeneration. In the integrator l o g i c a l - d e c i s i o n c i r c u i t s , two comparators are used i n p a r a l l e l , one having a reference l e v e l set to t r i g g e r at the 1/4 the maximum normalized sweep, and the other with a l e v e l set to t r i g g e r at 3/4 the maximum normalized - 23 * sweep. The two voltage l e v e l s from each comparator are used to bias the grids of pulse-gating tubes. The d e t a i l s of the arrange-ment w i l l be discussed i n the next section. In the zero comparator, a difference amplifier i s used before the actual comparator c i r c u i t , so that the f l i p - o v e r of the c i r c u i t w i l l occur on a very small input s i g n a l . The e \ m 4 (v) t ) (a) Upgoing, Er = v~ - (b) Downgoing, Er = o Figure 4-8. Comparators important point i s that the comparator turn o f f when the wave-form reaches zero, and not delay unnecessarily, or t r i g g e r prematurely. I f the comparator does not turn on and off at the proper point of the t r i g g e r i n g waveform, the action of the clamp i n the sweep c i r c u i t , which i s controlled by the comparator, w i l l be e r r a t i c , and the sweep w i l l be useless. Also, d r i f t errors w i l l occur. Therefore the design values of the comparator are c r i t i c a l . - 26 -5. Block-Schematic Description of the Integrator C i r c u i t s . Now that ^he integration procedure has been outlined and the basic c i r c u i t s reviewed, i t i s possible to discuss a c i r c u i t which performs the integration. It has already been seen that the coarse-channel of the integrator serves to count the accumulated fine-channel increments, and that the actual integration i s performed i n the f i n e channel. It has also been seen, i n section 2 , that two cycles are required for one inc r e -mental integration. Hence i f one complete int e g r a t i o n of the equation i s to be completed i n one revolution of the magnetic drum, then two basic integrators w i l l be required f o r each of the coarse and f i n e channels. Therefore, Coarse Integrator I s h a l l integrate the information i n the ODD channels and Coarse Integrator II s h a l l integrate the information contained i n the EVEN channels. S i m i l a r l y , the fine channel w i l l require an ODD and an EVEN integrator. The four basic integrators must be interconnected so that the derivative from the previous coarse-channel i s read into the fine-channel under consideration i n order to carry out the integration procedure. The basic block schematics w i l l now be described. 5-1. Coarse Channel Integrators. Figure 5-1(a) shows a block schematic of Coarse Integrator I. The block l a b e l l e d I i s a sweep c i r c u i t which i s actuated by f l i p - f l o p s FFI and FF7. Block C i s a zero comparator, and the block G following represents a sine clock pulse (SCP) selector c i r c u i t . The three c i r c l e s together represent cosine "CPi 24° Magnetic Drum Coarse Track Write ,n-l C O F71 (+1) FF7 (-1) (a) E F ' - ( A N D ) — L P - ( A N D ) — — OP - ( A M D ) — r n - l - e i — "To^  '.Ch/. CPI r n - l C O Case 1 Select LP CP2 EP OP LP (b) rn-l c l C P 3 Figure 5-1. The Three Possible Coarse-Sweep Output Voltages - 27 -clock pulse (COP) selector c i r c u i t s , which are the pentode AND gates reviewed e a r l i e r . The outputs of these.three gates are EP (early pulse), OP (zero pulse) and LP (late pulse). The c i r c u i t action w i l l now be described with reference to Figures 5-1 (a) and 5 - K b ) . Suppose that y C Q ^ i s stored as a pulse i n coarse channel 1 , and that i t i s desired to carry out an integration to f i n d y c { n ^ , which i s the value of at time t Q+ dt. F i r s t CPI (channel pulse 1) i s read from'the magnetic drum set to f l i p -f l o p F F 1 . The signal from FFI causes the output of sweep I to (n) increase p o s i t i v e l y . The next pulse read i s y.„ ;; t h i s pulse CO resets FFI and causes the sweep to terminate at a voltage dependent on the time-length between CPI and y C Q n ^ . Hence the p o s i t i o n of the function pulse has been translated into a voltage at the output of the sweep am p l i f i e r . While t h i s action i s taking place, the fine-channel comparator associated with Coarse Integrator I decides whether to select EP, OP or LP to set FF7 and i n i t i a t e the coarse channel downsweep. Once the s e l e c t i o n i s made, the downsweep begins at a normalized rate of (-1) u n t i l the output voltage reaches zero. At t h i s point, the zero comparator generates a pulse which resets FF7 and terminates the sweep. The same pulse generates a 10-microseeOnd gate which i s used i n conjunction with the SCP i n the selector gate G to obtain the pulse which represents the new variable, y ci'^« This pulse i s rewritten on the storage drum and, as w i l l be seen l a t e r , It i s used i n the EVEN f i n e channel to perform integration of the next-highest der i v a t i v e . It i s obvious from Figure 5-1(h) that the s e l e c t i o n of EP to i n i t i a t e the downsweep effects a subtraction of one pulse-position i n the value of y G i n ^ ; the selection of OP causes no change i n i t s value; and the s e l e c t i o n of LP causes an addition of one pulse p o s i t i o n to y c o n ^ . The three cases are i l l u s t r a t e d . The i n t e r p r e t a t i o n i s simply that i n the f i r s t case, the (n+l)st derivative i s negative over the i n t e r v a l under consideration, so that the value of the (n)th derivative i s decreasing. In the seoond case, the (n+l)st derivative i s r e l a -t i v e l y near zero, so that no change i n the (n)th derivative i s noticed. And i n the t h i r d case, the (n+l)st derivative i s posit i v e and has caused the f i n e channel containing the nth derivative to overflow i n the p o s i t i v e d i r e c t i o n , so that a count of +1 i s effected i n the coarse channel. A f t e r the sweep has terminated, the output holds at zero volts and awaits the next ODD channel pulse, i n t h i s case CP3. It i s apparent from Figure 5-1(h) that the integration consumes two cycles. Coarse Integrator I I , which accepts the information i n the EVEN channels, begins integration i n channel 2 (or cycle 2 ) , terminates i n channel 3» begins again i n channel 4, and so on, just the opposite of Coarse Integrator I. Hence a l l the stored information i s accounted f o r by the two c i r c u i t s . This action requires that the channel pulses be selected into ODD and EVEN channel pulses. Notice that the terms ODD and EVEN r e f e r to the integrators I and I I , and not to the - 29 -numbers of the channel pulses. This i s because there are an odd number of channels, so that a f t e r channel 15 passes through the ODD integrator (J), channel 1 i s read into the EVEN i n t e -grator ( I I ) . Therefore i n alternate revolutions of the storage drum, the integrators w i l l handle the opposite channels that they did i n the previous revolution. 5 - 2 . Fine Channel Integrators Integration and the l o g i c a l decision operation of selecting the downsweep-initiating pulses i s performed by the fine-channel integrators. The same basic components that appear i n the coarse integrators are used, except f o r the l o g i c a l -d i c i s i o n comparator arrangement. The action i s s l i g h t l y more complicated, since two more input f l i p - f l o p s are required, and scaling of the sweep must be effected. The schematic of Fine Integrator IV i s shown i n Figure 5-2(a), and the thr§§::possible sweep waveforms i n Figure 5-2(b). The input f l i p - f l o p s are FF5, FF6, FF11 and FFI2. The downsweep i n i t i a t i n g pulses, P-, PO and P+, selected by the comparator v-<v0<v+ together with t h e i r coarse-channel counterparts EP, OP and LP* are sine clock pulses which occur at 1/4-channel i n t e r v a l s . The schematic of the comparator block v-<:v0<v+ w i l l be described l a t e r i n t h i s section. To review the operation, r e f e r to Figures 5^2(a) and 5-2(b). Suppose that the operation begins with channel pulse. 2, CP2, and that the value-of the fine-channel function i s yfo* 1"" 1^. Consider t h i s to be an extension of the case considered previous-l y , so that while the value of y f ^ n _ 1 ^ i s being read into the Read CP? Magnetic Drum Fine Track FF6 (+1) F F i i (-£). I FF5 ( 4 ) FF12 (-1) I I I V—cv Q<v-(a) 0 To Coarse Down Gates Case 1 v 0> v+ Sexect P-&LP Add 1 i n Coarse Channel Case 2 v-<.v_< v+ Select CP&OP No Change i n Coarse Channel Case 3 v 0<v-Select P-&EP Subtract 1 i n Coarse Channel CP4 Figure 5-2. The Three Possible Fine-Sweep Output Voltages - 30 -fine channel, the value of y c | n ^ i s being found i n the opposite coarse integrator. Pulse CP2 sets FF5 and FF6, both of which cause a posit i v e sweep, and FF11, which causes a negative sweep. The normalized sweep rates caused by each of these f l i p - f l o p s i s indicated i n brackets i n the respective blocks. The standard sweep rate i s approximately 100 v o l t s per 1000 microseconds. As the storage drum rotates, y ^ 1 1 " 1 ^ i s read and resets FF6, y c ] [ n ^ i s obtained from the ODD coarse integrator and resets FF5, and P0, a " f i x e d " pulse, resets FF11, the operation assuming no p a r t i c u l a r sequence. The sweep rates due to each pulse input add as shown i n the diagram. It i s apparent from a consideration of Figure 5-2(b) that the output voltage of the sweep now represents y f i n + " i ) = yfoIi~1) + a + y c i n ) d t + a - The sweeps which 2 2 represent y G { n ^ + a and P0( - a) have been scaled by 1/2 to represent the l a s t two terms of the equation. In the three cases i l l u s t r a t e d , the dotted l i n e s show the path the sweep would take i f no count were transferred to the coarse scale v i a Coarse Integrator I I . At t h i s point i n the operation, the sweep output v o l t -age represents the fine-channel deri v a t i v e , or portion of the derivative, a f t e r one incremental integration. Now a dec i s i o n must be made by the comparator block as to which pulses to select to actuate the Coarse Integrator II and Fine Integrator IV downsweeps i n order to transfer a part of t h i s quantity ( i f necessary) to the coarse channel. Figure 5-3 shows how the comparators are arranged with the pulse AND gates so that the Integrator .Output Case 1 2 3 .