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Practical behavioral modeling technique of power amplifiers based on loadpull measurements

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Practical behavioral modeling technique of power amplifiers based on loadpull measurements
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Liu, Jiang
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Nonlinear system
Nonlinear modeling
Frequency-domain modeling
Large-signal network analysis
Memory effect
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ABSTRACT: Accurate linear and nonlinear models for devices and components are essential for successful RF/microwave computer aided engineering (CAE). The modeling techniques can be categorized in different levels based on the abstraction of the model as well as the application of the models at various design phases. This dissertation deals with behavioral modeling techniques for nonlinear RF components, especially amplifiers. There is an increasing demand for accurate behavioral models of RF and microwave components, or integrated circuit (IC) blocks used in wireless system designs. Accurate behavioral models help designers evaluate and select the appropriate components at simulation phase, thereby cutting development cost. However, there isnt a practical (or flexible) solution for accurate and effective behavioral model generation. This dissertation tries to tackle this problem. Power amplifiers and devices are the main components studied in this dissertation.The primary focus is on the characterization of the loadpull performance of power amplifiers and devices. Major contributions of this dissertation include development of advanced loadpull measurement procedures, large-signal load-aware behavioral model, and a load-aware behavioral model with memory-effect capabilities. There are two advanced loadpull measurements documented in this dissertation: the AM-PM loadpull measurement and the digital demodulation loadpull measurement. These two measurements may have been used internally by some research groups, however, according to the best knowledge of the author, they havent received much attention in the literature. This is the first published work on these two topics. It is shown in this work that the AM-PM performance can be strongly dependent on the load conditions. This property provides important information about the nonlinearities of power amplifiers and is used herein to create better behavioral models.This newly developed digital demodulation loadpull measurement procedure enables system designers to evaluate power amplifiers directly against digital communication system parameters such as error vector magnitude (EVM). Two example measurements are given to demonstrate the measurement system setup and the correlations between traditional nonlinear figure-of-merits and system metrics. A new behavioral modeling technique / procedure is developed based on loadpull AM-AM and AM-PM measurements. The large-signal scattering function theory is applied in the technique to formulate the model. The created model is able to automatically detect the load impedance and generate corresponding nonlinear properties. Three example models are presented to demonstrate the capability of this technique to predict accurately the output power contours, 50 ohm large-signal S21, and 3rd order intermodulation products (through additional file-based model).Finally, a modeling technique is demonstrated to enable predicting the linear memory effect within a varying load condition. The nonlinear block used in the traditional two-box model structure is replaced with the large-signal loadpull model mentioned above. By adding this new feature, the resulting model is able to predict the load-related AM-AM and AM-PM properties, which will improve the accuracy of ACPR prediction.
Thesis:
Thesis (Ph.D.)--University of South Florida, 2005.
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Includes bibliographical references.
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by Jiang Liu.
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PracticalBehavioralModelingTechniqueofPowerAmpliers BasedonLoadpull Measurements by JiangLiu Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofElectricalEngineering CollegeofEngineering UniversityofSouthFlorida Co-MajorProfessor:LawrenceP.Dunleavy,Ph.D. Co-MajorProfessor:HuseyinArslan,Ph.D. ThomasWeller,Ph.D. DennisKillinger,Ph.D. MiguelLabrador,Ph.D. DateofApproval: November07,2005 Keywords:nonlinearsystem,nonlinearmodeling,frequency-d omainmodeling, large-signalnetworkanalysis,memoryeect c r Copyright2005,JiangLiu

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DEDICATION Tomywifeandmyparentsfortheirsupportandencouragement

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ACKNOWLEDGEMENTS DuringmyjourneypursuingthisPh.Ddegree,lotsofpeopleha vegivenme selresshelpandencouragements.Thisdissertationwouldhavebe enimpossiblewithoutthem.Specialthankstomydissertationadvisors,LawrenceP .Dunleavyand HuseyinArslan,fortheirinvaluablesupport,inspirationandgui dance.Iwouldalso liketoexpressmyappreciationtomycommitteemembers,Dr.Th omasWeller, Dr.DennisKillingerandDr.MiguelLabrador.Theyhavebeen veryhelpfuland supportiveduringthisjourney. IwouldliketothankDr.JanVerspecht.Ihavebenetedalotfr omhisinsight andexperienceinthemodelingarea.Iamalsoverygratefulto Modelithicsforits resourcesandsupport.EspeciallyIwouldliketothankBillCla usenandJohnCapwell fortestingmodelsandgivingmefeedbacks. Mypresentandformercolleagueshavegivenmelotsofsupport. Iamverygrateful toBalajiLakshminarayananforbeingsuchawonderfulocemat eandforthoseactive discussions.IwouldliketothankAlbertoRodriguezforhisassistan ceinsolving measurementproblems.IalsowanttothankAnthonyWebsterandRav iVaranasi fortheproductivecollaborationandstimulatingdiscussions.I wishtothankTevk Yucek.Heisawonderfulfriendandhashelpedmeacademically andpersonally. Iwouldliketoexpressmyappreciationtomyparents,fortheir overwhelminglove andkindnessduringtheserstthirtyyearsofmylife.Specialt hankstomytwobig brothersandsister-in-lawsforsupportingmeworkingtowards myPh.Ddegree. Lastbutnotleast,Iwouldliketothankmylovelywife.Everyti mewhenI thoughtIcouldn'tnishthedegree,mywifehasbeenthere,en couragingmeand providingmethestrengthtocontinue.Withouthersupportand love,Idon'tknow howIcanachieveit.

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TABLEOFCONTENTS LISTOFTABLES iii LISTOFFIGURES iv ABSTRACT ix CHAPTER1INTRODUCTION 1 1.1Backgroundandmotivation 1 1.2Contributionofthedissertation 3 1.3Organization 4 CHAPTER2LITERATUREREVIEWONCURRENTBEHAVIORALMODELINGTECHNIQUESFORPOWERAMPLIFIERS6 2.1Introduction 6 2.2Introductionofnonlinearphenomena82.3ReviewofbehavioralmodelingtechniquesofPAs15 2.3.1Memorylessmodels 17 2.3.2Memoryeectmodeling22 2.4Proposedresearchtopics 30 2.5Conclusion 31 CHAPTER3ADVANCEDLOADPULLMEASUREMENTS32 3.1Introduction 32 3.2AM-PMloadpullmeasurementprocedure33 3.2.1Introduction 33 3.2.2IntroductionofatypicalVNAstructureandprocessingsteps 34 3.2.3AM-PMmeasurementthroughvectorreceiversetup353.2.4ExampleAM-PMresults37 3.3DigitalDemodulationloadpullmeasurementprocedure40 3.3.1DenitionandmeasurementofEVM403.3.2Measurementsystemandcalibrationconsideration413.3.3ExampleloadpullEVMmeasurementresults44 3.4Conclusion 49 i

