Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Edwards, Edward Murray
Master of Science - MSc
University of British Columbia
The requirements imposed upon a d.c. amplifier and reference voltage supply, suitable for measurement and control of signals of the order of 1 volt to an accuracy of 10 parts per million are investigated. A basic block design is proposed to achieve this goal using a transistor differential amplifier of new design and a highly regulated reference voltage supply. The detailed design procedure for these building blocks is then presented. Exact analysis of important characteristics of several relevant circuit configurations is presented. The unit under discussion was constructed and the measured performance was found to be in good agreement with the predicted performance.
AD.C. AMPLIFIER AND REFERENCE VOLTAGE SUPPLY SUITABLE FOR USE IN A MAGNET CURRENT REGULATOR by Edward Murray Edwards B . S c , U n i v e r s i t y of B r i t i s h C olumbia, 1959 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of P h y s i c s THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1964 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that per-mission f o r extensive copying of t h i s t h esis f o r s c h o l a r l y purposes may be granted by the Head of my Department or by hi s representatives. I t i s understood that.copying or p u b l i -c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of if shvo-<i*^~ The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada Date ABSTRACT The r e q u i r e m e n t s imposed upon a d.c. a m p l i f i e r and r e f e r e n c e v o l t a g e s u p p l y * s u i t a b l e f o r measurement and c o n t r o l of s i g n a l s of the o r d e r of 1 v o l t t o an a c c u r a c y of 10 p a r t s per m i l l i o n are i n v e s t i g a t e d . A b a s i c b l o c k d e s i g n i s proposed t o a c h i e v e t h i s g o a l u s i n g a t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r of new d e s i g n and a h i g h l y r e g u l a t e d r e f e r e n c e v o l t a g e s u p p l y . The d e t a i l e d d e s i g n procedure f o r th e s e b u i l d i n g b l o c k s i s then p r e s e n t e d . E x a c t a n a l y s i s of i m p o r t a n t c h a r a c t e r i s t i c s of s e v e r a l r e l e v a n t c i r c u i t c o n f i g u r a t i o n s i s p r e s e n t e d * The u n i t under d i s c u s s i o n was c o n s t r u c t e d and the measured performance was found to be i n good agreement w i t h the p r e d i c t e d performance * i ACKNOWLEDGEMENT The au t h o r wishes t o thank Dr. B. B a r r i e , the s u p e r v i s o r of t h i s p r o j e c t , f o r h i s encouragement and support throughout the course of t h i s work. He would a l s o l i k e t o thank Dr. J . B i c h a r d f o r h i s encouragement and i n t e r e s t . D u r i n g the l a t e r stages of t h i s work, the author has been employed by Dr« L. Young of the E l e c t r i c a l E n g i n e e r i n g Department of the U n i v e r s i t y . The author wishes t o thank Dr. Young f o r h i s u n d e r s t a n d i n g and encouragement. The a u t h o r i s i n d e b t e d t o the Defence Research Board f o r t h e i r f i n a n c i a l support and to the E l e c t r i c a l E n g i n e e r i n g Department f o r t y p i n g and p r i n t i n g the f i n a l t h e s i s * L a s t but by no means l e a s t , the auth o r wishes t o thank h i s w i f e f o r g r e a t p a t i e n c e , u n d e r s t a n d i n g and h e l p . v i i TABLE OF CONTENTS Page L i S "b Of F i gUT G S ttooDO**o«oe« S » O » « O S O A O O « « • 1^ L X S ~b O f Tctb X © S « » o o 0 » o o o o o o o o o e e a o o o s o o « » * o * O # * « * * V3l Acknowledgements « o a o . * o » * « o » 0 a * o e o « e » « « * v n X « X H~b 3? O (Xll C "b X O II Ooo<>9oooec<>o«o»««fic«o0«e«*ft« •*•<»« X 2* OutXine of System 2.1 G*eneZ*al e . o ° B » e e o » . o « » . . . o . o o e « » . . . . . . . * . 3 2.2 The D.C. Ampl i f i 6r< • I I > > I I < I I O I > I > < > < I > < < 3 2.3 The Temperature C o n t r o l System 3 2.4 R e g u l a t e d Power Supply ........ 4 2.5 Reference V o l t a g e Supply ..........*..••• 4 3. Module D e s i g n 3*1 The T w o - t r a n s i s t o r Compound B l o c k ....... 6 3*2 The Common—emitter Compound C i r c u i t ••«•• 8 3.3 C o n s i d e r a t i o n s i n the A m p l i f i e r D e s i g n •« 9 , 3*4 The Input Stage of the D.C. A m p l i f i e r ... 10 3*5 The Second Stage of the D.C. A m p l i f i e r 17 3*6 The E m i t t e r - f o l l o w e r T h i r d Stage of the D C . A m p i i f i e r . o o . e o a e . e o o e e . o . . . . . ^ * * . . 21 3»7 The Oven Temperature C o n t r o l System .««• • 22 3*8 The Common—collector R e g u l a t o r .... ...... 26 3«9 The Common-emitter R e g u l a t o r .....»«.»••• 29 3*10 M o d i f i c a t i o n of R e g u l a t o r Output Re S X S "b 3/11C e « o e « o o « » e » e © « t © o o e © o e * » * 30 3.11 Comparison of Common-emitter and Common-c o l l e c t o r R e g u l a t o r s ...<> ..<.........**.. . 30 3.12 The Temperature C o e f f i c i e n t of Breakdown-3.13'General Power Supply C o n s i d e r a t i o n s *..*• 35 i i I Page 3.14 The R e g u l a t e d Power Supply f o r the D.C. 3*15 The Reference Supply 38 3*16 The P r e - r e g u l a t o r s • 39 3•17 The OV en e f i o o o . o o e o o e « . . o e o . . o « e . « • •»•*'•• 39 4. Performance of Equipment 4.1 The D.C. A m p l i f i e r 44 4*2 The T e m p e r a t u r e - r e g u l a t o r System ........ 44 4„3 Power Supply Performance „............... 46 4»4 P r e — r e g u l a t o r Performance 48 Appendix 1» L i n e and Load R e g u l a t i o n Performance of R e g u l a t e d Power S u p p l i e s ......... 50 Appendix 2* D e r i v a t i o n of E q u a t i o n s P r e d i c t i n g Power Supply Performance 53 Appendix 3« D e r i v a t i o n of the Exact Parameters f o r an E m i t t e r - f o l l o w e r ................. 60 Appendix 4* D e r i v a t i o n of the Ex a c t Parameters f o r a Common-emitter A m p l i f i e r ...... 65 Appendix 5* D e r i v a t i o n of the Exact Parameters f o r a Common-emitter A m p l i f i e r w i t h E x t e r n a l E m i t t e r Impedance . . . . . . . . . . . . . 6 9 Appendix 6. D e r i v a t i o n of the Parameters of the Compound Stage Used i n the D i f f e r e n t i a l A m p l i f i e r « .:«. 74 Ref e r e n c e s . • • • o e o o o © « . o © « o o e o . « . . . . o . . . . . . . . « . * * • i i i LIST OP FIGURES Page 2- 1 B l o c k Diagram of D.C. A m p l i f i e r and Reference Supply ........ 5 3- 1 The Two T r a n s i s t o r Compound «.•••« 8 3-2 The B a s i c T w o - t r a n s i s t o r Compound Common—emitter A m p l i f i e r .............. 8 3-3 The Input Stage of the D.C. A m p l i f i e r . 11 3-4 T r a n s i s t o r w i t h B a s e - e m i t t e r R e s i s t o r * 12 3-5 The Second Stage of the D.C. A m p l i f i e r 18 3-6 The E m i t t e r - f o l l o w e r T h i r d Stage ...... 21 3-7 The Oven Temperature C o n t r o l Servo .... 23 3-8 The Common-collector R e g u l a t o r ........ 26 3-9 The Common-emitter R e g u l a t o r 29 3-10 Breakdown-diode V o l t a g e a t 10 m i l l i a m p s v s . Diode C u r r e n t f o r Zero Temperature C o e f f i c i e n t ...... 34 3-11 The R e g u l a t e d Power Supply f o r the D.C, Allipl 1 f 1 © I* » f r e o o o a o * 0 6 B B * o o e o e o o * 35 3-12 Complete Schematic of D.C. A m p l i f i e r . . 41 3-13 Complete Schematic of Power S u p p l i e s .. 42 3- 14 P a r t s L i s t f o r Temperature C o n t r o l l e r . 43 4- 1 V a l u e of R 302 v s . Oven Temperature ... 45 A l r r l Four T e r m i n a l Network R e p r e s e n t a t i o n of R e g u l a t o r 50 A2—1 P r e — r e g u l a t o r 53 A2-2 S i m p l i f i e d C i r c u i t of P r e - r e g u l a t o r ... 53 A3-1 E m i t t e r - F o l l o w e r 60 A4-1 Common—Emitter A m p l i f i e r . c . . . . . . . . . . 6 5 A5-1 Common—emitter A m p l i f i e r w i t h E x t e r n a l E m i t t e r Impedance o o . . . . . . . . . . . . 69 i v Page A5-2 S m a l l - s i g n a l H y b r i d E q u i v a l e n t C i r c u i t of Common-base T r a n s i s t o r w i t h E x t e r n a l E m i t t e r Impedance 69 A6-1 The T w o — t r a n s i s t o r Compound i n the Common-e m i t t e r C o n f i g u r a t i o n .................... 74 v LIST OP TABLES Page 4—1 P r e d i c t e d and Measured Parameters of the R e g u l a t e d Power Supply •.*.••..... 47 4—2 P r e d i c t e d and Measured Parameters of the Reference Supply 47 v i 1. INTRODUCTION A d.c. a m p l i f i e r and r e f e r e n c e v o l t a g e s u p p l y s u i t a b l e f o r use i n a magnet c u r r e n t c o n t r o l , or p r e c i s i o n p o t e n t i o m e t e r , was d e s i g n e d and b u i l t . I n the p a s t ^ " ^ ' ^ ^ such systems have u s u a l l y employed a m p l i f i e r s based on some m o d u l a t i o n t e c h n i q u e , such as a chopper-s t a b i l i z e d a m p l i f i e r . T h i s t e c h n i q u e u s u a l l y r e q u i r e s an a u x i l i a r y a.c. a m p l i f i e r t o extend the pass-band out to the r e q u i r e d few k i l o c y c l e s . The m o d u l a t i o n system i s v e r y s u s c e p t i b l e t o p i c k u p or n o i s e a t the modulator f r e q u e n c y . E l e c t r o n i c choppers can work a t much h i g h e r f r e q u e n c i e s than m e c h a n i c a l or magnetic choppers or m o d u l a t o r s . However z e r o -d r i f t a g a i n becomes a problem. Magnetic modulators and a m p l i f i e r s were i n v e s t i g a t e d . I t appeared h i g h l y u n l i k e l y t h a t the s t a b i l i t y r e q u i r e d c o u l d be a c h i e v e d w i t h these d e v i c e s . Consequently, a new t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r was d e s i g n e d which o f f e r e d s u p e r i o r performance. The new a m p l i f i e r has good z e r o - s t a b i l i t y , a low n o i s e f i g u r e and p r o v i d e s a d.c. to 20 k i l o c y c l e s per second band-w i d t h w i t h i n e x p e n s i v e d e v i c e s . S i n c e o n l y one a m p l i f i e r i s used i n s t e a d of sep a r a t e low and h i g h f r e q u e n c y a m p l i f i e r s , the g a i n i s c o n s t a n t and the phase s h i f t s m a l l up to the upper c u t o f f f r e q u e n c y . The new d e v i c e has o p e r a t e d f o r s e v e r a l days w i t h i t s i n p u t s h o r t e d . Under t h i s c o n d i t i o n the peak-to-peak voTtage d r i f t s were of the o r d e r of t h r e e m i c r o v o l t s , r e f e r r e d to the i n p u t . 