UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Coding for signals with occasional transients Reader, William Roland 1962

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1962_A7 R25 C6.pdf [ 4.4MB ]
Metadata
JSON: 831-1.0302292.json
JSON-LD: 831-1.0302292-ld.json
RDF/XML (Pretty): 831-1.0302292-rdf.xml
RDF/JSON: 831-1.0302292-rdf.json
Turtle: 831-1.0302292-turtle.txt
N-Triples: 831-1.0302292-rdf-ntriples.txt
Original Record: 831-1.0302292-source.json
Full Text
831-1.0302292-fulltext.txt
Citation
831-1.0302292.ris

Full Text

CODING FOR S I G N A L S Y I T H OCCASIONAL T R A N S I E N T S b y W I L L I A M ROLAND READER B . S c . , U n i v e r s i t y o f A l b e r t a , 1 9 5 3 A T H E S I S SUBMITTED I N P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D S C I E N C E I n 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 We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d 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 The 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 J u n e , 1 9 6 2 ABSTRACT T h i s i n v e s t i g a t i o n i s concerned w i t h improvements t h a t can be made i n communication systems to enable them t o t r a n s m i t e f f i c i e n t l y s i g n a l s c o n t a i n i n g o c c a s i o n a l t r a n s i e n t ; A method of i m p r o v i n g d e l t a m o d u l a t i o n by the use of v a r i a b l e s t e p s i z e i s d i s c u s s e d i n d e t a i l and the d e s i g n a.nd c o n s t r u c t i o n of a s u i t a b l e coder and s t e p s i z e c o n t r o l u n i t are d e s c r i b e d . The r e s u l t s of t e s t s ma^ de on the equipment con-s t r u c t e d are g i v e n . From these r e s u l t s i t i s co n c l u d e d t h a t c o n s i d e r a b l y b e t t e r response t o sudden l a r g e changes i n i n p u t s i g n a l can be o b t a i n e d w i t h o n l y s l i g h t d e t e r i -o r a t i o n i n the performance under normal c o n d i t i o n s of i n -put s i g n a l . The method used to e f f e c t t h i s improvement i s a p p l i c a b l e t o more complex m o d u l a t i o n schemes. V ACKNOWLEDGEMENT The a u t h o r i s i n d e b t e d t o t h e N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a f o r t h e i r s p o n s o r s h i p o f t h i s p r o j e c t a n d f o r a r e s e a r c h a s s i s t a n t s h i p , a n d t o t h e N o r t h e r n E l e c t r i c Company f o r t h e F e l l o w s h i p g r a n t e d t o h i m i n 1 9 6 0 . G r a t e f u l a c k n o w l e d g e m e n t i s g i v e n t o P r o f e s s o r F . K . B o w e r s f o r g u i d a n c e a n d e n c o u r a g e m e n t t h r o u g h o u t t h e p r o j e c t a n d t o D r . F . N o a k e s a n d t h e o t h e r members 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 D e p a r t m e n t 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 . 1 1 TABLE OF CONTENTS Page AbS"fcl?aC~fc o 0 o . 0 . 0 0 0 . 0 O 0 . 0 O O . 0 « © O O O O O O « © . « © O O 0 0 « O . O O O O O 0 « . L i s t of I l l u s t r a t i o n s c >> t <>>>»>» •<••<>••! o < • ) • • • • • « . « < • i v Acknowledgement o o o . 8 o « » . . 6 o ° » * « i > » » » » . . . « » . » « o « » « a » o ° ' > < > « J v 1. I n t r o d u c t i o n 1 2. T h e o r e t i c a l C o n s i d e r a t i o n s - 3 2.1 I n f o r m a t i o n Rate and System C a p a c i t y . . . . . . . . 3 2*2 " G e n e r a l l y C o r r e l a t e d " S i g n a l s ............. 4 2.3 R e d u c t i o n i n A c c u r a c y f o r T r a n s i e n t s ........ 5 2.4 D e s i r e d System C h a r a c t e r i s t i c s .............. 6 2.5 " G e n e r a l l y C o r r e l a t e d " S i g n a l s i n D e l t a MO d i l l ct~fc 1 Oil o o o t O 0 0 o e » 0 O i » » 0 - « o * * » » o » o o o e o o 0 o o o 0 o T 3. D e l t a M o d u l a t i o n 9 3.2 O v e r l o a d C h a r a c t e r i s t i c s . . . . . . . . . . . . . . . . . . . . 11 3.3 Q u a n t i z i n g Noise . . . . . . . . . . . o o . . . . . . . . . . . . . . 12 3»4 I n t e g r a t o r Waveform. . . . . . . a . . . . . . . . . . . . . . . . . 12 3*5 Transmiss i o n of DC S i g n a l s ................a 13 4. . A c c e l e r a t e d D e l t a M o d u l a t i o n 17 4.1 B a s i c Requirements......... *...............« 17 4.2 Coding f o r Step S i z e I n c r e a s e . . . . . . . . . . . . . . . 19 4»3 Rate of Step S i z e I n c r e a s e ................. 22 4.4 Maximum Step S i z e ...»*•••>»....«... ......... 24 i i i Page 4.5 Coding f o r Step S i z e Decrease. 25 4.6 Bate of Step S i z e Decrease................ 26 4.7 T r a n s m i s s i o n of DC S i g n a l s i n 5. System D e s i g n 32 5.1 D e s i g n Method and Requirements............ 32 5.2.1 C u r r e n t G e n e r a t o r . . . . . . . . . 36 5.3 Step S i z e C o n t r o l C i r c u i t . . . . . . . . . . . . . . . . . 38 5.3,1 D i g i t a l C o n t r o l C i r c u i t 38 5*3.2. Analogue C o n t r o l C i r c u i t . . . . . . . . . . . 44 60 R e s u l t s of T e s t s 46 6.1 Waveform Comparisons 46 6^2 D i s c u s s i o n r o f Waveforms.. 53 6.3 Method Used to Measure N o i s e . , . . * . . . 54 6.4 R.esults of Noise Measurements 57 7. C o n c l u s i o n s 60 7.1 C o n c l u s i o n s R e g a r d i n g the ADM System...... 60 7.2 A p p l i c a t i o n t o Other Systems.............. 60 Appendix I n s t r u m e n t a t i o n 63 A, Coderoo.o.o.o....«...o . .a«ft...ooo...ftoo 63 B. Step S i z e C o n t r o l C i r c u i t . . . . . . . . . . . . . . 68 Re f e r e n c e s 72 L I S T OP I L L U S T R A T I O N S F i g u r e P a g 3 . 1 S i m p l e D e l t a M o d u l a t i o n S y s t e m . » * 1 3 . 2 T y p i c a l W a v e f o r m s — S i m p l e DM S y s t e m 1 4 . 1 A c c e l e r a t e d D e l t a M o d u l a t i o n S y s t e m . . . . . . . . . . . 1 4 . 2 S l o p e o f V Q ( t ) f o r V a r i o u s P u l s e P a t t e r n s . . . . . 2 4 . 3 V a r i o u s A c c e l e r a t i o n M e t h o d s . . . . . . . . . . . . 2 4 . 4 T y p i c a l R e s p o n s e — A D M . . . . . . . . . . 2 4 . 5 I n t e g r a t o r C h a r a c t e r i s t i c s 3 5*1 D e l t a M o d u l a t i o n C o d e r — B l o c k D i a g r a m 3 5 . 2 C o d e r C u r r e n t G e n e r a t o r . . . . . . 3 5 . 3 S t e p S i z e C o n t r o l V o l t a g e . » » » • , » » . . » . . . . . . . . . . 3 5 . 4 D i g i t a l S t e p S i z e C o n t r o l U n i t — B l o c k D i a g r a m 4 5 . 5 T y p i c a l W a v e f o r m s — ADM S y s t e m 4 6 . 1 O s c i l l o g r a m . . . . . . * • , , . « # , * « , * * . » . . . . . . . « . . . , . . . 4 6 . 2 O s c i l l o g r a m . . 4 6 . 3 O s c i l l o g r a m . . . . . . . . . . . . 5 6 . 4 O s c i l l o g r a m . . . . . . . . . . o 5 6 . 5 O s c i l l o g r a m . . . 5 6 . 6 N o i s e M e a s u r i n g C i r c u i t . , . . . . * 5 6 . 7 G r a p h o f S i g n a l - t o - N o i s e R a t i o v e r s u s A m p l i t u d e 5 A - l D e l t a M o d u l a t i o n C o d e r — S c h e m a t i c D i a g r a m . . . . 6 A - 2 S t e p S i z e C o n t r o l C i r c u i t — S c h e m a t i c D i a g r a m 7 1. I N T R O D U C T I O N I n t h e p a s t f e w d e c a d e s t h e r e h a s b e e n a p h e n -o m e n a l i n c r e a s e i n c o m m u n i c a t i o n . R e c e n t l y t h i s g r o w t h h a s b e e n p a r t i c u l a r l y r a p i d i n t h e d i g i t a l f i e l d w h e r e m e s s a g e s a r e r e p r e s e n t e d b y d i s c r e t e e l e c t r i c a l i m p u l s e s , a s i n d a t a t r a n s m i s s i o n a n d p u l s e c o d e m o d u l a t i o n . To k e e p p a c e w i t h t h e e x p a n s i o n i n c o m m u n i c a t i o n , new a n d b e t t e r m e t h o d s o f s e n d i n g i n f o r m a t i o n m u s t be f o u n d . M u c h o f t h e w o r k now b e i n g d o n e i s c o n c e r n e d w i t h i n c r e a s i n g t h e jaumber o f m e s s a g e s t h a t c a n be s e n t o v e r e x i s t i n g s y s t e m s . T h i s i n c l u d e s s u c h p r o j e c t s a s s p e e c h b a n d w i d t h r e d u c t i o n a n d t a l k - s p u r t i n t e r p o l a t i o n . T h i s t h e s i s i n v e s t i g a t e s a more e f f i c i e n t m e t h o d o f t r a n s m i t t i n g a p a r t i c u l a r t y p e o f s i g n a l ; one w h i c h n o r m a l l y v a r i e s a t m o d e s t r a t e s b u t w h i c h o c c a s i o n a l l y h a s t r a n s i e n t s i n v o l v i n g much h i g h e r r a t e s o f c h a n g e . S u c h s i g n a l s a r e f o u n d i n many f i e l d s . The f o l l o w i n g s e c t i o n s d e s c r i b e a m e t h o d o f u s i n g r e d u c e d a c c u r a c y f o r t r a n s i e n t s so t h a t t h e i n f o r m a t i o n r a t e o f t h e s i g n a l d o e s n o t i n c r e a s e d u r i n g s u d d e n l a r g e c h a n g e s . The d e s i r e d c h a r a c t e r i s t i c s o f a n e f f i c i e n t s y s t e m a r e t h e n l i s t e d . D e l t a m o d u l a t i o n i s e x a m i n e d a s a n e x a m p l e o f a c o m m u n i c a t i o n s y s t e m w h e r e g r e a t e r e f f i c i e n c y i n t r a n s m i s s i o n 2 of s i g n a l s w i t h o c c a s i o n a l t r a n s i e n t s i s d e s i r a b l e and p o s s i b l e . The l a t t e r s e c t i o n s of the t h e s i s d e s c r i b e the d e s i g n and i n s t r u m e n t a t i o n of the m o d i f i c a t i o n t o d e l t a m o d u l a t i o n , d i s c u s s the r e s u l t s of t e s t s made on the new system, and p r e -sent s p e c i f i c and g e n e r a l c o n c l u s i o n s r e g a r d i n g an e f f i c i e n t method of t r a n s m i s s i o n of t h i s c l a s s of s i g n a l . 3 2 . T H E O R E T I C A L C O N S I D E R A T I O N S 2.1 I n f o r m a t i o n R a t e a n d S y s t e m C a p a c i t y The c a p a c i t y r e q u i r e d i n a c o m m u n i c a t i o n s y s t e m d e p e n d s o n t h e i n f o r m a t i o n r a t e o f t h e m e s s a g e t o be t r a n s -m i t t e d . The i n f o r m a t i o n r a t e o f a c o n t i n u o u s a m p l i t u d e -a n d b a n d - l i m i t e d s i g n a l , i n t u r n , d e p e n d s o n t h e b a n d w i d t h , ¥ , s i n c e a t l e a s t 2¥ s a m p l e s p e r s e c o n d a r e r e q u i r e d t o s p e c i f y i t . The r a t e a l s o d e p e n d s o n t h e r e q u i r e d a c c u r a c y i n a m p l i t u d e o f t h e s a m p l e , o n t h e p r o b a b i l i t y o f o c c u r r e n c e o f e a c h q u a n t i z e d a m p l i t u d e , a n d o n t h e a m o u n t o f c o r r e l a t i o n i n t h e s i g n a l . I f t h e s i g n a l i s q u a n t i z e d i n t o 2 n d i s t i n c t a m p l i -s t u d e l e v e l s , e a c h l e v e l i s e q u a l l y l i k e l y , a n d t h e r e i s no c o r r e l a t i o n , t h e n n b i t s a r e r e q u i r e d t o s p e c i f y e a c h s a m p l e . The i n f o r m a t i o n r a t e , a n d h e n c e t h e m i n i m u m s y s t e m c a p a c i t y f o r s u c h a s i g n a l , i s 2n¥ b i t s p e r s e c o n d . T h i s i s t h e c a p a c i t y o f a s t a n d a r d PCM s y s t e m s a m p l i n g a t t h e N y q u i s t r a t e . S i g n a l s w i t h t h i s i n f o r m a t i o n r a t e a r e e x t r e m e l y r a r e . E i t h e r t h e p r o b a b i l i t y o f o c c u r r e n c e o f some a m p l i -t u d e l e v e l s i s l o w e r t h a n o t h e r s o r t h e r e i s c o r r e l a t i o n among v a r i o u s p a r t s o f t h e s i g n a l . I t i s t h u s p o s s i b l e i n m o s t c a s e s t o r e d u c e t h e c a p a c i t y r e q u i r e d i n t h e c o m m u n i -c a t i o n s y s t e m . To t h i s e n d v a r i o u s s c h e m e s h a v e b e e n u s e d a n d many o t h e r s p r o p o s e d . 4 Some o f t h e m o s t e f f e c t i v e a n d p r a c t i c a l o f t h e s e s c h e m e s t a k e a d v a n t a g e o f t h e c o r r e l a t i o n among s a m p l e s o f t h e s i g n a l . I n t h i s m e t h o d a p r e d i c t i o n o f t h e n e x t s a m p l e v a l u e i s made a t b o t h t h e t r a n s m i t t e r a n d r e c e i v e r . The p r e -d i c t i o n i s b a s e d o n p a s t b e h a v i o u r o f t h e s i g n a l , t h e s i m -p l e s t t y p e b e i n g a p r e d i c t i o n t h a t t h e n e x t v a l u e w i l l be t h e same a s t h e p r e v i o u s v a l u e . One s u c h s y s t e m . - L s d i f f e r e n t i a l P C M . T h i s s y s t e m q u a n t i z e s , e n c o d e s a n d t x a j x s m i t s t h e d i f f e r -e n c e b e t w e e n t h e s a m p l e a n d a s u m m a t i o n pf...px.e.vj_aus. q u a n t i z e d d i f f e r e n c e s . The r e c e i v e r t h e n a d d s t h e q u a n ± i z . e d - d i f f e r e n c e t o t h e p r e v i o u s v a l u e t o o b t a i n t h e c o r r e c t o u t p u t . 