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CHAPTER4LARGE-SIGNALSCATTERINGFUNCTIONMODELBASED ONLOADPULLMEASUREMENTDATASETS54 4.1Introduction 54 4.2Introductionoflarge-signalscatteringfunctiontheory 56 4.2.1Small-signalnetworkanalysis564.2.2Theoryofthelarge-signalscatteringfunction584.2.3Creationofthelarge-signalscatteringfunctionmodel 60 4.3Currentloadpull-basedmodelingtechniqueandtheirlim itations63 4.4Behavioralmodelbasedonloadpullgainandphasecompressionmeasurements 65 4.5Experimentalresult1:measurement-basedbehavioralmode l70 4.5.1ExamplemodelofapackagedRFICLNA714.5.2ExamplemodelofaPAsample79 4.6Experimentalresult2:simulation-basedbehavioralmodel 85 4.7Conclusion 90 CHAPTER5MEMORYEFFECTMODELINGOFPOWERAMPLIFIERS INLOADPULLCONDITIONS92 5.1Introduction 92 5.1.1Filteringmodelingofmemoryeects945.1.2Neuralnetworkmodelingofmemoryeects95 5.2Limitationofcurrentmodelingtechniquesandproposedso lution96 5.3Experimentalresults 99 5.4Conclusion 109 CHAPTER6CONCLUSIONSANDFUTURESTUDY111 6.1Conclusions 111 6.2Recommendationforfuturestudies113 REFERENCES 117 ABOUTTHEAUTHOR EndPage ii

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LISTOFTABLES Table4.1Listofthe6exampleloadrerectioncoecientsusedt o testtheLNAmodel. 74 Table4.2Listofthe6exampleloadrerectioncoecientsusedt o testthePAmodel. 81 Table4.3Simulationtimecomparison:behavioralmodelvs.ci rcuitmodel90 Table5.1Theoptimized5-tapFIRcoecients.104Table5.2ComparisonofthesimulatedACPRforlowersideband (67.0+j*93.8ohm).Averageinputpowerissetat20dBm.108 Table5.3ComparisonofthesimulatedACPRforuppersideband (67.0+j*93.8ohm).Averageinputpowerissetat20dBm.108 Table5.4ComparisonofthesimulatedACPRforlowersideband (50ohm).Averageinputpowerissetat20dBm.108 Table5.5ComparisonofthesimulatedACPRforuppersideband (50ohm).Averageinputpowerissetat20dBm.109 Table5.6ComparisonofthesimulatedACPRforlowersideband (5ohm).Averageinputpowerissetat20dBm.109 Table5.7ComparisonofthesimulatedACPRforuppersideband (5ohm).Averageinputpowerissetat20dBm.109 iii

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LISTOFFIGURES Figure1.1Generationofbehavioralmodelfromdierentdat asources: measurement-basedorsimulation-based.3 Figure2.1AM-AMandAM-PMperformanceofISL3990PAat5.24GHz.1 0 Figure2.2Outputspectrumofanonlinearcomponentundertwo toneexcitation. 11 Figure2.3Illustrationofthethirdorderinterceptpointco ncept.12 Figure2.4Illustrationofthespectralregrowtheectandthe ACPR concepts. 13 Figure2.5MeasurementexampleofIMsofaMAX2371amplier.14Figure2.6Anexample1.9GHzPCSpoweramplier.16Figure2.7Comparisonofdierentmodelsforapoweramplier sample.20 Figure2.8MeasuredAM-AMofaMurataXM5060PAfor5GHz 802.11aWLANapplications. 23 Figure2.9MeasuredAM-PMofaMurataXM5060PAfor5GHz 802.11aWLANapplications. 24 Figure2.10Twoboxmodel:nonlineareectandmemoryeecta re separatedintotwoblocks. 25 Figure2.11Threeboxmodel:twolterfunctionsareusedtomo del thememoryeect. 26 Figure2.12Illustrationoftheparallelwienermodel.28Figure2.13IllustrationoftheVolterra-seriesbasednonline armodel.29 Figure3.1SystemdiagramofHP8719D. 35 Figure3.2DataprocessingrowdiagramoftheHP8719DVNA.35 iv

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Figure3.3AM-PMloadpullmeasurementsystemdiagram.37Figure3.4ComparisonofmeasuredAM-AMandAM-PMresults fromtheVNAandtheloadpullsystemfortheLNAsam-pleat900MHz. 38 Figure3.5AM-AMandAM-PMloadpullmeasurementresultsat 900MHzfortheLNAsample.39 Figure3.6AM-AMandAM-PMloadpullmeasurementresultsat 2.14GHzforthehighpowerGaAsFETsample.39 Figure3.7EVMmeasurementdiagram. 41 Figure3.8Illustrationofthedigitaldemodulationloadpul lmeasurementsystem. 42 Figure3.9ComparisonofthesystemEVMandmeasuredEVMof theDUT. 43 Figure3.10ComparisonofthesystemACPRandmeasuredACPR oftheDUT. 44 Figure3.11ComparisonofthesystemandDUTEVM.45Figure3.12TransducergainandEVMcontoursforexamplesourcepullmeasurement. 46 Figure3.13TransducergainandEVMcontoursforexampleloadp ull measurement. 47 Figure3.14Sourcepull/loadpullEVMmeasurements;Pinissetat 22dBm.47 Figure3.15ImprovementoftheEVMperformancebytuningthel oad.48 Figure3.16ComparisonoftheGTandEVMcontoursatconstant outputpowerlevelof15and18dBm.50 Figure3.17ComparisonoftheACPRandEVMcontoursatconstant outputpowerlevelof15dBmand18dBm.51 Figure3.18ComparisonoftheIP3andEVMcontoursatconstant outputpowerlevelof15dBmand18dBm.52 Figure4.1Twoportnetworkwiththevoltageandcurrentden ition.56 Figure4.2Theinputandoutputvariablesforatwo-portnetw ork usedinthelarge-signalscatteringfunctiontheory.59 v

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Figure4.3FunctionalblockoftheLSNA.61Figure4.4Theinterpolationandextrapolationproblemwit hthe le-basedmodel. 65 Figure4.5Diagramofatwo-portnetwork.66Figure4.6TherowchartoftheMatlabprogramcreatedforthe behavioralmodeloptimizationbasedontheloadpullAM-AMandAM-PMdatasets. 70 Figure4.7IllustrationoftheMAXIM2373LNAsample.71Figure4.8Comparisonofthemeasuredandsimulatedgainandpha se compressionat50ohm. 72 Figure4.9Thesimulatedoutputpowercontoursarecomparedw ith themeasurements. 73 Figure4.10Comparisonofsimulatedandmeasuredoutputpowerc ontours.74 Figure4.11ComparisonofthemeasuredandsimulatedIP3usingth e large-signalbehavioralmodel. 75 Figure4.12Illustrationofthesixloadimpedanceexampleson the SmithChart. 75 Figure4.13ComparisonofthemeasuredandsimulatedPoutandIM 3 at6loadimpedances. 77 Figure4.14Theerrorsofthesimulatedfundamentaltoneat6l oads areplotted. 78 Figure4.15Theerrorsofthesimulated3rdorderintermodula tion productsat6loadsareplotted.78 Figure4.16IllustrationoftheISL3984powerampliersample .79 Figure4.17Comparisonofthesimulatedandmeasuredgainandph ase compressionin50ohm. 80 Figure4.18Comparisonofthesimulatedoutputpowercontourw ith themeasureddataset. 81 Figure4.19ComparisonofthesimulatedIM3contourusingthebe havioralmodelwiththemeasureddataset.81 vi