2 An independent r e f e r e n c e v o l t a g e s u p p l y (which i s e x t r e m e l y s t a b l e under v a r y i n g l i n e v o l t a g e c o n d i t i o n s ) i s i n c l u d e d i n the system. I n p r a c t i c e , the s t a b i l i t y of the r e f e r e n c e v o l t a g e i s l i m i t e d o n l y by t h a t of the break-down-diode used as a r e f e r e n c e * 2. OUTLINE OF SYSTEM 3 2.1 G e n e r a l The b l o c k diagram of the system i s shown i n F i g u r e 2-1. The system c o n s i s t s of a d.c. a m p l i f i e r , temperature c o n t r o l and power a m p l i f i e r , a r e g u l a t e d power su p p l y w i t h p r e - r e g u l a t o r and a r e f e r e n c e s u p p l y w i t h p r e - r e g u l a t o r . The s p e c i f i c a t i o n s r e q u i r e d f o r measurement and c o n t r o l of s i g n a l s of about 1 v o l t to + 10 ppm f o l l o w . 2.2 The D.C. A m p l i f i e r The d.c. a m p l i f i e r must have a zero s t a b i l i t y of + 10 m i c r o v o l t s or b e t t e r . I t s h o u l d have an a v a i l a b l e output of s e v e r a l v o l t s . The g a i n s h o u l d be g r e a t enough, t h a t any . subsequent a m p l i f i e r need not be an u l t r a - l o w d r i f t t y p e . Input impedance s h o u l d be of the order of 100K ohms or g r e a t e r to a v o i d l o a d i n g the s o u r c e . S i n c e such a u n i t would be e x t r e m l y s e n s i t i v e , a h i g h degree of common—mode r e j e c t i o n i s e s s e n t i a l t o reduce the e f f e c t s of s t r a y p i c k u p . The output impedance s h o u l d be low enough to d r i v e a medium impedance meter or r e c o r d e r d i r e c t l y . A w e l l d e f i n e d s t a b l e v o l t a g e , g a i n would a l l o w d i r e c t use f o r low v o l t a g e l e v e l measurements. 2.3 The Temperature C o n t r o l System A u n i t w i t h the s e n s i t i v i t y and s t a b i l i t y of t h a t d e s c r i b e d above would be extemely d i f f i c u l t t o temperature compensate over a temperature range of any a p p r e c i a b l e e x t e n t . 4 I t was t h e r e f o r e f e l t t h a t the more d i r e c t approach of e n c l o s i n g a l l c r i t i c a l components i n an oven at c o n s t a n t temperature would be more f r u i t f u l . I t was f e l t t h a t the oven temperature s h o u l d be h e l d to + 0.1C° or b e t t e r i f p r a c t i c a b l e . 2.4 R e g u l a t e d Power Supply I t i s r e a s o n a b l e t o expect equipment of the n a t u r e of t h a t d e s c r i b e d above to be s e n s i t i v e to power s u p p l y f l u c t u -a t i o n s . ¥hile i t might be p o s s i b l e to compensate the u n i t s f o r s u p p l y f l u c t u a t i o n s , the temperature changes caused by changing power d i s s i p a t i o n and the changes of component parameters w i t h v o l t a g e would be e x p e cted t o cause problems more severe t h a n t h a t of the c o n s t r u c t i o n of a w e l l r e g u l a t e d power s u p p l y . I t was t h e r e f o r e d e c i d e d to d e s i g n a power s u p p l y w i t h r e g u l a t i o n a g a i n s t l i n e v o l t a g e changes of 0.001$ or b e t t e r . T h i s degree of r e g u l a t i o n p r e s e n t s s i m i l a r , but much l e s s severe^ problems t h a n mentioned above i n c o n n e c t i o n w i t h the a m p l i f i e r . I t was t h e r e f o r e d e c i d e d to d i v i d e the r e g u l a t o r i n t o two u n i t s ; a rough p r e - r e g u l a t o r (ifo) and a main r e g u l a t o r i n s i d e the oven. The power s u p p l i e s were d e s i g n e d to t o l e r a t e l i n e v o l t a g e v a r i a t i o n s from 90 to 135 v o l t s rms. 2.5 Reference V o l t a g e Supply A r e f e r e n c e v o l t a g e s u p p l y was i n c o r p o r a t e d to a l l o w d i f f e r e n t i a l measurements or c o n t r o l . The d e s i g n i s v e r y s i m i l a r to the s u p p l y d e s c r i b e d above. To a v o i d l i m i t i n g the a c c u r a c y of the system, t h i s r e f e r e n c e s u p p l y s h o u l d have a s t a b i l i t y of 0.0001$ or b e t t e r . 5 Input o-o-Reference o-Voltoge o-Reference Supply D.C. Amplifier Pre-regulator 2 Power Supply Temperature Sensor and Amplifier Pre-regulator I Heater Power Amplifier Output — — o Heater Transformer Rectifier Filter Transformer Rectifier Filter Transformer Rectifier Filter 115 V. A.C. F i g u r e 2-1* B l o c k Diagram of D.C. A m p l i f i e r and Reference Supply 3. MODULE DESIGN 6 3*1 The Two T r a n s i s t o r Compound B l o c k Appendix 5 g i v e s the g a i n of a common-emitter t r a n s i s t o r a m p l i f i e r w i t h an e x t e r n a l e m i t t e r impedance, Zg, and l o a d impedance as h-p h , Z-p 1-h , A v = -G (-IS 9b_E ) rb 1 + h f e ^ r b 1 + * where h., h „ h , h., h , Z E o b E l+h„ 1-h , f e rb In the u s u a l d e s i g n of common-emitter a m p l i f i e r s the major d e p a r t u r e of the g a i n from the i d e a l v a l u e , -G, i s due to the terms h^^/(l+h^^) and n-L^/Zg« The major source of n o n - l i n e a r i t y i s the term h-j^/Zg. s i n c e hu^ i s i n v e r s e l y p r o p o r t i o n a l to the e m i t t e r c u r r e n t . A g r e a t improvement i n b o t h the p r e d i c t a b i l i t y and s t a b i l i t y of the g a i n can be a c h i e v e d by l o w e r i n g the v a l u e of t u ^ and r a i s i n g the v a l u e of h^ e» The w e l l known D a r l i n g t o n compound r a i s e s h f g to the p r o d u c t of h f e l and h ^ g 2 of the two t r a n s i s t o r s used. U n f o r t u n a t e l y , however, the e f f e c t i v e v a l u e of t u ^ i s a c t u a l l y i n c r e a s e d somewhat and i s s t i l l p r o p o r t i o n a l to the r e c i p r o c a l of the e m i t t e r c u r r e n t . The two t r a n s i s t o r compound suggested h e r e , and shown 7 i n F i g u r e 3-1 a l s o r a i s e s the c u r r e n t g a i n to a p p r o x i m a t e l y the pr o d u c t of the c u r r e n t g a i n s of the i n d i v i d u a l u n i t s . However, h ^ i s reduced g r e a t l y ( t y p i c a l l y one o r d e r of magnitude) over e i t h e r a s i n g l e t r a n s i s t o r or the D a r l i n g t o n compound. I n a d d i t i o n , the " b a s e - e m i t t e r " v o l t a g e drop of the D a r l i n g t o n compound i s the sum of the two b a s e - e m i t t e r v o l t a g e drops w i t h a t t e n d a n t temperature c o e f f i c i e n t s . The " b a s e - e m i t t e r " v o l t a g e drop of the compound suggested here i s o n l y t h a t a s s o c i a t e d w i t h one t r a n s i s t o r . I n the c i r c u i t used i n t h i s work the c o l l e c t o r c u r r e n t of the f i r s t t r a n s i s t o r i s s e v e r a l t i m e s l a r g e r than the c o l l e c t o r c u r r e n t of the second t r a n s i s t o r d i v i d e d by i t s c u r r e n t g a i n . Thus the c o l l e c t o r c u r r e n t of the f i r s t t r a n s i s t o r v a r i e s o n l y s l i g h t l y over the o p e r a t i n g range of the compound. Since h ^ , f ° r the compound, i s p r i m a r i l y determined by h - j ^ j * h ^ , as w e l l as b e i n g s m a l l , w i l l be s u b j e c t t o much l e s s percentage v a r i a t i o n oyer the o p e r a t i n g range. The compound c i r c u i t i s a n a l y z e d i n d e t a i l i n Appendix 6 and o n l y the approximate v a l u e s of the parameters w i l l be reproduced h e r e . , h i b l whpre h» - — h f e 2 3„2 l b - h" 0 w n e r e n f e 2 - h„ _ ...3-2 f e 2 f e 2 i b 2 R B 2 h , ^ h , n + h., , h , 0 rb r b l l b l ob2 «v !_ . ^ob2 h , s h , , + , • ob o b i h„ , f e l h - h h" fe ~ f e l f e 2 1 + h„ n h " 0 h ..h., _ f e l f e 2 o b i i b 2 T — T 4- ^cbo2 v _ v cbo ~ c b o l + h f x ' BE ~ B E l 8 O C Q2 BO E F i g u r e 3-1. The Two T r a n s i s t o r Compound 3.2 A P r a c t i c a l Common—Emitter A m p l i f i e r S u i t a b l e F o r Use I n a D i f f e r e n t i a l A m p l i f i e r Employing the Two T r a n s i s t o r Compound e m i t t e r a m p l i f i e r to s t a b i l i z e g a i n , r a i s e i n p u t impedance, and make the a m p l i f i e r p r o p e r t i e s l e s s dependent on t r a n s i s t o r parameters i s w e l l known. T h i s t e c h n i q u e i s e s p e c i a l l y e f f e c t i v e w i t h the two t r a n s i s t o r compound d e s c r i b e d above. The a m p l i f i e r h e r e i n d e s c r i b e d employs d i f f e r e n t i a l l y - c o n n e c t e d common-emitter u n i t s i n c o r p o r a t i n g the t w o - t r a n s i s t o r compound w i t h e m i t t e r r e s i s t o r s . T h i s b a s i c b u i l d i n g b l o c k i s shown i n F i g u r e 3-2. F i g u r e 3-2. The B a s i c T w o — T r a n s i s t o r Compound Common-Emitter The t e c h n i q u e of u s i n g an e m i t t e r r e s i s t o r i n a common— <>-°v0 V, tr A m p l i f i e r 9 Appendix 5 g i v e s the v o l t a g e g a i n and i n p u t impedance of a common e m i t t e r a m p l i f i e r w i t h e m i t t e r r e s i s t o r as A = - G ( 5 l L - - 5 s A ) ...3-3 l + h f e l - h r b 1+q where A v g = common e m i t t e r v o l t a g e g a i n and R L G = —• h., B„ B,-,,, h„ h , h.,h , l b i E , EO \ . n i f e r b , , _ i b o b \ B — + ~W~ ' + ^ \ + ) *E0 "EO "E l+h„ 1-h , f e rb ^ 0 l b Gh , ob Z T™ = ( l + h f o ) Bp ^ ...3-4 rb +• ( l + G ) ( l + h f e ) h Q b B E l + h f e E 3.3 C o n s i d e r a t i o n s i n the A m p l i f i e r Design I t was d e c i d e d to d e s i g n a t h r e e stage a m p l i f i e r w i t h an o v e r a l l g a i n of lj , 0 0 0 o and a,n i n p u t impedance of about 100K ohms« The g a i n f i g u r e of 1*000 was chosen so t h a t an a u x i l i a r y a m p l i f i e r used t o i n c r e a s e the g a i n f u r t h e r c o u l d be 10 r e l a t i v e l y s imple w i t h o u t a d v e r s e l y e f f e c t i n g the zero s t a b i l i t y . The t h r e e stages were to c o n s i s t o f ; 1. A h i g h - g a i n v e r y l o w - d r i f t i n p u t stage w i t h good common-mode r e j e c t i o n 2. A medium-gain, l o w - d r i f t second stage 3. An e m i t t e r - f o l l o w e r output stage w i t h p r o v i s i o n s f o r common—mode feedback to the c u r r e n t - s o u r c e t r a n s -i s t o r of the i n p u t s t a g e . 