NonlinearRFCircuitsandNonlinearVectorNetworkAnalyzers With increasingly low-cost and power-efficient RF electronics being demanded by today’s wireless communication systems, it is essential to keep up to speed with new developments.Thisbookpresentskeyadvancesinthefieldthatyouneedtoknowabout andemergingpatternsinlarge-signalmeasurementtechniques,modeling,andnonlinear circuitdesigntheorysupportedbypracticalexamples. Topicscoveredinclude: • novellarge-signalmeasurementtechniquesthathavebecomeavailablewiththeintro- ductionofnonlinearvectornetworkanalyzers(NVNAs),suchastheLSNA,PNA-X, andSWAP • directextractionofdevicemodelsfromlarge-signalRFdynamicloadlines • characterizationofmemoryeffects(self-heating,traps)withpulsedRFmeasurements • interactivedesignofpower-efficientamplifiers(PAs)andoscillatorsusingultra-fast multi-harmonicactiveload-pull • Volterraandpoly-harmonicdistortion(X-parameters)behavioralmodeling • oscillatorphasenoisetheory • balancing,modeling,andpoly-harmoniclinearizationofbroadbandRFICmodulators • developmentofafrequency-selectivepredistortertolinearizePAs PATRICK ROBLIN is a Professor in the Department of Electrical and Computer EngineeringatOhioStateUniversity(OSU).HehasworkedatOSUsince1984,after receivinghisD.Sc.degreeinelectricalengineeringfromWashingtonUniversity.Heis thefounderoftheNonlinearRFResearchLaboratoryatOSUandpreviouslyco-wrote thebookHigh-SpeedHeterostructureDevices(CambridgeUniversityPress,2002). THE CAMBRIDGE RF AND MICROWAVE ENGINEERING SERIES SeriesEditor, SteveC.Cripps,DistinguishedResearchProfessor,CardiffUniversity Peter Aaen, Jaime Plá and John Wood, Modeling and Characterization of RF and Microwave PowerFETs Dominique Schreurs, Máirtín O’Droma, Anthony A. Goacher and Michael Gadringer, RF AmplifierBehavioralModeling Fan Yang and Yahya Rahmat-Samii, Electromagnetic Band Gap Structures in Antenna Engineering EnricoRubiola,PhaseNoiseandFrequencyStabilityinOscillators EarlMcCune,PracticalDigitalWirelessSignals StepanLucyszyn,AdvancedRFMEMS Forthcoming Matthias Rudolph, Christian Fager and David E. Root, Nonlinear Transistor Model Parameter ExtractionTechniques SorinVoinigescu,High-FrequencyIntegratedCircuits DavidE.Root,JasonHornandJanVerspecht,X-Parameters JohnL.B.Walker,HandbookofRFandMicrowaveSolid-StatePowerAmplifiers JohnWood,PeterAaenandMohamedSayed,ModernRFMicrowaveMeasurementTechniques RichardCarter,TheoryandDesignofMicrowaveTubes Anh-VuH.Pham,MorganJ.ChenandKuniaAihara,LCPforMicrowavePackagesandModules Nuno Borges Carvalho and Dominique Scheurs, Microwave and Wireless Measurement Techniques Nonlinear RF Circuits and Nonlinear Vector Network Analyzers Interactive Measurement and Design Techniques PATRICK ROBLIN OhioStateUniversity CAMBRIDGE UNIVERSITY PRESS Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,SãoPaulo,Delhi,Tokyo,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9780521889957 (cid:2)c CambridgeUniversityPress2011 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2011 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcatalogrecordforthispublicationisavailablefromtheBritishLibrary ISBN9780521889957Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. àGloria Contents Preface pagexi Acknowledgments xiv 1 Wirelesssignals 1 1.1 Modernwirelesscommunications 1 1.2 OFDMprimer 3 1.3 ImpactofclippingonOFDM 9 1.4 Spectralregrowthandclipping 12 1.5 Metrics 13 1.6 Multisine 14 References 15 2 Large-signalvectormeasurementtechniqueswithNVNAs 17 2.1 MeasurementofRFsignals 17 2.2 Principleofoperationofvectorlarge-signalmeasurements 19 2.3 Sampler-basedprincipleofoperation 23 2.4 Relativeandabsolutepowerandharmonicphasecalibrations 27 2.4.1 Calibrationforconnectorizeddevices 27 2.4.2 On-wafercalibration 33 2.5 TunerdeembeddingwiththeLSNA 35 2.5.1 Definitions 36 2.5.2 Extractionofβ ,γ ,andδ inTC 38 C C C 2.5.3 Extractionof(1/K )TP 38 C 2.5.4 ExtractionofLRRM(Z ) 39 x 2.6 ModulatedmeasurementsandIFcalibration 39 2.6.1 AbsolutetimereferencecalibrationforRFmodulatedmeasurements 40 2.7 BroadbandmeasurementswiththeLSNA 42 2.7.1 Principleofphasecalibration 44 2.7.2 Experimentalresultsanddiscussions 48 2.8 Pulsed-RFsmall-andlarge-signalmeasurements 51 2.8.1 Analysisofpulsed-RFsignals 52 2.8.2 PulsedI–V pulsed-RFmeasurementsystemwiththeLSNA 53 