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A small high-speed tunnel-diode memory. Walton, John Thomas 1964

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A SMALL HIGH-SPEED TUNNEL-DIODE MEMORY by JOHN THOMAS WALTON B.A.Sc* The U n i v e r s i t y of B r i t i s h Columbia, 1 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE In the Department of E l e c t r i c a l Engineering We accept t h i s t h e s i s as conforming to the standards r e q u i r e d from candidates f o r the degree of Master of A p p l i e d Science Members of the Department of E l e c t r i c a l Engineering The U n i v e r s i t y of B r i t i s h Columbia MARCH 1964 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department o r by h i s r e p r e s e n t a t i v e s . It i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permiss ion . Department of E l e c t r i c a l Engineering The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date March, 1964.  ABSTRACT The design of a 16 word 25 b i t tunnel-diode memory i s d e s c r i b e d . The memory i s word organized and employs d e s t r u c t i v e readout, the current change of state of the tunnel diodes being sensed. This arrangement r e q u i r e s only a r e s i s t o r and tunnel diode f o r each b i t s t o r e d . The d r i v e r c i r c u i t s f o r the memory serve three functions} 1) to couple i n t o the array the i n f o r m a t i o n to be s t o r e d , 2) to supply dc b i a s i n g to the array and, 3) to sense the current t r a n s i e n t on readout. Low impedance c i r c u i t s are r e q u i r e d , and two approaches are examined: the modified White emitter f o l l o w e r and the t r a n s -former coupled emitter f o l l o w e r . The former employs negative feedback to decrease i t s input impedance, while the l a t t e r employs a broadband transformer. The design of the modified White c i r c u i t n e c e s s i t a t e s an examination of the p r o p e r t i e s of t r a n s i s t o r s i n the 100 Megacycle frequency range. The c h a r a c t e r i s t i c s of a few high frequency^ t r a n s i s t o r s are shown. The transformer coupled c i r c u i t depends on the p r o p e r t i e s of the broadband transformer. These transformers are examined? and a design technique f o r v a r i o u s current r a t i o s i s g i v e n . Two sets of experimental r e s u l t s are d e s c r i b e d using 2X2 arrays to simulate the 16X25 memory. One employs 5 ma tunnel diodes, and the other 1 ma tunnel diodes„ Using the 1 ma array with transformer i n p u t , s u c c e s s f u l o p e r a t i o n with w r i t e pulses 10 nanoseconds wide i s demonstrated. i i ACKNOWLEDGEMENT The i n i t i a l work on t h i s t h e s i s p r o j e c t was s t a r t e d d u r i n g the Summer of 1962 while the author was employed at the Lawrence R a d i a t i o n Laboratory at Berkeley, C a l i f o r n i a . G r a t e f u l acknowledgement i s thus given to Mr. F.S« Goulding, who i n i t i a l l y suggested the t o p i c , to Mr. L. S c o t t , and to Dr. L.B. Robinson, w i t h whom the author had many u s e f u l d i s c u s s i o n s . At The U n i v e r s i t y of B r i t i s h Columbia, the author i s g r a t e f u l f o r the encouragement and ideas given him by h i s s u p e r v i s o r * P r o f e s s o r P.K. Bowers, and f o r the a s s i s t a n c e given him by Dr# P. Noakes and other members of the department. F u r t h e r , he i s g r a t e f u l f o r the help he r e c e i v e d from h i s f e l l o w graduate students. Acknowledgement i s given to NRC f o r a Research A s s i s t a n t -ship from Block Term Grant BT-68 and f o r a Studentship h e l d i n 1962-3. i x TABLE OF CONTENTS Page Ab S "b r c l C "b «..«««.. . . . . . . a . . . . . . . a a o a a a . a . a a a a . a a . . . LiS"fc O f 111 U S t r a l ; ionS • a a . a . a a . e a . . . a a a a a a a « . . « » * « v L i S "t O f Tab l e S ^ • a « s . * a 6 a « . . a . a a a a . a a a a a . a a a a a « . « « V 1 1 1 AcknOWl 6CLgemen"fc « . « o a o . a a a . a a a o o . a . . a a a « « a a . a s « . . . 1 ^ 1 a I n't T O d .UC~bion £ . e . . o « a a a a a . a a a a « a « a a a a a a a a a a e « * 1 1 «1 De S i g n Problem a e a a a a « . a a a a a a a a 8 « a . « a e e s * 1 1.2 Types of Memories ............. a • a . a . . . . • 1 2. Tunnel—Diode Arrays . . . . . . . . . . . . . a * . . . a . a . . . . . 8 2.1 P h y s i c a l P r o p e r t i e s of Tunnel Diodes .... 8 2.2 The Tunnel Diode as a Memory C e l l ....... 8 2.3 Array C o n f i g u r a t i o n s .................... 12 2.4 DC Aspects of the Array ................. 14 2.5 Tunnel-Diode Switching C h a r a c t e r i s t i c s • « 17 3. D r i v e r s f o r the Array .«•••..« 20 3.1 D r i v e r Requirements ..................... 20 3.2 P o s s i b l e D r i v e r C i r c u i t s 22 4. The M o d i f i e d White E m i t t e r Follower . . . . . . . a . . 27 4.1 DC Co n s i d e r a t i o n s . . . a . . . . . . . . . . . . . . . . . . . 27 4.2 High—Frequency C o n s i d e r a t i o n s ........... 34 5. The Transformer Coupled E m i t t e r Follower ..... 44 5.1 DC Co n s i d e r a t i o n s ......................« 44 5.2 HighMFrequency C o n s i d e r a t i o n s . a . . . . 46 o 6. Re s u l t s and Conclusions 50 6.1 Experimental Arrays ..................... 50 6.2 Comparison wi t h Other Devices 54 i i i Page 6.3 E x t e n s i o n of the Array ...... ............ 57 6.4 GoncilJlSiOnS . . . o o e o . e . e e . e o o o e o . o . a e . o . . . 58 Appendix I - Tunnel-Diode Switching C h a r a c t e r i s t i c s 60 Appendix I I - T r a n s i s t o r VHP Measurements ........ 64 A2.1 T r a n s i s t o r Parameters .................. 64 A2.2 C i r c u i t J i g Measurements ............... 71 Appendix I I I — R e s i s t o r - C a p a c i t o r Performance . ... 73 A3al R e s i s t o r Measurements . . « e .o ..<> o .. «... a • 73 A3.2 C a p a c i t o r Measurements ................. 75 Appendix IV — Broadband Transformers ........ ..... 78 A4.1 I n t r O d U C t i O n o o A o . . . o « o a c 0 « . o . o s o o . o o a e . 78 A4.2 Operation of B i f i l a r Transformers ...... 79 A4.3 Autotransformer Representation ......... 79 A4.4 Transmission Line Representation ....... 83 A4.5 Experimental Work ...................... 86 A4.6 Conclusions . . . . . . . . . o o a o o A a o o o o o . . . . . . . 89 Appendix V — MWEF Loop Gain . . . . . o . . . . . . . . . . . . . . . . . 90 Appendix VI — 2X2 Pulse Generator ................ 95 References . . . . . . . . . . . . . . . s o . . . . . . . . . . . . . . . . . . . . . . 100 i v LIST OF ILLUSTRATIONS Fi g u r e Page 1«1 B i t Organized Array . . . . . . . . . . . . . . . . . a o . . . 3 1 . 2 Vo rd~ Organi zed. Array o . o . o o . . o o « . . . o o a o o o « 3 2.1 Nondestructive Voltage D e t e c t i o n . . . « . « . 0 10 2.2 T r a n s i s t o r ^ T u n n e l Diode C e l l . . . . . . . . . a . . . 10 2.3 D e s t r u c t i v e Voltage D e t e c t i o n ............ 11 2.4 Nondestructive Current D e t e c t i o n ......... 11 2.5 D e s t r u c t i v e Current D e t e c t i o n . . .... .« ... . . . 12 2.6 P o s s i b l e A r r a y C o n f i g u r a t i o n s ....«......• 13 2.7 D e f i n i t i o n of Bin a r y States . . . . . a . . . . . . . » 14 2.8 Tunnel—Diode Design C h a r a c t e r i s t i c s ...... 15 2.9 Tunnel—Diode E q u i v a l e n t C i r c u i t ........«» 17 2.10 Tunnel—Diode Switching Current . . . c o o . . . . * 18 3.1 Examination of Y D r i v e r Admittance ....... 21 3.2 Block Diagram of D r i v e r C i r c u i t s ......... 22 3.3 A Simple E m i t t e r Follower ...............o 23 3.4 Comparison of y ^ with Y^ . . a o . . . . . . . . . . . . 24 i. 3.5 E v o l u t i o n of the M o d i f i e d White Emitter F O 1 X O 3? 4 > « a « e # o o o e e o 0 0 0 0 0 0 0 o e o o o o o o e o o o a * 2 f) 3.6 X and Y M o d i f i e d White E m i t t e r Followers . 26 3.7 X and Y Transformer Coupled E m i t t e r F o i l OWe r S . « . « . o . a o . o . . o o . « a o o o o o a . . . 0 0 . 0 0 0 26 4.1 The MWEF . . . . « « o « . « o . o o o . o . « oo o . . . o . o o o « . o 27 4.2 Power D i s s i p a t i o n as a F u n c t i o n of R 2 28 4.3 DC Output Voltage as a Fu n c t i o n of Temper-eft 113? 6 e « 0 O « « « # c o o 0 0 0 0 0 0 0 0 0 0 0 e o o o s 0 0 0 0 0 0 0 0 0 3 X 4.4 A Balance (X 3?cLlI* « o a « o o s o . 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 9 6 31 4.5 DC Compensated MWEF ........... o o . . . . . . . . . 32 4.6 Output Voltage S e n s i t i v i t y of the Y MWEF . 33 v F i g u r e Page 4.7 Output Voltage S e n s i t i v i t y of the X MWEF 33 4.8 The MWEF at High Frequencies ............ 35 4.9 T y p i c a l h ^ g Values ...................... 37 4*10 Current Gain f o r T d r i v e r of 1 ma Array . 39 4.11 L i m i t i n g Value of T d r i v e r Gain ......... 41 4.12 P o s s i b l e Detector C i r c u i t s .............. 42 5.1 X and Y TGEF . . . . . . o o o . . . . . . . . . . . . . . . . . . . 45 5.2 TCEF Admittance C h a r a c t e r i s t i c s ......... 47 5.3 Y. Drxver Gain . . . . . . . . . . . . o o a o o o o o o . . . . . . 48 6.1 Block Diagram of 2X2 Array .... ......«• ... 51 6.2 Read—Write S i g n a l s f o r Si n g l e C e l l ...... 51 6.3 Read—Write S i g n a l s f o r 2X2 Array ........ 52 6.4 D r i v e r Arrangement f o r 5 ma Array ....... 52 6.5 Waveforms f o r 5 ma Array ................ 53 6.6 TCEF D r i v e r C i r c u i t s .................... 54 6.7 Waveforms f o r 1 ma Array . . . . . . . . . . . . . . 5 5 6.8 "1" and "0" Output Pulses ............... 55 6.9 F u l l — W r i t e Pulse from Tektronix P u l s e r .. 57 A l . l Analogue Setup of Tunnel-Diode DEq ........ 61 A1...2 Analogue Setup f o r Generation of Input . * 62 A1.3 Tunnel—Diode Switching T r a j e c t o r i e s as Simulated on an Analogue Computer ....... 62 A2.1 Test Arrangement Block Diagram .......... 64 A2.2 Me asur ed h s o . o . o . o . o . o o o . 0 . 0 . 0 0 . 0 . 0 . . 65 f e A2.3 The [ y ] b Parameters f o r the 2N834 ....... 67 A2.4 The [y] Parameters f o r the 2N1143 ...*«> 69 A2.5 Comparison of Gain from the y'.s and from Measurements . . . . e o . . o . o o o o . o . o . . . o . o o o . . 72 v i F i g u r e Page A3.1 R e s i s t o r Measurements 74 A3«2 R e s i s t o r Mounting ..••«..« ...<>.... • 74 A3«3 C a p a c i t o r Measurements .-,. „ »»<> .« « . 76 A3«4 C a p a c i t o r Mounting ...«.»<,. „ „ o»<> „ <, » « »„ . o « « 75 A3«5 C a p a c i t o r s i n P a r a l l e l 0000000000000000000 75 A4«l 1:1 I n v e r t i n g Transformer o o o o o o o o o o o o o o o . 79 A4.2 Autotransformer E q u i v a l e n t of 1:1 Trans-A4.3 A 1:2 Current Transformer . o o o o o o o o o o o . . . . 80 A4.4 Examples of Autotransformer Design T G C lllT X C^ U G A o e e o o o e o o o o o o o o o o 00000000000040 8 1 A4.5 Response of 1:4 Transformer ...... . .. 82 A4.6 Response of 1:2 Transformer f o r DiffGrGn*fc f i n d i n g s o o o o oo o«o o o o o o«o o o o o o * « 83 A4.7 1:2 Transformer with Transmission Line Ec^LlXVclX 6Il"fc « « « * o o o e * e oo ooeo oeoo o « o o o o o o o « « 84 A4.8 T h e o r e t i c a l Response Curves <>... »o .« . « „ . . . 85 A4.9 Experimental Res u l t s o . o o o o o . o o o . o o ,<,<,. s « . 87 A4.10 Comparison of T h e o r e t i c a l and Experimental Re S u i t s #. .««..« 0000 0000 00000000 0000 00000. 88 A 5 o1 S i m p l i f i e d MWEF . o o o o o o o o o o o e o o o o o o o o o o o . . 90 A5.2 MVEF f o r Gain C a l c u l a t i o n s .0000.00000. ... 91 A5.3 Current Gains from y Parameters . . . o o o o . . . 93 A6.1 2X2 Pulse Generator Block Diagram .....•«. 95 A6.2 A s t a b l e , Monostable. and B i s t a b l e C i r c u i t s 96 A6 o 3 PulS e Shape r . .000000000.00000000000000.00. 97 A6.4 OR and AND—GATES 0000 0.. o o o o o o o . • • « • . • 98 A6 o 5 Delay C i r C U i t e o o o . o o o 000000000000000000.0 98 A6.7 Waveforms from 2X2 Pulse Generator . . 0 , . . . 99 v i i LIST OF TABLES Table Page .2.1 Bias Arrangements ...o .oo... o«. ...... .... 16 2.2 Current Requirements .................... 17. 2.3 Switching Current C h a r a c t e r i s t i c s ...... • 19 4.1 R e s i s t o r Values i n Ohms ................. 29 4.2 Current and Power D i s s i p a t i o n Ranges .... 30 A2.1 Frequency at which j h^ g j = 1 ............ 66 v i i i 1. INTRODUCTION 1.1 Design Problem This t h e s i s w i l l be concerned with the development of a small high—speed storage u n i t . The s p e c i f i c a t i o n s f o r t h i s u n i t were decided upon while the author was employed at the Lawrence R a d i a t i o n Laboratory at Berkeley, C a l i f o r n i a . In general the s p e c i f i c a t i o n s f o r the store were t h a t i t was to have a r e a d -w r i t e time of l e s s than 100 nanoseconds and- to h o l d 16 words of 25 b i n a r y b i t s each. The intended use f o r the store was i n f a s t - c o i n c i d e n c e n u c l e a r i n s t r u m e n t a t i o n and the s p e c i f i c a t i o n s were determined to make the device compatible with e x i s t i n g equipment. Furthermore, thd storage i s to be only temporary as the i n f o r m a t i o n i s subsequently t r a n s f e r r e d to a slower permanent memory. The store thus i s r e q u i r e d to act as a b u f f e r between the randomly o c c u r r i n g s i g n a l s of the nucl e a r d e t e c t o r s and the slower permanent memory and,is consequently c a l l e d a b u f f e r s t o r e . The technology of d i g i t a l storage has advanced c o n s i d e r a b l y i n the past decade. In hand with t h i s t e c h n o l o g i c a l advance has been the advance i n terminology. Thus i n the f o l l o w -i n g s e c t i o n s of t h i s chapter a b r i e f review of a few of the aspects of d i g i t a l storage technology and terminology w i l l be gi v e n . Furthermore, j u s t i f i c a t i o n w i l l be shown f o r the design d e c i s i o n s t h a t r e s u l t i n the array of Chapter 2. 1 02 Types of Memories Memory arrays f o r the storage of d i g i t a l i n f o r m a t i o n are c l a s s i f i e d a c c ording to l ) the type of addressing scheme, 2) the method of readout* and 3) the type of memory c e l l used i n the a r r a y . The way i n which the l o c a t i o n i s determined f o r d i g i t a l i n f o r m a t i o n to be read i n t o or out of the memory-is c a l l e d a d d r e s s i n g . Two c o n c e p t u a l l y d i f f e r e n t modes e x i s t ; s e q u e n t i a l addressing, and c o n d i t i o n a l or random a d d r e s s i n g . With the former i n f o r m a t i o n i s ordered s e q u e n t i a l l y with r e s p e c t to time, while with the l a t t e r no such temporal o r d e r i n g i s necessary. Consequently, i n f o r m a t i o n s t o r e d i n a random addressing (random access) a r r a y can be readout i n a time sequence d i f f e r e n t than t h a t used f o r reading i n ; whereas with s e q u e n t i a l addressing the input and output sequences are always the same. Random access memories have been the subject of much developmental work i n the past decade. This has been prompted by the concept of the stored-program d i g i t a l computer where the prograjti and data are st o r e d i n the machine. With t h i s con-cept, access to any p a r t of the memory f a c i l i t a t e s the programming and the l o a d i n g of data. The i n f o r m a t i o n s t o r e d i n a d i g i t a l memory i s i n b i n a r y ( 0 , l ) coded form. A s i n g l e d i g i t of the b i n a r y code, (0 or l ) , i s c a l l e d a b i t and f o r a given memory a f i x e d number of b i t s comprise an e n t i t y c a l l e d a word. The b i n a r y coding r e q u i r e s elements having two d i s t i n c t s t a t e s and these elements are u s u a l l y c a l l e d memory c e l l s , c e l l s , or b i t s . The memory c e l l s can be wired i n two d i s t i n c t p a t t e r n s r e s u l t i n g i n the b i t - o r g a n i z e d a r r a y and the word-organized a r r a y . These are i l l u s t r a t e d i n Figure's 1 . 