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UBC Theses and Dissertations

Aspects of delta modulation De Faye, Philippe John 1959

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ASPECTS OF DELTA MODULATION by PHILIPPE JOHN de FAIE B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1957 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 t h e s i s as conforming to the standards r e q u i r e d from candidates f o r the degree of Master of A p p l i e d Science,, Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OP BRITISH COLUMBIA MAY, 1959 i ABSTRACT The f i r s t part of t h i s t h e s i s d e s c r i b e s the design and c o n s t r u c t i o n of a pulse communications system c a l l e d d e l t a modulation* A simple t r a n s i s t o r i z e d coder and decoder was b u i l t to convert speech s i g n a l s i n t o b i n a r y p u l s e s , and back again* This system was t e s t e d i n s e v e r a l ways* the o i r c u i t performance was checked e l e c t r o n i c a l l y , and the q u a l i t y of t r a n s m i s s i o n through the system was judged by l i s t e n i n g t e s t s and by comparison w i t h s p e o i a l tapes c o n t a i n i n g c o n t r o l l e d amounts of s i g n a l and thermal noiseo The second part concerns the design and c o n s t r u c t i o n of a compressor and expandor t h a t can be used w i t h a d e l t a system i n order to improve i t s t r a n s m i s s i o n q u a l i t y . A f a s t - a c t i n g compressor and expander was co n s t r u c t e d u s i n g diode-bridges as n o n - l i n e a r elements. Tests of the two components used "back-to-back" showed a s a t i s f a c t o r y matching of t h e i r c h a r a c t e r i s t i c s . I f these components were used w i t h the d e l t a modulation system? there would be a c o n s i d e r a b l e i n c r e a s e i n the range of s i g n a l l e v e l s t h a t oould be t r a n s m i t t e d w i t h reasonable q u a l i t y . In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of E l e c t r i c a l Engineer-ing The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date May 15, 1959  i i TABLE OP CONTENTS Page A b s t r a c t . i L i s t of I l l u s t r a t i o n s ............ . . . . . i v Acknowledgement ........... v X 9 T h e O r y o o o e e o o e o c o o o o . o o o c o . . © * * . 1 l . l o I n t r o d u c t i o n - - o . - o . . . . . . o . o . . o o o o o o o o o o . . . o o 1 1<>2. Regeneration, of s i g n a l 2 1,3» Pulse code modulation „ 3 1«4« D e l t a . modulation ......................... 3 lo4»l<> P r i n c i p l e of op e r a t i o n .......... 4 1*4.2. Disadvantages .................... 7 1.4.3. S i g n a l - t o - n o i s e r a t i o .... ........ 9 l o 4 . 4 e Pulse generator c o n s i d e r a t i o n s . .. . 11 1 o 5 * ^ O III JJ) clU CL OI* S o o o o o o * « « * e * » * o o . e e « o o e o * « o o o o o 13 l»5«lo S y l l a b i c compandors ............... 14 1,5.2. Instantaneous compandors ......... 18 1,6. Operation of instantaneous compandors .... 18 1.6.1. The n o n ^ l i n e a r element .......... 18 1.6.2. A p p l i c a t i o n to d e l t a modulation... 20 1«7<> Methods of e v a l u a t i o n ................... 20 2o C o n s t r u c t i o n of a d e l t a modulation system ...... 23 2.1. Delta.coder . . . . o . o . . . . . . . . . . . . . . . . o . . 23 2.1,1, Timing generator *;. 23 2ol«2. Pulse generator and comparator ... 23 2olo3<> I n t e g r a t o r „. 28 2.1.4. DO a m p l i f i e r 29 2.1.5• Output c i r c u i t 30 2 O 2 O D©l"fcO»-Cl©COCL03? - o o o o - o e e o o o « o * * « « « ' e « « o » « « * * * « e 30 2 o 2 © 1 o Regenerator 0 0 0 0 «> . * Q 0 30 2 O 2 o 2 » Xlli/ & £>3? Q> "fc Or • o o » » « 6 e 0 o * « * « » * o o o * o o 30 i i i Page 3o Performance of the d e l t a modulation system .„ ....<> <> ~34 3»1« C i r c u i t r y operation. . 0 ............. 0 ....... . 34 3 o 2 « L i s t e u i n g t e s t s o . o . . • • . . . . o . . . . . . . . . . . . . . . . . . 34 3o2»l« Experimental r e s u l t s .. ........... 34 3«2»2. Comparison of c a l c u l a t e d and observed s i g n a l — t o - n o i s e r a t i o s . .............. 37 4. C o n s t r u c t i o n of the instantaneous compandor ....<,.. 39 4«1« Feedback a c t i o n . ............................ 39 4«2* C i r c u i t d e s c r i p t i o n ........... . . . o . . o o . . . . . . a 41 5« Performance of the instantaneous compandor ........ 44 ^ O 1 • S t a b i l i t y t, * o • • • o o * e o e « « o « » s « * o o o a o o o « « * e t t o o o 44 5o2. Compandor range 44 5*3® IlXS"fa0Ilill^) t 0S t S -- • - - 0 - s o - 0 a e - o « * « « o - « o o o o « » o * o « - » * o o o 4*7 5»4o T h e o r e t i c a l a p p l i c a t i o n to a d e l t a system o o * 48 60 Noise generator c o n s t r u c t i o n and performance « • o . o o 50 *J 9 CoilGlUSlOnS e o e o e e e o a s e o o e o o a o o s o o o o o o o o o o o o o t o o o 52 do References o o o 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 o o 54 i v LIST OP ILLTJSTEATIONS F i g u r e Page l o l . T y p i c a l d e l t a m o d u l a t i o n system .... ...o«. 5 1 . 2 0 Waveforms o f d e l t a m o d u l a t i o n . s y s t e m . 6 1 o 3 o Low s i g n a l l e v e l waveforms , . .. • . 8 1.4* S l o p e o v e r l o a d . ..... 9 1 o 5» Use of p o s i t i v e p u l s e s o n l y t o s i m p l i f y d e l t a modulat l O I l System . . . • • • o . . e o o o o . o o o o o o o o o o o 12 1 . 6 . E f f e c t of p u l s e w i d t h v a r i a t i o n 12 1 . 7 « Compandor a p p l i c a t i o n .-. . . . . . . . a . 15 1.8. S y l l a b i c and i n s t a n t a n e o u s c o m p r e s s i o n . ....... 0 . 16 1«9« T y p i c a l c o m p r e s s o r . g a i n . c h a r a c t e r i s t i c s ......... 17 1 o 10 . Two—diode c ompr e s s o r . . . . . . • • • . . . • . • • • • . 0 0 . . . . . . 18 1 . 1 1 . F o u r — d i o d e compressor .•••..••«•••...*.......».«'«. 19 1 0 1 2 . S l o p e c o m p r e s s i o n and e x p a n s i o n w i t h a d e l t a s ystem - . 21 1 .13- S i m p l i f i e d d e l t a c o d e r and decoder u s i n g s l o p e c o m p r e s s i o n and e x p a n s i o n ...o.oooo.... 21 2 . 1 . C i r c u i t d i a g r a m o f d e l t a coder 24 2 . 2 . O r i g i n a l f e e d b a c k c o u p l i n g . . o » o 0 . . . o e o . . o o o o . o o o . . 26. 2.3o F i n a l f e e d b a c k c o u p l i n g 28 2»4» Output c i r c u i t of d e l t a coder . ......oo... 31 2 . 5 . C i r c u i t d i a g r a m of d e l t a d e c o d e r ............... 32 4 . 1 . P r i n c i p l e o f o p e r a t i o n o f t h e i n s t a n t a n e o u s compandor .. ..... . 40 4 » 2 . C i r c u i t d i a g r a m of the compandor used " b a c k - t o — b a c k " .o»o...o 42 5 . 1 . G a i n and phase c h a r a c t e r i s t i c s o f a m p l i f i e r . . . o o 45 5«2o O v e r a l l compandor performance . 0 . . . . . . 0 0 0 0 0 0 0 0 0 0 46 5 . 3 . S i g n a l - t o - n o i s e r a t i o of a d e l t a s y s t e m , w i t h and w i t h o u t i n s t a n t a n e o u s a m p l i t u d e c o m p r e s s i o n 49 6 . 1 . C i r c u i t d i a g r a m of n o i s e g e n e r a t o r ............. 51 V ACKNOWLEDGEMENTS The a u t h o r i s i n d e b t e d t o t h e Defence R e s e a r c h B o a r d , Department of N a t i o n a l D e f e n c e , Canada, f o r a b u r s a r y and f o r t h e i r s p o n s o r s h i p of t h i s p r o j e c t . Acknowledgement i s v e r y g r a t e f u l l y g i v e n t o P r o f e s s o r P. Ko Bowers f o r h i s g u i d a n c e t h r o u g h o u t t h i s p r o j e c t , and t o Dr. F. Noakes f o r h i s a s s i s t a n c e t o the a u t h o r . Thanks a r e a l s o extended t o t h e o t h e r members of t h e s t a f f and t o t h e gr a d u a t e s t u d e n t s o f t h e E l e c t r i c a l E n g i n e e r i n g Department f o r t h e i r h e l p f u l sugges-t i o n s . The a u t h o r i s a l s o i n d e b t e d t o t h e B r i t i s h C o lumbia Telephone Company w h i c h g r a n t e d him a s c h o l a r s h i p i n 1957? t h u s e n a b l i n g him to c o n t i n u e w i t h h i s s t u d i e s . 