3.4 The Input Stage of the D#C. A m p l i f i e r The i n p u t stage c o n s i s t s of two a m p l i f i e r s of the type shown i n F i g u r e 3—2 connected d i f f e r e n t i a l l y w i t h a t r a n s i s t o r as a high-impedance c u r r e n t source i n the e m i t t e r l e a d s . To reduce problems a s s o c i a t e d w i t h leakage c u r r e n t , the t r a n s i s t o r s used i n the two a m p l i f i e r u n i t s were a l l s i l i c o n . The c i r c u i t i s shown i n F i g u r e 3-3. Q401 and Q402 are bonded t o g e t h e r , cap—to-cap w i t h Dow C o r n i n g 731 S i l i c o n e r u b b e r . T h i s assembly i s t h e n wrapped w i t h a l a y e r of t h i n i n s u l a t i n g t a p e , f o l l o w e d by two l a y e r s of copper tape s e p a r a t e d by i n s u l a t i n g t a p e . The whole assembly i s th e n wrapped w i t h another l a y e r of i n s u l a t i n g t a pe* The wrappings a c t as a th e r m a l f i l t e r t o keep the two t r a n s i s t o r s v e r y n e a r l y a t the same temperature even when the ambient temperature i s changing* The o t h e r p a i r s of t r a n s -i s t o r s i n the a m p l i f i e r are t r e a t e d s i m i l a r i l y . The compound b l o c k c o n s i s t i n g of Q402 and Q404 w i l l now be examined. The b a s e — e m i t t e r v o l t a g e of a s i l i c o n t r a n s i s t o r o p e r a t i n g a t 1 ma a t room temperature i s about 0.6 v o l t s . The common-emitter i n p u t impedance^ h. of such a t r a n s i s t o r i s 11 + I3V F i g u r e 3-3. The Input Stage of the D.C. A m p l i f i e r a p p r o x i m a t e l y ^ f g ^ 1 ^ ^ * where h ^ g i s the common-emitter c u r r e n t g a i n and, h ^ , the common-base i n p u t impedance, i s a p p r o x i m a t e l y 30 ohms. I f a r e s i s t o r Bg, i s p l a c e d between the base and the e m i t t e r , the i n p u t c u r r e n t t o the c o m b i n a t i o n (see F i g u r e 3-4) w i l l be I " = I B x V BE B + I c ^BE h FE Thus h " 0 PE ~ IB" h " — h 3-5 FE - n P E V B 1 ? . . . J D I c R b h P E "where I g " , Ig> IQ« Vgg? hpjj are d.c. l a r g e - s i g n a l parameters, However, HJJ + h. R„ + h„ h., i „ ^ i e B f e I D e l " = l B D b D h„ Rg Rg f e X c 1 f e ~ i " - n f e h h * " •^B i + f e i b where ig"> ig» i c« hf e» a r e s m a l l - s i g n a l parameters, F i g u r e 3-4. T r a n s i s t o r W ith B a s e - E m i t t e r R e s i s t o r I f the above mentioned parameters are 3-5 and 3-6, 3-7 and 3-8 are o b t a i n e d . s u b s t i t u t e d i n t o h — v» 2 FE _ FE ' n * * * ~ F E h f e " = h f e " ~ 3 - 8 *B" h f e I f h ^ e and h^^, are assumed to be a p p r o x i m a t e l y e q u a l , as i s u s u a l l y the case, i t i s seen t h a t h ^ may be c o n s i d e r a b l y reduced w i t h o u t s e r i o u s r e d u c t i o n of T h i s p e r m i t s l a r g e r c u r r e n t i n the i n p u t t r a n s i s t o r of a compound f o r a g i v e n compound c o l l e c t o r c u r r e n t . I f the c u r r e n t g a i n s of Q404 are t a k e n as h p g = h f g = 40 and R408 i s ta k e n as 5.6K ohms, the n hpg" =7.5 and h^ " = 33. Q404 i s a c t u a l l y o p e r a t e d a t a l i t t l e l e s s than 1 ma. However, the r e s u l t s quoted above are s t i l l a p p r o x i m a t e l y c o r r e c t o OC—201's were chosen f o r Q403 and Q404. Q402 i s oper a t e d a t a p p r o x i m a t e l y 100 jxa. From the d a t a sheet f o r a 2N697 a t I c=100 |j,a» h i b ~ 3 0 0 o h m s h f e - 50 h * 3: X 1 0 = 5 . ..3-9 rb h , ? 2 X 1 0 ~ 7 mhos, ob From the d a t a f o r the OC—201, h^ i s as quoted above, 40 and h o b = .5 \i mho. The presence of R408 l e a d s t o h^ " = 33 as s t a t e d above. Combining t h i s w i t h 3-9 and 3-2 g i v e s as the parameters of the compound Q402, Q404 and R408% h i b ~ 9 o h m h r b 1.8 X 1 0 ~ 4 h Q b * 2.1 X 1 0 ~ 7 , ...3-10 h_ « 2000 i e From 3-3 and 3-10 and t a k i n g G * 60 and and R E O = Jisr— - 850 ohms ob i b „ q * .011 + .01 + ^ - ) h f e -3 # 1 - .5 x 10 ^ 1 1 + h f e RT A V F = -G ((1 - .011 - .01 (-^2. + ^ - ) ) ) ...3-11 V h R E R E o 1 + .01 (^2. + 5L.) + . o n Z t t ;, = — — ° — — — X 10^ ohms lb -n + -021 (G + 1) K E .3-12 15 I t was d e c i d e d to use Rg = 100 ohms because a l a r g e r v a l u e would r e q u i r e a c o r r e s p o n d i n g l y h i g h e r v a l u e of R^ f o r the same g a i n and the stage would t h e n r e q u i r e a h i g h e r v o l t a g e to main-t a i n the d e s i r e d o p e r a t i n g c u r r e n t . Lower o p e r a t i n g c u r r e n t s would g i v e a h i g h e r v a l u e of h and lower v a l u e s of h ^ g and thus degrade the s t a g e . H i g h e r o p e r a t i n g v o l t a g e would r a i s e power d i s s i p a t i o n and aggravate the therm a l d r i f t s . V i t h Rg = 100 ohms, Ayg = -.9G and ZJE = 100K ohms/(.45 + .01 9 ( G + l ) ) . I f Rg was s e t equal t o R g Q , o n l y about 6 per cent more g a i n would be obtained,, I f i t i s assumed t h a t the second stage i n p u t impedance i s v e r y h i g h compared t o R^, the g a i n of the f i r s t stage w i l l be R406 p R406 R404 - ° y 100 Sin c e Ayg = 60 was d e s i r e d ^ R406 was chosen as 6.8K ohms to g i v e G = 68 and Ayg j u s t over 60. These v a l u e s g i v e Zj-g = 57K ohms. I f R401 and R402 are chosen as 150K ohms, the i n p u t impedance would be a p p r o x i m a t e l y 82K ohms between d i f f e r e n t i a l i n p u t s . R401 s u p p l i e s base c u r r e n t to the compound t r a n s i s t o r . I f R410 i s c o r r e c t l y chosen the v o l t a g e drop a c r o s s R402 w i l l be zero a t the d e s i r e d o p e r a t i n g p o i n t and zero i n p u t - v o l t a g e . Two of the above d e s c r i b e d elements are connected t o g e t h e r to form a d i f f e r e n t i a l a m p l i f i e r . Q403 i s the same type as Q404, s e l e c t e d f o r matched • Q401 i s the same type as Q402, s e l e c t e d f o r matched h^ and IQ^Q* The e f f e c t of the c o l l e c t o r - b a s e leakage c u r r e n t , IQ^Q? °^ the compound i s as f o l l o w s . The d i f f e r e n c e between the IQ-^Q of Q401 and t h a t of Q402 f l o w s t h r o u g h the source r e s i s t a n c e and c r e a t e s an o f f s e t v o l t a g e * AI^g^Rg. I t i s t h e r e f o r e d e s i r a b l e to have these IQBO' s a s s m a , H a s p o s s i b l e and as c l o s e l y matched as p o s s i b l e . The e f f e c t of the IQ^Q of Q403 i s s i m i l a r except t h a t the e f f e c t i v e v a l u e i s the a c t u a l v a l u e d i v i d e d by the c u r r e n t g a i n of the i n p u t t r a n s i s t o r , , Thus, i f these l e a k a g e s are of the same or d e r as the leakage of the i n p u t t r a n s i s t o r t h e i r e f f e c t w i l l be n e g l i g i b l e * The I Q B 0 o f Q40l a n d Q402 was -9 a p p r o x i m a t e l y 10 amp. R403 and R404 were hand wound w i t h advance r e s i s t a n c e w i r e on a s i l i c o n e r u b b e r form and matched to w i t h i n 0.05$. R405 and R406 were s e l e c t e d from a v a i l a b l e 6.8K ohm, itfo d e p o s i t e d carbon r e s i s t o r s . A p a i r was found t h a t matched to w i t h i n 0.1$. With the i n p u t s h o r t e d and the l o a d r e s i s t o r s matched, zero o u tput v o l t a g e w i l l be o b t a i n e d from the d i f f e r e n t i a l a m p l i f i e r i f the c o l l e c t o r c u r r e n t of the two compound " t r a n s i s t o r s " are e x a c t l y equals The e m i t t e r c u r r e n t s w i l l t h e n be v e r y n e a r l y e q u a l s i n c e the compound t r a n s i s t o r s have v e r y l a r g e , n e a r l y matched, c u r r e n t g a i n s . T h i s i m p l i e s t h a t the v o l t a g e drops a c r o s s the e m i t t e r r e s i s t o r s w i l l be v e r y n e a r l y e q u a l . T h i s i s o n l y p o s s i b l e i f the b a s e — e m i t t e r v o l t a g e s of the two compound " t r a n s i s t o r s " are equal f o r e q u a l c o l l e c t o r c u r r e n t . F o r t u n a t e l y t h i s parameter i s v a r i a b l e i n the c o m p o u n d - t r a n s i s t o r c i r c u i t u s e d . I f Rg ( F i g u r e 3-4) i s v a r i e d w h i l e I^, i s h e l d c o n s t a n t , I g " ( i n the compound c i r c u i t I g " i s c o l l e c t o r c u r r e n t of the i n p u t t r a n s i s t o r , F i g u r e 3 — l ) must be v a r i e d . When I g " i s v a r i e d the base e m i t t e r v o l t a g e w i l l v a r y . Thus Rg may be v a r i e d t o change the b a s e - e m i t t e r v d l t a g e of the compound a t c o n s t a n t 17 c o l l e c t o r c u r r e n t . S i n c e the b a s e - e m i t t e r v o l t a g e of a modern s i l i c o n t r a n s i s t o r i s a l r e a d y a q u i t e p r e d i c t a b l e parameter, o n l y a s m a l l c o r r e c t i o n i s n e c e s s a r y . T h i s can be e a s i l y a c c o m p l i s h e d w i t h o u t u p s e t t i n g o t h e r parameters of the c i r c u i t . l a r g e r (6.8K ohms i n s t e a d of 5.6K ohms) tha n R408 and shunted by a f i n e - a d j u s t network t h a t c o u l d v a r y the r e s u l t i n g r e s i s t a n c e from somewhat above to somewhat below 5.6K ohms. To a c c o m p l i s h t h i s R415 was made 10K ohms and R416 e x p e r i m e n t a l l y s e l e c t e d t o p l a c e the zero near the c e n t e r of the ad j u s t m e n t . T h i s a d j u s t - ment s h o u l d be made w i t h the i n p u t s h o r t - c i r c u i t e d . R409, R402j R413 and R414 are a s i m i l a r arrangement used to compensate f o r d i f f e r e n c e s i n base c u r r e n t r e q u i r e d t o e s t a b l i s h the d e s i r e d o p e r a t i n g p o i n t . The adjustment of R412 s h o u l d be made 9 a f t e r the adjustment of R415 9 w i t h the i n p u t o p e n — c i r c u i t e d . The zero adjustment s h o u l d t h e n be independent of source impedance. Q411 i s a high-impedance c u r r e n t source f o r the e m i t t e r c i r c u i t . The common-mode feedback s i g n a l , B, (see F i g u r e 3-3) i s g e n e r a t e d from a source of low impedance compared w i t h R411. Q411 i s thus o p e r a t i n g i n the common-base mode, and has an t h a t f l o w s w i l l be a p p r o x i m a t e l y e q u a l to. the v o l t a g e a t the base of Q411 d i v i d e d by R411„ 3.5 The Second Stage of the D.C« A m p l i f i e r For the reasons s e t out above R407 was made somewhat output conductance a p p r o x i m a t e l y e q u a l t o h ob° The a c t u a l c u r r e n t a p p r o x i m a t e l y 18 g r e a t e r g a i n which c o u l d be a d j u s t e d . The c i r c u i t i s shown i n F i g u r e 3-5. • + I3V < R424 Input I O-F i g u r e 3.