ITERATIVE SYNTHESIS EMITTER-FEEDBACK OP A FLAT-STAGGERED TRANSISTOR VIDEO AMPLIFIER by FRANK C H A R L E S CAMERON B.S., A THESIS Stanford University, SUBMITTED IN PARTIAL 1958 F U L F I L L M E N T OF THE R E Q U I R E M E N T S FOR THE D E G R E E MASTER OF A P P L I E D In the We a c c e p t this standards required degree of SCIENCE Department Electrical OF of Engineering thesis as from Master.of conforming candidates Applied to the for the Science Members of the D e p a r t m e n t of E l e c t r i c a l Engineering The University of AUGUST British 1962 Columbia In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for exte|^live copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of E l e c t r i c a l Engineering The University of British Columbia, Vancouver 8, Canada. Date ABSTRACT B r u u n and G r i n i c h designs for using stages alloy-junction The transistors cascades responses The design lation. ° amplifier drift- Equivalent are reviewed feedback sistors are drift- emitter circuits given parameters problem of this is of the by concerned the procedure use of necessary for stages Johnson— cases. Butterworth- w i t h an types of alternative to obtain pole-zero general to cancelto in- transistors. Johrison-Giacoletto newer the i n both produced sufficiently the lead cancellation. numerical method i s or d i f f u s i o n - t y p e s and p o l e s of using functions the spite here emitter hybrid-n treat emitter high-frequency tran- developed. is and the pole—zero amplifier Diffusion-type described Grinich and m o d i f i c a t i o n s attention Suitable by cascades without the i n the c i r c u i t , were used an i t e r a t i v e configuration zeros well video and d i f f u s i o n - t y p e - a l l o y - j u n c t i o n amplifiers Transfer either reported In addition, both : type research feedback which are of described configuration. described t h r o u g h use method u s i n g broadband clude common-emitter hybrid-n; e q u i v a l e n t amplifier type previously resistance-capacitance i n the Giacoletto have to of and cascades transistors with emitter feedback the of of the for property transfer defining synthesizing dependence, is type function this for this are described. stages i n the given. of are dependence flat of using commonSpecial amplifier that interdependent. are amplitude developed, response, A numerical in iterative method of solution is A numerical using 2N384 a response design example p-n-p is obtained when u s i n g the of delay, and t h a n by the small dc very emitter w i t h an i n p u t results iterative poses pair and t h a t are very Suggestions for are little good small or very or design to a is is linearity, for the two properties, bandwidths, or resistances. 50-JTL l i n e , design, obtained output is described. using circuit and construction necessary. of db, 49.6 pad and an for ob- particular theoretical equivalent an no designs large values development i i i there convergence the accurate adjustment given. Butter- shown t h a t Phase interstage to hybrid-it further the comparable shows sufficiently The amplification that (300x0. used connection the is the theoretical impedance-matching that for but given. of It amplitude an a m p l i f i c a t i o n of according Johnson-Giacoletto method The currents for indicate amplifier method, overshoot for Mc i s 6.5 G r i n i c h method resistance step-response emitter-follower modified to design maximally-flat g i v i n g maximum dc method g i v e The n u m e r i c a l m e t h o d fitted Test cps designs. An a m p l i f i e r . b u i l t but for amplifier G r i n i c h method. iterative Grinich e x c e p t when d e s i g n i n g very f r o m 40 resistance interstage designs. for a three—stage transistor the iterative db g r e a t e r value by this optimum f o r t a i n e d by 7.6 of compared w i t h an e q u i v a l e n t optimum i n t e r s t a g e true drift w i t h a passband worth type exists proposed. the method are the the pur- ACKNOWLEDGEMENT -—^ The Dr. of author would l i k e A . D . Moore, for this his afforded many h e l p f u l in the by like the supervising and g u i d a n c e throughout professor, the course of acknowledge the the programming UBC C o m p u t i n g C e n t r e , given by h i s fellow graduate assistand the students work* research Grant to staff suggestions experimental This Council thank the research,, He w o u l d a l s o ance help to (BT-68) was c a r r i e d out under granted to ix Dr« F * a National Noakes 0 Research T A B L E OF CONTENTS List of Illustrations List of Tables v i i i Acknowledgement . 1. Introduction 2. Transistor . . . ix 1 Equivalent Circuits Transistor 2.2 Physical 2.3 Admittance Parameters D i f f u s i o n Model The Operation . . . . . . . of the of . . . . Junction Transistor a Hybrid-ix . 26 Transistor 2.7 Modified Equivalent Circuit for Parallel Capacitance Feedback i n the E m i t t e r Lead High-Level Single-Stage Functions 35 Capacitance . 43 . Resistance. . 45 Injection A m p l i f i e r Response 51 Functions Current- . and . . . . 3.5 M a x i m i z a t i o n of . . 54 Voltage-Amplification for a Stage in Stagger-Tuned Cascade the . DC C u r r e n t iv a . Current-Amplification Representation Complex-Frequency Plane . . . The . 54 Amplification Functions Cascade 3.4 8 Equivalent The M i l l e r 3.3 . 11 2.6 3.2 6 One-Dimensional The D r i f t 3.1 . 6 2.5 2.8 . C i r c u i t Representation Johnson-Giacoletto Circuit 3. . 2.1 2.4 Page vi . . . in 55 the 59 . Amplification . 61 . 62 4. The 4.1 4.2 5. 6. 7. Iterative Method of The S y n t h e s i s Realization Problem . . . Approximation Function . . . 4.3 Realization 4.4 The Numerical — Iterative . 5.2 Grinich Designs 5.3 Designs U s i n g the 5.4 Characteristics 5.5 Pre-Design . . A p p r o x i m a t i o n and . . . . . . . 64 Design . . Using . . . Iterative of Construction Design 6.2 Low-Frequency 6.3 The E m i t t e r 6.4 Amplifier Conclusions « o the . . . 72 . . . . . 77 . . . 77 Transistor . . . 79 . . . . Method Physical . . . 88 . Realizability. 94 96 98 98 . 101 103 106 . . 69 . Results o . . and Performance . 66 . Follower . . . Method Considerations . . Amplitude . • . Transistor Iterative of . Considerations Test . . Equations . a Drift Prediction General « . RCA 2 N 3 8 4 G e r m a n i u m D r i f t 6.1 References Page 64 Network . The . Synthesis The M a x i m a l l y - F l a t . « . • . . The 5.1 Amplifier . Method Designs . Network . . . . v . . . . . . . . . . . . . . 115 117 LIST OF I L L U S T R A T I O N S Figure " 1. D i f f u s i o n model 2. C o m p o s i t e t r a n s i s t o r : (a) common-base (b) common-emitter c o n f i g u r a t i o n . . configuration, . . . . . Generalized elements extrinsic 3. 4. 5. 6. of Page a junction transistor Tt-equivalent circuit with . . . . 12 29 Johnson-Giacoletto equivalent c i r c u i t S i m p l i f i e d hybrid-TC circuit . . . . hybrid-TC common-emitter . common-emitter . . 32 . 3 3 equivalent 7. The circuit 8. Single-stage 9. S i m p l i f i e d hybrid-TC e q u i v a l e n t c i r c u i t for C ... Miller S i m p l i f i e d J o h n s o n - G i a c o l e t t o hybrid-TC c i r c u i t w i t h emitter feedback . equivalent circuit . equivalent Common-emitter transistor for the drift 37 amplifier for y^, . equivalent . . circuit . . . . 41 . . . . 44 modified 45 M 10. 28 11. Equivalent circuit 12. F i n a l form of the common-emitter w i t h emitter feedback . . the y-^-[ e a n d y2i • e equivalent • • 47 circuit 51 Equivalent 14. Cascaded 15. T h r e e - and f o u r - s t a g e B u t t e r w o r t h - t y p e d i s t r i b u t i o n s of p o l e s and z e r o s f o r a m a x i m a l l y - f l a t cascaded amplifier . 62 Amplifier pole locations c o m p l e x p o l e s ( Y} r e a l ) , ( imaginary) 70 17. for of . 4 6 13. 16. circuit i n terms equivalent emitter-feedback single-stage amplifier . amplifier . . . . . . 54 55 i n the s - p l a n e : (a) for and (b) f o r r e a l poles Low-frequency a m p l i f i c a t i o n , methods, Rj v a r i a b l e . . . vi i t e r a t i v e and . . . . . Grinich . . . 84 Figure Page 18. ^ T h r e e - s t a g e p o l e - z e r o c o n f i g u r a t i o n s f o r R-j- = 3 0 0 X 1 . : (a) G r i n i c h d e s i g n , and (b) d e s i g n b y t h e i t e r a t i v e me 19* A m p l i t u d e r e s p o n s e c u r v e s by the G r i n i c h and i t e r a t i v e methods f o r R j = 300.n.: (a) o v e r a l l a m p l i f i e r r e s p o n s e , and (b) i n d i v i d u a l s t a g e r e s p o n s e s . . . 86 20. Phase r e s p o n s e c u r v e s f o r R j = 3 0 0 H : (a) G r i n i c h d e s i g n , and (b) d e s i g n by t h e i t e r a t i v e method . 21. 22. . 87 R e s p o n s e t o a u n i t - s t e p f o r R^ = 3 0 0 X L : ( a ) G r i n i c h d e s i g n , and (b) d e s i g n by the i t e r a t i v e method . . 87 Successive cycles a m p l i f i e r w i t h Rj 92 i n the i t e r a t i v e = 300A . . diagram of the amplifier . an 23. Circuit 24. The t e s t 25. (a) T r a n s i s t o r c o m m o n - c o l l e c t o r a m p l i f i e r , and (b) low-frequency Common-emitter output 27. B l o c k diagram of generator . . 29. . amplifier . . T-equivalent 26. 28. test d e s i g n of stage to . 99 . . circuit feed . . . . . . . . 50-J1. l i n e test circuit using . . . . . . . 100 . . 103 . sweep-frequency 107 Amplitude response using sweep-frequency generator, (a) e x a c t d e s i g n v a l u e s , (b) m o d i f i e d d e s i g n v a l u e s f o r m a x i m a l l y - f l a t response . . . . . . . . B l o c k diagram of phase test measurements circuit for . . 30. T r i a n g u l a t i o n method of 31. Amplitude response 32. Phase 33. B l o c k diagram of response response test . phase curve curve . . amplitude . . . determination for the the test amplifier circuit for transient for measurements a m p l i f i e r response . to . . test 108 and . . . amplifier . . 108 . . 109 . . 110 . . 110 . 34. Test 35. Low-frequency amplitude response f o r amplifier . . . . . . . . . vii 105 112 a step-function input the t e s t . . . . . . 113 114 LIST OP T A B L E S Table Page I. Grinich designs II. Designs using w i t h R-j- v a r i a b l e the iterative variable . . . . method w i t h R . . . 83 T 90 v i i i ITERATIVE S Y N T H E S I S OF A FLAT-STAGGERED EMITTER-FEEDBACK TRANSISTOR VIDEO 1. Video television, the amplifiers radar, transistor posed soon to after transistor is pectancy. band, low-pass early transistor acteristics not necessary made to this network design This of obtain to size, been to low the proThe life ex- to only broad- fact that high-frequency char- circuit representation. "broad-band amplifier choice used consideration of power used equivalent The of 1948. high-gain, due broad-barid be of was and l o n g has suitable to design application in July transistor configuration The extremely partly stages. i n the amplifiers transistor a high-gain, from a q u a l i t a t i v e its small have for amplifier circuit device''" is the advanced systems. synthesis of d i d not importance low-pass m a i n l y due state cascade transistor c a n be models and the to of amplifiers. order prime ruggedness, i n the sufficiently In lar advent physical extent of these broad-band, Modern a c t i v e a limited was are attractive requirements* INTRODUCTION and communication the AMPLIFIER of the i n the of the it is particu- cascade following 2 3 three configurations emitter-input pedance, unity ciable The configuration a high (very initial output close voltage which give to is amplification.' characterized impedance, unity for current small load by The a low of cascaded video input amplification resistance), a m p l i f i c a t i o n w i t h no p h a s e - r e v e r s a l design common-base amplifiers was of im- less than and appre- the signal. based on this configuration cutoff to frequencies miniaturized the due the of the output pedance was necessary gain the transistors. necessary to bandwidths ple to achieve were cutoffs early broad-band video high collector of l o w common-base of to the transistor interstage impedance realize high video obtain low-frequency models. The u s e transformers the low to emitter of match input im- impedance-transformation number o f gains, difficult interstage to the A large extremely current-amplification and, to amplifier stages consequently, achieve transformers. due It to was video the also amplification with transformers, was multidifficult but 4 means for low—frequency The extremely The common-collector high input current power is at less gain is mon-collector ing impedance the least connection or output connection. gain is close come It is all possible unity. three if common-emitter of an lower output the impedance. voltage connections. for am- The impedance and com- match- amplifier. of impedance current of characterinput than the im- common- and c u r r e n t and g i v e s Very large advancement is magnitude) phase-reversal, common-base an phase-reversal, of both voltage connections. can have the configuration an o r d e r capable the With three (by with a signal of to higher stages but signal primarily common-emitter b a s e - i n p u t plification, have used The and c o n s i d e r a b l y is the input pedance cation is low output appreciable, w i t h no for available. configuration a very the a somewhat power or than u n i t y , i z e d by base base-input a m p l i f i c a t i o n c a n be plification the c o m p e n s a t i o n became am- the greatest current amplifi- amplification, the transistor current-amplification cutoff a^, art frequencies 3 in the large video-frequency power interstage t h e n be gain available transformers. This over allows a wide Direct use t o he band without made the o r RC c o u p l i n g b e t w e e n of the need for stages may employed. In the investigation special attention as configuration this for range. cascaded The will video be stages is of i s o l a t i o n and given to equivalent common-emitter offer the most circuits, representations suitable qualities amplification. video of transistor seems t o stagger-tuned multiplicative of is commonly u s e d amplification. generally so cascade dictated simplify A mismatch i n order the to achieving interconnection obtain individual in stage a good degree design. The 5 analysis video ter pole i n t r o d u c e d by Bruun amplifiers lead has been ger-tuning paper, by extended plane. cancelled by sistor i n the the cluding the The real emitter and G h a u s i , have cascade of mally-flat using RC e m i t t e r conjugate pole lead. alternate common-emitter feedback give i n the a Butterworth was used pole-pairs by Pederson resistive, to of pole-zero -cancellation. real produced to i n t r o d u c e d was a having and h i s methods of series-peaked, stag- complex- zero stage a l l In achieve i n the emit- then only a colleagues, re- Pepper broadbanding, in- and s h u n t - p e a k e d i n 8 pair in a common-collector-common-emitter synchronously-tuned response. broadbanding design feedback extraneous studied the use of 7 t e r s t a g e s , and the by Grinich: response introducing frequency the with resistance-capacitance maximally-flat Grinich's for were n o t Methods (identical) of considered stages to give multiple-stage feedback by al Pederson et due to maxifor their 4. overall low gain-bandwidth It cal) is method to of be shown i n t h i s network amplifiers tially gain, zero cancellation The b a s i s the that for drift to junction well as added circuit a on the circuit is plane of the is essentially (electric) alloy- junctions, and d i f f u s e d - a l l o y lead equivalent much l e s s manner than the network outlined hybrid-rc circuit equivalent is valid alpha-cutoff transistor. The v o l t a g e ^ - a n d c u r r e n t - a m p l i f i c a t i o n e x p r e s s i o n s rived for stage i n a cascade. best a single-stage represents design It emitter-feedback is shown t h a t a transistor frequency-dependent the as (drift) feedback i n the in modified parallel This which i s pole- lies then v a l i d , f o r then a frequency substan- 10 Johnson.. The with a built-in circuit emitter is work of modified Johnson-Giacoletto o n l y up t o a of small-signal chosen resistance-capacitance simplified. design synthesis suitable circuit micro-alloy, w i t h the the (numeri- t h a n does the and the is frequency by equivalent which exhibit A parallel i n series by B r u u n , equivalent transistors surface-barrier, to method y i e l d s amplifier transistor equivalent transistors transistors. is The for an i t e r a t i v e Grinich* method of hybrid-TC account field. this a given bandwidth* the The that applicable 9 G i a c o l e t t o , based by Johnson-Giacoletto slightly and t h a t this of circuit* developed for is scheme u s e d b y representation equivalent thesis synthesis common-emitter greater product. proceeds.. stage the amplifier current i n a cascade, amplification function For a p a r t i c u l a r is and f o r de- a amplification and the given, transistor are from complete which operating-point, 5 a c u t - a n d - t r y method y i e l d s for which the low-frequency A numerical design cascaded the an optimum i n t e r s t a g e amplifier,, d e s i g n method is It amplification is is is greatest interstage resistance. The amplifier, built design design procedure. to the for the large performance rate emitter of Rj, a maximum^ carried through for found that resistance, a of three-stage convergence currents a three-stage specifications, verifies and of large cascaded the 6 2.: T R A N S I S T O R E Q U I V A L E N T C I R C U I T S 2.1 Transistor The sidered to urately, for Circuit transistor, for be active a linear a three-terminal c i r c u i t design eters or the are ated of and on the the case of the of box'', t y p e used to analysis and c u r r e n t s , port parameters point at out which are that no approximations or 'exact' d e s c r i p t i o n of the may v a r y In this even for of each is design for partic- depends to be types both of is only a amplifier Although particular device. representation of type of made However, must be transistor is two-port a "black with terminal transistor are the it H e r e , we h a v e exclusively this on incorpor- of bandwidth. advantage the of used. two frequency. assumptions a single param- wide—band r e p r e s e n t a t i o n , major acc- two m e t h o d s is con- represented, two-port representation transistor c a n be o r more useful f o u n d by measurement advantage single-frequency eters of and r e p r e s e n t s foremost that a set Although these which deals The fact the a single uency. the usually in essentially problem of treatment ages this is d i s t i n g u i s h e d by t h e i r general of choice (two—port), narrow-band representation mentioned here method either i n t o which the are which are problem of by It p a r t i c u l a r method of Transistors systems, network. independent, The circuit four—pole circuit. not applications. type