1 and 1 . 2 f o r equal 3 V A D D R E S S I N G - S E L E C T O R S fa = 4 .71 - </) Ul 0! O O < v J<L \ \ \ \ \ \ \ \ \ * x til Xir^tAk——f*s——— f * - ^ * - * * ... I \ \ \ I I \ \ \ 1 \ \ \ I / / / S T / LINE B i r Y2 Y3 \ ¥4 \ / -A-/ 1 \ \ \ I I \ \ \ I I N \ \ \ / / / / C \ / / \ ^\—^ ^ —l tr | \ \ \ 1 \ \ W B I T L I N E S F i g u r e 1.1. B i t - O r g a n i z e d Array f o r N = 16 Words o b ii> Ul </) VJ z Ji tn ui a Q a < of 1 •XI f * = 4 B i t s Hi s f Each \ il ) K s / ' N 1 f* ) \ ( f ) \ ) K 1 / ) ^ 1 /" * I ) ( 1 f > <• \ / r ^ ) c > <• \ f ) \ p I. f* > \ ) f ) K r ^ 1 f > > ^ / 1 f k /• ) \ \ t t i t > \ V. t ' ( ) <• 1 ( ) \ > \ ' \ \ ( > \. ^ \ { \ / • \\ f > \ \ c J v * \ ) K \ t > \ \ f f ) \ f * \ \ ^ ) \ •1 r ) v. 1 f I ) ' c ) K 1 t ) y ) ( \ <. x . S f ) \ > C ) ^ \ r * \ \ \ ( ' \ XI6 J •> / * \^ / ) \ 1 y > \ d ) \ >~ U- 16 V/OW.T3S W = <* B I T Lines F i g u r e 1*2. Word-Organized Array f o r N = 16 Words of•w = 4 B i t s Each c a p a c i t i e s : N = 16 words of w = 4 b i t s each. In t h e - b i t organized array of F i g u r e 1,1, the memory c e l l s are arranged i n w pl a n e s . The f i r s t plane s t o r e s the f i r s t b i t of each word* the second plane the second b i t * and so on, To l o c a t e a word i n memory r e q u i r e s a coincidence between the X l i n e and T l i n e corresponding to the word. For example* to l o c a t e the word whose b i t s are stored i n the top l e f t corner of each plane, the X ( l ) l i n e and Y ( l ) l i n e must be a c t i v a t e d simultaneously by the addressing selectors,, The i n f o r m a t i o n i s then i n s e r t e d or withdrawn u s i n g the w b i t l i n e s . In the word-organized a r r a y of Figure 1.2, the b i t s of each word are st o r e d i n one h o r i z o n t a l row of c e l l s . The f i r s t b i t of each word i s s t o r e d i n the f i r s t column, the second b i t i n the second column* and so on. Here, however, no coincidence i s r e q u i r e d f o r l o c a t i n g a word i n the memory as the N X - l i n e s are t i e d d i r e c t l y to the N words i n storage. Thus a word i s l o c a t e d simply by a c t i v a t i n g i t s X l i n e * the i n f o r m a t i o n then being r e a d - i n or read—out on the v e r t i c a l b i t (or T) l i n e s * From the preceding i t i s seen that f o r N—word storage* a b i t - o r g a n i z e d memory r e q u i r e s 2jN addressing s e l e c t o r s while a word-organized memory r e q u i r e s N such s e l e c t o r s . -Consequently* f o r l a r g e systems* b i t o r g a n i z a t i o n i s u s u a l l y employed to reduce the number of addressing s e l e c t o r s . However, f o r small memories ( i . e . l e s s than 64 words^^) t h i s r e d u c t i o n does not warrant the i n c r e a s e d complexity r e q u i r e d f o r a c h i e v i n g the coinc i d e n c e s of the b i t - o r g a n i z e d a r r a y . As the work to be di s c u s s e d here i s concerned with the development of a small memory, the word-organized a r r a y i s p r e f e r r e d . 5 A second f e a t u r e i n the c l a s s i f i c a t i o n of an ar r a y i s the method of readout*, Readout i s the process of determining the i n f o r m a t i o n content of the memory c e l l s . Two techniques are p o s s i b l e : n o n - d e s t r u c t i v e and d e s t r u c t i v e readout. With non-d e s t r u c t i v e readout the memory c e l l s are u n a f f e c t e d by the read o p e r a t i o n . With d e s t r u c t i v e readout the c e l l s are a f f e c t e d as they are r e s e t to t h e i r quiescent s t a t e , the change of s t a t e , i f p resent, being d e t e c t e d . The type of readout d e s i r e d w i l l depend on the uses of the a r r a y . In some a p p l i c a t i o n s i t i s h i g h l y d e s i r a b l e to have no n — d e s t r u c t i v e readout. However, with temporary storage d e s t r u c t i v e readout i s p r e f e r a b l e as i t e l i m i n a t e s a c y c l e r e q u i r e d f o r r e s e t t i n g the c e l l s . In the previous d i s c u s s i o n on word-organized a r r a y s , i t was po i n t e d out t h a t only the X l i n e s (see F i g . 2b) need be e x c i t e d to l o c a t e a word i n the a r r a y . This f e a t u r e , coupled with d e s t r u c t i v e readout* can l e a d to very short readout times as the c e l l s can be o v e r d r i v e n to achieve a r a p i d change of s t a t e * Thus i t i s seen t h a t a word-organized d e s t r u c t i v e r e a d -out a r r a y b e s t meets the requirements of a b u f f e r s t o r e . The t h i r d c h a r a c t e r i s t i c of a b i n a r y storage u n i t i s the memory c e l l . For each b i t to be s t o r e d , there must be a device e x h i b i t i n g two s t a b l e s t a t e s * These s t a t e s can be e i t h e r n a t u r a l states of the dev i c e * or s t a t e s induced by dc or ac b i a s i n g . Examples of the former are ferromagnetic ( f e r r i t e c ores, t h i n f i l m s ) and superconductive memories, while of the l a t t e r 5 t u n n e l - d i o d e and parametric memories. Of these devices the tunnel diode at the present time has 6 the f a s t e s t switching time* I t must he noted however t h a t the switching time alone does not determine the access time (time r e q u i r e d f o r a read-write c y c l e ) of a storage u n i t . A d d i t i o n a l time i s l o s t due to the time f o r propagation of i n f o r m a t i o n through the s t o r e , f o r a m p l i f i c a t i o n of s i g n a l l e v e l s . f o r r eading and w r i t i n g t r a n s i e n t s to subside and f o r addressing the memory matrix,, C o n s i d e r i n g the f i r s t two of these, along (2) with the switching time of the dev i c e , Rajachman v ' has shown that f o r memories of l e s s than 1024 words an access time of 10 nanoseconds i s u l t i m a t e l y p o s s i b l e f o r a tunnel-diode s t o r e . This i s a f a c t o r of t e n b e t t e r than that which could be achieved by a comparable s i z e d ferromagnetic or superconductive unit© However^ f o r l a r g e r storage u n i t s the magnetic devices tend to be s u p e r i o r as t h e i r smaller p h y s i c a l s i z e and methods of f a b r i c a t i o n begin to have a grea t e r i n f l u e n c e on the access time than does the switching time. Thus the tunnel diode i s s u i t a b l e f o r small high—speed memories and at present i s the only device capable of r e a d i l y a c h i e v i n g access times of l e s s than 100 nanoseconds. Prom the preceding d i s c u s s i o n i t i s thus apparent t h a t a word-organized, d e s t r u c t i v e readout, tunnel-diode memory would best meet the requirements of the b u f f e r s t o r e . The memories as shown i n F i g u r e s 1.1 and 1.2 c o n s i s t of the memory c e l l s and addressing s e l e c t o r s . The addressing s e l e c t o r s i n t u r n are composed of l o g i c c i r c u i t s , d r i v i n g c i r c u i t s , and a dc supply,, The l o g i c c i r c u i t s decode the command signalswhich give the address of the r e q u i r e d word. The d r i v e r c i r c u i t s i n s e r t (or withdraw) i n f o r m a t i o n i n t o (or from) the a r r a y , w h i l e t h e dc s u p p l y e s t a b l i s h e s t h e two r e q u i r e d s t a b l e s t a t e s o f t h e t u n n e l d i o d e . Of t h e s e , o n l y t h e d r i v e r c i r c u i t a n d t h e dc s u p p l y w i l l be c o n s i d e r e d i n t h i s t h e s i s -8 2. TUNNEL-DIODE ARRAYS This chapter "will deal with the c h a r a c t e r i s t i c s of tunnel diodes and t h e i r a p p l i c a t i o n to d i g i t a l storage <> To t h i s end v a r i o u s c o n f i g u r a t i o n s of tunnel-diode c e l l s are examined* wi t h c o n c l u s i o n s drawn as to the optimum c o n f i g u r a t i o n from the p o i n t of view of minimum number of elements r e q u i r e d f o r a c e l l . The dc supply requirements f o r the array are then derived,, F i n a l l y , the s w i t c h i n g of a tunnel diode i s examined, and the bandwidth requirement of the a r r a y determined,, 2.1 P h y s i c a l P r o p e r t i e s of Tunnel Diodes In the i n v e s t i g a t i o n of the p r o p e r t i e s of h e a v i l y doped (3 V semiconductor pn j u n c t i o n diodes, E s a k i x i n 1957 developed a diode which e x h i b i t e d a v o l t a g e — s t a b l e negative conductance r e g i o n . This c h a r a c t e r i s t i c r e s u l t s from a t u n n e l i n g of e l e c t r o n s across the pn j u n c t i o n . As t u n n e l i n g i s a quantum mechanical process, the e l e c t r o n s t r a v e r s e the junction,-) at the speed of l i g h t . Consequently the diode i s an extremely high-frequency d e v i c e , i t s frequency response i n f a c t being l i m i t e d at s e v e r a l Kilomegacycles by i t s j u n c t i o n c a p a c i t a n c e . F u r t h e r , as the diode does not depend on m i n o r i t y c a r r i e r s , i t s behaviour should be f a i r l y w e l l independent of temperature, r a d i a t i o n e f f e c t s and surface contamination,, 2.2 The Tunnel Diode as a Memory C e l l In u s i n g tunnel diodes as b i n a r y c e l l s there are b a s i c a l l y (4) three approaches. These are the Goto P a i r v , v o l t a g e d e t e c t i o n , 9 and c u r r e n t detection,, The s t a t i c c h a r a c t e r i s t i c s of the l a t t e r are shown i n Fi g u r e s 2*1 and 2 . 2 . I t should be noted that the c o n f i g u r a t i o n s d i s c u s s e d here are the b a s i c memory c e l l and would be repeated throughout the memory. The Goto P a i r was r e p o r t e d e a r l y i n the development of tunnel-diode memory u n i t s and presents the f e a t u r e s of non" d e s t r u c t i v e readout and l o g i c g a i n ( i . e . a small input s i g n a l causes a large o u t p u t ) . The Goto P a i r has r e a l a p p l i c a t i o n as a memory c e l l only where l o g i c g a i n i s r e q u i r e d , and con-sequently w i l l not be used here,, Voltage d e t e c t i o n of the s i n g l e diode element a l s o lends i t s e l f to e i t h e r d e s t r u c t i v e or nondest r u c t i v e readout. Several schemes have been proposed f o r determining the voltage s t a t e of the tunnel diode i n a nondestructive manner. Among these are a combination of a diode and tunnel diode shown i n Fig u r e 2 . 1 a ^ ^ * and the tunnel d i o d e - t r a n s i s t o r combination of Figure 2 . 2 . Figure 2«lb shows the l o a d l i n e s f o r the operations of reading and w r i t i n g as w e l l as the quiescent s t a t e of the diode c e l l . To determine the state of the tunnel diode nortde s t r u c t i v e l y , a small p r e c i s e current pulse i s a p p l i e d to the read p i n . In an array t h i s p i n i s al s o connected to an output t r a n s i s t o r . The current that flows i n t h i s t r a n s i s t o r depends on the state of the tunnel d i o d e 0 The a p p l i e d current pulse here must be small so that i t does not cause the tunnel diode to switch. The or d i n a r y pn diode of Figure 2 . 1 not only i s o l a t e s the tunnel diode from the r e s t of the array during the switc h i n g p e r i o d , but i t a l s o provides a n o n l i n e a r l o a d l i n e to accentuate the d i f f e r e n c e i n current l e v e l s of the two p o s s i b l e v o l t a g e s t a t e s . The scheme here i s 10 Figure 2„1, Nondestructive Voltage D e t e c t i o n c l a s s i f i e d as v o l t a g e d e t e c t i o n as i t i s the v o l t a g e across the tunnel diode which d e f i n e s the c u r r e n t flow i n the pn diode* \NR.irE PIN •o READ PIN F i g u r e 2*2* T r a n s i s t o r - T u n n e l Diode C e l l The c i r c u i t of F i g u r e 2„2 i s i n essence the same as t h a t of F i g u r e 2»1 with the t r a n s i s t o r r e p l a c i n g the pn diode. How-ever w i t h t h i s , the i n t e r r o g a t i o n of the tunnel diode would he made on the c o l l e c t o r of the t r a n s i s t o r thus e l i m i n a t i n g the need f o r a c a r e f u l l y r e g u l a t e d read pulse amplitude,, For d e s t r u c t i v e " (6 ) readout of the v o l t a g e s t a t e , the c i r c u i t of Figure 2«3 could be used, the i n d u c t o r i n p a r a l l e l with the tunnel diode d e t e c t i n g the v o l t a g e change. -o -o O U T P U T F i g u r e 2*3* D e s t r u c t i v e Voltage D e t e c t i o n The preceding c i r c u i t s have det e c t e d the s t a t e of the tunnel diode by observing i t s v o l t a g e c o n d i t i o n s C i r c u i t s can a l s o be designed to determine the c u r r e n t s t a t e of the tunnel diode i n e i t h e r a d e s t r u c t i v e or n o n d e s t r u c t i v e manner, The c i r c u i t of Figure 2*4 would enable a n o n d e s t r u c t i v e determination of the c u r r e n t s t a t e to be made, This c i r c u i t i s the c u r r e n t (7) e q u i v a l e n t of Figure 2,2* The c i r c u i t shown i n Figure 2*5 has a p p l i c a t i o n i n d e s t r u c t i v e readout employing current d e t e c t i o n . This c i r c u i t employs the i n d u c t o r to d e t e c t the c u r r e n t change of s t a t e * The c i r c u i t as shown i n Figure 2.5 c o n s i s t s of a tunnel F i g u r e 2.4. Nondestructive Current D e t e c t i o n 12 diode, a r e s i s t o r and an i n d u c t o r . I f , however, the c i r c u i t i s used i n a word-organized a r r a y (Figure 1.2), the i n d u c t o r need not be repeated f o r each c e l l of the a r r a y . This i s apparent i O U T P U T F i g u r e 2.5* D e s t r u c t i v e Current D e t e c t i o n since any change i n the tunnel—diode current must a l s o occur i n the T l i n e s of the a r r a y * Thus, f o r " a word—organized cu r r e n t d e t e c t i n g a r r a y , the b a s i c memory c e l l c o n s i s t s of j u s t a r e s i s t o r and a tunnel diode* This c e l l has the l e a s t number of elements of the f o r e g o i n g * and consequently i s the one t h a t i s used i n the subsequent work* 2.3 A r r a y C o n f i g u r a t i o n s There are two c o n f i g u r a t i o n s