2 . 2 " G e n e r a l l y C o r r e l a t e d " S i g n a l s We h a v e a v a i l a b l e t h e n s y s t e m s s u c h a s PCM w h i c h a r e e f f i c i e n t i n t r a n s m i t t i n g u n c o r r e l a t e d s i g n a l s , a n d s y s t e m s s u c h a s d i f f e r e n t i a l PCM w h i c h a r e e f f i c i e n t i n t r a n s m i t t i n g c o r r e l a t e d s i g n a l s . T h e r e i s a c l a s s o f s i g n a l s , h o w e v e r , w h i c h f i t s i n n e i t h e r c a t e g o r y , T h e s e a r e s i g n a l s w h i c h a r e c o r r e l a t e d m o s t o f t h e t i m e b u t i n w h i c h o c c a s i o n a l " s u r p r i s e s " o r t r a n s i e n t s o c c u r . A n e x a m p l e i s a v i d e o s i g n a l w h i c h n o r -m a l l y c h a n g e s s l o w l y d u r i n g a s c a n e x c e p t a t b o u n d a r i e s b e -t w e e n l i g h t a n d d a r k o b j e c t s w h e r e t h e r e a r e s u d d e n l a r g e c h a n g e s i n l i g h t i n t e n s i t y . E x a m p l e s c a n a l s o be f o u n d i n t e l e m e t e r i n g , w h e r e t h e m e a s u r e d q u a n t i t y i s n o r m a l l y 5 s t e a d y , o r c h a n g e s g r a d u a l l y , e x c e p t d u r i n g a b n o r m a l c o n -d i t i o n s s u c h a s s w i t c h i n g o r b r e a k d o w n s . I f a " g e n e r a l l y c o r r e l a t e d " s i g n a l i s a p p l i e d t o a s y s t e m w h i c h i s c a p a b l e o f t r a n s m i t t i n g a n u n c o r r e l a t e d s i g n a l , t h e s y s t e m w i l l be o p e r a t i n g i n e f f i c i e n t l y m o s t o f t h e t i m e . I f , o n t h e o t h e r h a n d , i t i s a p p l i e d t o a s y s t e m w h i c h i s c a p a b l e o f t r a n s m i t t i n g o n l y c o r r e l a t e d s i g n a l s , t h e i n f o r m a t i o n c o n t a i n e d i n t h e t r a n s i e n t w i l l b e l o s t . 2 . 3 R e d u c t i o n i n A c c u r a c y f o r T r a n s i e n t s The p r o b l e m o f p r o v i d i n g a s y s t e m w h i c h w i l l a l l o w t r a n s m i s s i o n o f t h e t r a n s i e n t s a n d w h i c h o p e r a t e s w i t h a h i g h a v e r a g e e f f i c i e n c y i s a d i f f i c u l t o n e , p a r t i c u l a r l y i f t h e same a m p l i t u d e a c c u r a c y i s r e q u i r e d f o r t r a n s i e n t s as f o r n o r m a l c h a n g e s . A l t h o u g h m e t h o d s c a n be d e v i s e d t o do t h i s t h e y a r e n o t t o o p r a c t i c a l s i n c e c o m p l i c a t e d v a r i -a b l e - d e l a y n e t w o r k s a r e r e q u i r e d a t t h e t r a n s m i t t e r a n d r e c e i v e r . F o r t u n a t e l y t h e r e a r e many a p p l i c a t i o n s w h e r e a r e d u c t i o n i n a c c u r a c y i s t o l e r a b l e d u r i n g t r a n s i e n t s . F o r e x a m p l e , i n v i d e o t r a n s m i s s i o n , a d v a n t a g e may be t a k e n o f t h e i n a b i l i t y o f t h e eye t o d e t e c t t h e e x a c t s i z e o f a n y d i s c o n t i n u i t y ' ' " . O r , a s a n o t h e r e x a m p l e , i n t e l e m e t e r i n g t h e t r a n s i e n t s i g n a l w i l l o f t e n b e d i s -t o r t e d i n a n y c a s e due t o i n e r t i a i n p i c k - u p o r r e a d - o u t t r a n s d u c e r s o r t o o t h e r f a c t o r s . 6 On t h i s b a s i s , more o r l e s s p r a c t i c a l s c h e m e s f o r t h e e f f i c i e n t t r a n s m i s s i o n o f " g e n e r a l l y c o r r e l a t e d " s i g n a l s 2 a r e f e a s i b l e . One s u c h s y s t e m p r o p o s e d b y R . E . G r a h a m i s r a m o d i f i e d d i f f e r e n t i a l PCM s y s t e m . I n t h i s scheme t h e e r r o r i n a p r e d i c t e d v a l u e i s q u a n t i z e d u s i n g a n o n - l i n e a r q u a n t i z i n g s t a i r c a s e . T h i s p e r m i t s s m a l l e r r o r s t o be t r a n s m i t t e d more a c c u r a t e l y t h a n l a r g e e r r o r s . O t h e r m e t h o d s s u c h a s q u a n t i z i n g h i g h f r e q u e n c i e s m o r e c o a r s e l y 1 3 t h a n l o v f r e q u e n c i e s , a n d " s l o p e c o m p a n d i n g " , a r e b a s e d o n t h e same p r i n c i p l e o f r e d u c e d a c c u r a c y f o r p o r t i o n s o f t h e s i g n a l c o n t a i n i n g h i g h r a t e s o f c h a n g e . 2 . 4 D e s i r e d S y s t e m C h a r a c t e r i s t i c s We w i l l now c o n s i d e r a s y s t e m w h i c h o p e r a t e d e f f i c i e n t l y f o r c o r r e l a t e d s i g n a l s a n d a s s u m e t h a t i t h a s b e e n m o d i f i e d f o r t r a n s m i s s i o n o f " g e n e r a l l y c o r r e l a t e d " s i g n a l s . I f i t s c a p a c i t y i s n o t i n c r e a s e d , t h e m o d i f i c a -t i o n e n a b l i n g i t t o t r a n s m i t t r a n s i e n t s w i l l r e s u l t i n r e -d u c e d a c c u r a c y o f t r a n s m i s s i o n f o r some s i g n a l s w h i c h w o u l d p r e v i o u s l y h a v e b e e n t r a n s m i t t e d a c c u r a t e l y . T h i s i s b e -c a u s e a p o r t i o n o f i t s c a p a c i t y t o t r a n s m i t c o r r e l a t e d s i g n a l s m u s t be a s s i g n e d t o t h e t r a n s m i s s i o n o f t r a n s i e n t s . The d e s i r e d c h a r a c t e r i s t i c s o f t h e s y s t e m a r e a s f o l l o w s : 1 . The a c c u r a c y o f t r a n s m i s s i o n o f c o r r e l a t e d s i g n a l s s h o u l d be r e t a i n e d a s c l o s e l y a s p o s s i b l e . 2 . The r e s p o n s e t o t r a n s i e n t s s h o u l d be a s r a p i d a s p o s s i b l e , p r e f e r a b l y i n t h e o r d e r o f t h a t i m p o s e d b y b a n d w i d t h l i m i t a t i o n ( r i s e t i m e a b o u t O.35/W.0„ 3 . The a c c u r a c y d u r i n g t r a n s i e n t s s h o u l d be s u f f i -c i e n t t o show t h e m a j o r f e a t u r e s o f t h e t r a n s i e n t s i g n a l . 4 . N o r m a l a c c u r a c y s h o u l d be r e s t o r e d a s s o o n a s p o s s i b l e a f t e r a t r a n s i e n t . . 2 . 5 " G e n e r a l l y C o r r e l a t e d " S i g n a l s i n D e l t a M o d u l a t i o n T h i s p r o j e c t i n v e s t i g a t e s t h e p r o b l e m o f p r o v i d i n g e f f i c i e n t t r a n s m i s s i o n o f " g e n e r a l l y c o r r e l a t e d " s i g n a l s . B e c a u s e o f t h e d i f f i c u l t y o f e v o l v i n g p r a c t i c a l s y s t e m d e s i g n s f r o m a g e n e r a l t h e o r e t i c a l e x a m i n a t i o n , a m e t h o d o f i m p r o v i n g t h e e f f i c i e n c y o f one p a r t i c u l a r s y s t e m was d e v i s e d . The s y s t e m s e l e c t e d was d e l t a m o d u l a t i o n . The d e v e l o p m e n t o f t h i s m e t h o d , a s w e l l a s p r o v i d -i n g a more e f f i c i e n t d e l t a m o d u l a t i o n saheme f o r s i g n a l s o f t h i s t y p e , p e r m i t t e d some g e n e r a l c o n c l u s i o n s t o be made r e g a r d i n g e f f i c i e n c y i m p r o v e m e n t s i n o t h e r s y s t e m s f o r s i g n a l 8 w i t h o c c a s i o n a l t r a n s i e n t s . The f o l l o w i n g s e c t i o n s c o n t a i n a s h o r t d e s c r i p t i o n o f t h e s t a n d a r d d e l t a m o d u l a t i o n s y s t e m a n d i t ' s l i m i t a t i o n s . T h i s i s f o l l o w e d b y a d e t a i l e d e x a m i n a t i o n o f m e t h o d s o f i n -c r e a s i n g i t s e f f i c i e n c y f o r t r a n s m i s s i o n o f " g e n e r a l l y c o r r e -l a t e d " s i g n a l s . 9 3 . D E L T A MODULATION 3 . 1 D e s c r i p t i o n D e l t a m o d u l a t i o n (DM) i s a m e t h o d o f i n f o r m a t i o n t r a n s m i s s i o n e m p l o y i n g b i n a r y p u l s e s . I t d i f f e r s f r o m t h e w e l l k n o w n p u l s e c o d e m o d u l a t i o n s y s t e m i n t h a t a o n e - u n i t c o d e i s u s e d i n s t e a d o f a m u l t i - u n i t c o d e g r o u p . T h i s means t h a t t h e t r a n s m i t t e d p u l s e r a t e e q u a l s t h e s a m p l i n g r a t e . 4 A s i m p l e DM s y s t e m i s s h o w n i n F i g u r e 3 . 1 . a n d o p e r a t e s a s f o l l o w s . The p u l s e g e n e r a t o r i n t h e c o d e r p r o d u c e s a p o s i -t i v e p u l s e i f t h e e r r o r s i g n a l , v ( t ) , i s p o s i t i v e , a n d a n e q u a l n e g a t i v e p u l s e >if v ( t ) i s n e g a t i v e . The i n t e g r a t e d v a l u e o f t h e s e p u l s e s , V Q ( t ) , i s c o m p a r e d w i t h t h e i n p u t s i g n a l , v ^ ( t ) , t o o b t a i n v g ( t ) . P u l s e s a r e p r o d u c e d i n s y n c h r o n i s m w i t h t h e c l o c k , w i t h one p o s i t i v e o r one n e g a t i v e p u l s e i n e v e r y " t i m e s l o t " . The i n t e g r a t o r n e t w o r k i n t h e d e c o d e r i s i d e n t i c a l t o t h e i n t e g r a t o r n e t w o r k i n t h e f e e d b a c k l o o p o f t h e c o d e r . T h u s t h e d e c o d e r o u t p u t s i g n a l i s a l s o v Q ( t ) , a n d i s a s t e p w i s e r e p r o d u c t i o n o f t h e i n p u t s i g n a l . A n e x a m i n a t i o n o f t y p i c a l w a v e f o r m s ( F i g u r e 3 . 2 ) s h o w s t h a t t h e i n p u t s i g n a l h a s b e e n q u a n t i z e d i n b o t h t i m e a n d a m p l i t u d e . The i n t e g r a t i n g n e t w o r k i n t h e d e c o d e r i s U s u a l l y f o l l o w -e d b y a l o w - p a s s f i l t e r t o r e m o v e h i g h - f r e q u e n c y c o m p o n e n t s o f v ( t ) i n t r o d u c e d b y t h e q u a n t i z i n g p r o c e s s . c o d e r d e c o d e r c l o c k i n p u t s i g n a l + <g>. p u l s e g e n e r a t o r v ( t ) P v o ( t ) i n t e g r a t o r i n t e g r a t o r o u t p u t s i g n a l F i g u r e 3.1 S i m p l e D e l t a M o d u l a t i o n S y s t e m o 11 F i g u r e 3 . 2 T y p i c a l W a v e f o r m s - S i m p l e DM S y s t e m 3 . 2 O v e r l o a d C h a r a c t e r i s t i c s O v e r l o a d i n g o c c u r s i n d e l t a m o d u l a t i o n w h e n t h e r a t e o f c h a n g e o f i n p u t s i g n a l w i t h r e s p e c t t o t i m e e x c e e d s a c e r t a i n l i m i t . When t h i s h a p p e n s t h e i n t e g r a t o r v o l t a g e i s n o t a b l e t o f o l l o w , c a u s i n g t h e o u t p u t t o be d i s t o r t e d . The maximum s l o p e ( s l o p e - l i m i t ) i s g i v e n b y AV a _ AT w h e r e AV i s t h e h e i g h t o f e a c h s t e p , AT = j i s t h e s a m p l i n g i n t e r v a l , s f i s t h e p u l s e r a t e , s 3 . 3 . Q u a n t i z i n g N o i s e I n a l l b i n a r y p u l s e s y s t e m s , t h e s i g n a l i s d i s t o r t e d b y b e i n g a l l o w e d t o v a r y o n l y i n d i s c r e t e s t e p s . 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 . A s p e c i a l c a s e o f q u a n t i z i n g n o i s e i s c a l l e d t h e t h r e s h o l d e f f e c t . T h i s o c c u r s w h e n t h e a m p l i t u d e o f t h e i n p u t s i g n a l i s l e s s t h a n o n e - h a l f s t e p . The c o d e r t h e n t r a n s m i t s a r e g u l a r p u l s e p a t t e r n (+ - + - 4- - ) a n d no o u t -p u t i s o b t a i n e d f r o m t h e d e c o d e r . 3 . 4 I n t e g r a t o r W a v e f o r m I n t h e DM s y s t e m o f F i g u r e 3 . 