CONTRIBUTION TO TUE ANALYSIS AND DESIGN OF LINEAR AND PARAMETRIC AMPLIFIERS
A Thesis
Submitted for the degree of
DOCTOR OF PHILOSOPHY in the Faculty of Engineering
by
DHIREITECA N. N. S INHA
Department of Electrical Engineering Indian Institute of Technology
Delhi
1973ACKUOWIEDGEMSNTS
TI-Is work was sawried out under the supervision of Professor C.C. Dutta noy. The author wirOss to record his Aeop se:.se of gratitude to his supervisor for the able guidance a:-.d constant encouragement during the course of hie disSertation promlame, Professor P.S. Satsangi's h=elp
is 7,sco deeply apprecia7Jed for providim stimulatim:, advice regarding writing of the thesis. The author is thankful to
Dr. S.N. Gupta and Dr. A. Prabbakar for their useful suez*S- tions ELAI co; Herz a si::',cere appreciation is expressed to Pr. Ranjtt Kumar for the elegant typing.
Thanks are duo for their constant well.-wishes, to my
parents and family, in t3a.-oral, and my wife Mims in particular, Ithele ears and patience during the entire research schedule
doServe special admira'Aa:L.
D.N.N. $IWA
ABSMACT
The analysis and design of linear parametric amplificrs have been oonsidere in order to enhance their versatile appli- cations in both low-as well as high-frequency ranges. In the case of linear amplifiers, broadbandinC Of single and multi- stace amplifiers nas 'Alen investigated by using a new do:Ace
called active feedback look (AFB). This application of t e AFB has been found plausible because of the reasons tat t in both the low-and bigh-frecpency rezpotzes, the AM Pas easily maLoeuvrale rising caL,-freque:Jzy cilaracteristic. Furt:Alits for verification of the property of the APB and its app/ica tios, experimental data are also included.
As a nonlinear elemeLt is relevant for analysis anc_.
design of both parametric amplifiers an frequency converters, general real and reactive power relations in the element Ilays
beeL derive. co relations can be reduced to well known Manley and Rowe es relations under suitable constraints. In addition, classification of nonlinear elements has been carried out on the basis of these relations. Some of tlle relevant types, mentioned under the elassifteations are lose- less reaetancelecc clinear elements and lossy reactive nonm.
linear elements.
aa OOi shown that, usinc; /ossless reactanceleas nonlinear element, a creator value of conversion efficio:4y can be obtained than that possible from nonlinear reacta_ce.
In ladditIon e it x also been established that sucll typo Qf element Is idealy represented by a Jelephson junctio:,,
FLAlly, in Wall siznal sass. it ho ms been shown that, for the destj,:n of both parametric amplifiers and fre- quency converters, a loamy Matto* nonlinear element is better than an ideal nonlinear reactanee or resistance
Tie importance of element has been inferred on the Llasis of the derived expressions of the tolUiduser power fains.
Further, a formula for computing maims gain bandwidth pro- duct (GBW) of parametric amplifiers, bads also Leon ebtaine,:;.
Thie formula reveals that, for the case of lousy reactive
enlinear element, value of maximum (B is treater than that
obtaimble from reactive or resistive _o;Ilinear eleuents
16
20
23 23
3
33 TABLE OF CONTENS
Pale
ABSTRACT iv
LIST OF SYMBOL3
LIST OP :IMP:ZS xxl
LIST OP TABLES xxvi
LIST OF ABBRWIATIONS xxvi
CHAP, 1 INTRODUCTION 1
1.1 1,1 ear amplifier 2
2 Parano-ric amplifier 3 1 2.1 pitlo.1 of cofNerters ard
parametric an 7
1 2,2 Donf. of converters w:cl parametric amplifiers 1.3 Parametric amplification and
Josephson junction 1.4 Seope of this dissertation
1.4.1 Summary of Capters
CHA AN ACT/VE PEEDBA'T BLOCK AND ITS APPLICATIOM
2.1 Te transfer function of the APB 2.1.1 Condition of stability of
tl,e APB
2 1.2 Slope of the mein frequency characteristics of the APB 2.2 An application of the AP
2 2.1 Bandwidth and gain bandwidth product of the systou
2.3 Desi7n and experimental results of
the APB and the system 38 2 3.1 Discussions of the experimen-
tal results
2 Conclusion. 52
3 BOOSTINCI TATIMIDTH AND GAT 3 SAM- PROIXTCT OF LIMO AMMITIERS BY TM ME CP ACTVE PEET3r3k2 BLOCK
M-dificaticn.: of t'vm cascaded ei: to
amplifier and the APB 5 3,1.: Transfer function of the
cystem containing ridge'...T
and RC bilinear :petwork 62 3.2 Application of t:ne 4awicith booster
subsystemit multistaf7o amplifier 67 3.3 DesiFn and experimental results of
the systems 77
3.3.1 Discussion of experimental
resuris 80
3 4 conclusio%
4 GENERAL POWER RELATIONS IN, AND
PROPERTIES OP NONLINEAR ELEMENTS 86 4.1 General pmer relations in non.
linear elements 87
4.1.1 Maccification of non.
linear elements 93
(via)
4.12 Relation betweer ernerry of a nonlinear and Pt) and P
.3 Comments on Pan l's poi rolations
4.2 Derivaticin of cenversi'm if
and power 1-ain usin.;:: the power r, lationS
4 3 C ncluet.m
CAP
5 APPLICATION OF TT NNW RELATIONS AND DFXIVA/TON OP TRANSDUCER POWER lAINS5.1 Applioatio: of the power relations to ,IL oleme-te
5.1.1 31 nal waiysis of on- deal P/NL element ('Thzpe D) 5.1.2 POwer sins of PINL rosistaize
and nonideal prm clement 5 2 Transducer poweri.,.!ains of frequency
convertor o.r.d parametrio azaplifier 5.2.1souoar power -7air: a
iI' 171ttrthridtlle
a parametric amplifier 5.3 Conclusion
IT
102
105
109
114
130
21a
136
136
CTAPTER
6 -!Etts* L=Amin
POWER RELATIOM TV A JOSEPHSON JUNCTION6 / Derivatio- f t e reactive pmeor rctlevzio:la
6 1 Importance of tl'e viaOr
6.2 C7-ic-...43ion
mlationa
1 h:
cliAnat,
7 CONCLUSIONS i457.1 Main results of the thesis 145 2 Scope r)f further work '4)
APPENDIX
Brid:*ed-tr Network 1 52 II Bililear BC Network 156