1, THEOBY 1.1. INTRODUCTION There a r e many t y p e s o f communication systems i n use t o d a y . One o f t h e o l d e s t and s i m p l e s t methods i s the d i r e c t t r a n s m i s s i o n o f a u d i o s i g n a l s t h r o u g h conduc-t o r s , as i n t e l e p h o n e and t e l e g r a p h l i n e s . However, w i t h the i n c r e a s i n g demand f o r g r e a t e r communication f a c i l i -t i e s , c a r r i e r systems were i n t r o d u c e d so t h a t many c h a n n e l s c o u l d be accommodated by one p a i r o f c o n d u c t o r s or t r a n s m i s s i o n l i n k . These systems use t h e f r e q u e n c y d i v i s i o n p r i n c i p l e i n w h i c h each c h a n n e l i s a s s i g n e d a p a r t i c u l a r c a r r i e r f r e q u e n c y . These c a r r i e r f r e q u e n c i e s a r e t h e n u s u a l l y a m p l i t u d e o r f r e q u e n c y m o d u l a t e d by t h e s i g n a l , , But s i n c e d i r e c t t r a n s m i s s i o n and c a r r i e r systems r e q u i r e h i g h g a i n a m p l i f i e r s t o overcome l o s s e s , t h e y a r e v e r y s u s c e p t i b l e t o any n o i s e p r e s e n t i n t h e t r a n s m i s s i o n p a t h . However, o t h e r forms o f communication a r e a v a i l a b l e t h a t o p e r a t e on an e n t i r e l y d i f f e r e n t p r i n c i p l e . Shannon has shown t h a t a g i v e n s i g n a l o f bandwidth B and d u r a t i o n T can be c o m p l e t e l y d e s c r i b e d by 2BT +1 sample points' 1'. T h i s i s the b a s i s f o r a t y p e o f communication known as p u l s e m o d u l a t i o n . T h i s method samples the s i g n a l a t r e g u l a r t i m e i n t e r v a l s and t r a n s m i t s i n f o r m a t i o n p e r t a i n -i n g t o t h e sampled i n t e r v a l s o n l y . F o r example, t h i s 2 . i n f o r m a t i o n may be c o n t a i n e d i n t h e v a r y i n g a m p l i t u d e of the p u l s e s , or perhaps i n t h e w i d t h of the t r a n s m i t t e d p u l s e s * F u r t h e r m o r e , m u l t i p l e c h a n n e l s on one communi-c a t i o n l i n k a r e s t i l l p o s s i b l e , s i n c e any p a r t i c u l a r s i g n a l i s t r a n s m i t t e d o n l y d u r i n g c e r t a i n t i m e i n t e r v a l s , l e a v i n g t h e r e m a i n i n g t i m e a v a i l a b l e f o r o t h e r s i g n a l s . But t h e s e systems s t i l l a l l o w the c u m u l a t i v e a d d i t i o n o f n o i s e t h r o u g h -out t h e t r a n s m i s s i o n l i n k , w h i c h i s t h e main d i s a d v a n t a g e o f a normal c o m m u n i c a t i o n s y s t e m . 1 .2. REGENERATION OF SIGNAL What i s r e q u i r e d i s some method i n w h i c h t h e s i g n a l can be r e g e n e r a t e d a t each s t a g e , t h u s e l i m i n a t i n g any n o i s e t h a t may have been i n t r o d u c e d i n t h e p r e c e d i n g s t a g e s . The s u r e s t method o f t r a n s m i t t i n g a s i g n a l i s t o have o n l y two p o s s i b l e l e v e l s , say 0 or 1 v o l t . I n t h i s b i n a r y c a s e , u n l e s s the n o i s e i s a t l e a s t one h a l f t h e p u l s e h e i g h t , t h e r e c e i v e r w i l l be a b l e t o d i s t i n g u i s h whether a p u l s e i s p r e s e n t or n o t , and v / i l l be a b l e , t o r e g e n e r a t e t h e o r i g i n a l p u l s e d s i g n a l f o r f u r t h e r t r a n s m i s s i o n . However, i t i s now n e c e s s a r y t o d e v i s e a c o d i n g system so t h a t t h e o r i g i n a l c o n t i n u o u s s i g n a l can be e x p r e s s e d i n b i n a r y f o r m . I n t h i s c o d i n g p r o c e s s , t h e s i g n a l i s quan-t i z e d , t h a t i s , a s s i g n e d t o one o f s e v e r a l d i s c r e t e l e v e l s , and t h u s s u f f e r s some d i s t o r t i o n . . T h i s d i s t o r t i o n i s c a l l e d q u a n t i z i n g n o i s e ^ but as mentioned e a r l i e r , t h i s s h o u l d be t h e o n l y n o i s e p r e s e n t t h r o u g h o u t t h e t r a n s m i s s i o n s y s t e m . I t s h o u l d a l s o be p o i n t e d out t h a t a c o n s i d e r a b l y l a r g e r band-width, i s now r e q u i r e d . Thus, i n s t e a d o f a t r a n s m i s s i o n system o f low bandwidth but r e q u i r i n g e x p e n s i v e h i g h g a i n , low n o i s e a m p l i f i e r s , we now use a system o f g r e a t e r band-w i d t h w h i c h o n l y r e q u i r e s s i m p l e p u l s e r e g e n e r a t o r s as a m p l i f i e r s . 1.3. PULSE CODE MODULATION C u r r e n t l y t h e r e a r e two t y p e s o f systems w h i c h w i l l code a c o n t i n u o u s s i g n a l i n t o b i n a r y f o r m . I n one method., 2 c a l l e d p u l s e code m o d u l a t i o n , t h e i n p u t s i g n a l i s sampled a t a r a t e o f a t l e a s t t w i c e t h e b a n dwidth of t h e s y s t e m . These a m p l i t u d e samples are t h e n q u a n t i z e d i n t o a number o f d i s t i n c t l e v e l s , w i t h each l e v e l b e i n g a s s i g n e d a b i n a r y code. Thus the t r a n s m i t t e d s i g n a l i s a t r a i n o f grouped b i n a r y p u l s e s . F o r example, i f the s i g n a l i s s p l i t i n t o e i g h t l e v e l s , t h r e e b i n a r y p u l s e s w i l l be s u f f i c i e n t t o d e s c r i b e i t s s t a t e . However, a p u l s e code m o d u l a t i o n scheme i s r a t h e r d i f f i c u l t t o b u i l d , f o r b o t h t h e t r a n s -m i t t e r and r e c e i v e r a r e r e l a t i v e l y c o m p l i c a t e d . 1.4. DELTA MODULATION A s i m p l e r system, a l t h o u g h perhaps not so w e l l known, 3 4 5 i s c a l l e d d e l t a m o d u l a t i o n . i^^ > J a H e r e , as i n p u l s e code m o d u l a t i o n , the t r a n s m i t t e d s i g n a l i s u s u a l l y a t r a i n o f r e g u l a r l y spaced " 0 " o r " 1 " p u l s e s . These " 0 " or " 1 " p u l s e s , w h i c h a r e e a s i l y r e g e n e r a t e d , can c o n s i s t o f any two d i f f e r e n t p u l s e l e v e l s , f o r example, 3 v o l t s and -2 v o l t s , or perhaps 5 v o l t s and 0 v o l t s . F o r s i m p l i c i t y i n e x p l a n a t i o n , we w i l l c o n s i d e r the p u l s e s as b e i n g e i t h e r p o s i t i v e or n e g a t i v e , say v o l t and v o l t . 1 . 4 „ 1 . PRINCIPLE OF OPERATION The p r i n c i p l e o f o p e r a t i o n o f t h e c o d e r and d e coder i s q u i t e s t r a i g h t f o r w a r d . I t w i l l be e a s i e r , p e r h a p s , t o l o o k a t t h e d e c o d e r , or r e c e i v e r , f i r s t and see how t h i s c o n v e r t s t h e t r a i n o f p o s i t i v e and n e g a t i v e p u l s e s i n t o an a u d i o s i g n a l . I f t h e s e p u l s e s a r e j u s t p a s s e d t h r o u g h an i n t e g r a t o r , t h e form of the o r i g i n a l i n p u t s i g n a l w i l l be e v i d e n t i m m e d i a t e l y , as seen i n f i g u r e 1 , 2 .(b). Low-pass f i l t e r i n g w i l l t h e n produce an o u t p u t v e r y s i m i l a r t o the i n p u t shown above i n f i g u r e 1 . 2 . ( a ) . Now c o n s i d e r t h e a c t i o n of the c o d e r , or t r a n s m i t t e r , as shown i n b l o c k form i n f i g u r e 1.1, At e v e r y s a m p l i n g i n t e r v a l , as d e t e r m i n e d by t h e c l o c k , t h e p u l s e g e n e r a t o r w i l l produce e i t h e r a p o s i t i v e or n e g a t i v e p u l s e . I t w i l l produce a p o s i t i v e p u l s e i f t h e o u t p u t o f t h e comparator i s above a f i x e d r e f e r e n c e v a l u e , and s i m i l a r l y w i l l produce a n e g a t i v e p u l s e f o r a comparator output below t h i s v a l u e . The i n t e g r a t o r a c t s j u s t as i t does i n t h e d e coder p r e v i o u s l y d e s c r i b e d . Thus the c o m p a r a t o r sees t h e i n p u t s i g n a l and t h e f e d - b a c k i n t e g r a t e d f o r m of t h e p u l a e t r a i n , w h i c h i s an a p p r o x i m a t i o n t o the s i g n a l , as shown i n f i g u r e 1 . 2 . ( b ) . The a c t i o n o f the f e e d b a c k l o o p w i l l m a i n t a i n t h e c o r r e c t r e l a t i o n between the i n p u t and t h e i n t e g r a t e d p u l s e s . F o r example, c o n s i d e r t h e i n p u t and the i n t e g r a t e d wave-forms as b e i n g n e a r l y e q u a l . Now l e t t h e i n p u t i n -5-CLOCK u ( t ) i n p u t . v ( t ) e ( t ) -> p ( t ) TEANSMITTEE OE CODEE p ( - t ) - -1 LoPoPo I-1 w ( t ) o u t p u t EECEIVEH OB DECODEE F i g u r e , T y p i c a l d e l t a m o d u l a t i o n system p ( t ) p u l s e t r a i n 1 M I N I (o) F i g u r e 1 . 2 . Waveforms of d e l t a m o d u l a t i o n system c r e a s e , p r o d u c i n g a p o s i t i v e o u t p u t from t h e c o m p a r a t o r . T h i s w i l l a l l o w t h e p u l s e g e n e r a t o r t o send out a p o s i t i v e p u l s e , t h e r e b y i n c r e a s i n g t h e i n t e g r a t e d o u t p u t . Thus t h e out p u t f o l l o w s t h e i n p u t . The a n a l y s i s s i m i l a r l y h o l d s i f the s i g n a l d e c r e a s e s , f o r i n t h i s case a n e g a t i v e p u l s e w i l l be g e n e r a t e d t o r e d u c e the i n t e g r a t e d waveform a l s o o 1.4.2. DISADVANTAGES Thus t h e b a s i c o p e r a t i o n of the d e l t a coder i s q u i t e s t r a i g h t f o r w a r d . However, t h e r e a re s e v e r a l o b v i o u s s h o r t -comings i n t h i s system o u t s i d e o f the u s u a l c i r c u i t problems L i k e a l l p u l s e m o d u l a t i o n schemes, t h e d e l t a system s u f f e r s from q u a n t i z i n g n o i s e , as can be seen by t h e e r r o r s i g n a l e ( t ) i n f i g u r e 1.2.