t h a t could be used with c u r r e n t d e t e c t i o n i n a word-organized a r r a y . They are shown i n F i g u r e 2*6. For the arrangement of F i g u r e 2.6a (the E s a k i (8) A r r a y ) the X and X l i n e s r e q u i r e the same p o l a r i t y pulses f o r w r i t i n g . Furthermore,only one p o l a r i t y of dc b i a s i s i r e q u i r e d . However,on readout only one h a l f of the c u r r e n t change would flow i n the X l i n e s and t h i s i s a s e r i o u s drawback as the c u r r e n t change between s t a t e s i s small (e.g. about 0*5 ma f o r a 1 ma tunnel d i o d e ) * The c o n f i g u r a t i o n of Figure 2.6b r e q u i r e s two d i f f e r e n t dc supply v o l t a g e s and the d r i v e r s r e q u i r e opposite p o l a r i t y pulses f o r w r i t i n g . However, the e n t i r e c u r r e n t change now reaches the I l i n e s on readout. This i s the arrangement used i n the a r r a y . W 'BIT (Yl DRIVERS X2 X3 X5 > W O R D 5 (a) IS (b) F i g u r e 2»6i, P o s s i b l e Array C o n f i g u r a t i o n s 2.4 The DC Aspects of the Array The memory to be designed here i s t h a t of 16 words of 25 b i t s each. One of the design q u a n t i t i e s to be determined i s the dc supply requirements of the a r r a y . For t h i s , the tunnel-diode dc c h a r a c t e r i s t i c s are now examined. The tunnel—diode c h a r a c t e r i s t i c , shown i n Fig u r e 2.7* has three p o i n t s of i n t e r s e c t i o n with the quiescent l o a d l i n e : A* B, and C. Of these, only A and B are stable, s t a t e s , C (9) being u n s t a b l e . ' Thus the s t a t e s A and B can be used to correspond to the (0,1) coding of the b i n a r y system. In s t a t e B the t o t a l power d i s s i p a t e d i n the diode and r e s i s t o r i s l e s s than i n s t a t e A. Thus s t a t e B w i l l be used f o r the 0 s t a t e , W R I T E t£>r\V L I N E W R . \ T B C I N E F i g u r e 2.7* D e f i n i t i o n of Bi n a r y States since the diode spends most of i t s time i n t h i s s t a t e , being r e t u r n e d to i t by the read o p e r a t i o n . The diode then i s normally i n the B s t a t e * and the a p p l i e d v o l t a g e , V , must be 15 decreased to w r i t e a "1" i n t o the c e l l . The w r i t e procedure i n v o l v e s a coincidence between the X and T l i n e s of the word. This coincidence i s shown i n Figure 2.7 by drawing i n the h a l f -w r i t e and f u l l - w r i t e l o a d l i n e s . The read o p e r a t i o n i n v o l v e s i the X l i n e alone and i s shown as the read l o a d l i n e i n the f i g u r e . Since w i t h c u r r e n t d e t e c t i o n the l a r g e s t p o s s i b l e c u r r e n t change between s t a t e s A and B i s r e q u i r e d f o r ease i n d e t e c t i o n , the load l i n e should be as steep as the tunnel-diode c h a r a c t e r i s t i c s w i l l a l l o w . In t h i s r e s p e c t Germanium diodes are s u p e r i o r to S i l i c o n and Gallium Arsenide types. S i l i c o n diodes have a lower peak c u r r e n t to v a l l e y c u r r e n t r a t i o than Germanium, and Gallium Arsenide diodes have e x h i b i t e d r e l i a b i l i t y problems. Thus, Germanium tunnel diodes were used i n t h i s d e s i g n . Figure 2.8 shows the boundaries of the v a r i a t i o n i n the LN3713 1N3717 v l 58 mv 58 mv V 2 395 mv 395 mv V 3 315 mv 315 mv V 4 72 mv 72 mv h .975 ma 4. 58 ma .140 ma . 60ma H .075 ma .350 ma X4 1.075 ma 4.82 ma Figure 2.8. Tunnel-Diode Design C h a r a c t e r i s t i c s peak and v a l l e y c h a r a c t e r i s t i c s , d e f i n e d i n Figure 2.7, of the General E l e c t r i c 5 ma and 1 ma tunnel diodes. These boundaries are used to determine the l o a d i n g r e s i s t o r , R^, the quiescent a p p l i e d v o l t a g e , ^ aQ* ^ e V T ^ ^ e s i g n a l amplitude, V w , and the read s i g n a l amplitude, v r , a l l of which are i n t e r r e l a t e d . Thus,using F i g u r e 2.8 the f o l l o w i n g four equations can be w r i t t e n ; V a 0 + * VaO = + V l V a 0 - V2 - & VaO = + V 2 V a 0 - Vw + ^ V a 0 = H\ + v 3 V a 0 + V r - * VaO = URL + V where the values of i ^ , x^j e t c , are the values given f o r the boundary p o i n t s , and ^>VaQ i s the v a r i a t i o n i n the supply v o l t a g e . I f S^ aQ i s allowed to be 20 mv ( c f . S e c t i o n 4 . l ) , a ^ then the value s of Table 2.1 r e s u l t f o r the 1 ma and 5 ma diodes. I t should be noted that the values l i s t e d f o r v are r . minimum* A small v i s d e s i r a b l e so th a t the read s i g n a l does JEDEC NO. Peak Current (ma) Load Resistance (ohms) V a 0 < m v ) v (mv) wv ' v r(mv) 1N3713 1 645 666 322 86 1N37T7 4.7 130 676 334 77 Table 2.1. Bias Arrangements not a p p r e c i a b l y redude the s i g n a l from the tunnel diode. This i s examined f u r t h e r i n S e c t i o n 2.5. 17 The c u r r e n t r e q u i r e d f o r s t a t e s A and B i s obtained by-drawing the c a l c u l a t e d l o a d l i n e s on the dc c h a r a c t e r i s t i c s of the 1 ma and 5 ma tunnel d i o d e s . The r e s u l t s of t h i s are gi v e n i n Table 2.2 f o r a 16 word. 25 b i t a r r a y . Peak Current (ma) "A" State Current / Diode (ma) "B" State Current / Diode (ma) X Supply Current Range (ma) % Supply Current Range (ma) 1 0*975 0.48 12-24.6 7.7-15.6 4.7 4.58 2.8 70-115 44.8-73.4 Table 2*2. Current Requirements 2.5 Tunnel-Diode Switching C h a r a c t e r i s t i c s The tunnel diode and l o a d r e s i s t o r can be represented by the e q u i v a l e n t c i r c u i t of Fi g u r e 2.9^"^.' Here L represents S the t o t a l s e r i e s inductance of the c i r c u i t , R the t o t a l s e r i e s s 777 Figure 2.9. Tunnel-Diode E q u i v a l e n t C i r c u i t r e s i s t a n c e , C the junction, c a p a c i t a n c e , and f ( v ) the s t a t i c i - v c h a r a c t e r i s t i c s of the tunnel diode. This c i r c u i t i s d e s c r i b e d by the f o l l o w i n g d i f f e r e n t i a l equations; 18 - r r = V - R l - v dt a s Cdv . „/ N dt = 1 " f ( v ) where i s the dc b i a s v o l t a g e and v o ( t ) i s the input s i g n a l . a Using a Donner Analogue Computer these equations were solved f o r the change i n current t h a t . o c c u r s when the tunnel diode i s switched by a step input from, the "1" s t a t e to the "0" s t a t e . The d e t a i l s of t h i s computation are g i v e n i n Appendix I . Fi g u r e 2.10 shows the s w i t c h i n g c u r r e n t as a f u n c t i o n of time, with the magnitude of the : i n p u t , YQ , as a parameter. In each case here the r i s e time of the input was the same, about 15 nanoseconds. I f these curves are now approximated by s t r a i g h t l i n e s as shown on the 0.1 v o l t curve, then the v a l u e s S W I T C H IN& C U R R B M T v.o T I M E \M M A N O S E C O N D S Figure 2.10. Tunnel—Diode Switching Current l i s t e d i n Table 2.3 r e s u l t . From t h i s t a b l e i t i s seen that as the input s i g n a l v o l t a g e i s i n c r e a s e d , the switching time^T i s decreased. However^so a l s o i s the output s i g n a l c u r r e n t . The former e f f e c t i s due to the f a c t t h a t the rate of change of the tunnel-diode v o l t a g e i s p r o p o r t i o n a l to the d i f f e r e n c e between the s i g n a l c u r r e n t and the tunnel-diode c h a r a c t e r i s t i c The l a t t e r e f f e c t i s due to the input s h i f t i n g the second stable p o i n t , B. Input AI = Max I - Min I (ma) T ( nanoseconds) 0.1 0.54 3,3 0.2 0.44 3.0 0.3 0.40 2.5 Table 2.3. Switching Current C h a r a c t e r i s t i c s The bandwidth r e q u i r e d to tra n s m i t the cur r e n t s i g n a l shown i n Fig u r e 2.10 i s of the order of 0.35/T where T i s d e f i n e d i n the f i g u r e . Thus^using the values given i n Table 2 i t i s seen t h a t a 3 db bandwidth of the order of 110 - 140 Megacycles i s r e q u i r e d f o r t r a n s m i s s i o n of the c u r r e n t s i g n a l , with some response up to 300 Megacycles, to ensure smooth r o l l - o f f . 20 3. DRIVERS POR THE ARRAY In t h i s chapter the c h a r a c t e r i s t i c s r e q u i r e d of the d r i v e r c i r c u i t s are g i v e n . Prom these the c o n c l u s i o n i s drawn t h a t the d r i v e r s should be some form of an e m i t t e r - f o l l o w e r c i r c u i t . Two v a r i a t i o n s of an e m i t t e r — f o l l o w e r c i r c u i t are proposed f o r f u r t h e r study. These are i n v e s t i g a t e d i n Chapters 4 and 5. 3.1 D r i v e r Requirements The fundamental requirement of the d r i v e r c i r c u i t s i s the c o u p l i n g i n t o the a r r a y of the b i n a r y i n f o r m a t i o n to be s t o r e d . Por the tunnel—diode a r r a y t h i s means that the d r i v e r s should have a low output impedance. Any impedance due to the d r i v e r s w i l l have the e f f e c t of decreasing the steepness of the load l i n e on the tunnel-diode c h a r a c t e r i s t i c , and thus r e q u i r e a l a r g e r d r i v e v o l t a g e . Therefore, f o r w r i t i n g i n t o the a r r a y , the d r i v e r s should be v o l t a g e sources ( i . e . have zero output impedance)• A second requirement w i l l apply to the Y d r i v e r s only* they should act as d e t e c t o r s . That i s the Y d r i v e r s should be designed to have some means of d e t e c t i n g the c u r r e n t t r a n s i e n t which occurs i f the tunnel diode switches d u r i n g readout. This means the i n p u t admittance l o o k i n g from the array i n t o the Y d r i v e r should be g r e a t e r than the t o t a l admittance of the other c e l l s t i e d to that d r i v e r . Figure 3.1 shows what i s i n v o l v e d . Consider a c u r r e n t change in,say,the (XI, Y l ) c e l l of the f i g u r e . When t h i s c u r r e n t step reaches the p o i n t A, i t sees the 21 W O R D X> W O R D X7 F i g u r e 3 . 1 . E x a m i n a t i o n o f Y D r i v e r A d m i t t a n c e i n p u t a d m i t t a n c e -of t h e Y d r i v e r , y ^ , s h u n t e d b y t h e a d m i t t a n c e o f t h e o t h e r c e l l s t i e d t o t h e Y I l i n e . U s i n g t h e l o a d r e s i s t o r s d e r i v e d i n S e c t i o n 2 . 4 and n e g l e c t i n g t h e i m p e d a n c e o f t h e t u n n e l d i o d e s t h e m s e l v e s , t h e a d m i t t a n c e o f t h e o t h e r c e l l s t i e d t o t h e Y I l i n e w o u l d . b e o f t h e o r d e r o f 1 5 x l / 6 8 0 = 22 m mhos f o r t h e 1 ma a r r a y a n d 1 5 x 1 / 1 3 0 = 115 m mhos f o r t h e 5 ma a r r a y . (The a c t u a l m e a s u r e d a d m i t t a n c e i s g i v e n i n F i g u r e 3 . 4 ) . I d e a l l y , f r o m t h e p o i n t o f v i e w o f e l i m i n a t i n g c r o s s t a l k , ( i . e . s w i t c h i n g o f c e l l s o t h e r t h a n t h e d e s i r e d o n e s ) t h e i n p u t a d m i t t a n c e s h o u l d be i n f i n i t e . T h u s , f o r i n s e r t i n g a n d w i t h d r a w i n g i n f o r m a t i o n f r o m t h e a r r a y t h e d r i v e r a d m i t t a n c e s h o u l d be s e v e r a l h u n d r e d m m h o s . F i n a l l y , i t w o u l d be d e s i r a b l e t o h a v e t h e d r i v e r c i r c u i t s s u p p l y t h e dc b i a s i n g f o r t h e a r r a y . M o s t t r a n s i s t o r s r e q u i r e 5 -20 ma dc b i a s f o r opt imum o p e r a t i o n , a n d t h i s c u r r e n t c a n t h e n be u s e d f o r t h e a r r a y b i a s i n g . T h i s scheme p l a c e s some dc r e s t r i c t i o n s on t h e t r a n s i s t o r s t o be u s e d , b u t a p p e a r s t o be t h e m o s t e f f i c i e n t f r o m t h e p o i n t o f v i e w o f t o t a l c u r r e n t r e q u i r e d f o r the memory. T h i s , however, w i l l r e q u i r e that each d r i v e r have good dc s t a b i l i t y and i n a c h i e v i n g t h i s s t a b i l i t y (see S e c t i o n 4 . l ) some current e f f i c i e n c y i s l o s t . Furthermore, f o r some of the d r i v e r s , p a r a l l e l t r a n s i s t o r s w i l l be needed to meet the cu r r e n t demands. I t i s , t h e r e f o r e , not c e r t a i n t h a t t h i s c r i t e r i o n w i l l l e a d to more economical design than one i n which a l l or p a r t of the dc b i a s i n g i s obtained from a separate supply. B i a s i n g of the ar r a y r e q u i r e s that a p o t e n t i a l d i f f e r e n c e , , e x i s t between the X and T l i n e s . To conserve c u r r e n t , the p o t e n t i a l of the 25 Y l i n e s was made zero. The p o t e n t i a l of the 16 X l i n e s was then set at -V , t h i s being d i c t a t e d by the type o f . t r a n s i s t o r employed f o r the Y d r i v e r . The d r i v e r c i r c u i t s can thus be represented i n diagram form as shown i n Figure 3*2* O V J T f g T T F R O M WE.VtOF?Y COIAMAtlP C I R C U I T S X DJ5WBR S I G N A L S T O D C S U P P L Y <~^0 V O L T S j COMM4.V1C1 F R O I ^ L O & l t cvvuruiTS D R I V E I ? OUTPUT P R f l W CELLS -j^t— -5te.MA.LS TO cei-L<> D C su^PWY ( a V O U T S ) F i g u r e 3.2. Block Diagram of D r i v e r C i r c u i t s 3.2 P o s s i b l e D r i v e r C i r c u i t s The requirement of hig h input admittance l e d to the c o n s i d e r a t i o n of e m i t t e r - f o l l o w e r c i r c u i t s . A simple emitter f o l l o w e r i s shown i n F i g u r e 3.3. I f the r e s i s t a n c e of the base, , i s small then the input admittance i s e s s e n t i a l l y t h a t of I N P U T F R O M SVM5VLE ceUL F i g u r e 3.3. A Simple E m i t t e r Follower a grounded-base stage, y^]-,* Figure 3.4 the magnitude of the i n p u t admittance to the grounded-base stage of a t y p i c a l VHF t r a n s i s t o r i s shown as a f u n c t i o n of frequency. For comparison, the input admittance to 15 tunnel diode c e l l s , y^ , i s a l s o shown. From the f i g u r e i t i s seen t h a t the input admittance to the grounded-base stage i s comparable at h i g h f r e q u e n c i e s to the admittance of the 15 diode c e l l s f o r the 1 ma a r r a y , and i s about h a l f t h a t of the 5 ma a r r a y . In the 5 ma case i t would be p a r t i c u l a r l y expedient to i n c r e a s e the input admittance of the d r i v e r . Even with the 1 ma a r r a y about h a l f of the h i g h f r e -quency components are l o s t . A t t e n t i o n was t h e r e f o r e turned to methods of i n c r e a s i n g the input admittance of the simple emitter f o l l o w e r . .One c i r c u i t t h a t was examined was a t r a n s i s t o r v e r s i o n of the White Cathode F o l l o w e r ^ of F i g u r e 3.5a. A second c i r c u i t examined was the transformer coupled emitter f o l l o w e r c i r c u i t of F i g u r e 3.7. 24 F i g u r e 3.4. C o m p a r i s o n o f w i t h y ^ F i g u r e 3.5 shows t h e e v o l u t i o n o f t h e m o d i f i e d W h i t e e m i t t e r f o l l o w e r (mwef) f r o m t h e W h i t e C a t h o d e F o l l o w e r a n d t h e W h i t e e m i t t e r f o l l o w e r ( w e f ) shown i n F i g u r e 3.5b. The m w e f ^ 1 2 ^ i s s i m p l e r t h a n t h e w e f , a n d h a s an a d d e d a d v a n t a g e : t h e b i a s c u r r e n t s i n QI a n d Q2 m u s t b o t h f l o w i n t h e l o a d . T h u s , f a i r l y l a r g e ( i . e . 