Stability Analysis of Nonlinear Microwave Circuits (Artech House Microwave Library)

354 Pages·2003·6.2 MB·English

by  Almudena Suarez

Stability Analysis of
Nonlinear Microwave Circuits
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Stability Analysis of
Nonlinear Microwave Circuits
Almudena Suárez
Raymond Quéré
Artech House
Boston (cid:127) London
www.artechhouse.com
LibraryofCongressCataloging-in-PublicationData
Suárez,Almudena.
Stabilityanalysisofnonlinearmicrowavecircuits/AlmudenaSuárez,RaymondQuéré.
p.cm.—(ArtechHousemicrowavelibrary)
Includesbibliographicalreferencesandindex.
ISBN1-58053-303-5(alk.paper)
1.Microwavecircuits. I.Quéré,Raymond. II.Title III.Series.
TK7876.S762003
621.381’32–dc21 2002038278
BritishLibraryCataloguinginPublicationData
Suárez,Almudena
Stabilityanalysisofnonlinearmicrowavecircuits.—(ArtechHousemicrowavelibrary)
1.Microwaveintegratedcircuits–Design 2.Stability
I.Title II.Quéré,Raymond
621.3’8132
ISBN1-58053-303-5
CoverdesignbyGaryRagaglia
Chapters1,2,4,5,6byAlmudenaSuárez
Chapter3byRaymondQuéré
©2003ARTECHHOUSE,INC.
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Useofaterminthisbookshouldnotberegardedasaffectingthevalidityofanytrademarkor
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InternationalStandardBookNumber:1-58053-303-5
LibraryofCongressCatalogCardNumber:2002038278
10987654321
Contents
Preface xi
Acknowledgments xv
1 Steady-StateSolutionsofNonlinearCircuits 1
1.1 AutonomousandNonautonomousDynamicalSystems 2
1.2 OscillationsinLinearandNonlinearSystems 10
1.3 Phase-SpaceRepresentationofSolutions 16
1.3.1 TransientTrajectoriesandLimitSets 16
1.3.2 LimitCycles 19
1.3.3 InvariantSets 21
1.4 StabilityofLimitSets 29
1.4.1 ConceptofStability 29
1.4.2 StabilityTypes 31
1.4.3 CoexistingStableSolutions 42
1.4.4 QualitativeVariationsintheStabilityProperties 43
1.5 PoincaréMap 44
1.5.1 DefinitionofthePoincaréMap 44
1.5.2 PoincaréMapsofLimitSets 48
v
vi StabilityAnalysisofNonlinearMicrowaveCircuits
1.5.3 ChaoticSolutions 50
1.6 Entrainment:Phase-LockedSolutionsintheTorus 52
References 57
2 NonlinearAnalysisTechniques 61
2.1 Time-DomainSimulation 62
2.2 HarmonicBalanceforNonautonomousCircuits 66
2.2.1 Harmonic-BalanceEquations 67
2.2.2 NumericalResolutionoftheHarmonic-Balance
Equations 71
2.2.3 ContinuationTechniqueforHighAmplitudeofthe
RFGenerators 73
2.3 HarmonicBalanceforAutonomousandSynchronized
Circuits 75
2.3.1 AnalysisofFree-RunningOscillators 78
2.3.2 AnalysisofSynchronizedCircuits 86
2.3.3 AnalysisofSelf-OscillatingMixers 89
2.4 EnvelopeTransient 91
2.5 ContinuationTechniqueforTracingSolutionCurves
VersusaCircuitParameter 96
2.6 AnalysisofAutonomousandSynchronizedCircuitsin
ClosedHarmonic-BalancePrograms 99
2.6.1 AutonomousCircuits 100
2.6.2 SynchronizedCircuits 104
2.6.3 ContinuationMethodBasedontheUseofAuxiliary