(d). N a t u r a l l y as the s a m p l i n g speed i s i n c r e a s e d , t h e i n t e r v a l s between c o m p a r i s o n s w i l l be s h o r t e r , and t h e q u a n t i z i n g n o i s e w i l l be r e d u c e d . A n o t h e r s e r i o u s p r o b l e m , r e l a t e d t o t h e f i r s t , i s t h e t h r e s h o l d e f f e c t . T h i s i s t h e i n a b i l i t y o f the code r t o f o l l o w v e r y low s i g n a l l e v e l s , as i l l u s t r a t e d i n f i g u r e 1»3« Thus t h e coder i s i n s e n s i t i v e t o s i g n a l s s m a l l e r t h a n t h e p u l s e h e i g h t , and i n t h i s c a s e w i l l o n l y send out a l t e r n a t e p o s i t i v e and n e g a t i v e p u l s e s . A n o t h e r i m p o r t a n t c o n s i d e r a t i o n i n d e l t a m o d u l a t i o n i s t h e f a c t t h a t t h e system o v e r l o a d s not on the customary l a r g e a m p l i t u d e s , but r a t h e r on l a r g e s l o p e s . F o r a g i v e n s i g n a l u ( t ) = A s i n a ) g t where u) g i s t h e s i g n a l f r e q u e n c y , the maximum s l o p e i s Aw . Now t h e g r e a t e s t s l o p e t h a t t h e p(t) outpu-fc F i g u r e 1«3» Low s i g n a l l e v e l waveforms s t e p waveform can f o l l o w i s h max ~ 1_ f P where h i s t h e s t e p h e i g h t and f i s t h e p u l s e f r e q u e n c y . IP F i g u r e 1.4* S l o p e o v e r l o a d Thus Aid = h f s p or h f A - E (1) max 2'nt u ' s Thus by i n c r e a s i n g t h e p u l s e f r e q u e n c y f , not o n l y i s t h e q u a n t i z i n g n o i s e r e d u c e d , but t h e sy s t e m can h a n d l e g r e a t e r s l o p e s , and t h e r e f o r e g r e a t e r a m p l i t u d e s . 1.4.3. SIGNAL TO NOISE EATIO These t h r e e c h a r a c t e r i s t i c s of d e l t a m o d u l a t i o n , q u a n t i z i n g n o i s e , t h r e s h o l d e f f e c t , and s l o p e o v e r l o a d , make i t r a t h e r d i f f i c u l t t o e x p r e s s a s i g n a l - t o - n o i s e r a t i o f o r the system 1. As the s i g n a l l e v e l i n c r e a s e s , t h e n o i s e p r e s e n t changes a p p r e c i a b l y . However, i f we a r e c o n s i d e r i n g s i n e waves, and i f t h e s i g n a l - t o - n o i s e r a t i o i s t a k e n t o be the r a t i o o f the s i g n a l power t h a t o v e r l o a d s t h e system t o the l o w e s t s i g n a l t h a t i s j u s t e q u a l t o n o i s e , a q u a n t i t a t i v e f i g u r e can be o b t a i n e d . Prom e q u a t i o n ( l ) /A \ 2 h 2 f 2 '» • vF = St*" (2) * ' s where S i s t h e r o o t mean square power o f a s i n e rms u * wave o f f r e q u e n c y f which, j u s t o v e r l o a d s t h e s y s t e m . s Now i t can be shown^ t h a t t h e average t h r e s h o l d or low l e v e l n o i s e power i s g i v e n by ,2 N rms 1 (3) Thus t h e maximum s i g n a l - t o - n o i s e r a t i o , as d e f i n e d above, i s 2 S 3f R M S » - J 2 — (A) N 2 2 V 4 ' "rms 2TT£ a However, t h i s i s an u n r e a l i s t i c f i g u r e t o use a t h i g h s i g n a l l e v e l s , f o r t h e n o i s e t h a t accompanies l a r g e s i g n a l s i s c o n s i d e r a b l y l e s s t h a n t h a t a t t h e t h r e s h o l d l e v e l as g i v e n by e q u a t i o n (3)o T h i s l a r g e - s i g n a l n o i s e can be f assumed to have a f l a t f r e q u e n c y s p e c t r u m up t o about ^ . The n o i s e power i n t h e o p e r a t i n g band o f the d e l t a coder i s t h e n p r o p o r t i o n a l t o the h i g h e s t o p e r a t i n g f r e q u e n c y , f , 11* o f t h e s y s t e m or N rms oc (5) Thus the s i g n a l - t o - n o i s e r a t i o now becomes S 3 rms (6) N rms o The c o n s t a n t i s r a t h e r d i f f i c u l t t o c a l c u l a t e , due t o t h e h i g h degree o f n o n - l i n e a r i t y i n the n o i s e s i g n a l . The v a l u e o f c^ = 0.04» as d e r i v e d by P. de Jager"^, w i l l be used h e r e . 1.4.4. PULSE GENEEATOB CONSIDERATIONS s p e c i a l compandor may be used w i t h t h e d e l t a s y s t e m . T h i s w i l l be d i s c u s s e d i n t h e s e c t i o n on companding. However, t h e r e i s an i m p o r t a n t method of s i m p l i f y i n g t h e o p e r a t i o n o f a d e l t a c o d e r t h a t s h o u l d f i r s t be m e n t i o n e d . The i n t e g r a t o r s were p r e v i o u s l y d e s c r i b e d as r e c e i v i n g b o t h p o s i t i v e and n e g a t i v e p u l s e s . I n s t e a d , p u l s e s t h a t a r e e i t h e r p o s i t i v e or z e r o can be u s e d , f o r t h e i n t e g r a t o r can be a r r a n g e d so t h a t a c o n s t a n t c u r r e n t removes, d u r i n g e v e r y p u l s e i n t e r v a l , one h a l f o f t h e charge b r o u g h t t o i t by a p o s i t i v e p u l s e . t h e p u l s e g e n e r a t o r , s i n c e o n l y s i n g l e p o l a r i t y p u l s e s are-now r e q u i r e d . T h i s a c t i o n i s i l l u s t r a t e d i n f i g u r e 1.5. I n t h i s c o n n e c t i o n i t might be p o i n t e d out t h a t a l t h o u g h t h e a c t u a l p u l s e s i z e i s not c r i t i c a l , i t i s v e r y To improve the s l o p e o v e r l o a d c h a r a c t e r i s t i c s a T h i s p r o c e d u r e g r e a t l y s i m p l i f i e s t h e b u i l d i n g o f 12. p ( t ) [ . 1 , 1 1 P u l s e t r a i n v ( t ) I n t e g r a t e d waveform F i g u r e 1.5» Hse o f " p o s i t i v e p u l s e s o n l y t o s i m p l i f y d e l t a m o d u l a t i o n system v ( t ) a t coder P u l s e t r a i n , p ( t ) v ( t ) a t coder and decoder p ( t ) i n p u t , u ( t ) Waveforms when p u l s e w i d t h ' m o d u l a t i o n i s p r e s e n t u ( t ) Waveforms when no p u l s e width, m o d u l a t i on e x i s t s F i g u r e 1.6. E f f e c t o f p u l s e w i d t h v a r i a t i o n i m p o r t a n t t h a t t h e p u l s e a r e a does not v a r y f r o m one p u l s e t o t h e n e x t . C o n s i d e r a b l e d i f f i c u l t y was e n c o u n t e r e d i n making t h e s e p u l s e s u n i f o r m , f o r they t e n d e d t o i n c r e a s e s l i g h t l y i n w i d t h w i t h i n c r e a s i n g s i g n a l l e v e l . S i n c e t h e s e p u l s e s a r e r e g e n e r a t e d t o r e j e c t n o i s e and d i s t o r t i o n , the p u l s e w i d t h v a r i a t i o n s w i l l not appear a t t h e r e c e i v e r , but n e v e r t h e l e s s , t h e y w i l l h i n d e r the o p e r a t i o n of t h e d e l t a c o d e r . I f the p u l s e w i d t h i n c r e a s e s w i t h s i g n a l l e v e l , the i n t e g r a t e d waveform w i l l f o l l o w s m a l l s i g n a l s i n a c o n t i n u o u s f a s h i o n r a t h e r t h a n s t e p w i s e , p r o d u c i n g a p u l s e - s p a c e p a t t e r n i n s t e a d o f the c o r r e c t s i g n a l , as shown i n f i g u r e 1.6. 1.5. COMPANDOBS In s e c t i o n 1.4o4«» r e f e r e n c e was made t o t h e use o f compandors. The word "compandor" i s s i m p l y t h e c o n t r a c t i o n o f t h e two words, " c o m p r e s s o r " and "expandor". C o n v e n t i o n a l a u d i o systems a r e l i m i t e d i n t h e i r s i g n a l - t o - n o i s e r a t i o s by i n h e r e n t n o i s e i n the system and by t h e maximum s i g n a l t h a t can be h a n d l e d . F o r l o u d p a s s a g e s , t h e s i g n a l - t o - n o i s e r a t i o i s u s u a l l y a d e q u a t e , but low l e v e l s s u f f e r because t h e y a r e a p p r o a c h i n g t h e n o i s e l e v e l . Gompressors a m p l i f y t h e s e weak s i g n a l s more t h a n t h e s t r o n g ones b e f o r e t h e y a r e put i n t o t h e t r a n s m i s s i o n s y s t e m , t h u s r e n d e r i n g them f a r l e s s s u s c e p t i b l e t o any n o i s e i n the syst e m . A f t e r p a s s i n g t h r o u g h t h i s s ystem, t h e s i g n a l s a r e f e d t o an expander, w h i c h has n o n - l i n e a r a m p l i f y i n g c h a r a c t e r i s t i c s i n v e r s e t o th o s e o f t h e co m p r e s s o r . The combined e f f e c t i s t o i n c r e a s e the s i g n a l - t o - n o i s e r a t i o o f s m a l l s i g n a l s , but a t t h e 14. expense of d e c r e a s i n g t h a t o f l a r g e o nes. F o r example, c o n s i d e r a t r a n s m i s s i o n system i n w h i c h t h e output s i g n a l i s l i m i t e d t o 1 v o l t and i s accompanied "by 1 m i l l i v o l t o f n o i s e 1 . Thus t h e s i g n a l - t o - n o i s e r a t i o v e r s u s o u t p u t s i g n a l v o l t a g e i s as shown i n f i g u r e 1.7 • N o t i c e t h a t a t peak o u t p u t , t h e s i g n a l - t o - n o i s e r a t i o i s 60 d e c i b e l s , c e r t a i n l y more t h a n adequate f o r a l l a u d i o u s e s , s i n c e even a t a 30 db s i g n a l - t o - n o i s e r a t i o , t h e n o i s e i s b a r e l y p e r -c e p t i b l e . The a d d i t i o n of a compandor might produce t h e second c u r v e , r e s u l t i n g i n a c o n s i d e r a b l e l o w - l e v e l e x t e n s i o n o f the a c c e p t a b l e s i g n a l - t o - n o i s e r a t i o o f , s a y , 40 db. There a r e two g e n e r a l c l a s s e s o f compandors, s y l l a b i c 7 and i n s t a n t a n e o u s . B o t h t y p e s produce t h e r e s u l t s d es-c r i b e d above, a l t h o u g h t h e method of o p e r a t i o n v a r i e s con-s i d e r a b l y . S y l l a b i c compandors compress e n t i r e waveforms when l o u d p assages o c c u r , whereas t h e i n s t a n t a n e o u s t y p e o n l y com-p r e s s t h e h i g h e r i n s t a n t a n e o u s a m p l i t u d e l e v e l s . F i g u r e 1.8. i l l u s t r a t e s t h e s e two methods o f o p e r a t i o n . 