20 - 100 ma) q u i e s c e n t c u r r e n t s c a n be o b t a i n e d f r o m t h e mwef . 25 W h i t e C a t h o d e W h i t e E m i t t e r M o d i f i e d W h i t e F o l l o w e r F o l l o w e r E m i t t e r F o l l o w e r F i g u r e 3 .5 . E v o l u t i o n o f M o d i f i e d W h i t e E m i t t e r F o l l o w e r A s w i l l be shown i n S e c t i o n 4.2, t h e i n p u t a d m i t t a n c e t o t h e mwef i s a p p r o x i m a t e l y ( l + h f ^ ^ i b i ' w h e r e n f e 2 ^ s c o m m o n - e m i t t e r s h o r t - c i r c u i t c u r r e n t g a i n o f Q2, a n d y ^ i i s "the g r o u n d e d - b a s e i n p u t a d m i t t a n c e o f QI. S i n c e t h e Y d r i v e r a c t s as t h e d e t e c t o r , i t s h o u l d h a v e a l a r g e i n p u t a d m i t t a n c e o v e r t h e b r o a d e s t b a n d w i d t h p o s s i b l e . , T h e r e f o r e . , t h e Q2 t r a n s i s t o r o f t h i s d r i v e r s h o u l d be t h e b e s t . A s a t t h e p r e s e n t t i m e PNP t r a n s i s t o r s h a v e b r o a d e r b a n d w i d t h s t h a n N P N , Q2 o f t h e Y d r i v e r s h o u l d be P N P . H e n c e t h e Y a n d X m w e f 1 s a r e as shown i n F i g u r e 3.6. The o u t p u t s i g n a l f r o m t h e d r i v e r i s t a k e n f r o m t h e c o l l e c t o r o f Q2 o f t h e Y mwef b y u s i n g e i t h e r a t r a n s f o r m e r o r a l u m p e d d e l a y l i n e * C h a p t e r 4 d e a l s w i t h t h e s e c i r c u i t s i n d e t a i l . The s e c o n d m e t h o d i n v e s t i g a t e d o f i n c r e a s i n g t h e i n p u t 2fe O U T t P U T T O A R R A Y (a) Y mwef F R O M K R R A Y / F i g u r e 3.6, X and Y M o d i f i e d White Em i t t e r Followers admittance i s shown i n Figure 3,7. This uses the simple emitter r f o l l o w e r c i r c u i t and a broadband transformer. Here the i n p u t -2 admittance i s i n c r e a s e d by n , where n i s the e f f e c t i v e turns r a t i o of the transformer* These c i r c u i t s are i n v e s t i g a t e d i n Chapter 5 , with d e t a i l s of the transformers given i n Appendix IV, -*v, O U T P U T F R O M A R R A Y Figure 3.7. X and Y Transformer-Coupled E m i t t e r F o l l o w e r s ( t c e f ) 27 4. THE MODIFIED WHITE EMITTER FOLLOWER This chapter w i l l d e al with the modified White emitter f o l l o w e r (mwef) as shown i n Fi g u r e 4,1» The chapter begins w i t h a d i s c u s s i o n of the dc c h a r a c t e r i s t i c s of the mwef. The high-frequency c h a r a c t e r i s t i c s are then examined, the bandwidth l i m i t a t i o n s of the c i r c u i t being i n d i c a t e d . 4,1 DC C o n s i d e r a t i o n s As shown i n Table 2»2 of Chapter 2, the cur r e n t requirements of the array v a r y over a wide range. The power d i s s i p a t e d i n the t r a n s i s t o r s of a d r i v e r w i l l thus be dependent on the b i a s c u r r e n t r e q u i r e d by the a r r a y . This power dependence w i l l now be examined f o r the mwef. Figur e 4 „ 1 0 The MWEF High loop c u r r e n t g a i n i n the c i r c u i t of Figure 4,1 r e q u i r e s R 1 » R 2 ° However, good dc s t a b i l i t y of the Q 2 t r a n s i s t o r l i m i t s R-^  — IOR20 Hence i n the f o l l o w i n g R-^  = 10R2» Since R^>-R2« and since both t r a n s i s t o r s r e q u i r e b i a s c u r r e n t s of the same order of magnitude, V, should be grea t e r t h a n V2* H o w e v e r , a v a i l a b l e power s u p p l i e s l i m i t e d t h e s i z e of t h e r a t i o V j A g t o V 1 / V 2 = 2 . t i POVYEFS. D I S S I P A T I O N iH C I I L U l V V A T T i 500, F i g u r e 4 . 2 . Power D i s s i p a t i o n as a F u n c t i o n o f R 2 F i n a l l y , t h e t r a n s i s t o r s u s e d h a d a minimum o p e r a t i n g c o l l e c t o r v o l t a g e , V * o f a b o u t 6 v o l t s . F o r s m a l l power d i s s i p a t i o n t h e n , t h e maximum o u t p u t c u r r e n t , l Q m > s h o u l d o c c u r when V = V „ T h u s , w i t h R, = 1 0 R o , V , = 2 V 0 , a n d I n = I - a t c c m > 1 2 1 2 ' 0 0m V c = V c m , t h e t r a n s i s t o r power d i s s i p a t i o n c a n be e x p r e s s e d as P t = - 9 1 I 0 . B 2 [ X 0 m ~ X o ] + T0 V c m F r o m t h i s i t i s s e e n t h a t t h e l o w e s t p o w e r d i s s i p a t i o n o c c u r s when R 2 = 0 . H o w e v e r , f o r t h e t r a n s i s t o r s u s e d , t h e b a s e r e s i s t a n c e , ^ , was a b o u t 70 o h m s . H i g h - f r e q u e n c y g a i n r e q u i r e s 29 Rj> ( i . e . R^ i s by—passed at high f r e q u e n c i e s ) . Hence R-^  / should be of the order of 1 Kohm which means R2 should be about 100 ohms. The e f f e c t of R^ on the power d i s s i p a t i o n i s shown i n Fig u r e 4.2 f o r the 1 ma T mwef. As i s seen the v o l t a g e V 2 i s dependent of the R,^ v a l u e . The v o l t a g e i s , of course, a l s o dependent on the value of the maximum output c u r r e n t . For the four d r i v e r c i r c u i t designs r e q u i r e d ( i . e . two f o r the 5ma ar r a y and two f o r the 1 ma a r r a y ) , w i t h R^ = 100 ohms, the four v a l u e s range from 6.8 to 15 v o l t s . Consequently, f o r design convenience was chosen as 12 v o l t s (and hence V^ = 24 v o l t s ) . The r e s u l t i n g r e s i s t o r v a l u e s are giv e n i n Table 4.1, while the current and power d i s s i p a t i o n ranges are given i n Table 4.2. 1 ma tunnel diode 5 ma tunnel diode Xmwef Tmwef Xmwef Ymwef R l 2.7K 4.7K 680 IK R 2 330 470 68 100 Table 4.1. R e s i s t o r Values i n Ohms From Table 4.2 i t i s seen that i n the 5 ma array (both i n the X and T mwefs) Q2 must be a p a r a l l e l combination of t r a n s i s t o r s to s a t i s f y the power d i s s i p a t i o n l i m i t of about 180 m i l l i w a t t s (see Appendix I I ) . 30 D i s s i p a t i o n i n M i l l i w a t t s D r i v e r I 0(ma) Ql Xmwef 1 ma Max 15.6 31 75 Min 7.7 25 44 Xmwef 1 ma Max 24 .6 52 120 Min 12.0 41 67 Ymwef 5 ma Max 73.4 146 3 52 Min 44.8 118 260 Xwmef • 5 ma Max 115 220 186 550 405 Min 70 Table 4.2. Current and Power D i s s i p a t e d Ranges One f u r t h e r dc c o n s i d e r a t i o n i s the s e n s i t i v i t y of the output v o l t a g e of the mwef to changes i n temperature and supply v o l t a g e . This aspect w i l l now be examined: the r e s u l t s g i v e n here w i l l a l s o apply to the t c e f of Chapter 5. Examination of the mwef c i r c u i t shows that the output v o l t a g e i s d e f i n e d by a source v o l t a g e plus the base—emitter j u n c t i o n v o l t a g e of Q^* Since t h i s j u n c t i o n v o l t a g e i s known to vary at approximately —2mv/°C f o r Ge and -2,3mv/°C f o r S i , ^ 1 " ^ the output v o l t a g e w i l l be temperature dependent. Fi g u r e 4.3, shows t h i s f o r both the X and T mwefs. Also shown i s the temperature dependence of the output v o l t a g e f o r anemitter f o l l o w e r . The mwef v a r i a t i o n i s grea t e r at higher temperatures duq to c o l l e c t o r leakage c u r r e n t e f f e c t s . The r e s u l t s of 31 Fi g u r e 4.3. DC Output Voltage as a F u n c t i o n of Temperature Fi g u r e 4.3 c l e a r l y c a l l f o r some scheme to reduce the output v o l t a g e v a r i a t i o n . To t h i s end the balanced—pair c i r c u i t of Figu r e 4.4 was used. Examination of t h i s c i r c u i t shows that F i g , 4.4. A Balanced P a i r 33 i f i s d r i v e n from a v o l t a g e source v n , then the volt a g e at the base of Q2«, v 2 , i s given by the f o l l o w i n g ; KT T I e 2 ^ KT , Ieo2 ^_ v~ = — - I n 7 — + — In ^  + v, , 2 q I , q I , l y u e l ^ eo1 where I i s the emitter leakage c u r r e n t . T h u s , i f equal c u r r e n t s flow i n both t r a n s i s t o r s and the t r a n s i s t o r s are i d e n t i c a l , then v» = v, independent of temperature. (a) (b) Figur e 4„5. DC Compensated MWEF The e f f e c t of t h i s s t a b i l i z i n g network can be analyzed by c o n s i d e r i n g the v o l t a g e g a i n around the loop of Q^-Q^a The negative feedback of the loop reduces any e r r o r v o l t a g e by a f a c t o r of l/(l + where A v i s the magnitude of the loop v o l t a g e g a i n . This loop gain was c a l c u l a t e d and checked e x p e r i m e n t a l l y . For the T mwef the g a i n was found to be of the order of 100, while f o r the X mwef of the order of 65. The d i f f e r e n c e i n 33 Fig u r e Output Voltage S e n s i t i v i t y of the I MVEF Fig u r e 4,7. Output Voltage S e n s i t i v i t y of the X MWEF 34 these two gains i s due to the d i f f e r e n c e s i n the h ^ of the t r a n s i s t o r s employed. As shown i n Figure 4.3 the "compensated" output c h a r a c t e r i s t i c s are much more s a t i s f a c t o r y , though v a r i a t i o n s are s l i g h t l y l a r g e r than the v o l t a g e g a i n c a l c u l a t i o n s would p r e d i c t . This could he due to an unbalance i n the c h a r a c t e r i s t i c s of the t r a n s i s t o r s i n the dc p a i r . The v a r i a t i o n of the output v o l t a g e f o r changes i n l o a d c u r r e n t and f o r changes i n supply v o l t a g e was a l s o examined. For l o a d c u r r e n t changes from 5 ma to 30 ma i n both the X and Y mwef c i r c u i t s the output was observed to change l e s s than 3 mv. The s e n s i t i v i t y of the mwefs to supply-voltage changes i s shown i n F i g u r e s 4.6 and 4.7* The extreme s e n s i t i v i t y of the output v o l t a g e to v a r i a t i o n s i n the —12 v o l t supply i n Fig u r e 4.7 i s due to the f a c t t h a t the base vol t a g e of i s d e f i n e d by a simple r e s i s t a n c e c h a i n . This s e n s i t i v i t y due to the -12 v o l t supply could be e l i m i n a t e d i f a zener diode were used to d e f i n e the v o l t a g e on the base of Q^. The Y mwef does not e x h i b i t t h i s dependence as the base of there i s t i e d to ground. The preceding d i s c u s s i o n on dc s t a b i l i t y a p p l i e s p r i n c i -p a l l y to the d r i v e r s f o r the 1 ma a r r a y , although the v a r i a t i o n s f o r the 5 ma mwefs were e s s e n t i a l l y the same. Thus^from the r e s u l t s i t i s seen that a + 10 mv t o l e r a n c e can be achieved* and i n f a c t can be b e t t e r e d i f the vo l t a g e on the base of i s a c c u r a t e l y d e f i n e d . 4.2 High-Frequency C o n s i d e r a t i o n s \ \ In S e c t i o n 2.5 the bandwidth requirement of the t u n n e l -diode a r r a y was given as about 300 Megacycles. As l i t t l e i n f o r m a t i o n i s a v a i l a b l e about the performance of t r a n s i s t o r s , r e s i s t o r s , and c a p a c i t o r s i n t h i s frequency range, i t vas found necessary to make measurements on the elements to determine t h e i r VHP c h a r a c t e r i s t i c s * The r e s u l t s of these measurements are given i n Appendices II and I I I . i n the 50-350 Megacycle frequency range the elements a r e . s u b j e c t to the e f f e c t s of le a d inductance and p a r a s i t i c c a p a c i t a n c e . This complicates the c i r c u i t r e p r e s e n t a t i o n of these passive elements. With t r a n s i s t o r s the p i c t u r e i s even more i n v o l v e d as lumped element approximations to the t r a n s i s t o r equations become poor and as e f f e c t s of p a r a s i t i c capacitances begin to predominate. Thus^ adequate e q u i v a l e n t c i r c u i t r e p r e s e n t a t i o n i n t h i s frequency range i s cumbersome. Hence^in the f o l l o w i n g no attempt w i l l be made to give an e q u i v a l e n t c i r c u i t f o r the network. looked at as a grounded-base stage with feedback, the feedback loop being a grounded-emitter a m p l i f i e r . Prom the r e s i s t o r — c a p a c i t o r measurements i t i s seen that As i s seen i n Fig u r e 4.8a, the mwef c i r c u i t can be 777 (a) (b) Fi g u r e 4.8. The MWEF at High Frequencies 36 Assuming that the admittance l/R-^ can be neglected and that C i s a short c i r c u i t * then the mwef can be drawn as shown i n F i g u r e 4.8(b). F u r t h e r , i f i t i s assumed t h a t each t r a n s i s t o r , i s working i n t o a short c i r c u i t , then the loop c u r r e n t g a i n , A T, i s A I = 3 V I 1 = ~ k f e k f b * and the input admittance T^ , i s I + I I ^ y 1 2 _ i (]_ + _2 ) C ~ V - v v I ' ° v l v l x l = y i b ( l - h f b h f e > =• ^ i b ( l y ^ y ^ The r a t i o 1-^ /V^  = y ^ since i t was assumed t h a t the output of Q-^  i s shorted by the input of Q^. An exact expression f o r the loop g a i n i s d e r i v e d i n Appendix V where i t i s shown t h a t there i s a d i f f e r e n c e of about 4 db and 35 degrees between the two expressions at 350 Megacycles. However 5 f o r an i n i t i a l understanding of the problems a s s o c i a t e d with t h i s c i r c u i t the approximation i s e a s i e r to examine, and hence w i l l be used i n the f o l l o w i n g . The preceding thus shows that the input admittance to the i grounded-base stage i s i n c r e a s e d by 1 + A T. Hence^A T should be as l a r g e as s t a b i l i t y c o n s i d e r a t i o n s w i l l allow. I t i s seen from Equation ( l ) that.the input admittance i s zero when Aj = -1* Thus^ i n the complex plane- the c u r r e n t g a i n must avoid the (—1,0) p o i n t i f the network i s to be s t a b l e . N y q u i s t ^ ^ has extended t h i s concept of a v o i d i n g the (-1,0) I 3 7 p o i n t by s t a t i n g .that f o r a s i n g l e - l o o p s t a b l e a m p l i f i e r , the loop gain when p l o t t e d i n p o l a r form must not e n c i r c l e the (-1,0) p o i n t . This statement j>hen leads to the B o d e ^ 1 ^ c r i t e r i o n f o r s i n g l e - l o o p a m p l i f i e r s : the loop g a i n must be l e s s than u n i t y when the phase reaches -180 degrees. Thus,to determine the s t a b i l i t y of the mwef the loop g a i n , A T = -h„, h,, ' 1 ib fe - h ^ e must be examined. Shown i n Figure 4.9 i s a Bode p l o t of the t y p i c a l measured h„ valu e s f o r the 2N1141 PNP t r a n s i s t o r and the \ N d t a FREQ MC I Figure 4.9 . T y p i c a l h„ Values 2N2369 NPN t r a n s i s t o r . These are the common-emitter t r a n s i s t o r s f o r the T and X d r i v e r s r e s p e c t i v e l y . As can be seen from the f i g u r e the h ^ ' s a r e s i m i l a r : both are i n t h e i r 6 db/octave c u t - o f f r e g i o n , w i t h a phase l a g of gr e a t e r than 90 degrees. In the f o l l o w i n g only the ex p e r i m e n t a l l y measured r e s u l t s f o r the T d r i v e r of the 1 ma a r r a y w i l l be given, since t h i s was the most c r i t i c a l d esign problem. The Y d r i v e r c i r c u i t to be examined i s shown i n Fig u r e 4.8 with QT the 2N2369 t r a n s i s t o r and Q 2 the 2N1141. The short - c i r c u i t c u r r e n t gains of these t r a n s i s t o r s were measured, the 2N2369 as a grounded-base a m p l i f i e r , and the 2N1141 as a grounded-emitter. The product, h f e n f k » °f these measurements i s shown i n Fig u r e 4.10. Also shown i n the f i g u r e i s the a c t u a l measured s h o r t — c i r c u i t c u r r e n t g a i n of the* Y d r i v e r . The d i f f e r e n c e of about 80 degrees at 350 Megacycles between these two curves i s due,to two causes. F i r s t , i n the a c t u a l c i r c u i t there i s a 50 ohm r e s i s t o r on the base of Q N f o r impedance matching of the input s i g n a l to the a r r a y . This caused, an a d d i t i o n a l phase l a g of 35 degrees. Secondly,the assumption made i n d e r i v i n g the g a i n e x p r e s s i o n as ~ n f ^ n f e w a s "that Q-^ worked i n t o a short c i r c u i t . In f a c t the input impedance of Q 2 i s about 70 ohms - comparable to the Q-^ output impedance. This causes about a 40 degree a d d i t i o n a l phase l a g at 350 Megacycles. Thus 3the combination of these two p e r t u r b a t i o n s to the i d e a l mwef accounts f o r the measured phase: l a g and the r e s u l t a n t i n s t a b i l i t y of the network. A t t e n t i o n was thus turned to s t a b i l i z i n g t h i s network. Bode v ' shows that an i d e a l feedback a m p l i f i e r has a c u t - o f f 39 C-tAIN I N d b 5 0 ^OO " 2 . 