small-signal:applications, purposes, an e q u i v a l e n t representation ular Representation at by a set of a single volttwo- freq- representation so the that type, we h a v e 'exactness' examined is of in light certain an of param- considerably. thesis, a broad-band amplifier is t o be synthesized, and the sistor need is for a broad-band c i r c u i t representation apparent. approximated over single-frequency treatment leads transistor a set and of output, erties. ing range t e r m i n a l parameter quite n a t u r a l l y to of a set parameters, of two are several quadripole features of a purely internal physical behaviour of the separate transistor will describing familiar Also, have to be the several the approaches band equivalent circuit. band quadripole parameters, to is neglected is of of the a change o r TC-network as the of the most possible analysis lead an e q u i v a l e n t c i r c u i t where the i n evidence. The u s e are placed is for quadripole amplifier, the point. an of set form an by transistor. deriving a above a pa- c i r c u i t represents to a transistors of broadbroad- equivalent and G i a c o l e t t o . a theoretical transistor that 13 tively, to of these the common m e t h o d problem of shown b y P e t e r s o n are i n operating 12 T- These so representation F o l l o w i n g from the it the important of familiar device, the of empirical approach, equivalent less of lack- synthesis The type importance which are and a l l is at the prop- of modified for transistor. of be transfer device type representation can input modified types point, a transfer-function c i r c u i t elements are of this operating equivalent-circuit There analysis necessary. For This tran- the The m o s t is rameters an e x t e n s i o n describing immittances representation. since device quadripole parameters^ this fixed that the a matrix representation is w o u l d be by the measurements. features completely of a n d two d e s c r i b i n g f o r w a r d a n d r e v e r s e There i n the terminal behaviour a broad frequency i n terms four The of a suitable Alterna- t r a n s i s t o r model physical of phenomena o f an e q u i v a l e n t will the cir- 8 cuit representation of a transistor advantages over the quadripole contact is kept w i t h the easy to see w h i c h are transistor. dependent transistor the on the circuit advantage, an elements though, equivalent circuit frequency. Since ous of aspects easily tage the imation 2.2 transistor to i n the equivalent the Physical design, 'exact for the point circuit as only The m o s t a wide elements may b e it is choice of much less is one or is frequency are it range identified with is only of of vari- can The m a i n still of single independent circuit. that two important modification i n design equivalent circuit closer parameters over elements a device, affected. i n which the Since distinct the equivalent validity separate incorporated of the The of of operating may b e is operation desirable a high-frequency a number representation. physical the t h e n has be disadvanan approx- device. 1 Operation of the Junction Transistor i A short transistor the operation w i l l equivalent p-n-p may b e holes circuit. discussed in a and e l e c t r o n s the physical given This video-amplifier as leading to discussion w i l l this design. is the the be involved in development of confined polarity chosen The h ^ - p - n j u n c t i o n s i m i l a r manner by and by processes reversing the of the for the transistor interchanging sense to all the terms voltages currents. Junction and be junction transistor present and d e s c r i p t i o n of n-type silicon. transistors semiconductor I n the concentration of n-type donor are composed materials, usually semiconductor atoms, or of a c o m b i n a t i o n of p- either or material an e x c e s s of germanium there is electrons, a greater and in the p-type of acceptor trons). called semiconductor atoms, The or an excess r e g i o n where a p-n junction, rectifying, although tion i n that rent must be The material on b o t h the of p- differs sides of is holes a greater (i.e., and n - t y p e w h i c h has it there the a deficit materials interesting p-n-p nority carriers is composed p-n junction which acts (injector of holes) into as the n-type as minority carriers the base emitter, the tion of are the major is concentration into tric the across emitter t h a n does junccur- r e g i o n has the base region, other region is c o n t r o l l e d by the j u n c t i o n due to electron into by flow the i n the process be an e m p i r i c a l treatment is essentially to be riers m a k i n g many c o l l i s i o n s times during their effect transistor discussed process the base mi- region, of At much way. junc- This emission voltage the across base. with l i t t l e or no elec- circuit Diffusion individual d i r e c t i o n of region. n-type a built-in equivalent later). of therefore resistance of the higher emitter-base w i t h the and changing across low diffusion, (the i n the a random t h e r m a l travel of fields included by relatively of composed and the flow is a very flow base base junction to electrons from e l e c t r i c field will the forward- region. the are is the cross the material received being a collector to Hole-current aid flow end of a g r e a t many more h o l e s emitter-base base opposite current because than there holes at a an e m i t t e r p-n junction which acts there of and h o l e of and a r e v e r s e - b i a s e d impurity is rectifying junction electron junction transistor (conducting) This join elec- considered. biased holes. of property from an o r d i n a r y the concentration flow car- m o t i o n many On t h e average, 10 it acts to cause throughout plied of by charge of region is very trons, and the through the ing base transit carrier diffusion rived The electron reach the lowed to from in the the will is on the next the the given is the collector The effect of If recombine with taken by h o l e s the the recom- the t r a n s m i s s i o n of called sup-: nonuniformity considered. will is region, i n the that composed defined flow by bias base base elec- holes in cross- minority-car- of minority- dependence and i s to of the be de- so but that are the n-type is base The very : which immediately the i n the base region current al- p-type region. are impurity the prevented concentration than that flow across in the holes. through the * 8 t X base region from multiplication factor, by A f b = * (in holes much g r e a t e r the. m a j o r of the holes from e n t e r i n g a current a non-conducting region region. region so rendered region, prevented collector junction is collector to representation reverse through The h o l e - c u r r e n t to due junction potentials a large electrons base be showing junction is are the also for uniform section. by region layer. efficient become random m o t i o n i s base collector a means to gradient The m e a n t i m e the p-type*collector collector be this holes An a d m i t t a n c e enter n-type the time. collector entering of to collector Similarly, must region sense) collector i n the region. currents i n the few result diffusion density density carriers thin, base or density charge charge D i r e c t i v i t y to a concentration bination rier carrier a region. carrier the the emitter a^, 11 where ft = i n j e c t i o n e f f i c i e n c y - the f r a c t i o n of t o t a l current c r o s s i n g the e m i t t e r j u n c t i o n t h a t i s c a r r i e d by m i n o r i t y c a r r i e r s i n t o the base, 6 = transport factor r i e r s that reach a n d oc The quency, multiplication factor but quencies. a manner may b e It to considered decreases be hybrid-TC the principles of the fact amplifier available 2.3 circuit the that Admittance of real car- will function and c o n s t a n t with increasing of at fre- low fre- frequency in 2.3. the modified now b e diffusion the synthesis i n the The of be a complex i n Section derivation equivalent to is i n magnitude discussed A complete view injected = the i n t r i n s i c - a = the r a t i o of t o t a l c u r r e n t c r o s s i n g the c o l l e c t o r j u n c t i o n to the m i n o r i t y c u r r e n t a r r i v i n g at i t . current basic = the f r a c t i o n of these the c o l l e c t o r j u n c t i o n , made process. equivalent Johnson-Giacoletto starting This circuit is is from the necessary fundamental and a complete): u n i f i e d d e r i v a t i o n in to is not literature. Parameters theoretical of a One—Dimensional D i f f u s i o n Model analysis of the junction transistor for 14 small signals years before by the Shockley, ction the shortly eters of device the physically with to and f o l l o w i n g the transistor. T he the its that, of a was set of several A second theory made a number one-dimensional following paper of development. widening derivation theoretical classic realized. a n d Teal"'"'' e x t e n d e d i n conjunction thereafter, for was i n Shockley's space-charge-layer contributed junction described Sparks, transistor effects have was of by the authors admittance applies jun- A study of 16 Early 9 1 0 17 to ' 'is' param- d i f f u s i o n model analysis paper of the alloy- 12 junction as well Figure ity carriers (The grown-junction shows across symbols on L e t t e r 1 as the the and s i g n Symbols transistors d i f f u s i o n model base region of convention used for Semiconductor for transport a junction conform to Devices) of transistor. the' I R E Standards 19 E V v 0 Figure In order to continuity carrier 1. D i f f u s i o n model satisfy (hole) density generation of hole flow per librium hole density density i n the n-type and q to flow to i.e., the from holes the the per of holes n-type be point follows rate at used per i n the to effective is —^'J^/q. expressed -(p as - to that < 0 be rate to P the net the then the rate equi- actual hole in current den- rate hole of recombination (natural p r o p o r t i o n a l to T h e n the net rate of P^)/"Cp' Therefore, of rate the lifetime hole of a change plus be n hole the of the point p be characteristic charge, rate Let the charge, The n e t recombination is is be of equal material, and ^ hole time point. we d e f i n e equilibrium density. r e l a t i o n may b e that n-type material, If the at 0 transistor conservation u n i t volume the u n i t volume a junction so t h a t c > space charge regions x a n y p o i n t m u s t be an e x p o n e n t i a l of of c o n d i t i o n of u n i t volume material. sity carriers the r e l a t i o n may b e of the Y minor- the decay), deviation generation the of of continuity This equation i s v a l i d i n the base r e g i o n and assumes that generation i s not stimulated through some e x t e r n a l Now i t field is is agency« assumed that the e f f e c t of an a p p l i e d e l e c t r i c small so that the r e s u l t i n g d r i f t v e l o c i t i e s r i e r s can be superimposed on the thermal v e l o c i t i e s riers; hole i n other words, the system i s l i n e a r * then has two components, d i f f u s i o n component. of the car- of the car— The hole c u r r e n t a d r i f t or conduction component, and a The d i f f u s i o n component of h o l e - c u r r e n t den- s i t y at any p o i n t i s p r o p o r t i o n a l to the g r a d i e n t of the hole dens i t y at that p o i n t , i . e . , it i s due to a d i f f u s i o n p r o c e s s , and may be w r i t t e n as <Vdiff = where v -v*> ( i s the hole d i f f u s i o n constant i n n—type m a t e r i a l , and q ^ p i s the g r a d i e n t of the charge d e n s i t y . The minus s i g n ap- pears because hole motion must be such as to decrease The d r i f t the gradient. component of h o l e - c u r r e n t d e n s i t y at any p o i n t i s p o r t i o n a l to the a p p l i e d e l e c t r i c charge d e n s i t y at that p o i n t . f i e l d s t r e n g t h and the If a mobility the d r i f t v e l o c i t y per u n i t f i e l d i n t e n s i t y , Adrift pro- hole i s defined to be then = iyipE which gives f o r the t o t a l h o l e - c u r r e n t d e n s i t y J Since the d r i f t p = ^p^P - ^ pV ° D term i s n e g l i g i b l e we may w r i t e J when put i n t o Equation ( 2 - l ) this gives ....(2-2) p = - qD^yp; 14 a* i V°(VP)(-<ID ) j i _ r a p v P - pn V " / N * p' 9 + D_ V = - ....(2-3) P« p Since the diffusion region a n d x = W, E q u a t i o n ( 2 - 3 ) This the then i s holes injected It P , E the basic is given between p a r a l l e l planes may b e w r i t t e n the base now t o at x = 0 as r e l a t i o n which describes into convenient lies the behaviour of region. introduce an excess h o l e density, by P Substituting = i n Equation (2-4), ^P ~ p E we P E P n «.o (2-5) * 0 have ^ E 2 P E + D •p .2 ^ e I: 2 'x P where L_ = (D P P Equation split (2-4a) into a n ac p ) is = the 2 . ^ ^ < P p hole a linear a n d a dc _ J - , , L diffusion length differential i n n-type material. e q u a t i o n w h i c h may equation by assuming a s o l u t i o n of be the form P (x,t) Q = P e 0 U ) + P O L (x)exp(jat). ....(2-6.) The d c e q u a t i o n t a k e s the form <* eO ^__2 and t h e ac e q u a t i o n - ^(1 L x ary that P ^ = These g conditions •..-.( 2-4b) is -v—\ d noting P = 0 2 eO n T + j « f J ? i p equations imposed by e m i t t e r = 0 0 3 0 0 (2-4c) x must he s o l v e d w i t h b o u n d - and c o l l e c t o r voltages. 14 It for c a n be shown b y t h e u s e o f B o l t z m a n n s t a t i s t i c s an unbiased and p - t y p e j u n c t i o n the e q u i l i b r i u m hole regions are r e l a t e d P where is with mal respect 3 reverse—bias i n p-type potential (base), m a t e r i a l , V^ of the p-type a n d _A~^ region ~ kT/q = of the e l e c t r o n i c and T = absolute ). temper a t u r e . charge, therk = (At 300 K, junction, Note t h a t Vg i s hand, i f an e x t e r n a l t h e n t h e new v a l u e material i s , P (0) Q s m a l l and n e g a t i v e , i.e., in direction. On t h e o t h e r n-type ....(2-7) —1 A. - 1 0 / 2 6 v o l t " the region w i t h q = magnitude constant, density (barrier) to the n-type potential, Boltzmann's the = P expCA.Vg). n i n the n - by P^ i s t h e e q u i l i b r i u m h o l e the d i f f u s i o n j u n c t i o n densities that of h o l e (at the emitter - P expA(y + V B de b i a s is applied concentration to i n the junction), = P exp(AV ) n E ....(2-8a) 16 and, (at the c o l l e c t o r P (¥) = P expA(V Q Equations of total p terms The m o s t e 0 (0) P direct found by s o l v i n g e Q = P (expAV n (¥) n parameters. o f t h e more g e n e r a l l/Lp i s replaced by ( l + ja origin and t h a t i s taken then i n the form 0 t h e same i n terms - c 1) . (2-9b) density o f t h e symmetry ( x ) = A cosh(x /L^ is just only i s unaltered solution will about - ¥/2)/L p a r a m e t e r s may f o r t h e ac c a s e . equation the simplest i s t o be and then o b t a i n i n g the i n c r e - ac e q u a t i o n a n d d i f f e r s 2 are (2-9a) t h e dc e q u a t i o n ) equations 1) The ac a d m i t t a n c e the d i f f e r e n t i a l tage P conditions s o l u t i o n f o r excess hole case that - E = P (expAV t h e n be f o u n d b y n o t i n g t h a t in (2-8b) c densities, t h e dc e q u a t i o n conductance noted n t h e dc b o u n d a r y of excess hole and be c densities. P mental + V ) = P exp(Av ) B (2-8) then represent hole In junction), x = ¥/2. result a particular i n that It should by a change when advan- The dc s o l u t i o n i s + B s i n h ( x - ¥/2)/L . (2-10) Using P ( x the boundary ) = P n(e A V C conditions, + e ^ Y 2cosh(W/2L Equations E- 2) „. e ) h ( x Jg2 f (2-9), ) this •• becomes ....(2-11) p 2sihh(¥/2L ) p p 17 The h o l e is the current found from the form (for A is procedure the (x the = 0) P similar to for i n Equation hole Equation (2-2) ^p(x.t) °* P ^ x cross-sectional that dc using ^ AT. ^ p and-(noting current area (2-6), across of we the the base. can then emitter ( e that (x = write junction the = W) _ — E V x = 0 - l)coth(¥/L ) - (e^ C - V use is There sense that ^ e O of for U l)csch(¥/L ) p the collector dc h o l e current current across is i n the the a p-n-p If, collector F x = V ( n e A V E - l)csch(¥/L p of also transistor for Np a s neg- ,-...(2-13b) ) j made is ) as ^ p A L q A « • « « ( 2 1 3 cL P ) - (e A V C - l)coth(V/L A bility, a p AD I„ = qAD. ^Cp ~ ^ ~ p tion. By 0 x-direction) junction in in . . ....(2-12) ( x ) e,0 o n P A L where base field) / \ ( x ) A = —qAD P x - d i r e c t i o n i n the as T ative / \ (x) = J density electric effective expression positive hole-current negligible i where i n the the relationship, electron-current due a p-type the Einstein to the region, flow voltage u n is equilibrium electron |x p - from base across defined as density, the the P ) 14 AD^. to emitter emitter junc- electron as the mo- decay 18 time for electrons, then expressions derived Under for the emitter that L that and c o l l e c t o r the the primed the Then the refer total to dc and given intrinsic-cx large I E c A , A V J V = I parameter, can and c o l l e c t o r regions junctions to electron L n be to and currents are - 1) ....(2-14a) C - l) ...,(2-14b) V to at ""-Ep (2-13) compared dc the collector = electrons, R E A currents I The are refer the for from the and c o l l e c t o r unprimed q u a n t i t i e s quantities emitter distances E n length i n Equations i n the qAa N ' — — ( e A L ' n •= p t where those qAu N = — p - £ ( e I™ I diffusion boundaries emitter and to currents assumptions n the analogous electron a>"£ <<^l, as n emitter + I and the and c o l l e c t o r ""-En + a region region. the c emitter C n are ....(2-15a) « ....(2-15b) , mentioned in Section 2.2 is by a = 1 ...,(2-16a) H—— T Cp X and the emitter injection efficiency, Y = 1/(1 # > is + — ) • I Ep given by ....(2-l6b) 19 For practical junctions, quency junction transistors Ig <<^Ig n independent c l o s e l y , ^foc *= lQ ^C and p plane ^ at and a ^-Qp' n a n d may b e w i t h abrupt s taken o to I v Equations = ^ i ( e I p The may b e that A v E _ 1) + ^ 2 ( e G^^ = G ( e A V E - G + -^(e l) A 21 l^n P. £ 2 G ~ _ A _ ^P!£ 12 incremental -^coth(¥/L conductances slope form A V C - l) ,...( -17a) A V C _ i) ....( -17b) 2 2 of the c s c at dc h ( ¥ / (2-l8a) ) L . .. a g i v e n dc .(2-18b) operating characteristic curves point at i.e., g of i n the ) = G e E l l VQ = c o n s t ....(2-19a) E E = G e E 21 = const (2-19b) A because more A G^ found from the point, 2 fre- A G = — • and u n i t y " ^ ' ^ or (2-15) A where be are 1. ¥ e may now r e w r i t e and fl" h parallel G ^ a n d G^ Vj,; and, taking 21 ~ (which are into account u A U V e functions the V e of ¥) dependence are of independent ¥ on 16 , 20 ' " o^c 1 2 = const "e A E - 1 V / 1 L Av e / —-csch(¥/L E V)• £v c AV 1 C AL A E V -coth(W/L )^ n F - + csch(¥/L ) p G ^expCAVg) ....