-5. The Second Stage of the D.C. A m p l i f i e r The t r a n s i s t o r s used i n the second stage are germanium t r a n s i s t o r s . The b a s e - e m i t t e r v o l t a g e of a germanium t r a n s i s t o r a t 1 ma c o l l e c t o r c u r r e n t and room temperature i s t y p i c a l l y 0*1 v o l t compared w i t h 0.6 v o l t f o r s i l i c o n . I n o r d e r t h a t the t e c h n i q u e of u s i n g a r e s i s t o r between the base and the e m i t t e r , t o reduce h^g w i t h o u t s e r i o u s l y e f f e c t i n g h ^ . work e f f e c t i v e l y , i t i s n e c e s s a r y to i n c r e a s e the r a t i o of V-g-g/tUvj• A s i l i c o n diode has a v o l t a g e - c u r r e n t c h a r a c t e r i s t i c v e r y s i m i l a r to the base— v o l t a g e — e m i t t e r - c u r r e n t c h a r a c t e r i s t i c of a s i l i c o n t r a n s i s t o r . Thus the f o r w a r d v o l t a g e drop a t 1 ma c u r r e n t i s about 0.6 v o l t , and the dynamic impedance i s about 30 ohms. Q406, Q408, D402 and B418 form \a p-n-p compound t r a n s i s t o r complimentary t o t h a t shown i n F i g u r e 3-1. D402 r a i s e s the e f f e c t i v e b a s e - e m i t t e r v o l t a g e of Q406 from 0.1 v o l t to 0.7 v o l t a t 1 ma c o l l e c t o r c u r r e n t , w h i l e r a i s i n g the e f f e c t i v e h., from 30 ohms t o 60 ohms. U s i n g a 2N1305 f o r Q408, a 2N1304 f o r Q406, and a 1N465A f o r D402 g i v e s the f o l l o w i n g parameters f o r the compound t r a n s i s t o r thus formed* ¥ith the f o l l o w i n g v a l u e s f o r t r a n s i s t o r p arameters, x f e l 60 h f e 2 - 120 h., , = 300 ohms l b l h r M =" 7 X 10 -4 h =" .12 X 10 o b i -6 h., „ =* 30 ohms l b 2 h , 0 = 5 X 10 rb2 -4 h , . =• .34 X 10 obz -6 h "- 80 n f e 2 _ O U I , =0.1 ma c l I = 1 ma c 2 E q u a t i o n s 3-2 g i v e h., =2.5 ohms l b h , = 8 X 10 rb -4 «© * 3"~ X 3 h « .13 I 10" ob h„ *? 4700 i e Prom 3-3 and 3-13 t a k i n g G = 20 Eo I K ohm R R q = 0.016 + 2*5 X 10" 3 + R E o R E h f e 1 + h = 1 - 2 X 10 4 * 1 f e V E - G f l - *016 - 2.5 X l O "3 ! ^ - + ^§°) 20 1 + .016 + 2.5 X 1 0 _ 3 ( ^ - + ) 'E J I E 10 -5 .. .3-15 .047 Bg + (l+G) .13 X 10 -6 Fo r reasons s i m i l a r t o those o u t l i n e d r e g a r d i n g the c h o i c e of R404, R420 was s e t equal to 100 ohms. V i t h R420 = 100 ohms, e q u a t i o n s 3-14 and 3-15 become and A v E = - * 9 6 G 'IE 100K .20 + .013 (1+G) Ta k i n g S e t t i n g and G *? 'IE 20, 220K R422 = 3.3K R423 = 10K Thus G = 20 and R L = ^7p- // R422 ~ 2K A v E = ~ 1 9 An i d e n t i c a l u n i t i s used f o r the o t h e r h a l f of the second stage of the d i f f e r e n t i a l a m p l i f i e r w i t h a 2K ohm r e s i s t o r (R424) as an e m i t t e r c u r r e n t s o u r c e . 21 3.6 The E m i t t e r - F o l l o w e r T h i r d Stage of the D.C. A m p l i f i e r The t h i r d stage of the d i f f e r e n t i a l a m p l i f i e r i s a d i f f e r e n t i a l e m i t t e r - f o l l o w e r . I t s purpose i s to p r o v i d e a low output-impedance and thus make the g a i n more independant of l o a d i n g a t the o u t p u t . The c i r c u i t i s shown i n F i g u r e 3-6. e Output I o Output 2 + 13 V F i g u r e 3-6. The E m i t t e r F o l l o w e r T h i r d Stage Q4Q9 and Q410 are 2N1309 h i g h — g a i n germanium t r a n s i s t o r s . E425 and R426 are 8.2K ohms r e s i s t o r s ^ used to e s t a b l i s h the d e s i r e d 1 ma o p e r a t i n g c u r r e n t w i t h the common-mode A output a t +4 v o l t s , The output impedance of an e m i t t e r — f o l l o w e r i s g i v e n by R (Appendix 3) Z = oc l b h f e 1 + h , R ob g ...3-16 22 F o r a 2N1309 at I = 1 ma: c h f e - 1 9 0 h' * .4 X 1 0 " 6 mhos ob h., = 30 ohms l b R v a r i e s , depending on the s e t t i n g of R423, between 0 and 2K ohms* Thus the output impedance w i l l be between 60 ohms and 82 ohms« 3.7 The Oven Tem p e r a t u r e - C o n t r o l Servo The b a s e - e m i t t e r v o l t a g e of a s i l i c o n or germanium t r a n s i s t o r o p e r a t e d a t c o n s t a n t c o l l e c t o r c u r r e n t d ecreases a p p r o x i m a t e l y 2 M i l l i v o l t s f o r each c e n t i g r a d e degree r i s e i n temperature over a wide temperature range. T h i s v o l t a g e and i t s temperature c o e f f i c i e n t appear s t a b l e w i t h t i m e . T h i s phenomenum i s u t i l i z e d t o c o n t r o l the temperature of the oven. The c i r c u i t f o r the temperature c o n t r o l servomechanism i s shown i n F i g u r e 3-7. B a s i c a l l y the u n i t i s a d.c. a m p l i f i e r which i s not compensated f o r the e f f e c t of the change of the b a s e - e m i t t e r v o l t a g e of the i n p u t t a n s i s t o r w i t h t e m p e r a t u r e . I n f a c t the a m p l i f i e r i s d e s i g n e d t o emphasize t h i s e f f e c t . A germanium t r a n s i s t o r i s used f o r Q301. A s i l i c o n t r a n s i s t o r would have about s i x times as l a r g e a b a s e - e m i t t e r v o l t a g e w i t h about the same v a l u e of O BE of a p p r o x i m a t e l y b T —2 mv/C°. The b a s e - c i r c u i t v o l t a g e d i v i d e r , R301 and R302, 23 o + Heater 24V c -OVEN F i g u r e 3-7. The Oven Temperature-Control System R 302 —1 would then have to have about s i x times the r a t i o ( l + g~302") and the s e n s i t i v i t y of the c i r c u i t t o power s u p p l y v o l t a g e changes would be i n c r e a s e d by the same f a c t o r . T r a n s i s t o r Q301 i s o p e r a t e d i n the common e m i t t e r mode. The impedance of the b a s e - c i r c u i t v o l t a g e d i v i d e r must be much l e s s t h a n the common-emitter i n p u t impedance to maximize the v o l t a g e s e n s i t i v i t y of Q301* The performance of the c i r c u i t may be a n a l y s e d by r e p l a c i n g Q301 w i t h a h y p o t h e t i c a l t r a n s i s t o r w i t h q BE _ Q o T and h a v i n g a v o l t a g e g e n e r a t o r of 2 mv ( T Q - T) i n s e r i e s w i t h i t s base l e a d . U s i n g e q u a t i o n s A5—97 A5—12, and A5-13 of Appendix 5* and A4-9 of Appendix 4 the g a i n o f the a m p l i f i e r c o n s i s t i n g of Q301, Q302 and Q303 may be shown t o be A y E = 1.5 X 10 24 The e m i t t e r - f o l l o w e r , Q304 w i l l p r o v i d e an o u t p u t -impedance of a p p r o x i m a t e l y 250 ohms. R310 i n the c o l l e c t o r c i r c u i t of Q304 se r v e s to l i m i t the c u r r e n t through Q304 i n the event of o v e r l o a d or s h o r t c i r c u i t . The v o l t a g e a t the p o i n t marked V^ , i n F i g u r e 3-7 w i l l have a temperature c o e f f i c i e n t of — - = 1.5 X 1CT X (-2) mv/C° ...3-17 dT = 30 v o l t s / C }T and w i l l be generated by a source of a p p r o x i m a t e l y 250 ohms impedance. As w e l l as b e i n g s e n s i t i v e t o temperature changes, the u n i t i s s e n s i t i v e t o s u p p l y v o l t a g e v a r i a t i o n s . The u n i t t h a t was c o n s t r u c t e d gave an o p e r a t i n g p o i n t of 35°C w i t h R302 = 15K and R301 = 100 ohms. The d i v i d e r r a t i o f o r R302 and -3 R301 i s t h e n 6.7 X 10 . When t h i s i s m u l t i p l i e d by the 4 a m p l i f i e r g a i n , 1.5 X 10 , the r e s u l t i s 2 VT — - = 100 v o l t s / v o l t where = v o l t a g e a t t e s t p o i n t ( f i g u r e 3-7) Vg = s u p p l y v o l t a g e 2 5 <^T / <^T o / The r a t i o / = 3.1 C / v o l t i s the e r r o r i n o p e r a t i n g a v s ^T p o i n t t h a t would be caused by a change of 1 v o l t i n s u p p l y v o l t a g e * The power s u p p l i e s used i n t h i s equipment are capable of more t h a n s u f f i c i e n t r e g u l a t i o n t o keep t h i s source of e r r o r below a few m i l l i d e g r e e s f o r l i n e v o l t a g e s between 9 0 and 1 3 5 v p l t s r.m.s. The e f f e c t of the change of b a s e - e m i t t e r v o l t a g e of Q 3 0 2 w i t h temperature i s suppressed by the pr o d u c t of the v o l t a g e g a i n of Q 3 0 1 and one p l u s the r a t i o of output impedance of Q 3 0 1 t o the i n p u t impedance of Q 3 0 2 . T h i s q u a n t i t y i s a p p r o x i m a t e l y 3 3 0 . The temperature s e n s i t i v i t y of the base-e m i t t e r v o l t a g e of Q 3 0 2 o n l y changes the o v e r a l l s e n s i t i v i t y by about l / 3 $ . T r a n s i s t o r s f u r t h e r a l o n g i n the u n i t w i l l have even l e s s e f f e c t . The e f f e c t of the leakage c u r r e n t of Q 3 0 2 i s much more s e r i o u s . I f the IQ^Q of Q 3 0 2 changes by 1 jj,a, t h i s w i l l appear as a 1 aa change i n c u r r e n t through the output impedance of Q 3 0 1 w h i c h , i n c l u d i n g the e f f e c t of i t s l o a d r e s i s t o r , R 3 0 3 , i s 3 6 K ohms. The 1 \xa, change i n I Q B Q of Q 3 0 2 then appears as a 3 6 m i l l i v o l t change a t the output of Q 3 0 1 which i s e q u i v a l e n t to about l / 3 mv a t the i n p u t or about l / 6 C°. I t would t h e r e -f o r e be d e s i r a b l e to r e p l a c e Q 3 0 2 w i t h a low leakage s i l i c o n t r a n s i s t o r . S e l f h e a t i n g of Q 3 0 1 i s another p o t e n t i a l source of e r r o r and i n s t a b i l i t y . Q 3 0 1 , which i s r e q u i r e d t o d i s s i p a t e about \ mw, i s mounted i n a f i n n e d h e a t - s i n k which g i v e s an o v e r a l l o / c o l l e c t o r j u n c t i o n - t o - a m b i e n t t h e r m a l r e s i s t a n c e of about .2 C /mw. 26 The j u n c t i o n of Q301 would t h e n be e x p e cted to be a t about 0.05C 0 above ambient. S i n c e t h i s q u a n t i t y s h o u l d be s t a b l e to w i t h i n about 10$, the i n s t a b i l i t y caused s h o u l d be n e g l i g i b l e . The h e a t e r power a m p l i f i e r i s a common-emitter power s t a g e , w i t h a v o l t a g e g a i n of about 5, d r i v e n by an e m i t t e r -f o l l o w e r * B311, R312 and B 315 p r o v i d e adequate t h e r m a l . s t a b i l i t y . R313 and R314 l i m i t the power d i s s i p a t i o n i n the c o l l e c t o r c i r c u i t of Q305. The output v o l t a g e to the h e a t e r i s t h e n about 150 volts/C°. The oven w i l l t h e n be t u r n e d from f u l l on to f u l l o f f by an i n t e r n a l temperature change of about .15 C°. For the u n i t c o n s t r u c t e d , the v a l u e of R302 r e q u i r e d f o r 35°C o p e r a t i o n was a p p r o x i m a t e l y 15K ohms and dR302 w a g 3 T found t o be 250 ohms/C°. 