Table Of ContentAmal Banerjee
Performance
Evaluation
of Electronic
Oscillators
Automated S Parameter Free Design
with SPICE and Discrete Fourier
Transforms
Performance Evaluation of Electronic Oscillators
Amal Banerjee
Performance Evaluation
of Electronic Oscillators
Automated S Parameter Free Design with
SPICE and Discrete Fourier Transforms
AmalBanerjee
AnalogElectronics
Kolkata,India
SupplementaryMaterialscanbefoundonlineathttps://www.springer.com/us/book/
9783030256777.
ISBN978-3-030-25677-7 ISBN978-3-030-25678-4 (eBook)
https://doi.org/10.1007/978-3-030-25678-4
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Supplementary Online Software
Onlineathttps://www.springer.com/us/book/9783030256777canbefoundalinkto
software tools that can be used in conjunction with this book. These tools are a
systematicschemetoaccuratelyestimatetheperformancecharacteristicsofcommon
types of electronic oscillators. This scheme consists of three main steps—design,
followed by time domain performance analysis and finally by frequency domain
performanceanalysis.Thedesignstepfocusesonthekeyissue—willtheoscillator
startup?Thisisvital,asanoscillatorisanautonomousself-excitedcircuitanddoes
not need any external trigger. The supplied C computer language executables
guarantee the accuracy of the design calculations, each of which generate text
SPICE input format netlists. This scheme exploits the transient analysis feature of
thegoldstandardelectroniccircuitsimulationtoolSPICE(SimulationProgramwith
IntegratedCircuitEmphasis).Thelargesignaltimedomainperformancecharacter-
isticsofanoscillatorundertestistransformedtothefrequencydomainwithanother
supplied C computer language executable, which generates the power spectrum—
essentiallythefrequencydomainperformancecharacteristicsoftheoscillator.
v
Contents
1 IntroductionandProblemStatement. . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 IntroductionandProblemStatement. . . . . . . . . . . . . . . . . . . . . . . 1
2 ElectronicOscillatorFundamentals. . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 FundamentalOscillatorConfiguration:
Open-andClosed-LoopEquations—Loop
Gain—BarkhausenandNyquistConditions. . . . . . . . . . . . . . . . . 5
2.2 NegativeResistanceOscillators:Start-Up
andSteady-StateConditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 TraditionalElectronicOscillatorStart-Up
andSteady-StateAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 DifferentialOscillatorsasanAlternative
toFeedbackandNegativeResistanceOscillators. . . . .. . . . . .. . . 11
2.5 CommonOscillatorDesignEquationsandFormulas. . . . . . . . . . . 12
2.5.1 Common-EmitterColpittsResonatorFeedback
Oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.2 Common-EmitterClappResonator
NegativeResistanceOscillator. . . . . . . . . . . . . . . . . . . . . 14
2.5.3 Common-BaseColpittsResonatorFeedback
Oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.4 Common-BaseLCTankResonator
NegativeResistanceOscillator. . . . . . . . . . . . . . . . . . . . . 16
2.6 OscillatorNoise:PhaseNoise—AnIntuitiveApproach. . . . . . . . . 17
2.6.1 Leeson’sTheoryofOscillatorPhaseNoise. . . . . . . . . . . . 20
2.6.2 OscillatorNoise:APerturbationApproach
andCharacterization. . .. . . . .. . . .. . . . .. . . . .. . . .. . . 21
2.7 MultiplyingSignalstoGetNewSignals:Mixers. . . . . . . . . . . . . . 22
2.8 OutputBufferAmplifier:CoupleOutput
toExternalLoad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
vii
viii Contents
2.9 TheDiscreteFourierTransformandPower
SpectrumofaSignal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 AutomatedSParameter-FreeElectronicOscillator
Design,PerformanceEvaluationScheme,
andStep-by-StepDesignExamplesUsingSPICE,
DiscreteFourierTransform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 SParameter-FreeElectronicOscillatorDesign,
PerformanceEvaluationScheme. . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 VerificationofDiscreteFourierTransform