+ - -- — J^ND^ Er - + t Er - v - l + + -P~~ MGen (AND gTp ND ND EP) Early Pulse TOR Zero ^ Coarse Ch. -\0J Down Pulse " © Late O LP ^ Selector 3 Channel Pulse Ch.Pulse -(o) Fine Ch. Down. Pulse IP }'£ ^ Channel Pulse P- Selector Figure 5 - 3 . Fine Channel Schmitt Comparator Arrangement proper s e l e c t i o n i s made. Each of the.two-comparators comprising the block have two possible states, designated as the (+.). or the (-) state. A comparator i s i n the ( + ) /state i f the input voltage has exceeded the reference voltage, arid i s i n the (-) state i f the input i s less than the reference voltage. When a(+) signal i s delivered to one of the gates, that gate i s allowed to conduct, and when a(-) signal i s delivered, the gate blocks. Figure 5-3 i l l u s t r a t e s that the pulses EP and P-, OP and PO, and LP and P+, always occur together, and the comparators e f f e c t i v e l y choose one of these, p a i r s . Hence i n case 1 , the input, exceeds v+, and LP and P+ are chosen; i n case 2 , the Input voltage l i e s between v~ and v+, so that OP and PO are chosen; i n case 3 » the input i s less than v-, so that EP and P- are chosen. The corresponding - 32 -action of the coarse scale f o r the three cases i s to add one, do nothing, and subtract one, respectively. When the proper decision has been made, the coarse-channel downsweep pulse actuates the corresponding f l i p - f l o p , as discussed before, and the fine-channel downsweep pulse actuates (in t h i s case) FF12, causing a ;normalized sweep of -1 to be added to the e x i s t i n g waveform. When the fine-channel sweep zeros, the zero-comparator delivers a pulse which terminates the sweep, and which i s written on the drum to represent the integrated f i n e -channel value of the (n - l ) s t derivative, 7 f • Thus the c i r c u i t has accomplished one incremental integration. The Fine Integrator does not select one of the sine clock pulses to re-write on the drum because the f i n e scale operates i n an analogue fashion, whereas the Coarse Integrator selects a p a r t i c u l a r SCP, since the coarse channel operates i n a d i g i t a l , or incremental, fashion. T h e o r e t i c a l l y , no d r i f t w i l l occur i n the coarse channel, but the fine channel may f e e l the cumulative effects of small voltage d r i f t s i n the sweep c i r c u i t which might have only a minor effect i n the coarse channels. 5 - 3 . Combined Coarse and Fine Integrators. The arrangements of a l l four integrator units i s i l l u s t r a t e d i n Figure 5-4. The interconnection of the units i s self-evident from the foregoing discussion. It may be noticed that since the two integrators i n each scale handle the informa-t i o n i n alternate channels, certain pulses must be selected as ODD and EVEN i n order that the action does not become confused. v-<v0<vh-Figure 5 - 4 . Block Schematic of Combined Integrators - 33 -It has already been mentioned that the channel pulses, CP, are selected. In addition, P-(1/4-pulse), PO(centre pulse) and OP (zero pulse) must be selected into ODD and EVEN from t h e i r respective pulse t r a i n s before being applied to the comparator-controlled gates. Selection i s accomplished by using a signal from a "control f l i p - f l o p " which blankets alternate channels. The signal i s taken from one g r i d of the f l i p - f l o p . The signal from the opposite gri d i s used to gate any required pulse which occurs i n any of the remaining channels. Details of the s e l e c t i o n are given in' section 6. In Figure 5-4, blocks I and I I I are the ODD integrators, coarse and f i n e , and blocks II and IV are the EVEN integrators, coarse and f i n e . An example of a t y p i c a l integration i s shown. The action begins (for purposes of i l l u s t r a t i o n ) when block I begins to sweep on CPI and terminates on y G Q n ^ , both pulses being received from the magnetic drum read-head. Assuming that the fine-channel decision c i r c u i t s dictate no change f o r t h i s i n i t i a l step, the downsweep begins on OP and terminates when the sweep reaches zero v o l t s . The pulse terminating the sweep selects one of the SCP to be rewritten on the drum to represent y c c\ n) + a = y q i n ^ + a. While t h i s sweep-down i s happening, y ^ 1 1 " 1 ) i s being integrated i n the EVEN integrators II and IV. In Fine Integrator IV, the y G { n ^ found above is used i n the i n t e -gration process; then the comparators decide which pair of pulses to select to start the downsweep. The EVEN downsweep begins on either EP, OP or LP as channel 3 begins to pass under the read-head. Also while channel 3 i s passing, the variable pulse - 34 -y ( 3-[ n" 1^ i s read into the ODD integrator I to start another incremental integration. One of the inputs to ODD integrator III i s the pulse ^ j 1 1 " 1 ^ obtained above when the EVEN sweep terminates. Again a decision i s made by the f i n e - s c a l e compara-tors and the ODD sweepdown begins. The r e c y c l i n g action of the two sets of integrators i s apparent from the diagram. The basic process just outlined i s extended to include a l l storage channels. At the end of one revolution of the magnetic drum, one incremental integration of the entire equation has been accomplished. With regard to the comparator block v-<vo<v+, note that f o r s i m p l i c i t y only one lead i s shown to the AND gates, whereas i n a c t u a l i t y four separate inputs are required. This concludes the discussion of the integrator schematic c i r c u i t s . It should be noted here that the object of t h i s thesis i s not to obtain the integrator i n i t s f i n a l form, as has been outlined, but rather to devise the* basic units required and to perform tests i n d i c a t i v e of t h e i r r e l i a b i l i t y of operation. The complete operation of t h i s unit as outlined would require parts of the computer, notably the storage drum, which are riot yet available. In addition, i t w i l l be seen presently, a great deal of redesign of the c i r c u i t s i s necessary to obtain optimum opera-t i o n . The d e t a i l s of the basic c i r c u i t elements are presented i n sections 7 and 8 . - 35 -6. Description of the Control C i r c u i t s The operation of the integrator w i l l be c l a r i f i e d at t h i s time by a discussion of the control c i r c u i t s . These include a l l pulse-generation and gating c i r c u i t s . The l o g i c a l -decision c i r c u i t s referred to i n the l a s t section may also be considered as part of the control c i r c u i t s ; these w i l l be elaborated i n the next section. A l l pulses are i n i t i a l l y derived from the clock s i g n a l . The magnetic drum rotating at a fixed speed of six t y cps delivers from the clock track a sinusoidal signal of 93.6 -kc/sec. This clock signal i s amplified and d i f f e r e n t i a t e d before being applied to the pulse generator. The output of the pulse generator i s a pulse t r a i n which occurs i n time-coincid-ence with the negative-going sinusoidal signal at i t s zero voltage l e v e l (Figure 6-1). These are the sine clock pulses, or SCP. Simultaneously the clock signal i s inverted and passed through another pulse generator to give the cosine clock pulses, or CCP. Next the SCP are passed through three d i v i d e r stages which divide the clock PRF (pulse r e p e t i t i o n frequency) by 2, 13 and 4. The 13 c i r c u i t y i e l d s the 1/4 channel marker pulses, or 1/4 CMP, and the 4 c i r c u i t y i e l d s the channel marker pulses, or CMP. These l a t t e r pulses are used to gate the actual channel pulses, CP, used i n the integrator. This s e l e c t i o n of the o r i g i n a l SCP i s used to eliminate any possible d r i f t s or phase s h i f t i n the d i v i d e r chain. Pulse Gen. CP> Cosine-Clock Pulses M *2 P A l l M *4 /~~\ Channel Marker Pulses -*^JMP) tCMtf i-Channel eMarkers Sine-Clock Pulses k A A A A .. i ( i i M i l i L 10 Milliseconds T Clock Signal Sine-Clock Pulses Cosine-Clock Pulses S-2 Out 4-Channel Markers f l 3 Out Channel Markers 5-4 Out Figure 6-1. Pulse Generator and Dividers - 5 6 -To perform the pulse s e l e c t i o n i t i s f i r s t necessary to generate the coarse scale downsweep pulses EP, OP and LP (early pulse, zero pulse, l a t e pulse). This i s done as follows (Figure 6-2). F i r s t the CMP are used to t r i g g e r three 10-micro-second coincident delay f l i p - f l o p s . The three gating pulses obtained are applied to three AND gates which i n conjunction with the CCP t r a i n select EP, OP and LP. Then the OP (zero pulse) t r i g g e r s another 1 0-micro-second delay multivibrator to y i e l d the channel-gate pulse, CHG. This pulse blankets the SCP which w i l l eventually be selected as the channel pulses, CP, to be stored permanently on the magnetic drum. Before t h i s i s done, further s e l e c t i o n of the channel gates (CHG) into ODD and EVEN gates i s required. Another t r a i n of 10-microsecond gating pulses i s required f o r the 1/4-channel pulses, P-, OP and P+. To obtain these the 1/4 CMP (channel marker pulses') are used to t r i g g e r two coincident delay f l i p - f l o p s , one with a delay of 1 3-micro-seconds and the second with a delay of 10-microseconds i(Figure 6 - 3 ) . The s i g n a l from the l a t t e r i s the 1/4 CHG which occurs i n coincidence with the 1/4 channel pulses of the SCP t r a i n . To select P- and PO i n d i v i d u a l l y , two more coincident delay f l i p - f l o p s are used, each of delay time 3 0 0 microseconds. The LP pulse i s used to t r i g g e r the f i r s t f l i p - f l o p , and the si g n a l obtained i s used i n conjunction with the 1/4 CiiG t r a i n i n an i > i 1 • AND gate to select the P-G (P-gate). The' signal from the second coincident f l i p - f l o p i s s i m i l a r l y used to se l e c t the POG (PO gate). Selection of the actual pulses P- and PO i s now a Channel Markers CC Cosine-Clock Pulses Zero Pulses D 10 D 10 D 10 I ) LO EG 1 " OG LG AND AND AND L P J Late Pulse - ( E P ) -*""^CH^ Channel Gates Zero Pulse Ea r l y Pulse SCP CMP E G OG LG CHG i i 10 Milliseconds-9 Sine-Clock Pulses Channel Markers Early Gate Zero Gate Late Gate Channel Gate Figure 6-2. Ten-Microsecond Coincident Gates :.5^io i i _!_!_ P-i _ I i 1 f t PG P+- CP2 Channel "Markers 15 & 10 Coincident Gates i i i i •P- 300 Gate PO 300 Gate Control FF Out CHG ODD CHG EVEN P -Figure 6 - 3 * Channel Pulse Selection - 3 7 -simple matter, but t h i s i s not done u n t i l the pulse i s required at the f l i p - f l o p because the gating waveform i s much less sensitive to d i s t o r t i o n than i s the sharp pulse. In.1, the> pulse t r a i n s already discussed, c e r t a i n of the pulses must be selected further into ODD and EVEN pulses f o r use i n the integrators. The process w i l l be i l l u s t r a t e d with the channel pulses, CP (Figure 6 - 3 ) . The f i r s t step i s to t r i g g e r a "control f l i p - f l o p " with the CMP. This f l i p - f l o p i s designed for an output swing of ± 1 5 v o l t s . The outputs from both grids are taken one to an ODD AND gate and the other to an EVEN AND gate. The output of these gates are the EVEN and ODD channel gates, CHG. These i n turn are used to obtain the selected channel pulses, CP, by gating the SCP i n two a d d i t i o n a l AND gates. These pulses are then used to t r i g g e r the integrator input f l i p -f l o p s . The signal from the control f l i p - f l o p i s also used to L select alternate sets of downsweep pulses, EP, OP and LP i n the coarse channels, and P-, OP and P+in the f i n e channels. These pulses are then gated by the comparators, as stated previously. With regard to the previous discussion of the comparators, notice that the LP and P- pulses do not have to be blocked at any time by the comparator. This i s because they are the l a s t pulses i n the group to occur, and i f one of the previous pulses has been selected to t r i g g e r the downsweep f l i p - f l o p s , t h e i r a p p l i c a t i o n can have no further e f f e c t . The only pulses not yet mentioned are the function pulses which must be read from the drum and into the f l i p - f l o p s . - 38 -These are gated by a pentode AND gate placed between the read amplifier and the f l i p - f l o p input. The pentode gate