3«8 The Common-Collector R e g u l a t o r A v e r y common r e g u l a t o r i s the s o — c a l l e d e m i t t e r - f o l l o w e r , or common—collector, r e g u l a t o r shown s c h e m a t i c a l l y i n F i g u r e 3-8. +Vj o- 01 I — W V «i R — ° v 0 :(l-a)R. f ° V R S a R , F i g u r e 3-8. Common-Collector R e g u l a t o r The performance of t h i s r e g u l a t o r w i l l be a n a l y s e d by e v a l u a t i n g g and r as d i s c u s s e d i n Appendix 1, where g a i V = const o L e t V ^ be changed by A"V\ w h i l e V q i s h e l d c o n s t a n t by changing the l o a d as much as i s n e c e s s a r y . The i n p u t t o Q2 remains c o n s t a n t s i n c e V , and thus the output of a m p l i f i e r , A, remains constant.. The b a s e - e m i t t e r v o l t a g e of Ql w i l l change s l i g h t l y when V ^ i s changed. T h i s s m a l l change w i l l cause a n e g l i g i b l e change i n the c o l l e c t o r c u r r e n t of Q2. Thus the c o l l e c t o r c u r r e n t of Q2 may be regarde d as c o n s t a n t . Any change i n V-g-g^ w i l l be much l e s s than AV.« As V. i s i n c r e a s e d I w i l l i n c r e a s e 1 1 due t o the i n c r e a s e i n c o l l e c t o r - e m i t t e r v o l t a g e of Ql and due to the i n c r e a s e of base c u r r e n t t h r o u g h R« A I = A V. I + h AV. l ...3-19 R o e l f o r e V. - V R - h. PE1 l mm I max o 3-20 Sin c e a s m a l l v a l u e of R w i l l degrade the performance of the s u p p l y , we choose the l a r g e s t a c c e p t a b l e v a l u e and s u b s t i t u t e i t i n t o E q u a t i o n 3.19 f o r A I 28 I h„ A I = ( E M ^ e i h . J AV. ...3-21 V - V h P E l f e l o b l 1 i min o Tf h <v v. ± T . f e l ~ FE1' ° _ AV V - V i i min o To f i n d r the output r e s i s t a n c e , l e t V. be h e l d o r ' i c o n s t a n t and examine the change i n I , A I , due to a s m a l l change i n YQf ^ V q . The change i n v o l t a g e a t the base of Q2, A V ^ ? < l u e to A V w i l l be: o A V ^ = aA A V ...3-23 £3 Z O T h i s w i l l cause a change i n base c u r r e n t of Q2 which w i l l be a m p l i f i e d by Q2 and Ql t o g i v e aA A V A I = (1.+ h f e l ) h f e 2 2. ...3-24 i e 2 aA A V " h f e l h f e 2 i f h f e l » 1 h i e 2 u s i n g A V Q h. 0 = h „ ~ h . , 0 and r - — — i e 2 f e 2 i b 2 o A V h., . r = - 2. = i b 2 _ 3 _ 2 5 0 A I a (-A) h f e l 29 E q u a t i o n 3-25 n e g l e c t s the f a c t t h a t r e s i s t o r , R, shunts the i n p u t t o Q l . r Q w i l l i n p r a c t i c e be somewhat h i g h e r than p r e d i c t e d by 3-25. 3.9 The Common-Emitter R e g u l a t o r An a l t e r n a t i v e r e g u l a t o r c i r c u i t , the common-emitter r e g u l a t o r , i s shown i n F i g u r e 3-9. +V: o-I -o + V 0 ( l - a ) R , *R > a R i F i g u r e 3-9. The Common-Emitter R e g u l a t o r The parameters g and r Q are e v a l u a t e d as i n 3-8. I f V. i s i n c r e a s e d by AV. w h i l e V i s h e l d c o n s t a n t , I w i l l 1 J 1 o 7 i n c r e a s e due t o the i n c r e a s e d b a s e - e m i t t e r v o l t a g e on Q l . I w i l l i n c r e a s e f u r t h e r due to i n c r e a s e d c o l l e c t o r e m i t t e r v o l t a g e on Q2 c a u s i n g more base c u r r e n t t o f l o w i n t o Q l . I f i t i s assumed t h a t s A VBE1 « A V i and — » h . , g 02 1 6 1 where g Q2 = output conductance of Q2 30 t h e n „ _ L L _ > l f e l v " o b l " s o 2 g = A - i - = h , o l ( h r t K 1 + g„ 0) ...3-26 A V. 1 I f V q i s h e l d c o n s t a n t and the change i n I , A I , due to a change, A V q , i n V q i s examined, then the same argument used to o b t a i n E q u a t i o n 3-25 y i e l d s : r = ^ ...3-27 a(-A) h f e l where A i s the g a i n of the a m p l i f i e r , A, i n F i g u r e 3-9. 3.10 M o d i f i c a t i o n of R e g u l a t o r O u t p u t — R e s i s t a n c e by I n t e r -a c t i o n of Output V o l t a g e and Reference V o l t a g e I f a p a s s i v e r e f e r e n c e element ( e . g . a breakdown d i o d e ) i s d r i v e n by a r e g u l a t o r , the r e f e r e n c e v o l t a g e , V^^ w i l l , i n g e n e r a l * change w i t h a change of output v o l t a g e , V q . The a n a l y s i s f o r r must be m o d i f i e d to account f o r t h i s e f f e c t . 0 a v R The i n p u t t o the a m p l i f i e r u n i t becomes ( a — ) A V dY 0 o and t h u s * k j b 2 1 _ _ r _ ...3-2o A( a — ) * V o 3»11 Comparison of Common-Emitter and Common—Collector R e g u l a t o r s I t i s seen t h a t , f o r e q u i v a l e n t s u p p l i e s , the output r e s i s t a n c e s are the same. The i n p u t conductances d i f f e r . 31 g c c = y I m a I v + h f e l h o b l • ' ' 3 " 2 2 1 min o and >cE = h f e l ( S 0 2 + h o b l } ...3-26 I t may be seen from Appendix 1, Al»6 t h a t the l i n e r e g u l a t i o n f a c t o r , K, i s g i v e n by K = g r Q ...3-29 S i n c e r and r are a p p r o x i m a t e l y equal i f l o a d i n g K g due t o the d r i v e r e s i s t o r , R, may be n e g l e c t e d , j r ^ - = — — . cc ^cc The o p e r a t i n g c o n d i t i o n s of the r e g u l a t e d s u p p l y f o r the d*c* a m p l i f i e r w i l l be t a k e n as an example* I = 50 ma V T - V = 5V I mm o h f e l = 7 0 h = 3 X 1 0 ~ 6 mho ob i g Q 2 i s the output conductance of the common-emitter a m p l i f i e r , Q2, and i s g i v e n by A-4-15 i n Appendix 4 as 1 _ h f e 2 h i b 2 , , Z >o2 ~ 2 v l lob2 i lfe2 T h.^J + 2 U o b 2 n f e 2 " h. ~ 1 i b 2 i b 2 h f e 2 h l b 2 \ ..*3-30 32 i f h f e 2 » 1 and h r b 2 « 1 T y p i c a l v a l u e s f o r Q2 h , , = .4 X 10 6 mho ob2 h r b 2 = 7 X I D " 4 h ^ b 2 = 30 ohms h f e 2 = 5 0 These w i t h 3-29 g i v e g o 2 * 22 X I D " 6 U s i n g t h i s v a l u e i n 3-21 and 3-25 y e i l d s 1 - 1500 Z -6 -6 g g 0 = 22 X 10 ° - 1.5 X 10 ° o 2 1 + Z g ...3-31 g C E ^ 1.8 X 10 3 C l e a r l y the common-emitter r e g u l a t o r w i l l p e r f o r m more than f i v e t imes as w e l l as the common-collector r e g u l a t o r i n t h i s a p p l i c a t i o n . 33 3.12 The Temperature C o e f f i c i e n t of Breakdown-Diodes I t i s w e l l known t h a t l o w - v o l t a g e breakdown-diodes have a n e g a t i v e temperature c o e f f i c i e n t of v o l t a g e and h i g h - v o l t a g e d i o d e s have a p o s i t i v e temperature c o e f f i c i e n t . A v e r y s m a l l temperature c o e f f i c i e n t i s observed i n d i o d e s which break down a t about 5.5 v o l t s . I t i s a l s o w e l l known t h a t the temperature c o e f f i c i e n t i s a f u n c t i o n of c u r r e n t , becoming more p o s i t i v e a t h i g h e r c u r r e n t . These phenomena were i n v e s t i g a t e d and s e v e r a l s a l i e n t f e a t u r e s n o t e d . The breakdown v o l t a g e a t 10 ma and the o p e r a t i n g c u r r e n t t h a t produced zero average temperature c o e f f i c i e n t between 0°C o and 100 C were measured on f o u r t e e n d i o d e s . The r e s u l t i n g d i s t r i b u t i o n i s shown i n F i g u r e 3-10* The v o l t a g e - t e m p e r a t u r e c h a r a c t e r i s t i c s between -50 C and +100 C of these d i o d e s were measured a t the c u r r e n t which gave zero average temperature c o e f f i c i e n t . The r e s u l t s were f i t t e d t o the e q u a t i o n V = V (50°C) 1 + a(T - 50) + b(T - 5 0 ) 2 + c(T - 5 0 ) 3 + d(T - 5 0 ) 4 ...3-32 V i t h i n the a c c u r a c y of a v a i l a b l e t e s t equipment (.01$), i t was found t h a t a = 0 (by c h o i c e of o p e r a t i n g p o i n t ) ...3-33 b = .7 X 1 0 " 6 34 Diode V o l t a g e at lOma I 6.3 Diode C u r r e n t f o r Zero Temperature C o e f f i c i e n t (ma) F i g u r e 3-10. Breakdown-diode V o l t a g e a t lOma v s . Diode C u r r e n t f o r Zero Temperature C u r r e n t 35 3.13 General Power Supply C o n s i d e r a t i o n s There are f o u r r e g u l a t o r s i n the system. Two serve as rough p r e - r e g u l a t o r s and two as r e g u l a t o r s . These u n i t s are a l l common-emitter r e g u l a t o r s . The main r e g u l a t o r s have a d i f f e r e n t i a l a m p l i f i e r s t a g e . The p r e - r e g u l a t o r s do not have t h e i r own r e f e r e n c e d i o d e s but use the output of the main r e g u l a t o r s as r e f e r e n c e s . The p r e - r e g u l a t o r s a l s o use s m a l l amounts of open-l o o p feedback to improve t h e i r r e g u l a t i o n . 3.14 The R e g u l a t e d Power Supply f o r the D.C. A m p l i f i e r The c i r c u i t of the r e g u l a t e d power su p p l y f o r the d.c. a m p l i f i e r i s shown i n F i g u r e 3—11. I t i s of the common-emitter type w i t h a d i f f e r e n t i a l a m p l i f i e r w i t h a g a i n of about 5. F i g u r e 3.11 The R e g u l a t e d Power Supply f o r the D.C. A m p l i f i e r R208 i s p r e s e n t t o improve the t h e r m a l s t a b i l i t y of Q204 and a l s o 36 to r a i s e the g a i n of Q203 by i n c r e a s i n g the c o l l e c t o r c u r r e n t of Q203 and thus r e d u c i n g i t s R207 and R205 are p r o t e c t i o n r e s i s t o r s t o l i m i t the c u r r e n t s i n paths t h a t would o t h e r w i s e c o n t a i n o n l y f o r w a r d b i a s e d d i o d e s and t r a n s i s t o r s , w h i c h c o u l d be momentarily o v e r l o a d e d by t r a n s i e n t s . R206 serve s t o i n c r e a s e the c o l l e c t o r c u r r e n t of Q202 and improve the therm a l s t a b i l i t y of Q203. (See 3-5 and 3-6). D202 r a i s e s the b a s e - e m i t t e r v o l t a g e of Q203 as d i s c u s s e d i n 3.5. Q201, Q202j and R204 form a c o n v e n t i o n a l " l o n g - t a i l e d - p a i r " d i f f e r e n t i a l a m p l i f i e r . D201 i s the r e f e r e n c e diode s u p p l i e d w i t h c u r r e n t from the r e g u l a t e d output through R203. R202 and R201 form the sampl i n g d i v i d e r . The r e s i s t a n c e of R201 and R202 i n p a r a l l e l s h o u l d be much l e s s t h a n the i n p u t impedance of Q201 to a v o i d l o s s of g a i n . R203 i s chosen such t h a t i t passes the c o r r e c t c u r r e n t f o r zero temperature c o e f f i c i e n t t o the p a r t i c u l a r r e f e r e n c e diode used. The q u a n t i t y 1 + R202/R201 i s made equal to the d e s i r e d v a l u e of Vout/V r e f . and R204 i s a d j u s t e d t o make the base v o l t a g e of Q201 equal to the base v o l t a g e of Q202. C201 keeps the s u p p l y impedance low a t h i g h f r e q u e n c i e s and a l s o reduces the l o o p g a i n of the r e g u l a t o r t o below u n i t y a t f r e q u e n c i e s below which phase s h i f t s become e x c e s s i v e . R209 i s n e c e s s a r y to t u r n the u n i t on and reduce the power d i s s i p a t i o n i n Q204. The performance of the s u p p l y was e s t i m a t e d on the b a s i s of the f o l l o w i n g t y p i c a l p a r a m e t e r s . 