0 0 "300 -4-00 FREQ IN MC F i g u r e 4 . 1 0 . Current Gain f o r T D r i v e r of 1 ma Array 40 c h a r a c t e r i s t i c o f 12 d b / o c t a v e . F u r t h e r , h e i n d i c a t e s how t h e a m p l i f i e r b a n d w i d t h may be m a x i m i z e d p r o v i d e d t h a t t h e a c t u a l a m p l i f i e r h a s a n a s y m p t o t i c g a i n r o l l - o f f o f g r e a t e r t h a n 12 d b / o c t a v e . A s t h e g a i n r o l l - o f f h e r e i s o f t h e o r d e r o f 6 d b / o c t a v e , t h i s p r o c e d u r e c a n n o t be e m p l o y e d . Commonly u s e d b r o a d b a n d i n g t e c h n i q u e s a r e e q u a l l y i n a p p l i c a b l e as t h e y a r e c o n c e r n e d w i t h e x t e n d i n g o n l y t h e g a i n m a g n i t u d e t o t h e c u t — o f f r e g i o n . No a t t e n t i o n i s p a i d t o t h e p h a s e c h a r a c t e r i s t i c w h i c h h e r e w i l l be a t l e a s t 90 d e g r e e s when t h e b r o a d b a n d e d g a i n c h a r a c t e r i s t i c i n t e r s e c t s t h e c u t - o f f a s y m p t o t e . C o n s e q u e n t l y t h e o n l y a t t a c k a p p l i c a b l e i s t h a t o f a t t e n u a t i o n o f t h e g a i n . T h i s c a n be done b y s e v e r a l m e t h o d s . The s i m p l e s t m e t h o d i s t o r e d u c e t h e g a i n o f t h e t r a n s i s t o r b y u s i n g a n e m i t t e r r e s i s t o r . T h i s was u s e d w i t h t h e 1 ma m w e f . A l t e r n a t i v e l y , g a i n c a n be r o l l e d - o f f a t t h e c o l l e c t o r o f b y u s i n g a s e r i e s - R C n e t w o r k . W i t h t h e 5 ma mwef b o t h t e c h n i q u e s w e r e u s e d as t h e s t a b i l i z i n g e m i t t e r r e s i s t o r e x c e e d e d t h e dc b i a s e m i t t e r r e s i s t o r . F o r t h e T d r i v e r a l i m i t i n g v a l u e o f t h e e m i t t e r r e s i s t a n c e was f o u n d e x p e r i m e n t a l l y t o be a b o u t 220 o h m s . F o r v a l u e s s m a l l e r t h a n t h i s , t h e c i r c u i t was u n s t a b l e . The c l o s e d - l o o p g a i n was d e t e r m i n e d b y m e a s u r i n g t h e i n p u t a d m i t t a n c e w i t h t h e l o o p o p e n , YQ , a n d t h e n c l o s e d , Y C „ The l o o p g a i n t h u s / c a l c u l a t e d f r o m Y £ = YQ(1 + A T ) i s shown i n F i g u r e 4.11 (, ( s e e A p p e n d i x V ) . A s c a n be s e e n f r o m t h e f i g u r e , t h e d r i v e r i s o n l y c o n d i t i o n a l l y s t a b l e . The i n c r e a s e i n g a i n a t h i g h f r e q u e n c i e s i s due t o c u r r e n t f e e d t h r o u g h t h e b a s e - c o l l e c t o r j u n c t i o n 41 d e p l e t i o n capacitance of Q-. Fu r t h e r , a ga i n margin of 4 db G A I N IN d b -"2 - 4 -a / / / / / / / / / P H A S E ^ / \ \ -* \ P>14AS'= is* — 1 0 0 -\40 -\ao ->oo -.-8o 5 0 TOO 1O0 3 00 -4-00 FREQ \U V\C Figure 4.11. L i m i t i n g Value of T D r i v e r Gain at 200 Megacycles i s inadequate, as the gain of i n d i v i d u a l t r a n s i s t o r s of the same type can vary by t h i s amount. The r e s u l t s of F i g u r e 4.11 thus represent a bound on the upper l i m i t of allowable loop g a i n . As was i n d i c a t e d i n F i g u r e 3.7 the output from the ar r a y i s obtained from the Q 2 c o l l e c t o r of the T d r i v e r . The c u r r e n t . 42 i c , t h a t flows there i s giv e n by A I i = ( ')im "> c y A T where Aj i s the loop g a i n , y^ the admittance of the 15 other diode c e l l s t i e d to the X d r i v e r ^ and the t o t a l tunnel—diode switching c u r r e n t . ThuSjusing Figure 4.1I wit h about an 8 db gain margin, the c o l l e c t o r c u r r e n t w i l l be at l e a s t 12 db down at 150 Megacycles r e g a r d l e s s of what form the a c t u a l d e t e c t o r c i r c u i t takes* S e v e r a l arrangements are p o s s i b l e f o r the d e t e c t o r . A simple r e s i s t o r , R^, i n the c o l l e c t o r as shown i n Figu r e 4.11a would be s u i t a b l e provided i t d i d not s e r i o u s l y (a) (b) Fig u r e 4.12. P o s s i b l e Detector C i r c u i t s a f f e c t the dc b i a s i n g of Q^* The e f f e c t of on the dc b i a s i n g of Q 2 can be e a s i l y e l i m i n a t e d by us i n g a shorted delay l i n e as shown i n Fi g u r e 4.12(b). This was the arrangement used wi t h the f i r s t a r r a y d i s c u s s e d i n Chapter 6. In both F i g u r e s 4.12(a) and (b) the assumption i s made th a t the output i s f e d i n t o a r e l a t i v e l y high-impedance a m p l i f i e r , such as ah emitter f o l l o w e r . In both cases i t i s the v o l t a g e across Ry. t h a t i s d e t e c t e d . As the impedance on the c o l l e c t o r of must be small ( i . e . should be l e s s than 300 ohms f o r high f r e q u e n c i e s as l / v o e — 300 ohms) the output v o l t a g e w i l l be cor r e s p o n d i n g l y s m a l l . Por the 5 ma ar r a y i t was of the order of 100 mv, while f o r the 1 ma ar r a y i t was about 20 mv. Broadband transformers were a l s o examined f o r p o s s i b l e a p p l i c a t i o n i n the d e t e c t i n g c i r c u i t . High-frequency transformers are l o s s y and. t h e i r presence i n the c o l l e c t o r c i r c u i t of causes a l a r g e phase s h i f t i n the loop g a i n , thus r e q u i r i n g the g a i n to be f u r t h e r attenuated. I t i s thus seen that the mwef high—frequency response i s h i g h l y dependent on the h ^ g of the t r a n s i s t o r . As c u r r e n t l y a v a i l a b l e t r a n s i s t o r s are i n t h e i r 6 db/octave c u t -o f f r e g i o n f o r the 100 Megacycle frequency range, i t i s d i f f i c u l t to o b t a i n a s t a b l e c i r c u i t and s t i l l maintain any loop g a i n . For bandwidths below 50 Megacycles the c i r c u i t does have a p p l i c a t i o n . Thus., c i r c u i t s t h a t r e q u i r e t r a n s i s t o r feedback to improve t h e i r i nput admittance are not very s a t i s f a c t o r y at hi g h f r e q u e n c i e s . Consequently the use of passive elements was i n v e s t i g a t e d . Out of these c o n s i d e r a t i o n s came the t r a n s -former coupled emitter f o l l o w e r of the next chapter. 44 5. THE TRANSFORMER COUPLED EMITTER FOLLOWER In t h i s chapter the c h a r a c t e r i s t i c s of the transformer coupled e m i t t e r f o l l o w e r ( t c e f ) are d i s c u s s e d . This c i r c u i t employs a broadband transformer, the p r o p e r t i e s of which are examined i n Appendix IV. I t i s shown i n t h i s chapter t h a t , with the help of these transformers, an o v e r a l l a m p l i f i e r bandwidth of 250 Megacycles i s p o s s i b l e with an input admittance of g r e a t e r than 15 m i l l i m h o s * The t c e f c i r c u i t s c onsidered are only those f o r the 1 ma a r r a y n 5ol DC Co n s i d e r a t i o n s In Chapter 4 i t was shown that i f the d r i v e r s supply the dc b i a s i n g , then both the X and Y mwefs had p a r a b o l i c d i s s i p a t i o n curves. Here, only the Y t c e f w i l l e x h i b i t a p a r a b o l i c power dependence as the X t c e f i s j u s t an em i t t e r f o l l o w e r . As with R-^  of the mwef, R^ of Fig u r e 5.1 should be about 1 K—ohm. Thus u s i n g an a n a l y s i s s i m i l a r to that of S e c t i o n 4.1 wit h R^ = 1.2K, V = 24 v o l t s , the maximum power d i s s i p a t i o n i s about 127 m i l l i w a t t s . This can be handled by a s i n g l e t r a n s i s t o r . The maximum X t c e f t r a n s i s t o r d i s s i p a t i o n i s about 148 m i l l i w a t t s with a c o l l e c t o r supply v o l t a g e of -6 v o l t s . This power can again be handled by a s i n g l e t r a n s i s t o r . As was mentioned i n Chapter 4, the dc output v o l t a g e from an emitter f o l l o w e r c i r c u i t e x h i b i t s a temperature dependence. Hence the same dc compensation i s r e q u i r e d f o r the t c e f c i r c u i t as was r e q u i r e d f o r the mwef. The complete t c e f X and Y d r i v e r 45 c i r c u i t s a r e as shown i n F i g u r e 5 . 1 . OUT t F R O M (a) T D r i v e r (b) X d r i v e r F i g u r e 5 . 1 . X a n d T T C E F The t e m p e r a t u r e d e p e n d e n c e o f t h e dc o u t p u t v o l t a g e f r o m t h e s e c o m p e n s a t e d d r i v e r s i s s i m i l a r t o t h a t shown i n F i g u r e 4 . 4 , A c t u a l l y i t i s s l i g h t l y l e s s t h a n t h a t shown f o r t h e mwef as t h e r e a r e no l e a k a g e c u r r e n t e f f e c t s o f a s e c o n d t r a n s i s t o r t o c o n t e n d w i t h h e r e . The t r a n s f o r m e r shown i s a 1 : 2 b r o a d b a n d c u r r e n t t r a n s -f o r m e r ( see A p p e n d i x I V ) . W i t h t h e t c e f t h e dc b i a s i n g o f t h e a r r a y c o u l d be done t h r o u g h one arm o f t h e t r a n s f o r m e r * The t c e f ' s w o u l d t h e n be ac c o u p l e d t o t h e a r r a y . W i t h t h i s , t r a n s i s t o r s w i t h l o w e r power d i s s i p a t i o n b u t w i d e r b a n d w i d t h s c o u l d t h e n be u s e d . H o w e v e r , f o r c o n v e n i e n c e t h e same b i a s a r r a n g e m e n t was u s e d as w i t h t h e m w e f . T h i s i s shown i n F i g u r e 5 . 1 . 5.2 High-Frequency C o n s i d e r a t i o n s I f one assumes t h a t Q3 of Figure 5.1 i s a grounded-base stage, and t h a t i n the case of the Y d r i v e r the e f f e c t of the • l o a d may be1 n e g l e c t e d , then the input admittance to the t c e f 2 i s g i v e n by N y ^ , here N i s the e f f e c t i v e turns r a t i o of the transformer, and y ^ i s the grounded-base s h o r t - c i r c u i t i n p u t 2 admittance* I d e a l l y here N =4, and consequently the input admittance to the d r i v e r should be 4 y ^ as shown i n F i g u r e 5.2. The X d r i v e r c h a r a c t e r i s t i c s alone w i l l be considered, as the measured admittance to the two d r i v e r s was p r a c t i c a l l y the same. F i g u r e 5,2 shows the admittance c h a r a c t e r i s t i c s to the X d r i v e r with Q3 a 2N2369 t r a n s i s t o r . Also shown i s the admittance of the other tunnel-diode c e l l s t i e d to the X d r i v e r , X^, and the e f f e c t i v e turns r a t i o of the transformer. The f i g u r e demonstrates t h a t there i s only a s l i g h t improvement i n the admittance at f r e q u e n c i e s above 100 Megacycles. F u r t h e r i t i s seen t h a t the transformer turns r a t i o does not approach i t s i d e a l value of 2 u n t i l the frequency drops to about 20 Megacycles,, This, however, rep r e s e n t s an improvement over the mwef where the input admittance was a c t u a l l y decreased at f r e q u e n c i e s above 50 Megacycles by the presence of the feedback 1 o op. The next f e a t u r e to be examined i s the o v e r a l l d r i v e r c u r r e n t g a i n . With t h i s the Q4 t r a n s i s t o r i s a PNP 2N1141, Fi g u r e 5,3 shows the g a i n f o r the X d r i v e r f o r v a r i o u s values of l o a d r e s i s t a n c e on the c o l l e c t o r of Q4. The input admittance f o r the v a l u e s of load r e s i s t o r s considered was p r a c t i d a l l y the same. Also shown i n the f i g u r e i s the o v e r a l l g a i n when the 47 transformer 1 was e l i m i n a t e d * The d i f f e r e n c e between the short V8Q. ifeo. 140 \ 7 A \00 -4-0. 20 SO -40 50 bo "IO SO VOO "2.00 TWO 400 Figure 5.2* TCEF Admittance C h a r a c t e r i s t i c s - c i r c u i t load curves i s a l s o shown. This represents the l o s s i n c u r r e n t gain through the transformer, which f o r a 1:2 t r a n s -former should be =-6db« As can be seen from the f i g u r e the transformer response i s at best -5.7db» For comparison the response curve f o r the 1:2 transformer of Appendix IV i s a l s o g i v e n . This transformer was terminated i n 47 ohms. Agreement between these two curves improves as the input impedance of the t r a n s i s t o r approaches the 47 ohm l e v e l . F i g u r e 5.3. Y D r i v e r G a i n 49 Thus Fig u r e 5.3 demonstrates t h a t i t i s p o s s i b l e to achieve bandwidths of the order of 250 Megacycles . Now with the a c t u a l memory the c u r r e n t that flows i n the c o l l e c t o r of Q4 i s given by-5 i A . (1 + y A / y D ) where A i s the o v e r a l l system g a i n , y^ the admittance of the 15 other c e l l s t i e d to the y d r i v e r , y^ the admittance to the X d r i v e r , and i ^ , the t o t a l t u n n e l diode switching current,, Since A ^ ( nf e)g4» a Q4 t r a n s i s t o r with a higher gain would give an even b e t t e r bandwidth. This aspect i s considered f u r t h e r i n Chapter 6. 6. RESULTS AND CONCLUSIONS 50 In t h i s chapter the experimental r e s u l t s obtained u s i n g the c i r c u i t s of Chapters 4 and 5 to d r i v e the a r r a y w i l l be examined. The speed of the a r r a y i s compared wi t h that of e x i s t i n g f e r r i t e — c p r e arrays and with tunnel-diode l o g i c . Some i n d i c a t i o n i s a l s o given as to the l i m i t of the s i z e of an a r r a y t h a t can be b u i l t ^ u s i n g current d e t e c t i o n . F i n a l l y , a t t e n t i o n i s drawn to areas which c o u l d warrant f u r t h e r inve s t i g a t i o n . 