viii Contents 2.8.3 Measurementbandwidth 55 2.8.4 Envelopeanalysisofpulsed-RFsignals 56 2.9 Multiplerecordingofpulsed-RFsignals 58 2.9.1 MultiplerecordingforCWsignals 59 2.9.2 Multiplerecordingforjointlypulsedandmodulatedsignals 62 References 63 3 DevicemodelingandverificationwithNVNAmeasurements 66 3.1 Modelverification 66 3.2 Modelsymmetry 72 3.3 Deviceparasitics 75 3.4 Modelextractionfrompower-sweepmeasurements 81 3.5 Modelextractionfromdynamicloadlinemeasurements 83 References 87 4 CharacterizationandmodelingofmemoryeffectsinRFpowertransistors 89 4.1 ImportanceofmemoryeffectsinRFdevices 89 4.2 Distributedandtransientmodelsforself-heatinginpowertransistors 90 4.2.1 Steady-statethermalmodeling 90 4.2.2 Implementationofthedistributedthermalmodel 92 4.2.3 Transientthermalresponse 94 4.2.4 Modelingofthetransientthermalresponse 96 4.3 Identificationofself-heatingusingpulsedI–V pulsed-RFmeasurements 98 4.3.1 CWdynamicloadlinemeasurementsystem 99 4.3.2 PulsedI–V pulsed-RFloadlinemeasurementsystem 99 4.3.3 OriginoftheI–V kneewalk-outintheCW-RFloadlines 100 4.4 TrappinginGaNHEMTs 103 4.5 CharacterizationwithacombinedLSNA/DLOSsystem 105 4.6 Quasi-staticdeviceparasitics 108 4.7 Rateequationforphysicalmodelingoftrappingeffects 111 4.8 Two-trap-levelmodel 113 4.9 Cyclostationaryeffect 115 4.9.1 Theory 115 4.9.2 Experimentalinvestigations 116 References 120 5 Interactiveloadline-baseddesignofRFpoweramplifiers 124 5.1 Reviewofpoweramplifiersofvariousclasses(A–F) 124 5.2 Outputterminationwithload-pullmeasurements 134 5.2.1 Activeload-pullmeasurements 135 5.2.2 Real-timeactiveload-pullmeasurements 136 5.3 Class-FdesignwithRTALP 140 Contents ix 5.4 CompletedesigncycleforapHEMTamplifier 147 5.5 RTALPofPAsforpulsedI–V pulsed-RFclass-Boperation 150 5.6 P1dBcontourplot 154 5.7 Class-EPAoperation 155 References 158 6 Behavioralmodeling 160 6.1 BehavioralmodelforSISOandMIMOsystems 160 6.2 Volterramodeling 161 6.2.1 Volterraalgorithm 162 6.2.2 Modelderivation 165 6.2.3 Analyticexample 168 6.2.4 Modelextraction 171 6.2.5 Experimentalmodelextractionandvalidation 172 6.2.6 Phasereference 174 6.2.7 Poly-harmonicdistortionmodel(PHD) 175 6.3 Single-bandmulti-harmonicenvelopePAmodel 179 6.3.1 Inputsignal 180 6.3.2 OrthogonalChaillotexpansion 180 6.3.3 Memorylessnonlinearsystemmodeling 183 6.3.4 Quasi-memorylessnonlinearsystemmodeling 185 6.3.5 Power-seriesexpansion 186 6.3.6 Multi-pathmodelpartitioning 187 6.3.7 Time-selectivesingle-bandmulti-harmonicenvelope PAmodel 187 6.4 Two-bandfundamentalenvelopePAmodel 190 6.4.1 Nonlinearpower-amplifiercharacterizationwithNVNA 192 6.4.2 Extensiontohigher-ordernonlinearities 194 6.4.3 Modulatedtwo-bandmodel 195 6.5 Appendix:Volterraseriesexpansionforafour-toneexcitation 198 References 200 7 Kurokawatheoryofoscillatordesignandphase-noisetheory 201 7.1 Oscillatoroperatingpoint 201 7.2 Kurokawatheoryofoscillators 203 7.3 Vectormeasurementofdevicelinewithreal-timeactiveload-pull 207 7.3.1 Testoscillatorcircuit 207 7.3.2 Real-timemulti-harmonicactiveload-pullsystem 208 7.3.3 Experimentalresults 209 7.3.4 Self-oscillationtest 213 7.4 Impactofwhitenoiseonanoscillator 215 7.5 Impactof1/f noiseonanoscillator 222 7.5.1 DerivationofSa,1/f((cid:5)ω) 223 x Contents 7.5.2 Derivationof Sφ,1/f((cid:5)ω) 224 7.5.3 RangeofvalidityoftheKurokawaequations 227 7.6 Injectionlockingandadditivephase-noisemeasurements 229 7.6.1 Theory 229 7.6.2 Experimentalmeasurements 233 References 235 8 Design,modeling,andlinearizationofmixers,modulators,anddemodulators 237 8.1 VectorcharacterizationofanI–Qmodulator 237 8.1.1 BalancingofanI–Qmodulator 237 8.1.2 Kmodeling 238 8.1.3 I–QmodulatorcharacterizationwithLSNA 240 8.1.4 KmodelingofanI–QmodulatorandanI–Qdemodulatorchain 243 8.2 Polyphasemulti-pathtechnique 248 8.2.1 Nonlinearbehavior 249 8.2.2 Polyphasemulti-pathtechnique 249 8.3 Poly-harmonicmodelingofasingle-sidebandmodulator 253 8.3.1 Theory 253 8.3.2 Poly-harmonicpredistortionlinearizationtestresults 257 References 261 9 LinearizationofRFpoweramplifierswithmemory 262 9.1 Predistortionlinearizationandtheimpactofmemoryeffects 262 9.2 Predistortionforquasi-memorylessamplifiers 266 9.3 LinearizationforPAsmodeledwithmemorypolynomials 269 9.4 Two-bandfrequency-selectivepredistorter 274 References 279 Index 280