(2-20a) and g 22 A X C = <lA|J.pP e n L e A V A const E f" A E _ V e V e P C - 1 _ _ _ E G 22 e L -csch(¥/L E V c )• ^¥ AVr 1 o J Av [I A ± t h ( ¥ / L p ) _ s e c h ( ¥ / L ) p coth(¥/L ) + p p Av C - i ! + (1 K e A v E A L - s e c h W/L )c o t h ( V / L ) P (2-20b) where K-l e = A • E - 1 1 , , • c s c h ( ¥ / L )• A L , e 'A*V- RE V A C - l V ! —r-n: v e e Av A v ! E A L c' Av E For V first n < -0.5 volt, and V g ^ O . l term i n Equation (2-2l) volt ^¥ 7-—coth(¥/L ) ^ — P P > .. . .(2-21) (a t y p i c a l value), the predominates, andthe K 1 term i n C Equation (2-20b) If we predominates•„ let O 0 and = ¥ / p L G = ....(2-22a) —exp(AV™) ,.....(2-23) ¥ then the conductance parameters g and = G 0 rcoth0 cj written . . . . (2-24a) o g 2 1 = - G 0 O csch0 g 1 2 = - Gr - 0 O csch0 g The p a r a m e t e r l l may b e G 2 0Q 2 = - 0 c a n be „«,..( 2-24b) Q j ....(2-24c) Q ... , . ( 2 - 2 4 d ) coth0 . Q Q related to the low-frequency com- A mon-base noting small-signal forward current that Jfoc =1, through the ratio, = * a o = ^ o 8 a ' relation I p C ~ 21^ ll VQ .= c o n s t g To o b t a i n t h e g ~ = more g e n e r a l G 2l/ G ll admittance = s e c h ^o° A2-25&) parameters we now 1 replace l/L by (l + j»'T") /L 2 0' £ 0 ( 1 + O In the general form, 0 replaces so that j « 7p)'- 0Q and y ^ . ...,(2-22b) replaces g^ . , and 22 Equations (2-24) become y l l y 21 y 0* coth0' G = ~ G = - 2 K (2-26a) $ csch0 „...(2-26b) 0 csc.h0 . ,..(2-26c) ,y = - 0 coth0 and „...(2-26d) 00 The p a r a m e t e r signal 1 = c a n be 0 forward current related r a t i o : i n the to the common-base same m a n n e r a s small- i n Equation (2-25a) ' a fb - — 8 i x 1 ~ 21 ll = const y V ep r C / / y = s e c h ^ = ' cos*0 {l o + > T p ~T ) 2 9 a • o ( 2""~ 2'79') For 0 the first O <3Cl> = ¥/L two "t terms n e of hyperbolic cosine its expansion to series i 3 1/(1 + = ••• :•• ' —± 1 + 1 0 ( l + j«>r ) 2 1 p o + may b e that mately the the • ••. r 3<oT l0 p low-frequency value j3 * B /(l. + j « ^ 1 0 ) 2 0 p 0 of *1/(1 8, (2-27b) 2 2 o is approxi- i.e., + i0 2 Q = 1 ) = 8 / ( l + j«/« ) 0 .... o numerator term i n E q u a t i o n (2-27b) J3 then give f0Q) 1 + i0 Noting approximated by 0 ....(2-25b) ....(2-27c) 23 where, using the relation L 2 = D P <°0 = Here is Equation the frequency (2-27c) is ( L y at V ) 2 2 / P ^ , .P / L ] T n which the down t o \ of its 2D / ¥ . ....(2-28) 2 = squared magnitude low-frequency of value; 8 in it is 14 the is a-cutoff here with a frequency observed single The that time error reduced by o r i g i n a l l y defined 8 behaves i n the a refinement To f i n d cutoff where f nority the = D i t ^ 2(L /W) p Pritchard. is apparent o f frequency is = /% 0Q 2 i s through the at which the down t o \ 'of its t h e f 0 diffusion base region* squared for ¥/L 8 then behaves = 8 sech( p ) ' D The p (2-28) < 0.3, ....(2-27d) time dc v a l u e of value of is mi8Q and 8 i n Equation is called t h e oc- 21 cutoff frequency, then takes 8 which is a^. the form = sech0* found to be This ^ requires that B sech(j2.43.tt/a> )2 0 a good a <* T'-Q = 2 . 4 3 , > 0i A 8 sech0 o approximation to 8 for and 8 . ,,.(-2-27e) BQ ^> 0 . 9 . Also 0'/sinh0' *=" 0/sinh0 for 0 < 1. is as (t r a n s i t ) magnitude low-frequency the from Equation and t h e r e f o r e 2 8 sech(ja7r 0 )^ carriers (2-27d) to 2 = i.e., due Prom E q u a t i o n ( 2 - 2 7 a ) , 8 system, It (2-27b) a> , M . ^ 20. al,'. i n Equation that fi)> a first-order et approximation used 21 more p r e c i s e l y , Q Shockley constant. frequency near as by ....(2-29) 24 The v a l u e the of is o> a 1.22 commonly measured more accurate our purposes. ¥e are times value. 2 the (2-26), y and Referring to 0Q = W-/L frequency short-circuit and too complex csch0 = -(G/K) 0 y 2 2 = ( G / B K ) 0 coth0, parameters .. ,.(2-30b) csch0 ....(2-30c) .,..(2-30d) Q L for ,.(2-30a) 2 J be as 1 Equation is w h i c h may admittance (2-29) and (2-17a), we see that for V Q <^ -0,5 v V G -7^(1 E E G NI A 1 9 + ^ ) l l A ....(2-31) G ( 2 - 2 5 a ) , w i t h 6Q )> 0 , 9 (2-3l) is and V g ^ O . l dominant, volt, and from E q u a t i o n (2-24a), g For are y term i n Equation and but 4 = - G 0 using Equation (2-19a) 2 al, G A first ' 3 1 E the 2 2 L Then, ' et approximations y G ^ -^4 F 2 Shockley ( /Po^ ^ coth0 = volt, I 2 (2-27e), l l <0Q o f Other available "^ ' c a n now w r i t e from Equations the n = G 0 O coth0 Q = G <[0.3, which is easily junction transistor, g l l = G / | 3 0 l i e A v A I E ^ attained 0QCoth0Q = = E -«ee A I E . ....(2-32) i n a good a n d high- therefore °* ' 0 ( " 2 3 3 a ) 25 and, from Equation (2-24d), g Then, from the fact 22 = / 0 Q 8 that = K V A = K g cc* ....(2-33d) = C*Q "= 8Q, g and 21 g T h e n we may r e w r i t e 1 2 = " = - a O oc g g Q Equations & c o t h c ....(2-33b) c ....(2-33c) # (2-30) as follows: 0 y l l = y 21 = ~ a 0 g ee ^ c s c n 0 .,.,(2-34b) y 12 = " a 0 g cc & c s c h 0 . ...(2-34c) y 22 = g g ee ee cc ^ c o t h ! ....(2-34a) ^ (2-34d) l where 0 = (j2.43co/a> ) a = a-cutoff a fbO g = a Q = A l e e IE and These g c c 2 , frequency low-frequency factor, = for the d i f f u s i o n model, common-base current amplification = q.Ig/kT = t h e l o w - f r e q u e n c y e m i t t e r a d m i t t a n c e , as g i v e n b y S h o c k l e y e t a l , E 10 /26 3 mhos a t . . 3 0 0 ° K, = the low-frequency c o l l e c t o r p r a c t i c a l v a l u e s of K ) . then are one-dimensional the admittance (<C!g s h o r t - c i r c u i t admittance parameters d i f f u s i o n model of the for e e for junction transistor, the valid 26 under V c < 2.4 the assumptions -0.5 The ^ W / L The as racy for (XQ^>0«9, V g ^ O . l volt, and volt. Johnson-Giacoletto have 0.3, transistor few frequency equivalent elements, linear of video-frequency be developed with corresponding or mum d e p e n d e n c e measurement so that are the also which is i n the various i n the important that case is the cir- associated some physical phenomena, operating i n equivalent the equivalent, have point circuit or accu- over elements transistor on the simple, valid the transistor as sufficient present circuit particular elements retain s h o u l d be desirable the regions It Circuit s h o u l d be and y e t design. It represent of circuit possible interest, range. cuit significance as amplifier range Hybrid—TC E q u i v a l e n t mini- and ease of considerat- ions. The into two analysis sections, one-dimensional the in modified Section resenting arrived sistor at the first theory These the of equivalent which deals effect of sistor are theory. extrinsic ite have added The been for the elements transistor. gives is published. of ' defined y.-parameters were by given parameters, rep- first intrinsic Johnson"^ but To t h i s not intrinsic a complete broken tran- similar 18 elements the by is idealized well one-dimensional configuration "extrinsic" combination which an minority-carrier diffusion, common-base since with admittance IT analyses circuit and c o r r e s p o n d i n g short-circuit theoretically i n the to "intrinsic" transistor, Shockley 2.3. the leading "intrinsic" covered by transistor representation of the with the tran- Shockley the compos- 27 Practically, circuit takes mittance minal parameters in added of to are are are the the = the 2(a). shown i n F i g u r e lead (b' junction space-charge-layer) transition itance, both tion charge across ances the are neglected so which are the equivalent admittance The the are g^ = t h e elements difference configuare: r^^ of the and the ac- collector-junction / transition (depletion-layer a n d C, = C = "tc c the w i t h the not ter- terminal resistance commonly c a l l e d collector collector capac- equilibrium condi- potential series measurable set lead and hence up resistare circuit. parameters for configuration admittance found. connection and e l e c t r o s t a t i c they the range. E m i t t e r and c o l l e c t o r small that common-emitter for ad- these common-emitter to base associated separation i n the common-base metallic (more junctions. The the of due capacitance, capacitance are The . e x t r i n s i c . e l e m e n t s A = emitter C, and from Extrinsic circuit account = internal base); conductance; of and compared w i t h the i n the resistance the short-circuit d i f f u s i o n model frequency is tive of the equivalent and compared w i t h the model. circuit between or then measured over four the theoretically i n t r i n s i c model to base The c i r c u i t elements theoretical semiconductor leakage obtained Such an e q u i v a l e n t series d e f i n i t i o n of then measured t e r m i n a l parameters ration of a one-dimensional equivalent parameters parameters are of transistor corresponding terminal method following pattern. parameters intrinsic the the the the c a n be parameters. The intrinsic transistor easily found from transformation the equations are y lle = y l l + y 12 + y 21 + y 22 in .-..(2-35a) 28 y and which are matrix 12e = " ( y 12 + y 22 } 21e = " ( y 21 + y 22 } y related to 2 2 e the = y 2 ....(2—35b) ...(2-35c) ...o(2-35d) 2 terminal voltages and c u r r e n t s l l e y 12e b e 1 ... X 21e y Figure circuit of the istor, 2(b) the y shows 22e the transistor. g } » ^^ > n e a n < composite common-emitter The y - p a r a m e t e r s i n the g ! ^ c are of the the added l l y 12 y 21 y 22 'te c ° t c + i b Iv! be be C (a) Figure The as the 2. transiselements, C c y l l e 12e y 21e y •"•c 22e x c V. ce te (b) C o m p o s i t e t r a n s i s t o r : (a) common-base c o n f i g u r a t i o n , (b) common-emitter c o n f i g u r a t i o n admittance sum o f repre- AAA y bb box extrinsic e y equivalent intrinsic C. 1 tc o- (2-36a) c iVe v m i n o r i t y - c a r r i e r admittances and r ^ c the equation y sent by matrix i n Equation a symmetrical matrix, (2-36a) representing may b e the written passive 29 elements, trolled and a n o n - s y m m e t r i c a l m a t r i x , representing the source, l l e y y 0 12e 0 b 'e (2-36b) + y This 12e then leads y to 22e the Lumped—element ted section priate sums common-base power of Figure ( y 21e ~ ^-equivalent y 12e of o b t a i n e d by the elements Equations phase slope introduced by u s i n g parameters of correct is the Equations for correct the at (2-26) exact so that squared-magnitude dc. approximate Excessive form of the Using Equations that, half- function common-base 22e +y- L2e ( |21e" y I I tr Figure the error would I o- appro- form of the dot- be y- (2-34). y e 3. i n the approximating the y-parameters is , c 'e shown i n F i g u r e obtained from the of V 0 circuit representations 3 are } and d i f f e r e n c e s frequency and the con- 12e ) V be V ce —o e 3. Generalized TX-equivalent extrinsic elements (2-35), from Equation (2-26), (2-2l), (2-33a), circuit (2-33d), with and the fact 30 K-l * J - the element values 0 0 of Figure „ l l _ * J _ J^L<^! 3 may b e w r i t t e n 0 l l e y " y + 12e y 22e y 21e + 12e y - = 12 y y l l y + y + y 21 ~ Weesi'nitff = Mcc—^ 22 12e = " 12 = 12e = 12 -(cosh0 - l) ^ ~l} ....(2-37a) --.(2-37b) 0 sinh0' cc y cosh as (2-37c) and " y Using cy, and t h a t y " y the facts tt a 21 e e that 0' sihh0'' (2-37d) ^$>1 n e a r <c = 2 . 4 3 , the magnitude the half-power frequen- 0'/sinh0' of the term c a n be a p p r o x i m a t e d b y 1 0' slnh0 1 + ....(2—38a) j0.263»/tt 5 This is s i m i l a r to the approximation by Bruun except that 0> /0.263 r e p l a c e s h i s tt /0.256. E q u a t i o n (2-38a) i s than r e c t e d t o y i e l d t h e c o r r e c t p h a s e s l o p e a t dc so t h a t a a 0' , sinh0' e -j0.142«./co a (2-38b) + j0.263Wto a * l cor- 0 The term —r(cosh0 sinh0 - l) = 0 tanh(0/2) i s then expanded i n a 31 series, and n o t i n g omitting terms expansion, from Equation (2-25b) that 3Q = 1 - 0 ^ / 2 , of degree greater than two i n t h e with 0 ' ,| (cosh0' - l) * ( l - a 0CQ = 8Q = We m a y t h e n w r i t e l l e - y 1 + 2 y e 12e = ( 1 = (1 - a 0 " O a ) g c ) g c + 22e + y 12e = V c c , e a n where at d y 21e " <j±e the l a s t analysis circuit, cuit a O ee u ee 5 2 1 5 g -j0.142«/« + j 0 < 2 ee<° ./« c c .263«/. j 0 g 1 * 1 jl.21 g two a p p r o x i m a t i o n s equivalent is shown / f i ) cx ••••(2-40a) ....(2-40b) a a * a ^ ; - ( 2 - 4 0 ^ ) a T~ 63a/a " a O ee a ••••(2-40d) g U e e are permissible c i r c u i t which results called for operation with from t h e above the Johnson-Giacoletto i n Figure 4. The e l e m e n t s are simply the i n t r i n s i c elements equations, The 12e " l^e I + as w^tt . The of y ee (2—37) -j0.142«/a + (2-39) a 1. Equations e y ) + jl.215a/a> u the s u b s t i t u t i o n y series we may w r i t e smh0 with and r the added i n t r i n s i c elements extrinsic hybrid-n; equivalent of the equivalent derived elements from the described are g^, e = emitter diffusion conductance = ( l - o^Jg C^, e = emitter diffusion capacitance = 1.215g type /tt cir- diffusion previously. 32 g b'c b 'c g and It lent diffusion conductance = (l collector diffusion capacitance =.1.215g = i n t r i n s i c transconductance m g °ce is collector = collector-emitter important circuit b Y *> + to are note that independent - «o)g cc /« = oc„g O ee e diffusion conductance all elements of of frequency. the = oc-.g 0°cc above equiva- b v v + ce Figure 4. Johnson-Giacoletto hybrid-ic equivalent c i r c u i t Bruun has s i m p l i f i e d the cation to video amplifiers, tances of g^, , g^, to that c of and C ^ , as C , which accounts lateral nature ration. The of the equivalent is are c for g ce is circuit, shown i n F i g u r e assumed transistor conductance common-emitter the i n the 5. negligible major for The with p o r t i o n of common-emitter omitted because it appliadmitrespect the b i - configu- shunts the 6 small load amplifier •C^ , is resistance used considered assumed capacitance. here. negligible Equations ylie 12e y i n the The optimum d e s i g n emitter with respect (2-40) transition to may t h e n b e = g_A* 'ee + of the video capacitance, emitter expressed jl.215«/« a the diffusion as ....(2-41a) 33 - 22e y and where it is y of the the a y ~ 12e g a O g which l i m i t Figure the Q diffusion high-frequency as to process o b t a i n an performance a guide to the be 6 ee persion but Simplified equivalent fundamental in transit finite, base time quency, oc^ b e g i n s to an a—cutoff have of layer. to of a^g V, ' 0 e e be 1.215g The m o s t the c -o be 5. of transistor. + Figure idea choice tt + (2-41d) a ). 5 i n order T h i s may s e r v e high-frequency = l / ( l - q u a l i t a t i v e l y the of oa o .. ee 0 and a ' cc (2-41c) o 0 = circuit transistor. suitable 12e y " ....(2-41b) consider equivalent junction = 0 that us effects + 21e noted Now l e t and v 12e y V ee ce oc hybrid-TC c o m m o n - e m i t t e r circuit cause the of cutoff minority carriers T h i s means decrease frequency beyond across the the a certain disthin, fre- that the t r a n s i s t o r may b e oa^c It has been frequency is inversely proportional frequency, so that is shown b y said Shockley 15 et the al that square of the the a-cutoff base w i d t h and hence increases r a p i d l y as to the 34 base is effect C made thinner. of is I n the represented by the emitter circuit, diffusion the capacitance, b 'e ' The other capacitance transition capacitance. across p - n j u n c t i o n due any up a c r o s s region ance the of charge. "where into The the density and donor atoms are i n the and n - t y p e the electric to widen or increase of the exists the C^ , e much s m a l l e r of is but into carriers by mobile across layer, is serve the and the than the low. Accepas to terminate tends decrease the emitter emitter diffusion collector they capacitance. than the collector unbal- "depletion- in a transition much g r e a t e r n- junction resulting set the charge junction potentials, is capacitance a thin instead or a junction potential holes across neutralized g there a with a resultant mobile regions, is £ capaci- transition ca- b c ' 1 pacitance, C.^. and e m i t t e r The effective i n Figure diffusion admittance, tional C.j. to circuit c = C , resistance giving 1 5 is y^, to c then behaves > c, , , bb' b e' i~Tl p-region , , , tance, the applied tance, lead diffusion of C , electrostatic depletion-layer capacitance, ' the depletion transition is circuit, the not capacitance, C, , circuit, An a p p l i e d b i a s the i n the Because diffusion are field. or narrow to potential tor p- i n the On o p e n j u n c t i o n by and e l e c t r o n s layer," r simplified equivalent and C c to all composed of the discussed later. like a lowpass filter effective an e m i t t e r lead between internal sum o f the to The i n t e r n a l base cutoff effect. an i n c r e a s e emitter composed i n the to of base emitter , and a M i l l e r - a d m i t t a n c e term be and the rise admittance proporinput the emitter baseadmit- A reduction emitter of cutoff frequency. 2.5 The D r i f t It has transistor short the Transistor been depends transit—time collector, resistance. the (b) junction high-frequency fulfillment of injected the to collector the demands an upper the on the low Prior conflicting placed cy shown t h a t capacitance, and of the these on t h e of a requirements: from the development limit three carriers imposed by frequency of operation three emitter (c) drift low to base transistor, requirements operation (a) of had high-frequen- transistors. 25 Kroemer in the base to move realized c o u l d be reduced i n an e l e c t r i c a comparatively that slow field process the minority-carrier considerably rather t h a n by because of emitter very low v a l u e the base and d e c r e a s e d constant in i n the at electric base The drift the field of a p-n-p transistor net N(x) = 0 is field that carriers were which random n a t u r e . control the The impurity it was very high through the base region This parallel is at the to a d i s t r i b u t i o n introduces a to the diffusion direction region. to x collector. drift related N(x) so exponentially the F, where region to the diffusion, its new p r i n c i p l e i n t r o d u c e d b y K r o e m e r w a s concentration if transit-time — net the is by the drift impurity concentration field i n the intensity, base region by = N(0)exp(-AFx) impurity emitter defined side (electron) of the base (2-42) concentration region, and i n the A ^ - base, = kT/q = 36 thermal potential. The fined (normalized) N(¥) Inj^y A where F = drift and used free for to ¥ = base compare transistor. the drift the which y, . = AF¥ field is de- .....