6.1 Experimental Arrays I n i t i a l i n v e s t i g a t i o n on the tunnel-diode array was c a r r i e d out u s i n g two d r i v e r s , X and Y, and a s i n g l e diode c e l l . The r e s u l t s of t h i s i n d i c a t e d that current d e t e c t i o n was p o s s i b l e . However,to determine i f the s w i t c h i n g of one tunnel diode would a f f e c t another i n the a r r a y , a 2x2 matrix was b u i l t f o r both the 5 ma and 1 ma tunnel diodes. This array was b u i l t on a p r i n t e d - c i r c u i t board w i t h a minimum amount of copper removed. The arrangement of the a r r a y i s shown i n F i g u r e 6,1. The presence of the other 14 words and 23 b i t s was simulated u s i n g an RC combination on each l i n e as shown. Only the r e s u l t s f o r the 2x2 array w i l l be given, as the performance of the a r r a y i s of more i n t e r e s t than that of a s i n g l e diode c e l l . F u r t h e r , the d i f f e r e n c e i n the output s i g n a l was s l i g h t : the r i s e time and pulse height of the output being about 2 nanoseconds slower and 5 mv smaller f o r the array than f o r the s i n g l e c e l l . 51 X2 L-AAA.-rAA-'V I ™ ! ^ - xA/V\rj-*V\AA--2 v •MAArrjVVNA-Figu r e 6.1. Block Diagram of 2x2 Array The pulse sequence r e q u i r e d f o r w r i t i n g i n t o and r e a d i n g out of a s i n g l e diode c e l l i s shown i n F i g u r e 6.2. Y IT i rr W , i £ R E A D F i g u r e 6.2. Read—Write S i g n a l s f o r S i n g l e C e l l For d r i v i n g the 2x2 a r r a y the pulse sequence of F i g u r e 6.3 was used. Note that the X h a l f — w r i t e pulse i s wide enough to allow each of the two c e l l s on the X l i n e to be set s e p a r a t e l y . This permits the presence of c r o s s - t a l k to be determined. A pulse generator was designed to produce the pulse sequence of F i g u r e 6.3 (see Appendix VI) » With t h i s the X h a l f - w r i t e pulses 52 were about 100 nanoseconds wide while the Y h a l f - w r i t e and X read pulses were about 30 nanoseconds wide. ¥ ¥ ' "WRITE | R E A D F i g u r e 6.3. Read-Write S i g n a l s f o r 2x2 Array The exact c o n f i g u r a t i o n s f o r the X and Y d r i v e r s employed with the 5 ma ar r a y are shown i n Figure 6.4. The output, shown i n Figure 6.5, i s a pulse r a t h e r than a step due to the presence -2N8"M-- 1 1 V (a) Y MWEF D r i v e r (b) X MWEF D r i v e r Figure 6.4. D r i v e r Arrangement f o r 5 ma Array 53 of the shorted delay l i n e on the output. These output pulses had about a 15 nanosecond r i s e time and were about 35 nanoseconds wide. F u r t h e r ^ i t should be noted here that when the diode c e l l does not switch ( i . e . when a "0" i s p r e s e n t ) , the output pulse i s i n i t i a l l y of the opposite p o l a r i t y to the pulse when the diode switches. 1'. O o A-, O U T \r \ 5 c — —t/s*>. W R 1 ( T E » E S | i i i • ij i 1 i 1 1 I C O M V ! ! i i 1 I N j j ( i T I M E F i g u r e 6.5. Waveforms f o r 5 ma Array When the mwef i s used with the 1 ma tunnel-diode a r r a y , output pulses of the order of 20 m i l l i v o l t s are produced. This was considered inadequate as i t was intended t h a t t h i s s i g n a l should d r i v e a tunnel-diode gate f o r which 100 m i l l i v o l t s was r e q u i r e d to ensure r e l i a b l e o p e r a t i o n . The exact c o n f i g u r a t i o n s f o r the X and Y d r i v e r s f o r the 1 ma a r r a y are shown i n F i g u r e 6.6, The output waveforms are shown i n F i g u r e 6.7. These f i g u r e s i l l u s t r a t e the output f o r three d i f f e r e n t storages* The waveforms have a r i s e time of about 10 nanoseconds* This i s shown i n F i g u r e 6.8, which also shows (a ) Y T C E F D r i v e r (b) X T C E F D r i v e r F i g u r e 6,6, T C E F D r i v e r C i r c u i t s t h e o u t p u t s i g n a l when a "0" i s p r e s e n t . The o u t p u t h e r e i s a p u l s e due t o t h e RC e m i t t e r t i m e c o n s t a n t w h i c h was c h o s e n t o d i f f e r e n t i a t e t h e c u r r e n t s t e p i n p u t f r o m t h e a r r a y . T h u s , u s i n g t h e t c e f c i r c u i t i t i s p o s s i b l e t o a t t a i n t h e d e s i r e d o u t p u t s i g n a l l e v e l o T h i s d e m o n s t r a t e s t h e s u p e r i o r i t y o f t h e t c e f c i r c u i t o v e r t h e mwef f o r t h i s a p p l i c a t i o n , 6,2 C o m p a r i s o n w i t h O t h e r D e v i c e s To e v a l u a t e t h e f o r e g o i n g r e s u l t s , a c o m p a r i s o n s h o u l d be made w i t h t h e o p e r a t i n g s p e e d s of b o t h f e r r i t e c o r e s a n d t u n n e l — d i o d e l o g i c . P r e s e n t l y a v a i l a b l e f e r r i t e c o r e s h a v e a b o u t 20 n a n o s e c o n d r i s e t i m e s when d r i v e n b y a h e a v y c u r r e n t p u l s e ( i . e . 350 ma a n d 1Q0 n a n o s e c o n d s w i d e ) . The a r r a y s b u i l t w i t h t h e s e c o r e s h a v e a r e a d - w r i t e c y c l e t i m e o f a b o u t 250 n a n o s e c o n d s . kVOLT-A.G.E F i g u r e 6 „ 7 . ' W a v e f o r m s f o r 1 ma A r r a y IO MS' F i g u r e 6 , 8 . " 1 " a n d " 0 " O u t p u t P u l s e s 56 By comparison the tunnel-diode a r r a y has about a 1G nanosecond r i s e time when d r i v e n by a 100 m i l l i v o l t , 30 nano-second wide p u l s e . Furthermore^as shown i n F i g u r e 6.7 the tunnel—diode a r r a y has about a 200 nanosecond read-write c y c l e time. This does not represent the l i m i t . The long c y c l e time here r e s u l t s from the t r a n s i e n t due to the h a l f - w r i t e pulse oh the X l i n e s . For t e s t purposes these pulses were chosen to be about 100 nanoseconds wide. I f both h a l f - w r i t e pulses were made 30 nanoseconds wide (as i s the Y h a l f - w r i t e p u l s e ) , then the read-write c y c l e time would be about 60 nanoseconds« To determine whether the a r r a y would accept pulses s h o r t e r than t h i s , a T e k t r o n i x P r e t r i g g e r Pulse Generator was used to produce the e n t i r e w r ite p u l s e . This pulse was of the order of 10 nanoseconds wide and i s shown i n Figure 6.9. This then i n d i c a t e s that a read—write c y c l e time of the order of 2Q nanoseconds might u l t i m a t e l y be p o s s i b l e . This corresponds to an o p e r a t i n g frequency of 50 Megacycles which i s about a f a c t o r of 10 f a s t e r than f e r r i t e - c o r e a r r a y s . This speed should i n t u r n be compared with present t r a n s i s t o r - t u n n e l diode l o g i c speeds which are r e p o r t e d to be (16) of the order of 250 Megacycles . However^transistor l o g i c (17) has a present l i m i t of about 100 Megacycles , and the a r r a y speed would be adequate f o r t h i s . One f i n a l aspect should perhaps be noted i n the comparison of tunnel—diode with f e r r i t e - c o r e memories. At the present time,, tunnel diodes are about 100 times as expensive as f e r r i t e 57 \ 1 j i i 1 < i j 1 i | r lOO MV T I N E V G U f - . ' * * " -F i g u r e 6.9. F u l l - W r i t e Pulse Produced Using a Tektronix Pulse Generator and J e r r o l d RF Attenuator c o r e s . Consequently the f a c t o r of 10 i n c r e a s e i n speed must be weighed a g a i n s t a f a c t o r of 100 increase i n c o s t . This i s one reason f o r l i m i t i n g the s i z e of tunnel—diode memories. The aspect of memory s i z e i s considered f u r t h e r i n the next s e c t i o n . 6.3 E x t e n s i o n of the Array The extent to which the s i z e of the a r r a y can be i n c r e a s e d depends on the c i r c u i t s used to driv-e i t . The t c e f c i r c u i t i s more f l e x i b l e than the mwef as i t s o v e r a l l system ga i n can be a l t e r e d without a f f e c t i n g i t s s t a b i l i t y . Consequently i t alone w i l l be considered here. The a r r a y s that have been d i s c u s s e d are of 16 word 25 b i t c a p a c i t y . I f the requirement that the d r i v e r s supply the de b i a s i n g i s removed, then l a r g e r a r r a y s become p o s s i b l e . The 58 extension, however, i s l i m i t e d by the admittance of the array i t s e l f . As the a r r a y s i z e i s i n c r e a s e d i t s impedance becomes sm a l l e r , causing a g r e a t e r mismatch f o r the t r a n s f o r m e r s . The transformers used r e q u i r e d about a 40 ohm load f o r matching. Consequently^array s i z e s v a s t l y d i f f e r e n t than that designed would perhaps r e q u i r e transformers with d i f f e r e n t c h a r a c t e r i s t i c impedances. This a p p l i e s p a r t i c u l a r l y to the X d r i v e r s . Por the Y d r i v e r , however, there i s the a d d i t i o n a l requirement t h a t i t d e t e c t the s w i t c h i n g c u r r e n t . The c u r r e n t t h a t flows i n the Y d r i v e r i s dependent on the number of c e l l s shunting i t . Thus any i n c r e a s e i n word c a p a c i t y w i l l r e s u l t i n l o s s of s i g n a l c u r r e n t . This of course can be countered by u s i n g a higher g a i n t r a n s i s t o r i n the grounded-emitter stage, or by decreasing the amount of d i f f e r e n t i a t i o n ( i . e . extending the band width to lower f r e q u e n c i e s ) i n t h i s stage. The s i z e of the a r r a y i s a l s o dependent on the type of tunnel diode used. Por diodes with peak c u r r e n t s g r e a t e r than 1 ma the mismatch on the transformer w i l l occur f o r smaller s i z e d a r r a y s . This would have a tendency to reduce the number of b i t s , but the number of words c o u l d be i n c r e a s e d due to the l a r g e r s w i t c h i n g c u r r e n t . Use of diodes with peak c u r r e n t l e s s than 1 m could i n c r e a s e the b i t c a p a c i t y , but not the number of words* 6*4 Conclusions The f e a s i b i l i t y of d e t e c t i n g the c u r r e n t change of s t a t e has been demonstrated i n t h i s t h e s i s . The method i s a p p l i c a b l e , however,only to small s i z e a r r a y s as the shunting admittance of 59 the a r r a y i t s e l f causes s i g n a l l o s s e s . Consequently,driver c i r c u i t s are r e q u i r e d which have a high input admittance r e l a t i v e to the a r r a y admittance. The i n v e s t i g a t i o n of h i g h input admittance c i r c u i t s l e d to the c o n s i d e r a t i o n of the mwef and the t c e f c i r c u i t s . Con-s i d e r a t i o n of the mwef showed t h a t i t s a p p l i c a t i o n here was l i m i t e d due to the i n a b i l i t y to s t a b i l i z e the network i n the 100 Megacycle frequency range and s t i l l m aintain loop g a i n . The t c e f c i r c u i t , on the other hand, employed a b i f i l a r wound 1:2 t r a n s -former to achieve an improved i n p u t admittance. This l e d to an i n v e s t i g a t i o n of a few of the p r o p e r t i e s of b i f i l a r wound t r a n s -formers. D e s i r e f o r good c o u p l i n g and the d e s i r e f o r broadband response are not compatible, and r e q u i r e that a compromise be made. A technique f o r d e s i g n of these transformers was developed. Throughout t h i s work d i f f i c u l t i e s were encountered r e s u l t i n g from an e a r l y assumption that i t would be economical to supply the dc to the a r r a y through the d r i v e r c i r c u i t s . The i n i t i a l d r i v e r , c i r c u i t considered was the mwef which employs two t r a n s i s t o r s and could be made to handle the cur r e n t r e q u i r e d . However,as the t c e f c i r c u i t appears to be su p e r i o r i t would, i n fu t u r e i n v e s t i g a t i o n s , be wise to d i s c a r d the b i a s i n g aspect f o r the d r i v e r s , and i n s t e a d ac couple them to the a r r a y . A d d i t i o n a l work c o u l d be done on i n c r e a s i n g the bandwidth of the d r i v e r c i r c u i t s . T h i s coupled w i t h the use of f a s t e r tunnel diodes could perhaps l e a d to access times of the order of 10 nanoseconds. More work co u l d a l s o be done on the broadband t r a n s f o r m e r s . E x t e n s i o n of the b i f i l a r technique to t r i f i l a r and higher order windings may be v e r y p r o f i t a b l e . 60 APPENDIX I TUNNEL-DIODE SWITCHING CHARACTERISTICS The d i f f e r e n t i a l equations governing the sw i t c h i n g of the tunnel diode are as given i n S e c t i o n 2.5: L | r = V - V - RI dt a c | = I - f (v) = 1 - 1 ' • Time s c a l i n g these by s e t t i n g t = CT/b r e s u l t s i n L b 5 ? = V a - V - R I and s e t t i n g L = 5 x l 0 ~ 9 i l , C •= 5 x l O ~ 1 2 c , b = 2 x l 0 1 0 , the d i f f e r e n t i a l equations become 20 1 ^1 _ v - V - RI .02 c |5 = I ~ I' ' d j which when the ranges of the v a r i a b l e V and I are examined can be w r i t t e n i n terms of machine parameters i , v as 4000 1 | i = 5 0 x l 0 3 (v - v) - 200 Ri 10 3 c = 200 i - 200 i ' 3 where i = 50 x 10 I and v = 200 x V. S u b s t i t u t i n g i n the values of R, JL, and c as R = 680, 1 = 1 , and c = 1 y i e l d s 0.1 |j = 0.25 (v - v). - 0.68 i 2.5 j j j = 0.1 i - 0.11' The d i o d e f u n c t i o n g e n e r a t o r a s s o c i a t e d w i t h t h e D o n n e r C o m p u t e r was s e t up t o g e n e r a t e t h e i ' f u n c t i o n , w h i c h i s t h e t u n n e l - d i o d e s t a t i c i - v c u r v e . T h u s t h e a n a l o g u e c i r c u i t i s as shown i n F i g u r e A l . l . to io is •O -0.681 -o-GENERATOR A.1 F i g u r e A l . l . A n a l o g u e S e t u p o f T u n n e l - D i o d e D E q . The i n p u t v o l t a g e was g e n e r a t e d b y s o l v i n g a n e q u a t i o n o f t h e f o r m + a X = K . d t T h i s e q u a t i o n * w h e n w r i t t e n i n t e r m s o f m a c h i n e p a r a m e t e r s , becomes , • v- . — x dx 0 &3 140 w h e r e x = 200X, V Q = 200V n where V n i s t h e a m p l i t u d e o f t h e s t e p 0 0 62 f u n c t i o n as d e f i n e d i n Figure 2.11, and 0 = 2 x l 0 ^ t . The c i r c u i t arrangement then i s as i n Fig u r e Al<>2. ;, Figure A1.2, Analogue Setup f o r Generation of Input F i g u r e A1.3. Tunnel-Diode Switching T r a j e c t o r i e s as Simulated on an Analogue Computer 63 The switching t r a j e c t o r i e s are shown i n Figure A1.3 f o r the three input s i g n a l s considered. Figure 2.11 shows the same t r a j e c t o r i e s p l o t t e d a g a i n s t time. I t should a l s o be noted here that while the F i g u r e A1.3 has 1 ma as i t s peak current the r e s u l t s obtained here apply almost e q u a l l y to the 5 ma tunnel diode. That t h i s i s so can be seen from the f a c t t h a t the d i f f e r e n t i a l equations are not a f f e c t e d by the s u b s t i t u t i o n of R' = R/m, L' = L/m, C' = mC, and i ' = mi. Since f o r the 5 ma tunnel diode Rr- — l/5R n , 5 ma ' 1 ma' C r — 5CT , and ic — 5 i n the only approximation i n v o l v e d 5 ma 1 ma 5 ma 1 ma J rr i s f o r L. T h i s r e s u l t s as the inductance a s s o c i a t e d with the tunnel diode i s due to the leads and hence i s independent of the tunnel diode s i z e . However as the inductance considered i n the switching of the 1 ma case i s small i t does not p l a y a very important r o l e i n determining the o v e r a l l switching time. Thus to an accuracy of about 10% the 1 ma curves can be used to represent the 5 ma tunnel diode. 