ExecutableAccuracy. . . . . . . .. . . . . . . . . . .. . . . . . . . . .. . . . . 32
3.3 1800MHz(1.8GHz)Common-Emitter
NegativeResistanceClappResonatorGSM
CarrierFrequencyOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 1000MHz(1GHz)Common-EmitterNegative
ResistanceClappResonatorOscillator. . . . . . . . . . . . . . . . . . . . . 40
3.5 750MHzCommon-EmitterNegativeResistance
ClappResonatorOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6 500MHzCommon-EmitterNegativeResistance
ClappResonatorOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.7 1000HzCommon-EmitterFeedbackColpitts
ResonatorOscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.8 500MHzCommon-EmitterFeedbackColpitts
ResonatorOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.9 750MHzCommon-BaseFeedbackColpitts
ResonatorOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.10 500MHzCommon-BaseFeedbackColpitts
ResonatorOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.11 Common-BaseNegativeResistance100MHz
ParallelRLCResonatorOscillator. . . . . . . . . . . . . . . . . . . . . . . . 54
3.12 1000MHzDifferentialOscillatorUsingCMOS
Level3MOSFET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.13 750MHzDifferentialOscillatorUsingCMOS
Level3MOSFET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.14 500MHzDifferentialOscillatorUsingCMOS
Level3MOSFET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.15 14MHzCrystalOscillatorUsingCMOSLevel3MOSFET. . . .. . 65
3.16 750MHzCommon-EmitterNegativeResistanceClapp
ResonatorOscillatorwithNonidealResonatorInductor. . . . . . . . . 66
3.17 SchottkyDiodeRingDouble-BalancedMixer
LO250MHzRF500MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Contents ix
3.18 SchottkyDiodeRingDouble-BalancedMixerLO250
MHzRF500MHz:UnequalLoadSourceResistances. . . . . . . . . 70
3.19 Common-CollectorBufferAmplifierInput
Frequency500MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 ConclusionsandFutureWork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
AppendixA:HFA3134DataSheetandSPICEDeviceModel. . . . . . . . . . 77
AppendixB:ListofSuppliedCComputerLanguage
ExecutablesforLinuxandWindows. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
AppendixC:DownloadingandInstallingMinGW. . . . . . . . . . . . . . . . . . 81
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Chapter 1
Introduction and Problem Statement
1.1 Introduction and Problem Statement
An electronic oscillator is truly unique as it generates the periodic, time-varying
current and voltage waveforms that trigger and drive all other electronic circuits.
Theseperiodic,time-varyingcurrentandvoltagewaveforms,calledsignals,would
neverexistwithoutacircuitthatconvertsdirectcurrent(DC)electricalenergyinto
periodic time-varying alternating current (AC) electrical energy. By definition, an
electronicoscillatorisanautonomous,self-triggeredcircuit,existingandthrivingon
inherent(DCpowersupply,activedevice)nonlinearpropertiesandinstabilities,and
isthereforetrulyanonlinearcircuit.Anoscillator“self-excites”itselfintogenerating
itsperiodic,time-varyingcurrent–voltageoutput.
Clearly, design and performance evaluation of electronic oscillators is a chal-
lenging task, because it is autonomous and requires no input trigger. The designer
cannot analyze the output for a given known input, for a new oscillator design. In
addition except for negative resistance oscillators, there is no necessary and
sufficient condition that will guarantee start-up of oscillations. In the worst case,
the designer may end up with an oscillator that will oscillate, but never start up!!
These very exciting issues and their solutions will be examined in minute detail in
subsequentchapters—infactChap.3isdedicatedentirelytodesignexamples,with
performance evaluation of common oscillator types used in key RF–microwave
applications,application-specificintegratedcircuits(ASIC),etc.