1.5.1. SYLLABIC COMPANDORS S y l l a b i c compandors a r e more c o m p l i c a t e d t h a n i n s t a n t -aneous t y p e s , but u n f o r t u n a t e l y the l a t t e r r e q u i r e a c o n s i d e r a b l y l a r g e r b a n d w i d t h due t o t h e i n t r o d u c t i o n o f h i g h e r f r e q u e n c i e s by t h e c o m p r e s s i o n p r o c e s s . Hence s y l l a b i c compandors a r e o f t e n f o u n d i n t e l e p h o n e c a r r i e r equipment, where bandwidth r e q u i r e m e n t s a r e v e r y i m p o r t a n t . I t s a c t i o n i s s i m i l a r t o t h a t o f a u t o m a t i c - g a i n - c o n t r o l of r a d i o r e c e i v e r s , but s i n c e t h e g a i n i s c o n t r o l l e d by t h e s i g n a l i t s e l f r a t h e r t h a n by some c a r r i e r f l u c t u a t i o n , i t 60 1 10 100 1000 Output v o l t a g e (mv) -60 -40 -20 0 Lb "below overload Curve #1. Normal s i g n a l - t o - n o i s e r a t i o Curve #2. S i g n a l - t o - n o i s e r a t i o a f t e r companding Figu r e lo7» Compandor a p p l i c a t i o n F i g u r e 1 * 8 « S y l l a b i c and i n s t a n t a n e o u s c o m p r e s s i o n 17. i s q u i t e c o m p l i c a t e d and has a tendency t o o v e r l o a d on i n i t i a l l o u d t r a n s i e n t s . 1.5.2. INSTANTANEOUS COMPANDORS On t h e o t h e r hand, i n s t a n t a n e o u s c o m p r e s s i o n , as t h e name i m p l i e s , does not r e l y on t h e p a s t h i s t o r y o f t h e wave-f o r m , hut r a t h e r a c t s on t h e s i g n a l i n s t a n t a n e o u s l y , com-p r e s s i n g h i g h a m p l i t u d e s as t h e y o c c u r . Thus an i n s t a n t -aneous compandor i s a n o n - l i n e a r d e v i c e , o p e r a t i n g on t h e v a r y i n g a m p l i t u d e o f t h e s i g n a l . 1.6. OPERATION OF INSTANTANEOUS COMPANDORS A t y p i c a l g a i n c h a r a c t e r i s t i c f o r a compressor i s a l o g a r i t h m i c r e s p o n s e combined w i t h a l i n e a r r e g i o n , as shown i n f i g u r e 1.9« The expandor works i n a s i m i l a r f a s h i o n , i t s c h a r a c t e r i s t i c s b e i n g o b t a i n e d by i n t e r c h a n g i n g t h e o r d i n a t e and a b s c i s s a i n f i g u r e 1.9» 1.6.1. THE NON-LINEAR ELEMENT Dio d e s a r e v e r y w e l l s u i t e d f o r use as compandors s i n c e they p o s s e s s a l m o s t l o g a r i t h m i c v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s . The s i m p l e s t form o f a compressor c o n s i s t s o f two d i o d e s and a r e s i s t o r . B 'WW——— V i n out F i g u r e 1.10. Two-diode compressor For low s i g n a l l e v e l s , -the diodes have a f i x e d r e s i s t a n c e , say R q . Thus the low l e v e l a t t e n u a t i o n i s given by B /2 B B + B /2 o' 2B +B Now, as the s i g n a l i s i n c r e a s e d , the impedance of the forward-biased diode decreases, thus i n c r e a s i n g the a t t e n u -a t i o n of the c i r c u i t . . However, a more e f f e c t i v e compression can he made by r e p l a c i n g the r e s i s t o r B by two back-to-back s e r i e s d i o d e s . Now, as the input s i g n a l v o l t a g e i s r a i s e d , the impedance of the s e r i e s diodes w i l l i n c r e a s e , s i n c e one of them w i l l be back-biased. The p a r a l l e l diodes w i l l act as b e f o r e , t h e i r impedance decreasing w i t h i n c r e a s i n g s i g n a l . Thus the o v e r a l l compression r a t i o i s c o n s i d e r a b l y l a r g e r than i n the previous case of a r e s i s t o r and two d i o d e s . In 1 out F i g u r e 1.11. Four-diode compressor 1.6.2. APPLICATION TO DELTA MODULATION In s e c t i o n 1 , 4 , 4 . , i"t was mentioned t h a t a compandor could be used w i t h a d e l t a modulation system. But i t i s c l e a r that the instantaneous amplitude compressor j u s t d e s cribed w i l l not improve the o p e r a t i o n of a d e l t a coder. Because the coder overloads on s l o p e s , and not amplitudes, a compressor i s r e q u i r e d t h a t w i l l reduce any high, slopes that w i l l occur at the .input. This may be accomplished by f i r s t d i f f e r e n t i a t i n g the input s i g n a l and a p p l y i n g i n s t a n t -aneous amplitude compression to the d i f f e r e n t i a t e d waveform. F i n a l l y , i n t e g r a t i o n w i l l r e s t o r e the s i g n a l to one which has smaller maximum slopes than the o r i g i n a l . This s i g n a l i s then f e d i n t o a c o n v e n t i o n a l d e l t a system. The r e c e i v e r i s a standard decoder, but f o l l o w e d by a slope expandor, that i s , a d i f f e r e n t i a t o r , expandor, and i n t e g r a t o r . A f t e r s t u d y i n g f i g u r e 1.12., i t i s evident t h a t a c o n s i d e r -able r e d u c t i o n i n components i s p o s s i b l e , as shown i n f i g u r e 1.13. Thus a normal amplitude compandor and one d i f f e r e n -t i a t o r must be added to a d e l t a systeim i n order to g a i n the advantages of compression te c h n i q u e s . 1.7. METHODS OF EVALUATION Before d e s c r i b i n g the equipment b u i l t i n t h i s p r o j e c t some mention should be made of methods of e v a l u a t i n g the t r a n s m i s s i o n q u a l i t i e s of systems such, as these. S e v e r a l good q u a l i t y tape r e c o r d e r s and a noise gener a t o r are d e s i r a b l e f o r t h i s purpose. Tape reco r d e r s are 21. u(t) D. I SLOPE COMPRESSOR P.G, p ( t ) DELTA CODER P ( t ) ^ L.P, 4> w(t) DELTA DECODER SLOPE EZPANDOR Figur e 1*12« Slope compression and expansion w i t h a d e l t a system u(t) P.O. P ( t ) .(t) L P I + w(t) Figur e 1«13» S i m p l i f i e d d e l t a coder and decoder u s i n g slope compression and expansion a v a i l a b l e w i t h s i g n a l - t o - n o i s e r a t i o s between 48 cLb t o 60 db and w i t h f r e q u e n c y r e s p o n s e s up t o 8 Kc o r 12 Kc a t a t a p e speed of 7"& i n c h e s per s e c o n d . P r a c t i c a l e v a l u a t i o n s i n -v o l v e r e c o r d i n g s t a n d a r d s i g n a l s , and t h e n comparing them w i t h s i g n a l s passed t h r o u g h t h e system under t e s t . I t i s - . 4 a l s o u s e f u l t o have r e c o r d s o f s t a n d a r d s i g n a l s w i t h added n o i s e a t known s i g n a l - t o - n o i s e r a t i o s . The l i s t e n e r may t h e n judge whether t h e s i g n a l p a s s e d t h r o u g h t h e system sounds b e t t e r o r worse t h a n t h e same s i g n a l added t o con-t r o l l e d amounts o f n o i s e . I n t e l l i g i b i l i t y t e s t s may a l s o be p e r f o r m e d . I n t h i s case,.random words, p h r a s e s , or numbers are f e d t h r o u g h th e system under t e s t , and a r e t h e n s t u d i e d f o r t h e i r ease of i n t e l l i g i b i l i t y by h a v i n g a group o f p e o p l e g i v e t h e i r v e r s i o n s o f t h e s i g n a l Jaeard. However, c o m p a r i s o n t e s t s , and e s p e c i a l l y i n t e l l i g i b i l i t y t e s t s r e q u i r e a l a r g e number of l i s t e n i n g ^ s e s s i o n s b e f o r e a good q u a n t i t a t i v e measure of the system under s t u d y can be o b t a i n e d . I t i s d i f f i c u l t t o s o r t out v a r i a t i o n s i n p e r s o n a l l i s t e n i n g h a b i t s from the a c t u a l v a r i a t i o n s t h a t a r e b e i n g s t u d i e d i n t h e s y s t e m . Thus f o r a good e v a l u a t i o n o f an a u d i o s y s t e m , a l i s t e n i n g t e s t , combined w i t h d a t a on f r e q u e n c y r e s p o n s e , s i g n a l - t o -n o i s e r a t i o , and o t h e r p h y s i c a l p a r a m e t e r s s h o u l d be g i v e n whenever p o s s i b l e . CONSTRUCTION OF DELTA MODULATOR 2.1, DELTA CODER 2.1.1. TIMING GENERATOR The a c t u a l c o n s t r u c t i o n of the d e l t a modulator began w i t h the b u i l d i n g of the t i m i n g generator, or c l o c k , as i t i s shown on the block diagram of f i g u r e 1. I t i s a standard a s t a b l e m u l t i v i b r a t o r designed to operate at 100 Kc. This frequency-was chosen because i t i s high enough to giv e a good reproduc-4 t i o n of audio s i g n a l s . Very low c o l l e c t o r load r e s i s t a n c e s were used, r e s u l t i n g i n s w i t c h i n g c u r r e n t s of 18 ma, to reduce v a r i a t i o n of the cl o c k frequency. The r i s e time of the p o s i -t i v e going c o l l e c t o r swing, which i s used to t r i g g e r the pulse generator, i s about 0.1 microseconds. The t i m i n g generator and the other components of the coder are i l l u s t r a t e d i n the c i r c u i t diagram of f i g u r e 2.1. 