64 APPENDIX I I TRANSISTOR VHP MEASUREMENTS In t h i s appendix the high-frequency performance of s e v e r a l t r a n s i s t o r types i s examined* Prom t h i s examination some i n d i c a t i o n i s given of the v a l i d i t y of the measurements made on the s h o r t — c i r c u i t gains of the mwef and t c e f . The measurements on the t r a n s i s t o r parameters were r e q u i r e d f o r an understanding of the performance of the mwef. The t r a n s i s t o r s , because of the intended a p p l i c a t i o n of t h i s c i r c u i t , were r e q u i r e d to have at l e a s t a 300 m i l l i w a t t d i s s i p a t i o n i n f r e e a i r . This power c o n d i t i o n e l i m i n a t e d many of the higher frequency t r a n s i s t o r s c u r r e n t l y a v a i l a b l e . The measurements were c a r r i e d out us i n g the General Radio 1607-A T r a n s f e r F u n c t i o n and Immittance B r i d g e . The 'block diagram of the t e s t arrangement i s shown i n Fig u r e A2.1. GR U n i t O s c i l l a t o r s 50-250 Mc 250-920 Mc GR 1607-A Bridge and Mounts SIGNAL FREQUENCY Input Supply Bias Supplie s GR U n i t Detector and IF A m p l i f i e r Output Supply GR Un i t O s c i l l a t o r 65-500 Mc LOCAL OSCILLATION Fi g u r e A2.1. Test Arrangement Block Diagram A2.1 T r a n s i s t o r Parameters The t r a n s i s t o r s l i s t e d i n Table A2.1 were examined. 65 SO \00 7.00 30O FV-eeouEHCY IN MC F i g u r e A2.2. M e a s u r e d h. 66 Quantity j Manuf a c t u r e r T r a n s i s t o r JEDEG No. Type T y p i c a l f. T from Manu. Average f from T Measurements 6 Motorola 2N834 NPN 3 50 Mc 360 Mc 6 T.I. 2N1143 PNP 300 Mc 350 Mc 2 F a i r c h i l d 2N2369 NPN 625 Mc 450 Mc 2 T.I. 2N1141 PNP 480 Mc 550 Mc Table A2.1* Frequ ency at Which h„ J i e := i (t> The measured h„ T s of these t r a n s i s t o r s are shown i n Figure A2.2< f e Two sets of parameters are c o n v e n t i o n a l l y used w i t h t r a n s i s t o r s : the h y b r i d parameters, and the admittance para-meters. In the a n a l y s i s of the mwef loop g a i n , the admittance parameters were found more convenient to use than the h y b r i d . Consequently o n l y the admittance parameters were measured — both f o r the grounded—base and grounded-emitter a m p l i f i e r s . The Jjyj k parameters can be r e a d i l y obtained from the y g parameters and v i c e v e r s a , and i n f a c t t h i s was done as a check on the accuracy of the measurements. For the t r a n s i s t o r s s t u d i e d there was found to be about a 10$ d i f f e r e n c e between the two methods of f i n d i n g [ y ] b # The admittance parameters were obtained f o r the b i a s c o n d i t i o n s e x i s t i n g when the 1 ma mwef Y - c i r c u i t has an output c u r r e n t of 7.7 ma. The r e s u l t s of these measurements are shown i n F i g u r e s A2„ .3 and A2.4. The admittance parameters shown are i n d i c a t i v e of the orders of magnitude t h a t were observed f o r a l l t r a n s i s t o r s c o n s i d e r e d . The admittance parameters are roughly independent of 6 7 « » » *• •OO TOO 1)00 -400 F i g u r e A2 03(b)„ y Q b f o r the 2N834 F i g u r e A2.3(d). y r b f o r the 2N83.4 69 IN M I L L i M H O S . •20.4 F i g u r e A 2 „ 4 ( b ) 0 y f o r the 2N1143. 70 Figure A2,4(d). y r e f o r the 2 N 1 1 4 3 71 c o l l e c t o r v o l t a g e f o r v o l t a g e s g r e a t e r than 5 v o l t s . The parameters are more dependent on c o l l e c t o r c u r r e n t . In p a r t i c u l a r , the forward transadmittance, y^, changes about 50% f o r a change i n cu r r e n t from 5 to 15 ma. A2.2 C i r c u i t J i g Measurements As i n d i c a t e d i n Chapters 4 and 5 measurements were made on the gain of the two d r i v e r c i r c u i t s considered. The c i r c u i t s were b u i l t on p r i n t e d c i r c u i t boards with minimum copper removed. These were then mounted on the GR 1607-P601 Ungrounded Component Mount. With the measurements of the mwef c i r c u i t i t was found necessary to add an a d d i t i o n a l low—pass f i l t e r on the supply l i n e s to the Bridge to prevent the c i r c u i t from o s c i l l a t i n g . Using the measurements of the previous s e c t i o n , the short - c i r c u i t c u r r e n t gain f o r the mwef was c a l c u l a t e d from Equation A5.3 of Appendix V. A comparison of t h i s r e s u l t with the r e s u l t obtained from the measurements u s i n g the mwef c i r c u i t j i g i s shown i n Figure A2.5. As can be seen from the f i g u r e , the experimental curve i s about 20% above the c a l c u l a t e d curve. This e r r o r i s t o l e r a b l e since t r a n s i s t o r s of the same type can va r y as much as 50% i n t h e i r c h a r a c t e r i s t i c s . 72 F i g u r e A2.5» C o m p a r i s o n o f G a i n F r o m y ' s a n d F r o m M e a s u r e m e n t s 73 APPENDIX I I I RESISTOR - CAPACITOR PERFORMANCE In t h i s appendix the r e s u l t s of measurements made i n the 50 to 350 Megacycle frequency range on l/2 watt carbon r e s i s t o r s and 75 v o l t ceramic c a p a c i t o r s are examined. A3.1 R e s i s t o r Measurements The r e s u l t s of the r e s i s t o r measurements are shown i n F i g u r e A3.1. A r e s i s t o r can be represented as an i n d u c t o r i n s e r i e s with a p a r a l l e l r e s i s t a n c e - c a p a c i t a n c e c i r c u i t . This can be s i m p l i f i e d to a s e r i e s r e s i s t a n c e - i n d u c t a n c e c i r c u i t , or to a p a r a l l e l r e s i s t a n c e - c a p a c i t a n c e combination, depending on the value of the r e s i s t o r . For the r e s i s t o r s measured the s e r i e s - R L combination was found to h o l d f o r values l e s s than 100 ohms, while the p a r a l l e l - R C h e l d f o r values g r e a t e r than 100 ohms. The range of valu e s of the p a r a s i t i c inductance and capacitance was 5-12 nanohenries f o r the inductance, and 0.5-1 p i c o f a r a d f o r the c a p a c i t a n c e . The measurements were made u s i n g the General Radio 1607-A B r i d g e . The components were mounted on the Component Mount with the arrangement shown i n Fig u r e A3.2. —H U { * - "Oio C O P P E R . i-uas, Figure A3.2* R e s i s t o r Mounting OtiMS, 75 A3.2 C a p a c i t o r Measurements The r e s u l t s of these measurements are shown i n Figure A3.3. A ca p a c i t o r , can be represented as a s e r i e s inductance-capacitance c i r c u i t . Examination of the inductance showed that i t was a t t r i b u t a b l e to the leads and was of the order of 10 nanohenries f o r a l l the c a p a c i t o r s considered. The measurements were done u s i n g the General Radio 1607-A B r i d g e . The c a p a c i t o r s were mounted as shown i n Fig u r e A3.4 on the Component Mount. 0\ b C O P P B R . LUG-F i g u r e A3.4. C a p a c i t o r Mounting A technique employed i n high—frequency work i s that of p a r a l l e l i n g c a p a c i t o r s i n order to achieve a lower l e a d inductance. This can,however, cause c o m p l i c a t i o n i f a c a p a c i t o r which looks i n d u c t i v e i s shunted by one which i s s t i l l c a p a c i t i v e . T h i s produces a p a r a l l e l - L C c i r c u i t which w i l l resonate. At the resonant frequency the c i r c u i t w i l l have a high impedance. Fi g u r e A3.5 shows what i s i n v o l v e d . J 1 1 F i g u r e A3.5* C a p a c i t o r s i n P a r a l l e l rzi IN OHMS n 1 , 1 1 T A N K C ^ C U l T / / 1 1 1 1 / \ s \ \ \ \ / \ / ' \ ">?* 1 \ 1 \ owe \ \ \ \ / / \ / \ / \ \ \ \ \ \ \ \ / y V /\ \ \ / \ / i \ / • \ \ / y / • / / / / r V / / \ V \ 5-0 lOO "500 F i g u r e A3«3. Cap a c i t o r Measurements 77 The resonant frequency f o r t h i s c i r c u i t i s given as 1/2TC J (L-J^ + L 2 ) C 1 C 2 / ( C 1 + C 2 ) . The frequency response f o r a 50 pF combination i s shown i n Figure A3.3. 78 APPENDIX IV BROADBAND TRANSFORMERS A4*l I n t r o d u c t i o n This appendix deals w i t h the p r o p e r t i e s of broadband transformers i n the 50 to 450 Megacycle frequency range. T h e o r e t i c a l and experimental r e s u l t s are given which i n d i c a t e the range of a p p l i c a t i o n . Conventional transformers are c h a r a c t e r i z e d by having a leakage inductance, a magnetizing inductance, and an i n t e r -(18) winding c a p a c i t a n c e v • ••• The bandwidth of these devices i s l i m i t e d by the leakage inductance and the i n t e r w i n d i n g capacitance* The transformers d e s c r i b e d here are b i f i l a r wound. This means that each t u r n i s p a i r e d with another c a r r y i n g , i d e a l l y , an equal and opposite c u r r e n t . The i n t e r w i n d i n g capacitance thus becomes a component of the c h a r a c t e r i s t i c impedance of the r e s u l t i n g t r a n s m i s s i o n l i n e . Hence }the input and output windings can be c l o s e l y spaced together to o b t a i n good c o u p l i n g and s t i l l achieve a wide bandwidth. The winding arrangement f o r a 1:1 i n v e r t i n g transformer i s shown i n F i g u r e A4.1. The primary i s the s o l i d l i n e , while the secondary i s d o t t e d . For h i g h e r r a t i o t r a nsformers, as w i l l be i n d i c a t e d , the primary and secondary are not d i s t i n c t . The simple 1:1 transformer, however, i s considered f o r an i n i t i a l e x p l a n a t i o n of the o p e r a t i o n of these transformers. F i g u r e A 4 . 1 1 : 1 I n v e r t i n g Transformer A 4 . 2 Operation of B i f i l a r Transformers The o p e r a t i o n of the f o r e g o i n g 1 : 1 transformer and other b i f i l a r transformers can be e x p l a i n e d by assuming the current flow components shown i n the f i g u r e . For the symmetrical components, i g , the magnetic f i e l d s almost c a n c e l , and the inductance i s s m a l l . With the unsymmetrical (i- u) component, the magnetic f i e l d s add, and the mutual inductance w i l l be a p p r e c i a b l e . As can be seen from the f i g u r e , the e f f e c t of the un-symmetrical c u r r e n t flow i s to reduce the output c u r r e n t . How-ever, f o r an output v o l t a g e there must be some(i u) c u r r e n t flow ( i . e . there must be a net f l u x c i r c u l a t i n g i n the c o r e ) . Consequently, from the p o i n t of view of o b t a i n i n g an output v o l t a g e without a p p r e c i a b l y d i s t u r b i n g the symmetrical ( i ) s c u r r e n t s , the inductance to the ( i u ) c u r r e n t s should be l a r g e . Thus a lar g e number of turns would be d e s i r a b l e . However,as w i l l be shown i n S e c t i o n A 4 . 4 , a long transformer l i n e l ength i s d e t r i m e n t a l to the transformer high—frequency response. A 4 . 3 Autotransformer Representation I f the assumption i s made th a t the mutual reactance i s s u f f i c i e n t to ensure that only symmetrical c u r r e n t s flow, then 80 the o p e r a t i o n of the transformer of Fig u r e A4.1 can be represented u s i n g the autotransformer of Figure A4.2. Fi g u r e A4.2. Autotransformer E q u i v a l e n t of 1:1 Transformer This r e p r e s e n t a t i o n of the transformer i n terms of an autotransformer becomes quite u s e f u l i n the design of higher r a t i o d e v i c e s . An example which i l l u s t r a t e s t h i s i s the 1:2 cu r r e n t transformer of Figure A4«3. The a c t u a l w i r i n g arrange-ment i s shown i n F i g u r e A4.3a» while the autotransformer e q u i -v a l e n t i s shown i n Figure A4*3b« In bothjthe symmetrical current flow i s i n d i c a t e d . r e s u l t i n g autotransformer e q u i v a l e n t c i r c u i t , i t i s easy to design a transformer of any d e s i r e d c u r r e n t r a t i o , i n v e r t i n g or non-(a) (b) F i g u r e A4.3. A 1:2 Current Transformer Using the concept of symmetrical c u r r e n t flow and the 81 i n v e r t i n g , A few f u r t h e r examples are given i n Figure A4.4, (c) 1:4 N o n i n v e r t i n g Cascaded (d) 1:4 N o n i n v e r t i n g D i s t r i b u t e d i F i g u r e A4.4, Examples of Autotransformer Design Technique I t should be noted t h a t each of these transformers would be wound on one f e r r i t e cor'e. When the p e r m e a b i l i t y of t h i s core i s h i g h , the same flux' threads each t u r n . Consequently, i n the case of higher c u r r e n t r a t i o transformers, the voltage induced per t u r n i n each stage should be the same. For example, consid e r the 1:4 transformer of F i g u r e A4.4c - i f the f i r s t stage has 2N t u r n s , the second should have N t u r n s . E x p e r i m e n t a l l y t h i s was found to be necessary f o r optimum o p e r a t i o n below 100 Megacycles. However,above 100 Megacycles t h i s was not r e q u i r e d . In p a r t i c u l a r , two 1:4 transformers were wound, one with 4 turns on each stage, and the second with 8 turns and then 4 t u r n s . The responses f o r these were measured u s i n g the General Radio 1607-A i i ! 82 T r a n s f e r F u n c t i o n B r i d g e , a n d a r e shown i n F i g u r e 4 . 5 . As c a n be s e e n t h e r e s p o n s e f o r t h e e q u a l t u r n t r a n s f o r m e r i s b e t t e r above FREQUENCY IN (MC , , 1 . i 1 •*— *-•SO \00 ISO 200 TLSP 30O 350 -400 F i g u r e A 4 . 5 . R e s p o n s e o f l s 4 T r a n s f o r m e r 100 M e g a c y c l e s . T h i s i n d i c a t e s t h a t a t t h e s e f r e q u e n c i e s t h e f l u x must r e t u r n t h r o u g h t h e a i r s u r r o u n d i n g t h e t r a n s f o r m e r r a t h e r t h a n t h r o u g h t h e f e r r i t e . F r o m t h e s e r e s u l t s i t i s i n d i c a t e d t h a t a s h o r t l i n e l e n g t h i s d e s i r a b l e f o r h i g h - f r e q u e n c y a p p l i c a t i o n s . To d e t e r m i n e t h e e f f e c t o f l i n e l e n g t h on t h e t r a n s f o r m e r p e r f o r m a n c e i t i s c o n v e n i e n t t o u s e a t r a n s m i s s i o n l i n e e q u i v a l e n t c i r c u i t (19) f o r t h e t r a n s f o r m e r . A4«4- T r a n s m i s s i o n L i n e R e p r e s e n t a t i o n F r o m t h e a s p e c t o f a c h i e v i n g a m a g n e t i z i n g i n d u c t a n c e , a l a r g e number o f t u r n s i s d e s i r a b l e , u n t i l t h e c a p a c i t a n c e a s s o c i a t e d w i t h t h e t u r n s b e g i n s t o l i m i t t h e r e s p o n s e „ The e x p e r i m e n t a l r e s u l t s o f v a r y i n g t h e number o f t u r n s on a 1:2 t r a n s f o r m e r a r e shown i n F i g u r e A4.6. H e r e i t i s s e e n FREQUENCY IN MC H 1 1 1 1 1 1 1  5 0 t O O \ 5 Q ^ 0 0 - Z S O - 5 0 O - 5 S O 4 0 0 F i g u r e A4.6* R e s p o n s e o f 1:2 T r a n s f o r m e r f o r D i f f e r e n t W i n d i n g s t h a t t h e 4 - t u r n t r a n s f o r m e r i s b e t t e r t h a n t h e 8 - t u r n f o r f r e q u e n c i e s g r e a t e r t h a n 400 M e g a c y c l e s . T h i s r e s u l t f u r t h e r 84 i n d i c a t e s t h a t f o r high—frequency performance the l i n e l e n g t h should be s h o r t . The e f f e c t of l i n e l e n g t h and i n t e r w i n d i n g capacitance can best be s t u d i e d i f the transformers are viewed as a t r a n s m i s s i o n l i n e . I f the assumption i s made t h a t the cur r e n t s f l o w i n g are symmetrical, then the b i f i l a r windings can be approximated by l o s s l e s s t r a n s m i s s i o n l i n e s . In p a r t i c u l a r ^ the t r a n s m i s s i o n l i n e e q u i v a l e n t f o r the 1:2 transformer i s shown i n F i g u r e A4.7. The output c u r r e n t (1^ + I^) can be obtained as © + v, - ® T7T Figure A4.7. 