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Figure4.20Illustrationofthesixloadimpedanceexamplesuse dto testthebehavioralmodeldevelopedfortheISL3984ontheSmithChart. 82 Figure4.21ComparisonofthemeasuredandsimulatedPoutandIM 3 at6loadimpedances. 83 Figure4.22Theerrorsofthesimulatedfundamentaltoneat6l oads areplotted. 84 Figure4.23Theerrorsofthesimulated3rdorderintermodula tion productsat6loadsareplotted.84 Figure4.24Comparisonofthesimulatedgainandphasecompressio n under50ohmcondition:behavioralmodelvs.circuitmodel.8 6 Figure4.25ComparisonofthesimulatedPoutcontoursfromthe behavioralmodelandthecircuitmodelatconstantPinof10dBm. 87 Figure4.26ComparisonofthesimulatedPoutcontoursfromthe behavioralmodelandthecircuitmodelatconstantPinof30dBm. 87 Figure4.27ComparisonofthesimulatedIM3contoursfrombeha vioralmodels:oneoptimizedwithloadpullAM-PMinfor-mationandonewithout. 88 Figure4.28ComparisonofthesimulatedIM3contoursfromtheb ehavioralandcircuitmodels. 89 Figure4.29ComparisonofthesimulatedIM3fromthecircuitmo del andthebehavioralmodels. 89 Figure5.1Examplemeasurementsetuptoobtainthetime-domai n testsignal. 93 Figure5.2Modeldiagramcombininglinearlteringandnonl inear look-up-table(LUT)sections. 94 Figure5.3Diagramoftheproposedmemoryeectmodelwiththe load-relatednonlineargain/compressioncharacterizationfeatureintegrated. 97 Figure5.4Simulationschematicsetup:WLAN54MbpsOFDM sourceisused. 100 vii

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Figure5.5ComparisonofstaticanddynamicAM-AMandAM-PMeects. 101 Figure5.6ExtractedlinearmemoryeectfromthedynamicAMAMandAM-PMeect. 101 Figure5.7Thememoryeectbehavesindependentlyontheloa d impedances. 102 Figure5.8BadextractionofthelinearAM-AMandAM-PMdistortio n.103 Figure5.9IllustrationofinruenceofnonlinearAM-AMandAMPMcompressionontheoutputspectrum.104 Figure5.10Illustrationoftheeectofthelinearblock.105Figure5.11Comparisonofthesimulatedlinearmemoryeect:c ircuit modelvs.behavioralmodel. 105 Figure5.12Comparisonofthesimulatedoutputpower:behavio ral modelvs.circuitmodel. 106 Figure5.13Vericationofthebehavioralmodelwitha6MBps WLAN signal. 107 Figure5.14Comparisonofthesimulatedandmeasuredoutputspec trumoftheexamplepoweramplier.107 viii

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PRACTICALBEHAVIORALMODELINGTECHNIQUEOFPOWER AMPLIFIERSBASEDONLOADPULLMEASUREMENTS JiangLiu ABSTRACT Accuratelinearandnonlinearmodelsfordevicesandcompone ntsareessential forsuccessfulRF/microwavecomputeraidedengineering(CAE). Themodelingtechniquescanbecategorizedindierentlevelsbasedontheabstr actionofthemodel aswellastheapplicationofthemodelsatvariousdesignphase s.Thisdissertation dealswithbehavioralmodelingtechniquesfornonlinearRF components,especially ampliers. Thereisanincreasingdemandforaccuratebehavioralmodels ofRFandmicrowavecomponents,orintegratedcircuit(IC)blocksusedin wirelesssystemdesigns.Accuratebehavioralmodelshelpdesignersevaluateandse lecttheappropriate componentsatsimulationphase,therebycuttingdevelopment cost. However,thereisn'tapractical(orrexible)solutionforaccu rateandeective behavioralmodelgeneration.Thisdissertationtriestotack lethisproblem.Power ampliersanddevicesarethemaincomponentsstudiedinthis dissertation. Theprimaryfocusisonthecharacterizationoftheloadpull performanceofpower ampliersanddevices.Majorcontributionsofthisdissertati onincludedevelopment ofadvancedloadpullmeasurementprocedures,large-signallo ad-awarebehavioral model,andaload-awarebehavioralmodelwithmemory-eect capabilities. ix

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Therearetwoadvancedloadpullmeasurementsdocumentedint hisdissertation: theAM-PMloadpullmeasurementandthedigitaldemodulationl oadpullmeasurement.Thesetwomeasurementsmayhavebeenusedinternallybysom eresearch groups,however,accordingtothebestknowledgeoftheauthor ,theyhaven'treceivedmuchattentionintheliterature.Thisistherstpubl ishedworkonthesetwo topics. ItisshowninthisworkthattheAM-PMperformancecanbestrongl ydependentontheloadconditions.Thispropertyprovidesimportan tinformationabout thenonlinearitiesofpowerampliersandisusedhereintocr eatebetterbehavioral models. Thisnewlydevelopeddigitaldemodulationloadpullmeasure mentprocedureenablessystemdesignerstoevaluatepowerampliersdirectlyag ainstdigitalcommunicationsystemparameterssuchaserrorvectormagnitude(EVM) .Twoexample measurementsaregiventodemonstratethemeasurementsystemsetu pandthecorrelationsbetweentraditionalnonlineargure-of-merits andsystemmetrics. Anewbehavioralmodelingtechnique/procedureisdevelope dbasedonloadpull AM-AMandAM-PMmeasurements.Thelarge-signalscatteringfunctio ntheoryis appliedinthetechniquetoformulatethemodel.Thecreated modelisabletoautomaticallydetecttheloadimpedanceandgeneratecorrespond ingnonlinearproperties. Threeexamplemodelsarepresentedtodemonstratethecapabil ityofthistechnique topredictaccuratelytheoutputpowercontours,50ohmlarge -signalS21,and3rd orderintermodulationproducts(throughadditionalle-b asedmodel). Finally,amodelingtechniqueisdemonstratedtoenablepred ictingthelinear memoryeectwithinavaryingloadcondition.Thenonlinear blockusedinthe traditionaltwo-boxmodelstructureisreplacedwiththelar ge-signalloadpullmodel mentionedabove.Byaddingthisnewfeature,theresultingmo delisabletopredict x

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theload-relatedAM-AMandAM-PMproperties,whichwillimprove theaccuracyof ACPRprediction. xi