amplifies the pulse enough to enable i t to t r i g g e r the input f l i p - f l o p s . This concludes the discussion of the control c i r c u i t s . The derivation of any further pulses required for the integrator i s merely a r e p e t i t i o n or extension of the; p r i n c i p l e s and; c i r c u i t s already discussed. With these p r i n c i p l e s i n mind, a l l phases of the integration may be understood. The d e t a i l s of the control and l o g i c a l decision c i r c u i t s are given i n section 7 , and of the integrators, i n section 8 . - 3 9 -7. C i r c u i t Details of the Control,System The control c i r c u i t s , discussed i n section 6, include, the pulse-derivation c i r c u i t s and the comparator decision c i r c u i t s . These w i l l now be described i n d e t a i l . Where a c i r c u i t i s used i n several s i m i l a r applications, mention i s made of i t s s p e c i f i c uses. 7-1. The Clock Amplifier and Limiter The clock amplifier i s shown i n Figure 7-1. This c i r c u i t amplifies the 93.6 kc/s, 1 v o l t peak-to-peaki clock signal from the read-head to an amplitude of 550 v o l t s peak-to-peak. A tuned plate load i s used, and the output i s taken through a cathode follower to a diode c l i p p i n g c i r c u i t . From here the signal i s amplified and d i f f e r e n t i a t e d to provide the negative 1 ' , clock pulses. The various waveforms accompany the c i r c u i t of Figure 7-1. The output PRF (pulse recurrence frequency) i s i ' known as" the sine-clock PRF (SCP) , which has been discussed previously. A PRF displaced i n phase by 1 8 0 ° from the sine-CIOGJC pulses i s obtained by inverting the clock s i g n a l and passing i t through a similar l i m i t i n g c i r c u i t ; ' t h i s s i g n a l i s the cosine-clock PBF (CCP), or cosine-clock pulses. In the c i r c u i t , inductor Lg i s used to dc-restore the g r i d of the amplifier. This inductor offers a high-impedance to the clock signal inputs but i s a low-resistance path f o r any charge which tends to accumulate on the g r i d ; hence the gri d i s e f f e c t i v e l y clamped at zero vo l t s , and the output pulses correspond accurately to the points where the sinusoidal C4 =tSR7 OUT P l a t e o f T I G r i d o f T3 - 5 u s e c ^ — lDji s e c -O u t p u t o f T3 550v r 3 v 11 r R l 5 6 0 K io# R 2 I K n t t R3 3 9 K » t t R 4 3 3 0 K It n R5 6 8 K 2W i t R 6 27Qohm iw ti 5% R 7 , 9 1 0 o h m IT R8 270K I t t i R9 10K 1W 10% R I O 1 0 K i t C I . 0 5 m f d 2 0 % 02 5 0 0 mmfd rt C3 25 n i t C 4 . 0 1 m f d i t L l 6 mh L 2 5 - 3 5 •" T I 6 A U 6 T& 1 2 A T 7 D l 1 N 1 9 1 F i g u r e 7 - 1 . C l o c k A m p l i f i e r a n d L i m i t e r C i r c u i t s c l o c k s i g n a l c r o s s e s the zer o a x i s . The r e s i s t o r R5 i s p l a c e d i n s e r i e s w i t h the c o u p l i n g c a p a c i t o r 04 i n o r d e r t o p r e v e n t e x c e s s i v e c u r r e n t i n t o t h e d i o d e - c l i p p i n g arrangement. There i s a s m a l l phase s h i f t t h r o u g h R5C4, but t h i s i s n e g l i g i b l e . At t h i s p o i n t i n t h e o p e r a t i o n , t h e c l o c k p u l s e s a r e a c c u r a t e i n t i m e > but t h e y a r e n e c e s s a r i l y s m a l l . To be u s e f u l , t h e y must be a m p l i f i e d i n two s e p a r a t e p u l s e g e n e r a t o r s , o r p u l s e - s h a p i n g c i r c u i t s . A t t h e o u t p u t o f t h e l i m i t i n g c i r c u i t t h e p u l s e s have an a m p l i t u d e of -20 v o l t s and a r i s e - t i m e of 1/2 m i c r o s e c o n d . I n t h e p u l s e g e n e r a t o r s t h e y w i l l be a m p l i f i e d and shaped t o +jp0 v o l t s a m p l i t u d e and 3 m i c r o s e c o n d s w i d t h . 7-2. The P u l s e G e n e r a t o r The sche m a t i c of t h e d e l a y f l i p - f l o p - ^ used as a p u l s e g e n e r a t o r i s shown i n F i g u r e 7-2. T h i s c i r c u i t g e n e r a t e s low-impedance c l o c k p u l s e s f o r use i n t h e v a r i o u s g a t i n g c i r c u i t s . The c i r c u i t a c t i o n w i l l now be summarized. I n t h e quiesicent s t a t e , T2 i s c o n d u c t i n g h e a v i l y , s i n c e i t i s b i a s e d o n l y by a IK cathode r e s i s t o r , and T I i s almost a t c u t o f f s i n c e i t i s b i a s e d by a 4.7K cathode r e s i s t o r . T h e r e f o r e t h e output f rom t h e cathode of T I i s j u s t above ze r o v o l t s . The p l a t e o f T l i s down s l i g h t l y from the v o l t a g e w h i c h would be e s t a b l i s h e d by t h e p l a t e c u r r e n t a l o n e because o f a s m a l l c u r r e n t f l o w i n g t h r o u g h R7-R6-D1-R2. The i n p u t s i g n a l i s t h e SCP o r CCP PRF. As soon as a Plate of T l Grid of T2 iOjisec-1 20v "•7. ' 30v JL |5v Rl 2 7 K 10% R2 270K tt R3 1M « iti R4 22K tt tt R5 630K n tt R6 470K tt tt R7 15K 1W tt R8 4.7K iw tt R9 22K,. 1W t» RIO IK'4. tt R l l 2.2M ft CI '1000 rrimfd 20$ C2 50 " tt T l ;^-12AT7 T2 n Dl )1N67A D2 Cathode of T l - OUT Figure 7-2 Clock Pulse Amplifier -41-t r i g g e r occurs, Dl conducts and the pulse charges C2 negatively. The plate current of T2 diminishes because of t h i s negative-going grid s i g n a l , regeneration through G2 and C l begins, and within a very short time (1/2 microsecond) T2 i s cut o f f and TI is conducting heavily. At t h i s time, the plate of TI i s down and diode Dl i s blocked. Since C2 i s now disconnected from the t r i g g e r source, i t s charge leaks o f f through R l l , causing the g r i d of T2 to r i s e exponentially toward zero, where i t i s normally clamped by diode D2. As soon as. the g r i d r i s e s high enough that T2 begins to come out of clamp, regeneration occurs through Cl and C2, and the tube currents are restored very rapi d l y to t h e i r o r i g i n a l states. As t h i s happens, the plate of TI r i s e s i n potential and once more the diode D2 i s allowed to conduct current. Now the c i r c u i t i s ready to accept the next t r i g g e r pulse. For the c i r c u i t values shown, the output i s a pulse of 50 v o l t s amplitude and 3 microseconds duration (Figure 7-2). The duration of the pulse depends upon the i n i t i a l voltage l e v e l s , the shape of the t r i g g e r pulse, and the time-constant R11C1. 7 - 3 . Division-by-Two and Division-by-Four C i r c u i t s The divisipn-by-two and division-by-four c i r c u i t s are e s s e n t i a l l y the same monostable f l i p - f l o p with d i f f e r e n t time-constants and grid-return voltages. The division-by-two c i r c u i t , shown i n Figure 7 - 3 , i s a cathode- and p l a t e - t o - g r i d coupled monostable f l i p - f l o p . The input PRF i s the sine-clock PRF, and the output i s 46.$ ,kc/s , i l l u s t r a t e d i n Figure 7 - 3 . The c i r c u i t U-lOus - J Clock Pulses - IN 30v Plate of T2 HI 100K 10% R2 IK tt n R3 47K 1W ii R4 IK tt it R5 10K w tt R6 1M £w it R7 330K n tt R8 15K tt it R9 2.7K tt tt P I 200K n it C l 25 mmfd 20% C2 .01 mfd n C3 100 mmfd ti T1,T2 D1.D2.D3 20v I-12AT7 1N191 Divided PRF - OUT Figure 7-3. Division-by-Two C i r c u i t and Waveforms -42-action i s as follows: I n i t i a l l y , T2 i s conducting and the voltage drop across R4 biases T l to cutoff. The plate of T l i s down s l i g h t l y due to a small current flowing through R3-D1-R2-R1. For d i v i s i o n by two with the components shown, the grid-return v o l t -age Er i s approximately 200 v o l t s . The grid of T2. i s clamped at + 1 5 v o l t s i n the' quiescent' state. When an input pulse i s applied, the g r i d of T2 i s driven negative and released from i t s clamp. Regeneration occurs through the common cathode r e s i s t o r R4 and, i n a very short time, T l i s conducting and T2 i s biased to cutoff. Because the plate of T l i s down, the c i r c u i t i s i s o l a t e d from the t r i g g e r source through diode Dl. Now the charge on the coupling capacitor CI, which i s holding T2 i n clamp, begins to leak o f f exponentially through R6 to the return voltage Er. The time-constant C1R6 and the return voltage are chosen so that while T2 i s s t i l l i n clamp, a second t r i g g e r pulse passes at the input and i s blocked by Dl. In between t h i s pulse and the next t r i g g e r pulse, the g r i d of T2 r i s e s high enough to overcome the bias imposed by the current of T l through R4. Regeneration then occurs and restores the c i r c u i t to i t s o r i g i n a l state, with T2 conducting and T l cut o f f . The c i r c u i t i s then ready to accept another t r i g g e r pulse. The output PRF i s taken from the plate of T2. It w i l l be noticed that "the c i r c u i t a c t i o n i s very s i m i l a r to that of the pulse generator, but cathode coupling - 4 3 -instead of double plate-to-grid coupling i s employed. Also, Er can be changed to a l t e r the delay time of the c i r c u i t . The delay time depends upon the tr i g g e r shape, i n i t i a l voltage settings, and the time-constant ClR6, as well as upon Er. The division-by-four c i r c u i t divides a PRE of 3.6 kc/s to 0 . 9 kc/s. To obtain t h i s d i v i der, the following changes are made in Figure 7-3: Cl = ,002mfd R6 = 2.2 M 1/2W 10% R° = 6 8 K 1/2W 10% 7-4. Phantastron_Division-bj-Thirteen C i r c u i t . The phantastron divider,2 > 4 shown i n Figure 7-4, divides the output of the f i r s t d ivider stage from 46 . 8 kc/s to a 3.6 kc/s PRF. The phantastron i s e s s e n t i a l l y a M i l l e r sweep generator which has a. l i n e a r timing waveform, rather than the exponential waveform of the multivibrator c i r c u i t s already discussed. The l i n e a r waveform gives increased timing s t a b i l i t y . A p o s i t i v e t r i g g e r of 15 v o l t s i s required to obtain a 2 5-volt negative pulse' from the cathode. The c i r c u i t action w i l l be described b r i e f l y . In the quiescent state, screen current flows to r a i s e thecathode potential to +40 v o l t s . Since the suppressor i s biased at +25 v o l t s , plate current i s cut o f f . When a t r i g g e r is received at the suppressor, plate current s t a r t s to flow, causing a sharp drop i n po t e n t i a l at the plate. This drop; however, i s coupled to the control g r i d , so that the plate current i s limi t e d to a small value. At the same time the cathode C l D l ± P l a t e o f T I 3 5 v C a t h o d e o f T I r D i v i d e d P R F - O U T I I H 1 i i tkl m 2 0 v s e c -^ 5 v R l 1 0 0 K 1( R 2 6 8 K it tt R3 6 . 8 K tt tt R 4 6 . 9 M tt tt R 5 22K tt ft! R 6 4 . 7 K tt ft P I 2 0 0 K tt tt C l 1 0 0 mmfd 2( G2 50 tt tt G3 2 5 0 tt ft C 4 . 