(2-43) intensity width, drift transistor The p a r a m e t e r field^free transistor, to the generally and ip = 8 , (electric) lies for a field- between = 0, "maximum-field" transistor. The gion parameter, by ^ - is base-field drift field and i n c r e a s e s reduces the the oc-cutof f transit-time frequency of i n the the base re- transistor. a g i v e n base w i d t h i n a germanium t r a n s i s t o r , an improvement a factor high sity of near eight the emitter the low tor capacitance tion c a n be attained. leads impurity density layer. performance produces because limit tion transistor the is, advantage sistor, it is the of quite the necessary An e q u i v a l e n t collector due to a further base high-frequency To t a k e mon-emitter near the a low base-lead and conductance This also to Also, the leads wider operation. This naturally, called modify circuit configuration, for the the Figure 6, the drift the collec- of the deple- transiscapacitance drift of junc- transistor. drift tran- circuit. transistor been den- collector of by and low improved type equivalent has to and c o l l e c t o r improved c a p a b i l i t i e s to resistance, improvement resistance impurity For i n the developed com- by 26 te¥inkel, i n the same f o r m as the Johnson—Giacoletto hybrid-n 37 circuit commonly u s e d The v a l u e s number of of the for alloy-junction circuit elements multiplying factors that diffusion transistors c a n be f o u n d b y means o f depend on the drift a field only. b b i b r cc S-AA/V 'be 'te be be o- e Figure Using (2-38), fusion 6. Common-emitter e q u i v a l e n t f o r the d r i f t transistor a method identical an a p p r o x i m a t i o n transistor c a n be a fb The numerical excess drift phase value (at transistor of 2 written „ a 0 ^ ' 2 that as -j0.215«/« + in deriving + j<o"Jp) l 2 Equation for a dif- 27 e I used = sech0Q(l ja/tt a (2-27f) a in this A similar a s oc^ 0.215 w )« i for to circuit expression expression for is called alpha of the the ^ ^-jOco/c^ a fb where ljf, of 0 = the oc f b excess ^ a 0 1 phase e (2-27g) + at ja/a a^, a related to the phase angle, by 0 = - \fj - TC/4. (2-44) 38 For the field-free transistor, transistor, 0 . 2 1 5 ^ 6 ^ 1 6 = 0.215 radian, radian; depending for on t h e the drift drift-field parameter. In the istic of oc^ mon-emitter common-emitter is extremely small-signal the of important current oc„ By configuration, = may b e seen a f (2-27g) exponential t e r m c a n be approximated by the where one—half of at its a f e + ja> (1 squared low-frequency frequency is f that, for first two a<^fi> , a terms ~ 29 parameter, a , this given a 0> Q magnitude is given n) 0 at T a Q " l of oc^ + is down to by • 1 point by ....(2-45b) a e) + a ). value e convenient ( Q which the a a = oc /(l - Q <°,V-P~ = ( ! It and n o t i n g expansion, a frequency com- ....(2-45a) i n Equation series character- from the . b substituting its phase ratio — 1 The as the ....(2-46) a^9 to introduce a new cutoff 39 which c a n be suitable effects considered for of to common-emitter excess is most u s e f u l frequency at which the «/w ^>(l a - an e f f e c t i v e representation, a ) to note that magnitude fe <o(l 0 the compensated is is 0<°a + a a> at also frequency for the approximately the equal to unity, i.e., then Q a is this of a This alpha-cutoff phase. It for be a = frequency at 1 + = a 9) 1 0 a = «„. T aQ Q which the real part of oc^ is equal 30 to one-half The ter a i n the low-frequency parameter, value. co^, because it is applicable to equivalent expressions requires phase, its frequency t h a n (o directly « of to be for much more the specified w h e r e a s tt^ a l o n e is is a more easily measured c i r c u i t work; elements to attractive include of the the parame- and i s i.e., the equivalent effects of more use of circuit excess sufficient. 26 teWinkel the (for excess-phase 7^9), has given parameter, an e m p i r i c a l e x p r e s s i o n w h i c h 9, to the base-field relates parameter, as 9 = 0.221 A second expression effective a-cutoff relates + 0.098 ^ the frequency, radian. a-cutoff a^,, by frequency, (2-48) (o^, to the 40 (0 = ^ P = Equation 2.43 used be transistor, + a„9 (2-49) i n the transistor 1 * 1.21 suggests d e r i v a t i o n of r e p l a c e d by o r more w a + 0 . 0 9 7. then that the r e l a t i o n (6^ E q u a t i o n (2-27e) Tj) 2.43 = + 0.18 a>^^C^ s i m p l y by o..a(2-49) for the diffusion for the drift 2 . . The { . . l a t t e r =F = expression 31 was used by authors of Stephenson the for preceding the four diffusion transistor references for the and by drift the transis- tor . Equations l l e y " y + (2—40) 12e y 12e = ( = ~ 1 then ( 1 a 0 ) " a 0 g cc become ee ) g 5s «/» + ee J cc + g a / a ) T ....(2-50b) -j0.117«/a y 22e + y *21e 0 1 Using of lent *12e = O « c c i V j b T 2 p £ 7 « ^ " ^ c c - y, 12e = oc„g — 0 e 0 J e an e x a c t \j , t e W i n k e l h a s where J g e e C, . b'e e i -j0.117a/a ;—• = a g jp.216a/« . /a' for for e e ^ T y^ , g e = + y^2e expressed = g e e /a' . . . . (2-50d) e low frequencies may b e = g /«m. ee T b 0 T y^, + J g . A + shown t h a t of ""(2-50c) T expression c i r c u i t elements 'b'e T a e and ....(2-50a) T the """ n ^ e r m equiva- as + j«C b t e ....(2-51) ....(2-52) s 41 By p l o t t i n g y^, has found i n the g that, that on t h e axis. good to pass through This of a series is accurate factor P accounts to parameter the to J ^ P/g the i n the frequencies. 7. part The is bination of a'/g assumed higher their b t e centres the a impedance i.e., , a/a^ - ^ 1 . field on frequencies considering +l/3-C for < to The and i s multiplying related graphically 0.51 a n d C, , be determined circuit may b e 'b'e , for by y^, is s i m p l i f i e d to just as i n the the , shown at lower in Figure parallel com- Johnson-Giacoletto D-.e ee hybrid-u by at nearly 0 < Y ^ < 9 . equivalent F o r «/«_, ^ 0 . 2 , very and c a p a c i t a n c e , ^ P for imaginary lie te¥inkel range 0.167 The variable, curves that e e drift with o r i g i n and have obtained w i t h i n 1$ for ; the resistance b'e which the suggests a p p r o x i m a t i o n c a n be consist plane u p t o tt/to^, = 2 , semicircles real complex equivalent circuit. It has been shown t h a t g this change g e de- 32 creases slightly with increasing but 1 neglected. ybe Figure = 7. y i l e T he + y a'/g B a for y^, 'ee 12( equivalent small circuit >P/g ee is 42 The te¥inkel expression for y ~ v a N is related m = ! + 08ee j W 12e & ^ g i s 0 v e by n graphically ....(2-53) V to Vp i n t h e 0.333 for This y as y where = 21e m representation for is m a n d w i t h i n Vfo i n m a g n i t u d e w/fi> crude, but is The commonly u s e d T = 0.5. The used for ^0.87 0 ^V? ^ 9 . y 6% f o r range w i t h i n ifo i n p h a s e for a/tt^ 0.25, approximation y the sake of for w i t h an e r r o r % a g is n overall tt/coVp 0.5, of again only quite simplicity. lumped r e p r e s e n t a t i o n of the distributed 33 base resistance ment, to be practical been shown, a reasonable applications Because emitter has of the diffusion approximation; of the drift increase capacitance is a diffusion junction t r a n s i t i o n capacitance, the ter, is diffusion not conductance is for the even fusion capacitance is collector pacitance to drift transistor, the due at also high the which the drift that is for most larger The transistor for is the drift here the at emitter than the that emit- collector than for The the transistor the high doping frequencies. smaller measure- frequency, drift transistors. t r a n s i t i o n capacitance anyway. adequate cutoff T h i s means e for fusion for C^ , negligible smaller is of transistor. less transistor. transistor it methods in effective than for of by v a r i o u s the dif- collector dif- transistor, but dominating ca- 43 It is seen hybridan equivalent with a d d i t i o n of the f o r a/a^, < ^ 1 , then that circuit is valid C, , t h e ty e • for the the Johnson-Giacoletto drift transistor emitter—junction transition 32 34 ' capaci- tance. The accounted effect for of the collector lead—resistance, i n a manner g i v e n by G r i n i c h , but it r is '.may cc " be usually neglected. O t h e r more e l a b o r a t e e q u i v a l e n t c i r c u i t s h a v e b e e n p r o 35 posed, but they are u n n e c e s s a r i l y complex f o r our p u r p o s e s . 2.6 The M i l l e r Capacitance The m a i n e f f e c t analogous been the that of the 5 shown b y B r u u n . collector—base mately by to to of 1 Prom F i g u r e tion is it is = - ( y 21e effect reference base-emitter to 8, showing the seen " y that 12e O ee L g the s intrinsic C the ) R equivalent low-frequency , leads + L r has transistor, approxi- '^fjiller* & i bb + a ' / g ee v e n . . (2-54a) c i r c u i t of voltage as an ampli- amplifica- a V g ee F~ + ' r , \ ! + a ' / g bb ee R R i n a manner i n vacuum t u b e s , capacitance, 7 g ee l 36 for low-frequency base-collector voltage amplification + V, v~ accounted t r a n s i t i o n capacitance, Stiller stage, c a n be c Miller With an e q u i v a l e n t fier C ....(2-55a) \ 44 and f o r a'/g S 6 6 + r,^ this becomes 0 0 v ^ - " ( y 21e - y 12e L ) R " = a .(2-55b) O ee I/ g R (y i--V e be ) V 9 1 2 *L Figure 8. Single-stage The e f f e c t ternal base the voltage ty, C can therefore c and e m i t t e r C If of the M i l l e r Miller amplifier equivalent = C c ( a + capacitance e e ~ a ^L» parallel with the cuit a better this capacitance is g R in- the (2-54c) effect plus uni- by t h e n m o d i f i e d as current generator c a n be than C approximately equal approximation, but much g r e a t e r O ee L c* and t r a n s i t i o n c a p a c i t a n c e s , A capacitance between (2-54b) represented represents e represented g may b e circuit is ^ ff> circuit O eeV a The c a p a c i t a n c e , fusion l a m p l i f i c a t i o n , o& equivalent o by "Miller The be V of the to i n Figure the Miller C c t o make t h e 9. emitter dif- capacitance. s h o u l d be added equivalent i n a p p l i c a t i o n s where ciris low neglected. The m o d i f i e d J o h n s o n - G i a c o l e t t o h y b r i d - i t e q u i v a l e n t in cir- 45 cuit are fits well transistor described alloy-type drift transistors are transistors r - with plane-parallel i n one-dimensional well •u o types A x/ / well as by this represented bb A as V - form. [rile* y 12e equivalent ^ + 2.7 9. As was the is choice the of ( y cuit with Circuit for Feedback mentioned circuit transistor The t e C diffusion circuit. M ] } i n the Emitter earlier, to be the used. common-emitter feedback feedback, Z , g is b'e Resistance- of circuit configuration in ) V Lead method Th e yi2e circuit Parallel series simplified Johnson-Giacoletto emitter + 21e- S i m p l i f i e d hybrid-TC e q u i v a l e n t modified for CL,.,, Miller resistance-capacitance lead. C and B Modified Equivalent Capacitance that Surface-barrier alloy-junction be Figure junctions shown design to be with w i t h the depends used on here parallel common emitter hybrid-u equivalent cir- i n Figure cir- 10. This 5 cuit will be analyzed From F i g u r e 10 H using the it seen is method = Ve^lle of Bruun. that + y 12e + ^ C ± e ) ..-.(2-56a) 46 X so 2 = V e ^ l e that V, , b'g = V, , b'e = e^lle ( = V e t and I = 1 1 bb + , b + ( y e + 2 y 1 y2ie Z e ( -ll y + e Z e ( 1 l l e + Z (y = V 2 y lle ( y I, i i j z 2' i q I 1 or i (I + •1 + ( l -+ y e - e y - y i l l e + + ^ + 1 2 2 e 2 1 e ) ) v t e C } + e b ' + } > C te ] V (2-58a) j«C .J te + . (2-58b) g J" te>'' + C (yno+ y i c -o 2 e Z l_l Figure T h e n we can 10. ••••(2-57) } ft b + + a C 21e t e C J te' + ^ y 2 1 e y 21e + lle 12e l J 12e y y .(2-56b) ^12^ " 2=<y2ier - a y 12e>Ve O ee be g V S i m p l i f i e d Johnson-Giacoletto hybrid-Tt equivalent c i r c u i t with emitter feedback define i l T b'g ( 1 + y l l e + y 12e V^lle + + y J' 21e a C + te ) ^ t e * . . . . (2-59a) 47 and The y 2 1 V g ' - ^21e1 + circuit Z e ( l l e y c a n be y + y 12e ) 21e ...(2-59b) ^ t e + 5 redrawn i n terms of the parameters i l l e a n d y 21e It back the _ equivalent i y 2 1 = e is a s s seen impedance, transistor 21e b°' i w n that Z , g Figure n the is to 11. effect modify equivalent of the the c i r c u i t by external emitter feed- admittance parameters of the | l + Z (y-^ e factor e + + ^ te>]' C L bb o-wv + 21e bg bg Figure 11. E q u i v a l e n t c i r c u i t i n terms y Further Miller-effect Equation v lie a n d y 2 ie s i m p l i f i c a t i o n , c a n be admittance (2-54a), term, w i t h the of achieved g i v e n by by lumping the a relation similar modified emitter d i f f u s i o n and to tran- i sition admittance The stage . p -•y le"L 2 which replaces term, V voltage + Z Equation e amplification is ( Y 2o1l eo ~ = i -Q « e ( y l l e + 1 2y^oJ e " L^ y now (for coR^C<<C[l) c R J / X 2 1 e + (2-60) jrt^) (2-55b). The M i l l e r - e f f e c t a d m i t t a n c e may t h e n b e written as 48 lie y = ^ C ( y 1 + c 1 w h i c h may be s i m p l i f i e d , to " y 12e + Z (y, e lle -i J + ) R L ..(2-61a) 21e y ^°-te\ + u s i n g t h e same argument as t h a t this case plification, lle ^ - ! J^(y le z (y - 2 + e l l y e + 12e y 2 1 c L * J-C ) C R e t o (2-61b) ) the approximation i s rather crude but i s used simplicity. f o r the sake of f o r l o w s t a g e am- C o m b i n i n g t h e m o d i f i e d sum o f t h e e m i t t e r transition admittances y y l l e . + In y lle w i t h the M i l l e r - e f f e c t + lle 12e + + Z ^ + e ( y te t o C ile (y-Q e + y + y with 0 21e ^ + (2-62a) * n ^ C d i f f u s i o n and admittance ' t e y 12e e s a L c C ) ....(2-62a) we m u s t n ) R gives m e o b t a i n an a p - manner as used (2-37), y 21e t e r m 0 coth0 terms t t ( y 21e 21e^ = y l l + y 12 = S g o = P The J + to expand E q u a t i o n to the term Equations lie y 1 order proximation for leading Equation (2-54c), to y In 21e is e e g o 0 ' ( c o t h 0 ' - |csch0') ee 0 whe r e K~ <3C[ 1. expanded i n a power of degree greater c o t h .(2-37e) 0 series, t h a n t w o , we have and o m i t t i n g 49 •rile + y 21e g - - where use is made of e + J O . S W ^ ) d e g (l 'ee Q 0Q <^0- a n + ;j0.667to/to ) O a a (2-50e) rp o ~ Q 8 ~ ¥ e may now e x p a n d E q u a t i o n ( 2 ^ 6 2 a ) , using Equations (2-50), as n y ln i e* +^ l y 1 j i a ' [l •+ < A ( C / g + T T le ^'/See^ 1 + Z 1 (a'/g ee )[l L e ( t e l l e y W c + e e + y 21e ! 1 J^te*] + + . jft/ttj, + . Z (y e lie + y + jtoC 21e )1 te J (2-62b) i where l/« = ^ [ l r and Here, the frequency c a n be T 1 A frequency of seen effective H + <> (C the by eff T t e + a e e /g e e R C )] L - G a'HA> ....(2-63) T + oc R C ). L 0 p a r a m e t e r to^ i s transistor ( ) the .,..(2-64) c effective half-power internal-base-emitter (2-52) and circuit. (2-54c) to This give capacitance = = shown i n F i g u r e + ^ (C /g combining Equations input C t e b'e C + C te + C M = g ee / t t T + C te + a 0 ee L c g R C *ee /*T H 9. Combining t h i s to r = g /a'c ee eff b w i t h E q u a t i o n (2-63) = l / r , , C „„. b'e eff gives an 50 If Z i s defined g as the p a r a l l e l combination of R and C , g e then R R 1 + jfi>R C e e where <o, 1 The d e n o m i n a t o r 1 + Z (y e + y n e l/RC . e e A (2-66) of Equation (2-62) + 3«C ) = 1 + Z [ g 2 1 e e t e 1 (1 i + g R ) ee e + jw K g See^ + U 1 e 1 (1 + g + jft)/a and M 0.667 A Finally, + « T Equation lle Thus, equivalent ure 12. + (l + J0.667*-) R (0.667 e V 1 1 + + y l l e the f i n a l * C T .«ee i B t e jacj + /g e e ) 1 J ) +j«/« (2-67) R M/cc j/(l e e c e t e ( l + T /g e e (2-62a) g y e e 9 = [ l / ^ + g 2 e e may t h e n b e w r i t t e n —r-^ R ) w h e r e l /« (2-65) 1 + jtt/aj e + e e g e e (2-68) e (2-69) •• « • - takes the form W<* )(l + r a ' ( l + g R ) e e R )(l e + W^) j«A> )2 form of the common-emitter c i r c u i t with emitter feedback i s that ....(2-62c) transistor shown i n F i g - 51 b b b h + lie 2 J bg bg = y ie bg V 2 g Figure 2.8 12. F i n a l form of the common-emitter c i r c u i t with emitter feedback High-Level The jection quency Injection preceding theory. for Equation For small (2-28) development has a diffusion transistor, emitter i n the w By extending emitter almost the currents = 2.43D a should a which for is the actual increases with high-frequency an advantage Such is (o a a-cutoff obtained by in-* fre- developing P is (2-70) high-level shown t h a t I ) E less this (large frequency = 4 . 8 6 D /V . than t h i s emitter by J is for the (2-71) a correction current. operation with diffusion case injection give increasing the the on l o w - l e v e l /W . i n using high-level not based 2 has <o (high However, ' c a n be to include 38 Rittner which been form theory currents), doubled, equivalent factor Nevertheless, transistors, there injection. drift transistor. It has 52 been pointed drift out by transistor Kroemer tends to that at operate high as levels a diffusion of injection, the transistor. The 32 minority-carrier to increase level, rocal transit quite rapidly and t h e r e f o r e relation higher to current creasing ed f r o m the the at i n the base emitter a-cutoff transit levels. emitter time currents frequency, time, increase is much more has been above a quite in transit shown certain which bears decreases This current region a recip- rapidly time with r a p i d t h a n w o u l d be at in- expect- theory. 39 It a ^ might increases creasing be to here that a maximum a n d t h e n emitter and d r i f t mentioned current. This Webster decreases effect is has shown steadily noted with i n both that in- diffusion transistors. The low-frequency emitter-base conductance, g e e > has been 32 shown to creasing rents. vary to The capacitance For a significant increasing above effects to quite markedly effects approximately The with a minimum and t h e n high-level non-linear amount the emitter with cause simple vary the increasing operation, which like tend there the injection for large level, emitter.cur- emitter-base emitter diffusion current. appear to be transistor to behave theory de- a variety not of even predicts. t r a n s i t i o n capacitance is quite independent 33 of emitter sistance, tion r^^, level, It the current, is but is and Das very tends obvious nearly to shown t h a t constant, decrease then hybrid-TC e q u i v a l e n t has that circuit very some are of not the base-lead independent slightly the at circuit correct for of re- the high injec- levels. elements high of injec- 53 tion levels. equivalent design ter Until circuit procedure currents currents is an a n a l y t i c a l for based not which are equivalent circuit transistor and i s high or injection levels on t h e equivalent considered well Figure suited 12 i s for of is circuit worthwhile. w i t h i n the" r a n g e of e m p i r i c a l r e l a t i o n to established, for However, low-level large for a emit- emitter injection, a valid representation use the i n c i r c u i t design of the the problems. 54 3. 3.1 A M P L I F I E R RESPONSE FUNCTIONS Single-Stage The equivalent now e n a b l e functions for us to for cascades circuit Current- for and V o l t a g e - A m p l i f i c a t i o n circuits calculate derived current- a common-emitter of a such single s ^> and stage previous with emitter The N o r t o n f o r m o f stage shown i n F i g u r e is chapter voltage-amplification stages. r , i n the Functions feedback the and equivalent 13. ' bb i bg v ' V ?' 