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CHAPTER1 INTRODUCTION 1.1Backgroundandmotivation Computeraidedengineering(CAE)softwarepackagesplayanim portantrolein researchanddevelopmentofwirelesscommunicationsystems.The yhelppredict thecomponentorsub-systemperformancepriorthehardwarepro totypeimplementation,cutthedevelopmentcostandreducethetimetomarket .Accuratemodelsfordevices/sub-systemsarethekeyforthesuccessfulapplicat ionofCAEsoftware.Ifthemodelsarenotaccurate,nomatterhowfastorprec isethesimulators are,thenalsimulationresultswon'tmatchprototypemeasure ments.Asignicant amountofresearchhasbeendevotedtowardsthedevelopmento fvarioustypesof devices/componentsmodels. Ingeneral,therearethreetypesofmodelingtechniqueswid elyusedinCAE tools.Theyarephysicaldevicemodeling,equivalentcircuit modelingandbehavioral modeling.Physicaldevicemodelsprovidethemostcomplexand completeinformationaboutthedevicestudied;howevertheyrequiresubstantia lcomputerresources, detaileddeviceinformationtypicallyunavailabletodesig ners.Physicalmodelsare thereforenotsuitableforcircuitdesigns. Equivalentcircuitmodelscanbeconsideredasanabstraction ofthephysicalmodels;circuitsofelementalelectricalcomponentsarearrang edinphysically-motivated topologiestorepresenttheelectricalcharacteristicsofth edevices.Themainchal1

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lengeofthistechniqueistondapropercircuitstructurean doptimizetheelements' valuestomatchtheperformanceofthedevices. Behavioralmodelsareanotherlevelofabstractionofthedev ice.Theyareasetof mathematicalexpressions,andcorrespondingttingcoecient s,thatcanrepresent theinput-outputrelationship.Behavioralmodelsprovidet heminimalsetofinput informationaboutthedeviceconstructionascomparedtooth ertwotypesofmodels. Theyalsorequiretheleastamountofsimulationtimeandaresuit ableforsystem leveldesigns[1]. Behavioralmodelscanbederivedfromtwodierentapproach es.Therstapproachistomeasuresamplesofthecomponentofinterestandtoc reatethemodel basedonthemeasurementresults.Thesecondapproachistousesimul ationdata fromlow-levelmodels(physicalmodelsorequivalentmodels) andcreatethebehavioralmodelsforhigherlevelsimulationtoreducethesimulat iontimes.Figure1.1 illustratesthetwoapproaches. Behavioralmodelingisreceivingmoreandmoreinterestrece ntly.Thisisbecauseoftheincreasingintegrationlevelinwirelessproducts, e.g.cellularphonesand personaldigitalassistants(PDA).Designersprefertousingo-th e-shelffunctional components,likelownoiseampliers(LNA)andpowerampliers( PAs),directlyin theirproductstominimizethediscretecomponentsinthesyste mandcutthenal cost.Accuratebehavioralmodelsforthesecomponentsarevery importantforthis practicetobesuccessful. Thishasmotivatedtheresearchworkdocumentedinthisdissert ation.Specically,thisdissertationtriestoaddressthebehavioralmodel ingproblemsforpower ampliers,whichareanimportantcomponentincurrentwirel esssystems. 2

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E C C S R BB' RR Collector Emitter BaseSubstrate Model Behavioral Measurement-basedBehavioral model generation generation Behavioral model Simulation-based B E Figure1.1Generationofbehavioralmodelfromdierentdat asources:measurementbasedorsimulation-based.1.2Contributionofthedissertation Anidealbehavioralmodelforanpowerampliershouldbeablet opredictthe nonlinearperformance,suchasgaincompressionandintermodu lationdistortionat dierentinputpowerlevelsundervarioussource/loadcondi tions.Moreover,itshould beabletopredictthedynamiceectsofampliersundermodu latedsignalstimuli. Lotsofresearchusingdierentapproacheshasbeendonetoach ievethisgoal.However,accordingtotheliteraturereviewthatisgiveninCha pter2,thisgoalhasn't beenmetyet. Thedissertationdocumentsabehavioralmodelthatcanmeetth erequirementof anaccuratenonlinearpowerampliermodelthrougheasilyob tainedmeasurements. Thecontributionofthisdissertationcanbesummarizedasthef ollowing: 3

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Twoadvancedloadpullmeasurementprocedureshavebeendeve lopedforbehavioralmodeling; Abehavioralmodelingtechniqueisdemonstratedtocreatela rge-signalscatteringfunctionmodelbasedonloadpullgainandphasecompressi on;example modelshavebeenillustratedshowingtheeectivenessofthist echnique; Anewbehavioralmodelisproposedtocombinetheloadpullmod elwiththe linearlteringmodeltoenablethepredictionofmemoryee ctatdierent loadconditions;thisfeaturemakesthemodelreadyforaccur atesystemlevel modeling. 1.3Organization Theorganizationofthisdissertationislistedbelow.Inchapt er2,adetailliteraturereviewaboutthecurrentbehavioralmodelingeort sisprovided.Dierent techniquesareintroducedbrieryandtheirlimitationsare discussed. Inchapter3,twoadvancedloadpullmeasurementproceduresa represented,namely loadpullAM-PMmeasurementandloadpullEVMmeasurement.Itissh owninthe chapterthattheloadimpedanceswillaectthephasecompressi onpropertyofampliers.Thisinformationisusedlatertodevelopthelarge-si gnalbehavioralmodels. AlsotheEVMofanamplierundervariousloadconditionsismeasu redandcomparedwiththeintermodulationdistortion.Similaritiesar eobservedforthesetwo gure-of-merits. Chapter4isdevotedentirelytointroducetheproposedmodel ingtechniquebased onloadpullgainandphasecompressionmeasurements.Generalrev iewofthelargesignalscatteringfunctiontheoryisgiven.Theproposedmodel exploitsthesame conceptbyextendingthesmall-signalS-parametermodeltoad dressthenonlinear 4

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eects.Anoptimizationprocessisdevelopedtotthemodelpar ameterstomatchthe measurementdatasets.Threeexamplemodelsarepresentedthatsh owthecapability ofthismodelingtechniqueforpredictingnonlinearperfor manceundervariedload situations. AnewbehavioralmodelisproposedinChapter5topredictthem emoryeect undervariedloadpullconditions.Thisisachievedbycombin ingthemodeldesignedin Chapter4andalinearlteringfunction.Experimentalresul tsaregivenoutproving theeectivenessofthismethod.InChapter6,conclusionsare drawnandfuture studiesarerecommended. 5