37 f e ob h rb l b h oe h. l e Q204 70 3 X 10 4 X 10 1 2 X 10 70 -6 -4 Q203 +D202 50 *4 X 10 7 X 1 0 ~ 4 60 -6 Q201 and Q202 50 .2 X 1 0 " 6 mho 7 X 1 0 ~ 4 150 ohms mho ohms D201 250 ohms 6 v o l t s Prom 3-30 g Q of Q202 = 5 X 1 0 ~ 6 mho. These v a l u e s are s u b s t i t u t e d i n t o 3-26 to o b t a i n 1.2 X 10""3 mho ...3-34 To the above v a l u e of g must be added 1/820 mho due to the presence of R209 (820 ohms) to y i e l d g = 2.4 X 1 0 ~ 3 mho The impedance a t the base of Q203 i s a p p r o x i m a t e l y h f ^ h ^ + i„ h , RT f e ob L r ^ ) / ( l + h_pQ ^ T ) i n p a r a l l e l w i t h R206, t h a t i s , about 1.5K, 38 The g a i n of the a m p l i f i e r i s then RT A 1 i-t rv j-= -2 h — = 5 l b The f a c t o r \ appears due to the f a c t t h a t a s i n g l e - e n d e d output i s b e i n g t a k e n from a d i f f e r e n t i a l a m p l i f i e r . The a t t e n u a t i o n of the v o l t a g e d i v i d e r i s a = .45 ^ R R /V >. r- • , v f = = .05 « . a 6 0 r R + R 203 S u b s t i t u t i o n of these v a l u e s i n t o 3-25 y e i l d s Tq = 0.4 ohm ...3-36 and s i n c e K = gr 0 K = 10 ...3-37 3.15 The Reference Supply The d e s i g n of the r e f e r e n c e supply i s s i m i l a r t o t h a t of the r e g u l a t e d s u p p l y f o r the d.c, a m p l i f i e r . The parameter a was chosen to be \» S i m i l a r c a l c u l a t i o n s t o those of 3.14 show K £ 1 0 ~ 3 ...3-37 The r e f e r e n c e v o l t a g e output i s t a k e n d i r e c t l y from the r e f e r e n c e d i o d e . Any change i n output v o l t a g e of the r e g u l a t o r i s t h e n 39 f u r t h e r a t t e n u a t e d by | ^ * 40 X 1 0 ~ 3 * v o Thus K „ =" 40 X 1 0 " 6 ...3-38 r e i 3.16 The P r e - r e g u l a t o r s The p r e - r e g u l a t o r s are s i m p l e r t w o - t r a n s i s t o r r e g u l a t o r s u s i n g the output v o l t a g e of the main r e g u l a t o r s as r e f e r e n c e s * The v o l t a g e d i v i d e r s are i n the e m i t t e r s of the d r i v e r t r a n s i s t o r s . T h i s r e s u l t s i n the d r i v e r t r a n s i s t o r s o p e r a t i n g i n the common—base mode w i t h g _ = h The d e t a i l e d d e s i g n °o2 ob2 c a l c u l a t i o n s are g i v e n i n Appendix 2 and the c i r c u i t diagrams i n F i g u r e 3-13. 3*17 The Oven The oven i s a 6 i n c h by 3 i n c h by 5 i n c h box f a b r i c a t e d of \ i n c h t h i c k aluminium* The t o p and bottom are i n s u l a t e d w i t h about 1 i n c h of s t y r o f o a m . The s i d e s are wrapped w i t h f i b e r g l a s s tape on which i s wound a 25 ohm nichrome h e a t e r . The h e a t e r i s h e l d i n p l a c e w i t h another l a y e r of tape and o u t e r p a n e l s of f i b r e b o a r d . The f i b r e board p a n e l s a l s o p r o v i d e some the r m a l i n s u l a t i o n * The g a i n of the temperature c o n t r o l system i s s e t a t about \ the v a l u e r e q u i r e d t o s u s t a i n o s c i l l a t i o n s * The p e r i o d of the damped o s c i l l a t i o n s which occur when f i r s t 40 s w i t c h e d on i s about 6 minutes* A f t e r about 2 hours of o p e r a t i o n the temperature appears t o have s t e a d i e d down t o w i t h i n a few hundredths of a c e n t i g r a d e degree .from the e q u i l i b r i u m v a l u e . F i g u r e 3-12. Complete Schematic of D.C. A m p l i f i e r F i g u r e 3-13. Complete Schematic of Power S u p p l i e s R 301 100 ohm C301 .1 u f a R 302 see f i g . 4-1 Rr^03 47 K Q 301 2N 1303 R 304 3.3 K Q 302 2N 1305 R 305 330 Q 303 2N 1304 R 306 8.2 K Q 304 2N 1305 R 307 560 Q 305 2N 1305 R 308 1.5 K Q 306 2N 250 R 309 6.8 K R 310 2.7 K R 311 3.3 K R 312 330 R 313 270 R 314 680 R 315 5 ohm/5 watt see F i g u r e 3-7. F i g u r e 3-14. P a r t s L i s t f o r Temperature C o n t r o l l 44 4. PERFORMANCE OF EQUIPMENT 4.1 The D.C. A m p l i f i e r The a m p l i f i e r o utput was connected t o a s t r i p c h a r t r e c o r d e r and the system r u n f o r s e v e r a l days w i t h the i n p u t s h o r t e d * D u r i n g the f i r s t day a stea d y d r i f t of about 1 m i c r o v o l t per hour ( r e f e r r e d t o the i n p u t ) was obse r v e d . A f t e r the f i r s t 24 hours the d r i f t remained below + 2 m i c r o v o l t s . Source r e s i s t a n c e s up to about 1,000 ohms made no a p p r e c i a b l e d i f f e r e n c e . A source r e s i s t a n c e of 10K ohms gave r i s e t o about 6 m i c r o v o l t s p e a k — t o -pe ak of v e r y l o w - f r e q u e n c y n o i s e . 100K ohms source r e s i s t a n c e gave about 40 m i c r o v o l t s . The f r e q u e n c y response of the a m p l i f i e r was down 1 db a t 10 k c , 3 db a t 20 k c , and 6 db a t 40 k c . The broad—band n o i s e f i g u r e was found to be about 3 db w i t h a 10K ohm source impedance and about 6 db w i t h a IK ohm source impedance* The i n p u t impedance was measured as 120K w i t h the v o l t a g e g a i n s e t a t 1,000. 4.2 The Temperature R e g u l a t o r System The temperature c o n t r o l u n i t was p l a c e d i n an oven w i t h a thermometer. The temperature was s l o w l y r a i s e d w h i l e the output of the c o n t r o l u n i t was m a i n t a i n e d c o n s t a n t at 1 v o l t by v a r y i n g R302. The r e s u l t i n g d a t a i s p l o t t e d i n F i g u r e 4-1. From the sl o p e of the p l o t of R302 v s . t e m p e r a t u r e , i t was dete r m i n e d t h a t a 250 ohm change i n R302 corresponds to a change of 1°C. R302 was the n v a r i e d a t c o n s t a n t temperature and i t was found t h a t 10 ohms change i n R302 caused the output of temperature 45 46 c o n t r o l a m p l i f i e r (V^ of F i g u r e 3-7) to change 1 v o l t . I t i s thus seen t h a t |JT = 250 ohms/c° = 2 5 v o l t s / G o m e a s u r e d d i 10 ohms/V This v a l u e compares f a v o r a b l y w i t h the e s t i m a t e d v a l u e (3-17) of 30 volts/C°. The h e a t e r c u r r e n t r e q u i r e d t o r a i s e the oven temperature from 25°C to 35°C was measured and found t o be 0.6A. The h e a t e r c o n t r o l and power a m p l i f i e r can s u p p l y about 1.4 times t h i s amount of c u r r e n t or about t w i c e the power. I t i s t h e r e f o r e e x p e c t ed t h a t the oven and temperature c o n t r o l w i l l f u n c t i o n p r o p e r l y i n ambient temperatures from about 15°C to j u s t under 35°C. 4.3 Power Supply Performance The output impedance and l i n e r e g u l a t i o n f a c t o r of the r e g u l a t e d power s u p p l y were measured and compared to the p r e d i c t e d v a l u e s . A change i n l o a d c u r r e n t of 11 millamps was found to cause a change i n output v o l t a g e of 5 m i l l i v o l t s from which r Q = 0.45 ohm. The output v o l t a g e changed 6 m i l l i v o l t s f o r an i n p u t change of 5 v o l t s . The l i n e r e g u l a t i o n f a c t o r , K, i s th e n -3 1.2 X 10 . P r e d i c t e d and measured v a l u e s are compared i n t a b l e 4-1. 47 P r e d i c t e d Measured r 0,4 ohm 0.45 ohm o K 1 0 " 3 1.2 X 1 0 " 3 Table 4-1. P r e d i c t e d and Measured Parameters of the R e g u l a t e d Power Supply-S i m i l a r t e s t s performed on the r e f e r e n c e s u p p l y gave the r e s u l t s of Table 4-2. P r e d i c t e d Measured K 1 0 ~ 3 1.4 X 1 0 " 3 3 V R 4 X 1 0 ~ 2 2 X 1 0 ~ 2 d V o K .'f 40 X 1 0 " 6 < 50 X 1 0 ~ 6 Table 4-2. d V R The d i s c r e p a n c y i n ^ y was due to the f a c t t h a t r e f e r e n c e diode used had a dynamic r e s i s t a n c e of o n l y 27 ohms i n s t e a d of the 50 ohms a n t i c i p a t e d from the d a t a s h e e t . The v a l u e o f K ' o b t a i n e d by m u l t i p l y i n g the measured * VR v a l u e s of K and r = - , namely o K „ = 28 X 1 0 ~ 6 r e f i s p r o b a b l y more a c c u r a t e t h a n the v a l u e a c t u a l l y measured, s i n c e the change i n r e f e r e n c e v o l t a g e caused by a 5 v o l t change i n i n p u t v o l t a g e was o n l y a few tim e s the t h r e s h o l d of d e t e c t a b i l i t y on the measuring equipment used. 48 4.4 P r e - r e g u l a t o r Performance I t was found p o s s i b l e t o a d j u s t the p r e - r e g u l a t o r s t o g i v e l e s s t h a n 15 m i l l i v o l t s o u tput change f o r 15 v o l t s i n p u t change^ t h a t i s , K = 10 « & ' ' p r e - r e g The o v e r a l l l i n e r e g u l a t i o n f a c t o r f o r the r e f e r e n c e system should t h e n be K r e f t o t a l = 3 0 X 1 0 " 9 The r e f e r e n c e s u p p l y and p r e - r e g u l a t o r operate a t a nominal i n p u t of 22 v o l t s and a nominal output of 5.6 v o l t s . A 10$ change i n l i n e v o l t a g e would t h e n be expected to produce about 0»07 m i c r o v o l t change i n 5.6 v o l t s or about 0.0013 ppm. A change of a.c. l i n e v o l t a g e from 90 to 135 v o l t s (+ 20$) caused a change i n r e f e r e n c e v o l t a g e of l e s s t h a n the l i m i t of r e s o l u t i o n of the measuring system used (about 2 (ov). The use of h i g h q u a l i t y s h i e l d e d l i n e i s o l a t i o n t r a n s f o r m e r s would g r e a t l y reduce the problems of 60 c y c l e c o u p l i n g when w o r k i n g w i t h h i g h impedance s o u r c e s . A v o l t a g e d i v i d e r , c o n s i s t i n g of a 1000 ohm p r e c i s i o n r e s i s t o r and a decade r e s i s t a n c e box, was p l a c e d a c r o s s the o u t -put of the r e f e r e n c e s u p p l y * A s t a n d a r d c e l l was connected i n s e r i e s - o p p o s i n g t o the v o l t a g e a c r o s s the 1000 ohm r e s i s t o r and the r e s u l t a n t v o l t a g e was f e d i n t o the a m p l i f i e r . The r e s i s t a n c e box was a d j u s t e d f o r zero output v o l t a g e from the a m p l i f i e r and the a m p l i f i e r output was connected to a r e c o r d e r . D u r i n g s e v e r a l days of o p e r a t i o n the d r i f t never exceeded 5 m i c r o v o l t s r e f e r r e d t o the i n p u t , t h a t i s , about p a r t s per m i l l i o n . 