1:2 Transformer w i t h Transmission Line E q u i v a l e n t e (1 + co s K 2RT + (R + 2RT )cos0Q. L s L y + (R LR + Z j p s i n J0 where (3 i s the phase constant f o r the l i n e , ZQ i t s c h a r a c t e r i s t i c impedance, and JL i t s e f f e c t i v e l e n g t h . Maximum power t r a n s f e r occurs when L = 0, and 4R = R,. Further, an optimum value f o r g L •> ZQ can be found by minimizing the c o e f f i c i e n t of the s i n (3JL term as ZQ = 2R^. S u b s t i t u t i n g the values of ZQ and R^ and n o r m a l i z i n g the equation^ (I, + 1^(1,+ I 0 ) computed. These are p l o t t e d i n Fig u r e A4.8. values were 85 I n F i g u r e 4 . 4 , two w i r i n g a r r a n g e m e n t s were shown f o r a 1 : 4 t r a n s f o r m e r . N o r m a l i z e d c u r r e n t e x p r e s s i o n s w e r e d e r i v e d f o r t h e s e u s i n g t h e same a p p r o a c h as f o r t h e 1 : 2 t r a n s f o r m e r . I n t h e c a s e o f t h e c a s c a d e d 1 : 4 a r r a n g e m e n t , t h e e x p r e s s i o n was e v a l u a t e d f o r e q u a l t u r n s on b o t h s t a g e s , a n d f o r t h e r a t i o o f 2 t u r n s t o 1 . T h e s e r e s u l t s a r e shown i n F i g u r e A 4 . 8 , NORMALIZED (MAfiHlTUPef' F i g u r e A 4 . 8 . T h e o r e t i c a l R e s p o n s e C u r v e s I t i s s e e n f r o m t h i s f i g u r e t h a t t h e 1 : 4 t r a n s f o r m e r s do n o t h a v e a s b r o a d a b a n d w i d t h as t h e 1 : 2 . T h i s r e s u l t s f r o m m i s m a t c h i n g b e t w e e n t h e v a r i o u s s e c t i o n s o f l i n e s u s e d t o compose t h e s e t r a n s f o r m e r s . F u r t h e r , t h e 1 : 4 t r a n s f o r m e r w i t h e q u a l 8 6 t u r n s on e a c h s t a g e i s s u p e r i o r t o t h e one w i t h t h e r a t i o o f 2 t o l i F i n a l l y , t h e d i s t r i b u t e d t h r e e - s t a g e t r a n s f o r m e r a p p e a r s t o be b e t t e r t h a n t h e two—stage w i t h t h e r a t i o o f 2 t o 1 t u r n s . I n a l l o f t h e s e i t i s s e e n t h a t i t i s d e s i r a b l e t o h a v e as s h o r t a n e f f e c t i v e l i n e l e n g t h as p o s s i b l e , A4<>5 E x p e r i m e n t a l Work T h r e e 1:4 a n d s e v e r a l 1:2 t r a n s f o r m e r s were b u i l t . The t r a n s f o r m e r s were c o n s t r u c t e d on 0.2" d i a m e t e r f e r r i t e c o r e s . Two d i f f e r e n t t y p e s o f f e r r i t e c o r e s were e m p l o y e d . One was s p e c i f i e d f o r a p p l i c a t i o n s b e l o w 100 K i l o c y c l e s , w h i l e t h e o t h e r was i n t e n d e d f o r a p p l i c a t i o n b e l o w 10 M e g a c y c l e s . H o w e v e r , i n t h e f r e q u e n c y r a n g e o f i n t e r e s t t h e r e was p r a c t i c a l l y no d i f f e r e n c e i n t h e r e s p o n s e o f t r a n s f o r m e r s wound o n t h e two d i f f e r e n t f e r r i t e s . T h i s , o f c o u r s e , i s due t o t h e f a c t t h a t a t h i g h f r e q u e n c i e s t h e p e r m e a b i l i t i e s o f b o t h f e r r i t e s w o u l d be p r a c t i c a l l y u n i t y . The b i f i l a r l i n e was made b y t w i s t i n g two p i e c e s o f #34 w i r e t o g e t h e r . T h i s l i n e when c o a t e d w i t h G l y p t a l V a r n i s h h a d a c h a r a c t e r i s t i c i m p e d a n c e o f a b o u t 80 ohms, f r o m 50 M e g a c y c l e s t o 500 M e g a c y c l e s . F o r c o m p a r i s o n w i t h t h e t h e o r e t i c a l c u r v e s o f S e c t i o n A4.4 t h e n o r m a l i z e d e x p e r i m e n t a l c u r v e s f o r t h r e e o f t h e t r a n s -f o r m e r s a r e shown i n F i g u r e A4.9. The l o a d i m p e d a n c e f o r t h e r e s p o n s e c u r v e s shown was 47 o h m s . The e f f e c t o f h i g h e r i m p e d a n c e s i s t o r e d u c e t h e c u r r e n t o u t , w h i l e l o w e r i m p e d a n c e i n c r e a s e s i t . The c h o i c e o f 47 ohms was d i r e c t e d a t s i m u l a t i n g t h e l o a d t h e t r a n s f o r m e r s w o u l d be w o r k i n g i n t o i n t h e i n t e n d e d 87 c i r c u i t a p p l i c a t i o n o f C h a p t e r 5* \.o. .fe. -. MORMAL\ZED(GAIN> 1.2. F R E Q U E N C Y \N M C F i g u r e A4.9. E x p e r i m e n t a l R e s u l t s The c u r v e s f o r t h e 1*4 t r a n s f o r m e r shown i n F i g u r e A4.9 i n d i c a t e t h a t t h e t w o - s t a g e t r a n s f o r m e r i s b e t t e r t h a n t h e • d i s t r i b u t e d t y p e - T h i s i s c o n t r a r y t o t h e r e s u l t o f S e c t i o n 4.5, b u t c o u l d be e x p l a i n e d b y t h e i n c r e a s e d c o m p l e x i t y o f the w i r i n g f o r t h e d i s t r i b u t e d f o r m . T h i s p o i n t was n o t p u r s u e d f u r t h e r as t h e r e s u l t s i n d i c a t e d t h a t t h e h i g h e r c u r r e n t - r a t i o t r a n s -f o r m e r s do n o t h a v e as w i d e a b a n d w i d t h as t h e 1:2. A d i r e c t c o m p a r i s o n b e t w e e n t h e t h e o r e t i c a l a n d e x p e r i m e n t a l r e s p o n s e i s n o t p o s s i b l e w i t h o u t k n o w i n g t h e |3 L t e r m o f t h e e x p e r i m e n t a l r e s u l t s . F o r t h e 1:2 t r a n s f o r m e r , t h e pi t e r m c a n be r e a d i l y o b t a i n e d f r o m t h e s h o r t - c i r c u i t a d m i t t a n c e m e a s u r e m e n t s . The s h o r t - c i r c u i t a d m i t t a n c e i s g i v e n a t t h e 88 g e n e r a t o r e n d b y y _ c o s 3  sc - 3 Z Q s i n 3S2. ' K n o w i n g ZQ f o r t h e b i f i l a r w i n d i n g s , ^ 3 t- c a n be c a l c u l a t e d . T h i s c o u l d be done f o r t h e 1 : 4 t r a n s f o r m e r as w e l l , b u t t h e s h o r t c i r c u i t a d m i t t a n c e e x p r e s s i o n i s c o n s i d e r a b l y more c o m p l i c a t e d . F i g u r e A 4 . 1 0 t h u s shows t h e d i r e c t c o m p a r i s o n b e t w e e n t h e t h e o r e t i c a l a n d e x p e r i m e n t a l v a l u e s f o r t h e 1 : 2 t r a n s f o r m e r s . F i g u r e A 4 . 1 0 . C o m p a r i s o n o f T h e o r e t i c a l a n d E x p e r i m e n t a l R e s u l t 89 A4.6 Conclusions The cu r r e n t r a t i o s f o r the experimental transformers are of course l o v e r than the t h e o r e t i c a l ones as the c u r r e n t flow i n the b i f i l a r l i n e i s not e n t i r e l y symmetrical. However^ as S e c t i o n 4.4 i n d i c a t e d ^ t h e l i n e l e n g t h cannot be i n c r e a s e d to improve t h i s symmetrical c u r r e n t flow without decreasing the bandwidth. Thus> f o r these transformers a compromise must be made between cu r r e n t r a t i o and bandwidth. For the 1:2 transformer used with the t c e f of Chapter 5t an 8-turn transformer was found most s a t i s f a c t o r y f o r the frequency range of i n t e r e s t * 90 APPENDIX V MWEF LOOP GAIN In t h i s appendix the loop g a i n i s d e r i v e d i n terms of the y parameters. A comparison i s made between the exact expression, the s h o r t - c i r c u i t loop g a i n , and the i d e a l i z e d loop g a i n . C o n s i d e r i n g the c i r c u i t shown i n Fig u r e A5.1 the network r admittance matrix j Y i can be r e a d i l y obtained from V,. m Figure A5.1. S i m p l i f i e d MWEF ( Y i b + y Q e ) ( y r b + y f e ) (y*>, + y „ J (yn-h + y,-J or ..(A5.1) To o b t a i n the loop g a i n the c i r c u i t of Figure A5 ..2 i s used. 91 Figure A5.2, m irr MWEF f o r Gain C a l c u l a t i o n s ^ i b 0 " V l " = y f b (y + y- ) w oe J l e y J re X V 2 . 0 ^oe 73 S e t t i n g V 3 = V 1 , and I 2 = 0, the c l o s e d - l o o p c u r r e n t g a i n i s h.1 _ y o e ( y 0 b + y i e } • y f e ( y f b + O T 1 V 1 l J y^(y.-h - y ^ y ™ + y r J (A5.2) i b V J o b ' " i e ' " r b ' T b "re' S e t t i n g = 0 the s h o r t - c i r c u i t loop c u r r e n t gain i s ~ y f e y f b 1. ^ s c y i b ( y 0 b + y i e } - W f b ..(A5.3) Assuming t h a t y ± e > y Q b and t h a t y l b y i e > y r b y f b ) t h e a P P r o x i m a t e e x p r e s s i o n ~ y f e y f b  y i b y i e ..(A5.4) of Chapter 4 r e s u l t s . These three Equations (A5.2, 5»3 and 5,4) 92 were evaluated u s i n g the y parameter values of Appendix II and are shown i n Figure A5.3.. As can be seen from the f i g u r e ^ t h e s h o r t - c i r c u i t loop g a i n and c l o s e d - l o o p gain are p r a c t i c a l l y i d e n t i c a l . However., the simple approximation of Chapter 4 i s i n e r r o r about 4 db and 40 degrees at 350 Megacycles. As the loop gain i s determined i n Chapter 4 by measuring the input admittance w i t h the loop open and then c l o s e d , the v a l i d i t y of t h i s procedure w i l l now be examined. With the loop c l o s e d the input admittance i s given by „ _ A ( y j b + y 0 e ) ( y 0 b + y i e } - ( y f b + y r e ) ( y r b + y f e > c = A n = y o b y i e where A = det JY j and A - ^ i s the 1,1 minor of [ I j . Now i f the input admittance i s then measured with the loop open and the output shorted, t h i s i s T - —— i { y i b(y. 0b + y i e ) - yr b y f b y o b + y±e Now I 0 ( l + A I)=Y C, or (1 + A T ) = - . ...(A5.5) y i b ( y 0 e + y±e ) - W f b S o l v i n g f o r A T y o e ( y o b + y i e 5 *- y f b y f e - y r e ( y r b + y f e ) A I = y i b i y o b + y i e 5 " y r b y f b (3-AIU IN ells 94 Comparing t h i s with A5.2 i t i s seen that the expressions are p r a c t i c a l l y i d e n t i c a l since y ^ > y r g and y £ e > y r b (see Appendix II ) • Hence A-j- = I ^ / l | and the g a i n obtained from the admittance measurements i s the closed—loop g a i n . One f u r t h e r p o i n t should perhaps be noted. From A5.5 an a l t e r n a t e approach to network s t a b i l i t y can be seen. With Equation 5.1 a necessary and s u f f i c i e n t c o n d i t i o n f o r the e x i s t e n c e of [ v ] with [ i ] = 0 i s t h a t det [ l ] = A = 0. From Equation A5.3 i f A = 0 then 1 + A-j- = 0 and hence Aj = -1. This c o n d i t i o n was d e r i v e d i n Chapter 6 by c o n s i d e r i n g the input admittance to the mwef. 95 APPENDIX VI 2X2 PULSE GENERATOR This appendix d e s c r i b e s the pulse generator that was designed to d r i v e the 2x2 a r r a y of S e c t i o n 6.1. To achieve the d e s i r e d r i s e times of about 20 nanoseconds 5' 2N708 t r a n s i s t o r s were employed almost e x c l u s i v e l y throughout the generator. This t r a n s i s t o r has a t y p i c a l f^, of about 4 0 0 Megacycles. The b l o c k diagram f o r the device i s shown i n Figure A6.1. The numbers t h a t appear i n t h i s f i g u r e correspond to s i m i l a r numbers i n the f a l l o w i n g f i g u r e s . Figure A6.1. 2X2 Pulse Generator Block Diagram The a s t a b l e , b i s t a b l e , and monostable c i r c u i t s are the 96 (a) Astable 33K ^ FROM 2 o o F < O R c H I J  (V) ( y ™<xsz 777 |4 0 P D I O O T J—ll—L ^ J _ | L _ $ o -2.N10S .1 L < 1 -o_ (b) Monostable AAM n o - n . "1 <"Vio-n. i e p i I — o (c) B i s t a b l e Figure A 6 « 2 e Astable. Mono stable^ and B i s t a b l e C i r c u i t s 9 7 standard c o l l e c t o r - b a s e cross-coupled c i r c u i t s . These are shown i n F i g u r e A6,2« The ast a b l e and b i s t a b l e provide the c l o c k and g a t i n g pulses r e s p e c t i v e l y * The monostable provides a 100 nanosecond wide pulse delayed some 20 nanoseconds w i t h r e s p e c t to the t r i g g e r p u l s e ; a comparable delay occurs i n the t r i g g e r i n g of the b i s t a b l e . follower—grounded emitter a m p l i f i e r which d r i v e s a shorted delay l i n e w i t h about 15 nanoseconds delay. This gives an output-pulse about 30 nanoseconds wide which i s f e d i n t o the OR-GATE? and the AND-GATE shown i n Figure A6,4„ I t should be noted that the AND—GATE has a v a r i a b l e b i a s supply which f o r the X l i n e s permits the height of the read pulse to be v a r i e d independently of the w r i t e p u l s e , A delay of about 50 nanoseconds between the YI and Y2 outputs i s achieved by us i n g the c i r c u i t of Fig u r e A6<,5<, The pulse shaper (shown i n Fig u r e A6 83) i s an emitter _ J l J l o © o < 3 ) o + 6v -|| t»7<i»^-O — | i 53o p r F i g u r e A6«3«. Pulse Shaper F R O M I O K T P R O M * .1 — [ j i r © © Tlx H1 < 1 W D M (a) O R - G A T E (b) AND—GATE F i g u r e A6<,4. OR a n d AND G a t e s F i g u r e A 6 . 5 * D e l a y C i r c u i t Figure A6.6 shows the a c t u a l output waveforms observed u s i n g a Tektronix 581 o s c i l l o s c o p e . F i g u r e A6«6« Waveforms from 2x2 Pulse Generator (100 ns/div, 200 mv/div) 1 0 0 REFERENCES I . Sims, R.C., Beck* E.R.j and Kamm, V.C., "A Survey of Tunnel Diode D i g i t a l Techniques", FIRE, V o l . 49* No. 1 pp. 136—146, January 1.961. .2. Rajachman, J.A.* "Computer Memories - Future P o s s i b l e Developments", RCA Review, pp. 137-152, June 1962. 3. E s a k i , L., L e t t e r to the E d i t o r , P h y s i c a l Review, V o l . 109, No.2* 1958. 4. Goto, et al., " Esaki Diode High Speed Logic C i r c u i t s " j IRE Trans a c t i o n s on E l e c t r o n i c Computers, V o l . EC9, pp. 25-29-, March I960. 5. Payton, "A P r a c t i c a l . Non—Destructive Random Access Tunnel. Diode Memory", WESCON 1962, Part 4. 6. Rajachman, J.A.^ "Computer Memories - A survey of the S t a t e - o f - t h e - A r t " , PIRE, V o l . 49? No. 1* pp. 1 0 4 - 1 2 7 9 January 1961„ 7. Sims, et a l , op. a 1 •>, p. 138. 8. Rajachman, op. e i t * ^ p. 125. 9. Salama, C.A.T., "The S t a t i c and Dynamic C h a r a c t e r i s t i c s of Series—Connected Tunnel Diodes and t h e i r A p p l i c a t i o n s i n D i g i t a l C i r c u i t s " , M,A.Sc.  Thesis j, U#B.C, p. 17, December 1962. 10. Salama, C.A.T., op. c i t . , p. 17. I I . F a r l e y , Elements of Pulse C i r c u i t s , London, Metheun and Co., 1953. 12. Goulding, F.S., P r i v a t e Communication. 13. Joyce, M.V., and Clar k e * K.K 0, T r a n s i s t o r Network A n a l y s i s * Reading* Mass., Addison-Yesley, I960;, p. 23. 14. Bode, H.Y., Network A n a l y s i s and Feedback A m p l i f i e r Design, P r i n c e t o n * Van Nostrand, 1945, p. 151. 1.5. Bode, H.V., op. cit-«-* Chapter 18. 1.6. Meyers* P., "Trends on Nanosecond Switching", Ele c t r o n i c s , V o l * 3 6 | No. 38j, pp. 35-38, September 20, 1963. 17. Meyers, P., op. c i t * * p. 36. 101 18. Millman, J . , and Taub, H., Pulse and D i g i t a l Ci: New Xork, McGraw-Hill, 1956, Chapter 9. 19. R u t h r o f f , C.L., "Some Broad-band Transformers", PIRE, V o l . 47 No. 8. pp. 1337-1342, August 1959. 

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