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CHAPTER2 LITERATUREREVIEWONCURRENTBEHAVIORALMODELING TECHNIQUESFORPOWERAMPLIFIERS 2.1Introduction Generallyspeaking,themodelsusedinCAEtoolscanbegroupedi ntothreecategories:physicaldevicemodels,equivalentcircuittransistor modelsandbehavioral models.Physicaldevicemodelsarebasedonthedescriptionofca rriertransport physics.Thesekindofmodelsprovideinvaluableinsightintoho wthedevicesoperate aswellastheirelectricalproperties,suchasDC,ACandtransi entperformances. However,Thecompletenessofthesemodelsrequiredetailed(of tenproprietary)informationaboutdevicegeometriesandfabricationpropert ies.Themodelsgenerate hugedemandforcomputingpower,aswell.Therefore,theyar enotsuitableforcircuit designs. Equivalentcircuitmodelsarecomposedofelectricalelemen tssuchasresistors, capacitors,inductors,andnonlinearcurrentorvoltagesourc es,whichcancharacterize theelectricalpropertiesoftransistors.Thereareallkindso fequivalentcircuitsfor dierenttypesoftransistors,suchasBJT,CMOSorMESFET.Thisk indofmodeling techniquedoesn'tdependonthedevicephysicstoderivetheel ectricalproperties fromthecarriertransportequations.Comparedwithphysicald evicemodels,the equivalentmodelsrequiremuchlesscomputationpower.Howev er,thelimitation associatedwiththismodelingtechniqueisthatitisdicultt ocomeupwitha suitablecircuitstructureandttheparameterstomatchthem easuredproperties. 6

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Behavioralmodelsprovideanotherlevelofabstractiontore presentthedevice performance.Theyareasetofmathematicalexpressionsthatde scribetheessential electricalproperties.Mostofthetime,onlytheinput-outpu trelationshipisofinterest.Sothebehavioralmodelingreducestondasuitableeq uationtomatchthe outputtotheinput.Typically,asimulationusingbehavioral modelswillrequirethe leastamountoftime.Thecostofthistechniqueisthatthemode lisonlyasaccurate asthedatagivenandtheappropriatenessoftheequationstor epresentthemeasured behavior. Inthisresearch,thefocusisonthebehavioralmodelingofno nlinearpowerampliers.Powerampliers(PAs)arecriticalcomponentsinwire lesscommunication systems.Oftentheyarethenalstageforthesignalamplication .Theyprovidehigh gaintotheinputsignal,enablingthesignaltotransmitthroug htheradiochannel andbedetectedbythereceiver.Ontheotherhand,theycancr eatelargein-band andout-of-banddistortionandinterferencethatneedstobe takencareof,otherwise theoutputsignalwon'tbedetectedcorrectly.Hence,theirpe rformance,toalarge extent,decideswhetherthewholesystemcanworkproperlyorn ot.Accuratemodels ofPAsarerequiredforsystemevaluationandverication. Numerousmodelingtechniqueshavebeenreportedinthepastsev eralyears.The researcheortsrangefromsimulatingthecompressionproperti esofaPAunderonetonestimulustocapturingtransientinput-outputrelationsh ipinthetime-domain. InSection2.3,thebasictheoriesofthesemodelingtechnique sarereviewedand summarized.Despitethesereportedtechniques,therearestillso mequestionsthat needtobeanswered.InSection2.4,severaloftheproblemsare pointedoutforthe currentresearchmethods.Theseproblemswillbeaddressedinthe dissertation.To begin,let'sbrieryreviewinthefollowingsectionthebasicn onlinearphenomenathat areincurredbythePAs. 7

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2.2Introductionofnonlinearphenomena Thepowerampliers(PA)nonlineareectsareusuallypresente dinfrequency generationanddistortion.Typicalnonlinearphenomenainc ludethefollowing: harmonicdistortion AM-AMandAM-PMconversion intermodulationandinterceptpoint adjacentchannelpowerratio dynamicrange. Thefollowingexampleisprovidedtoillustratetheseconcept s. OnesimplewayanonlinearPAcanberepresentedisbythepolyno mialfunction showninEquation2.1: y ( t )= k 1 x ( t )+ k 2 x ( t ) 2 + k 3 x ( t ) 3 (2.1) where x ( t )and y ( t )aretheinputandoutputsignalofthecomponentrespectively .We willusethisrepresentationofPAnonlinearitytoillustratea nddenetheabovelisted nonlinearphenomena.Assumetheinputsignal x ( t )isasinglestimulusfrequency, i.e. x ( t )= A cos( !t )(2.2) bysubstituting x ( t )intoEquation2.1,followingexpressionisobtainedthrough expansion: y ( t )= 1 2 k 2 A 2 +( k 1 A + 3 4 k 3 A 3 )cos( !t )+ 1 2 k 2 A 2 cos(2 !t )+ 1 4 k 3 A 3 cos(3 !t )(2.3) 8

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Althoughthereisonlyonefrequencyexcitation attheinput,severalnewfrequencies,2 and3 ,aregeneratedduetothenonlinearoperationofthePAs.These frequenciesaredenedastheharmonicsoftheexcitationfr equency,i.e. m! ,where misaninteger.Oftentheexcitationfrequencyisalsocalled fundamentalfrequency. Theharmonicdistortion(HD)isdenedastheratiooftheharmo nictothefundamentalresponse.Forthesingle-toneexampleshownabove(Equat ion2.3,thesecond harmonicdistortiondenotedas HD 2 canbewrittenas HD 2 = k 2 A 2 2 k 1 A (2.4) Noticethatthefundamentaltoneconsistsoftwoitems,onefromt heoriginalinput andtheotherfromthethirdordermixingproductof2 ! k 3 x ( t ) 2 .Thispart isconsideredasinterferencefromhigherorderharmonicsth atcontaminatestherst orderlinearresponse.WhencomputingtheHD,onlytheresponseof thefundamental frequencyshouldbeconsidered. AM-AMandAM-PMaredenedastheshiftinamplitudeorphaseofthef undamentaltoneattheoutputportduetothechangesintheinpu tsignalamplitude. Forthisexample,thefundamentaltoneattheoutputis k 1 A + 3 4 k 3 A 3 ,includinga lineartermandthecontributionofthe3rdordermixingprod uct.Becausetheoutput powerisnite, k 3 hastobeanegativevaluetomakeastablesystem.Thiscauses compressioninthefundamentalfrequencypowerlevel.Thisis denotedasAM-AM eectorgaincompression.OnegureofmeritforAM-AMisthe1dBc ompression point(P1dB),wherethegaindecreasesby1dBcomparedtotheo riginalvalue. Furthermore,ifthe3rdorderproductisnotin-phasewiththe input,thatwould causethephaseshiftinthefundamentaltone,whichcanbeeasily observedinthe 9

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frequencydomainaccordingto: Y ( )= k 1 A + 3 4 k 3 A 3 e j (2.5) where isthephasedierenceofthelinearand3rdterm.Thiseectis referredto AM-PMconversion.Obviously,AM-PMoccurswhenthePAisdriveni ntoahigh compressionregion.Figure2.1showstheAM-AMandAM-PMeectofan ISL3990 poweramplier.Thecompressionandphaseshiftofthefundament altoneareobvious withtheincrementoftheinputtone.The1dBcompressionpoint occursattheinput levelof-6dBm. 13 14 15 16 17 18 19 20 21 22 23 24 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 0 2 4 6 8 10 12 14 Pout (dBm) Phase Variation (degree) Pin (dBm) Output Power and Phase vs. Input Power Gain Phase Figure2.1AM-AMandAM-PMperformanceofISL3990PAat5.24GHz. Nowlet'sassumetheinput x ( t )isatwo-toneexcitation,i.e. x ( t )= A ( cos ( 1 t )+ cos ( 2 t ))(2.6) theexpansionofEquation2.1leadstotheresultshownfollowin g: 10