2 5 m f d tt T I T 2 D l 6 & S 6 £ - 6 A L 5 1 N 1 9 1 I n p u t P R F - I N F i g u r e 7 - 4 . P h a n t a s t r o n D i v i s i o n - b y - T h i r t e e n C i r c u i t - 4 4 -current, and hence the screen current, i s greatly reduced, so that a large p o s i t i v e step appears at the screen. A f t e r t h i s i n i t i a l sharp drop, the M i l l e r sweep action begins (Figure 7-4J. The control g r i d : i s now free and has a large p o s i t i v e bias, and the plate-to-grid coupling condenser C2 forms a negative feedback loop. Electron current flows from the tube into the l e f t side of C2, and through R4 to Er. Therefore the l e f t side of C2 must drop i n p o t e n t i a l at a rate dependent upon R 3 C 2 . This requires a plate current which increases l i n e a r -l y with time u n t i l f i n a l l y the tube "bottoms", or runs against the knee of the plate c h a r a c t e r i s t i c . Since further drop i n the plate voltage i s impossible, and the increasing current cannot be further supplied, the right side of C2 r i s e s exponentially toward Er u n t i l the g r i d supplies the current. Now the screen current again increases, the control g r i d i s i n clamp, and the tube returns to i t s quiescent state and awaits the next trigger' pulse. With the component values shown, a d i v i s i o n r a t i o of 13 i s obtained by adjusting Er i n the neighbourhood of 220 y o l t s . It has been stated i n the l i t e r a t u r e 3 that with a stable power supply and p r e c i s i o n components, r e l i a b l e d i v i s i o n by 30 has been achieved. Therefore a r a t i o of 13 appears to be well within the stable range of operation of the phantastron. With the suppressor t r i g g e r i n g employed here, the source i s not disconnected during the plate rundown, but the wave-forms are not adversely affected. The phantastron d i v i d e r out-put pulse, as mentioned e a r l i e r , i s a 3 .6 kc/s PRF which triggers -45 the division-*by-four d i v i d e r . 7-5. The 1 0-Microsecond Coincident Gates It has already been seen that the output PRF of the division-by-four circuut triggers three coincident gates which supply the early (EP) , zero (OP), and l a t e (LP) 1 0 microsecond gating pulses. The c i r c u i t used i s the pulse generator of 50v 1 EPG E a r l y Pulse Gate OPG Zero Pulse LPG Late Pulse Gate Interstage Coupling C i r c u i t CCP Cosine- Clock Figure 7-5:. Coincident Down-Gate Waveforms Figure 7 - 2 with the following change to increase the width of the output pulse from 3 microseconds to 1 0 microseconds: R l l = 1 . 5 1 1 1 / 2 W 1 0 % . The waveforms f o r the coincident gate - 4 6 -c i r c u i t s are shown i n Figure 7-5» With a stable power supply the c i r c u i t i s very r e l i a b l e , but the timing r e s i s t o r and condenser, R l l and C2, are quite c r i t i c a l . With the 20% capacitors a v a i l a b l e , i t was necessary to make up the exact resistance required with a combination of smaller values. For a design which Is c r i t i c a l and which has to be standardized, i t i s advisable to use components of 5% t o l e r -ance throughout. The cathode waveform of the EP i s d i f f e r e n t i a t e d to supply the t r i g g e r f o r the OP gate, and that of the OP gate supplies the tr i g g e r f o r LP. Diode-coupling between gates i f employed to bias o f f a small amount of high-frequency leak-through which appears on the output waveform of the f i n a l d i v i d e r stage (the t r i g g e r f o r the EP gate). A c i r c u i t i d e n t i c a l to the coincident gates i s used to supply the channel-gate pulse. As mentioned e a r l i e r i n connection with the block schematics, t h i s gate i s triggered by zero pulse (OP). The tr i g g e r pulse i s selected In a pentode AND gate, to be described l a t e r i n t h i s section. ... The 1/4-ehannel gate is a 10-microsecond gate l i k e those already discussed. To obtain t h i s 'gate, however, a 15-microsecond coincident gate, triggered on the channel-marker pulses (CMP), must supply the required t r i g g e r pulse. For a 15-microsecond delay time, R l l of the previously-described c i r c u i t must be increased to 2 megohms. The output of the 1/4-channel gate is used i n conjunction with two 300-microsecond selector - 4 7 -pulses to obtain the ind i v i d u a l P- and PO gating pulses. 7-6. The 300-Microsecond Coincident Gates and Triode AND Gate Two 300-microseeond coincident gates are used to supply the selector pulses f o r the P- and PO gates of the 1/4-channel gate t r a i n . The c i r c u i t of the coincident gates i s the same as that of Figure 7-2 but for the following changes:• C2 = 6 2 0 mmfd 2 0 % R l l = 4.7M 1/2W 1 0 % The components i n these gates are not too c r i t i c a l so long as the waveforms blanket the P- and PO pulses. The f i r s t gate i s triggered by l a t e pulse (LP), and the second by the t r a i l i n g edge of the output from the f i r s t . The two pulses obtained are added to the P- and PO gates at the g r i d of a triode AND gate,-^ shown in Figure 7-6. The triode i s biased to cutoff except when the selected pulse causes i t to come out of clamp. Then the tube conducts, and the selected pulse appears at the output. The main objection to t h i s gate i s that the selected pulse i s attenuated, and there i s always some i n t e r a c t i o n of the pulse sources. I f a larger pulse i s necessary, a stage of ampli-f i c a t i o n could be used before the tri o d e gate. This would also i s o l a t e the sources. As i t happens, the 1 5 - v o l t pulse obtained from the present arrangement i s just s u f f i c i e n t to operate, a pentode clock-pulse selector gate, since the suppressor of such a gate i s biased to cutoff at - 2 0 v o l t s . Rl 39K £W XVTO R2 270K » » R3 1M ..» .. " R4 IK " " CI ,.,01 mfd C2 .001 •» T l J-12AT7 Grid of T l -^10;is 18v 20v . L "llv Cathode of T l - OUT Figure 7-6. Triode AND Gate and Waveforms - o Rl 1M £W 10$ CI .01 mfd R2 68K n t? R3 27K n f t T l 6AS6 R4 10K tt « R5 22K t t n R6 270K n H SCP - Input 1 Coincident Gate- In.2 T 50v .L T 150v 1 Selected SCP - OUT Figure 7-7. Pentode AND Gate and Waveforms - 4 8 -7 - 7 . The Zero- and Late-Pulse Selector Gates The zero pulse (OP) and late pulse (LP) must be derived separately f o r t r i g g e r i n g the channel and 1/4-channel coincident gat,es. This i s accomplished using a pentode AND g a t e , ^ shown schematically i n Figure 7 - 7 . This gate i s t y p i c a l of the pulse-selector gates used extensively i n the sweep t r i g g e r i n g c i r c u i t s . Its operation w i l l be reviewed b r i e f l y . Normally, both grids are biased to cutoff, so that no plate or screen current flows with no s i g n a l applied. The cosine-clock pulses are applied to the control g r i d , and the OP or LP selector pulses to the suppressor. With the plate current biased to cutoff by the suppressor, a small screen current w i l l flow whenever a cosine-clock pulse brings the control g r i d ou-t of clamp. However, nothing as yet appears at the plate. When a gatingpulse occurs at the same time as one of the clock pulses, both grids are released and the tube i s allowed to act as an amplifier f o r the duration of the gating pulse. This allows just one of the clock pulses to be amplified, so that a large negative pulse appears at the plate of the tube. The large gain of the tube causes the output pulse to be sharpened considerably. With large input pulses, output pulses of 5 0 - 3 0 0 v o l t s and of 0 . 2 microsecond rise-time are e a s i l y obtained. The c i r c u i t i s ideal for t r i g g e r i n g sweep input f l i p - f l o p s because, in addition to supplying a large t r i g g e r pulse, i t normally - 4 9 -conducts no plate current, thus saving on power supply require-ments. 7-8. Control F l i p - F l o p and Channel Gates The control f l i p - f l o p , bistable multivibrator triggered by the channel-marker pulses (CMP), supplied from each gri d a posit i v e output voltage which blankets alternate channels from CMP}, to CMP^ + 1 . The output from each g r i d i s taken through a cathode follower to a. group of gating c i r c u i t s to select the required ODD and EVEN pulse groups. The pulses which must be so selected are the 1/4-channel (P-), centre-channel (PO), channel (CP), and l a t e (LP) pulses. The schematic c i r c u i t of the control f l i p - f l o p , cathode followers and channel gate selectors i s shown in Figure 7-8. Selection of the P-,lP0 and LP pulses w i l l be reviewed presently. The control f l i p - f l o p c i r c u i t i s i d e n t i c a l to the sweep input f l i p - f l o p s previously mentioned. The c i r c u i t i s designed for a g r i d swing of ±15 v o l t s . The exact voltage swing i s not too important, so long as a suitable amplitude i s obtained for gating requirements. In the number of c i r c u i t s b u i l t ' , the outputs vary between 12 and 20 v o l t s amplitude, which i s quite s a t i s f a c t o r y . It i s important that the plate and grid-biasing r e s i s t o r s be well matched f o r symmetrical operation. In a general analysis of the f l i p - f l o p design problem, which has a unique solution f o r a p a r t i c u l a r tube and output voltage, i t was found that i f the r e s i s t o r errors were i n the same d i r e c t i o n ( i . e . high or low) then f o r a r e s i s t o r tolerance of 5%, and a O u t p u t o f T l 1 5 v 5 0 v 1 C h a n n e l G a t e s - I N 1 R l R 2 R3 R 4 R5 R 6 R 7 R8" R9 R I O R l l R 1 2 R13 C I C'2 C3 56K 2 7 0 K 56K ». 1 8 0 K " 270Kww » 15K " 1 8 0 K 27K 6 8 K 1M 27K 2 2 0 K 18K 100 mmfd 50 » .01 m f d tt 5% tt » tt re rt 20% t t t t T 3 0 0 v 1 T l T 2 T3 , T 4 D l 5 7 5 1 1 2 A X 7 6 A S 6 1 N 1 9 1 S e l e c t e d CHG - OUT 1 F i g u r e 7 - 8 . C o n t r o l F l i p - F l o p a n d C h a n n e l G a t e s -50-matched tube, the error i n the output swing i s approximately 1 0 % . Since the operation of the f l i p - f l o p i s very s t r a i g h t - -forward, i t w i l l not be reviewed here, except to say that a 3 0 -volt t r i g g e r pulse i s required to effect a change i n state. The input and output waveforms are I l l u s t r a t e d with the c i r c u i t diagram. In the channel-gate arrangement, the control f l i p - f l o p outputs are added at the suppressor grids of two pentode selector gates. The suppressor i s normally biased to cutoff, so tjiat only wh,en the positive-going waveform appears does the tube conduct. The channel-gate t r a i n i s applied to both control grids through a small decoupling condenser, so that alternate channel gates appear inverted at the pentode output. The two outputs are then taken to separate phase inverters which give both p o l a r i t i e s of the ODD and EVEN channel gates at t h e i r outputs. Now that the gates are selected, the ODD and EVEN channel pulses are selected i n another gating c i r c u i t and applied to the ODD and EVEN sweep input f l i p - f l o p . These c i r c u i t s w i l l be reviewed i n section 8. 