2 1 e b g 1 v o g Figure It the = - I Equivalent circuit stage a m p l i f i e r useful single-stage cation G. i is 13. to define amplifier. function two The - [1+ the single- amplification functions short-circuit current-amplifi- Z e ( y n e + y 2 1 e ( y + 21e " yi2e J«P. )][l+(Z t e ) Z S .+ r a b b ) ( y | i e + .... with for is " s for a low-frequency y ^ ) ] (3-la) value -oc^a'R G .(0) 1 R^ + r A voltage-amplification 1 s 2 s = b b + a ' / g' e_e function, + a*R i n terms . (3-lb) Q of measured voltages, 55 V G = V m with = - = i V t 1 = M + l l e y a low-frequency + y le In vm amplification system. the It overall individual 3.2 is R Ig, R all are , + a /g ee b bk a single-stage meet the stage to Functions for + a R + y lie)] (3-2b) Q a m p l i f i e r has of insufficient a video cascade (broadband) amplifier just interstage a Stage a cascaded resistances, the stages product of so that the in a Cascade emitter-feedback Rj, and a l l amplifier, emitter currents, identical. i r-AAH +E -in(k-l) 1 "Rn Je el Figure The the y amplification functions. 14 s h o w s assumed ob( ne r L requirements then necessary Amplification where = amplification function is Figure V to + • o••(3~•2a) b general, 1 C value Q (0) ^ te)] I + 2 -a a G ( y21e R (k-l) 1 14. C a s c a d e d l o a d impedance interstage resistance, T 'R-, _lc e ( ink >1)B T E 1 J c ek emitter-feedback of a stage R , T inn Rn R ek en 1 en amplifier i n a cascade i n p a r a l l e l with consists the of i n p u t imped- ance of the f o l l o w i n g The script input stage, impedance "k", is Z^^.^)* of a t y p i c a l seen from F i g u r e f o r low frequencies, impedance Lk = I B Z in(k+1) (2-26c), of a t y p i c a l 1 Z = B I 1 sub- + + . . . . (3-3a) this becomes (3-3b) + a'R , . ek b load by the + y, ' ' ) ^lle/k from E q u a t i o n R- i = r ' + a ' / g ink bb ee The denoted 13 t o b e Z- , = r , ' + 1/(y-, ' ink bb lie and stage, r stage bb yij ( (Rj r + b b is yii^k-n + e ) ( y therefore i { e + y i ; i ) e k + 1 ....(3-4a) which reduces R The stage at low frequencies T 1 Lk = 'R The stage I R I equivalent i n a cascaded ' bb + + a'/g„„ + a R ^ { > ' + a'/g + a'R bb ee e (k+1) ! e r circuit amplifier, I 1 + Z e yile ( + noting 13 a p p l i e s that Z g to a single = R j a n d Z-^ = Z ^ . function for a is ~ k of Figure current-amplification G l (3-4b) k + 1 e short-circuit i n a cascade to ^ l e + ( y 21e " ^ t e f l 1 yi2e + < I R ) R + I ' b ^ l i e + ^li^k] ....(3-5a) The symbol " " signifies " i n parallel with" 57 with a low-frequency value -a a'R , / n G (0) l = , • k I R The m e a s u r a b l e in a cascade + r bb 1 /See a + a R • ....(3-5b) ek a stage is " L ; voltage-amplification function for Q vmk + T + Z e ( l l e y + y ( y 21e 21e " yi2e ^ t e ^ + ) Z 1 Lk + r bb ( lie y + y lie>k] ....(3-6a) reducing at low frequencies to -a a'R , , ,> ^ . r bb + a ' / g ee + a ' R e k ' 0 G It is function is function by v m k seen (0) = then that related to the the L k measurable .... (3-6b) voltage-amplification short-circuit current-amplification Lk i k 7 ~ — ^L(k-l) Z G The optimum i n t e r s t a g e low that we may n e g l e c t put impedance The resistance vmk of the the resistance following stage, a n d we may G (see • ••* Section v a r i a t i o n with frequency correction factor ratio = G i.e., Z^ i n E q u a t i o n (3-7a) n is ( ~ 3 3.5) of 7 a ) is the in- R^ « n then a constant write vmk = G i k p ^ k i ' L(k-l) so ....(3-7b) 58 A similar analysis lent R , T of the current c a n b e made u s i n g source, and the i n t e r s t a g e 1^'» with which i t i s i n p a r a l l e l , voltage-amplification the Thevenin giving the f u n c t i o n f o r a stage equiva- resistance, open-circuit i n a cascade as (V ) Q vk _ ~ V Q P C s - I " 1 V^lle + + ^ l e ^21. - ^te'H + *12e I )R 1 * ( E I + » b T ) ( ' l i . + . • . • (3—8) This caded expression short-circuit is identical to the isolated-stage current-amplification function of cas- Equation (3-5a). The for overall a cascaded stage short-circuit amplifier functions, is just as mentioned G Likewise, the overall i current-amplification the product earlier, = TT measurable G i of the i n d i v i d u a l and i s given k function by ." ....(3-9) voltage-amplification function is n G and is related vm = TT G vmk t o G^ b y R G = G . -4 vm I + Z. , i S i . T vm It is obvious (3-10) that the overall ....(3-11) Z m l open-circuit voltage-amplification 59 function is identical fication f u n c t i o n by Because amplifier the examine 3.3 the the overall short-circuit comparing Equations overall depends amplification to on the functions (3-5a) and amplification function position of the of the poles for Current-Amplification Representation (3-8). of the cascaded and z e r o s individual stages, amplification expressions current-ampli- we m u s t a stage i n the of in a the now cascade. Complex-Frequency Plane To e x t e n d the complex-frequency The v a r i a b l e cy v a r i a b l e be be be (3-5a) i n the cascaded This (2-62c), expression and - (2-67), a a'u A R to the p = for general case shall replace a normalized of the jco b y p. complex-frequen- later. is the current-amplification function amplifier c a n be to more + jco, we reserved defined Equation used form. variable, s will to analysis design, expanded in its most to general using Equations (2-50d), give T (3-12) ( R l + r bb } p + .co. co. + co + 1 r <°2 ee g The subscript This p, "k" w i l l rational may b e w r i t t e n 1 r ( R I be + r bb } + a g dropped while function r 1 of the discussing (1 ee ( + R I !ee e) R + r a single complex-frequency bb } stage. variable, as N(p) G 1 ( P ) = K D ( P ) ' (3-13) 60 Here the the zero numerator of t r a n s m i s s i o n of the stage factor = p + <o N(p) which depends o n l y By proper at any p o i n t . , . .(3-14) 1 on t h e e x t e r n a l f e e d b a c k adjustment The i s d e f i n e d by of these on t h e n e g a t i v e denominator elements, R t w o e l e m e n t s we may p l a c e real and C „ g G the zero axis-. polynomial to-.to a ( l + g R ) 1 r e e e. to, + to + . ^ .2g „e„e( R I + r b b') 1 D(p) P A + 2 v 1 r b T + to,to 1 defines the poles e o o o( 3 - 1 5 ) 5 r 1 R ) a '(1 + g ee e g ( R + r, J ) ee I bb'. + 6 6 v T of t r a n s m i s s i o n , or p o i n t s of i n f i n i t e amplifi- cation The transistor operating ing ing are seen t o depend upon the some o f w h i c h only transistor parameters depend on t h e t r a n s i s t o r parameters, includ- and t o a l i m i t e d at a particular operating point, a r e to-^, to > to^, a n d R . to-^ a n d to d e - on t h e f e e d b a c k extent 2 elements, x R g on t h e v a l u e 2 a n d C , a n d to^ d e p e n d s o n G of R e used i n the follow- stage. Alternatively, are quadratic elements. a given important pend I parameters, the feedback the T of t h i s p o i n t , and upon t h e e x t e r n a l c i r c u i t For R zeros R , o C , R , q T f o r a given and I g (which transistor, determines g the four parameters ) . The i n t e r s t a g e ee • Q Q 61 resistance, R , is T chosen current-amplification. large as and C , maximize As w i l l be shown l a t e r , Thus noted poles and zeros are once The that the we may f i n d form of of a stagger-tuned Stagger-Tuned order to the as multiple the achieve That poles cascade, A stagger-tuned readily to thereby t h a n does Grinich has The pattern passband as more lo- (3-12) design. like amplifier, cancellation maximum a t t a i n a b l e the ammust amplifica- bandcentre than appearing case of a single lends i n the video amplifier about i n the response a better for of rather syn- amplifier itself functions a quite by the complex-frequency amplification-bandwidth cascade. a maximally-flat cascaded pole-zero l i m i t s the and z e r o s synchronously-tuned designed stagger-tuned g of zero amplifier cascaded amplifier prescribed generally the the and z e r o s which acts pole-zero giving poles i n the cascaded approximating its of function desired, (identical) of cascaded the Equation bandwidth necessary the distributed stage. adjustment the is, response chronously-tuned R Cascade i n d i v i d u a l stages are are positions the achieve which point of use as positions. An a m p l i f i c a t i o n f u n c t i o n the s h o u l d be parameters pole-pair. to lation. this Ig the function worth) zero low-frequency of stagger-tuned. product at and design interdependent; we k n o w t h e plification, plane, effective the location In tion the pole s h o u l d be suggests be to It cation 3.4 as c o n t r o l l i n g both g the practical. so all-pole using method (Butter- pole-zero imposes amplification. a cancel- restriction As an example, 62 typical three- and f o u r - s t a g e pole-zero patterns of the type 40 used by G r i n i c h are to obtain a Buttervorth shown i n F i g u r e yield is of type and erly of discussed no p o l e - z e r o this method of t r a n s m i s s i o n to all-pole step poles i n the cancellation. than that following chapter T h i s method should o b t a i n e d by the Grinich. Because poles be current amplification greater method of 15. A d e s i g n method w i l l i n which there distribution design, responses compare the as it design allows exist, is well two d e s i g n in contrast necessary as zeros the to to as w e l l as the B u t t e r w o r t h - investigate the a m p l i f i c a t i o n response phase to prop- methods. s-plane Figure 3.5 15. Maximization In T h r e e - and f o u r - s t a g e B u t t e r w o r t h - t y p e d i s t r i b u t i o n s of p o l e s and zeros f o r a m a x i m a l l y f l a t cascaded a m p l i f i e r of choice for of terstage DC C u r r e n t e x i s t i n g designs"''^ maximized by the the case of as dc current an optimum i n t e r s t a g e no e m i t t e r resistance the Amplification feedback. g i v e n by B r u u n , This amplification is resistance, optimum v a l u e but modified to Rj p-k» 0 of in- include 63 the effect of excess phase, is -1 R Iopt where R for I°°V a»/g e e r ee + ' / g ee bb ^>B + T R These expressions feedback are the of design, ing solution. is serves to find either tion. but iterative R and C g It a good Rj p-j.» 0 side + a ' / g ee ....(3-16b) ao s h o u l d be is not v a l i d as bb bb interstage the Rlopt T r m o d i f i e d when t h e effects of emitter included. Using mum v a l u e .(3-16a) a to method resistance g are evident when u s i n g starting not that the point. of network must be the value for chosen found u n t i l the above iterative method maximum dc is of method, (3-16), the before there A cut-and-try starting with Equations find synthesis, a starting converg- choosing although method is it used and d e v i a t i n g current opti- to amplifica- 64 .4... THE I T E R A T I V E - METHOD OF. NETWORK 4.1 The Synthesis Methods two problems The Problem of of approximation function,, called specified frequency the for the commonly called the number freedom For the of numerator just or single stage of four degrees are to available be due to the of more of finding to most are: methods by the the a suitable approximate a commonly u s e d ap- maximally-fHat am- delay, sum o f less From E q u a t i o n cascade number of on t h e number transfer number placed of more degrees the number should imposed by 3.3; the on the this it interdependence system. of of the imposed seen that a maximum However, may b e requirements less degrees is afford ra- of function the (3-12) a available available approximation. i n Section the is, i n the than the for explained i.e., that restrictions, amplifier a constraint on t h e polynomials, freedom amplification Formal solve a p p r o x i m a t i o n when u s i n g depends function, one the of as realizability, of or restrictions. a of coefficients and denominator conditions to and m a x i m a l l y - f l a t function, conditions, is three amplifier function amplification freedom that function, The accuracy i n the variable of attempt realization. is amplitude, Realization linear-phase. approximation independent problem low-pass, attainable degrees, of and response. equal-ripple tional synthesis approximation plitude, The A p p r o x i m a t i o n and modern network approximation proximations - SYNTHESIS only two considered for physical of the zeros and are not generally poles function. of network synthesis ap- 65 plicable to because of the synthesis restrictions acterization of lent composed circuit It cuit as is also external possible the to so obtained by This formal ence of of pole-zero dition) the under polynomial be of for ization, two specified the as by elements the useful char- transistor, by an equiva- matter, the cir- c i r c u i t be as is adjusted easily networks simple w h i c h may has the been to be active net- i n the pres41,42 described work is previously. that the upon the numer- denominator function. method involves determining amplification function function poles response directly design that (the i n designing prescribed the of transistor difficult method solution. of the simultaneous the excludes transfer the to a practical method response to is due amplifier depend restriction related w o u l d be iterative must configuration circuit The the often case, the This methods. this the present a way p r e s c r i b e d external at (zeros) (poles) the proximate the definitely method amplifier equivalent finished condition for polynomial In in that, synthesis circuits. elements. realizability restrictions polynomial the lumped known c o n f i g u r a t i o n A necessary ator on t h e transistor the An i t e r a t i v e works of amplifier element, important that linear placed active the and e c o n o m i c a l . of (the zeros the realizability ap- approximation of the con- numerator amplification circuit to parameters function and the condition). requirements, a p p r o x i m a t i o n and real- to analytical but provides satisfy by a numerical procedure means, for arriving 66 4.2 Approximation The mise quency in range of percent. to It plifier is of almost the the is also the The finity, number i.e., at familiar function is i.e., one N(p) input is is a compro- over variety), usually and less for the relatively approximation to amplitude of the origin for fre- linear overshoot than ten handle all pole-zero starting a useful in am- i n which the for flat all-pole not necessarily maximally-flat of equal G(p) to trans- are unity. of its at roots poles function is function, to r the 3 but amplifier it amplifier is designs. mathematically the efficient with finite in- It is unit half- of stages important although functions at ....(4-1) in certain most plane = -1. usedf '^ our left-half at amplifier. maximally-flat zeros is zero Butterworth^ function many o f lead the (3-13) become r^ -order cancellation point of one low-pass i n which 2 not the is G(j<c) (Butterworth) (-s ) is of all-pole b b a n d w i d t h has function derivatives i n Equation known that, the This response is requirements amplitude minimum-phase simplest function response constant phase a step-function maximally-flat bandcentre, power has interest, maximum p o s s i b l e well and t r a n s i e n t Function design. The fer It function response amplitude-response steady-state amplifier. (when t h e The M a x i m a l l y - F l a t A m p l i t u d e maximally-flat between a video - as The a maximally- simpler, network; unless does i.e., zeros may p o s s i b l y zeros perturb have 44 higher tions figures of from those merit. given The finite by E q u a t i o n (4-1) by the an amount pole posi depending 67 on t h e p r o x i m i t y o f t h e z e r o s The g e n e r a l transfer to the poles. function of a multistage a m p l i f i e r may be w r i t t e n a s , a l+ , •. • • • + a , s + a + , s = K ^ i " „_ ± 0 s + b s + . . . . + b s + b^ r-1 1 0 s G(s) m m n m 1 r where m <^r. i.e., N(s) i s given, Equation a) 1 n a l l finite we w o u l d l i k e zeros to find G(0) The amplifier cutoff of G ( s ) are known, a G(s) i n the form of number o f p o l e s , be m a x i m a l l y - f l a t a t z e r o b) normalization, r with a fixed G(s) w i l l ....(4-2) v n Assuming that (4-2), - r, such that frequency, s = 0, G(;jl) so t h a t frequency, « u , i s used the normalized frequency for frequency variables are defined by s It i s convenient p/« = £ + j f t . A t o work w i t h the f u n c t i o n G(s)G(-s) On t h e r e a l - f r e q u e n c y the equal even powers to zero The be axis, above restated as of s thereby at the = K this amplification function, only (4-3) u 2 N(s)N(-s) is just G(jft) having ....(4-4) D(s)D(-s) the squared magnitude This function a l l odd-order contains derivatives origin. requirements o n t h e a p p r o x i m a t i o n f u n c t i o n may follows: a) G(s)G(-s) must be m a x i m a l l y - f l a t a t s = 0 , a n d b) 2 G(jl) = G (0). 2 2 of 68 Prom E q u a t i o n ( 4 - 4 ) , written as G(s)G(-s) a Taylor = K (c 2 series + c s Q 2 the about + 2 expression the + c + c where c To make setting equal the to cessive of these of the that zero number as c^, etc., 2 set are of to it s ( 2 r ( r " l ) + l ) + c * + 2 s r 2 at of zero ••"( - ) o ) 4 possible successive used 5 of means G(s)G(-s) the It the specify be of 2 r - l , but of suc- can derivatives function, to of zero. s = 0 is an even are frequency derivatives s h o u l d be at r ....(4-6) through choice is freedom l ) 2 be only r-1 coefficients and therefore maximal-flatness frequency. In order to satisfy and denominator of conditions G(s) Z It available s h o u l d be i n G(s) noted since i n Equation (4-2). is f i x e d by is used the dc in setting that N(s) is These (a) must be / \ / \ / 2\r D(s)D(-s) = ( - s ) pear + s ) many as zero zero f u n c t i o n , because degrees l can as 2 i.e., c , c a n be 2 ( r - 2 maximum number o f derivatives r-1 merator the r maximally-flat s = 0, coefficients G(s)G(-s) at at ( origin G(s)G(-s) = G (0)/K . Q maximum p o s s i b l e zero shown t h a t only 2 G(s) 2 for + r there (b) related are r+1 half-power by 4 4 ' 4 2 the K, r+1 b ^ , b-^, ••• a n d one frequency. nu- ' ^ 4 . . (4-7) degrees known, because are: above, N(s)N.(-s) . N(jl)N(-jl) amplification level, the and of freedom unknowns b r _2 • degree of ap- Here K freedom The r e m a i n i n g r-1 69 degrees of freedom are available the amplification function, 4.3 Realization The function - r e a l i z a b i l i t y requirement upon u s i n g the given positions, transfer itance amplification (3-15), the It resulting has been feedback, zeros are stage by a transfer zeros those with if, from of the the that, given for a resistance-capac- the zero i n the found from the pole positions. polynomial for may b e w r i t t e n a f t e r of upon poles compute p o s i t i o n of f u n c t i o n may b e denominator to zeros shown b y G r i n i c h ^ amplifier the fulfilled of dependence derivatives Equations is dependence common-emitter emitter The is prescribed function. transistor adjusting The N e t w o r k D e s i g n i n which there pole for a single stage, n o r m a l i z a t i o n i n the current- Equation simplified form D(s) The ure 16, zeros of = s Equation + 2 tfs + 2 (4-8) (4-8) 2 located, as shown i n Fig- at s k'*k = ^ where The pole are ^ , pole-pair positions y A radius, ~\Jf 2 - ^V? ± 3 ? - 2 - ft is the 2 tf' ....