PAGE 25

y ( t )= k 2 A 2 +( k 1 A + 9 4 k 3 A 3 )( cos ( 1 t )+ cos ( 2 t )) + 1 2 k 2 A 2 ( cos (2 1 t )+ cos (2 2 t )) + k 2 A 2 ( cos ( 1 t 2 t )+ cos ( 1 t + 2 t )) + 1 4 k 3 A 3 cos (3 1 t )+ cos (3 2 t )) + 3 4 k 3 A 3 ( cos ( 2 t +2 1 t )+ cos ( 2 t +2 1 t ) + cos ( 1 t 2 2 t )+ cos ( 1 t +2 2 t ))(2.7) Forthiscase,besidestheharmonicsofthefundamentalinputt ones,morefrequencycomponentsareobservedthatobeytherelationship m! 1 n! 2 ,themixing ofthetwoinputexcitationtones.Thesecomponentsaredened astheintermodulation(IM)products.Figure2.2showsatypicaloutputspectr umofanonlinear component. DC Figure2.2Outputspectrumofanonlinearcomponentundertwo -toneexcitation. OfthemultipleIMproducts,2 1 2 and2 2 1 areofmostinterestbecause theyareclosetothefundamentalfrequencyanddiculttolt erout.Thepowerlevel ofthesetwoIMs, 3 4 k 3 A 3 ,isproportionaltothecubeoftheinputsignalamplitude A 11

PAGE 26

whilethefundamentaltoneattheoutputisapproximatelyli neartothat,assuming theinputpowerlevelislowandneglectingcontributionfro motherIMproducts. Thereisa3:1ratiobetweentheamplitudesoftheIM3andthef undamentaltone, whichcanbeobservedfromFigure2.3. Noise Floor IP3 1dB Fund. tone 3rd IM P1dBInput Power Level (dBm) OutputLevel(dBm) Dynamic Range 1 1 1 3 Figure2.3Illustrationofthethirdorderinterceptpointco ncept. Ascanbeseen,theextrapolationofthepowerofthefundamenta landthethird orderIM(IM3)productswillintersect.Theintersectionpoin tisdenedasthethird orderinterceptpoint(IP3).Althoughthispointistotallya theoreticalvalue,itisa usefulquantitytoestimatetheIM3distortion. Fordigitalcommunicationapplicationswherecomplexmodu lationtechniquesare utilized,thesinusoidalrepresentationofthestimulussignali snolongervalidto simulatethedistortioneect.Forthissituation,ACPRisofte nusedtorepresent thedistortioneect.Asthenameimplies,ACPRrepresentsthespe ctralleakageto thenearbychannelsduetothedistortioneectandisquanti edasthepowerratio betweentheadjacentchannelandthemainchannels,asdened inEquation2.8: 12

PAGE 27

ACPR = P adjacent P main (2.8) Obviously,theACPRmeasurementdependsonthedenitionofth emainchannel andtheadjacentchannel(whichisoftengivenoutinthespeci cationsofwireless communicationsystems,likeW-CDMAorIS-95).Figure2.4illust ratesthespectral regrowtheect.Signicantpowerleakageoutofthemaincha nnelcanbeseeninthe gure. -2 -1 0 1 2 -120 -100 -80 -60 -40 -20 0 20 Frequency (MHz)Power (dBm) Lower Adjacent Channel Upper Adjacent Channel Main Channel Figure2.4Illustrationofthespectralregrowtheectandthe ACPRconcepts.The mainchannelandadjacentchannelaregiveout,whichwillbe usedforACPRcalculation. Anotherimportantconceptisthedynamicrange(DR),showninF igure2.3,that denestheregionwherethenonlinearcomponentpreservesli nearperformancedue tolowpowerinput.Itislimitedatthelowersidebythenoisero orwhiletheupper levelisusuallyequalto1dBcompressionpoint. ThemeasurementresultofarealPAisgivenoutinFigure2.5tod emonstrate theIMeect.MeasuredIM3,IM5andIM7(third,fthand7thord erIMproducts) 13

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andthefundamentalfrequencyareillustrated.Noticetherei sadropinIM3power levelaroundaninputpowerof-13dBm.Thisphenomenonisoft encalledas\sweet spot"wheretheIMdistortionwillbemuchbetterthanatotherp owerlevels.Thisis causedbythedestructivesummationofdierentcontributorst otheIM3.Thiseect canbeexploitedinPAdesignstogethigheroutputpowerlevel andeciencyandat thesametimemaintainlowIM3distortion. -120 -100 -80 -60 -40 -20 0 20 -45 -40 -35 -30 -25 -20 -15 -10 -5 Product Power (dB)Pin (dBm) Comparison of the power of fundamental and IM products Fund 3rd IM 5th IM 7th IM Figure2.5MeasurementexampleofIMsofaMAX2371amplier. Obviously,theexamplemodelshowninEquation2.1cannotpred ictthehigher orderIMproducts,simplybecauseoftheloworderofthepolynom ial.Thisalso demonstratestheimportanceofmodelingforaccuratesimulat ionandpredictionof circuit/systemperformance.Inthefollowingsection,curren tstateofartmodeling techniquesforPAsareintroducedindetail. 14

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2.3ReviewofbehavioralmodelingtechniquesofPAs TherearetwopracticalapproachestomodelPAs:circuit-leve lmodelingand behavioralmodeling.Incircuit-levelmodeling,onehasto haveagoodknowledgeof thePA'sstructure;themodelperformancereliesgreatlyonth eaccuratemodelforthe nonlineardevicesusedinthecircuit.Figure2.6givesanexa mple1.9GHzPCSpower amplierdesignusingapackagedFETdevice,lumpedcomponent sanddistributed matchingcircuits.TheaccuracyofthesimulationofthePAdep endsonthemodels fortheelementsinthecircuits,especiallythenonlinearFET device.Usuallythe nonlineardevicessuchasBJTsorMOSFETarerepresentedbyane quivalentcircuit, inwhichoneorseveralnonlinearelementsareincluded.These nonlinearelements areoftenreferredasthebasicnonlinearities[2].Typicaln onlinearelementsinclude: nonlinearconductance nonlineartransconductance nonlinearresistance nonlineartransresistance Behavioralmodeling,ontheotherhand,issimplyamathemati caland/ordatale-basedcharacterizationoftheessentialnonlinearproper tiesofthegivencircuit [1].IttreatsthePAsystemasablackbox;theonlythingthatma ttersisthe relationshipbetweentheinputandoutputsignals.Oncetheinp ut/outputsignals areobtained,eitherfrommeasurementsorsimulation,mathem aticalequations,datale-basedlook-up-table(LUT)orneuralnetworkstructuresca nthenbecreatedto replicateandpredicttheperformanceofthePAs.Thismethodi sespeciallyuseful forsystemengineerswhoareonlyinterestedintheinteraction ofthePAswithother blocksinasystem.That'sbecausebyusingbehavioralmodels,the simulationtime 15