1 t h e i n t e g r a t o r e m p l o y -e d may be a l o n g - t i m e - c o n s t a n t RC c i r c u i t w h i c h g i v e s a c l o s e a p p r o x i m a t i o n o f a s t e p o u t p u t f o r a n i n p u t p u l s e o f l a r g e a m p l i t u d e a n d s h o r t d u r a t i o n . T h u s p o s i t i v e s t e p s a r e p r o -d u c e d b y a p o s i t i v e p u l s e a n d n e g a t i v e s t e p s b y a n e g a t i v e p u l s e . I n m o s t c o m m u n i c a t i o n c h a n n e l s , h o w e v e r , i t i s s i m p l e r t o t r a n s m i t b i n a r y p u l s e s a s e i t h e r p u l s e o£ n o -p u l s e c o r r e s p o n d i n g t o a 1 o r a 0 , i n s t e a d o f a p o s i t i v e p u l s e a n d a n e g a t i v e p u l s e . I n t h e c o d e r a n d d e c o d e r t h e 13 1 a n d 0 p u l s e s a r e t h e n c o n v e r t e d i n t o s h o r t p o s i t i v e a n d n e g a t i v e p u l s e s t o g i v e a s t e p w a v e f o r m a t t h e i n t e g r a t o r . A l t e r n a t i v e l y j a p o s i t i v e s t e p a t t h e i n t e g r a t o r c a n be p r o d u c e d b y u s i n g a d o u b l e - s i z e p u l s e f o l l o w e d b y a l i n e a r o c c. d e c a y a n d a n e g a t i v e s t e p b y u ^ i n g t h e d e c a y o n l y ' ' • Y e t a n o t h e r p o s s i b i l i t y i s t o u s e p o s i t i v e a n d n e g a t i v e p u l s e s w h o s e d u r a t i o n i s e q u a l t o t h e s a m p l i n g i n t e r v a l j w h i c h r e s u l t s i n a r a m p w a v e f o r m a t t h e i n t e -g r a t o r . T h i s l a t t e r m e t h o d was u s e d i n t h e s y s t e m c o n -s t r u c t e d , 3 . 5 T r a n s m i s s i o n o f -DC; S i g n a l s I n many a p p l i c a t i o n s t h e t r a n s m i s s i o n o f d c i n p u t s i g n a l s i s a r e q u i r e m e n t , a n d s o a b r i e f r e v i e w o f t h e m e t h o d o f d c t r a n s m i s s i o n i n DM f o l l o w s . D e l t a m o d u l a t i o n i n i t s s i m p l e s t f o r m c a n t r a n s m i t d c l e v e l s b u t t h e t r a n s m i t t e d p u l s e p a t t e r n i s t h e same f o r a n y l e v e l , t h a t i s , a p a t t e r n c o n s i s t i n g o f a l t e r n a t e : 1 a n d 0 p u l s e s . A c h a n g e i n d c l e v e l i s t r a n s m i t t e d b y a l t e r i n g t h i s r a t i o o f 1 a n d 0 p u l s e s , b u t w h e n t h e new d c l e v e l i s r e a c h e d , t h e p a t t e r n a g a i n b e c o m e s r e g u l a r . A d i f f i c u l t y i s e n c o u n t e r e d i n t h i s m e t h o d h o w e v e r , s i n c e , i n t h e c a s e o f a n e r r o r i n t r a n s m i s s i o n t h e e f f e c t o f t h e e r r o r i s p r e s e n t i n t h e o u t p u t i n d e f i n i t e l y , t h a t i s , e r r o r s a r e c u m u l a t i v e • 14 A m e t h o d o f o v e r c o m i n g t h i s d i f f i c u l t y , c a l l e d " e x p o n e n t i a l d e l t a m o d u l a t i o n , " was i n v e s t i g a t e d b y 6 J . H o l z e r . I t c o n s i s t s o f t h e u s e o f a f i n i t e - t i m e -c o n s t a n t i n t e g r a t o r i n t h e c o d £ r f e e d b a c k l o o p a n d i n t h e d e c o d e r , i n s t e a d o f a p e r f e c t ( i n f i n i t e - t i m e - c o n s t a n t ) i n t e g r a t o r . The r e s u l t i s a d i f f e r e n t p u l s e p a t t e r n f o r e v e r y s e p a r a t e d c l e v e l o f i n p u t s i g n a l a n d t h u s a n e r r o r i n t r a n s m i s s i o n w i l l h a v e a m e a s u r a b l e e f f e c t o n t h e d e -c o d e r o u t p u t f o r a f i n i t e t i m e o n l y . The u s e o f a f i n i t e - t i m e - c o n s t a n t i n t e g r a t o r , a s w e l l a s b e i n g more p r a c t i c a l , p l a c e s a d e f i n i t e l i m i t o n t h e a m p l i t u d e o f i n p u t s i g n a l t h a t c a n be h a n d l e d . I n a t y p i c a l a r r a n g e m e n t w i t h t h e c a p a c i t o r - s h u n t i n g r e s i s t o r c o n n e c t e d t o t h e m i d - p o i n t o f t h e i n t e g r a t o r v o l t a g e r a n g e , t h i s l i m i t i s r e a c h e d w h e n a s i g n a l o f s u c h l e v e l a s t o c a u s e t r a n s m i s s i o n o f a l l p u l s e s o r a l l s p a c e s i s a p p l i e d t o t h e i n p u t . F u r t h e r m o r e , t h e s l o p e l i m i t o f a n e x p o n e n t i a l DM s y s t e m now d e p e n d s o n t h e d c v o l t a g e l e v e l a t t h e i n t e g r a t o r a n d o n t h e d i r e c t i o n o f c h a n g e o f t h e i n p u t s i g n a l . B e c a u s e o f t h i s i t i s d e s i r a b l e t o l i m i t t h e i n t e g r a t o r a m p l i t u d e r a n g e o v e r w h i c h t h e s y s t e m n o r -m a l l y o p e r a t e s so t h a t t h e s l o p e l i m i t r e m a i n s f i n i t e . F o r e x a m p l e , i f t h e r a t i o o f s l o p e l i m i t a t z e r o l e v e l t o t h a t a t maximum a m p l i t u d e , V^. , i s t a k e n a s 2 , t h e n t h e c o r r e s p o n d i n g p u l s e p a t t e r n f o r a dc s i g n a l o f maximum a m p l i t u d e i s 1 1 1 0 1 1 1 0 1 1 1 0 P o r , i f t h e p a t t e r n b e c o m e s 1 1 1 1 1 1 1 1 1 1 1 1 t h e n , a t t h e i n t e g r a t o r , a n e g a t i v e s t e p i s r e p l a c e x i b y a p o s i t i v e s t e p a t e v e r y f o u r t h p u l s e , a n d t h e v o l t a g e , w i l l i n c r e a s e a t a r a t e o f 2 s t e p s i n 4 p u l s e s , w h i c h i s a ' , « a s l o p e o f 2* The i n t e g r a t o r t i m e c o n s t a n t , A , c o r r e s p o n d i n g t o t h i s c o n d i t i o n i s f o u n d a s f o l l o w s : V S AV i _ —IS. _ 2 R R R d v = 0 a t * w h e r e C i s t h e i n t e g r a t o r c a p a c i t a n c e , R i s t h e i n t e g r a t o r s h u n t i n g r e s i s t a n c e , n i s t h e t o t a l n u m b e r o f s t e p s i n t h e i n t e g r a t o r a m p l i t u d e r a n g e i g i s t h e c u r r e n t i n R H e n c e dv o _ nAV _ nAV d t ~ 2RC - 2X 16 B u t f o r a r a t i o o f 2 : 1 i n s l o p e m a 2 a nAV 2 2 1 X nAV a a n d s i n c e a AV AT X nAT The s t a n d a r d DM s y s t e m , b e c a u s e o f i t s i n h e r e n t s l o p e l i m i t a t i o n i s u n s u i t a b l e f o r t r a n s m i s s i o n fif s i g n a l s w i t h o c c a s i o n a l t r a n s i e n t s . I n t h e f o l l o w i n g s e c t i o n s a m e t h o d o f o v e r c o m i n g t h i s l i m i t a t i o n i s d e v e l o p e d . T h i s m e t h o d , b e c a u s e i t u s e s a c h a n g e i n s l o p e , h a s b e e n c a l l e d " a c c e l e r a t e d d e l t a m o d u l a t i o n . " m e t h o d t h e u s e o f a p e r f e c t i n t e g r a t o r i n t h e c o d e r f e e d -b a c k l o o p i s a s s u m e d . The e f f e c t Of u s i n g a f i n i t e -t i m e - c o n s t a n t RC c i r c u i t a s i n t e g r a t o r t o a l l o w t r a n s -m i s s i o n o f dc s i g n a l s i s t h e n c o n s i d e r e d . I n d e v e l o p i n g t h e f u n d a m e n t a l a s p e c t s o f t h i s 17 4 . A C C E L E R A T E D D E L T A MODULATION 4 . 1 B a s i c R e q u i r e m e n t s A s i n d i c a t e d i n S e c t i o n 3 . 2 t h e maximum r a t e o f c h a n g e o f a DM s y s t e m i s d e p e n d e n t o n t h e s i z e o f e a c h s t e p a n d o n t h e p u l s e r a t e . One w a y o f i m p r o v i n g t h e r e s p o n s e i s t o i n c r e a s e t h e p u l s e r a t e , b u t t h i s o f c o u r s e , means a g r e a t e r t r a n s m i s s i o n b a n d w i d t h i s r e q u i r e d , , A n o t h e r w a y i s t o i n c r e a s e t h e s i z e o f e a c h s t e p , t h a t i s , u s e c o a r s e r q u a n t i z a t i o n , b u t t h i s h a s t h e d i s a d v a n t a g e o f i n c r e a s i n g t h e q u a n t i z i n g n o i s e f o r a l l i n p u t s i g n a l s . I t s h o u l d be p o s s i b l e , h o w e v e r , t o u s e a l a r g e r s t e p s i z e o n l y w h e n s u d d e n l a r g e c h a n g e s o c c u r i n t h e 6 i n p u t s i g n a l a n d t h e n o r m a l s t e p s i z e a t a l l o t h e r t i m e s » B y t h i s means t h e o r i g i n a l a c c u r a c y w o u l d be r e t a i n e d f o r s m a l l c h a n g e s i n i n p u t s i g n a l b u t a c l o s e r r e p r e s e n t a t i o n o f t r a n s i e n t s w o u l d be o b t a i n e d . B e c a u s e o f t h e i n c r e a s -e d s t e p s i z e i t i s l i k e l y t h a t a n o v e r s h o o t w i l l o c c u r . T h e t i m e r e q u i r e d f o r t h e a c c u r a c y t o b e r e s t o r e d a f t e r a t r a n s i e n t w i l l d e p e n d o n t h e a m o u n t o f t h i s o v e r s h o o t . A b a s i c s y s t e m of a c c e l e r a t e d d e l t a m o d u l a t i o n (ADM) f o r o b t a i n i n g t h e r e q u i r e d c h a r a c t e r i s t i c s i s s h o w n i n F i g u r e 4 . 1 * c o d e r c l o c k d e c o d e r i n p u t s i g n a l v . ( t ) % ( t ) p u l se g e n e r a t o r T ( t ) i n t e g r a t o r T , ( t ) s t e p s i z e c o n t r o l i n t e g r a t o r t * ( t ) s t e p s i z e c o n t r o l o u t p u t s i g n a l v 0 ( t ) F i g u r e 4»1 A c c e l e r a t e d D e l t a M o d u l a t i o n S y s t e m 19 4 . 2 C o d i n g f o r S t e p S i z e I n c r e a s e The d e c i s i o n t o c h a n g e s t e p s i z e m u s t be d e r i v e d f r o m e i t h e r t h e i n t e g r a t o r v o l t a g e , v ( t ) o r , a s s h o w n i n F i g u r e 4*1 f r o m t h e t r a n s m i t t e d p u l s e s , v ( t ) . T h a t i s , a s s u m i n g no o t h e r c o m m u n i c a t i o n p a t h b e t w e e n t r a n s m i t t e r a n d r e c e i v e r , t h i s i n f o r m a t i o n m u s t be c o n -t a i n e d w i t h i n t h e t r a n s m i t t e d p u l s e t r a i n a n d d e r i v e d f r o m i t b y t h e r e c e i v e r . S i n c e i n DM o n l y t w o d i f f e r e n t s i g n a l s a r e t r a n s -m i t t e d , a 1 o r a 0, t h e i n f o r m a t i o n r e g a r d i n g s t e p s i z e m u s t be a c e r t a i n s e q u e n c e o f p u l s e s w h i c h w i l l be c a l l e d t h e " a c c e l e r a t i o n s i g n a l . " The p u l s e s c o n s t i t u t i n g t h i s a c c e l e r a t i o n s i g n a l w i l l , h o w e v e r , s t i l l r e t a i n t h e i r DM s i g n i f i c a n c e , a 1 p r o d u c i n g a p o s i t i v e s t e p a n d a 0 p r o -d u c i n g a n e g a t i v e s t e p . I n d e l t a m o d u l a t i o n w h e n s l o p e o v e r l o a d o c c u r s , t h e c o d e r t r a n s m i t s e i t h e r a l l 1 ' s o r a l l O ' s . T h e r e f o r e ^ t h e a c c e l e r a t i o n s i g n a l w i l l be made u p o f a c e r t a i n n u m b e r o f p u l s e s , a l l o f t h e same t y p e . I f a l a r g e n u m b e r o f p u l s e s a r e u s e d a s t h e a c c e l e r a t i n g s i g n a l , t h e r e w i l l be a l o n g d e l a y b e f o r e t h e o u t p u t o v e r t a k e s t h e i n p u t . On t h e o t h e r h a n d , i f t h e a c c e l e r a t i o n t a k e s p l a c e a f t e r o n l y a f e w s t e p s i n t h e same d i r e c t i o n , q u a n t i z i n g n o i s e w i l l be i n c r e a s e d f o r r e l a t i v e l y s m a l l r a t e s o f c h a n g e o f i n p u t s i g n a l * 2 ° ( a ) s l o p e = a 1 1 1 1 1 l 1 ( b ) s l o p e = | 1 1 1 0 1 1 1 0 1 1 1 ( c ) s l o p e = | 1 1 0 1 1 0 l 1 0 1 1 0 1 1 0 1 1 F i g u r e 4 . 2 S l o p e o f v ( t ) f o r V a r i o u s P u l s e P a t t e r n s T h i s i s i l l u s t r a t e d i n F i g u r e 4 . 2 w h e r e t h e o u t p u t s i g n a l s l o p e c o r r e s p o n d i n g t o v a r i o u s p u l s e p a t t e r n s i s s h o w n . T h e s e s l o p e s a r e e x p r e s s e d i n t e r m s o f a , t h e maximum s l o p e i n a n o r m a l DM s y s t e m . F r o m p a t t e r n 4 . 2 ( c ) i t c a n be s e e n t h a t i f t h e d e c i s i o n t o a c c e l e r a t e w e r e b a s e d o n t w o s u c c e e d i n g p u l s e s b e i n g t h e s a m e , a c c e l e r a t i o n w o u l d o c c u r f o r a n y c h a n g e i n i n p u t s i g n a l ( o f s u f f i c i e n t d u r a t i o n ) w i t h a s l o p e e x c e e d i n g —^ . A s a c o n s e q u e n c e t h e q u a n t i z i n g n o i s e w o u l d i n c r e a s e f o r i n p u t s i g n a l s w i t h s l o p e s b e t w e e n a a n d a . 