Traditionalelectronicoscillatordesigntechniqueisbasedonthesmallandlarge
signal S (scattering) parameters. The small signal S parameters for a selected
transistor (RF–microwave bi-junction or field effect transistor) are supplied by the
manufacturer for corresponding specific transistor biasing conditions and target
oscillationfrequencies.ThedesignerfirstusesthesuppliedsmallsignalSparameters
toverifyifthetransistorisunstableattheselectedtargetoscillationfrequency,and
compute the reflection coefficients at the input–output ports of the transistor. An
unstabletransistorisessentialforoscillationstart-up.ThelargesignalSparameters
©SpringerNatureSwitzerlandAG2020 1
A.Banerjee,PerformanceEvaluationofElectronicOscillators,
https://doi.org/10.1007/978-3-030-25678-4_1
2 1 IntroductionandProblemStatement
areusedtoanalyzethesteady-stateoscillations.TherearemajordrawbackstotheS
parameter (small, large signal) based electronic oscillator design scheme, to be
examined in detail in Chap. 2. Unlike small-signal S parameters, large-signal S
parameters for the same transistor must be determined with expensive computer-
aideddesign(CAD)toolsortestequipmentasvectornetworkanalyzers.
ThisbookhasdemonstratedanewSparameter-freeelectronicoscillatordesign
and performance evaluation scheme that exploits the properties of a new breed of
RF–microwave transistors which do not require the circuit designer to use any
(large,smallsignal)Sparameterstodesignacircuitusingthattransistor.Infact
thedata sheetofsuchatransistordoesnotcontainanysmall-signalSparameters
andcorrespondingbiasingconditions,atall.
Simply designing an oscillator does not guarantee that the physical device will
start up and oscillate—this must be verified, using the gold standard SPICE (Sim-
ulationProgramwithIntegratedCircuitEmphasis)circuitsimulator.Thisisessen-
tial,sinceanoscillatorisautonomous,andthereisnowaythedesignercanpredict,
atdesigntime,iftheoscillatorwillstartupandoscillate.Chapter2enumeratesthe
design equations and calculation steps in detail to design common RF–microwave
electronic oscillators (common emitter-negative resistance, common emitter feed-
back,common base-negativeresistance,common-basefeedback,differential, etc.);
Chap. 3 contains an exhaustive list of design examples to illustrate how, e.g., a
1800MHz(1.8GHz—GSMcarrierfrequency)commonemitter-negativeresistance
oscillatormaybedesignedwithoutusingany(small,largesignal)Sparameters
anditstimedomainstart-upandsteady-statebehaviorbeanalyzedusingSPICE.
SPICE transient analysis of an electronic oscillator does not provide complete
information about the performance characteristics of electronic oscillator design,
becauseofitsautonomousandnonlinearnature.Itisimpossibleforthedesignerto
predictorestimatethedeviationbetweenthetargetfundamentalfrequencyandthe
actualoutputfundamentalfrequency,fromtheoscillator’stimedomainperformance
characteristics. To estimate andmeasure these key performance characteristics,the
time domain oscillator output must be transformed to the frequency domain, using
thepowerfuldiscreteFouriertransform(DFT)algorithm.DFTenablesthecalcula-
tion of the power spectrum of the frequency domain signal (transformed from the
timedomain).Theactualfundamentalfrequencyandthefirstfewharmonics,aswell
asdistributionofsignalenergyamongthesemeasuredfrequencies,canbeextracted
from the power spectrum. This has been clearly demonstrated for each design
exampleinChap.3.
It must be noted that the electronic oscillator design and DFT transformation
computationsarecomplicated,multistep,andthustimeconsuminganderrorprone.
Inparticular,theDFTtransformationandpowerspectrumcalculationsarebasedon
complex numbers and their complex conjugates, and so are impossible to do
manually for any real-world data set. To address these issues, a set of simple,
versatile C computer language executables are provided. These C computer lan-
guage executables have been supplied for both the popular Linux and Windows
operating systems. The C computer language executables for each oscillator type
(e.g., common emitter-negative resistance) implement the S parameter-free