(4-9) \ geometric mean o f the ? and the average pole-pair v = s k 0 p o s i t i o n , ~Y» - X = ( s k -*- g i s v e n 0 o(4-10) by •(4-11) s )/2. + 0 k s-plane Figure If D(s), of Equation nomial of equations 16. we the A m p l i f i e r pole locations complex poles ( real), (YJ imaginary) equate to Equation the Equating 2 y = ^ and equating of the denominator current-amplification function (3-15)) for coefficients i n the s - p l a n e : (a) f o r and (b) f o r r e a l p o l e s the the corresponding (4-8), zero the we positions coefficients + fi r + constant from the of (corresponding coefficients can then f i n d the gives + r of the required pole-pair s polynomial, to poly- design positions. ....(4-12a) ftog_(R T coefficients b b ) gives + g R ) ee e I (R, + r ') ee I bb . l + Substituting tion (2-68) the expression 1 + n Solving R g ^ r Equations yields (4-13) B f o r te^ ( n o r m a l i z e d t o i " ^ ) ^; r+ 1 and x i n t o E q u a t i o n (4-12a) a^Q 71 a'(1 gives ^;^f , ( T g e ( e (4-12b) the design °^ E q u a - I R e M ) O O C O o (4-12b) + bb) r and (4-13) simultaneously for equations 1 l A! + e e ('^1: g + r )J b b ..(4-14a) a . (R_ + r M ee I bb J and «ee R I + r These expressions normalized parameter, ft ." 2 ....(4-15a) 0 may b e s i m p l i f i e d s o m e w h a t ELQ* "ft: a'H resulting f bb> g ee e a ( B such 1 define that a + *ee 1 i f we ( R I + r b b } a + g e e ( I R J ...(4-16) + r bb) in Q ayflj - M^ 2 - flgflp ....(4-14b) 72 and where R a = e g from Equation + ( R I bb r (2-64) T t e /g (2-69) T By e l i m i n a t i n g expressed R e (4-3), + r b b may b e m o r e conven- and R g ..(4-15c) )H- compensating using the capacitor, C , g defining Equations may (2-66) be and giving C Equations equations zeros ee as = (Bj from t e E q u a t i o n (4-15b) The h i g h - f r e q u e n c y found W e ) + e e M £ 0.667 + «> C /g iently o o o (o4 - 1 5 b ) } ee H = 1 +« (C and from E q u a t i o n + of (4-14b) which state the transfer the e and = l/tt.R . 1 e (4-15c) co ( 4 - 1 7 ) are then the two r e a l i z a b i l i t y requirement f u n c t i o n to the poles for the design relating the known c i r c u i t configuration. 4.4 The Iterative The to solve Method iterative a variety of method of synthesis network problems has p r e v i o u s l y been concerned w i t h used vacuum-tube 73 41 amplifiers, distributed vacuum-tube 44 networks, and interstage 4 6 47 stagger-tuned author's to multicavity klystron amplifiers, knowledge, networks this is the involving solid-state The m e t h o d a l t e r n a t e s and r e a l i z a t i o n , first the taking and f i n d i n g from t h e s e scribed configuration; to approximates from the known as network find the the a new desired corresponding the is pole of poles differ must be process, vergent. the from the found. If, The iterative In the of positions this, plane particular the are poles t h a n w o u l d be is a new some set lie closer of trans- in a pre- network an of satisfied set, approximation new s e t so are cycles the differs amount of poles because of the the new set of iterative process the is con- error of amount. in this paper, real axis." to real axis an a l l - p o l e a The a new on the the zeros, zeros. again prescribed tend to for by continued u n t i l to case of poles set decreases, constrained the applied Each pole application treated lie the along w i t h the Prom t h i s previous than been from t h i s previous no l o n g e r process of function. the approximation error To network which, on s u c c e e d i n g a p p r o x i m a t i o n becomes l e s s zero poles r e a l i z e d which gives is set obtained approximation error. again zeros of has requirements a realizable response approximation requirement set of it ' devices. two zeros set time an assumed mission then used first 48 of the Because the maximally-flat s- func- tion. The erties. lour iterative However, 45 may o c c u r , method g e n e r a l l y degenerative, a n d no w a y of shows good oscillatory, anticipating convergence or divergent such behaviour propbehavis known. 74 The iterative method may b e restated more specifically 42 for the design 1. in this Start of with G(s) plane paper as an i n i t i a l for roots n = number worth all-pole ) 2 s of amplifier finding the zeros is 2 r •= 2 n as the poles left-half- + 1 = 0 n i n the from the given ....(4-1) This maximally-flat the tion the response stages. Realize ^ of of where where 3. definition a maximally-flat (_ 2. follows: is just the Butter- d i s t r i b u t i o n of prescribed poles by E q u a t i o n using (4-10) poles. configuration, the and relation ^ by Equa- (4-11). Form the denominator isfy approximation the polynomial from the c o n d i t i o n as given zeros in to sat- Equation (4-7) N(s)N(-s) D(s)D(-s) = (-s ) 2 2 n + ....(4-7) D(s)D(-s) and f i n d its (-s ) " 2 The 2 left-half zeros + from • t o plane f c — roots > — 2 of = 0. Equation ....(4-18) (4-18) are the 75 new p o l e s w h i c h make t h e a m p l i f i c a t i o n function, G(s), maximally-flat. 4. Compare t h e new s e t o f p o l e s w i t h the p r e v i o u s s e t o f poles: a) I f t h e y a r e d i f f e r e n t , the s o l u t i o n has v e r g e d ; u s i n g the p o l e s f o u n d Step b) 2 and r e p e a t the i n Step not 3, con- r e t u r n to cycle. I f t h e y a r e t h e same ( w i t h i n t h e p r e s c r i b e d a p p r o x i mation error), the s o l u t i o n has then only necessary to f i n d elements R^ and converged, and the v a l u e s of the from E q u a t i o n s (4-15c) i t is circuit and (4-17). The iterative method i s b a s i c a l l y v e r y s i m p l e , b u t f a c t o r i z a t i o n of p o l y n o m i a l s i n Step 3 n e c e s s i t a t e s Use was the t h e use high-speed digital computer. made o f an Alwac electronic digital computer, a m e d i u m - s i z e machine w i t h an of a III-E 8,192- word m a g n e t i c - d r u m memory. A p r o g r a m has video amplifier S t e p s 1-4 above. been w r i t t e n f o r the d e s i g n of a f o r up able stages i n cascade, to a u n i t and phase-frequency Autograph programs were w r i t t e n u s i n g a 6-26 system w h i c h has digits i n the m a n t i s s a . response output curves s t e p i n the t i m e domain, i n a f o r m f o r r e c o r d i n g on t h e M o s e l e y through following Programs have a l s o b e e n w r i t t e n w h i c h the a m p l i t u d e - f r e q u e n c y the r e s p o n s e to e i g h t transistor 6 binary digits X-Y suit- Recorder. The floating-point-arithmetic i n t h e e x p o n e n t and A s u b r o u t i n e p r o g r a m made t h e Computing C e n t r e was and used 26 b i n a r y available f o r s o l v i n g the h i g h - order polynomials floating-point decimal fraction unit digits. using system which A second expansions step. Bairstow's was is method; equivalent subroutine used for it to used seven forming i n determining an 8-24 significant partial- response to a 77 5o N U M E R I C A L D E S I G N S The m e t h o d cancellation to amplification of design employed by G r i n i c h uses obtain a stagger-tuned function. To e x t e n d drift transistor clude the effects using the 2N384 g e r m a n i u m d r i f t signs are possible pole-zero that for tially his design equations of excess phase; if the cancellation. It all-pole maximally-flat analysis to must be several will be method a m p l i f i c a t i o n , at modified to a given will the in- be given More e f f e c t i v e is used shown f o r iterative include designs transistor. iterative a g i v e n bandwidth the greater the pole-zero rather a number method g i v e s transistor dethan of designs substan- operating point. 5.1 The R C A 2 N 3 8 4 G e r m a n i u m D r i f t As stated transistor tor previously, performance capacitance, low are: alpha-cutoff amplifier d e s i g n m u s t be requirements low b a s e - l e a d emitter effective Giacoletto the Transistor for high-frequency resistance, t r a n s i t i o n capacitance, frequency. well The transistor represented hybrid-n equivalent by the c i r c u i t besides low and collechigh chosen for the modified Johnson- f i t t i n g the above requirements. The RCA 2 N 3 8 4 a l l o y - t y p e P - N - P germanium d r i f t transistor 33 3 2 29 4 9 fits the above r e q u i r e m e n t s have s t u d i e d the parameters well. RCA 2 N 3 8 4 d r i f t and t y p i c a l operating A number transistor, of authors and the characteristics are ' ' '50' following taken from 51 their ratory findings as well measurements. as One from the of the manufacturer's objectives data in this and design labo- pro- 78 cedure was t o u s e t y p i c a l rameters to achieve a low value order of c o l l e c t o r a low interstage a converging, resistance, due to the effects begins to of the parameter designs: = 50-S2. common-base factor a^ common-emitter factor = emitter 7 'ee + 0.7 pf = 2 pf = 0.984 current= 60 t r a n s i t i o n capacitance = 35 p f = 5.5 low-frequency common—base conductance E = 1.3 current- base f i e l d parameter A l at an = 2 u ( l 0 0 Mc) oc^ = l o w - f r e q u e n c y amplification C, 'te deterioriate values, resistance = low-frequency amplification solution for injection. = collector capacitance plus glass header, metal case, and i n t e r lead capacitance e in as p o s s i b l e , b u t frequency a assures be shown l a t e r , o f 25° C , t o be u s e d i n t h e base—lead for physically-realizable of h i g h - l e v e l a> = a l p h a - c u t o f f C As w i l l performance The f o l l o w i n g i s a l i s t bb design. I j , must be as l a r g e I g ^>2 m a , h i g h - f r e q u e n c y temperature a general The c h o s e n v a l u e capacitance. for ambient of the t r a n s i s t o r p a - p o i n t f o r t h e t r a n s i s t o r was c h o s e n as and I j , = 2 ma. to achieve values as f a r as p o s s i b l e The d c o p e r a t i n g = -12 v o l t s , (average) emitter = I (ma)/26 = 0 . 0 7 7 xx (I = 2ma). E E The effective alpha-cutoff .= effective frequency frequency common-base i s , using Equation (2-49), alpha-cutoff = 2u(58.5 M c ) . 79 5.2 G r i n i c h Designs Using a Drift Transistor The d e s i g n m e t h o d u s e d b y G r i n i c h equivalent Bruun. c i r c u i t with emitter He u s e s a cascaded transfer function, pensated by a capacitor and a r e a l zero made pairs cle, feedback to coincide o f t h e above obtained. form, lost w h i c h c o u l d be u s e d , of:the real cascading response is cir- i n the Butterworth o f one s t a g e say, to further other (normalized) two d e g r e e s includes the effect to cancel of freedom increase of the emitter f r e q u e n c y , to^, r e l a t e d b'e From E q u a t i o n 0.09y^), i n the p a i r , pole-pair the the are amplifi- transition ca- by defining to the emitter a modified diffusion ca- by C drift pole G^g, f o r a d i f f u s i o n t r a n s i s t o r alpha-cutoff pacitance on the u n i t com- a single By stagger—tuned two-pole pair. Grinich pacitance, and the the zero. t o be m a x i m a l l y - f l a t By c o n s t r a i n i n g the s i n g l e stage conjugate plane, a resistor o n l y to produce By p l a c i n g a l l the poles of the other the resistor hybrid-TC to give feedback a complex an a l l - p o l e zero cation an e m i t t e r w i t h and cancel t h e f u n c t i o n i s made sense. of t r a n s i s t o r s t ° produce the i n the form given by i n the complex—frequency having an emitter pole feedback pair one u s i n g employs = > *eeK 1 215 (2-49), + = 1 a g ee / a T 21 the effects ....(5-la) of excess phase in i s r e p l a c e d b y to^ - to /(1.215 + « /l.215 and Equation (5-la) b»e t e = ' ^eeK' to include transistor, C C becomes + C te = g e e / a r ....(5-lb) , 8 0 Using the parameters given i n the preceding s e c t i o n f o r the 2N384 drift transistor, fied cutoff frequency at the s p e c i f i e d operating p o i n t , the modi- is to* ='2TC-(50.2 M C ) . The r e s u l t a n t modified expression 1 f o r the amplification- bandwidth product^'^ GB, f o r a stage i n a cascaded a m p l i f i e r without emitter feedback is <4/2 71 GB = 1 + (1 + r bb R-r + a a'Tg , / g v ee . . . . ( 5 - 2 ) ee By modifying the c u r r e n t - a m p l i f i c a t i o n expression used by G r i n i c h we o b t a i n (s + G . ( s ) = Ks 2 + [ f i d 0 +* B e \ & ) Q) ± + g R ) e e e' + 6 » o9 o(5 3) — where Q"-l . = a,/V 1' u = l• / u eC ( a B J 2TI(GB) 0 u « g R u ee I . . . . ( 5 - 4 ) T e and (6 = a m p l i f i e r c u t o f f u normalization. By equating the c o e f f i c i e n t s frequency used f o r of the denominator polynomial 81 of Equation (5-3) to the corresponding coefficients of the poly- nomial D(s) the in resulting design the manner = s equations + 2 2Ts + ^ Grinich's method are 2 for indicated i n Section 2 obtained 4.3 1 ? = - — ( s\ ^ 2 and R e For the single located the g case real ee of pole L l± h a stage of the having the choosing zero, the of A special • a n odd number e Equation case of of P B for R , an e m i t t e r resistor, is P e e B ), it g ....(5-7) e c a n be used to cancel i.e., " 1 )* (5-6b) g (5-6b) i n order e low-frequency + g = ^ - ^ 7 ^ ee Equation stages • ( l (5-5), • t The 0 proper value e 1 only at R of . ...(5-6a) current-amplification function s = - Q and by l ) . to is place i -i = Z—(rY~ ~ e e S^O l ) - used i n the a pole at design s = ....(5-6c) g current- and -1, voltage-amplification 82 expressions are the same as those i n S e c t i o n 3.2$ from Equation (3^5b) G. ( 0 ) R and from E q u a t i o n -ocQa'Rj , bb /See = — I + r + — a + j e a R (3-6b) i G v r ("0 ) r An upper h a l f - p o w e r all designs. stage F o r ease a m p l i f i e r was normalized Mc), Q j b e the poles given for able* the pears I gives curves the r e l a t i o n s , w i t h R^, These that (Equation relatively results the 6.5 Mc w a s specified For t h i s a Grinich design for three- case the is shown in t r a n s i s t o r , w i t h te^: = 2TXX optimum i n t e r s t a g e value (3-16)), I o 0 Iopt = 4 the plotted for Bj p^. meaningless 6 of a ' 17. a number o f designs resistance, i n Figure a stage without when e m i t t e r feedback configuration for as using the is a Grinich the vari- 17-.•from w h i c h i t computed from B r u u n ' s to is dc-amplification versus interstage are 0 4 Figure results applicable The p o l e - z e r o of resistance = 282x5. comparison w i t h the interstage-resistance above e 7.74. R Table •+ a ' R * 1 example. for R is of 2N384 d r i f t From E q u a t i o n ( 3 - 1 6 ) , which T e c a l c u l a t i o n and c o n s t r u c t i o n , a c h o s e n as U s i n g the = 0 b frequency d i s t r i b u t i o n of F i g u r e - . 1 5 (a) v r (6.5 of -oc„a R + a 7 g ap- expression feedback, is used. three-stage Rj (a) 220 240 270 300 330 390 470 560 680 820 1000 1200 1500 0.314 0.292 0.265 0.242 0.224 0.193 0.163 0.139 0.116 0.098 0.081 0.068 C.055 0.580 0.601 0.626 0.648 0.666 0.695 0.723 0.745 0.765 0.784 0.795 0.808 0.820 R el 11.0 13.8 17.7 21.8 25.8 33.8 44.8 56.6 72.6 91.5 115 142 182 R e2 28.4 31.4 36.0 40.6 45.1 54.3 66.5 80.5 98.6 120 148 179 224 B e3 58.3 61.0 65.2 69.7 74.3 83.8 97.0 157 189 224 276 G il 7.70 7.60 7.49 7.40 7.30 7.20 G i2 4.80 4.88 4.97 5.05 5.12 G i3 2.90 3.04 3.23 3.38 G (0) 107.2 113.0 120.0 G (0) 40.60 41.06 41.58 ± ± (db) 112 133 7.08 7.02 6.95 6.90 6.88 6.83 6.80 5.23 5.34 5.40 5.50 5.55 5.60 5.65 5.69 3.52 3.74 3.96 4.13 4.30 4.45 4.55 4.66 4.75 126.2 132.0 141.0 150.0 157.0 164.5 170.5 175.5 180.0 184.0 42.02 42.41 42.9c* 43.52 43.92 44.32 44.63 44.87 45.11 45.30 i 00 Table I Grinich designs with R T variable 51 •• 50 I t e r a t i v e Method Designs - 49 t 48 47 4 6 •• G (0) ± \ 45 " : ( d b )I 4 4 •• Grinich 43 Three-Stage 4 2 " f u Designs Amplifier 2N384: = 6 . 5 Mc 2 ma 41 te= P <o = 2TT(58O5 C 4 0 •- 3 5 f T /) MC) =5.5, 3 9 •• 200 Figure 17. 300 400 Low-frequency 500 600 700 amplification, iterative 800 900 and G r i n i c h 1000 methods, 1100 1200 Rj variable 85 amplifier is figuration ative shown i n F i g u r e of the method. a value stage equivalent In both The amplitude and phase shown i n F i g u r e s shows its response cutoff that at 6.5 frequency the with time the above domain, to The the the for responses the iter- of 300Si., frequency-dependent input. response phase cutoff is response frequency overshoot is product a bandwidth of for the design and 20 r e s p e c t i v e l y . a unit-step a risetime-bandwidth nanoseconds using resistance appreciable 19(a) amplitude Mc. designed conr- used. are seen comparison w i t h the amplifier avoids 18(a) is for cases, an i n t e r s t a g e which d e f i n i t e l y l o a d i n g $ was 18(a) 6.5 is flat 19(a) with relatively seen i n Figure about 8.1$ for 0.370 Mc. The or 21 it a 3 db linear as of Figure Figure From F i g u r e indeed of to 20. In a unit-step a risetime 50$ time of delay a input, 57 is 53 nanoseconds. s—plane Figure 18. Three-stage (a) G r i n i c h method p o l e - z e r o c o n f i g u r a t i o n s f o r R-j- = 3 0 0 - n . : d e s i g n , and (b) d e s i g n by t h e iterative 0 86 Grinich Design ( G . ( 0 ) = 4 2 . 0 2 db) -3 rl o - Design by the Iterative Method( G ( 0 ) = 49.61. db) -6-- •H -P o i •H <HH •H - 9 " PH Ci) -12 a> OS (a) 1.5 4- 2.5 3 f -+- 4 Iterative Grinich (b) Figure 1.5 19. 2.5 3 6.5 8 10 6.5 8 10 (Mc) Design Design A m p l i t u d e response c u r v e s by the G r i n i c h and i t e r a t i v e methods f o r Rj = 300XL : (a) o v e r a l l a m p l i f i e r response, and (b) i n d i v i d u a l s t a g e r e s p o n s e s 240 T D e s i g n by the I t e r a t i v e Method 200 + Grinich Design 150 + 8 6, .7 10 11 12 13 14 (Mc) 2 0 . Phase r e s p o n s e c u r v e s f o r R = 300.rx: (a) G r i n i c h d e s i g n , and (b) d e s i g n by the: i t e r a t i v e method 5 Figure 1.1 f T r 6 7 (sec. R e s p o n s e t o a u n i t - s t e p f o r R-j- =^300jn_: ( a ) G r i n i c h d e s i g n , and (b) d e s i g n b y t h e : . i t e r a t i v e : method L Figure 21. 