7 - 9 . Late Pulse (LP) Triode-Pent^ode Gates-, The l a t e pulses, ODD and EVEN, are selected f o r use i n the sweep f l i p - f l o p s i n a pentode-triode gate, shown i n Figure ; 7 - 9 . Two si m i l a r gates are required, actuated by the two signals from the control f l i p - f l o p , f o r the ODD and EVEN integrators. The control f l i p - f l o p signal i s applied to the g r i d of the triode, so that when t h i s signal i s p o s i t i v e , the pentode i s biased to cutoff by the current through the common cathode r e s i s t o r . When -51-Rl R2 R3 R4 R5 R6 R7 R8 15K 27K 6SK .68K 1M 10K 22K 270K 1W n tt tt tt it it tt tt ft tt it it n C l .01 mfd C2 .05 n TI i-12AT7 T2 6AS6 T -15v i T 50v 1. Input 1 - Control FF Input 2 - LP Gate 150v L r OUT - Late Pulses Figure 7 - 9 . Late-Pulse Triode-Pen'tode Selector Gate the signal goes negative, the t r i o d e i s cut o f f and the c i r c u i t acts l i k e th-e pentode AND gate of section 7 - 7 . The cathode must be by-passed to preserve the high gain of t h i s type of gate, 7 - 1 0 . The P- and PO Pulse Selector, Gates The P- and PO pulses, ODD and EVEN, are selected i n a pentode AND gate which combines two signals at the suppressor to bring the tube into the conducting state. The signals are the control f l i p - f l o p output and the P- or PO coincident gates. The sine-clock pulses are applied to the control g r i d , and both grids are normally biased to cutoff. -52-The c i r c u i t action i s i d e n t i c a l to that of the gate of section 7-7 except f o r the addition of the two signals at the suppressor. Since both signals are derived at low-impedance; sources, and the g r i d draws very l i t t l e current, the adding c i r c u i t i s quite e f f i c i e n t . There i s v i r t u a l l y no i n t e r a c t i o n . of the sources. The suppressor i s biased such that the posi t i v e part of the control f l i p - f l o p waveform brings the tube to the verge of conduction, and the added coincident pulse brings i t into the conducting state. The 15-volt coincident pulse i s just s u f f i c i e n t to produce a usable selected SCP trigger-pulse at the plate. Because of the rather c r i t i c a l grid-bias values f o r t h i s amplitude of input pulse, the power supply must be very stable. The only pulse c i r c u i t s which remain to be discussed are the sweep f l i p - f l o p t r i g g e r i n g c i r c u i t s . These w i l l be l e f t to section 8, which w i l l also describe the sweep amplif i e r and zero-comparator c i r c u i t s . 7-11. The Fine-Channel Schmitt Comparators and Associated Gates The block schematic arrangement of the f i n e - s c a l e l o g i c a l - d e c i s i o n comparators was discussed i n section 5. It remains to i l l u s t r a t e the d e t a i l s of the c i r c u i t and i t s i n t e r -connection with the pentode selector gates. The c i r c u i t of one of the comparators and the associated down-gates i s shown i n Figure 7-10. It has already been mentioned that the Schmitt d i r e c t -coupled comparator i s a bistable c i r c u i t which changes state Sweep Input to TI Plate of T2 - OUT 7 130v 7 13 Ov 10 msec 9 Plate of TI - OUT Rl 47K 1W 5% R2 82K it tt R3 180K £w it R4 47K tt it R5 150K n 10% R6 180K n it C l .05 mfd 20% G2 .01 tt « T1,T2 T3,T4 T5 T6 T7 T8 I-12AT7 I-12AX7 6AS6 tt tt it OP Gate P+ Gate EP Gate CP Gate Dl 1N191 Figure 7-10* Fine-Scale Schmitt Comparators and Down-Gates - 5 3 -whenever the input voltage r i s e s above a p a r t i c u l a r reference l e v e l . The required t r i g g e r voltage Er i s the difference between the negative bias voltage and the voltage at which tube T l begins to come out of clamp. The c i r c u i t returns to i t s quiescent state when the input f a l l s below that same l e v e l , barring the small hysteresis effect which i s always p r e s e n t . 1 0 For t h i s p a r t i c u l a r a pplication, a small hysteresis e f f e c t , or f a i l u r e of the c i r c u i t to t r i g g e r back at the same voltage that i t triggered forward, i s of no si g n i f i c a n c e . The cathode follower of the comparator i s arranged so that the output when applied to a pentode gate w i l l cause the gate to open when the comparator i s i n the (+) state, and w i l l cause the gate to block when i t i s i n the (-) state. For the AND gates shown, the comparator must supply a signal which i s just below the suppressor cutoff bias i n the (+) condition, so that the coincident pulse w i l l turn the tube on the rest of the way. In the (-) state, the comparator must supply a signal which w i l l cause the gate to block the 5 0-volt coincident pulse. The c i r c u i t shown,, s a t i s f i e s t h i s requirement with an output si g n a l of -30 volts i n the "on" or (+) condition, and a signal of -150 v o l t s i n the " o f f " or (-) condition. B r i e f l y , the c i r c u i t a ction i s as follows: In the quiescent state, both comparators of the block v - < ' V o < v + are i n the o f f condition (Tl o f f , T2 conducting), so that the two output signals cause the gates to block. If the sweep input r i s e s above v-, the f i r s t comparator t r i g g e r s , and i f i t r i s e s above v+, the second comparator also t r i g g e r s . The T l g r i d bias l e v e l s are - 5 4 -such that the f i r s t comparator triggers at 1/4 the maximum normalized sweep (approximately 25 volts) and the second compara-tor triggers at just below 5/4 the maximum normalized sweep (approximately 75 v o l t s ) . The second unit i s set at just below 7^ v o l t s to allow time for P+ to be gated should that pulse be chosen to i n i t i a t e the downsweep. The comparator outputs combine i n the arrangement of Figure 5 - 3 to select the proper pair of pulses f o r tr i g g e r i n g the coarse- and fine-channel downsweeps. This concludes the discussion of the integrator control c i r c u i t s . Section 8 describes the c i r c u i t d e t a i l s of the sweep input f l i p - f l o p s , the sweep amplifiers, and the zero comparators. 8. Integrator C i r c u i t D etails - 5 5 -This section i s concerned with the d e t a i l s of the i n -put f l i p - f l o p s and t h e i r associated gates, the diode gate sweep inputs, the sweep amplifiers, and the zero comparators. These w i l l be described i n order i n the following sections,, 3-1. Sweep Input F l i p - F l o p s The sweep amplifier requires a positive or negative step voltage input to produce respectively a negative or a p o s i -t i v e ramp output. The input f l i p - f l o p s , triggered by appropriate pulses, supply t h i s voltage. The f l i p - f l o p s are standardized to del i v e r an output of ±15 v o l t s , and are i d e n t i c a l to the control f l i p - f l o p discussed e a r l i e r . A t y p i c a l input f l i p - f l o p and i t s gates are shown i n Figure 8-1. The c i r c u i t action i s as follows: The two pentode gates, TI and T2, receive pulses from the magnetic drum read-head or from some part of the control c i r c u i t s . In the former ca&e, the magnetic drum i s positioned so that, for example, the CP1 gating pulse from the control c i r c u i t s appears at the same time as CP1 (channel pulse 1) read from the drum. This pulse i s amplified i n TI to trigger the f l i p - f l o p . The f l i p - f l o p i s now i n the "set" condition, and i t s output s i g n a l turns on T2 to allow i t to accept the function pulse from the drum. For the example chosen, the function pui.se i s y C Q . This pulse resets the f l i p - f l o p through T2, and the sweep input i s turned o f f . Now the input tubes are i n t h e i r o r i g i n a l states, with TI ready to accept the next channel pulse, and T2 turned o f f . CHG 1 n CPI +15 0 -15 n-1 CHGI 3 Selected Channel CP2 n-2 c CP3 Gate - IN 1 Drum Read IN 2 OUT to Sweep Amplifier Rl 68K 1056 CI R2 27K tt C2 R3 1M it C3 R4 10K tt R5 18K « R6 270K tt R7 4.-7M tt D1,D2 R8 56K tt 5% T l R9 180K tt T2 RIO 270Kww tt T3, T4 R l l 15K tt 5% T5 R12 68K 2W 10% .05 mfd .01 » 100 mmfd tt tt 1N191 Germanium 6AS6 CP Selector ft py ft 5751 Input F l i p - F l o p I-12AT7 Cathode Follower Figure 8 -1. Sweep Input F l i p - F l o p and Selector Gates -56-This f l i p - f l o p therefore reads the information i n the t, ODD channels into the sweep-amplifier. An i d e n t i c a l arrange-ment reads the Information i n the EVEN channels into the opposite sweep. Obviously a t o t a l of four such "read-in" units are required f o r the four sweep c i r c u i t s . In the coarse channels, another f l i p - f l o p i s required to supply the signal for the down-sweep. As discussed i n section 5 , t h i s f l i p - f l o p turns on with a s e l e c t e d e a r l y , zero or l a t e pulse input, and turns o f f with a pulse from the zero compar-ator when thesweep reaches zero v o l t s . The output signal i s po s i t i v e , since i t must produce a negative-going ramp. The two f l i p - f l o p s must be i n the correct i n i t i a l state to produce the sweep i n the required manner. As mentioned i n section 5, the fi n e - s c a l e sweeps require two a d d i t i o n a l f l i p - f l o p s . These units are i d e n t i c a l to those already discussed, but f o r a d i f f e r e n t input arrange-ment. The f i r s t of t-hese f l i p - f l o p s t r i g g e r s on the channel pulse and resets on the centre-channel pulse, PO. The si g n a l from t h i s unit causes a negative sweep which when added to the e x i s t i n g sweep, e f f e c t i v e l y subtracts a i n the integration operation. 2 The second f l i p - f l o p reads the coarse-channel v a r i a b l e , scaled by dt, int o the-fine scale. Therefore t h i s unit i s set by the channel pulse and i s reset by the pulse representing the new coarse-channel variable as i t i s generated by the coarse-scale zero comparator. This f l i p - f l o p e f f e c t i v e l y adds to the sweep n. 1 the quantity y c ~ - a . The sealing by | of these two inputs 2~~~i i s accomplished i n the sweep input diode gates (section $-2). - 5 7 -It i s clear that the input f l i p - f l o p s are elements which translate a pulse p o s i t i o n into a signal of accurately-determined time-duration. When t h i s voltage or si g n a l i s applied to the sweep amplifier, a corresponding p o s i t i v e or negative ramp of accurately-known amplitude i s produced. The sweep c i r c u i t which accomplishes t h i s action w i l l now be described. 8-2. The Sweep Amplifier One of the most c r i t i c a l designs encountered i n the 3,10 integrator c i r c u i t s i s that of the sweep amplifier. The four amplifiers must a l l sweep at precisely the same rate f o r the same input s i g n a l . As mentioned before, i t i s not important that the gain of the amplifiers i s a constant, but the time-constants of the d i f f e r e n t feedback networks must a l l be the same. How t h i s i s accomplished w i l l be seen l a t e r i n t h i s section. The basic function of the sweep c i r c u i t has already been described. The c i r c u i t d e t a i l s are shown i n Figure 8"-2. The zero comparator (section 8-3) i s also shown. The sweep amp-l i f i e r has two stages. The f i r s t stage T l i s a difference ampli-f i e r having a gain of approximately 50. The second stage, a pen-tode amplifier, has a gain of about - 7 0 . The open-loop gain of the amplifier i s therefore approximately -3500, This gain i s quite s u f f i c i e n t to achieve the accuracy expected i n the i n t e -gration. The mathematical errors inherent i n t h i s type of approxi-mate integration w i l l probably exceed any error introduced from the sweep amplifier. The o v e r a l l gain i s negative i n order that negative feedback can be used. H I 270Kww to 1($ R9 100K 10% Cl .01 mfd 1% Tl,T-5 5751 R3 180K t » 5% t t RIO 27K tt 5% C2 .01 » 20% T4,T6 12AT7 R4 180K 1W R l l 56K n ft C3 12 * -el e c t r o l y t i c T3 12AX7 R5 18K f t t t R12 1.5K n « C4 .05 " 20% 50 mmfd " T2 6AK5 R6 27Gohm iw t t R13 10K w tt C5 R7 33K t» 10% R14 330K n 10% 5% ,2,3,4 1N461 ,6,7 1N191 R8 1M t t t t R15 150K tt Dl - R16 15K t t n D5 Figure 8-2. Diode Gate, Sweep Amplifier and Zero Comparator -58-The amplifier has two feedback loops, an inner p o s i t i v e loop and an outer negative loop. The inner loop, from the cath-ode of T2 to the cathode of T l through R7, compensates f o r the loss i n gain i n T2 caused by not bypassing the cathode, thereby avoiding the use of a bypassing capacitor. The outer loop formed by the capacitor CI and the input r e s i s t o r together cause the amplifier to act as an integrator. The time constant R1C1 determines the rate of the sweep. More w i l l be said about t h i s i n the discussion of the diode gates l a t e r i n t h i s section. One important aspect of the c i r c u i t not yet considered i s the clamping tube T3. This tube, a back-coupled 12AX7, Is biased to cutoff during the entire sweep, so that the grid of T2 i s free to receive the negative input s i g n a l during t h i s time. The signal f o r the clamp i s obtained from the zero com-parator; t h i s w i l l be made clear i n the next section. As soon as the sweep returns to zero and t r i e s to go negative, a p o s i -t i v e signal of a few m i l l i v o l t s from the comparator-drives the clamp tube i n t o conduction, thus dc-restoring the coupling capacitor C2, and e f f e c t i v e l y holding the grid of T2 at zero v o l t s . The clamp tube acts l i k e a diode except that the action i s made very fast through the use of the g r i d , and the back-resistance i s much higher than conventional germanium or s i l i -con junction diodes. Because of t h i s high back-resistance, the capacitor C2 can be made quite small and the time-constant of the coupling c i r c u i t s t i l l remain very large. The capacitor C3 i s dc-restored by the germanium diodes D5 and D6 i n Figure 8-2. A large capacitor i s required - 5 9 -R l R l 2 7 0 K ww \% C I . 