50 APPENDIX 1. LINE AND LOAD REGULATION OP REGULATED POWER SUPPLIES The r e g u l a t o r i s regard e d as a f o u r - t e r m i n a l network ( F i g u r e A l - l ) w i t h c h a r a c t e r i s t i c s d e s c r i b e d by E q u a t i o n s A l - 1 and A l - 2 . AAA Oe—>-t——-'VVV Oe— V S Q ! r s fv F i g u r e Al-1.. F o u r - T e r m i n a l Network R e p r e s e n t a t i o n of R e g u l a t o r where where d l — dV + g„dV. r o B f 1 o . . . A l - 1 3V r = — o I V. i and S4 31. ^ V i g d l — dV + g.dV. r o toi l r . . . A l - 2 3V r = -* ~ 3 1 , 51 and • i av. The l i n e r e g u l a t i o n f a c t o r , K, i s d e f i n e d by E q u a t i o n A l - 3 . K dV o d V i . . * A l - 3 I f the i n p u t v o l t a g e i s changed, b o t h the output v o l t a g e and c u r r e n t w i l l change. These changes are r e l a t e d b y j d i = ±- dV o bL o . . . A l - 4 E q u a t i o n A l - 4 i s s u b s t i t u t e d i n t o E q u a t i o n A l - 1 , and the r e s u l t i n g e q u a t i o n s o l v e d f o r K as d e f i n e d by E q u a t i o n A l - 3 K = g r RT o L f RT + r L o •«.Al-5 S i n c e a s u p p l y w e l l r e g u l a t e d a g a i n s t l o a d v a r i a t i o n s , w i l l have r R T, the a p p r o x i m a t i o n A l - 6 i s j u s t i f i e d . O Li to .* . . A l - 6 The output r e s i s t a n c e , r, i s d e f i n e d by E q u a t i o n A l - 7 . dY c d i . . . A l - 7 52 I f the output c u r r e n t i s changed, b o t h the output v o l t a g and i n p u t v o l t a g e w i l l change. The i n p u t v o l t a g e change and the i n p u t c u r r e n t change are r e l a t e d by E q u a t i o n A l - 8 . 1 d I i — = g g = - ( d e f i n i t i o n of g g and r ) „.*Al-8 s i E q u a t i o n AI—8 i s s u b s t i t u t e d i n t o E q u a t i o n AI—2 and the r e s u l t i s s o l v e d f o r dV. i n terms of dV . 1 o dV. = dV . . . A l - 9 r r ( g i + g s ) E q u a t i o n AI—9 i s s u b s t i t u t e d i n t o E q u a t i o n 1—1 and the r e s u l t i s s o l v e d f o r r u s i n g E q u a t i o n A l - 7 to y i e l d : r = r i ...Al-10 o g f r o ( g i + g s ) r r I n the r e g u l a t o r s c o n s i d e r e d here d l ^ = dI Q« Thus g^ = g = r . I f these approxima" output impedance i s found to be: and r ~ Q pr o x i m a t i o n s are made i n AI—10, the r = r ( l + g„r ) »•» .AI—11 o tof s Sin c e g ^ r g « l i n the r e g u l a t o r s and power s u p p l i e s c o n s i d e r e d ? 53 APPENDIX 2. DERIVATION OF EQUATIONS PREDICTING POWER SUPPLY PERFORMANCE !• P r e - r e g u l a t o r R5 AAA-Q I R4 R2 \ 0 2 / R3 R7« R 6 R7 A R8 • V A r VR -o A F i g u r e 1. P r e - r e g u l a t o r F i r s t , c o n s i d e r the s i m p l i f i e d c i r c u i t of F i g u r e 2. 01 Z. *" R 7 N 02 R6 V R v 2 F i g u r e 2. S i m p l i f i e d C i r c u i t of P r e - r e g u l a t o r C a l c u l a t i o n of g' and tq the f o r c i r c u i t of F i g u r e 2. We s e t AV'2 = 0, assume A V ' R = 0 and c a l c u l a t e g*• The output c u r r e n t w i l l i n c r e a s e when i s i n c r e a s e d f o r two r e a s o n s ; (a) VQ^i i n c r e a s e s and causes a s m a l l i n c r e a s e i n c o l l e c t o r c u r r e n t of Q l . (b) ^CB2 ^ n c r e a s e s a n d causes a s m a l l i n c r e a s e i n c o l l e c t o r c u r r e n t of Q2 which i s m u l t i p l i e d by the c u r r e n t g a i n of Q l . When a t r a n s i s t o r i s o p e r a t e d w i t h non-zero impedance i n both e m i t t e r and base c i r c u i t s , i t cannot, s t r i c t l y s p e a k i n g , be s a i d t o be o p e r a t i n g e i t h e r common-base or common-emitter. How-ev e r , i f the e m i t t e r — c i r c u i t impedance i s much l a r g e r t h a n the base c i r c u i t impedance d i v i d e d by h ^ e , the c i r c u i t may be re g a r d e d as common-base w i t h n e g l i g i b l e e r r o r . S i m i l a r i l y , i f the e m i t t e r - c i r c u i t impedance i s much l a r g e r t h a n the base-c i r c u i t impedance d i v i d e d by hfes> the c i r c u i t may be s a i d to approximate a common—emitter. The v o l t a g e r e f e r e n c e , V R , w i l l n o r m a l l y be a l o w -impedance s o u r c e . Thus Q2 may be regard e d as a common—base c o n f i g u r a t i o n and i t s output conductance w i l l be h^^* The b a s e - c i r c u i t impedance f o r Ql i s the output impedance of Q2, which i s ^ / n G> J2* ^ n e e m i " t " t e r - c i r c u i t impedance seen by Ql i s the i n t e r n a l impedance of the power s o u r c e . ^)•0]:)2, ^ o r ^ e s u p p l i e s c o n s i d e r e d here w i l l be ^ 1 micro mho. I f we assume h^.^ — .100, Ql w i l l p e r f o r m as a common-emitter as l o n g as r « 10K ohms which w i l l c e r t a i n l y be the case f o r a source J r e a s o i i ab l e t r a n s f o r m e r — r e c t i f i e r - f i l t e r system. T h e r e f o r e the 55 out p u t admittance of Ql w i l l be b Q e ^ , Thus: d I = h o e l d V l + h f e l h o b 2 d V l — A 2 " 1 = h f e l ( h o b l + h o b 2 > d V l J h t e l ^ ^ b ^ 1 ' = h f e l f i L o b l + h o b 2 ) - ' k 2 ~ 2 I f we now assume a change i n output v o l t a g e AV 2, w i t h h e l d c o n s t a n t , we can c a l c u l a t e AI and thus r . The j u n c t i o n ° R 6 of B7 and R6 may be regard e d as a source of v o l t a g e , V" = =,—•—=— z 5 7 w i t h i n t e r n a l impedance, R' = p p d r i v i n g the e m i t t e r of 6 7 Q2.. AV" 2 AI„ 0 = ...A2-3 R' + h., 0 i b 2 6 A V R 6 + R 7 2 R,R 7 6 7 h R 6+ R ? AV 1 R 7 + h i b 2 R 7 R 6 56 AI c2 / h f b 2 / A I E 2 =• A I E 2 ...A2-4 AI f e l c2 ..A2-5 h f e l A Y ' 2 R 7 + h i b 2 + IT> 6 R 7 R + h (1 + ^L) AV' 7 l b 2 R 6 ••»A2-6 AI f e l K ' = = < hobl + hob2> | R 7 + W 1 + 5^> ] *.*A2—7 R e t u r n i n g to the c i r c u i t of F i g u r e 1, we s e t R^t R^ and Rr- - oo and examine the e f f e c t of R c. 5 o V - V - IR V2 _ V 2 a£ .*.A2-8 V , R - V R + I R 8 • •.•A2-9 From A2-8 ^ i ^ i dV R' + Rc 3" d i "8 R .•.A2-10 and from A2-9 DVR< d l - tt8 ...A2-11 combining A2-10 and A2-11 we have r = r V R - 1) : *V , 2 VR« A2-12 I f I i s h e l d c o n s t a n t , I must remain c o n s t a n t and t h e r e f o r e I g ^ -tB2 a n d VBE2 r e m a i n c o n s t a n t . Summing c u r r e n t s a t the j u n c t i o n o f R^ and R^ g i v e s Vt - (v.t _ v ) R, R 'BE2 y T _ V'R ~ VBE2 + ± E 2 -7 ,*A2-13 Taking d i f f e r e n t i a l s i n A2-13 w i t h I = c o n s t a n t y i e l d s dv-«2 - dV-t.R d V R I R, 7 R, d V * 2 = D V*R R7 (RT + fc) = d V 6 7 R£ + R.-7 ! 6 7 R R^-.•A2-14 58 thus + R~ — '- •..A2-15 R 6 ; S u b s t i t u t i n g A2-15 i n t o A2-12 y i e l d s R r = R ' — Ro Tr- ...A2-16 O O o xtg L e t us now examine the e f f e c t of R^, R 2 and R^* I f R-^ and R 2 are chosen such t h a t a t the nominal v a l u e o f R l V, (nom) ± = V„ 0(nom) •**A2-17 1 V R 2 t h e n the c u r r e n t t h r o u g h R^ i s zero a t nominal s u p p l y v o l t a g e . I f i n c r e a s e s ( a t c o n s t a n t I ) c u r r e n t w i l l f l o w t h r o u g h R^ and cause V g 2 to r i s e thus t e n d i n g t o reduce V-g-g-p and t h e r e f o r e ^E2* ^ h ^ s w i l l * i n turn-, tend t o reduce I . I f the v a l u e s are chosen c o r r e c t l y i t s h o u l d be p o s s i b l e t o j u s t o f f s e t the tendency of I t o i n c r e a s e w i t h i n c r e a s i n g V^. The c u r r e n t t h r o u g h R 3 i s AV^/R* A V t l = A V 1 R ^ + R 2 - * A 2 - 1 8 AT i = v i - Vnom) R , 3 = ( R 1 / / R 2 + R 3 + h i b 2 / / R 6 ) T h i s c u r r e n t causes A I c 2 = | h f b 2 | A I E 2 = + A I E 2 = " ZR3 — A 2 - 1 9 R l h f e l AI = h„ , AI „ = -h„ n I„„ = -AV, f e l c2 ~ f e l R3 ~ 1 R±+ R 2 R* 3 •••A2-20 5 I _ R l h f e l _ „ dY± - - R l + R 2 g'T t g' R^ i s n e c e s s a r y t o s t a r t the s u p p l y s i n c e w i t h Ql non-c o n d u c t i n g t h e r e i s no power to the r e f e r e n c e s e c t i o n * R,-lowe r s g t o (g* + ^— ) + g" and R^ improves the t h e r m a l 5 s t a b i l i t y of Ql but l o w e r s the e f f e c t i v e v a l u e of ^ to R 4 APPENDIX 3o DERIVATION OP THE EACT PARAMETERS FOR AN EMITTER-FOLLOWER I t has been found d e s i r a b l e t o work i n terms of "mixed h-parameters", i*e<» n £ e * n r b » n 0t> s i n c e "these are u s u a l l y s p e c i f i e d and and h Q b are q u i t e p r e d i c t a b l e . The i m p o r t a n t mid-band parameters of an a m p l i f i e r are i t s v o l t a g e g a i n , A y» i t s c u r r e n t g a i n , A — , i t s i n p u t impedance, , and i t s output impedance, Z » out F i g u r e A3-1. E m i t t e r - F o l l o w e r I n terms of common c o l l e c t o r h-parameters v o l t a g e g a i n = A. vc h. 1 + h Z T , I C v oc L\ h r c ~ "ZT ( _ ) L h, f c •*..A3-1 c u r r e n t g a i n = A- = s i c f c 1 + h Z T oc L ...A3-2 61 output impedance = Z Q C = — »».A3-4 h„ h h _ f c r c I C g where Z T = l o a d impedance, and Z = g e n e r a t o r impedance. g These w i l l be c o n v e r t e d t o mixed h-parameters. ^h„, (1 - h J - h ,h., h f e = _ : thi o b _ i b ...A3-5 (1 + h f b ) ( l - h r b ) + h o b h . b 1 - h 1 + h f e = rb (1 + h f b ) ( l - h r b ) + h o b h . b ««*A3-6 ^ + W*1 ~ h r b } + h o b h i b = ~ ~ ~ ~ — A 3 " 7 1 + h f e , h ., h .., 1 + h f b = — i - 2 k ^ b _ i A 3 _ 8 1 1 +' h. 1 - h ' i e rb N - . . = — ...A3-9 (1 + h f b ) ( l - h r b ) + h o b h . b S u b s t i t u t i n g A3-7 i n t o A3-9 y i e l d s 1 + h f h i c = h . b — e- M . A 3 - 1 0 ^ ^"rb 62 1 + hp, h „ = «..A3-11 r c ^ + V ( l - h r h ) + h o b h i b S u b s t i t u t e A3-7 and A3—8 i n t o A3-11 to o b t a i n , h ,h., 1 + h„ b ^ : 1 _ ob i b ^ , f e ^ " 1 + h f e 1 ~ h r b 1 ~ h r b i 1 + h-pa — — h o b > W ,*.A3-12 1 - h , 1 - h , rb rb h f c = - ( 1 + h f e ) .*.A3-13 h Q C = ^ = ...A3-14 (1 + h f b ) ( l - h r b ) . + h Q b h i b S u b s t i t u t e A3-7 i n t o A3-14 t o o b t a i n 1 + h h f e oc 1 - h ob •••A3-15 rb S u b s t i t u t i n g A3—10* A3-?129 A3-13, and A3-15 i n t o A3-1 g i v e s A 1-h 1 - ( l + h f e ) oh i b rb 1 - h rb h., l+h'„ i b f e Z L X - h r b 1+h 1 + f e 1-h h o b Z L rb 1 + h f e • * *A3-16 63 whi c h s i m p l i f i e s t o 1 - h r b V = T T T — • • • A 3 - 1 7 S u b s t i t u t e A3—13 and A3-15 i n t o A3-2 to get 1 + h f e A. = - — ...A3-18 l+h„ 1 + T T ^ h o b Z L ^ r b S u b s t i t u t i n g A3-10, A3-13 and A3-15 i n t o A3-3 g i v e s ( l + h f ) 1+h ( 1 + h f e ) 1 _ h r b Z. = h., — + — :— ,..A3-19 I C xb -, , n , 1, 1 - 1 : 1 T. -i . 