15 88 5.3 Designs U s i n g the A number o f using the outlined Iterative three-stage computer programs i n Section Method a m p l i f i e r designs written for (4-16), depends stages. This is does not restrict In the This fier the where noise because stage. have of or first the following product somewhat, pedance of greater stages, but effect, the This gives = R j r the stage first most increase been order to i d e n t i c a l values of the the the noise stages least ampli- amplifier figure a r b i t r a r i l y arranged of so for convenience by r e a r r a n g i n g the tuning the loading started bb + a '/gee effect of assuming ^ for 1 + of the identical i o r the QQ^ V te/gee C as to in amplification-bandwidth input g a i n e d w o u l d p r o b a b l y be by a pattern current-amplification function is advantage A design purely the i d e n t i c a l values H of has the stage following whose n < ii idual v stages + from E q u a t i o n Wc* (4-16) load ima small re- stages. from Equation (2-64) and method, a high-gain low-level increase since on the or feedback, to on t h e placement for to possible, a stage made a typical by G r i n i c h , contributes have The d e s i g n may b e sistances, the tends stages may b e second-order stage feedback Suceeding It neglected specify for a small extent advantageous progressively design. to apparently is iterative given QQJ^? following designs, feedback. been 4.4. The n o r m a l i z e d p a r a m e t e r , by E q u a t i o n the have 89 The iterative convergence method i s applied for several of the poles, and a p p r o x i m a t e values s k' k' s of R g a n d z e r o s > cycles (until ^ i k ' ''" are then found using k s a PP r a o a c n rough ed) , Equation (4-15c) n + ? 2 0 R where ek^ ( I R from Equations * Q + (2-69), (4-10), M ^ and As an a l t e r n a t i v e made for values of 2 based of R the load resistance g ^ The v a l u e s the of Q g k iterations (4-15c) iterative plotted 1 a r e r B I method, i n Figure T + k M <> 2 t e /g 'ee t s )/2. k + r stage + | bb ' a + / g initial e to give guess e + a of R j . improved estimates (3-4b) R + ' e(k+l) " a E (usually the c i r c u i t be ' e(k+l) to a converging the r e s u l t s can often using Equation aVgee ^^en m o d i f i e d then give I I gives T upon t h e known v a l u e bb are continued and (4-17) Table the k + « C a good f o r each = R 0 and (4-11), are then used k - ft Q 0 = s,_*s w to the above, e The v a l u e s 0.667 A - ft = ( s o f & ^f _ T - 2 ^ Q 2 only solution. element o f a number w i t h R j as t h e v a r i a b l e . 17 a l o n g w i t h t h e r e s u l t s s l i g h t l y ) , and Equations values. of designs using The r e s u l t s from the Grinich are _ A>i _ ^-02 _^03 _n _ii 12 1 3 i s _ s 2' 2 s _ " R el R e2 R e3 G i l G i2 G i3 " G (0) ± " G.(0) ' * (db) 300 330 390 470 560 680 820 1000 1200 0.358 0.334 0.296 0.258 0.226 0.196 0.169 0.146 0.127 0.352 0.328 0.288 0.251 0.220 0.189 0.163 0.140 0.122 0.349 0.325 0.286 0.249 0.217 0.187 0.161 0.138 0.120 0.443 0.626 0.751 0.840 0.909 0.970 1.019 1.063 1.096 1.174 1.129 1.145 1.173 1.202 1.228 1.250 1.271 1.286 0.360 0.364 0.385 0.406 0.427 0.449 0.466 0.483 0.497 0.360 0.364 0.385 0.407 0.428 0.449 0.467 0.484 0.498 0.441 0.598 0.665 0.697 0.716 0.729 0.737 0.743 0.747 0.769 0.735 0.726 0.724 0.724 0.724 0.724 0.724 0.724 +J0.308 +J0.336 +J0.369 +J0.392 +J0.409 +j 0 . 4 2 3 +J0.433 ±3 0 . 4 4 1 +j 0 . 4 4 8 0.387 0.377 0.368 0.362 0.356 0.352 0.349 0.346 0.344 +j 0 . 9 0 0 +J0.902 +J0.906 +j0.910 +J0.912 ±j0.915 ±j0.916 +J0.918 +J0.919 0.05 0.70 3.11 6.81 11.30 18.30 27.20 40.50 56.70 12.78 15.23 20.92 28.80 38.00 51.46 69.00 93.30 125.0 130.4 142.4 162.3 189.0 222.0 272.0 333.0 420.0 527.0 15.88 16.48 16.65 16.50 16.23 15.62 15.00 14.10 13.25 9.50 9.55 9.46 9.31 9.15 8.90 8.50 8.07 7.55 2.01 2.04 2.14 2.23 2.28- 2.29 2.27 2.22 2.14 302.5 321.0 336.5 343.0 339.0 318.0 290.0 252.0 214.0 49.61 50.13 50.50 50.69 50.60 50.05 49.25 48.03 46.60 Table II. Designs using the iterative method w i t h R T variable 1 91 designs ative of Table I. method becomes levels, which y i e l d Grinich there is The method ratio levels, levels of though is Figure the of The get be iterations, solve four the It to response the less at iter- impedance negligible chosen, fre- designs the R-j- = 3 0 0 X 1 . , amplification using corresponds to a voltage gain ratio higher significant; at of interstage very high or 6.2:1. imped- ~ impedance l o a d i n g p r o b l e m , where neither to be about next shown, close fifteen More on t h e section. w i t h the major successive to that zeros the the closest The w i t h the convergence iterations matter p o r t i o n of to real the i n d i v i d u a l stages in final dotted lines of after were that needed to origin. will approxi- time Used i n each poles are only convergence Each i t e r a t i o n took two steps pole-pair. polynomial ^hich arises noted two for are d i s t r i b u t i o n of R^ = 3 0 0 x i . . w h i c h goes w i t h each sixth-degree the and the problem for accuracy. s h o u l d be (Butterworth) plane and z e r o s minutes, curves of here a power initial design though i n the cancelling level This capacitive s o l u t i o n seems discussed mately the zero three-place interstage a m p l i f i c a t i o n t h a n do or complex-frequency the the applicable. both poles indicating three the 22 s h o w s s o l u t i o n of values 2.5:1, of method produces db i n c u r r e n t design. quite lower iterative somewhat still we r u n i n t o i n the of advantage requirement greater 7.6 the the impedance of almost d e s i g n method i s poles the an advantage advantage, ance At At the the substantially iterative current satisfy loading, designs. figure, apparent* which e a s i l y quency-dependent the Prom t h i s cycle. come v e r y The to close amplitude- shown i n F i g u r e 19(b) s-plane * 0 -1.532 x =. p o l e position 0 = zero position = p o l e and zero paths to convergence •= f i n a l p o l e - p a i r a n d associated zero Figure 22. Successive cycles i n the i t e r a t i v e a n a m p l i f i e r w i t h R-j- = 300-CL. -1.0 design of 93 for comparison w i t h the 19(a), for the The be first discussed have for same and e from the has next essentially section. and C R - = 130.4A, C low-frequency voltage =--15.88 G. (0) = -9.50 G = -2.01 i 3 retical seen 19(b) design. At initially Grinich time which the at is of frequencies a rate the somewhat The -302.5 ~ the is pf. which i s phase overshoot higher the stages are Figure cutoff^ the the than that is is 9.9% f o r than the 21 shows the 19(a) comparable for relatively figure and it of the 8.1% for the is off comparable linear. a unit-step theo- Grinich amplification falls response about amplitude- From F i g u r e than for greater db. theoretical input. flatter above 49.61 amplifier. a unit-step amplitude design. domain, to stages is a n d 20 show t h e curves response that (0) amplification i phase-response to pf, = 579 G (0) G (0).= Figures and t h i r d = 1811 2 amplification for 2 overall second a result e3 ±1 and the Figure values ei The no f e e d b a c k , The = 12.78.n-, e 2 design, I^. feedback-element R Grinich a stage i n the their R curves In the input, Grinich 94 design. to The risetime-bandwidth a risetime essentially delay 5.4 is of the 58 58 n a n o s e c o n d s same Although tion are may b e for two ling. of the properties, haviour for the the as mentioned 0.378, corresponding Mc b a n d w i d t h . design. The This is 50% t i m e encountered. Figure designed real pole-zero pairs a result, the infinite. is 4.4, 18(b) which are shows some shows the of the compensating an example of the good conver- abnormal final Here, essentially resistor and i t s This generally w i t h R^ = 300-fl.. feedback zero, Method in Section amplifier become Grinich method the As a 6.5 Iterative iterative comes a p p r o x i m a t e l y to as for is nanoseconds. Characteristics gence product be- soluthere self-cancel- first stage capacitor be- tends degenerative ef- 44 feet mentioned by Another Chang. characteristic tremely rapid for in five or six iterations. closest to the o r i g i n was zero this of and the pair large cancelling pole was made was the tendency come first stage to for as the to to of of case last first a second zero the stage stage. came real cancelling pole. The R . T arrived critical exat pole-zero pair The of the amplifier, As the interstage more slowly. pole-zero pair most real was self-cancelling. this the of convergence solution being convergence o r i g i n was low values the the The d i d the that approximately lower, self-cancelling. closest verge to w i t h the In this belonged resistance due R^, n o t e d was pair belonged This to to be- the pole-zero pair and s l o w e s t to con- 95 A s R j was first stage made became and e v e n t u a l l y even smaller, closest crossing led to oscillatory was o b t a i n e d by u s i n g to over the the pair approaching right network this of the the slowly half-plane, process, because of it Although a converging an a v e r a g i n g a physically-realizable pole-zero origin into behaviour. the which solution d i d not yield right-half-plane zero. The in the critical design is parameter QQ» Q U This the is given Q [l T L critical pole designs converge faster fixed zeros transistor externally to parameters C , be small to make small, in the requirements a given c g e but crease i n interstage resistance values of and f o r tions of current large negligible = 0. is (lj;) less a n < these C , and C ^ , i • The right- by the the transistor large, and tt^ requirements are disregarded they i n emitter are we should in conflict with performance. current make Q Q resistance frequency-dependent for and by e and/or smaller. we r u n i n t o h i g h - l e v e l interstage small, determined transistor will For tendency is s h o u l d be high-frequency an i n c r e a s e lems, e e )] 0 L c J c because transistor, emitter b b + a R C )] * r ^ , and C^. , a transistor for ee r parameter a', parameters a', the + and t h e r e This parameters, of te realizability (4-16) position for occur. variable choice by E q u a t i o n a ' f l + <*JC / g ° physical + a ' / g ^ T the half-plane governing an i n - For injection exceed the loading. For For t h i s large prob- restricpar- 96 ticular QQ design, <C 0 . 3 6 0 . physically This I-g, = 2 m a , R-j- = 3 0 0 r i - , is very nonrealizable The reasons where amplifier of physical will design realizability, shown i n t h e 5.5 P r e - D e s i g n P r e d i c t i o n of possible a particular the the c r i t i c a l pole and/or ly design. no p r o b l e m s bility poles (move will will be upper occur. necessarily real lie extremely are large. within are not the fast and the pole critical and t h e r e the not startis QQ are of 1^, general- than the real r e g i o n where amplifier realizable problems the closest on the approach realizable bandwidths, case, or values of the is critical pole physical to some not i n d i v i d u a l stage the realiza- tend to have to possible. bandwidths greater o r i g i n may a g a i n physically real c r i t i c a l distance solution is poles cut- solution small bandwidths, closer For In this lim- before section, For large bounds poles extremely o r i g i n and a p h y s i c a l l y separation, previous is origin), the large within prescribed realizable = 0. and lower the for realizability. the For a restricted, p r e d i c t i o n whether w i t h i n which a p h y s i c a l l y toward which y i e l d s Realizability physically convergence of Mc, section. a rough i n the is u lie Physical give physical Yhen any position to position for exist frequency possible. of value <o , following As m e n t i o n e d R-j- ( s m a l l ^ Q ) , There off to solution will ing the bandwidth, as is to = 6.5 u solution. its It be close a n d f* realizable lie solutions possible. As an example, approximate upper cutoff frequency bounds 97 were found drift quite upper 300-n., the realizable 5.5 two transistor is for for three-stage w i t h 1^,-2 small, cutoff ma. physically frequencies bounds amplifier were solutions very existed designs the F o r R-j- = 5 6 0 . n - , a c a s e realizable between solutions were 4 Mc a n d 6 0 M c . much c l o s e r for using upper together, cutoff and 2N384 where possible For Rj = physically frequencies between Mc a n d 12 M c . For stages, define poles cascaded physical amplifiers containing greater r e a l i z a b i l i t y becomes more Through f u r t h e r investigation, a region complex-frequency must lie of to the assure it of a numbers problem. s h o u l d be plane no r i g h t - h a l f - p l a n e of possible to w i t h i n w h i c h the zeros. 98 6. The for transistor a three—stage 300x1.. put It was = - 2.67 interstage give ues cascade of 50-rx. db) to a low output is on the line 50-Si. and a t w o - s t a g e impedance of the The side to to of the compensate (pad was 300-XL used output amplifier. 23, w i t h t h e o r e t i c a l nominal r e s i s t o r out- 300-xu input l o a d i n g the stage of designed the is and emitter-follower without third 5 and l o a d r e s i s t a n c e s an a m p l i f i e r w i t h i n p u t shown i n F i g u r e low i n Chapter A m i n i m u m - l o s s p a d was shown i n b r a c k e t s . chosen build match the resistance used a m p l i f i e r designed w i t h source to resistance, interstage circuit video decided impedances loss to A M P L I F I E R C O N S T R U C T I O N AND PERFORMANCE design values p a r t i a l l y for The used val- were emitter-lead resistance. 6.1 General Design Considerations Standard high-frequency stage the layout complete eight were inches cury battery Figure The 5/l6 The employed. a m p l i f i e r was l o n g by provided at P r o v i s i o n was in were both also square. BNC c o a x i a l dc i n t e r n a l mounting of The test inline purposes, about connectors power terminals. a 15-volt amplifier is mershown 24. individual transistor 2N384 h a s base i n an aluminum box along with external for with s h i e l d i n g and g r o u n d i n g enclosed inches ends made For w i t h a n ON-OFF s w i t c h . inch i n length tween two construction techniques and were a fourth lead and c o l l e c t o r to leads soldered connected were cut directly to minimize the to approximately into the an i n t e r n a l feedback circuit. shield be- capacitancej designed Figure 23. emitter-follower output amplifier Circuit diagram of the test amplifier 100 101 this lead tion was is grounded. that o c ^ be The only criterion for w i t h i n 25$ of its transistor nominal value of selec- 60 for l g .= 2 m a . 6.2 Low-Frequency For to design biasing the low-frequency for Considerations video and s t a b i l i z a t i o n r e a s o n s , extending cutoff, 40 c p s , f^, made of 13.8 R-j- = 3 0 0 - n . \if f o r coupling as capacitors, capacitors age which causes current, by u s i n g heavy capacitors to The made use to practical dc . The a typical sensitive to to feedback ensure temperature resistance not used bypassed. The for emitter that change. value i n multistage currents, for single to high of use leak- biasing. and it electrowas found coupling-. resistance dc a a value their leakage emitter i n each the compensation p r o b l e m has stage currents The p o r t i o n o f high-frequency bypassing of feedback the of desirable emitter electrolytics emitter not c o u p l i n g because l o w dc basis s h o u l d have is difficulties with very total large for low-frequency 15-^if C-j-, Normally, i t electrolytic been chosen R C - c o u p l i n g , and on the the possible was not amplifiers. interstage, lytic is a m p l i f i e r w i t h a passband Use was But, it are has in- feedback is been w e l l heavily discussed 52 by M u r r a y , reactance using of the the low-frequency emitter bypass T-equivalent capacitor is circuit. given by The 102 where R s p = source G . (R , ei _ " R and resistance G i< el R present) - °) ' „ = emitter feedback broadbanding resistor used for high-frequency R -. = e m i t t e r f e e d b a c k el stabilization resistor used for dc n where the elements shown i n F i g u r e 25(b), and of the are low-frequency (for the r^ = base r = collector r c e = emitter For the current frequency, resistance = 12A set at R total emitter 520-fi. t o 2 are are (= 4 MXL) for Ij, = 2 ma. (6-1) is e l . be d o w n 3 db a t = 1/2 a partic- feedback give good shown i n F i g u r e s h u n t e d w i t h 0«2-p,f ....(6-2) C , ^ .= - l / f l ^ X , , - , . de 1 Ode ceramic 23. .,..(6-3) resistance, current The r e s u l t i n g d e s i g n v a l u e s capacitors transistor)? then and been « a m p l i f i c a t i o n to P The circuit, ( = 200-fiu) The d o m i n a n t r e s t r i c t i o n o n E q u a t i o n Cde current resistance E X emitter T-equivalent 2N384 d r i f t resistance = 25/l (ma) ular : for R . ' e l + R , , eh' has stability. the emitter A l l electrolytic capacitors to ensure bypassing capacitors good high- 103 frequency 6.3 performance The E m i t t e r In the last order stage ter-follower its Follower to of in r b The 4. , = r + out e ( 1 + is ( output impedance without it necessary to transistor T-equivalent ! + a low amplifier, 53 Stansel. It given by R the pair. low-frequency R achieve f b common—collector circuit evident _ a 1 was )(r are then c r emit- amplifier and 25, as that e R ) ....(6-4a) L " " f b ^ ^ C —— : -— 1 + / r, + R c' b s + an shown i n F i g u r e + r )/(r + b use loading } ....(6-5a) 1 r v and G (0) vm Figure Here, then a^ the b = b 25. c (a) (b) (1 - a f b )r b .«..(6—6a) + RL T r a n s i s t o r common—collector a m p l i f i e r , low-frequency T-equivalent c i r c u i t = (r^ + r ) / ( r b above + relations + * " ) , and i f b become we assume that and r <^r , b c 104 R. in = r, b + - b r R + r The v o l t a g e off with fo) der to e ( r . + - input r < b. r R a s )r b c^ + R > a ' ( r e (6-4b) V ' + ....(6-5b) s>] ) - , f ,.. + RL) E f o r c + • ( 1 V ' + b U quite ....(6-6b) + b constant impedance, to beyond however, which i s the falls reason for the quite using a-cutrapidly two cascade. and the used by the drawing r ^ + frequency, The f i r s t plifier, - The increasing in ( r amplification is frequency. stages ' e , = r + —rlr out e a l - e and G a a emitter-follower output stage emitter-follower 1^, = 1 m a , a n d t h e give adequate R The v o l t a g e is pair = 32.4A/ R.. m4 = 48.8 k a , ' a m p l i f i c a t i o n of the vm4 fourth fifth. is t o be stage voltage. out4 and G the the output output G is o u t = 5 are = °* ,(0) = 0*815. 9 6 6 the 12*., k n , am- current first = 3 ma i n have R. _ = 3 . 6 8 m5 stages of 4 ma, w i t h the drawing Ig ( 0 ) vmD The t o t a l We t h e n B stage or- 105 For the emitter-follower R . n - 4 9 k ^ , and G ¥e t h e n have although stage of the quite is output another, c a n be made common-emitter Figure The v a l u e slight - of the equal loss to i n the does not overlooked, is it impedance, l o a d the last passband. by the is method of use possible of to case for stage w i l l have to close emitter db. in this to output 2.06 and a h i g h i n p u t a high level, to u n i t y . achieving a heavily design the be but for an 50--n_ l i n e . included the Figure loaded to overall 26 s h o w s a ampos- stage. 26. Common-emitter output amplification the buffer i n p u t impedance plification sible matchj - 1 2 ^ , t dependent, often Here, impedance u impedance and t h a t stage. An e m i t t e r - f o l l o w e r the o = 0,79 ~ frequency impedance, common-emitter raise (0) R a m p l i f i e r w i t h i n the There exact y m a low output which low output pair, resistor or greater is stage to chosen feed to than u n i t y , common-collector buffer 50-.fi- l i n e make to the dc compensate stage. The voltage for low- , 106 frequency voltage amplification G .