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Figure2.6Anexample1.9GHzPCSpoweramplier. willbedecreasedsignicantly,thereforeincreasingtheengi neers'productivity.Infact, behavioralmodelingisindispensablebecauseitispracticall yimpossibletosimulate theentiresystematthetransistorlevelwiththecomplexdigita llymodulatedsignal astheinput[1]. Theinput-outputrelationshipofaPAisdescribedbythenonli nearparameters introducedintheSection2.2.AM-AMandAM-PMaretwomostwidely usedparametersinPAbehavioralmodeling,becausetheseparameterscap turesignicantpart ofthePAnonlinearitiesandtheycanbeeasilymodeled.Amode lthatpredictsonly theAM-AMandAM-PMeectsisoftenreferredtoamemorylessmodel ,ormild memorymodel.Here\memoryless"PAmeansthatthecurrentoutpu tsignalfrom thePAunderstudyisonlydeterminedbythecurrentinputsigna landisnotaected bypreviousinputoroutputsignalsamples.A\memory"modelind icatesthatthe currentoutputsignalisaectedbyboththepresentinputaswe llaspreviousinput/outputsignals.The\memory"eectcanbeobserved,inthef requency-domain, astheasymmetricIMDperformanceofIMproducts,e.g.powerle veldierencesfor 16

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theupperandlowerIM3andIM5.OritisshownasthedynamicAM-AM and AM-PMcurvesbylookingatthetime-domainsignalsamples.Theme moryeectis causedbyseveralissues,includinginputandoutputtunednetwor k,lowfrequency dispersion,electrothermalinteractionsandbiascircuitry [3],[4].Memoryeectsof aPAinruencetheperformanceofthesystemsignicantly,andth erefore,needtobe treatedcarefully[5].2.3.1Memorylessmodels AmongthevarietiesofthemathematicalexpressionsforAM-AMand AM-PM modeling,Saleh'smodelandthepolynomialfunctionsareut ilizedandreportedextensivelyintheliterature.Equation2.1giveninSection2. 2isatypicalpolynomial modelforaPA.Themodelcanbeeasilycreatedusingcurve-ttin galgorithmifthe measureddataisavailable.Onecanuseseparateexpressionstomo deltheAM-AM andAM-PMrespectively,orusingcomplexpowerseriestointegra tethetwoeects together[6].Byincreasingtheorderofthepolynomial,accu ratereplicationofthe AM-AMandAM-PMdatacanbeobtained.Thepolynomialmodelsarew idelyutilizedforPAcharacterization[6,7,8,9,10,11].Zhoupoint edoutthatpolynomial isnotsuitableforstrongnonlinearitiessuchashardlimiters butareappropriatefor weaklynonlineardevices[12].Asignicantlimitationofth ismethodisthatthe modelmaybehavebadlyforextrapolation. Salehproposedin[13]tworationalfunctionstomodeltheAM-AM andAMPMeectsofatravelling-wavetubeamplier(TWTA).Thismod elisutilizedin [14,15,16,17].ThemodelsaregivenoutinEquation2.9andE quation2.10: A ( r )= a r 1+ a r 2 (2.9) 17

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( r )= r 2 1+ r 2 (2.10) Theapplicationofthismodelneedstobecarefulbecausethis modelwasdeveloped primarilyforTWTAsanditmaynotsuitableforsolid-statepower amplier(SSPA) modeling.Asmentionedin[18],SSPAshaveamorelinearperfor manceinthesmallsignalregion(lowpower)thanTWTAsinthesaturationregion(h ighpower);the outputpoweroftheSSPAstendstoapproachasymptoticallyasat urationvaluewhile TWTAsmaypresenta\roll-over"eect. Ghorbani[19]proposedasimilarmodelandaddedtwomorettin gelementsto remedythelimitationoftheSaleh'smodel,asshowninEquati on2.11and2.12. Intuitively,thelastiteminthefunctionshouldhelpcompensa tingthe\roll-over" eect. A ( r )= x 1 r x 2 1+ x 3 r x 2 + x 4 r (2.11) ( r )= y 1 r y 2 1+ y 3 r y 2 + y 4 r (2.12) Rapp[20]presentedanAM-AMmodelthataimsatSSPAs.InEquation 2.13, isthesaturationlevelattheoutputand isthesmoothingfactor[18]. A ( r )= r (1+( j r j ) 2 ) 1 2 (2.13) White[18]comparedtheprevious3mathematicalmodelsandp roposedanew4 parameterexpressionthataimsatKa-bandSSPAs,asgivenoutinE quation2.14. ComparedtothelimitationsinRapp'smodelinreproducingt hegradualtransition betweenlinearregionandsaturationregion,theWhite'smod elusesanexponential termtodescribethisgradualtransitionandaRayleightermto linearizethetypical 18

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operatingoftheKa-bandSSPAs. A ( r )= a (1 e br )+ cre dr 2 (2.14) WhitealsoproposedanAM/PMmodel,giveninEquation2.15.Howev er,this modelisnotgoodforthispurpose,sinceitcannotrepresentthe nonlinearprogression ofthephasechangeswithrespecttotheinputamplitude. ( r )= 8><>: f (1 e g ( r h ) ) ;r h 0 ;r
PAGE 34

theinputsignalexceedsthemeasurementrange,theperforman ceoftheextrapolation fromdierentmodelsisquitedierent.Polynomialmodelan dWhitemodelincrease signicantly.Rappmodeliskeptrat,simulatingthesaturatio nlevel.AndtheTanh modelpresentsthedecrement.Sincetheoutputpowerofagene ralpoweramplier tendstodroptosomeextentwhentheinputpowerhitsthesatura tionregion,the TanhmodelandtheSalehmodelaremorerealistic.Amongthesetw omodels,Tanh modelhasabettermatchformeasurementdataset.Therefore,t heTanhmodelhas thebestperformanceamongthesixmathematicalmodelsforthi sexampleamplier. 12 14 16 18 20 22 24 26 28 30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Pout (dBm)Vin (Volts) Comparison of Different Models for AM/AM Fitting poly model rapp model white model tanh model saleh model Ghorbani model measured Figure2.7Comparisonofdierentmodelsforapoweramplier sample.Thispower amplierisdesignedfor802.11aWLANapplicationsat5.2GHz. Besidesthemathematicalmodelsdescribedabove,severalothe rmodelsarealso reported.Hischkeetal.[22]appliedthirdordersplinefuncti oninampliermodeling.Splinefunctioniscomposedofmultiplepolynomialsc onnectedatspecied breakpoints.Comparedtopolynomialfunctions,ithasmorere xibilityandisgood 20