1 rb r b l+b„ 1 + — h , Z, 1-h v o b L rb w hich s i m p l i f i e s t o l+h„ + Z T f e l b L ...A3-20 i c 1-h , , rb 1+h,, 1 + — h , Z T 1-h 0 rb S u b s t i t u t i n g A3-10, A3-12, A3-13 and A3-15 i n t o A3-4 g i v e s oc ...A3-21 1+h l ^ h rb 1+h (1 -1+h f e h o b + 1-h f e 1-h rb h i b h o b > rb 1+h f e 1-h rb h., + Z i b i 64 S i m p l i f y i n g , 1-h h., + -, ,, r b Z l b 1 + n f e « 2 — • • • • » o o A 3 ~* 2 2 OC • 1 + h , Z ob g I n summary; 1-h rb 1+h vc ..A3-17 f e 1 + l b ' i c 1+h 1 + f e 1-h rb h vZ T ob L ...A3-18 1+h Z. i c f e h., + ZT l b L 1-h ...A3-20 rb 1+h 1 + f e 1-h rb ob L h., + y-T-^ Z i b l + h f e g oc ..A3-22 1+h , Z ob g APPENDIX 4. DERIVATION OF THE EXACT PARAMETERS FOR A COMMON EMITTER AMPLIFIER •AAV—» Zg <• out in - • o F i g , A 4 - l 0 Common—Emitter A m p l i f i e r P u r s u i n g the l i n e of r e a s o n i n g used i n Appendix 3 we s t a r t from the e q u a t i o n s v o l t a g e g a i n , A y E h. 1+h Z T l e oe L h re f e a o A. 4 c u r r e n t g a i n , Aj-g = f e 1+h. Z T oe L o. A4 h„ h Z T 1 e re L i n p u t impedance, Z j E = t u g - Y+h—Z— oe L output impedance, Z OE h„ h fe re oe h. +Z l e g h 9 o A.4-66 where Z-^ = l o a d impedance and Z^ = g e n e r a t o r impedance 1+h h h. = h f e i e i c i b 1-h rb from Appendix 3 ..»A4-5 h = 1-h = -z—^-re r c 1-h rb l + h f 1 - h ^ o b ^ i b ^ r b rb. u s i n g h ^ c from Appendix 3 -A4-6 1+h fe h = h = n i . ^ - u oe oc 1-h , ob rb h , from Appendix 3, .oA4-7 h ^ e i s used as i s e E q u a t i o n s A4-5, A4-r6, and A4-7 are s u b s t i t u t e d i n t o A4-1, g i v i n g L-hrb 1+h f e h vh..-h 1—h ^ pb i b rb 1 + ± e h 7 1+h. h., 1-h , ob L f e i b rb 1-h , Z T rb L ,A4-8 S i m p l i f y i n g we have h f e 1-h rb *VE i b 1+h f e 1 + ( h f e h rb h ob 1+h f e i b 1-h )Z T rb .A4-9 67 E q u a t i o n 7 i s s u b s t i t u t e d i n t o e q u a t i o n 2 g i v i n g A = tS. ...A4-10 ^ r b E q u a t i o n s 5, 6, and 7 are s u b s t i t u t e d i n t o e q u a t i o n 3 l + h f e - . i ^ f e ' l ^ T faobhib-"rb'ZL ^ I E ~ i b 1-h , " 1-h , rb r b -. , 1 + h f e 1-h , ob L rb S i m p l i f y i n g 11!. y i e l d s ..*A4-11 h~ h , h , 1 + 4+h- h . K + 1-h , J Z L ; t± h . » — ...*A4-12 'IE - l - h r b \ b 1 + h 1 + I Z h T h o b Z L rb E q u a t i o n s 5* 6* and 7 are s u b s t i t u t e d i n t o e q u a t i o n 4, to g i v e , Z 0 E " !+ bfe h f e ^ . h h - h _ ! £ h _ - I f - i - h , W i b " h r b l - h r b ob l - h r b r b _ 1 + h f e -, u i e h.,+ Z l - h r b i b g «<> *A4-13 68 S i m p l i f i e d 13 y i e l d s 1-h , Z r b OE ~ h ^ h„ h o b + <hob + -fj 1+h- h., 1 + _ i b + 1-h , Z rb g .•.A4-14 AI so, 1 _ ob Z n„ ~ g 0 E 1-h , OE rb + * rh o b h f e 'fe 1-h rb l + h f e h i b h , h ,h„ rb \, i / ob f e ) + 2 \ '1-h rb 1+h f e h 1-h •f e rb rb 1+h f e h »>*A4-15 i b 1+h 1 + f e 1-h rb ^ i b Z g APPENDIX 5. DERIVATION OP THE EXACT PARAMETERS FOR A COMMON-EMITTER AMPLIFIER WITH EXTERNAL EMITTER-IMPEDANCE. -AAA—o— A II o F i g u r e A5—1* Common-Emitter A m p l i f i e r w i t h E x t e r n a l Emitter-Impedance The. a m p l i f i e r of F i g u r e A5-1 d i f f e r s from a common—emitte a m p l i f i e r o n l y i n h a v i n g an e x t e r n a l emitter-impedance* There-f o r e i f a s e t of h—parameters (the h'-parameters) i s found f o r a d e v i c e c o n s i s t i n g of a t r a n s i s t o r w i t h a r e s i s t o r i n the e m i t t e r l e a d , the h*—parameters may be used w i t h the r e s u l t s of Appendix 4 t o p r e d i c t the performance of the a m p l i f i e r . h'-parameters e e "ib 'e o - —A A A — o — A A A — > F i g u r e A5—2; S m a l l — s i g n a l H y b r i d E q u i v a l e n t C i r c u i t of Common-Base T r a n s i s t o r w i t h E x t e r n a l Emitter-Impedance 70 Prom F i g u r e A5—2 i t i s c l e a r t h a t h* = h., + Z„ »..A5-1 l b l b E h* = h , •••A5-2 rb rb h ' f b = h f b /.*.AM h , o b = h o b — A 5 - 4 I t o n l y remains to determine h ' ^ e t o complete the s e t of mixed h-parameters* I f i n F i g u r e A5-1 i s reduced t o zero an e m i t t e r — f o l l o w e r r e s u l t s , w i t h l o a d Z-g* The c u r r e n t g a i n of t h i s e m i t t e r -f o l l o w e r i s j u s t h*-. = — (l+h' £ e ) o From A3—18 i n Appendix 3 h» = - ^ ••••A5-5 1 + h f e 1 + I ^ T T h o b Z E rb T h e r e f o r e , f e 1 + h f e 1 + h f e 1-h , ob E rb ••»A5-6 1+h f e h f e ™ 1-h , h o b Z E rb 1+h-1-h , ob E rb 71 I n E q u a t i o n s A4—9, A4-10, A4-12 and A4-14, h ^ e appears i n the forms h f g , h f e / ( l + h f e ) and ( l + h f e ) / ( l - h r b ) . Hence, h* „ h„ h , Z-n, f e f e ob E AC- 7 1+h* - l+h„ " 1-h , *».A>W f e f e rb and, 1+h 1 f e rb 1+h 1-h rb f e (I+h f e > h o b Z E ...A5-8 A m p l i f i e r Performance I f E q u a t i o n s ( l ) t h r o u g h (4) and (6) through (8) are s u b s t i t u t e d i n t o E q u a t i o n A4—9 of Appendix 4, the r e s u l t may be ex p r e s s e d as shown i n E q u a t i o n ( 9 ) . h„ h ,Z„ 1-h , AT r / f e ob E \ rb Q VE = ~ G ( I T h — - T=h^ > 1 + 7 - ***A5-9 where G = Z L / Z E t and h., h„ h , h . , h , i b , n, „ , n 1 f e r b , i b ob \ g =; -g- + Gh z + G ( j ^ — - + -T-hT ) E f e rb I t i s noteworthy t h a t g may be m i n i m i z e d f o r g i v e n v a l u e s of G and h—parameters by a p r o p e r c h o i c e of Zg t h u s , 72 d Z E Z E o b S e t t i n g Bg/dZg = 0 and d e s i g n a t i n g the v a l u e of Zg which r e s u l t s Z-gQ y i e l d s h i b Z E 0 = / O h ^ - ***A5-11 and h., Z-r,n Z-n h„ h , h.,h , xb / EG , E \ . r i f e rb , l b o b x , 0 Z E 0 Z E Z E 0 i + h f e r b I f E q u a t i o n s ( l ) t h r o u g h (4) and (6) t h r o u g h (8) are s u b s t i t u t e d i n t o E q u a t i o n A4^12 of Appendix 4, the r e s u l t may be e x p r e s s e d as shown i n ( 1 3 ) . Z ' l E = ( l + h f e ) Z E • i ...A5-13 i - h r b + ( i + G ) ( i + h f e ) h o b z E 1±ZL ( l - h r b ) + (l+G) h d + h f e ) z E • o b where g and G are as p r e v i o u s l y d e f i n e d . S i m i l a r l y A' T i s 73 g i v e n by E q u a t i o n (14) a s , 11 ( ^ r b ) h f e - ( l + h f e ) h Q B Z E I E - l - h r b + U . + G M l + h f e ) h o b Z E - •••A5-14 and Z'QJ, by E q u a t i o n ( l 5 ) > 1-h rb OE h + (h + ^ ( l " h r b ) h f e - < I + h f e > h o b Z E W ( h o b + Ty h T - T z g i - h r b + ( i + h f e ) ( h o b z E + fe-i b _ E> ...A5-15 APPENDIX 6. DERIVATION OF THE PARAMETERS OF THE COMPOUND STAGE USED IN THE DIFFERENTIAL AMPLIFIER I f two t r a n s i s t o r s are connected as shown i n F i g u r e A6—1, t h e y can be r e g a r d e d as one d e v i c e , A s e t of h—parameters (the h M — p a r a m e t e r s ) may be d e r i v e d i n terms of the h-parameters of the i n d i v i d u a l t r a n s i s t o r s t o d e s c r i b e the o p e r a t i o n of the compound p a i r * F i g u r e A6-1* Two-^Transistor Compound i n the Common—Emitter C o n f i g u r a t i o n The commons-emitter h"—parameters are d e f i n e d by E q u a t i o n s ( l ) and ( 2 ) * v " = h". i " + h" v" .**A6-1 b l e b re c h" i " + h" v" ..*A6-2 f e b oe c Ql i s connected i n the common-emitter c o n f i g u r a t i o n and can be d e s c r i b e d by E q u a t i o n s (3) and ( 4 ) , v r t, = h. , i " + h .v . b i e l b r e l c l •••A6-3 i , = h„ ,i'\ + h ,v , •*«A6-4 c l f e l b o e l c l Q2 i s connected i n the common-collector mode and i s t h e r e f o r e d e s c r i b e d by E q u a t i o n s (5) and ( 6 ) . • v , = h. ^ i , ^ + h -v" = -h. _ i , + h ~v" c l i c 2 b2 r c 2 c i c 2 c l r c 2 c .••A6-5 i " = h„ 0 i , 0 + h _v" = -h„ 0 i , + h 0 v " c f c 2 b2 oc2 c f c 2 c l r c 2 c S o l v i n g E q u a t i o n (3) f o r v ^ g i v e s V L = I T T v " b - h ^ 7 i M b •••A6-7 r e l r e l whic h when s u b s t i t u t e d i n t o E q u a t i o n (4) g i v e s the r e s u l t i - (h - h i e l h ° e l ) i " + h ° e l v» c l ~ ^ n f e l h , ; 1 b + h , v b r e l r e l ...A6-8 E q u a t i o n s (7) and (8) are combined w i t h E q u a t i o n (5) and the r e s u l t i s s o l v e d f o r v", . b /, b f e l b " r e l ' ' 1 i c 2 \ . ,. , b r e l b ' r c 2 i e l 1+h -, h. 0 ' b 1+h -, h. ~ o e l i c 2 o e l i c 2 . A6-9 76 E q u a t i o n (9) i s s u b s t i t u t e d i n t o E q u a t i o n (8) t o y i e l d , h f e l h o e l h r c 2 ^ 1 = 1+h A. , l"b + 1+h , V " c — a 6 " 1 0 o e l i c 2 o e l i c 2 E q u a t i o n (10) i s s u b s t i t u t e d i n t o E q u a t i o n (6) t o g i v e , i« _ _ h f c 2 h f e l .„ , h o e l h r c 2 h f c 2 x „ c - 1+h n h . 0 1 b + v o c 2 1+h v h . . ; v c o e l i c 2 o e l xc2 .•.A6-11 I f E q u a t i o n s (9) and (11) are now compared w i t h E q u a t i o n s ( l ) and ( 2 ) , i t i s c l e a r t h a t , h f e l h r e l h i c 2 h". = h. , - , , f f ...A6-12 l e l e i 1 +h , h. _ o e l i c 2 h " r e - l ^ h 2 ' "-A6-13 o e l i c 2 h " f e = l + h f 6 ' h f C ' ..»A6-14 o e l i c 2 h ,h nh„ ^ I I o e l r c 2 f c2 k , , K n ' Q = h - r—T- r . . .A6-15 oe oc2 1+h , h. o e l i c 2 These e q u a t i o n s are now c o n v e r t e d t o g i v e the h"^-parameters i n terms of the mixed h-parameters by s u b s t i t u t i n g (see Appendices 3 and 4)s 1 + h f e h. = h. = h., ., , X t f ...A6-16 l e i c i b 1-h , rb 1 l + h f h = 1-h = -T~~T-— (^—T h ,h.,—h , ) re r c 1—h , v l — h , ob i b r b ' rb r b 77 1+h h = h oe oc f e 1-h rb lob where h f c = - ( l + h f e ) These s u b s t i t u t i o n s y i e l d the r e s u l t s h l e = B h i b l 1+h 1 ° h r b 2 A , , h o b l h i b l h f e l + h i b 2 (I=E + f e 2 r b l 1+h f e l ,•.A6-17 r e v 1-h h o b l h i b l r b l r b l 1+h f e l h o b 2 h i b 2 . 1+h fe 2 1-h rb2 *.A6-18 h f e h f e l ( l + h f e 2 } 1+h 1 + f e l 1+h f e 2 1-h r b l 1-h rb2 h o b l h i b 2 ...A6-19 h " = B ( h . , + t-T^ oe x o b i l+h„ -| i e l hob2> ...A6-20 1+h f e l 1+h f e 2 1-h B = r b l 1-h rb2 1+h 1 + f e l 1+h f e 2 1-h r b l 1-h rb2 h o b l h i b 2 .A6—21 I t i s u s u a l l y the case t h a t h ^ g ^ 1 and h b << 1* Making the a p p r o x i m a t i o n s l + h f e = h ^ g and 1—'h- ^ = 1 i n E q u a t i o n s (16) t h r o u g h (21) one o b t a i n s . 78 and h h. rJ i e i b h f e •..A6-22 h ob h f e h h h. t\j oe i e rb 'fe re h". = h % i e f e L i b l l f e 2 + h i b 2 ( h o b l h i b l + h r b l } J ••••A6-23 h h » r e * h»,„ ( h ^ h r b l f e v l l o b l i X i b l ~ h f e i / V h f e 2 " o b 2 i b 2 ' h» = h" (h , , oe f e o b i n + ^ 2 ) f e l h" % h f e l h f e 2 f e l + h f e I h f e 2 h o b l h . b 2 E q u a t i o n s (23) are s u b s t i t u t e d i n t o E q u a t i o n s (22) h " i b = hft + h i b 2 ( h o b l h i b l + h r b l > «A6-24 i e 2 h " r b = h * b l + h i b l h o b 2 + h " f e h i b l h i b 2 ^ o b l ^ ob2 ob o b i h f e l h f e l h f e 2 f e l + h f e l h f e 2 h o b l h i b 2 REFERENCES Johnson, S . D * a n d S i n g e r , J.R., Rev. S c i . I n s t * 29* 1026, (1958). G a r v i n , R,L.», Rev. S c i . I n s t . 29, 223, (1958) The E n g i n e e r i n g S t a f f of Texas I n s t r u m e n t s L t d . , T r a n s i s t o r C i r c u i t D e s i g n , New Yo r k , T o r o n t o , London, M c G r a w - H i l l Book Company I n c . , 1963, pages 96-98.
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Physics
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A D.C. amplifier and reference voltage supply suitable for use in a magnet current regulator
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