0 1 m f d 1% D ' s 1 N 4 6 1 S i l i c o n J u n c t i o n R l ( a ) 3 0 K P o t . 2 7 0 K ww 1 N 4 6 1 D i o d e s . 0 1 1% C a p a c i t o r " M e t a l C o n t a i n e r " • " P i n B a s e F i g u r e 8-3. S w e e p I n p u t D i o d e G a t e h e r e s o t h a t t h e f e e d b a c k c u r r e n t , i s n o t a p p r e c i a b l y i m p e d e d . I f t h e i m p e d a n c e p r e s e n t e d b y t h i s c a p a c i t o r w e r e l a r g e , t h e s w e e p w o u l d be a t t e n u a t e d a n d t h e f u l l l i n e a r r a n g e o f t h e a m p -l i f i e r w o u l d n o t b e u s e d t o b e s t a d v a n t a g e . T h e a c t i o n o f t h e d i o d e - g a t e i n p u t w i l l now be 9 r e v i e w e d . T h i s t y p e o f g a t e ( F i g u r e 8 - 3 ) h a s a p o s i t i v e a n d a n e g a t i v e i n p u t . W i t h n o s i g n a l a p p l i e d , a c u r r e n t f l o w s t h r o u g h P I - R 1 - D 1 - D 2 - * R 1 - P 2 . I f a n e g a t i v e v o l t a g e i s a p p l i e d t o i n p u t C f r o m a f l i p - f l o p , d i o d e D3 : c o n d u c t s , c a u s i n g : a d r o p i n -60-p o t e n t i a l a t t h e a n o d e o f D l , T h e r e f o r e D l b l o c k s , , a n d , t h e .. i n p u t g r i d i s c o n n e c t e d t h r o u g h D2-R1-P2 t o t h e n e g a t i v e s u p p l y . T h e p o w e r s u p p l y i s s t a b i l i z e d s o t h a t t h e o u t p u t r a m p r i s e s a t a . f i x e d r a t e d e p e n d e n t o n t h e t i m e - c o n s t a n t R1C1 ( a p p r o x i -m a t e l y ) . p o s i t i v e s u p p l y i s c o n n e c t e d t o t h e g r i d t h r o u g h P1-R1-D1, a n d B - i s i n t e g r a t e d t o g i v e a n e g a t i v e r a m p o u t p u t . T h e s l o p e o f t h i s r a m p i s t h e n o r m a l i z e d (-1) s w e e p s p o k e n o f e a r l i e r , w h e r e a s t h e s l o p e g i v e n b y t h e c a s e a b o v e i s t h e n o r m -a l i z e d (-1) s w e e p . T h e s t a n d a r d s w e e p c a u s e d b y o n e i n p u t i s e a s i l y c a l c u l a t e d f r o m t h e e q u a t i o n I f i t i s a s s u m e d t h a t t h e i n p u t r e s i s t a n c e i s 300K, t h e i n p u t s i g n a l i s e^ -300v, C l i s .01 m f d , a n d t h e i n t e g r a t i o n t i m e i s 1000 u s e e , then i t i s f o u n d f r o m t h e a b o v e f o r m u l a t h a t e 0 = 100v. o b t a i n e d b y s i m p l y a d d i n g a n o t h e r p r e c i s i o n r e s i s t o r i n s e r i e s w i t h e a c h h a l f o f t h e d i o d e g a t e ( F i g u r e 8 - 3 ( a ) ) . T h e s w e e p r a t e o b t a i n e d i s n o t e x a c t l y h a l f t h e s t a n d a r d b e c a u s e t h e o r i g i n a l i n p u t r e s i s t a n c e i s n o t e x a c t l y R l , b u t i s R l i n s e r i e s w i t h PI i n s e r i e s w i t h t h e f o r w a r d r e s i s t a n c e o f d i o d e D l . T h e e r r o r d u e t o t h i s d i f f e r e n c e i s v e r y s m a l l i n d e e d , e s p e c i a l l y s i n c e i t i s t a k i n g p l a c e i n t h e f i n e s c a l e . N o t i c e t h a t t h e t w o a d d i t i o n a l r e s i s t o r s a r e p l a c e d e x t e r n a l t o t h e p l u g - i n u n i t i n o r d e r t h a t t h e u n i t s b e i n t e r c h a n g e a b l e . C a l i b r a t i o n I f n o w a p o s i t i v e s i g n a l i s a p p l i e d t o i n p u t D , t h e A s w e e p r a t e o f a p p r o x i m a t e l y h a l f t h e s t a n d a r d , i s -61-of the various time-constants i s performed i n an RC bridge, designed s p e c i f i c a l l y f o r t h i s purpose. Potentiometers PI and P2 are required to compensate for variations i n the capacitor CI i n the d i f f e r e n t c i r c u i t s , since t h i s element i s the least exact of the bridge elements. It i s apparent, then, that so long as the amplifier has s u f f i c i e n t gain and i s stable, and the input c i r c u i t i s c a l -ibrated, the ramp voltage output w i l l have an accurate and con-sistent slope. Proper c a l i b r a t i o n of the time-constants of the input c i r c u i t s assures r e p e a t a b i l i t y among the four c i r c u i t s . In addition, the resistance of each half of the i n d i v i d u a l gates must be the same to assure that the p o s i t i v e and the negative ramps have the same sweep r a t e . 8-3. The Zero Comparator 10 The zero comparator d e l i v e r s an output pulse whenever the down-going sweep reaches zero v o l t s . The c i r c u i t i s shown i n Figure 8-2, tubes T5 and T6. For r e l i a b l e operation, i t i s imperative that the comparator pulse coincide very c l o s e l y with the time that the sweep reaches zero. Any error i n the t r i g g e r -ing time w i l l be r e f l e c t e d as a cumulative error i n the i n t e g r a -t o r variable undergoing operation. The comparator consists of a direct-coupled f l i p - f l o p , T 6 , preceded by a difference a m p l i f i e r , T5« In the quiescent state, the input i s at zero v o l t s , and T6(a) i s cut o f f by the cathode current flowing through T6(b). The clamp tube T3 i s ac coupled from T 6(a); i t s g r i d i s at zero v o l t s i n the quies-- 6 2 -cent state, so that the grid of T2 i s clamped at zero. When the sweep sta r t s to go p o s i t i v e , a large p o s i -t i v e signal (amplification 60) appears at the output of T5 and t r i g g e r s the f l i p - f l o p . The f l i p - f l o p bias l e v e l s are adjusted so that i t w i l l t r i g g e r on a 3-volt s i g n a l ; t h i s corresponds to something le s s than the f i r s t 0.1 v o l t r i s e of the sweep voltage. When regeneration occurs, T6(a) conducts heavily and i t s current bieases T6(b) to cutof f . Simultan-eously, the grid of T3 i s driven negative, so that T3 i s biased to cutoff and the grid of T2 i s fr e e . After a decision i n the f i n e - s c a l e , the sweep-down begins. When the sweep f a l l s to approximately 0.1 v o l t s , the grid of T6(a) begins to cut o f f , regeneration occurs, and the o r i g i n a l tube currents are quickly restored. As soon as the f l i p - o v e r i s accomplished, a negative pulse from the d i f f e r -entiated plate waveform of T6(b) turns o f f the f l i p - f l o p which supplies the si g n a l f o r the downsweep, and the sweep i s clamped at zero by the clamp tube, T 3 . In the coarse scale, the negative t r i g g e r from the comparator i s used to generate the 10-microsecond coincident pulse required to gate the sine-clock pulse representing the integrated v a r i a b l e . In the fin e scale, a p o s i t i v e pulse i s taken from T6(a) to represent the variable d i r e c t l y . This concludes the discussion of the c i r c u i t d e t a i l s of the integrator. The r e s u l t s of the t e s t s of the basic u n i t s and a summary a r e presented i n section 9. - 63 -9. Testing the C i r c u i t s 9-1. Introduction In t e s t i n g the apparatus, the main object was to determine whether the sweep c i r c u i t s could function as a dynamic storage unit. The arrangement i s t e c h n i c a l l y described as a pulse-selection analogue dynamic storage u n i t . The d i g i t a l computer cburiterpart of t h i s unit i s a dynamic storage r e g i s t e r . The basic mechanism of t h i s type of r e g i s t e r i s the f o l l o w i n g : ^ The word (pulse t r a i n ) i s introduced at one end of a delay l i n e whose delay time i s equal to the time-duration of the word, and the output signal i s returned to the delay-line input so that the word continues to c i r c u l a t e around a closed path. The test devised uses the two coarse-scale units, and comprises three basic steps. F i r s t the sweeps are made to function from a selected group of pulses. When they are functioning properly, the two c i r c u i t s are connected i n series so that the information injected into the f i r s t c i r c u i t i s read into the second c i r c u i t . Next, the output of the second c i r c u i t i s returned to the input of the f i r s t , and the synchronizing source disconnected, so that the injected information i s re-cycled between the two sweeps. The f i n a l t e s t i s to inj e c t a pulse which ef f e c t s a small subtraction from the value of the stored function. A f t e r subtraction, the sweep recycles the remaining information. Details of the'test procedure w i l l now be described. FFI (-1) CPI P- OP P cPout 11 Pout CP3 P -FFI Output FF2 Output Sweep I Output Figure 9-l» Block and Waveforms f o r Coarse Integrator I 9-2. Basic Operation of the Sweep C i r c u i t s . The block-schematic arrangement f o r the f i r s t test of the sweeps i s shown i n Figure 9 - 1 , where the ODD coarse-channel sweep and i t s waveform are i l l u s t r a t e d . The f l i p - f l o p FFI i s triggered by channel pulses CPI, C P 3 , etc., and i s reset by the ODD P-pulses. That i s , P- i s used to simulate the function - 65 -pulse which, i n the normal operation of the computer, would be read from the magnetic drum. The downsweep, controlled by F F 7 , i s i n i t i a t e d ' b y the zero pulse, OP, which i s selected into ODD and EVEN pulses f o r purposes of the t e s t . The OP i s the down-sweep pulse which corresponds to a decision i n the f i n e scale to produce no change i n the coarse-scale value of the function. The comparator pulse resets F F 7 . For t h i s group of f i x e d pulses, the selected output pulse should correspond exactly to the P- EVEN pulse i f the ODD c i r c u i t i s functioning properly. As nearly as could be deter-mined by the oscilloscope, the coincidence between the output pulse and the P- EVEN puise which i s generated from the clock signal Is within 1 microsecond. The r e s u l t s of t h i s test indicate the following: F i r s t , the input f l i p - f l o p s , sweep amplif i e r and zero comparator must a l l be functioning s a t i s f a c t o r i l y i n order to produce the waveforms shown. The fact that the output pulse coincides within 1 microsecond with the selected P- pulse indicates that the zero comparator i s functioning according to design. With the second coarse-channel triggered' by the CP2, GP4, etc., P-EVEN, and OP pulses, a s i m i l a r r e s u l t was obtained. The ampli-tudes of the two di f f e r e n t sweeps were not quite the same because of a s l i g h t unbalance i n the time-constants. For purposes of t h i s t e s t , t h i s difference i s of no consequence. In the fine-channel c i r c u i t s , however, the exact c a l i b r a t i o n of the time-constants i s very important, because the sweeps t r i g g e r comparators which select the downsweep-initiating pulses for - 66 -both the coarse and f i n e - s c a l e c i r c u i t s . A mismatch here may seriously affect the action of these comparators and t h e i r selector gates. 