Generators 106
References 111
3 LocalStabilityAnalysis 117
3.1 StabilityConceptforLinearandNonlinearCircuits 118
3.1.1 StabilityofLinearCircuits 119
3.1.2 StabilityofNonlinearCircuits 128
Contents vii
3.2 DerivationoftheCharacteristicSysteminthe
Harmonic-BalanceFormulation 131
3.2.1 ExpressionoftheCharacteristicSystem 132
3.2.2 StabilityAnalysisofLumpedCircuits 135
3.2.3 StabilityAnalysisofDistributedCircuits 142
3.2.4 CharacteristicLoci 147
3.2.5 TheNegativeImpedanceApproach 151
3.3 TheOpen-LoopApproach 152
3.3.1 TheBode,PlatzkerApproachforLinearCircuits 153
3.3.2 ExtensionoftheMethodforMultibiasCircuits 160
3.3.3 ExtensionoftheApproachtoLarge-SignalPeriodic
Steady-StateRegimes 161
3.3.4 Large-SignalStabilityAnalysisUsingaSimplifiedFilter 168
References 171
Appendix3A 172
4 BifurcationAnalysisofNonlinearCircuits 177
4.1 LocalBifurcations 178
4.1.1 LocalBifurcationsfromtheDCRegime 179
4.1.2 LocalBifurcationsfromthePeriodicRegime 188
4.2 BifurcationsofthePoincaréMap 196
4.2.1 Flip-TypeBifurcations 201
4.2.2 Direct-TypeBifurcations 204
4.2.3 Hopf-TypeBifurcations 209
4.3 GlobalBifurcations 211
4.3.1 SaddleConnection 212
4.3.2 Saddle-NodeLocal/GlobalBifurcation 213
4.4 AnalysisofBifurcationsfromtheHarmonic-Balance
CharacteristicSystem 216
4.4.1 BifurcationsfromtheDCRegime 217
4.4.2 BifurcationsfromthePeriodicRegime 219
4.5 Harmonic-BalanceAnalysisofBifurcationswiththe
AidofanAuxiliaryGenerator 228
viii StabilityAnalysisofNonlinearMicrowaveCircuits
4.5.1 AutonomousPeriodic 230
4.5.2 PeriodicRegimewithExternalExcitation 231
4.5.3 AutonomousQuasiperiodicRegime 233
References 240
5 GlobalStabilityofMicrowaveCircuits 243
5.1 GlobalBehaviorofFree-RunningOscillators 244
5.2 GlobalBehaviorofSynchronizedOscillators 247
5.3 GlobalBehaviorofFrequencyDividersbyTwo 252
5.3.1 DesignConceptsandApplicationsofFrequency
Dividers 252
5.3.2 ParametricStabilityAnalysisofFrequencyDividers
byTwo 255
5.3.3 ImprovementintheFrequency-DividerDesign 262
5.4 GlobalBehaviorofSelf-OscillatingMixers 266
5.4.1 DesignConceptsandApplicationsofSelf-Oscillating
Mixers 266
5.4.2 SteadyStateoftheSelf-OscillatingMixer 268
5.4.3 ParametricAnalysisoftheSelf-OscillatingMixer 269
5.5 GlobalBehaviorofFrequencyDoublers 273
5.5.1 DesignConceptsofFrequencyDoublers 273
5.5.2 ParametricAnalysisofFrequencyDoublers 273
5.6 GlobalBehaviorofPhase-LockedLoops 278
5.6.1 GeneralEquationsofthePhase-LockedLoop 279
5.6.2 ParametricAnalysisofthePhase-LockedLoop 281
5.6.3 UseofthePoincaréMaptoDeterminetheOperating
BandsofthePhase-LockedLoop 290
References 292
6 BifurcationRoutestoChaos 295
6.1 Homoclinicity 296
6.2 QuasiperiodicRoutetoChaos 302
6.3 Period-DoublingRoutetoChaos 305
Contents ix
6.4 Torus-DoublingRoutetoChaos 311
6.5 Intermittence 315
References 320
AbouttheAuthors 323
Index 325