(0) is = l/G vm5 (0) = A 1.045 vm4 w h e n R _ = 14.4x1. e5 Although be u s e d in the as test By output peak the the output stage, the common—collector cascade p a i r was could used amplifier. operating voltage is stage, into a 50-xz. l i n e limited output voltage output common-collector-common—emitter is to about and about 0.15 at low current levels, a low l e v e l . The m a x i m u m 0.30 v o l t the volt for for the the peak-to- emitter-follower common-emitter output stage. 6.4 Amplifier Test Results A number of different amplitude response and phase responses low-frequency input, stage necessary it was i n order sweep-frequency a sweep-frequency amplifications, amplitude expected to generator displayed on an o s c i l l o s c o p e of bypassing, for 500 k c flat coupling, to a some measurements, step-function 900-B) 20 M c . The detected and was used and a l s o and g r o u n d i n g . the test circuit used. would amplitude was response i n adjusting i n checking Figure 27 be response, used the the shows s diagram of made: amplitude small adjustment Model response been response. maximally-flat to have generator, response (Jerrold band from elements that achieve sweep t h e back measurements using point-by-point frequency and low—frequency Since a using response to was feed- adequacy the block 107 SweepFrequency Generator Jerrold Model 900-B Figure The element c a n be 27. values after compared w i t h the were a m p l i f i e r w i t h the modified design values shown f o r are adjustment 1 Mc different design values t a k e n of exact for comparing design compensating capacitors the second and 12$ f o r the accuracy In resistors stage are to which the Order to phase in ranges they display both and the i n Figure 23; brackets. oscilloscope find response very are to the for amplifier with These 28; the are markers somewhat the third lower, stage. upper half-power the signals The l o w - f r e q u e n c y measured; 29. the were The m o s t seen These measurements used value the of that are within an and meas- generator amplifier. test for known. frequency each but 4$ are a m p l i f i e r , a VHF s i g n a l a m p l i f i c a t i o n of desirable is by about d i s p l a y e d and measured:on voltage above it design values, t r a n s i s t o r parameters the of close values along w i t h a wideband d i f f e r e n t i a l and o u t p u t Figure given and a d j u s t e d the used using shown on F i g u r e design values frequency feedback was Display maximally-flat response. the the the CRO apart. In ure are o Detector Jerrold Model 50-D B l o c k diagram of t e s t c i r c u i t sweep-frequency generator Photographs the Video Amplifier under t e s t 50-n G = 50 db Fixed Atten. 4 0 db The input oscilloscope. stage circuit was also shown attenuation would be in 108 (a) Figure equal of to fixed output, (b) 28. Amplitude response u s i n g sweep-frequency generator, (a) e x a c t d e s i g n v a l u e s , (b) m o d i f i e d d e s i g n v a l u e s for maximally-flat response the a m p l i f i c a t i o n of attenuation was and d i f f e r e n c e RF S i g n a l Generator Radiometer Type MSllh Figure 29. 50-n. the test available. v o l t a g e s were Fixed Atten. 4 0 db amplifier, but The m a g n i t u d e s of o n l y 4 0 db the input, measured. Video Amplifier under t e s t B l o c k diagram of t e s t c i r c u i t and phase measurements u Wideband Differential Input to CRO for amplitude 109 The phase shown i n F i g u r e was determined by 30 f o r each the measured method of triangulation frequency. (V Figure The - V.) o 1 3 0 , T r i a n g u l a t i o n method of resulting amplitude Figures 31 but upper half-power the response curve. The h i g h e r that to gradual the fact sistor actually Figure 7) frequencies input the because cies Miller frequency cutoff base-emitter Miller the of element collector the to thought to a conductive broaden the stage; partly w i t h C^-i (see has been at neghigher shunted by introduces been n e g l e c t e d . response. values. tran- is at high- (the decrease this component the be of fact the this l o a d impedance following the design to circuit i n series Mc, design stages than the tends to in flat, i n the due two response; capacitance l o a d i n g which has tends input is response, last is shown than 6.5 as is flat smaller to broaden the term contains which also above sharply the are response 7 Mc r a t h e r as of chosen a resistive capacitance frequency-dependent the the which tends lected. ~ Ttlso, the has were responses achieve capacitors falloff that fall to determination amplitude is half-power elements stages) The frequency upper the The does not compensating high-frequency due curve i n adjusting frequency and phase a n d 32 r e s p e c t i v e l y . and the phase In addition, higher On t h e frequen- other hand, 110 I 1 1 1 1.5 2 Figure 31. Figure 1 1 2.5 3 , 1 — I 4 5 f Amplitude response 32. Phase response 1 6.5 (Mc) curve I 1 8 for f (Mc) curve f o r 1 II 10 12 15 20 the test the 1 test > - 25 amplifier amplifier Ill the assumption Miller for is admittance the l a s t taken (OCQRJ^^^I) i n t h e justified see E q u a t i o n which has an a m p l i f i c a t i o n account, the amplifier amplification is hardly the t e s t than predicted. accounting the stage term stage into bandwidth for of large It amplifier f o r the M i l l e r difficult the errors admittance If s h o u l d have i s therefore cascade whether of two. (2-54) this a smaller to predict i n approximation should increase or in decrease bandwidth. The m e t h o d small angles, phase shift This b u t the phase at the higher i s also compensating than probably curve is relatively frequencies accurate linear for with than i n the design that the less curve. high-frequency stages are smaller values. stage G G vml (0) v m l 2 were found t o be =-12.7 - is (0) = -310 ~ 49.83 d b , s h o u l d be compared G amplifications vm (°> amplification G which i s not very of the high-frequency low-frequency and the t o t a l phase due t o t h e f a c t capacitors the design The f o r measuring w i t h the design ( 0 ) + G pad= - ( 1 8 ' 2 values " 2 ' 6 of 7 ) =-15.53 G vm2<°> - - vm3 = - G and the total first which is sistance The 2 ' 9 0 8 ' amplification G The ( 0 ) 1 0 stage (0) due to the — 3X1, w o u l d e following = -352 - ^ 5 0 . 9 3 amplification probably (i" g v m stages are is lower presence account i n close than of for db. the design value, some e m i t t e r - l e a d the lower re- amplification)., agreement w i t h the design values. The using the response test response is of the spaced of the leading test Figure of signal was measured 33. Tektronix T y p e 581 CRO & Type N Sampling Unit Video Amplifier under t e s t the amplifier. step-function edge input B l o c k diagram of t e s t c i r c u i t f o r t r a n s i e n t response measurements a photograph 80-nanosecond is 33. step-function Fixed Atten. 4 0 db 50xx Figure 34 a circuit Tektronix Type 111 Pre-Trigger Pulse Generator Figure to of 1-nanosecond per the step-function input The u p p e r m o s t display input waveform. input waveform; centimeter. The and is The m i d d l e the lower grid the display lines display output is are the Figure amplifier response centimeter. is faster ment of The the source plug-in with grid lines was low-frequency s i m i l a r to Wave is was step- 10-nanoseconds design value. No v a l i d amplitude response was that of Figure was 545A o s c i l l o s c o p e about was 44 cps used as for which measure- available. measured u s i n g 29 e x c e p t (Model AG-10) per 50 n a n o s e c o n d s , equipment preamplifier) frequency by a w i t h the a n d a T e k t r o n i x Type half-power to possible Generator dual-trace spaced approximately 58-nanosecond overshoot circuit Sine-Square Test a m p l i f i e r response function input risetime than the The test 34. used that for a a Heathkit the signal ( w i t h a Type display. shown i n F i g u r e CA The 35. lower 114 0 f /o -3 o/ (design) / (measured) / G (0) 50.93 db G(0) vm 49.83 db y m 7 / -6 + -10 10 20 Figure 35. -f- 40 50 100 f 200 (cps) Low-frequency amplitude f o r the t e s t a m p l i f i e r 500 response •4- 1000 115 7 . CONCLUSIONS Two p r i n c i p a l c o n c l u s i o n s this work. The applicable to amplifiers, iterative the design leading to method of of designs o b t a i n e d by the Giacoletto hybrid-n equivalent in of the the test For up t o with a fixed 7.6 db w a s corresponding was less linear the dc and t h e r e varying the interstage of meaningless small, the For of dc when u s i n g indeed video i n some a useful respects representa- frequency range used using 2N384 drift delay more I n the emitter stages. but for amplifier phase the was used over response in designs low-frequency a cut-and-try It advantage observed method, that the by B r u u n and G r i n i c h optiis feedback. one Since tuning patterns amplifier, the an and overshoot design, optimized by the 2 ma, three-stage was resistance successive of However, t u n i n g p a t t e r n u s e d was different improve the resistance. interstage for three-stage for current design. method. a m p l i f i c a t i o n was feedback the frequency, emitter achieved current The of The m o d i f i e d J o h n s o n - c i r c u i t gives throughout is transistor performing better cutoff Grinich iterative mum v a l u e synthesis G r i n i c h method. transistor Mc u p p e r the using network results amplifier. a 6.5 transistor of drift drawn from the emitter-feedback than those tion c a n be were more of progressively the not loading effect investigated stages this greater is for m i g h t be the used to performance. low v a l u e s emitter current, of interstage convergence resistance was slow and/or low and problems values of \ 116 physical r e a l i z a b i l i t y appeared. realizability Further has been w o r k c a n be As a u s e f u l has suggested done designs byproduct w i t h up t o Several w o u l d be desirable realizability operating currents, of to the being used eight stages. areas for for future impedance point. It would also be and l e t interstage them be and to possibly problems. quite far further as are program ampli- apparent. ensuring or transistor useful to remove and e q u a l to allow impedance maximize the dc It physical level resistances as a computer study design variables, stages physical maximally-flat a means o f interstage equal these research, any of predicting direction* investigate i n p u t and output concerned, of of of avoiding at restrictions ling possible for in this been w r i t t e n capable tude A method the emitter easy hand- matching current is am- plification. A study circuit stage of high-level c o u l d be v e r y signal-handling useful, injection effects especially on the equivalent i n r a i s i n g the output capabilities. 7 It peaked with has of worthwhile peaked shown b y P e p p e r transistor video pole-zero product been to a m p l i f i e r , w h i c h has dependence, any of the apply amplifiers to and P e d e r s o n gives the the iterative o b t a i n the greatest shunt- function gain-bandwidth techniques. method to the a transfer greatest common b r o a d b a n d i n g that the design possible It of may be shunt- amplification. 117 REFERENCES 1. Bardeen, J . , and B r a t t a i n , W . H . , "The T r a n s i s t o r , A S e m i c o n ductor T r i o d e , " P h y s i c a l Review, 74:230-1, ( J u l y 15, 1948) 2. Ryder, 3. Wallace, R . L . , J r . , a n d P i e t e n p o l , W . J . , "Some C i r c u i t e r t i e s and A p p l i c a t i o n s of N - P - N T r a n s i s t o r s , " IRE, 39:753-67, (July, 1951) 4. Spilker, J . 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M . , "Design Theory of J u n c t i o n T r a n s i s t o r s , " 32:1271-1312, (November, 1953) 18. Zawels, 1, BSTJ, J . , " P h y s i c a l T h e o r y f o r a New C i r c u i t R e p r e s e n t a t i o n of J u n c t i o n T r a n s i s t o r s , " J . of A p p l . P h y s . , 25:97681, (August, 1954) 19. " I R E S t a n d a r d s on L e t t e r Symbols f o r Devices," (56 I R E 2 8 . S i ) , P r o c . I R E . (July, 1956) Semiconductor 44:934-37, 20. Early, J . M . , " P - I - N - P and N - P - I - N J u n c t i o n T r a n s i s t o r T r i o d e s , " B S T J , 3 3 : 5 1 7 - 3 3 , (May, 1954) 21. P r i t c h a r d , R . L . , "Frequency V a r i a t i o n s of C u r r e n t - A m p l i f i cation Factor for Junction Transistors," Proc. IRE, 4 0 : 1 4 7 6 - 8 1 , (November, 1952) 22. M i d d l e b r o o k , R . D . , and S c a r l e t t , R . M . , "An A p p r o x i m a t i o n the Alpha of a J u n c t i o n T r a n s i s t o r , " Trans. IRE, ED-3:25-29, (January, 1956) 23. Macnee, A . B . , " A p p r o x i m a t i n g the A l p h a of a J u n c t i o n s i s t o r , " Proc. IRE, 45:91, (Correspondence), ary, 19571 24. Walker:, R . L . , "A S t a t i s t i c a l Study of T r a n s i s t o r H i g h - F r e quency E q u i v a l e n t C i r c u i t s , " S t a n f o r d E l e c t r o n i c s Laboratory Technical Report, No. 23, Stanford U n i versity,(September, 1957) 25. Kroemer, H . , "The D r i f t T r a n s i s t o r , " pp. 2 0 2 - 2 2 0 , (1956) 26. teWinkel, J . , "Drift Transistors," 36:280-88, (August, 1959) 27. P r i t c h a r d , R . L . , " E l e c t r i c - N e t w o r k R e p r e s e n t a t i o n of T r a n sistors - A Survey," Trans. IRE, CT-3:5-21, (March, 1956) Transistors Electronic I, to Tran(Janu- RCA L a b s , and Radio Eng., 119 28. P e d e r s o n , D „ 0 , , " A N o t e on S i m p l i f i e d T r a n s i s t o r E q u i v a l e n t C i r c u i t s , " I n s t i t u t e of E n g i n e e r i n g Research R e p o r t , S e r i e s #60, I s s u e #229, U n i v e r s i t y of C a l i f o r n i a , (February, 1959) 29. Hyde, F . J . , "The C u r r e n t G a i n s of of J u n c t i o n T r a n s i s t o r s , " 18, Paper #2937E, D i f f u s i o n and D r i f t Types P r o c . I E E , 106B, s u p p l , 15- ( M a y , 19597"^ 30. Cripps, L . G . , " T r a n s i s t o r High-Frequency Parameter f^," Elect r o n i c and R a d i o E n g . , 3 6 : 3 4 1 - 4 6 , (September, 1959) 31. Stephenson, W . L . , "Transistor Cutoff Frequency." and R a d i o E n g . , 3 5 : 6 9 , ( F e b r u a r y , 1958) 32. Das, M . B . , and B o o t h r o y d , A . R . , " D e t e r m i n a t i o n of P h y s i c a l P a r a m e t e r s of D i f f u s i o n and D r i f t T r a n s i s t o r s , " Trans. IRE. ED-8.,#1:15-30, (January, 1961) 33. Das, M . B . , "On t h e D e t e r m i n a t i o n of t h e E x t r i n s i c E q u i v a l e n t C i r c u i t Parameters of D r i f t T r a n s i s t o r s , " J o u r , of E l e c t r o n i c s and C o n t r o l . 8 : 3 5 1 - 6 3 , (May, 1960) 34. Wolfendale, E . , "Alloy-Diffused Transistors," 33:88-93, (February, 1961) 35. A l m o n d , J . , and M c l n t y r e , R . J . , "The E q u i v a l e n t C i r c u i t t h e D r i f t T r a n s i s t o r , " RCA R e v i e w , 1 8 : 3 6 1 - 8 4 , (September, 1957) 36. Miller, Electronic Electronic Eng,, of J . M . , "Dependence of the I n p u t Impedance of a Three E l e c t r o d e Vacuum Tube u p o n t h e L o a d i n t h e P l a t e C i r c u i t , " N a t ' l . Bureau of Standards Scientific Papers, 15,#351:367-85, (1919-1920) r 37. Das, M . B . , and B o o t h r o y d , A , R . , "Measurement of E q u i v a l e n t C i r c u i t Parameters of T r a n s i s t o r s at V H F , " P r o c . I E E , 106, s u p p l . 1 5 : 5 3 6 - 4 9 , (May, 1959) 38. Rittner, E . S . , " E x t e n s i o n of the Theory of the J u n c t i o n T r a n s i s t o r , " P h y s i c a l Review. 9 4 : 1 1 6 1 - 7 1 , (June 1954) 39. Webster, 40. Butterworth, less 41. Moore, 1, V . M . , "On t h e V a r i a t i o n o f J u n c t i o n - T r a n s i s t o r Current-Amplification Factor with Emitter Current," Proc, IRE, 42:914-20, (June, 1954) S . , "On t h e T h e o r y o f F i l t e r A m p l i f i e r s , " Engineer, 7:536-41, (October, 1930) Wire- A . D . , " S y n t h e s i s of D i s t r i b u t e d A m p l i f i e r s f o r P r e scribed Amplitude Response," E l e c t r o n i c s Research L a b o r a t o r y T e c h n i c a l R e p o r t , N o . 53', S t a n f o r d U n i versity, (September 1, 1952) 120 42. C a r y o t a k i s , G . A . , Demuth, H . B . , and Moore, Network S y n t h e s i s , " IRE C o n v e n t i o n (1955) A.D. , "Iterative Record, pt.2:9-16, 43. Landon, V . D . , "Cascade A m p l i f i e r s w i t h Maximal RCA R e v i e w , 5 : 3 4 7 - 3 6 2 , (January, 1941) 44. C a r y o t a k i s , G . A , , " I t e r a t i v e Methods i n A m p l i f i e r I n t e r s t a g e Synthesis," E l e c t r o n i c s Research Laboratory Technical R e p o r t , N o . 8 6 , S t a n f o r d U n i v e r s i t y ; , (May 2 , 1955) 45. Chang, 46. Auld, 47. Schrack, 48. Yuan, J . T . , "On t h e S e l e c t i o n o f T u n i n g P a t t e r n s i n S t a g g e r Tuning M u l t i c a v i t y K l y s t r o n A m p l i f i e r s , " M.A.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, (August, 1960) 49. Hyde, F . J . , "The I n t e r n a l C u r r e n t G a i n o f Proc. IRE, 46:1963, (1958) 50. G r i s w o l d , D . M . , a n d C a d r a , . V . J . , "Use o f t h e RCA 2N384 D r i f t T r a n s i s t o r as a L i n e a r A m p l i f i e r , " , I R E N a t i o n a l C o n vention Record, v o l . 6 , pt,3:49-56, (1958) Flatness," C»Y„, "A Study of the I t e r a t i v e Method of Network Synthesis," Stanford Electronics Laboratory Technical R e p o r t , No. . 4 4 , S t a n f o r d U n i v e r s i t y , ( J u l y 2 8 , 1958) B . A . , I s a a c s , A . T . , and M o o r e , A . D . , "An I t e r a t i v e N u m e r i c a l Method f o r Stagger-Tuning M u l t i c a v i t y K l y s t r o n A m p l i f i e r s , " IRE Canadian C o n v e n t i o n R e c o r d , p p . 4 6 9 , (1958) 51. F . G . , "On t h e O p t i m i z a t i o n of t h e D r i f t L e n g t h of Stagger-Tuned M u l t i - C a v i t y K l y s t r o n A m p l i f i e r s for S m a l l S i g n a l s , " M.A.Sc» T h e s i s , U n i v e r s i t y of B r i t i s h C o l u m b i a , ( J u n e , 1960) Drift Transistors," RCA S e m i c o n d u c t o r P r o d u c t s B o o k l e t . Form #SCD108B, RCA S e m i c o n d u c t o r a n d M a t e r i a l s D i v i s i o n , S o m e r v i l l e , New J e r s e y , (1959) 52. Murray, R i P . , "Emitter Bypassing i n Transistor C i r c u i t s , " Trans. IRE, AU-5.#3:71-2. (May-June, 1957) 53. Stansel, F i R . , "The C o m m o n - C o l l e c t o r T r a n s i s t o r A m p l i f i e r a t Carrier Frequencies," Proc. IRE, 41:1096, (September, 1953)
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Iterative synthesis of a flat-staggered emitter-feedback transistor video amplifier Cameron, Frank Charles 1962
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