3 I f , h o w e v e r , i n s t e a d o f t w o s u c c e s s i v e p u l s e s , t h r e e w e r e c h o s e n , a c c e l e r a t i o n w o u l d o c c u r f o r a n y i n p u t s i g n a l h a v i n g s l o p e s e x c e e d i n g ^ ( c u r v e ( b ) , F i g u r e 4 , 2 ) . Q u a n t i z i n g n o i s e i n t h i s c a s e w o u l d be i n c r e a s e d f o r i n -p u t s i g n a l s w i t h s l o p e s b e t w e e n ^ a n d a . A s t h e b e s t c o m p r o m i s e b e t w e e n d e l a y a n d q u a n t i z -i n g n o i s e , t h i s l a t t e r s e q u e n c e was c h o s e n a s t h e a c c e l e r a t i n g s i g n a l . T h a t i s , w h e n e v e r t h r e e p u l s e s o f t h e same t y p o c c u r i n s e q u e n c e , t h e f o u r t h s t e p w i l l be l a r g e r i f t h e f o u r t h p u l s e i s a l s o o f t h e same t y p e . U n l e s s v Q ( t ) h a s r e a c h e d v ^ ( t ) a f t e r t h e f o u r t h p u l s e , t h e f i f t h a n d s u c c e e d i n g s t e p s s h o u l d a l s o be l a r g e r t h a n n o r m a l u n t i l a p u l s e o f t h e o p p o s i t e t y p e a p p e a r s w h e n t h e s t e p s w i l l , i n some f a s h i o n , r e t u r n t o n o r m a l s i z e » The t i m e d e l a y o c c u r r i n g a f t e r a s u d d e n j u m p o f v ^ ( t ) b e f o r e t h e f i r s t s t e p o f i n c r e a s e d s i z e , w i l l d e p e n d o n t h e p a r t i c u l a r c o n d i t i o n o f t h e c o d e r a t t h e t i m e o f t h e j u m p . I f t h e j u m p o c c u r s a l m o s t AT s e c o n d s a f t e r a s t e p i n t h e same d i r e c t i o n , t h e d e l a y w i l l be 2AT s e c o n d s . I f t h e j u m p o c c u r s j u s t a f t e r a s t e p i n t h e o p p o s i t e d i r e c t i o n t h e d e l a y w i l l be 4AT s e c o n d s . D i s c u s s i o n s i n t h e f o l l o w i n g s e c t i o n s a r e b a s e d o n a mean d e l a y o f 3AT s e c o n d s . 22 4 . 3 R a t e o f S t e p S i z e I n c r e a s e H a v i n g now e s t a b l i s h e d a m e t h o d o f i n i t i a t i n g t h e s t e p s i z e i n c r e a s e , t h e n e x t s t e p i s t o i n v e s t i g a t e t h e v a r -i o u s p o s s i b l e r u l e s g o v e r n i n g t h e a m o u n t o f i n c r e a s e . I t i s now n e c e s s a r y t o c o m p r o m i s e b e t w e e n ( l ) , a s m a l l i n c r e a s e i n s t e p s i z e a n d c o n s e q u e n t l y f u r t h e r d e l a y i n r e s p o n s e i f t h e c h a n g e i n v ^ ( t ) i s l a r g e , a n d ( 2 ) , a l a r g e i n c r e a s e i n s t e p s i z e a n d h e n c e p o t e n t i a l l y g r e a t e r q u a n t i z i n g n o i s e . B y u s i n g a v a r i a b l e s i z e i n c r e a s e , h o w e v e r , i t i s p o s s i b l e t o m i n i m i z e b o t h d i s a d v a n t a g e s . T h u s f o r t h e f o u r t h p u l s e a s m a l l i n c r e a s e i n s i z e w o u l d be m a d e , f o r t h e f i f t h a l a r g e r i n c r e a s e , a n d so o n . I n t h i s w a y t h e d e c r e a s e i n a c c u r a c y i s a f u n c t i o n o f t h e c h a n g e i n v ^ ( t ) . T h i s v a r i a b l e i n c r e a s e c a n be made i n a n u m b e r o f w a y s , two o f w h i c h a r e s h o w n i n F i g u r e 4 . 3 , w h e r e s t e p s i z e a n d r e s u l t i n g o u t p u t v o l t a g e a r e p l o t t e d a g a i n s t t i m e f o r a s t e p i n p u t o c c u r r i n g a t t = 0 . F o r n o r m a l DM (no a c c e l e r a t i o n ) t h e s t e p s i z e i s c o n s t a n t , a n d V Q ( t ) i n c r e a s e s w i t h s l o p e a . I n F i g u r e 4 . 3 ( b ) t h e s i z e o f s t e p i n c r e a s e s a s a l i n e a r f u n c t i o n o f t i m e a f t e r t h e a c c e l e r a t i o n s i g n a l . H e r e , t h e c o n d i t i o n t h a t t h e s t e p s i z e i n c r e a s e be s m a l l a t f i r s t i s m e t , b u t t h e r e w o u l d s t i l l be c o n s i d e r a b l e d e l a y i n m a t c h i n g v ( t ) t o v . ( t ) i f t h e j u m p i n v . ( t ) 0 1 j 1 w e r e l a r g e . 23 s t e p s i z e v I I 1 I I 1 II s t e p s i z e ( a ) n o r m a l DM s t e p s i z e ( b ) l i n e a r i n c r e a s e I 0 t ( c ) e x p o n e n t i a l i n c r e a s e F i g u r e 4 . 3 V a r i o u s A c c e l e r a t i o n M e t h o d s 24 F i g u r e 4 . 3 ( c ) shows a m e t h o d w h e r e b y t h e s t e p s i z e i n c r e a s e s a t a n e x p o n e n t i a l r a t e , d o u b l i n g f o r e a c h s u c c e s s i v e p u l s e a f t e r t h e a c c e l e r a t i n g s i g n a l . T h e r e i s no f i r m c r i t e r i o n w h i c h p e r m i t s t h e s e l e c -t i o n o f one m e t h o d o f s t e p s i z e i n c r e a s e o v e r a n o t h e r i n a g e n e r a l s y s t e m . I n a p a r t i c u l a r a p p l i c a t i o n t h e s p e e d o f r e s p o n s e o f i n p u t a n d o u t p u t d e v i c e s c o u l d be u s e d as t h e b a s i s f o r t h e c h o i c e . F o r t h e p r e s e n t s t u d y t h e v e r y f a s t a c t i o n o f t h e e x p o n e n t i a l i n c r e a s e i n s t e p s i z e o u t w e i g h s t h e d i s a d v a n t a g e s o f t h e r a t h e r l a r g e o v e r s h o o t . F o r t h i s r e a s o n t h e e x p o n e n t i a l i n c r e a s e w i l l be u s e d a s i l l u s t r a t i o n i n t h e f o l l o w i n g s e c t i o n s . 4 . 4 Maximum S t e p S i z e The maximum d e s i r a b l e s t e p s i z e i s r e l a t e d t o t h e n u m b e r o f s t e p s c o v e r i n g t h e a m p l i t u d e r a n g e o f t h e s y s t e m . F o r e x a m p l e , i n a n e x p o n e n t i a l l y a c c e l e r a t e d s y s t e m w h e r e t h e r a n g e o f a m p l i t u d e i s c o v e r e d i n 1 0 0 n o r m a l s i z e s t e p s , t h e maximum s i z e s t e p t h a t c o u l d be u s e d i s 6 4 A V . T h a t i s , i f a j u m p i n i n p u t f r o m m i n i m u m t o maximum a m p l i t u d e o c c u r r e d , t h e s t e p s w o u l d h a v e t h e f o l l o w i n g s i z e s i n t e r m s o f AV 1 , 1 , 1 , 2 , 4 , 8 , 1 6 , 3 2 , 64 g i v i n g a t o t a l c h a n g e i n o u t p u t o f 129AV o f w h i c h 29AV i s o v e r s h o o t . 25 The a m o u n t o f o v e r s h o o t c o u l d b e r e d u c e d a p p r e c i a b l y t h o u g h , f o r c h a n g e s i n i n p u t r a n g i n g f r o m 66AV t o 97AV b y m a k i n g t h e maximum s t e p s i z e 3 2 A V . T h i s w o u l d mean o f c o u r s e t h a t f o r a f u l l s c a l e j u m p , one more p u l s e p e r i o d w o u l d be r e q u i r e d t h a n p r e v i o u s l y . The s t e p s i z e s w o u l d b e , a g a i n i n t e r m s o f AV 1 , 1 , 1 , 2 , 4 , 8 , 1 6 , 3 2 , 3 2 , 32 The l i k e l i h o o d o f j u m p s i n i n p u t o f 97AV t o 1 0 0 A V i n a n o p e r a t i n g s y s t e m i s q u i t e r e m o t e a n d s o , f o r t h e 1 0 0 s t e p s y s t e m , a maximum s t e p s i z e o f 32AV i s b e t t e r t h a n 6 4 A V . S i n c e a maximum o f 9 s t e p s i s r e q u i r e d a f t e r a j u m p i n i n p u t t h e t i m e f o r a n y s i n g l e j u m p w o u l d n e v e r e x c e e d 9 A T . T h i s f i g u r e i n c l u d e s 3AT f o r t h e a c c e l e r a t i o n s i g n a l a n d 6AT f o r t h e a c c e l e r a t i n g t i m e . B y s i m i l a r r e a s o n i n g i t c a n be s h o w n t h a t t h e maximum s t e p s i z e f o r a l i n e a r l y - a c c e l e r a t e d s y s t e m s h o u l d n o t e x c e e d 13AV a n d t h a t t h e t i m e r e q u i r e d f o r a f u l l - s c a l e j u m p i s 1 5 A T . 4 . 5 C o d i n g f o r S t e p S i z e De/crease The s e q u e n c e o f p u l s e s u s e d t o i n d i c a t e t h a t v ^ ( t ) h a s b e e n e x c e e d e d c a n be e x t r e m e l y s i m p l e . I n f a c t , t h e f i r s t p u l s e o f o p p o s i t e s e n s e w i l l i n d i c a t e t h a t t h e i n t e -g r a t o r v o l t a g e h a s e x c e e d e d t h e i n p u t v o l t a g e a n d t h a t t h e n e x t s t e p , w h i c h w i l l be i n t h e o p p o s i t e d i r e c t i o n , s h o u l d be r e d u c e d i n s i z e . The v a r i o u s r a t e s a t w h i c h t h e s i z e o f t h e s t e p c a n be r e d u c e d a r e a s n u m e r o u s a s f o r a c c e l e r a t i o n . The r e q u i r e m e n t i s , o f c o u r s e , t h a t t h e c o r r e c t v a l u e o f o u t -p u t s i g n a l be a p p r o a c h e d a s q u i c k l y a s p o s s i b l e , b u t b e -c a u s e o f t h e l a r g e q u a n t i z i n g i n t e r v a l c o r r e s p o n d i n g t o t h e i n c r e a s e d s t e p s i z e i t i s n e c e s s a r y t o h u n t f o r t h i s c o r r e c t v a l u e . The p r o c e d u r e i s c o m p l i c a t e d b y t h e a d m i s s i o n o f o t h e r s u d d e n c h a n g e s i n v ^ ( t ) o c c u r r i n g a s h o r t t i m e a f t e r t h e i n i t i a l j u m p . I n d e e d t h e p o s s i b i l i t y o f s u c h b e h a v i o u r i s t o be e x p e c t e d i n many t e l e m e t e r i n g a p p l i -c a t i o n s w h e r e a d i s t u r b a n c e may c o n t a i n many t r a n s i e n t s . T h u s i f a j u m p i n v . ( t ) i s f o l l o w e d a f e w p u l s e p e r i o d s l a t e r b y a n o t h e r j u m p i n e i t h e r t h e same o r o p p o s i t e d i r e c t i o n , t h e s y s t e m m u s t a c c e l e r a t e t o f o l l o w t h e s e c o n d j u m p w i t h a m i n i m u m d e l a y . To a c c o m p -l i s h t h i s t h e same a c c e l e r a t i n g s i g n a l c a n be u s e d a s b e f o r e , t h a t i s , t h r e e s t e p s o c c u r r i n g i n t h e same d i r e c -t i o n d u r i n g d e c e l e r a t i o n w i l l i n d i c a t e t h a t v ^ ( t ) h a s a g a i n c h a n g e d a n d t h a t s t e p s i z e s h o u l d a g a i n be i n c r e a s e 4 . 6 H a t e o f S t e p S i z e D e c r e a s e One e x t r e m e o f s t e p s i z e r e d u c t i o n w o u l d be t o r e v e r t i m m e d i a t e l y t o a n o r m a l i n t e r p r e t a t i o n o f t h e c o d e w h i c h w o u l d mean a s m a l l r e c o v e r y t i m e i f t h e o v e r s h o o t were smal l , but a large recovery time and quite poss ibly i n s t a b i l i t y i f the overshoot were large . The other extreme would be to decrease step size by a small amount each per iod , but th is would again re su l t i n a large recovery time. The optimum rate , assuming equal p r o b a b i l i t y for the correct value to l i e within any quantum AV i n the f i n a l step before dece lerat ion , i s an exponential decrease i n which the size of step i s halved for each succeeding p u l s e . . Decelerat ion at th i s rate means that for a max-imum step size of 32AV the integrator voltage arr ives to within ^AV of the correct value of v Q ( t ) af ter 5 steps unless 4 of these steps are successively i n the same d i r e c -t i o n , i n which case i t w i l l take 6 steps. This gives a stable system since any o s c i l l a t i o n s about the correct value of v (t) are quickly damped out. Figure 4.4 shows some examples of the response of the ADM system to a step-input s i g n a l . These examples i l l u s t r a t e the three-step acce lerat ion s ignal and exponential step size increase and decrease c h a r a c t e r i s t i c s . 4.7 Transmission of DC Signals i n ADM Use of a f in i te - t ime-constant integrator as described i n Section 3.5 w i l l permit the system to t rans -mit dc s igna l s . For such a system the slope l i m i t depends upon the dc l e v e l , and hence there i s no unique slope be-yond which acce lerat ion i s des i rab le . I t i s poss ib le , 28 v . ( t ) - | j = k R = -v Q ( t ) V Q ( t ) v o ( t ) (a) 54AV jump (b) 33AV jump (c) 64AV jump F i g u r e 4«4 T y p i c a l Response -ADM 29 however, to define two "acceleration l ines" , as shown i n Figure 4.5. Below the upper acce lerat ion l i n e , input signals with prolonged pos i t ive slopes w i l l not cause acce lerat ion , and above i t they w i l l cause acce lerat ion . In Figure 4.5(a) the DM slope l i m i t and ADM a c c e l -erat ion l i n e are plotted as functions of integrator voltage for an inf in i te - t ime-constant in tegrator . In th i s case the acce lerat ion l ine i s hor izonta l at ^ . For a f i n i t e -time^constant integrator using the same acce lerat ion s i g n a l , the acce lerat ion l i n e can be found by subtracting a 2 from the DM slope l i m i t for a p a r t i c u l a r integrator time constant. Figure 4,5 (b) shows the c h a r a c t e r i s t i c for an integrator with a time constant nAT. A time constant of nAT as derived i n Section 3.5, corresponds to the DM slope l i m i t at zero dc l eve l being twice the DM slope l i m i t at maximum dc l e v e l . As shown, the acce lerat ion l ine approaches zero as V i s reached. This also follows from an examination of the pulse pattern for a dc s ignal of V . For th is voltage, the code 1 1 1 0 1 1 1 0 i s continuously transmitted, and thus for any increase i n v . ( t ) when i t i s close to V an i n -J l m crease i n step size w i l l occur. If a l l dc leve ls are to be transmitted without acce lera t ion , then the integrator time const&nt , A, cannot be less than nAT. On the other hand, a value of A of more than nAT 30 coarse trans * f ine trans coarse trans ADM Coarse t r a n s no trans . f ine t rans -niss ion rans. DM -a ADM a 2 "0" - V m ADM _a 2 DM - a slope slope l i m i t acce lerat ion l ine m acce lerat ion l i n e . ^  sl_ope_ JL imit_ i n t e -grator voltage f ine trans . coarse trans * f ine trans• DM (a) I n f i n i t e Time Constant {X - oo ) no trans* slope ADM no trans DM (b) F i n i t e Time Constant (X = nAT) Figure 4*5 Integrator Charac ter i s t i c s 31 w o u l d mean t h a t dc a c c u r a c y w o u l d be more d i f f i c u l t t o m a i n -t a i n i n t h e c a s e o f b o t h e r r o r s i n t r a n s m i s s i o n a n d d r i f t s i n t h e c o d e r a n d d e c o d e r c i r c u i t r y . T h e r e f o r e a v a l u e o f A o f nAT was c h o s e n . 