9 - 3 . Dynamic Storage Test The b l o c k - c i r c u i t and waveforms f o r the test as a dynamic storage are i l l u s t r a t e d i n Figure 9 - 2 . The c i r c u i t action i s as follows: I n i t i a l l y , with switch SI i n p o s i t i o n 1, the simulated function pulse P- i s injected into the EVEN sweep, v i a FF2. The output of t h i s c i r c u i t i s the selected SCP which should correspond to the P- ODD pulse, and i s used to terminate the ODD upsweep as i l l u s t r a t e d (point 1 1 on the waveforms). The output of the ODD sweep should then correspond to the second P-pulse. It appeared upon examination of the open-loop waveforms that the sweeps were functioning properly. At t h i s time, the switch SI was thrown to p o s i t i o n 2 , disconnecting the P- pulse input and i n j e c t i n g the Pout pulse i n i t s place. If the two pulses 1 corresponded exactly before switching, and i f the switch was disconnected somewhere during the l e v e l portion of the two sweeps, then the pulse recycled with no noticeable change i n the sweep waveforms. Of course, t h i s switching procedure i s crude, because there i s a time l a s t -ing over several cycles that the loop i s disconnected. The switching i n t e r v a l i s i l l u s t r a t e d i n Figure 9 - 2 . While the source i s disconnected, the sweeps must hold at either 0 v o l t s or at V v o l t s , i n order that the operation continue as before (point 2 on the waveforms) once the switching complete. OP CPI Pout II P- or OP CP2 Po.ut (1) Switching Interval (2) OP CP3 Pout II Sweep I Output Sweep II Output (3) Figure 9-2. Dynamic Storage System and Waveforms ... - - 6 7 . -It would not be d i f f i c u l t to devise an electronic switch which would remove t h i s e r r a t i c behaviour during switch-ing, but i t was found that a successful switchover could be made i n about 50 percent of the number of attempts, so that a more elaborate setup i s impractical. Once the switchover was completed successfully, the stored pulse usually recycled f o r anywhere from several seconds to 10 or 20 minutes. The factors which cause the pulse to be lo s t are, (1) accumulated d r i f t due to small voltage v a r i a t i o n s i n the sweep which eventually cause the pelector gate to choose a pulse on either side of the recycling pulse, and (2) mechani-cal disturbances of the tubes, which are r e f l e c t e d i n the sweep waveforms. In the f i r s t case, the s e l e c t i o n of a pulse other than the recycled pulse would i n eff e c t cause an addition or subtraction on the stored pulse which would throw the sweep o f f scale i n either d i r e c t i o n i n a, matter of a few milliseconds. Therefore i t was impossible to detect the exabt cause for the . loss of the pulse. Probably the best c r i t e r i a of how well the c i r c u i t i s storing information i s the Figure 9-3 showing the output pulse from the ODD sweep, triggered on the injected P- pulse, which i s now disconnected from, the c i r c u i t . Since the leading edge of the P- pulse i s about 0 .2 microseconds long, there w i l l not be more than t h i s amount of deviation i n the t r i g g e r i n g point. The output shows, then, that the 3 0 0-volts drop of the leading edge of the pulse which i s being recycled l i e s within 1 micro-- 68 -• 1 j usee 1 »*i i i > i i V -Figure 9 - 3 . Recycled Function Pulse Triggered on P-second of the leading edge of the injected pulse. It i s f e l t that with the ex i s t i n g gating methods, t h i s performance i s unsurpassable. It i s possible that with d i f f e r e n t gating methods and f l i p - f l o p s (for example, using very fast-switching, low-impedance t r a n s i s t o r s ) much better r e s u l t s can be achieved. 9-4. Incremental Subtraction from the Stored Pulse. In the operation of the integrator, i t i s necessary that a small increment be added to or subtracted from the stored pulse without causing the c i r c u i t to go unstable. This action was simulated i n a test arrangement which makes use of the dynamic storage just described. The i n j e c t i o n tube and i t s connection f o r e f f e c t i n g a subtraction i n the stored pulse i s shown i n Figure 9-4. It is more convenient to perform a subtraction rathe? than an. addition because of the arrangement of the e x i s t i n g c i r c u i t s . F l i p - f l o p 8 of the previous c i r c u i t receives the OUT Zero Gates OG 111 Early Gates EG Conduction Region - TI Rl 15K 1W R2 56K £» R3 1M » Cl 100 mmfd C2 .01 mfd TI 4-12AT7 T2 6AS6 - _ 5 =100 10% ft Injected Early Gates Figure 9-4. Incremental Subtraction by Pulse Injection . - 69 -injected pulse from the tube T2. This tube i s already i n the c i r c u i t of 9-2, but i s not shown, The addit i o n a l c i r c u i t r y required i s the i n j e c t i n g tube T l which supplies the early gate to the OP gating tube, T2. The action i s described b r i e f l y : I n i t i a l l y , T l i s biased to cutoff and S2•.••is i n po s i t i o n 1. To perform subtraction, the c i r c u i t i s f i r s t made to function as a dynamic storage. When the sweeps are functioning properly, switch 32 i s closed. This introduces a step of B+ v o l t s at input 3 ; the step i s d i f f e r e n t i a t e d at the g r i d of T l to form a short pulse. This pulse i s added to the incoming EG- pulses, as shown i n Figure 9-4, and the added pulses bring T l into conduction and thus allow several pulses to be gated. The addition of these pulses at the g r i d of T2 allows the EP pulse to t r i g g e r into F F 8 i n front of the OP pulse f o r several cycles of operation. Suppose f o r example that two EP pulses are gated. The f i r s t pulse w i l l cause an incremental subtraction i n the ODD sweep, and the new value w i l l be cycled to the EVEN sweep. Therefore the amplitude of the sweep w i l l drop approximately 1/100 of the maximum sweep voltage, or about 1 v o l t . If now a second EP pulse i s gated, the ODD sweep subtracts another i n c r e -mental po s i t i o n from the stored pulse, which i s again cycled to the EVEN channel. It i s evident that i f a burst of EP pulses i s injected, as i s done here, then the sweep waveform w i l l decrease i n amplitude several v o l t s with each burst, or each time the switch S2 i s closed. A f t e r each burst, the OP pulses take over once more, and the amplitude of the sweep holds at whatever value - 70 -i t has reached. This type of subtraction was achieved success-f u l l y with the c i r c u i t i l l u s t r a t e d . There i s no obvious reason why addition could not be carried out with equal ease. It would be necessary to devise a c i r c u i t which would block the OP pulse and inject instead the LP pulse for a few cycles of operation. The ultimate test would involve use of the magnetic storage drum for introducing the variables. Because of the complexities involved, and the improvements which f i r s t should be made i n the integrator, such a test i s not fe a s i b l e at t h i s time. On the basis of the tests outlined, i t may be stated that the design of the basic integrator units has been successful. 9 - 5 . Summary and Recommendations. Prom the tests of the, basic c i r c u i t s , i t can be concluded that integration based on the method outlined i n the thesis i s f e a s i b l e and worthy of further study. The present arrangement of gating tubes and sweep, amplifiers w i l l probably give r e s u l t s to an accuracy commensurate with the errors introduced by truncating the Taylor series a f t e r the f i r s t d erivative. As was pointed out i n section ]5, i t should be emphasized that an integrator error of even 5 percent to 10 percent i s tolerable i n many problems of systems simulation, since the integrator error does not accumulate as do the errors i n the other arithmetic c i r c u i t s . However, assuming that an accuracy of 1 percent i s desired over a reasonably long i n t e -gration, the following recommendations are made: - 7 1 -1. Accurate t r i g g e r i n g of the zero comparator i s worthy of further study, because the comparator action probably contributes more to d r i f t than any other single element i n the c i r c u i t . If the comparator has a t r i g g e r i n g error of 1 microsecond (this appears to be the approximate error i n the exi s t i n g arrangement), and i f t h i s error accumulates, then i n 1 0 incremental integrations the t r i g g e r i n g point could d r i f t enough to cause the addition or subtraction of 1 i n the coarse scale. This magnitude of error i s int o l e r a b l e f o r any precise problem solutions. 2. C a l i b r a t i o n of the sweep amplif i e r time-constants i n the'plug-in units of Figure 8 - 3 was found to be very c r i t i c a l . It i s recommended that the carbon-resist-ance potentiometers be replaced with j?K or 10K wire-wound trimmers i n order to better define the c a l i b r a -t i o n point. 3 . With regard to the mathematical errors involved, a d e f i n i t e improvement can be made by simply extending the p r i n c i p l e of operation outlined to .include higher-order d e r i v a t i v e s . For any precise solutions , involving a lengthy computer run, t h i s i s imperative. This i s t h e o r e t i c a l l y possible because the higher derivatives are already present as function pulses stored on the magnetic drum. Before attempting t h i s , however, the long-term d r i f t s t a b i l i t y of the c i r c u i t s should be investigated. This would include the d r i f t effects inherent i n the storage drum, which have not been at a l l considered i n t h i s t h e s i s . The c i r c u i t s , p a r t i c u l a r l y the f l i p - f l o p s and selector gates, could be greatly s i m p l i f i e d by the a p p l i c a t i o n of fast-switching t r a n s i s t o r s (Pulse  and D i g i t a l C i r c u i t s . 