2 .1 .2. PULSE GENERATOR AND COMPARATOR The pulse generator and comparator were designed and b u i l t up as a s i n g l e u n i t . The pulse generator i s an e m i t t e r -coupled monostable u n i t capable of being t r i g g e r e d by the p r e v i o u s l y d e s c r i b e d c l o c k p u l s e s . In the normal or o f f -s t a t e of the monostable c i r c u i t , t r a n s i s t o r T, i s conducting - - - • •• J i n i t s a c t i v e r e g i o n . I t i s drawing about 5 ma s i n c e i t s base i s clamped to —1.5 v o l t s by diode Dg. The feedback loop from the dc a m p l i f i e r i s in t r o d u c e d at D^ through R^. Since the vo l t a g e at the c o l l e c t o r of Tg v a r i e s from - 3 . 1 to -3»5 v o l t s , t h i s w i l l vary the current DC AMPLIFIES 5? Diodes = CK762 (Baytheon) B.^330 = 200 (Texas) ' B 2=1K = 2N247 (B.C.A.) fi3=1K « 1N497 B 4=330 B C=10K 5 B^=680 Bg=6•8K B o =270 B l 6 = 5.6K C 5= .45 B 1 2=1K G1 =850jx^f. C 6 =.015 Hf. ^ 1 3 " ^ ' ^2 -850u-Uf. A l l r e s i s t o r s B 1 4 = 1.5K C 3 = 33nnf• i w a 1 ; t c a r b o n B 10" 1.8K B 1 5 = 4.7K 0^=270 HHf. F i g u r e 2 . 1 . C i r c u i t d i a g r a m o f d e l t a coder through. DL v i a B C . Thus the c u r r e n t i n t h e d i o d e w i l l range f r o m l lHc = °* 0 1 M A T 0 IQ'K = 0*0-5 ma To unhook , t h i s c u r r e n t w i l l have t o he d e l i v e r e d t h r o u g h hy t h e p o s i t i v e g o i n g c l o c k waveform. T h i s w i l l a l l o w t h e v o l t a g e a t t h e cathode o f t o r i s e t o -1.5 v o l t s , p e r -m i t t i n g c o n d u c t i o n t h r o u g h S i m i l a r l y , any p o s i t i v e p u l s e w h i c h p a s s e s t h r o u g h w i l l have t o unhook Dg and "begin t o t u r n t r a n s i s t o r T^ o f f . At t h i s p o i n t , the mono-s t a b l e c i r c u i t w i l l f l i p o v e r and pass about 6.4 ma i n t o T^ f o r 1 m i c r o s e c o n d . Thus as t h e f e e d b a c k v o l t a g e v a r i e s , t h e monostable may or may not be t u r n e d on, d e p e n d i n g upon t h e amount of c u r r e n t f l o w i n g i n when a c l o c k p u l s e a r r i v e s . F o r example, i f t h e f e e d b a c k v o l t a g e i n c r e a s e s f rom say -3.2 v o l t s t o a p p r o x i m a t e l y -3*5 v o l t s , t h i s w i l l r e s u l t i n more of the p o s i t i v e c l o c k p u l s e c u r r e n t b e i n g used t o unhook , l e a v i n g an i n s u f f i c i e n t amount o f c u r r e n t l e f t t o unhook Dg, and T^. C o n s i d e r a b l e d i f f i c u l t y was e x p e r i e n c e d i n t h i s p a r t o f t h e c o d e r . The t h r e e - d i o d e c o n f i g u r a t i o n was r e q u i r e d f o r t h e f o l l o w i n g r e a s o n . I t i s i m p e r a t i v e t h a t t h e t o t a l c harge coming out o f t h e monostable r e m a i n c o n s t a n t . Now when t r i g g e r e d , T^ w i l l r e m a i n on u n t i l i t s e m i t t e r f a l l s t o w i t h i n a p p r o x i m a t e l y 0.2 v o l t s o f the base of T^. At t h i s p o i n t T^ w i l l b e g i n t o conduct a g a i n and the c i r c u i t w i l l r e t u r n t o i t s o r i g i n a l s t a t e . Thus t h e p u l s e w i d t h or on-t i m e depends not o n l y upon C^Bg, but a l s o upon the v o l t a g e on t h e "base of T^« 26, O r i g i n a l l y a s i m p l e r c o u p l i n g o f t h e f e e d b a c k v o l t a g e t o the monostable c i r c u i t was t r i e d . T h i s c o n s i s t e d o f c l a m p i n g t h e base w i t h a s i n g l e d i o d e and f e e d i n g t h e base t h r o u g h a r e s i s t o r as shown i n f i g u r e 2.2. f e e d b a c k v o l t a g e B c l o c k p u l s e s -1 .5 v T. F i g u r e 2.2,. O r i g i n a l f e e d b a c k c o u p l i n g T h i s c i r c u i t would produce t h e d e s i r e d c o m p a r i s o n a c t i o n , but due t o the non-zero f o r w a r d r e s i s t a n c e o f t h e d i o d e , t h e v o l t a g e a t the base of T^ would v a r y s l i g h t l y between p u l s e s because of v a r i a t i o n i n f e e d b a c k v o l t a g e . T h i s v o l t a g e v a r i a t i o n i s g i v e n by the e x p r e s s i o n base B + R, where = f o r w a r d r e s i s t a n c e o f the d i o d e 6 0 0 ohms ( a p p r o x i m a t e l y ) E = 3.6 K ^ = f e e d b a c k v o l t a g e v a r i a t i o n , maximum v a l u e o f 0.4 v. Thus the base o f T^ may v a r y by 400 x 600 < P. 3600 + 600 c 6 0 m v and the mo n o s t a b l e p u l s e w i d t h w i l l n o t be c o n s t a n t . The a c t u a l p u l s e width, v a r i a -t i o n i s g i v e n by dT ^ n „ v ^ \ = 0.66 x ^ — o where 7q i s the minimum T^ base v o l t a g e d u r i n g the exponen-t i a l t i m i n g decay, and i s about 0.4 v o l t s . Thus f o r a minimum p u l s e w i d t h v a r i a t i o n o f one p a r t i n f i v e h u n d r e d , i t w i l l be n e c e s s a r y t o keep d V Q c o n s t a n t t o w i t h i n 4 To = 9 . 6 & 0 0 = L - A " S i m i l a r l y , t h e base o f T^ must be h e l d c o n s t a n t t o w i t h i n 1.2 mv. S i n c e t h e base o f changed by 60 mv when a v a r i a -t i o n of o n l y 1.2 mv c o u l d be t o l e r a t e d , a n o t h e r c o u p l i n g network was r e q u i r e d . The d i o d e arrangement o f f i g u r e 2.3 g r e a t l y r e d u c e s t h i s base v o l t a g e v a r i a t i o n . Now t h e v a r i a t i o n on t h e base o f caused by a change i n the f e e d b a c k v o l t a g e i s r e d u c e d t o A 7 f D H f 2 A \ a s e * ( E f + B 5 ) ( B f + \ ) ( ? ) where B^ = f o r w a r d r e s i s t a n c e o f d i o d e 600 ohms ( a p p r o x i m a t e l y ) backward r e s i s t a n c e o f d: 1 Megohm ( a p p r o x i m a t e l y ) 28. c l o c k p u l s e s " R C=10K 5 - 3 . 0 v < f e e d b a c k v o l t a g e F i g u r e 2 . 3 . F i n a l f e e d b a c k c o u p l i n g F o r the same 0 . 4 v o l t change i n t h e f e e d b a c k v o l t a g e , t h e base v o l t a g e v a r i a t i o n , as c a l c u l a t e d by e q u a t i o n (7) i s now o n l y 0 . 0 1 mv. Thus t h e p u l s e w i d t h v a r i a t i o n due t o impr o p e r base c l a m p i n g i s e f f e c t i v e l y e l i m i n a t e d . The o u t p u t from t h e monostable c i r c u i t was o b s e r v e d a c r o s s a 100 ohm dummy l o a d . The'average c u r r e n t was 6 .4 ma, l a s t i n g f o r 1 m i c r o s e c o n d . I n o t h e r words, t h e p u l s e g e n e r a t o r i s c a p a b l e , once e v e r y s a m p l i n g p e r i o d , o f p r o -v i d i n g 6 .4 z 10 coulombs of charge f o r t h e i n t e g r a t o r . 2 . 1 . 3 . INTEGRATOR The i n t e g r a t o r c o n s i s t s o f a r e s i s t o r - c o n d e n s e r c o m b i n a t i o n and .a c u r r e n t generator'. I n o r d e r t o i n t e -g r a t e p r o p e r l y down t o 200 c p s , EC was chosen such t h a t Since the input impedance to the dc a m p l i f i e r i s about 3 0 0 0 ohms, the t o t a l r e s i s t a n c e seen by i s i « 5 • tHi -  3,3 E G. was then chosen at 0 . 4 5 m i c r o f a r a d s , producing a time - 0 constant of 1 . 6 m i l l i s e c o n d s . With a charge of 6 . 4 x 1 0 coulombs per p u l s e , the step s i z e at C,. i s given by T T Q 6 . 4 x 1 Q ~ ^ . . „ V , = 3 = — 7 = 1 4 » 2 mv a 1 ; e p C 0 . 4 5 2 C 1 0 " 6 The c u r r e n t generator i s r e q u i r e d to remove the aver-age current of % x 1 0 0 , 0 0 0 x 6 . 4 x 1 0 * " ^ » . 3 2 ma coming from the pulse generator, and to set the dc l e v e l at the top of the d i v i d e r c h a i n , and H'^ .^ The n o - s i g n a l pulse-space p a t t e r n i s adjusted by means of B ^ i ' w n l ° n v a r i e s the c u r r e n t drawn o f f the i n t e g r a t o r . The audio s i g n a l i s added to the coder through the c a p a c i t o r d i v i d e r c h a i n , and Cg. 2 . 1 . 4 . DC AMPLIFIEB The dc a m p l i f i e r , Tg i s used to a m p l i f y the d i f f e r e n c e s i g n a l and to provide a convenient p o i n t from which to take the feedback s i g n a l . Since the vo l t a g e g a i n i s about 5 0 , the 1 4 mv i n t e g r a t e d step, a f t e r being reduced to 7 mv at the base of Tg, appears as about 3 5 0 mv at the c o l l e c t o r . As p r e v i o u s l y d e s c r i b e d , t h i s v o l t a g e i s fedback v i a B,-to the cathode of D^, and c o n t r o l s the output of the pulse generator. 2.1.5. OUTPUT CIRCUIT The output c i r c u i t , shown i n f i g u r e 2 . 4 i s simply a pulse a m p l i f i e r and i n v e r t e r , T^ , f o l l o w e d by an e m i t t e r -f o l l o w e r , Tg. The t r a i n of p o s i t i v e output pulses are obtained from the common e m i t t e r s of T^ and T^, which go negative w i t h each pulse produced by the monostable c i r c u i t . 