32 5. SYSTEM DESIGN 5.1 D e s i g n Method and Requirements I n d e c i d i n g the d e s i r a b l e c h a r a c t e r i s t i c s of the ADM system, i t s p r o p e r t i e s i n response to a l a r g e s t e p -v o l t a g e i n p u t were c o n s i d e r e d . I t was a l s o r e q u i r e d ( S e c t i o n 4.2) t h a t f o r i n p u t s i g n a l s w i t h s l o p e s l e s s than the a c c e l e r a t i o n l i n e , the system a c t i n an i d e n t i c a l man-ner to a normal d e l t a m o d u l a t i o n system. Between these two extremes l i e s an a r e a i n which the p r o p e r t i e s of ADM had to be i n v e s t i g a t e d . Of s p e c i a l i n t e r e s t i s the r e g i o n between the a c c e l e r a t i o n l i n e and the DM s l o p e l i m i t , where an i n -c r e a s e i n n o i s e was e x p e c ted i n ADM when compared w i t h d e l t a m o d u l a t i o n . A study was a l s o r e q u i r e d of the be-h a v i o u r of ADM i n response to many typ e s of i n p u t s i g n a l s , i n c l u d i n g those w i t h c o n t i n u a l l y changing s l o p e s such as s i n e waves, and s i g n a l s which might cause i n s t a b i l i t y or l a r g e amounts of d i s t o r t i o n such as p u l s e s of s h o r t d u r a t i o n . There are two methods of a s c e r t a i n i n g the p e r f o r m -ance of a complex m o d u l a t i o n p r o c e s s ; by i n s t r u m e n t a t i o n and by computer s i m u l a t i o n . I n the former method g r e a t care must be t a k e n l e s t s p u r i o u s n o i s e and d i s t o r t i o n i n the a p p a r a t u s l e a d to m i s i n t e r p r e t a t i o n of the r e s u l t s . However, i n s t r u m e n t a t i o n y i e l d s some v a l u a b l e knowledge of the problems i n v o l v e d i n c o n s t r u c t i o n of an o p e r a t i n g system and of the complexity of the apparatus r e q u i r e d . T h i s i s an important c o n s i d e r a t i o n i n the present case, since the c h i e f m erit of d e l t a modulation as compared to pulse code modulation i s s i m p l i c i t y i n coder and decoder c o n s t r u c t i o n . Computer s i m u l a t i o n has the advantage of y i e l d i n g the r e q u i r e d performance c h a r a c t e r i s t i c s f r e e from the v a g a r i e s of a p a r t i c u l a r i n s t r u m e n t a t i o n method and o f t e n more q u i c k l y , but f o r the above reasons i t was decided to use the i n s t r u m e n t a t i o n method. Equipment was c o n s t r u c t e d with a p a r t i c u l a r a p p l i c a t i o n i n mind; t h a t of a low-speed t e l e m e t e r i n g channel, with the f o l l o w i n g c h a r a c t e r i s t i c s : pulse r a t e : f = 2 0 pps s t o t a l amplitude range: 4 v o l t s amplitude q u a n t i z i n g accuracy: +0.5$ Prom these requirements the system parameters are found as f o l l o w s : t o t a l number of steps i n amplitude range: n = ^ " o T ^ 100 normal step s i z e : AV = 4 v o l t s = 40 mv 100 sampling i n t e r v a l : AT = — ^ 7 ; = 50 msec; ^ s 20 pps DM slope l i m i t at mid-range dc input s i g n a l : 40 mv „ „ , , / a =' en = ° « 8 v o l t s / s e c 50 msec ADM^  a c c e l e r a t i o n l i n e at mid-range dc input s i g n a l : ^ = 0.4 v o l t s / s e c i n t e g r a t o r t i m e c o n s t a n t : A = nAT = 100 x 50 msec = 5 s e c m a x . s t e p s i z e : 32AV = 32 x 40 mv = 1 .28 v o l t s 5.2 DM C o d e r I n o r d e r t o c o m p a r e t h e v a r i o u s . c h a r a c t e r i s t i c s o f DM a n d A D M , a c o d e r a n d a s e p a r a t e s t e p s i z e c o n t r o l u n i t w e r e b u i l t . B y d i s a b l i n g t h e s t e p s i z e c o n t r o l u n i t t h e e q u i p m e n t c o u l d be o p e r a t e d a s a n o r m a l DM s y s t e m . S i n c e t h e f e e d b a c k v o l t a g e , - V Q ( t ) i s t h e same a s t h e d e c o d e r o u t p u t v o l t a g e i t was n o t n e c e s s a r y t o c o n s t r u c t a d e c o d e r f o r t e s t s o f s y s t e m r e s p o n s e . A b l o c k d i a g r a m o f t h e c o d e r i s s h o w n i n F i g u r e 5.1 a l o n g w i t h t h e w a v e f o r m s a t v a r i o u s p o i n t s i n t h e c i r c u i t c o r r e s p o n d i n g t o a m i d - r a n g e dc i n p u t s i g n a l . The o p e r a t i o n i s q u i t e s t r a i g h t f o r w a r d , h o w -e v e r a f e w e x p l a n a t o r y n o t e s a r e g i v e n b e l o w . A c o m -p l e t e c i r c u i t d i a g r a m a n d a d e t a i l e d d e s c r i p t i o n o f t h e i m p o r t a n t p a r t s o f t h e c i r c u i t a r e g i v e n i n t h e A p p e n d i x . R e f e r r i n g t o F i g u r e 5.1 a n i n p u t s i g n a l , v ^ ( t ) , i s a d d e d t o t h e f e e d b a c k v o l t a g e , - V Q ( t ) + S i n c e t h e l a t t e r i s a n i n v e r t e d a n d q u a n t i z e d r e p r o d u c t i o n o f t h e i n p u t s i g n a l t h e sum o f t h e two v o l t a g e s t e n d s t o be a c o n s t a n t v a l u e . A d e v i a t i o n f r o m t h i s c o n s t a n t v a l u e v ± ( t ) i n p u t s i g n a l - v ( t ) adder c l o c k JlfLAJ" JLUJL d i f f e r e r i -t i a t o r l a m p l i f i e r / c l i p p e r i n t e -g r a t o r A = RC i ( t ) gate binary" ( S c h m i t t c u r r e n t g e n e r a t o r ITU V ( t ) p output to decoder x ( t ) i_n_r v ( t ) [" s t e p s i z e | '— § 1 c o n t r o l c c t . I Note: Waveforms shown c o r r e s p o n d to mid-range dc i n p u t s i g n a l . F i g u r e 5.1 D e l t a M o d u l a t i o n Coder B l o c k Diagram,, u> : _ _ _e ^ 36 y i e l d s an e r r o r s i g n a l which i s a m p l i f i e d and c l i p p e d and t h e n sampled by the gate a t r e g u l a r i n t e r v a l s . These s h o r t samples s w i t c h the b i n a r y t o s t a t e 2 i f they are above V a or to s t a t e 1 i f t h e y are below . The coder output p u l s e s from the AND c i r c u i t are produced by c o i n c i d e n c e of the c l o c k and b i n a r y s i g n a l s . Thus no p u l s e s are t r a n s m i t t e d w h i l e the b i n a r y i s i n s t a t e 1 and p u l s e s are t r a n s m i t t e d w h i l e i t i s i n s t a t e 2. The i n t e g r a t o r i s a s t o r a g e c i r c u i t w i t h time c o n s t a n t A. whose v o l t a g e , - v Q ( t ) , i s v a r i e d by the c u r r e n t g e n e r a t o r which s u p p l i e s p o s i t i v e c u r r e n t f o r b i n a r y s t a t e 1 and n e g a t i v e c u r r e n t f o r b i n a r y s t a t e 2. The feedback v o l t a g e , - v Q ( t ) , i s thus always e i t h e r i n -c r e a s i n g or d e c r e a s i n g . 5.2.1 C u r r e n t G enerator A more d e t a i l e d diagram of the p o r t i o n of the c i r c u i t shown s i m p l y as c u r r e n t g e n e r a t o r i n F i g u r e 5.1 i s shown i n F i g u r e 5.2. The v o l t a g e , v ( t ) , from the s s t e p s i z e c o n t r o l c i r c u i t v a r i e s l i n e a r l y w i t h r e s p e c t to time d u r i n g p e r i o d s of s t e p s i z e i n c r e a s e and p e r i o d s of s t e p s i z e d e c r e a s e . The f u n c t i o n g e n e r a t o r , i n c l u d e d as p a r t of the c u r r e n t g e n e r a t o r , produces a c u r r e n t which i s an e x p o n e n t i a l f u n c t i o n of v ( t ) . i ( t ) x ( i - ) *• — i v ( t ) s ' s t e p s i z e c o n t r o l v o l t a g e f u n c t i o n g e n e r a t o r i ( t ) s w i t c h x ( t ) s w i t c h i n g s i g n a l from b i n a r y Note: x ( t ) i s the complement of x ( t ) - ( i ( t ) x ( t ) \ phase i n v e r t e r ( t ) x ( t ) + i ( t ) i n t e g r a t o r c o n s t a n t c u r r e n t source F i g u r e 5° 2 Coder C u r r e n t Generator V-0 38 The s i g n a l x ( t ) from the b i n a r y c i r c u i t s w i t c h e s i ( t ) e i t h e r d i r e c t l y to the i n t e g r a t o r or t h r o u g h a phase i n v e r t e r w hich produces - i ( t ) . The i n v e r t e r i s o p e r a t e d w i t h a c o n s t a n t output c u r r e n t of - I j so t h a t changes i n i t s o u tput are d i r e c t l y p r o p o r t i o n a l to changes i n i t s i n p u t . T h i s c u r r e n t i s b a l a n c e d by a c u r r e n t of +1^ from a s e p a r a t e s o u r c e . 5.3 Step S i z e C o n t r o l C i r c u i t Two d i f f e r e n t schemes were i n v e s t i g a t e d f o r o b t a i n i n g the s t e p s i z e c o n t r o l s i g n a l , v ( t ) ' . These were:a d i g i t a l c o n t r o l c i r c u i t and an analogue c o n t r o l c i r c u i t . S i n c e the d i g i t a l c o n t r o l c i r c u i t was found t o be the b e t t e r of the two, i t i s d e s c r i b e d i n d e t a i l i n S e c t i o n 5.3.1. A b r i e f d e s c r i p t i o n of the o t h e r scheme i s g i v e n i n S e c t i o n 5.3.2. 5.3.1 D i g i t a l C o n t r o l C i r c u i t The s t e p s i z e c o n t r o l c i r c u i t i s r e q u i r e d t o produce an output v o l t a g e , v ( t ) as shown i n s F i g u r e 5.3. F o r normal s t e p s i z e a t the i n t e g r a t o r , v g ( t ) i s a dc v o l t a g e , V q. I f t h r e e s t e p s i n sequence are i n the same d i r e c t i o n , v ( t ) must i n c r e a s e l i n e a r l y w i t h r e s p e c t to time w i t h a s l o p e of dv V s s dT~ = 4AT F i g u r e 5«3 Step S i z e C o n t r o l V o l t a g e ( f o r a c c e l e r a t i o n s i g n a l a t t = 2AT and d e c e l e r a t i o n s i g n a l a t t = t , ) The i n c r e a s e must c o n t i n u e u n t i l e i t h e r the maximum v o l t a g e (V + VgO c o r r e s p o n d i n g t o a s t e p s i z e of 32AV i s r e a c h e d , or the d e c e l e r a t i o n s i g n a l i s g i v e n , i n which case v ( t ) must i m m e d i a t e l y drop by an amount 4^1 ' A T = . * V s ' so t h a t the f i r s t s t e p i n the o p p o s i t e d i r e c t i o n w i l l be one h a l f of the s i z e of the p r e v i o u s s t e p . The v o l t a g e must,then c o n t i n u e to decrease w i t h a s l o p e of V _ s 4AT u n t i l the minimum v a l u e , V , i s reached. Should the o v e r l o a d i n g s i g n a l be of such am p l i t u d e t h a t a s t e p s i z e of 32AV i s used, the f i r s t s t e p s i z e i n the o p p o s i t e d i r e c t i o n s h o u l d be 16AV so t h a t no sudden decrease i n v ( t ) i s n e c e s s a r y . s As d i s c u s s e d i n S e c t i o n 4.5, i f , d u r i n g the d e c e l e r a -t i o n p e r i o d , t h r e e s u c c e s s i v e s t e p s are i n the same d i r e c t i o n , the s t e p s i z e decrease must be h a l t e d as i l l u s t r a t e d by the d o t t e d p o r t i o n of the waveform of F i g u r e 5.3(g). The b l o c k diagram of t h i s c o n t r o l c i r c u i t i s shown i n F i g u r e 5.4. I t o p e r a t e s on a d i g i t a l b a s i s , t h a t i s , i t counts the 1 and 0 p u l s e s and i f the c o r r e c t sequence o c c u r s , i t s w i t c h e s ramp and s t e p g e n e r a t o r s b i n a r y x ( t ) AND #1 c l o c k ^ — *mry AND #2 Storage c o u n t e r #1 r e s e t r e s e t S torage c o u n t e r #2 OR b i n a r y ( S c h m i t t s t e p g e n e r a t o r r a i gene. np r a t o r b u f f e r / l i m i t e r v ( t ) s c o n t r o l v o l t a g e F i g u r