10, pp 598-606). In the prototype integrator, approximately 100 vacuum tubes are used. Some of these tubes are applied to other parts of the computer as well, but about 75 of them are used just f o r the integrator. This does not' include the ring counter (Appendix B), which could also benefit by a p p l i c a t i o n of t r a n s i s t o r c i r c u i t s . Of these 75 tubes, about 55 are used f o r pulse gating requirements, and 13 of them are bistable f l i p - f l o p s . These 48 tubes could be e a s i l y replaced by t r a n s i s t o r s , as i n the l i t e r a t u r e c i t e d ; t h i s would save enormously on space and power requirements, and would greatly simplify the c i r c u i t r y . The c i r c u i t of the sweep amplifier could also be s i m p l i f i e d by a p p l i c a t i o n of the c i r c u i t shown schematically i n Figure 9 - 5 . This i s a two-stage balanced a m p l i f i e r with direct-coupling between the stages, but with ac-coupling at the output. If the output stage uses a wide grid-base tube (eg. 12AU7) then the d r i f t i n the f i r s t stage can be tolerated, so long as the tube i s s t i l l operating i n the l i n e a r portion of i t s - 73 plate c h a r a c t e r i s t i c s . This arrangement eliminates the interstage ac-coupling network, composed of the condenser C2 and the clamp tube T 3 of Figure 9-2. Rl A / W W - O OUT Clamp Figure 9-5. Proposed Sweep C i r c u i t The above are a few of the points which require further study before construction of the f i n a l prototype integrator i s attempted. From the r e s u l t s of the i n v e s t i g a t i o n outlined i n t h i s t h e s i s , there appears to be no great obstacle' i n the way of a t t a i n i n g integration to 1 percent accuracy. -74-Appendix A, Recording Devices The integration operation i s very f a s t , and1 f o r many applications a continuous recording device i s imprac-t i c a l because of the lengthy response time of the recorder. The recorder i s therefore usually more of a sampling device, and the integration operation i s stopped while the record is; being taken. In order to see the high-speed variations taking place during integration, an oscilloscope would be required. Such a device would be useful only as a q u a l i -t a t i v e measure of the operation, that i s , to see whether or not the integrator i s working. One possible system of reading the functions at a p a r t i c u l a r point i n the operation i s i l l u s t r a t e d i n the F i g -ure A - l . In order to use t h i s system, the erase and rewrite operations must be blocked, so that the sweep c i r c u i t s are continously reading out a fixed value of the function. I f sampling at a certain i n t e r v a l i s required, an electronic switching device which blocks the operation af t e r a s p e c i f i e d number of incremental integrations can be used. Assuming that the operation has been blocked, the c i r c u i t of Figure A - l w i l l function as follows: Channel pulse 1 sets FF1 and FF2. The outputs of these two f l i p - f l o p s are of opposite p o l a r i t y and are added i n the c i r c u i t represented by block A (or they are of the same p o l a r i t y i f the adder has a negative i n p u t ) . The adder del i v e r s a positive or negative output during the time that Figure A - l . Servo Read-Out System -75-the two signals do not cancel- one ano^liwrv: *Ehe f l i p - f l o p FF1 i s rest by: the function pulse Py. Channel pulse 1 also sets FF3 i causing the Sweep I to begin sweeping p o s i t i v e . Assume that the potentiometer driven by the servo motor i s set near the voltage which (when translated into a pulse position) represents Py. Now Sweep I r i s e s u n t i l i t reaches the voltage s e t t i n g of the potentiometer; then the comparator generates a pulse Px, which i s an approximation to Py. The pulse Px resets FF3, and sets FF2 and FF4- The Sweep I f a l l s u n t i l the zero comparator resets FF4» It may be seen from the waveforms that a posi t i v e or negative sig n a l i s obtained at the output of the adding c i r c u i t . This si g n a l i s detected and then integrated i n a RC c i r c u i t to give at the input to the servo amplifier an error signal proportional to the area of the adder output .pulse. The amplifier then app-l i e s the signal to the motor, and the servo positions the potentiometer accordingly. Since the function pulse i s being read continuously, the servo should position the potentiometer at the correct voltage representation of Py within a very b r i e f time. An alternate method of recording i s to use a si m i l a r arrangement, but to set the potentiometer manually. The pulses Px and Py could be observed on an os c i l l o s c o p e . Either method should give accurate r e s u l t s , but the servo system i s simpler to operate. The functions i n any channel can be read by t h i s method by selecting the desired channel-pulse input from the r i n g counter. This could be done very e a s i l y with a rotary switch connected to the various ring-counter outputs. -76-Appendix B. The Ring Counter The r i n g counter i s used to generate the i n d i v i d u a l channel gates. The c i r c u i t i s shown block-schematically i n Figure B - l ( a ) . The device consists of 15 astable mult i v i b -rators ( A l , A2, A3, A15)'connected i n series and closed i n a loop. Each such multivibrator or counter has two unstable states, and the time duration of each state, f o r a fix e d num-ber of counters i n the r i n g , i s determined byrthe frequency of a synchronizing pulse. The d e t a i l s of a p a r t i c u l a r counter i n the ri n g are shown i n Figure B-l(b). Tube T2 i s the counter, T l i s the synchronizing tube, and T3 i s the AND gate which uses the s i g -nal from t h i s p a r t i c u l a r counter to select a p a r t i c u l a r channel gate pulse. The c i r c u i t action i s as follows: The synchron-i z i n g tube i s triggered from the channel-marker pulses, which occur just before the channel pulses. In order to obtain a signal from the r i n g counter which blankets the channel-gate pulse, the "synchronous multivibrator" (Tl) i s given a period of about 500 microseconds, so that i t s output pulses from the pulse transformer i s approximately l£0° out of phase with the channel pulse PRF. At any instant of time, only one of the counters i s i n the (1) state (T2(a) conducting, T2(b) cut o f f ) , and the remainder are i n the (0) state. Say for example that A l i s conducting, and that the current which i t draws through the common cathode of T2(a) sets a l l the other counters into the (0) state. (a) Ring Counter Block Schematic m Synchronous Multi Basic Counter Gaitfl CHGi OUT ..ommon Cathode (b) C i r c u i t D e t a i l s Rl 1M 10% R5 39K 1W. 10% R2 100K tt R6 56K iw ft R3 100K 1W tt R7 33K tt tt R4 150K £w tt R8 56QK n ft R9 330K ft n RIO IK n tt PI 50K pot. CI .001 mfd C2 .0027 n C3 .02 rt C4 .25 " C5 250 mmfd Figure B - l . The Ring Counter -77-Suppose now that a pulse i s injected into the second-ary of the pulse transformer from the synchronous multivibrator. This pulse drives the common cathode p o s i t i v e , causing the cur-rent i n T2(a) of Al to diminish. Regeneration occurs, and immed-i a t e l y a f t e r the pulse has passed, Al i s triggered into the (0) state. Simultaneously, A2 i s triggered into the (1) state, because i t i s the only one of the 15 counters which receives a t r i g g e r pulse on both the cathode of T2(a) and the grid of,, T2(b), the l a t t e r from the d i f f e r e n t i a t e d plate waveform of T2(b) of A l . Therefore the r i n g counter has changed by one the po s i t i o n of the conducting multivibrator around the r i n g . The next t r i g g e r pulse causes A2 to return to the (0) state, and tr i g g e r s A3 into the (1) state. This action i s repeated around the loop, so that each of the 15 counters conducts f o r 1/15 of the t o t a l time. I f the synchronizing s i g n a l i s a PRF of 1000 cps, then each counter unit w i l l be on f o r 1 millisecond, and o f f f o r the next 14 milliseconds. The output from each counter i s a 45-volt pulse, l a s t i n g about 1 millisecond, from the grid of T2(a). The output from each counter i s taken to a triode AND .gate, i d e n t i c a l to T3 i n Figure B - l ( b ) , where i t i s added to the 10-microsecond channel-gate pulse t r a i n . Therefore the output of Al i s CHG1, and of A2 i s CHG2, and so on up to CHG15. These output pulses are then applied to pentode AND gates to select the sine-clock pulses which represent the channel pulses, CPi. These pulses are then used i n the general programming of the computer, and no t s p e c i f i c a l l y for the integrator. - 7 8 -A p p e n d i x C , L i s t o f R e f e r e n c e s 1 . . B e r r y , T . M . , " P o l a r i z e d L i g h t S e r v o S y s t e m , " T r a n s a c t i o n s o f t h e A . I . E . E . t v o l . 6 3 n o . 4 ( A p r i l 1 9 4 4 ) p p . 1 9 5 - 1 9 7 . 2 . B u s h , V . , " T h e D i f f e r e n t i a l A n a l y z e r , A New M a c h i n e f o r S o l v i n g D i f f e r e n t i a l E q u a t i o n s , " J o u r n a l o f F r a n k l i n  I n s t i t u t e , v o l . 2 1 2 , n o . 4 ( O c t o b e r 1 9 3 1 ) p p . 4 4 7 - 4 4 8 . 3 . C h a n c e , B . , H u g h e s , V . , M a c N i c h o l , E . F . , S a y r e , D . , a n d W i l l i a m s , F . C . , W a v e f o r m s . New Y o r k , M c G r a w - H i l l , 1 9 4 9 ( R i d e n o u r , L . N . , e d . , M . I . T . . R a d i a t i o n L a b o r a t o r y S e r i e s , v o l . i 9 ) . ~ ~ ' ' : ! ; 4 . F i n k , H . J . , " P r e c i s i o n F r e q u e n c y C o n t r o l o f a M a g n e t i c D r u m , " M . A . S c . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1 9 5 6 . 5 . J o h n s o n , C . L . , A n a l o g C o m p u t e r T e c h n i q u e s , New T o r k , M c G r a w -H i l l , 1 9 5 6 . 6 . K o r n , G . A . a n d K o r n , T . M . , E l e c t r o n i c A n a l o g u e C o m p u t e r s , New Y o r k , M c G r a w - H i l l , 1 9 5 2 . 7 . M c G u i g a n , J . H . , " C o m b i n e d R e a d i n g a n d W r i t i n g o n a M a g -n e t i c D r u m , " P r o c e e d i n g s o f t h e I . R . E . , v o l . 1 4 , n o . 1 0 , ( O c t o b e r 1 9 5 3 ) p p . 1 4 3 8 - 1 4 4 4 . 8 . M e n e l e y , C . A . a n d M o r r i l l , C D . , " A p p l i c a t i o n o f E l e c t r o n i c D i f f e r e n t i a l A n a l y z e r s t o E n g i n e e r i n g P r o b l e m s , " P r o c e e d - i n g s o f t h e I . R . E . , v o l . 4 1 , n o . 1 0 ( O c t o b e r 1 9 5 3 ) p p . 1 3 5 2 -TJW. 9 . M i l l m a n , J . a n d P u c k e t t , I . H . , " A c c u r a t e L i n e a r B i d i r e c -t i o n a l G a t e s , " P r o c e e d i n g s o f t h e I . R . E . , v o l . 4 3 , n o w l , ( J a n u a r y 1 9 5 5 ) , p p . 2 9 - 3 7 . 1 0 . M i l l m a n , J . a n d T a u b , H . , P u l s e a n d D i g i t a l C i r c u i t s , New Y o r k , M c G r a w - H i l l , 195K. 1 1 . P a r k , W . J . , " A r i t h m e t i c C i r c u i t s f o r a T i m e - S e q u e n t i a l P u l s e - P o s i t i o n M o d u l a t i o n A n a l o g u e C o m p u t e r , " M . A . S c .  T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1 9 5 8 . 1 2 . P a y n t e r , H . M . , e d . , A P a l i m p s e s t o n t h e E l e c t r o n i c A n a l o g  A r t , B o s t o n , M a s s . , G e o . A . P h i l b r i c k R e s e a r c h e s , I n c . , 1 9 5 5 . 1 3 . R i c h a r d s , R . K . , A r i t h m e t i c O p e r a t i o n s i n D i g i t a l C o m p u t e r s , V a n N o s t r a n d , 1 9 5 4 . 1 4 . R u b i n o f f , M . , " A n a l o g u e v s . D i g i t a l C o m p u t e r s - A C o m p a r -i s o n , " P r o c e e d i n g s o f t h e I . R . E . , v o l . 4 1 , n o . 1 0 , (October" 1 9 5 3 ) p p . 1 2 5 4 - 1 2 6 2 . 

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