2.2 DELTA DECODER The r e c e i v e r c o n s i s t s of a regenerator and an i n t e -g r a t o r o n l y . A low-pass f i l t e r has not been i n c l u d e d , s i n c e f i l t e r i n g i s u s u a l l y accomplished a u t o m a t i c a l l y by the audio monitoring device being used. 2 . 2 . 1 . REGENERATOR The regenerator i s an e m i t t e r - c o u p l e d monostable f l i p -f l o p which i s t r i g g e r e d by the incoming p o s i t i v e p u l s e s . I t s design i s s i m i l a r to the pulse generator i n the coder. However, i n t h i s case i t i s not so d i f f i c u l t to keep the pulse width constant, and furthermore, any s m a l l v a r i a t i o n i n the pulse width w i l l not s e r i o u s l y hinder the o p e r a t i o n of the r e c e i v e r . The regenerated pulse i s about 1 v o l t i n amplitude and 1 microsecond l o n g . F i g u r e 2,5 i s the c i r c u i t diagram of the complete decoder. 2 . 2 . 2 . INTEGRATOR 1 In the normal s t a t e of the i n t e g r a t o r , T^ 1 i s held on by 3*27' a n < i ^12 i s o : f f because i t s base i s at +1.5 v. A p o s i t i v e pulse from the regenerator w i l l t u r n o f f , a l l o w i n g a c u r r e n t to flow out of T^g i n t o Bgg f o r about 31. E 17 I B 18 input from B Q |f -4.5T I -6Y -^•output pulses Ov B 1 7 - 1M G 7 » 50 H|if B 1 8 8 6. 8K * ?» Tg, = 2N247 H 1 9 - 15K D 4 = 1N497 Figur e 2 . 4 » Output c i r c u i t of d e l t a coder 32 i PULSE BEGENEEATOR \ INTEGEATOB T r a n s i s t o r s - CK762 B e s i s t o r s - •§• w a t t , c a r b o n B20 »= 4.7K H 25 = 3.3K C 8 » 100 B 2 1 - 3.3K B 26 • 180 V = 330 \X\if B22 = 560 B 2 7 « 220K °10 = 330 \i\Xf E23 = 470 B28 - 10K *11 = 200 W* E 2 4 =- 6*8K B 2 9 - 3.9K C12 = 0 .5 F i g u r e 2 ,5. C i r c u i t d i a g r a m o f d e l t a decoder 1 microsecond. Since Bgg a l l o w s 15 ma to f l o w i n T^g f o r t h i s 1 microsecond, the average c o l l e c t o r c u r r e n t i s | § - 0.75 ma Thus w i t h set at 3»9 E» the c o l l e c t o r v o l t a g e w i l l vary around -3 v o l t s . With t h i s load r e s i s t o r , and w i t h chosen as 0.5 m i c r o f a r a d s , a 2 m i l l i s e c o n d i n t e g r a t i n g time constant i s obtained. The step s i z e i s given by 34. 3. PEBFOBMANCE OF THE DELTA MODULATION SYSTEM 3.1. CIBCUITEY OPERATION The d e l t a m o d u l a t i o n c i r c u i t r y d e s c r i b e d i n t h e p r e v i o u s f* 1^ s e c t i o n worked q u i t e s a t i s f a c t o r i l y . The c l o c k , a f t e r i n i t i a l a d j u s t m e n t t o 100 Kc, r e q u i r e d no f u r t h e r a t t e n t i o n t h r o u g h o u t the p r o j e c t . However, the s e t t i n g of t h e n o - s i g n a l p u l s e -space p a t t e r n was r a t h e r c r i t i c a l . A l t h o u g h i t i s t h e o n l y a d j u s t m e n t n e c e s s a r y i n t h e o p e r a t i o n o f t h e d e l t a c oder and d e c o d e r , i t must be made a t t h e b e g i n n i n g o f any t e s t p r o c e d u r e . The s t a b i l i t y of t h i s s e t t i n g c o u l d be im-p r o v e d by i n c r e a s i n g t h e charge d e l i v e r e d f r o m the p u l s e g e n e r a t o r . T h i s would r e d u c e t h e e f f e c t of any p u l s e -space v a r i a t i o n s caused by h a v i n g an i m p r o p e r amount o f c u r r e n t w i t h d r a w n from the c u r r e n t g e n e r a t o r , T^. F u r t h e r -more, t h i s g r e a t e r charge would i n c r e a s e t h e range o f t h e f e e d b a c k v o l t a g e , and t h u s make t h e comparator a c t i o n e a s i e r . The o v e r a l l f r e q u e n c y r e s p o n s e o f t h e d e l t a system i s u n i f o r m t o w i t h i n 1 db over t h e o p e r a t i n g range o f 200 cps to'5 Kc. The t o t a l power consumed by t h e cod e r and decoder r e s p e c t i v e l y i s 220 m i l l i w a t t s and 50 m i l l i w a t t s . 3.,2. LISTENING TESTS 3.2,1, EXPEBIMENTAL BESULTS I n e v a l u a t i n g t h e o p e r a t i o n o f t h e d e l t a s y s t e m , one must c o n s i d e r c a r e f u l l y t h e t y p e of s i g n a l b e i n g u s e d . At a f i r s t g l a n c e , the pe r f o r m a n c e o f the s y s t e m appears t o de-c r e a s e w i t h i n c r e a s i n g f r e q u e n c y , s i n c e t h e s i g n a l - t o - n o i s e r a t i o s d e v e l o p e d e a r l i e r a r e i n v e r s e l y p r o p o r t i o n a l t o 35. f r e q u e n c y . I f t h e s i g n a l s had t h e sp e c t r u m o f w h i t e n o i s e , t h i s would c r e a t e a s e r i o u s d i f f i c u l t y . F o r t u n a t e l y , w i t h a u d i o s i g n a l s the h i g h e r ; f r e q u e n c i e s , on t h e a v e r a g e , c o n t a i n l e s s energy t h a n the l o w e r ones, and i n t h i s r e s p e c t the d e l t a system o v e r l o a d c h a r a c t e r i s t i c s a r e w e l l s u i t e d t o a u d i o s i g n a l s . As i n a l l a u d i o s y s t e m s , t h e i n p u t s i g n a l l e v e l i s most i m p o r t a n t . I n t h i s c a s e , t o o low a s i g n a l l e v e l i n t o t h e coder w i l l r e s u l t i n a poor s i g n a l - t o - n o i s e r a t i o , f o r "both the t h r e s h o l d e f f e c t and q u a n t i z i n g n o i s e w i l l he i n -c r e a s e d . On the o t h e r hand, t o o h i g h an i n p u t s i g n a l l e v e l w i l l produce c o n s i d e r a b l e s l o p e o v e r l o a d . The a c t u a l s i g -n a l s chosen were spoken passages and s e v e r a l m u s i c a l e x c e r p t s , i n c l u d i n g b o t h v o c a l and i n s t r u m e n t a l p o r t i o n s . These s i g n a l s - w e r e v a r i e d c o n s i d e r a b l y i n a m p l i t u d e so t h a t b o t h the t h r e s h o l d e f f e c t and the o v e r l o a d c h a r a c t e r i s t i c s o o u l d be heard e a s i l y . F o r b e s t o p e r a t i o n , t h e i n p u t l e v e l was a d j u s t e d so t h a t t h e r e was o n l y a s l i g h t o v e r l o a d i n g of l o u d p a s s a g e s . Under t h e s e c o n d i t i o n s the spe e c h s i g n a l s were c o m p l e t e l y i n t e l l i g i b l e . N e v e r t h e l e s s , t h e e f f e c t of the d e l t a m o d u l a t i o n on t h e s e spoken passages was e a s i l y heard. A r e a s o n a b l y s t e a d y q u a n t i z i n g n o i s e was p r e s e n t , and s o f t p a s s a g e s , n o t i c e a b l y a t the end of words, s u f f e r e d from t h e t h r e s h o l d e f f e c t . T h i s r e s u l t e d i n a r a t h e r a b r u p t e n d i n g o f low l e v e l p a s s a g e s . On t h e o t h e r hand, t h e e f f e c t o f the d e l t a m o d u l a t i o n on m u s i c a l s i g n a l s was much more d i f f i c u l t t o p e r c e i v e . Thus i t can be seen t h a t i t i s v e r y d i f f i c u l t t o d e s i g n a t e one p a r t i c u l a r e x p e r i m e n t a l 36. s i g n a l - t o - n o i s e r a t i o f o r t h i s d e l t a s y s t e m . I n t h e o r y , one s h o u l d s u b t r a c t t h e o r i g i n a l s i g n a l f r o m the d e l t a modulated message i n o r d e r t o o b t a i n an e x p e r i m e n t a l s i g n a l - t o - n o i s e r a t i o . S i n c e t h i s p r o c e d u r e would be d i f f i c u l t t o u n d e r t a k e w i t h t h e equipment a v a i l a b l e , a c o m p a r i s o n approach was made i n s t e a d . As mentioned i n s e c t i o n 1 .7*t t e s t t a p e s o f known s i g n a l - t o - n o i s e r a t i o s were made f o r t h i s c o m p a r i s o n . The 0 db s i g n a l - t o - n o i s e t a p e was p r e p a r e d w i t h t h e a i d of the "TO"" meter o f the Ampex tape r e c o r d e r . The r e l a t i v e l e v e l s of s i g n a l and n o i s e were a d j u s t e d u n t i l . . . i t h e s t e a d y m e t e r - r e a d i n g o b t a i n e d w i t h t h e n o i s e p r e s e n t a l o n e was t h e same as t h e peak m e t e r - r e a d i n g of t h e s i g n a l by i t s e l f . I n v i e w of t h e l a r g e dynamic range o f the s i g n a l , t h i s was a d i f f i c u l t a d j u s t m e n t , and may w e l l have been i n e r r o r by 5 or even 10 db. Once t h i s 0 db t a p e has been made, i t i s easy t o p r e p a r e f u r t h e r t a p e s w i t h s i g n a l - t o - n o i s e r a t i o s i n c r e a s i n g e x a c t l y i n s t e p s of 5 db, up t o 30 db. I n comparing t h e s e t a p e s w i t h the d e l t a m odulated speech s i g n a l , t h e 25 db s i g n a l - t o - n o i s e r a t i o appeared t o be t h e closest match, t o t h e o r i g i n a l s i g n a l . However, as mentioned e a r l i e r , t h i s c o m p a r i s o n i s d i f f i c u l t t o make. F i r s t l y , one t e n d s t o c o n c e n t r a t e on the n o i s e a s s o c i a t e d w i t h t h e low l e v e l s i g n a l s r a t h e r t h a n on t h a t accompanying l a r g e s i g n a l s . S i n c e t h e p r e p a r e d t a p e s were r a t i o s o f peak s i g n a l s t o average n o i s e , t h i s t e n dency would produce 37-a p e s s i m i s t i c c o mparison o f t h e d e l t a system's s i g n a l - t o -n o i s e r a t i o . F u r t h e r m o r e , t h e ear i s c e r t a i n l y n o t capa-b l e of a c c u r a t e l y d i s t i n g u i s h i n g l e v e l s any c l o s e r t h a n about 3 db. Thus i n q u o t i n g a s i g n a l - t o - n o i s e r a t i o o f 25 db f o r t h i s d e l t a m o d u l a t i o n s y s t e m , one must r e a l i z e t h e c o n d i t i o n s under w h i c h t h i s f i g u r e was o b t a i n e d . 