e 5.4 D i g i t a l Step S i z e C o n t r o l U n i t ~- B l o c k Diagram t o produce the r e q u i r e d v o l t a g e , v ( t ) . The a c t u a l c i r c u i t S i s not as f o r m i d a b l e as would appear from the b l o c k diagram s i n c e much of i t can be b u i l t u s i n g s i m p l e diode c i r c u i t s , A complete c i r c u i t diagram and d e s c r i p t i o n are a g a i n g i v e n i n the Appendix, however an a b b r e v i a t e d d e s c r i p t i o n of the method of o p e r a t i o n f o l l o w s . AND c i r c u i t s #1 and #2 produce p u l s e s c o r r e s p o n d -i n g to the c o i n c i d e n c e of c l o c k p u l s e s and b i n a r y p u l s e s , x ( t ) , and c l o c k p u l s e s and complementary b i n a r y p u l s e s , x ( t ) . F i g u r e 5*5 shows r e p r e s e n t a t i v e waveforms f o r a t y p i c a l i n p u t s i g n a l . The s t o r a g e c o u n t e r s are r e q u i r e d t o count by t h r e e and must be r e s e t t o b e g i n c o u n t i n g a g a i n i f a p u l s e of the o p p o s i t e type o c c u r s . T h i s type of cou n t e r a c t s on the t r a i l i n g edge of the pulse; so t h e r e i s no output when an i n p u t p u l s e i s f o l l o w e d i m m e d i a t e l y by a r e s e t p u l s e . I n the absence of r e s e t p u l s e s the cou n t e r s t e p s t o a h i g h e r l e v e l w i t h each s u c c e e d i n g i n p u t p u l s e . These s t o r a g e c o u n t e r s , w h i l e s i m p l e i n o p e r a t i o n , p r o v i d e d a f l e x i b l e and r e l i a b l e c o u n t i n g d e v i c e which was e a s i l y adapted t o the r e s e t t i n g r e q u i r e m e n t s . The b i n a r y , a c t i n g as a v o l t a g e l e v e l d e t e c t o r , i s s w i t c h e d t h r o u g h the OR c i r c u i t by a v o l t a g e between the second and t h i r d l e v e l c o r r e s p o n d i n g t o a sequence of t h r e e 1 or 0 p u l s e s . U n t i l a r e s e t p u l s e produced 43 c l o c k i n p u t Jin i iAnmni in i iJui fwinjLa i n t e g r a t o r coder b i n a r y x ( t ) AND #1 AND #2 c o u n t e r #1 c o u n t e r #2 c o n t r o l c i r c u i t b i n a r y c o n t r o l v o l t a g e v s ( t ) n _ n j ; u~L_j~L_rLr if-irnjiruwirij—inn i i j i n r i n^ju~inr F i g u r e 5,5 T y p i c a l Waveforms ; ADM System by s w i t c h i n g of the b i n a r y i n the coder causes the c o u n t e r v o l t a g e to drop t o i t s normal v a l u e , i t remains above the t r i g g e r i n g l e v e l , h o l d i n g the b i n a r y on. The l e a d i n g edge of the b i n a r y p u l s e s t a r t s the g e n e r a t o r which produces the f i x e d - s l o p e ramp v o l t a g e , w h i l e the t r a i l i n g edge causes the s t e p g e n e r a t o r to add a n e g a t i v e s t e p of f i x e d a m plitude and r e v e r s e s the s l o p e of the ramp. The b u f f e r / l i m i t e r stage s e t s the c o r r e c t v a l u e s of V and (V + V ) and removes the o O S s t e p v o l t a g e when i t i s not r e q u i r e d , (as shown i n F i g u r e 5.3 ( e ) , ( f ) and (g) ). 5.3 .2 Analogue C o n t r o l C i r c u i t The second of the two methods of o b t a i n i n g a s t e p s i z e c o n t r o l s i g n a l c o n s i s t s of t a k i n g the i n p u t to the c o n t r o l c i r c u i t from the i n t e g r a t o r r a t h e r t h a n from the p u l s e t r a i n Df F i g u r e .4.1. The d e c i s i o n to change s t e p s i z e i s t h e n based on the s l o p e of the i n t e -g r a t o r s i g n a l averaged over a s u i t a b l e p e r i o d . I n an e x p o n e n t i a l system t h i s means t h a t the a c c e l e r a t i o n l i n e w i l l have a c o n s t a n t v a l u e independent of the v o l t a g e l e v e l , i n s t e a d of v a r y i n g a c r o s s the i n t e g r a t o r range as i n the d i g i t a l c o n t r o l scheme. There i s an e s s e n t i a l disadvantage i n the analogue method, however, s i n c e the c o n t r o l c i r c u i t a c t s on p a s t p u l s e s t h e r e b y c a u s i n g a d e l a y i n s t e p s i z e 4-5 change which i s e s p e c i a l l y troublesome i n response to the d e c e l e r a t i o n s i g n a l . . A l s o , a l t h o u g h the analogue scheme appeared to be r e l a t i v e l y s i m p l e , i n the a c t u a l c o n s t r u c t i o n a number of problems were encountered such as t h r e s h o l d l e v e l s t a b i l i t y and dc r e s t o r a t i o n . Because of these d i s a d v a n t a g e s the analogue c o n t r o l c i r c u i t was d i s c a r d e d i n f a v o u r of the d i g i t a l c o n t r o l c i r c u i t d e s c r i b e d i n S e c t i o n 5.3.1 and the l a t t e r was used f o r system t e s t s and measurements. 4 6 6 . . R E S U L T S OF T E S T S Two m e t h o d s w e r e u s e d t o c o m p a r e t h e p e r f o r m a n c e o f t h e a c c e l e r a t e d d e l t a m o d u l a t i o n s y s t e m w i t h t h a t o f o r d i n a r y d e l t a m o d u l a t i o n . The f i r s t o f t h e s e c o n s i s t e d o f O b s e r v i n g 'p,n a n o s c i l l o s c o p e a n d o n a c h a r t r e c o r d e r t h e r e s p o n s e o f t h e t w o s y s t e m s t o many t y p e s o f i n p u t s i g n a l s , b u t e s p e c i a l l y t o " g e n e r a l l y c o r r e l a t e d " s i g n a l s . The s e c o n d m e t h o d was a q u a n t i t a t i v e m e a s u r e -m e n t o f o v e r l o a d d i s t o r t i o n a n d . q u a n t i z i n g n o i s e , made b y t a k i n g t h e mean s q u a r e o f t h e d i f f e r e n c e b e t w e e n v ^ ( t ) a n d v Q ( t ) . F r o m t h i s , a n e x p r e s s i o n o f s i g n a l -t o - n o i s e r a t i o f o r a s i n e wave i n p u t s i g n a l o f v a r y i n g a m p l i t u d e was o b t a i n e d . The m a i n p u r p o s e o f t h e s e m e a s u r e m e n t s was t o d e t e r m i n e t h e c o s t o f t h e i m p r o v e -m e n t i n t r a n s i e n t r e s p o n s e i n t e r m s o f d e t e r i o r a t i o n o f s i g n a l - t o - n o i s e r a t i o f o r s i g n a l s w i t h s l o p e s n e a r t h e s l o p e l i m i t . I t s h o u l d be n o t e d t h a t t h e s e t e s t s w e r e made w i t h o u t t h e u s e o f a n o u t p u t f i l t e r a n d so a l l c o m p o n e n t s o f t h e n o i s e w e r e p r e s e n t , i n c l u d i n g h i g h -f r e q u e n c y c o m p o n e n t s t h a t w o u l d i n m o s t a p p l i c a t i o n s : be f i l t e r e d o u t . 6 . 1 W a v e f o r m C o m p a r i s o n s F i g u r e s 6 . 1 t o 6 . 5 a r e o s c i l l o g r a m s o f o u t -p u t s i g n a l s (v ( t ) ) . I n a l l c a s e s t h e u p p e r t r a c e i s the DM response and the lower t r a c e i s the ADM response except i n F i g u r e 6.1 where b o t h t r a c e s are f o r ADM. F i g u r e 6.1 T h i s o s c i l l o g r a m shows the ADM output f o r a s e r i e s of s t e p i n p u t v o l t a g e s and i l l u s t r a t e s the v a r i o u s amounts of o v e r s h o o t f o r d i f f e r e n t s i z e s t e p s . I n the upper t r a c e the output i s i n i t i a l l y a t V m and i s reduced by st e p s of the f o l l o w i n g s i z e s u n t i l -V i s reached: 1.2, 1.0, 0.8, 0.5, 0.3 and 0.2 v o l t s . I n the lower t r a c e the output i s i n i t i a l l y a t -V and i s i n c r e a s e d by steps of the same s i z e as b e f o r e but i n the r e v e r s e o r d e r . The e f f e c t of the e x p o n e n t i a l i n t e -g r a t o r c h a r a c t e r i s t i c i s shown by the d i f f e r e n c e i n the amount of overshoot f o r equal but o p p o s i t e s t e p s o c c u r r i n g a t d i f f e r e n t i n t e g r a t o r v o l t a g e s . The t o t a l t r a c e time i n b o th cases i s a p p r o x i m a t e l y 10 seconds. 49 F i g u r e 6.2 I n t h i s example the i n p u t s i g n a l was a 0.07 pps square wave w i t h an amplitude of a p p r o x i m a t e l y 4 v o l t s peak-to-peak. The r e l a t i v e a b i l i t y of DM and ADM t o f o l l o w a sudden change i n i n p u t i s c l e a r l y shown, f o r w h i l e the DM response f o l l o w s w i t h i t s maximum p o s s i b l e s l o p e and reaches the c o r r e c t output o n l y a f t e r a l o n g d e l a y , the ADM output v e r y q u i c k l y reaches the c o r r e c t v a l u e , and a f t e r a s h o r t i n t e r v a l of l a r g e q u a n t i z i n g n o i s e , a g a i n f o l l o w s the i n p u t s i g n a l w i t h the d e s i r e d a c c u r a c y . j N j \ J U 50 F i g u r e 6.3 These t r a c e s show the response to a square-wave i n p u t s i g n a l of 0 . 4 pps and a p p r o x i m a t e l y 4 v o l t s peak-to-peak. At t h i s f r e q u e n c y the DM output has become a t r i a n g u l a r waveform of much s m a l l e r a mplitude than the i n p u t s i g n a l w h i l e the ADM output s t i l l shows the g e n e r a l form of the i n p u t s i g n a l and reaches the c o r r e c t a m p l i t u d e . F i g u r e 6.4 T h i s shows the response t o a 4 v o l t peak-to-peak sine-wave i n p u t s i g n a l of f r e q u e n c y 0.07 cps which causes a s m a l l amount of o v e r l o a d d i s t o r t i o n f o r DM, and i l l u -s t r a t e s the r e a c t i o n of ADM to a s i g n a l w i t h a c o n t i n u a l l y v a r y i n g s l o p e . I t can be seen t h a t the ADM response g i v e s a b e t t e r g r o s s a p p r o x i m a t i o n to the s i n e wave but has, over most of the c u r v e , c o n s i d e r a b l y g r e a t e r h i g h -f r e q u e n c y q u a n t i z i n g n o i s e . 52 F i g u r e 6.5 T h i s o s c i l l o g r a m was t a k e n f o r a p e r i o d of 50 seconds w i t h a sine-wave i n p u t s i g n a l of f r e q u e n c y 0.2 cps and v a r y i n g i n amplitude from 0 to 4 v o l t s peak-to-peak i n 40 seconds. I t shows the l i m i t i n g i n o u t -put which o c c u r s i n the DM system which i s a b l e to f o l l o w o n l y about the f i r s t two c y c l e s of the i n p u t s i g n a l . The ADM system g i v e s a good r e p r e s e n t a t i o n of the i n p u t f o r a l l a m p l i t u d e s from zero t o the maximum. 6 . 2 D i s c u s s i o n of Waveforms. I n a d d i t i o n to the system parameters f o r which the waveforms shown were ob s e r v e d , v a r i o u s o t h e r v a l u e s of the parameters were used i n o r d e r t o check t h a t the b e s t v a l u e s had been s e l e c t e d . A l t h o u g h some of these d i f f e r e n t v a l u e s showed b e t t e r r e s u l t s f o r c e r t a i n types of i n p u t s i g n a l s , i t was found t h a t the parameters s e l e c t e d proved most advan-tageous f o r a v a r i e t y of i n p u t s . For example, a d e l a y i n r e d u c i n g s t e p s i z e a f t e r the d e c e l e r a t i o n s i g n a l gave b e t t e r a b i l i t y t o f o l l o w v e r y s h o r t i n p u t p u l s e s but caused e x c e s s i v e r e c o v e r y time f o r s t e p i n p u t s . A l e n g t h e n i n g of the a c c e l e r a t i o n s i g n a l from t h r e e to f o u r p u l s e s gave l e s s q u a n t i z i n g n o i s e f o r c e r t a i n s i g n a l s w i t h s m a l l s l o p e s , but i n c r e a s e d the q u a n t i z i n g n o i s e f o r s i g n a l s w i t h l a r g e r s l o p e s and a l s o i n c r e a s e d the d e l a y i n r e s p o n d i n g t o s t e p s . The advantage of v a r y i n g the s t e p s i z e i n c o r r e s -pondence w i t h the amplitude of the o v e r l o a d i n g s i g n a l i s demonstrated i n F i g u r e s 6.1 and 6.4 where, f o r s m a l l o v e r -l o a d i n g s i g n a l s , the o v e r s h oot i s s m a l l . The r e c o v e r y time a f t e r a c c e l e r a t i o n f o r v a r i o u s amounts of overshoot can be seen from the o s c i l l o g r a m s . T h i s time i s q u i t e s h o r t i n a l l c a s e s , the l o n g e s t p e r i o d b e i n g t h a t a s s o c i a t e d w i t h r e -a c c e l e r a t i o n which o c c u r s m a i n l y a t the extremes of 54 t h e a m p l i t u d e r a n g e . A n e x a m p l e i s i n t h e l a s t s t e p o f t h e l o w e r t r a c e o f F i g u r e 6 . 