B.1 A typical single BJT transistor common-emitter amplifier used for

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thesis.
Application of Nonlinear Transistor
Characteristics
A thesis
submitted in fulfilment
of the requirements for the degree
of
Doctor of Philosophy in
Physics and Electronic Engineering
at
The University of Waikato
by
Toby Balsom
2014

Abstract
Thisresearchpresentsthreeworksallrelatedbythesubjectofthird-orderdistor-
tionreductioninnonlinearcircuits. Eachoneisanovelextensiontoprevious
workinthatbranchofelectronicsliterature. Allthreefollowtheprocedureof
presentinganovelalgebraicproofandfollowingupwithsimulationsand/or
measurementstoconfirmthetheoreticalresult. Theworksaregenerallythemed
aroundnonlinearlow-frequencybipolartransistorcircuits.
Firstly,aninvestigationisconductedintoawelldocumentedeffectinbipolar-
junctiontransistors(BJTs)calledinherentthird-orderdistortionnulling. This
effectisshowntobeafundamentalresultofthetransistor’stransferfunction
actinguponaninputsignal. TheproofofasingleBJTemitter-followeramplifier’s
inherent null is examined which is well documented in the literature. This
forms the basis for a novel extension in Darlington transistors where theory
suggeststhethird-ordernulloccursatdoublethecollectorcurrentofasingle
BJT.DiscretemeasurementsofaCA3083transistorarrayareundertakenand
comparedwiththeoryandsimulationdata. Thesemeasurementsconfirmtheory
withreasonableaccuracy.
Atemperatureandprocessvariationindependentbiascircuitisdevelopedto
solveoneissuewithusingthird-orderdistortionnulling. Thisworkisinteresting
inthatitbranchesintoseriesresistancecompensationfortranslinearcircuits
andstandsasausefulcircuitinitsownright. Usingstacksofmatchedforward-
biased semiconductor junctions which conform to translinear conditions, a
bias current can be generated which theoretically removes temperature and
series resistance dependence on the particular BJT used. This proves useful
forthepreviousworkindistortionnulling,butalsoallowsdirectandaccurate
measurementofseriesresistance. Again,simulationandmeasurementdatais
i
ii
obtainedfromdiscretemeasurementsoftheproposedcircuit,andtheresults
conformwiththeorytoareasonabledegree.
Lastly, this work presents the analysis of a cascoded-compensation (Cas-
comp)amplifier. Itpresentsthefirstfullynon-linearderivationoftheCascomp’s
transferfunctionanditsassociatedharmonicandintermodulationdistortion
components. Thederivationrevealsaninterestingcharacteristicinwhichthe
third-orderintermodulationdistortionhasmultiplelocalminima. Thischarac-
teristichasnotyetbeenpresentedintheliterature,andallowsbetteroptimisa-
tionofCascompamplifiersinanyapplication. Again,thischaracteristicandits
potentialbenefitsareconfirmedwithsimulationanddiscretemeasurements.
Observationsofthepresentedworksarediscussedandbuiltuponinthelast
chapter. Thisleadstosuggestionsonfutureresearchtopicsbranchingonfrom
theseworks.
Acknowledgements
ToJonathan,BillandMarcusfortheinspiration,guidanceandwisdom. ToMark,
Kyle,SteveandBensonfortheentertainingdiversionsandenlighteningsupport.
ToTraceyandmyfamilyfortheloveandsacrifice.
iii

Table of Contents
Abstract i
Acknowledgements iii
TableofContents iv
ListofFigures viii
ListofTables xiii
1 Outline 1
1.1 ThesisMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Third-OrderDistortionNull . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 TranslinearExtraction . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 CascodedCompensation . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.4 AimsandGoals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 OriginalWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Introduction 7
2.1 DefinitionofDistortion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 MeasuresofDistortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 HarmonicDistortion . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 IntermodulationDistortion . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Third-OrderInterceptPoint . . . . . . . . . . . . . . . . . . . . . . 14
2.3 DistortioninBJTCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 BJTModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
v
vi TABLEOFCONTENTS
2.3.2 BJTDistortionCharacteristics. . . . . . . . . . . . . . . . . . . . . 19
2.3.3 EffectsofFrequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.4 HeterojunctionBipolarTransistors . . . . . . . . . . . . . . . . . 22
2.4 BJTNon-idealities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2 ParasiticResistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.3 Base-widthModulation . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.4 NonlinearBeta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.5 ProcessVariation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.6 SummaryofNon-idealities . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 LinearisationTechniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5.1 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5.2 Feedforward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5.3 Predistortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5.4 HarmonicTermination. . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 GeneralLiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Third-OrderDistortionNull 39
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 TheoreticalProof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4 DarlingtonBJTNull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.1 TheoreticalPlotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.7.1 Practicalimplementation . . . . . . . . . . . . . . . . . . . . . . . . 55
3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 TranslinearExtraction 57
4.1 TranslinearPrinciple. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1.1 NonidealTranslinearPrinciple . . . . . . . . . . . . . . . . . . . . 60
4.2 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 SeriesResistanceCompensation . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 ExpansionoftheTranslinearLoop . . . . . . . . . . . . . . . . . 64
TABLEOFCONTENTS VII
4.3.2 SeriesResistanceExtraction . . . . . . . . . . . . . . . . . . . . . . 66
4.3.3 ApplicationtoAmplifierBiasing . . . . . . . . . . . . . . . . . . . 67
4.4 ExtractionCircuitDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.1 TranslinearStackRatios . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4.2 MultiplierDividerdesign . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.3 BiasDriverCircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.5.1 MultiplierOutputError . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.2 AmplifierBiasCurrentError . . . . . . . . . . . . . . . . . . . . . . 74
4.5.3 IM3NullError . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.6 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.6.1 SeriesResistanceMeasurements . . . . . . . . . . . . . . . . . . . 77
4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.8 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5 CascodedCompensation 81
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 CurrentTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 FullTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4.1 MainAmplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4.2 IdealErrorAmplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4.3 AmplifierCoefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4.4 Non-IdealErrorAmplifier . . . . . . . . . . . . . . . . . . . . . . . . 90
5.5 CascompBiasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5.1 FundamentalGain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5.2 Third-OrderGain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6.1 CircuitSchematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6.2 Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.7 ProcessErrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.7.1 TransistorParameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.8 ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.8.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.8.2 VerificationofOptimisationBenefits. . . . . . . . . . . . . . . . 107