3.2.2. COMPARISON OF EXPERIMENTAL AND THEORETICAL SIGNAL-TO-NOISE RATIOS I n c a l c u l a t i n g t h e s i g n a l - t o - n o i s e r a t i o s f o r t h i B d e l t a s y s t e m , i t was assumed, t h a t f o r t h e purpose o f g e n e r a t i n g q u a n t i z i n g n o i s e , speech a c t s e f f e c t i v e l y as a s i n e wave o f f r e q u e n c y f = 800 c p s , s i n c e i t i s known t h r o u g h e x p e r i m e n t a l t e s t s ^ t h a t the maximum s i g n a l power f o r a u d i o s i g n a l s i s c o n t a i n e d a p p r o x i m a t e l y i n t h e 800 cps r e g i o n . Now, f r o m e q u a t i o n (4) we g e t one s i g n a l - t o -n o i s e r a t i o s t h e r a t i o o f t h e maximum 800 cps s i g n a l w h i c h j u s t o v e r l o a d s t h e system to t h e t h r e s h o l d n o i s e power. T h i s i s g i v e n by 2 S 3 3C, 100 11 Si 2lt x 0.8 The e x p e r i m e n t a l l y o b s e r v e d v o l t a g e s a t t h e i n p u t t o t h e coder which produced o v e r l o a d and t h r e s h o l d s i g n a l s r e s -p e c t i v e l y were 7»5 v o l t s and 0.15 v o l t s , o r a s j g n a l - t o -n o i s e r a t i o o f I = ~"o7i5 = 5 0 = 3 4 d * ( ± 1 d 1 o ) T h i s f i g u r e i s i n e x c e l l e n t agreement w i t h the t h e o r e t i c a l v a l u e o f 33.8 db. 3 8 . On t h e o t h e r hand, as p o i n t e d out i n s e c t i o n 1 . 4 « 3 » , a more u s e f u l s i g n a l - t o - n o i s e r a t i o i s t h a t c a l c u l a t e d from the amount of n o i s e a c t u a l l y accompanying l a r g e s i g n a l s , r a t h e r t h a n f r o m t h a t p r e s e n t a t t h e t h r e s h o l d l e v e l . T h i s r a t i o i s g i v e n more c l o s e l y "by e q u a t i o n (6) and i s c a l c u l a t e d t o be _ j - . -04 x i o o 3 m 1 > 2 3 x 1 Q 4 • „ 4 1 . d l > 5 3c .8 where 5 Kc was s u b s t i t u t e d f o r t h e b a n d w i d t h , f Q , and 800 cps was chosen as t h e s i g n a l f r e q u e n c y , f Q . T h i s i s i n c o n s i d e r a b l e d i s a g r e e m e n t w i t h t h e e x p e r i m e n t a l f i g u r e o f 25 db quoted i n the l a s t s e c t i o n , but f o r t h e r e a s o n s g i v e n t h e r e , t h i s i s not s u r p r i s i n g . CONSTRUCTION* OF—THE • INSTANTANEOUS COMPANDOR The compandor " b u i l t i n t h i s p r o j e c t i s t h e i n s t a n t a n -eous t y p e d e s c r i b e d i n s e c t i o n 1.5»2. The f o u r d i o d e s , as shown i n f i g u r e l o l l - , produce t h e d e s i r e d c o m p r e s s i o n c h a r a c -t e r i s t i c s . However, a matched expandor i a more d i f f i c u l t t o c o n s t r u c t . The method used here i s i l l u s t r a t e d i n f i g u r e 4*1* The sys t e m i n c o r p o r a t e s a h i g h - g a i n a m p l i f i e r and a n o n - l i n e a r n e g a t i v e f e e d b a c k network c o n s i s t i n g o f t h e same d i o d e c o n f i g u r a t i o n as used i n t h e compandor. 4.1 FEEDBACK ACTION The a c t i o n of t h e expander i s as f o l l o w s . V ^ i s t h e compressed i n p u t s i g n a l t o t h e expandor. Thus f o r a d i o d e c o m p r e s s i o n r a t i o of say a^, t h a t i s c l t h e i n p u t t o t h e a m p l i f i e r w i l l be —•—— • a l Now, s i n c e A]^$> ~ , t h e c l o s e d l o o p g a i n i s P • AJ 1 5 c 2 1 But t h e f e e d b a c k v o l t a g e f a c t o r i s ^ — =» 8 » out Thus A f * a 2 And so the o u t p u t s i g n a l i s W . » A_ x V , out f c l or . a 2 X Y i n out = »i F i g u r e 4»1«. P r i n c i p l e o f o p e r a t i o n o f t h e instantaneous compandor Thus i t can he seen t h a t i f the two d i o d e c o m p r e s s i o n r a t i o s a r e made e q u a l , t h e o u t p u t w i l l f o l l o w t h e o r i g i n a l i n p u t s i g n a l . 4.2. CIRCUIT DESCRIPTION The c i r c u i t d i a g r a m o f t h e i n s t a n t a n e o u s compandor i s shown i n f i g u r e 4.2. C o n s i d e r a b l e t i m e was spen t i n c h o o s i n g 8 d i o d e s . 4 w i t h s i m i l a r f o r w a r d c h a r a c t e r i s t i c s , and 4 w i t h s i m i l a r backward c h a r a c t e r i s t i c s . The s h u n t i n g r e s i s t o r s R^ and R ^ l i m i t the h i g h a m p l i t u d e c o m p r e s s i o n r a t i o t o 159*1, and t h e s h u n t i n g r e s i s t o r Rg matches t h e low a m p l i -tude c o m p r e s s i o n r a t i o s a t 12.5*1« I d e n t i c a l e m i t t e r f o l l o w e r s w i t h i n p u t impedances of about 140 K and output impedances of 150 ohms were used b o t h t o p r e v e n t l o a d i n g o f t h e d i o d e s and t o p r o v i d e a c o n v e n i e n t m i x i n g p o i n t f o r t h e s i g n a l and f e e d b a c k v o l t a g e . A The e f f e c t i v e open c i r c u i t g a i n i s a b o u t TJ s i n c e b o t h s i g n a l s a r e r e d u c e d t h r o u g h e i t h e r R^ or R^ t o one h a l f o f t h e i r o r i g i n a l v a l u e s . The a c t u a l r e d u c t i o n i s s l i g h t l y more, s i n c e t h e i n p u t impedance t o t h e a m p l i f i e r i s 4000 ohms . S i n c e an i n p u t s i g n a l o f 35 v o l t s , p e a k - t o - p e a k , i s r e q u i r e d t o produce a 159*1 c o m p r e s s i o n w i t h t h e d i o d e s a v a i l a b l e , a ste p - u p t r a n s f o r m e r was needed i f t h e s u p p l y v o l t a g e was t o be kept a t -6 v o l t s . When used w i t h a 40.1 impedance r a t i o t r a n s f o r m e r , C l a s s A o p e r a t i o n w i l l produce a p p r o x i m a t e l y 6~\j 40 or 38 v o l t s p e a k - t o - p e a k o u t p u t • COMPBESSOB EZPANDOB B 8 B 10 T FX T. B 12 out » 5 D° B 13 •5T ts 8 0 0 K V - 1.5K G l * = 5|if "a S3 90K =10 3S 6 8 K *2 ' • 5*rf-E 3 E 4 = 330K =11 s 500K °3 ' « 3 0(if 2 . 8 K =12 « 3 3 °4 • * . 0 2 u f »5 E 6 1.5K =13 270 C 5 ' = 3 3 0 K B U XS 2 2 K e 6 ' = #0025^ E7 S 3 3 0 B 15 » 3 3 0 K V • a 8 S 4.7K =16 2 . 8 K T T. l ' T 4 m 2N224 = GK762 = 2N247 D 1,D 2,D 5,D 6 - 1N158 3>3,B4,D7,D8 = 1N497 f F l m Hammond trans-former #842 F i g u r e 4«2« C i r c u i t diagram of the compandor used •''back-to-back" ro To p r e v e n t low f r e q u e n c y o s c i l l a t i o n s i n the c i r c u i t , t he c o u p l i n g t i m e - c o n s t a n t s , although, a l l g r e a t e r t h a n 1 m i l l i s e c o n d , were s t a g g e r e d c o n s i d e r a b l y , t h e l a r g e s t b e i n g about 1 second. I n o r d e r t o produce the s t a b i l i t y d e s c r i b e d i n the n e x t s e c t i o n , s e v e r a l p h a s e - l a g networks a r e i n c l u d e d i n t h e a m p l i f i e r . I t was a l s o n e c e s s a r y t o use f o r t h e t r a n s -f o r m e r Tjp^ a h i g h q u a l i t y a u d i o t r a n s f o r m e r (Hammond type 842) r a t h e r t h a n t h e m i n i a t u r e (Texas t y p e 302) o r i g i n a l l y t r i e d . PERFORMANCE OP THE INSTANTANEOUS COMPANDOB 5.1. STABILITY F i g u r e 5«1» I s "the o p e n - c i r e u i t g a i n and phase c h a r a c -t e r i s t i c f o r the a m p l i f i e r t a k e n w i t h the f e e d b a c k l o o p d i s c o n n e c t e d from the d i o d e s and grounded. Because o f the n o n - l i n e a r i t y i n t h e f e e d b a c k l o o p , t h e g a i n and phase margins must.be s a t i s f i e d o v e r a c o n s i d e r a b l e range o f 8 8 s , from 8 = ^ 2 5 t o 8 = y ~ • I t can be seen f r o m t h e grap h t h a t t h e c i r c u i t i s s t a b l e . F o r 8 =,^r^ t "the c r i t i c a l v a l u e o f t h e g a i n i s 21.9 db. and a t t h a t p o i n t , the g a i n m a r g i n i s 8 db and the phase m a r g i n i s 60°. F o r a l l s m a l l e r v a l u e s of 8 t h e g a i n and phase m a r g i n s a r e l a r g e r . 5.2. COMPANDOB BANGE F i g u r e 5 .2. i l l u s t r a t e s t h e o v e r a l l a c t i o n of t h e compandor. The f i r s t c u r v e i s t h e compressor c h a r a c t e r i s t i c s . N o t i c e t h a t below the b r e a k p o i n t t h e r e i s a c o n s t a n t 12.5*1 r e d u c t i o n . Above t h i s p o i n t c o m p r e s s i o n i n c r e a s e s a l m o s t l o g a r i t h m i c a l l y u n t i l a maximum c o m p r e s s i o n o f 159&1 o c c u r s a t t h e o v e r l o a d p o i n t o f 35 v o l t s p e a k - t o - p e a k . The compressor r e d u c e s the s i g n a l r a n g e s from 1 = 50«9 db - - . 