1 . E v e n i n s u c h c a s e s a s t h i s , t h e t o t a l o f d e l a y t i m e p l u s a c c e l e r a t i o n t i m e p l u s r e c o v e r y t i m e i s s t i l l o n l y a f r a c t i o n o f t h e t i m e r e q u i r e d f o r t h e o u t p u t o f t h e DM s y s t e m t o a r r i v e a t t h e c o r r e c t v a l u e . B e s i d e s t h o s e i n p u t s f o r w h i c h t h e r e s p o n s e i s s h o w n i n t h e o s c i l l o g r a m s many more i n p u t s i g n a l s w e r e u s e d , i n c l u d i n g r a n d o m v a r i a t i o n s s u c h a s c o u l d be e x p e c t e d i n some t e l e m e t e r i n g o r o t h e r a p p l i c a t i o n s . F o r e v e n t h e m o s t e r r a t i c o f t h e s e , no i n s t a b i l i t y was d e t e c t e d , a n y o s c i l l a t i o n s b e i n g q u i c k l y damped o u t . A t t h e e x t r e m e e n d s o f t h e a m p l i t u d e r a n g e s l i g h t o s c i l l a t i o n s o c c u r a f t e r t h e d e c e l e r a t i o n p e r i o d b e c a u s e , a s was s h o w n i n S e c t o r i o n 4 . 7 , t h e a c c e l e r a t i o n l i n e a p p r o a c h e s z e r o . E x a m p l e s o f t h e s e may b e s e e n i n F i g u r e 6 . 2 . 6 . 3 M e t h o d U s e d t o M e a s u r e N o i s e B e c a u s e t h e s p e e d o f o p e r a t i o n s e l e c t e d f o r t h e c o n s t r u c t e d s y s t e m was so low, a n a n a l o g u e c o m p u t e r , a s s h o w n i n F i g u r e 6 . 6 , was u s e d t o o b t a i n a c c u r a t e n o i s e m e a s u r e m e n t s . The q u a n t i t y m e a s u r e d was t h e e r r o r s i g n a l , w h i c h i n t h i s c a s e , was t h e sum o f t h e i n p u t s i g n a l , v ^ ( t ) a n d t h e i n t e g r a t o r v o l t a g e , - v Q ( t ) . A l t h o u g h t h i s e r r o r was c o m p o s e d o f q u a n t i z i n g n o i s e p l u s o v e r l o a d d i s t o r t i o n , f o r s i m p l i c i t y i t w i l l be r e -f e r r e d t o a s s i m p l y n o i s e . The t e s t i n g c i r c u i t was a d d e r / a m p l i f i e r  5 -24**]" computer a m p l i f i e r 0.000 5 |xf 1 1 meg V . ( t ) o *VW-^  1 15K - v o ( t ) . k,v 1 n 22 meg — v w — R-^~ 2 mej 100K —Wv--WV-k 0 v 2 n -4v s q u a r i n g c i r c u i t > < f u n c t i o r g e n e r a t o r 100K —vw-i n t e g r a t o r 100K —»N^-C 2=l[xf R 2= 10 meg 0 "TJ-lOOv Note: changed f o r s c a l e change F i g u r e 6.6 Noise Measuring C i r c u i t U l 56 ca l ibra ted by replac ing -v (t) with a f ixed vol tage . fo l lows: The s ignal - to-noise r a t i o (SNR) was obtained as v (t) = v . ( t ) - v (t) n i o where v (t) = instantaneous noise vol tage . The mean-square value of noise i s n T, R 2 C 2 k- v * dt 3 n and s i m i l a r l y for v^ where T^ . i s the tes t ing time k^ i s a constant determined by the computer arrange-ment R^t a r e v a l n e s of resistance and capacitance i n the computer in tegrator . Then the s ignal - to -noise r a t i o i s given by SNR = 10 log I \ n 2 dt 10 log v 2 dt n db 57 The n o i s e s a m p l e i s n o t a r a n d o m f u n c t i o n b u t c o n t a i n s c o m p o n e n t s o f t h e i n p u t s i g n a l f r e q u e n c y , a s w e l l a s o f t h e s a m p l i n g f r e q u e n c y . F o r t h i s r e a s o n t h e l e n g t h o f t h e m e a s u r e d s a m p l e was made a m u l t i p l e o f t h e p e r i o d o f t h e i n p u t s i g n a l , a n d o f s u f f i c i e n t d u r a t i o n t o a v e r a g e t h e v a r i a t i o n s f r o m p e r i o d t o p e r i o d . F o r e x a m p l e , i n t h e t e s t s u s i n g a n i n -p u t s i g n a l o f 0 . 2 c p s , t h e n o i s e was i n t e g r a t e d o v e r 1 0 c y c l e s o r 50 s e c o n d s . 6 . 4 R e s u l t s o f N o i s e M e a s u r e m e n t s T y p i c a l r e s u l t s o f n o i s e m e a s u r e m e n t s f o r t h e DM a n d ADM s y s t e m s a r e s h o w n o n t h e g r a p h o f s i g n a l - t o - n o i s e r a t i o v e r s u s a m p l i t u d e o f i n p u t s i g n a l f o r a 0 . 2 c p s s i n e ^ w a v e i n p u t ( F i g u r e 6 . 7 ) . M e a s u r e m e n t s w e r e a l s o made f o r o t h e r f r e q u e n c i e s o f i n p u t s i g n a l w i t h s i m i l a r r e s u l t s , t h e o v e r a l l s i g n a l - t o - n o i s e r a t i o b e i n g g r e a t e r a t l o w e r f r e q u e n c i e s a n d l e s s a t h i g h e r f r e q u e n c i e s . The d e l t a m o d u l a t i o n c h a r a c t e r i s t i c e x h i b i t s t h e u s u a l b e h a v i o u r5 a s i g n a l - t o - n o i s e r a t i o i n c r e a s i n g w i t h a m p l i t u d e u n t i l s l o p e o v e r l o a d o c c u r s a f t e r w h i c h i t d r o p s o f f s h a r p l y a n d t h e n a p p r o a c h e s a s y m p t o t i c a l l y t o z e r o d b . The a c c e l e r a t e d d e l t a m o d u l a t i o n s i g n a l - t o - n o i s e r a t i o i s i d e n t i c a l t o t h a t o f TJjM f o r a m p l i t u d e s g i v i n g s l o p e s b e l o w t h e a c c e l e r a t i o n l i n e . J u s t a b o v e t h i s l i n e a s l i g h t i m p r o v e m e n t i n SNR o v e r DM o c c u r s , c a u s e d H. ON * Q-H. P H tr o K> CO H-JQ p P t-j i 1 c+-O 1 1 P o M H" P 03 d CD C !m <i O H- h—1 O ct-< l >q CD CD W W CD P fe-3 d H-1 H" c PJ CD Hj O H. O to o •d W C/2 H-a t si p. < CD M P d pi c+-S i g n a l - t o - n o i s e r a t i o i n db VJl s t-1 to 4 O VJl —(— O VJl —I 1-O to VJl a c c e l e r a t i o n l i n e DM s l o p e l i m i t maximum am p l i t u d e (V ) m 59 b y a s l i g h t a c c e l e r a t i o n w i t h l i t t l e o r no o v e r s h o o t . T h i s s l i g h t i m p r o v e m e n t i s l e s s n o t i c e a b l e a t o t h e r f r e q u e n c i e s o f i n p u t s i g n a l . The e x p e c t e d d e t e r i o r a t i o n i n SNR a s c o m p a r e d t o DM o c c u r s f o r a m p l i t u d e s s l i g h t l y b e l o w t h a t c a u s i n g DM o v e r l o a d d i s t o r t i o n . T h i s d e t e r i o r a t i o n i s l e s s t h a n was a n t i c i p a t e d , b e i n g a s s h o w n , o n l y a b o u t 2 d b . T h u s f o r s i n e - w a v e i n p u t s i g n a l s t h e p e n a l t y p a i d f o r t h e i m -p r o v e m e n t i n r e s p o n s e t o s u d d e n j u m p s i s i n d e e d q u i t e s m a l l . A l t h o u g h f o r l a r g e r a m p l i t u d e s t h e SNR o f ADM d r o p s o f f s o m e w h a t f r o m i t s maximum v a l u e , i t t h e n r e m a i n s a l m o s t c o n s t a n t f o r i n c r e a s i n g i n p u t v o l t a g e , s h o w i n g t h a t t h e n o i s e v o l t a g e i n c r e a s e s i n d i r e c t p r o p o r t i o n t o t h e i n p u t s i g n a l v o l t a g e . T h i s means t h a t f o r a s p e c i f i e d m i n i m u m s i g n a l - t o - n o i s e r a t i o t h e r a n g e o f i n p u t s i g n a l s t h a t c a n be h a n d l e d b y ADM i s much g r e a t e r t h a n C a n be h a n d l e d b y D M . F o r e x a m p l e , i n F i g u r e 6 . 7 f o r a m i n i m u m SNR o f 15 db t h e a m p l i t u d e r a n g e o f ADM i s o v e r 4 t i m e s a s g r e a t a s t h a t o f D M , i n d i c a t i n g a n i n c r e a s e i n d y n a m i c r a n g e o f o v e r 12 d b . S i n c e t h e ADM n o i s e c o n t a i n s a l a r g e r p e r c e n t a g e o f h i g h -f r e q u e n c y c o m p o n e n t s t h a n t h e DM n o i s e , u s e o f a l o w - p a s s f i l t e r i n t h e o u t p u t w o u l d show a n e v e n g r e a t e r a d v a n t a g e f o r A D M . . ) 60 7. CONCLUSIONS 7.1 C o n c l u s i o n s Regarding the ADM System The o b j e c t of t h i s work was to i n v e s t i g a t e a method of i n c r e a s i n g the e f f i c i e n c y of systems t r a n s m i t t i n g s i g n a l s c o n t a i n i n g o c c a s i o n a l t r a n s i e n t s . Because of the d i f f i c u l t y of a g e n e r a l t h e o r e t i c a l i n v e s t i g a t i o n , a method was developed p e r t a i n i n g s p e c i f i c a l l y t o d e l t a m o d u l a t i o n . S e l e c t i o n of optimum parameters f o r t r a n s m i s s i o n of t h i s type of s i g n a l produced the ADM system. R e s u l t s of t e s t s on t h i s system show t h a t a v e r y s i g n i f i c a n t improvement i n t r a n s i e n t response has been o b t a i n e d w i t h no i n c r e a s e i n t r a n s -m i t t e d p u l s e r a t e . The expected i n c r e a s e i n q u a n t i z i n g n o i s e f o r s i g n a l s near the DM s l o p e l i m i t was s m a l l . A l t h o u g h more c i r c u i t r y i s r e q u i r e d f o r ADM than f o r DM the equipment i s s t i l l r e l a t i v e l y s imple compared t o o t h e r b i n a r y p u l s e systems, 7.2 A p p l i c a t i o n t o Other Systems The ADM system can be summarized as f o l l o w s . F o l l o w i n g an a c c e l e r a t i o n s i g n a l d e r i v e d from the p u l s e t r a i n , b o t h the t r a n s m i t t e r and r e c e i v e r i n t e r p r e t the s u c c e e d i n g p u l s e s i n a d i f f e r e n t manner, and con-s e q u e n t l y i n c r e a s e the s i z e of s t e p s a t the i n t e g r a t o r . A f t e r the t r a n s i e n t c o n d i t i o n has passed, normal i n t e r p r e -t a t i o n of the p u l s e s i s resumed. T h i s concept of changing the meaning of the code to accommodate o c c a s i o n a l t r a n s i e n t s i h the s i g n a l w i l l now be examined i n a more g e n e r a l sense* 61 The i d e a o f c h a n g i n g t h e m e a n i n g o f a c o d e i s n o t a new o n e . V a r i o u s s y s t e m s h a v e b e e n d e v e l o p e d w h i c h o p e r a t e o n t h i s b a s i s . H o w e v e r , i n f o r m i n g t h e r e c e i v e r o f c o d e c h a n g e s i s u s u a l l y a c c o m p l i s h e d b y u s i n g a s e p a r a t e s u p e r v i s o r y c h a n n e l . F o r i n s t a n c e a d d i t i o n a l p u l s e s c a n b e t i m e - m u l t i p l e x e d w i t h t h e m e s s a g e t r a n s m i s s i o n . , S u c h a s u p e r v i s o r y c h a n n e l m u s t be c a p a b l e o f f a s t a c t i o n , h o w e v e r , a n d b e c a u s e o f t h i s , a c o n s i d e r a b l e f r a c t i o n o f t h e t o t a l c h a n n e l c a p a c i t y w o u l d be n e e d e d i f e v e n o n l y one c o d e c h a n g e i s u s e d . A l t h o u g h a n i m p r o v e m e n t i n e f f i c i e n c y c a n be o b t a i n e d b y t h i s m e t h o d t h e e q u i p m e n t r e q u i r e d i s q u i t e c o m p l e x . A n e x a m p l e o f s u c h a s y s t e m a p p l i e d t o v i d e o t r a n s m i s s i o n i s d e s c r i b e d i n R e f e r e n c e 7 . I n t h e p r e s e n t c a s e t h e i n f o r m a t i o n f o r c o d e c h a n g e i s d e r i v e d f r o m t h e t r a n s m i t t e d m e s s a g e i t s e l f . I f t h e s i g n a l b e h a v e s i n a c e r t a i n m a n n e r ( i n d i c a t i n g i m p e n d i n g o r i n c i p i e n t o v e r l o a d ) b o t h t h e t r a n s m i t t e r a n d r e c e i v e r k n o w t h a t t h e n e x t c o d e p u l s e s a r e t o b e i n t e r p r e t e d i n a d i f f e r e n t w a y . T h i s p r o c e s s may be d e s c r i b e d ss a " s e l f -a d j u s t i n g 1 1 c o d e * A f i x e d c a p a c i t y s y s t e m u s i n g a " s e l f - a d j u s t i n g " c o d e t o a l l o w t r a n s m i s s i o n o f t r a n s i e n t s w i l l i n e v i t a b l y c a u s e d e g r a d a t i o n f o r some d t h e r s i g n a l s w h i c h o t h e r w i s e w o u l d be t r a n s m i t t e d a c c u r a t e l y . H o w e v e r , t h e o v e r a l l q u a l i t y o f t r a n s m i s s i o n w i l l b e b e t t e r t h a n f o r a s y s t e m w i t h a n o n - a d j u s t i n g c o d e . 62 From the experience gained with ADM we can conclude that "sel f -adjust ing" codes show promise as a general method of improving the e f f i c i ency of systems transmitt ing "generally correlated" s igna l s . Their app l i ca t ion might also be extend-ed to s ignals containing occasional disturbances of other kinds than transients} for instance, to s ignals containing occasional large amplitudes. 63 A P P E N D I X I n s t r u m e n t a t i o n The v a r i o u s s t a g e s o f t h e c o d e r a n d s t e p s i z e c o n t r o l u n i t a r e , f o r t h e m o s t p a r t , s t a n d a r d c i r c u i t s a n d r e q u i r e no e x p l a n a t i o n o t h e r t h a n t h e c i r c u i t d i a g r a m s . T h e r e a r e , h o w -e v e r , a f e w s e c t i o n s w h e r e some e x p l a n a t i o n i s n e c e s s a r y . The d e s c r i p t i o n s r e f e r t o t h e b l o c k d i a g r a m s , F i g -u r e s 5 . 