0«1 0 22 t o about ~QQQ'"" = 28.8 db, r e s u l t i n g i n a net compandor ad-vantage o f 22 db. The l i n e a r i t y of the e n t i r e system i s a l s o shown i n f i g u r e 5«2. The ou t p u t v o l t a g e , shown as t h e second c u r v e , v a r i e d f r o m t h e i n p u t by l e s s t h a n 1 db over 1 most o f t h e o p e r a t i n g r a n g e . These r e a d i n g s were t a k e n a t 1000 10 K 100 K 1 M f r e q u e n c y F i g u r e 5»1. G a i n and phase c h a r a c t e r i s t i c s o f a m p l i f i e r 40 10--Compreasor Input (volts) Curve #1 Expandor Output (volts) Curve #2 0.1 0.03 159*1 , Compandor advantage = 22 db 12.5*1 4-,005 •©! 0.1 0 . 4 Compressor Output Expandor input (volts) Figure 5*2. Overall compandor performance - 47. 23°C. Input-output l i n e a r i t y was a l s o measured at both 19° 0 and 28° C. Maximum v a r i a t i o n between these readings was s t i l l l e s s than 2 db. 5.3. LISTENING" TESTS - >' Due to the high negative feedback, the frequency r e s -ponse of the compandor was uniform to 1.5 db from 50 cpa "to 20 Kc. T o t a l harmonic d i s t o r t i o n i n the output s i g n a l was measured w i t h the H e a t h k i t Harmonic D i s t o r t i o n Meter. D i s t o r t i o n v a r i e d both w i t h frequency and s i g n a l amplitude. A minimum d i s t o r t i o n of 0»6% was observed at 1000 cps, and i t i n creased to 5% at 8 Kc and to 2.5% at 200 cps. With respect to s i g n a l amplitudes, minimum d i s t o r t i o n occurred i n the 1 v o l t to 10 v o l t range. On l i s t e n i n g to s i n g l e t e s t f r e q u e n c i e s passed through the compressor and expandor, i t was noted t h a t at 200 c p s , 2.5% d i s t o r t i o n i s q u i t e a u d i b l e , whereas 4»85& d i s t o r t i o n at 5 i s very d i f f i c u l t to p e r c e i v e . However, as a more r e a l i s t i c t e s t of the compandor, speech and music were played through the system. On both speech and music m a t e r i a l , i t was very d i f f i c u l t to observe any d i s t o r t i o n i n the s i g n a l as i t was passed through 22 db of compression and expansion. The performance of the compandor would be improved c o n s i d e r a b l y i f a transformer s i m i l a r to Tj,^ were used at the input to the diode compressor. This would match the frequency c h a r a c t e r i s t i c s of the compressor and expandor d i o d e n e t w o r k s more c l o s e l y . F u r t h e r m o r e , a b e t t e r m a t c h i n g of t h e i n d i v i d u a l d i o d e s w i t h o u t the use o f s h u n t i n g r e s i s -t o r s would i n c r e a s e t h e companding range o f t h e sys t e m . 5.4. THEORETICAL APPLICATION TO DELTA SYSTEM A l t h o u g h t h e compandor b u i l t i n t h i s p r o j e c t was not used w i t h t h e d e l t a c o d e r and d e c o d e r , a t h e o r e t i c a l e v a l -u a t i o n of i t s performance w i t h a t y p i c a l d e l t a system was made. As mentioned e a r l i e r i n s e c t i o n 3*2.2., t h e s i g n a l -t o - n o i s e r a t i o accompanying l a r g e s i g n a l s i n a d e l t a s y s -tem i s about 40 db w i t h o u t t h e a i d o f a compandor. T h i s i s shown by the s t r a i g h t l i n e o f f i g u r e 5.3* l a r e a l i t y , the l o w - l e v e l n o i s e i n a d e l t a s y s t e m , due t o t h e t h r e s h -o l d e f f e c t , i s q u i t e predominant near t h e o r i g i n and causes a v a r i a t i o n from l i n e a r i t y i n t h i s r e g i o n . However, the s t r a i g h t l i n e a p p r o x i m a t i o n shown w i l l c e r t a i n l y be s u f f i c i e n t f o r c o m p a r i s o n p u s p o s e s . Now w i t h a compressor p l a c e d b e f o r e t h e d e l t a c o d e r , and an expandor f o l l o w i n g t h e r e c e i v e r , the c a l c u l a t e d a l t e r -a t i o n i n t h e s i g n a l - t o - n o i s e r a t i o i s shown i n t h e second c u r v e . N o t i c e t h a t t h e s i g n a l - t o - n o i s e r a t i o accompany-i n g h i g h s i g n a l s i s s t i l l adequate f o r n o r m a l u s e , and t h a t the l o w - l e v e l s i g n a l - t o - n o i s e r a t i o has been con-s i d e r a b l y i n c r e a s e d . 4 0 30 i n s t a n t a n e o u s ^ (cLb) 2 0 # 2 ^ — ^ ^ ^ 6 0 0 ^ - 1 0 . 4 0 2 S i g n a l i n db b e l t> 0 * ow o v e r l o a d Curve #1 - 40 db S/N BATIO SYSTEM Curve # 2 - SAME SYSTEM^'BUT SUBJECTED TO COMPBESSION-EXPANSION F i g u r e 5.3. Signal-r-to-noise- r a t i o of. a . d e l t a .system, w i t h and w i t h o u t i n s t a n t a n e o u s a m p l i t u d e commpression NOISE GENEBATOE CONSTEUCTION AND PEEFOEMANCE A s i m p l e G a u s s i a n w h i t e n o i s e g e n e r a t o r was a l s o b u i l t t o p r e p a r e t h e s t a n d a r d n o i s e l e v e l t e s t t a p e s mentioned i n s e c t i o n 3 * 2 . 1 . A two-sta g e a m p l i f i e r , shown i n f i g u r e 6 . 1 . , p r o d u c e d a v o l t a g e g a i n o f 700 from 100 cps t o 20 Kc. Freque n c y spectrum measurements were made w i t h a G e n e r a l B a d i o t y p e 736-A Wave A n a l y s e r , w h i c h has a 4 cps m e a s u r i n g bandwidth between 20 cps and 15 Kc. W i t h a 1N34 d i o d e as a n o i s e s o u r c e , t h e f r e q u e n c y spectrum o f t h e n o i s e g e n e r a t o r was c o n s t a n t t o w i t h i n 3 db from 100 cps t o 10 Kc. 470-IK 1N34A 47K out 82K< _ + GK762 5\if CK762 Ov F i g u r e 6.1. C i r c u i t diagram of the noise generator CONCLUSIONS The d e l t a m o d u l a t i o n system b u i l t i n t h i s p r o j e c t was a f a i r l y s i m p l e one. A p a r t f r o m t h e two t r a n s i s t o r " c l o c k " , f o u r t r a n s i s t o r s were used i n the coder and f o u r i n t h e d e c o d e r . Some r e d u c t i o n might be made i n even t h i s number. The c i r c u i t worked s a t i s f a c t o r i l y , and was r e a s o n -a b l y s t a b l e ; i t c o u l d be improved f u r t h e r by i n c r e a s i n g t h e " l o o p g a i n " i n t h e c o d e r . The t r a n s m i s s i o n t e s t s d e m o n s t r a t e d a l l t h e e x p e c t e d d e f e c t s o f d e l t a m o d u l a t i o n : t h r e s h o l d e f f e c t , q u a n t i z i n g n o i s e , and o v e r l o a d i n g . The q u a n t i z i n g n o i s e sounded somewhat worse t h a n e x p e c t e d . N o n e t h e l e s s , speech p a s s e d t h r o u g h t h e system was p e r f e c t l y i n t e l l i g i b l e , and the q u a l i t y o f music t r a n s m i s s i o n was s u r p r i s i n g l y h i g h , c o n s i d e r i n g t h e l i m i t e d b a n d w i d t h , - 200 cps t o 5 Kc. There i s t h u s no doubt t h a t d e l t a m o d u l a t i o n i s a t r a n s m i s s i o n system t h a t can be b u i l t u s i n g s i m p l e c i r c u i t s t o a c h i e v e r e a s o n a b l e q u a l i t y . The compressor and expandor b u i l t were matched v e r y w e l l , and gave c o n s i d e r a b l e "compandor a d v a n t a g e " . By b e t t e r c h o i c e o f d i o d e s , t h i s advantage might be i n c r e a s e d s t i l l f u r t h e r . C o n s i d e r a b l e d i f f i c u l t y was e x p e r i e n c e d i n t h e c o n s t r u c t i o n o f t h e expandor w i t h i t s n o n - l i n e a r f e e d -=back: l o o p and i t s t e n d e n c y t b o s c i l l a t e . A f o r w a r d -a c t i n g expandor might he w o r t h e x p l o r i n g . I n t h e t i m e a v a i l a b l e f o r t h i s p r o j e c t , i t was not p o s s i b l e t o combine the compandor c i r c u i t w i t h t h e d e l t a m o d u l a t i o n s y s t e m , but t h e r e seems no doubt t h a t t h i s can be done s u c c e s s f u l l y * r e s u l t i n g i n c o n s i d e r -a b l e improvement i n t h e t r a n s m i s s i o n q u a l i t y o f the system* 54. EEFEEENCES 1* Shannon, CE.., and Weaver, W., "The M a t h e m a t i c a l Theory, o f Communication." U n i v e r s i t y o f I l l i n o i s P r e s s , Urbana, I l l i n o i s , 1949* 2, B l a c k , H.S., " P u l s e Code M o d u l a t i o n . " B e l l L a b s . E e c o r d , V o l . 25, page 265, J u l y , 1947* 3. de J a g e r , F . , . " D e l t a m o d u l a t i o n . " P h i l l i p s R e s e a r c h R e p o r t s , V o l . 7, page 442, 1952. 4» Bowers, F.K. "What Use i s D e l t a m o d u l a t i o n . t o t h e T r a n s m i s s i o n E n g i n e e r ? " Communications  and E l e c t r o n i c s . " Number 30, page 142, 1957. 5. B e n n e t t , W.R., " S p e c t r a o f Q u a n t i z e d S i g n a l s . " B e l l System T e c h n i c a l J o u r n a l , V o l . 27, page 446, 1948. 6. van der Weg, H . " Q u a n t i z i n g N o i s e o f a S i n g l e I n t e g r a t i o n D e l t a M o d u l a t i o n System w i t h an N - d i g i t Code." P h i l l i p s R e s e a r c h R e p o r t s , V o l . 8, page 367, 1953. 7. M a l l i n c k r o d t , C O . , " I n s t a n t a n e o u s Compandors." B e l l . T e l e p h o n e System T e c h n i c a l P u b l i -c a t i o n s , Monograph 1895* 

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