1 , 5 . 2 a n d 5 . 4 a n d t o t h e t y p i c a l w a v e f o r m s , F i g u r q ; 5 . 5 , a s w e l l a s t o t h e c i r c u i t d i a g r a m s o f t h e c o d e r a n d c o n t r o l c i r c u i t , F i g u r e s A - l a n d A - 2 r e s p e c t i v e l y . A . C o d e r ( c f . F i g u r e A - l ) B i n a r y The b i n a r y i s a S c h m i t t t r i g g e r w i t h a h y s t e r e s i s v o l t a g e o f 1 . 6 v o l t s . I t s i n p u t i s n o r m a l l y c l a m p e d b y t h e g a t e t o - 1 0 . 1 v o l t s w h i c h i s i n t h e c e n t r e o f t h e h y s t e r e s i s r a n g e . O p e n i n g o f t h e g a t e a p p l i e s a 0 . 1 5 msec s a m p l e o f t h e a m p l i f i e d a n d c l i p p e d e r r o r s i g n a l t o i t s i n p u t . T h i s s a m p l e s w i t c h e s t h e b i n a r y t o s t a t e 2 i f i t i s a b o v e - 9 . 3 v o l t s o r t o s t a t e 1 i f i t i s b e l o w - 1 0 . 9 v o l t s . I n t e g r a t o r The i n t e g r a t o r c o n s i s t s o f a 3 0 0 \if c a p a c i t o r s h u n t e d b y a n 18K r e s i s t o r . T h i s r e s i s t o r i s c o n n e c t e d t o t h e - 4 v o l t s u p p l y i n o r d e r t o e s t a b l i s h t h e m i d - p o i n t 64 o f t h e i n t e g r a t o r v o l t a g e r a n g e . T h i s r a n g e i s f r o m - 2 t o - 6 v o l t s c o r r e s p o n d i n g t o a n i n p u t v o l t a g e r a n g e o f - 6 t o - 2 v o l t s . T h i s l a r g e v a l u e o f c a p a c i t a n c e was c h o s e n so t h a t t h e c u r r e n t s f e e d i n g t h e i n t e g r a t o r a r e o f s u f f i c i e n t m a g n i t u d e t o swamp v a r i a t i o n s due t o t e m p e r a t u r e . S i n c e X = RC = 5 s e c C = 3 0 0 |xf 5 3 0 0 x 1 0 6 •= 1 6 . 7 K The v a l u e o f 1 6 . 7 K i s t h e t o t a l r e s i s t a n c e s h u n t i n g C , i n -c l u d i n g t h e 1 8 K r e s i s t o r a n d t h e i n p u t r e s i s t a n c e o f T i l . The c u r r e n t f o r n o r m a l s t e p s i z e i s lo ~ L AT = 3 0 0 x 1 0 " 6 x 0 . 8 = 0 . 2 4 ma a n d t h e c u r r e n t f o r maximum s t e p s i z e i s I = 0 . 2 4 x 32 max = 7 . 6 8 ma The s t a b i l i t y o f t h i s p o r t i o n o f t h e c i r c u i t p r e s e n t s t h e m o s t c r i t i c a l d e s i g n p r o b l e m i n t h e c o d e r . I n o r d e r t o o b t a i n a d c v o l t a g e a c c u r a c y o f ± 0 . 5 $ t h e d e v i a t i o n o f t h e sum o f f i x e d c u r r e n t s p l u s a v e r a g e v a l u e o f s w i t c h e d 65 current from zero, must not exceed \ AV 20 mv _ R ~ 16.7K ~ L ' Z The d r i f t can be held to a small value by using matched complementary t rans i s tors for T9 and T10 and a common head's ink . This problem, of course, i s not pecul iar to ADM but exists i n any exponential DM system. Current Generator As explained prev ious ly , the steps at the integrator are obtained by feeding a c lo se ly contro l led current into or out of the storage capacitor for a def in i te time i n t e r v a l . The amount of current flow into the capacitor i s determined by the voltage at the base of t rans i s tor T8. For a normal step size of 40 mv th i s voltage i s +10.5 vol ts , and a corresponding current of 0.24 ma flows through diode D2 to charge the storage capac i tor . During th i s i n t e r v a l t rans i s tor T7 i s held cut -of f by the voltage from the binary through T6. When a step i n the other d i r e c t i o n i s required, T7 i s turned on by applying about -10 vo l t s to i t s base. This ra ises the emitter of T7 to -10 vo l t s and cuts off diode D2. The c o l l e c t o r current of T8 now flows through the co l l e c t or resistance of T7 which causes an increase i n current i n t r a n s i s t o r T9 and consequently discharges the 66 s t o r a g e c a p a c i t o r * The v a l u e o f t h i s d i s c h a r g e c u r r e n t i s t h e same ( 0 . 2 4 ma) a s t h e f o r m e r c h a r g i n g c u r r e n t . T h e r e i s a c o n t i n u o u s c u r r e n t , - 1 ^ f l o w i n g i n T9 w h e t h e r T7 i s o p e n o r c l o s e d * T h i s i s b a l a n c e d b y a c o n -s t a n t c u r r e n t , +1^ f e d i n t o t h e c a p a c i t o r b y c u r r e n t g e n e r a t o r T 1 0 so t h a t t h e n e t c u r r e n t i s z e r o . The d i o d e a n d r e s i s t o r c i r c u i t c o n n e c t e d t o t h e e m i t t e r o f T8 m a k e s u p t h e e x p o n e n t i a l f u n c t i o n g e n e r a t o r * D e s i g n o f t h i s f u n c t i o n g e n e r a t o r . w a s s i m p l i f i e d a n d t h e a p p r o x i m a t i o n i m p r o v e d b y i n c l u d i n g t h e i n t e g r a t o r c h a r a c t e r i s t i c s . P o r t h i s p u r p o s e t h e i n t e g r a t o r was c o n -s i d e r e d a s h a v i n g a n i n f i n i t e t i m e c o n s t a n t i n a c c o r d a n c e w i t h t h e r e q u i r e d s y s t e m c h a r a c t e r i s t i c s . I n t h i s w a y , b y m a t c h i n g t h e i n t e g r a t o r v o l t a g e a t t h e s a m p l i n g p o i n t s w i t h t h e i d e a l e x p o n e n t i a l c u r v e , a p i e c e - w i s e - l i n e a r c u r r e n t c o u l d be u s e d . The o n l y e r r o r t h e n , was t h a t s m a l l a m o u n t i n t r o d u c e d b y t h e e f f e c t o f t h e f i n i t e t i m e c o n s t a n t o f t h e i n t e g r a t o r . I t s h o u l d be p o i n t e d o u t t h a t a n y s u c h e r r o r s w o u l d n o t r e s u l t i n s y s t e m e r r o r s s i n c e a n i d e n t i c a l a r r a n g e m e n t w o u l d be u s e d i n t h e d e c o d e r . clock. .differentiator binary (3chwitt t r i j « « r ) » inverter s t e p Size controI vof taae Vj(t) input voltage (-(, to -Zv ) D4 68A$ S 6 8A IK 4.7 k +70 A +'2v i + 6 v +12 v F i g u r e A - l Delta Modulat ion Coder — S c h e m a t i c Diagram Note 1.t M i .5isWj T l , T Z , T 6 , T 7 . T 6 \ T I I . T I Z . T I 3 : 2 N 4 0 4 T 3 , T 4 , T 5 • 2N39S . T 9 : 2 N I J 0 4 T I4 : 2N-IJ.75 , TIO •  2 N 4 0 4 diodes : IN497 2. output to receiver is taken front step site control c i r c u i t ON 6 8 B . S t e p S i z e C o n t r o l C i r c u i t ( c f . F i g u r e A - 2 ) S t o r a g e C o u n t e r s The c o u n t e r s a r e s t a n d a r d t w o - d i o d e s t o r a g e t y p e , w i t h t h e a d d e d f e a t u r e o f r e s e t c o n t r o l . T h i s r e s e t o c c u r s w h e n t h e c o d e r b i n a r y s w i t c h e s , c a u s i n g a n e g a t i v e p u l s e t o a p p e a r o n t h e r e s e t l i n e . T h i s may o c c u r a t a n y s t a g e i n t h e c o u n t i n g s e q u e n c e , a n d a f t e r a r e s e t p u l s e c o u n t i n g s t a r t s a g a i n f r o m z e r o , The o u t p u t o f t h e c o u n t e r s a c t u a l l y l a g s t h e c o d e r b i n a r y b y o n e f u l l s a m p l i n g i n t e r n a l . A o n e - h a l f p e r i o d d e l a y i s i n t r o d u c e d b e c a u s e t h e AND c i r c u i t s o p e r a t e o n t h e n e g a t i v e - g o i n g p o r t i o n o f t h e c l o c k w a v e f o r m i n s t e a d o f o h t h e p o s i t i v e — g o i n g p o r t i o n . I n a d d i t i o n ^ t h e c o u n t e r s i n t h e m s e l v e s h a v e a n i n h e r e n t o n e - h a l f p e r i o d d e l a y . A s p o i n t e d o u t i n S e c t i o n 5 . 3 , t h i s t o t a l d e l a y e n a b l e s t h e r e s e t p u l s e , a c t i n g w i t h o u t d e l a y o n t h e ' n e x t . , c o d e r b i n a r y d e c i s i o n , - t o c a n c e l a p u l s e b e f o r e i t i s c o u n t e d . Ramp a n d S t e p G e n e r a t o r I n t h e r a m p a n d s t e p g e n e r a t o r , t r a n s i s t o r T4 i s n o r m a l l y h e l d o f f b y a n e g a t i v e v o l t a g e f r o m t h e b i n a r y * T r a n s i s t o r T5 i s c o n d u c t i n g , i t s c o l l e c t o r c u r r e n t , I - , f l o w i n g t h r o u g h d i o d e D18 w h i c h c l a m p s t h e 20 p f c a p a c i -t o r v o l t a g e t o a p p r o x i m a t e l y +10 v o l t s . D i o d e s D 1 6 , D l 7 a n d D19 a r e r e v e r s e b i a s e d . Vhen the b i n a r y s w i t c h e s , T4 i s turned' on. The c o l l e c t o r c u r r e n t I , of T4 i s t w i c e t h a t of T5, A c u r r e n t c4 e q u a l to ( l c 4 - ^- c^ = d i s c h a r g e s the 20 [if c a p a c i t o r a t a c o n s t a n t r a t e , d r o p p i n g the v o l t a g e a t the base of T6 and c u t t i n g o f f D l 8 , T h i s n e g a t i v e - g o i n g ramp v o l t a g e con-t i n u e s u n t i l e i t h e r i t i s clamped to - 2,5 v o l t s by D19 dr the b i n a r y a g a i n s w i t c h e s . When the b i n a r y s w i t c h e s back t o i t s normal condi-t i o n a n e g a t i v e s t e p t u r n s T4 o f f and through the 0.6 jxf c a p a c i t o r and diode D16 drops the base v o l t a g e of T5 and opens D17. The c o l l e c t o r c u r r e n t of T5 i s thus g r e a t l y i n c r e a s e d fDr a s h o r t i n t e r v a l . The time c o n s t a n t of the c i r c u i t i s such t h a t a p o s i t i v e 2.5 v o l t s t e p appears on the 20 (j,f c a p a c i t o r . W i t h T4 o f f , the c a p a c i t o r , a f t e r the i n i t i a l s t e p i s charged a t a c o n s t a n t r a t e by c u r r e n t I ,-. d i o d e s C j D16 and D17 a g a i n b e i n g r e v e r s e - b i a s e d * T h i s produces a p o s i t i v e - g o i n g ramp which c o n t i n u e s u n t i l c l a m p i n g by D18 oc c u r s or the b i n a r y a g a i n changes i t s s t a t e . Thus the v o l t a g e a t the base of T6 v a r i e s between + 1 0 v o l t s and -2.5 v o l t s . B u f f e r / L i m i t e r Diode D20 performs the f i n a l c lamping of the con-t r o l v o l t a g e , r e d u c i n g i t s l i m i t s t o + 1 0 . 5 and 0 v o l t s . F i g u r e 5.3 shows the waveforms produced by the c i r c u i t , except t h a t i n the c o n s t r u c t e d u n i t a n e g a t i v e g o i n g c o n t r o l v o l t a g e was used i n s t e a d of a p o s i t i v e going'y^oltage as shown. The s l o p e of v ( t ) , from S e c t i o n 5.3.1 i s S dv dT V 4AT 10 4 x 50 x 10 -3 = 50 v o l t s / s e c or 2.5 v o l t s per sampling i n t e r v a l . From which "c5 dV = c d t and 20 x 10 x 50. • = 1 ma c4 = 2 1 c5 = 2 ma AND •! Storage counter * I I T 1 - -v f ( t ) output pulses to receiver 1 AND »2 1 ftorage counter *Z KJole I. transistor* T l . : 2 N 395 T 2 : 2 . N I J 7 J T3, T 5 . T 6 : 2N404-T 4 : i N I J 0 4 diodes IN+57 * pad to (jive count by 3 Off/ - lOv + I0v + I2v adjust for positive-goin^ 6lope on F i g u r e A-2. .Step Size. Cowtrol Circuit — Schematic Diagram 72 R E F E R E N C E S K<T-etzmer, E . R . , " R e d u c e d - A l p h a b e t R e p r e s e n t a t i o n o f TV S i g n a l s " , I R E C o n v e n t i o n  R e c o r d ^ P a r t 4 , 1 9 5 6 „ G r a h a m , R . E . , " P r e d i c t i v e Q u a n t i z i n g o f T e l e -v i s i o n S i g n a l s " , I R E WESCON  C o n v e n t i o n R e c o r d , P a r t 4 , 1 9 5 8 . de F a y e , P . J . , ' " A s p e c t s o f D e l t a M o d u l a t i o n , " 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 9 . de J a g e r , F . , " D e l t a m o d u l a t i o n , A M e t h o d o f PCM T r a n s m i s s i o n U s i n g t h e 1 - U n i t C o d e " , P h i l i p s R e s e a r c h R e p o r t s , V o l u m e 7 , 1 9 5 2 . H o l z e r , J . , " E x p o n e n t i a l D e l t a M o d u l a t i o n f o r M i l i t a r y C o m m u n i c a t i o n s " , S i g n a l  C o r p s E n g i n e e r i n g L a b o r a t o r i e s , ' F o r t M o n m o u t h , N . J . T e c h n i c a l Memorandum N o . M - 1 7 7 7 , 1 J u n e 1 9 5 6 . B o w e r s , F . K . , " D e l t a m o d u l a t i o n f o r C h e a p a n d S i m p l e T e l e m e t e r i n g " , I R E WESCON  C o n v e n t i o n R e c o r d , P a r t 5 , 1 9 5 9 . K i t s o p o u l o s , S . C . , a n d K r e t z m e r , , E . R . , " C o m p u t e r S i m u l a t i o n o f a T e l e v i s i o n C o d i n g S c h e m e " , P r o c e e d i n g s o f t h e I R E , J u n e 1 9 6 1 . < 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0302292/manifest

Comment

Related Items