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atmodelingsharptransitions.However,sincemostPAshavesmoothtr ansitioncharacteristics,itisnotagoodoptionconsideringtheaddedcompl exity. O'Tooleetal.[23]usedneuralnetwork-Besseltransformtomode lthebehavioral ofamemorylessPA.ThereportedACPRsimulationresultusingwide bandcode divisionmultipleaccess(WCDMA)signalshows1dBimprovementov ertraditional behavioralmodels.Fourier-exponentialseriesisalsoapplie dtomodelPAs'transfer characteristicstohelpdesignecientpredistorter[24]. Honkanenetal.[25]and[26]proposedabipolarampliermodel thathasa substantiatedsemi-physicalbasis.Thetransfercharacteristicof thebipolaramplier atlowinputpowerregionisrepresentedbyanexponentialfun ctionthattakesinto accountthebiascondition.Thesaturatedregionismodeledb yRapp'smodelto capturethesmoothtransitionbetweenthetworegions.Across-ov erfactorisaddedto modeltheweakconductionofthetransistorsatverylowinputp owerlevels.Usually thiseectisconcealedbynoiseroorandcannotbeobservedfro mgaincompression measurement.Two-tonemeasurementsarerequiredtorevealit .Thedetailedmodel islistedinEquation2.18 V out ( V in )= sign( V in ) V 0 out ( j V in j ) (1+( V 0 out ( j V in j A 0 ) 2 p ) 1 2 p (tanh( j V in j )) 1 c (2.18) where V 0 out ( j V in j )is: V 0 out ( j V in j )= 8><>: e kV b ( e kV in 1) ;V in + V b V in;tr v ( V in + V b )+ b e kV b +1 ;V in + V b >V in;tr 21

PAGE 36

GoodIM3andIM5simulationresultsarereported.Thelimitati onofthemodelis thatthismethodisbasedontheBJTphysicsandcannotbeusedfor FETampliers duetothephysicaldierencesoftheinput/outputtransferpr ocesses. 2.3.2Memoryeectmodeling ThememoryeectofaPAdescribestheinput-outputrelationsh ipintime-domain andcanbeobservedindynamicAM-AMandAM-PMcurves.Wheninspecte din frequencydomainusingtwo-tonemeasurements,itisshowninthe IMasymmetryand IMDvariation[27].Thememoryeectismoresignicantinsyste msthathavelarge signalbandwidth,e.g.WCDMAmulti-carriersystemand802.11a WLANsystem. Reasonsforthememoryeectinclude([27],[28]and[29]): frequencyresponseofthematchnetworks, Non-constantimpedanceinDCbiascircuits, nonlinearcapacitancesofthetransistors, andself-heatingeects Asanexampleofthememoryeect,aMurataGaAsXM5060powerampl ier samplewasmeasuredatdierentcarrierfrequencies.Figure2. 8andFigure2.9illustratethevariationofthegainandphaseofthepoweramplier atdierentfrequencies [30][31].Accordingtothegures,thisamplierhaslessdistor tionatthehigherfrequencies(higherP1dBandlessAM-PMdistortion)andasmallerga incomparedto lowerfrequencies.Noticethatthevariationofthegain/phase maybedierentfor dierentPAs,dependingonthecircuitdesign. BasedonthefactthattheAM-AMandAM-PMcurvesaresimilartoeach other, Poza[32]wasabletosimulatethefrequencyeectbyscalingan dshiftingthegain 22

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21 22 23 24 25 26 27 28 29 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 Gain (dB)Pin (dBm) Gain vs. Input Power and Frequencies 5.18GHz 5.20GHz 5.22GHz 5.24GHz 5.26GHz 5.28GHz 5.30GHz 5.32GHz 5.745GHz 5.765GHz 5.785GHz 5.805GHz Figure2.8MeasuredAM-AMofaMurataXM5060PAfor5GHz802.11aWLANapplications. 23

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0 5 10 15 20 25 30 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 Phase (degree)Power (dBm) AM-PM effects at different frequencies 5.18GHz 5.20GHz 5.22GHz 5.24GHz 5.26GHz 5.28GHz 5.30GHz 5.32GHz 5.745GHz 5.765GHz 5.785GHz 5.805GHz Figure2.9MeasuredAM-PMofaMurataXM5060PAfor5GHz802.11aWL AN applications. 24

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filter AM-AMAM-PM Figure2.10Twoboxmodel:nonlineareectandmemoryeecta reseparatedinto twoblocks[13].curves.Thisisastraightforwardapproachandcanbeeasilyimp lemented.The downsideisthatthecurvesmeasuredatdierentfrequenciesm aynotmaintaintheir shape,whichdeterminesthatthismethodisatbestanapproxim ation.Salehextendedhismemorylessmodel[13]byndingthemodelparamete rsatanyfrequency andgroupingthemtogethertoprovidefrequencydependency .Thelimitationofthis method,similarlytoPoza'smodel,liesinthattheshapeofthe curvesisdetermined bytherationalfunctionsandisnotrexibleforPAswithvaryi ngshapesofAM-AM andAM-PMcurves.Elaboratettingalgorithmsareneededforb estt. Thedisadvantageofthepreviousmethodsisthattheyuseone-t onemeasurement results,assumingthememoryeectcapturedinthiswayisaccura telyenough.However,aspointedoutin[33],whenawidebandsignalispassedthr oughthesystem, themodelcannotpredicttheinteractionbetweentheinstant aneoustones.Another limitationisthatthemodelcannotpredictthevariationin theAM-AMandAM-PM withvaryingtonespacings,whichusuallyappearsintwo-tonem easurementresults. Tocapturethedynamicpropertiesofthegainandphasecompre ssion,several modelshavebeenproposed,e.g.[32,13,34,35].Generally,t hesemodelshave atwo-boxorthree-boxstructure,asshowninFigure2.10andFi gure2.11.The underlyingassumptionisthatthenonlineareectandthememo ryeectcanbe separatedwithoutlosingaccuracy. 25

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filter AM-AMAM-PM Memoryless NL model Memory Effect filter Figure2.11Threeboxmodel:twolterfunctionsareusedtomo delthememoryeect [35]. Launay[34]appliedmovingaverage(MA)ltertoaddressthepr oblem,whichis showninEquation2.19and2.20.Onefrequencyischosenasther eferenceandthe coecientsofthenonlinearmodelisderivedbyttingthemo deltotheAM-AMand AM-PMmeasuredresults.Atthisfrequency,thelterattenuatio nisunitary.Then thecoecientsofthelterareestimatedbysolvingEquation2 .21 G (~ z )= X a n ~ z n (nonlinearmodel)(2.19) H ( f )= P 1 X k =0 a k ( V e ) e j 2 kf=P (ltermodel)(2.20) P 1 X k =0 a k ( V e ) e j 2 f j T e k = V e ( f ref ) V e ( f j ) (2.21) f j isthe j th frequency, T e isthesamplingperiod,andPisthesizeoftheMAlter. Similarly,amulti-tappolynomialmodelisproposedin[5]an d[36].Thismethod characterizesthein-phaseandquadraturecomponentssepara tely.Atwo-tapmodel showstheestimatedACPRerroriswithin0.7dB[36].In[37]the authorsused aWienerltertomodelthesmall-signalmemoryeectandtheSa lehmodelfor nonlinearity.TheWienerlterusedinthiscasebasicallyisac onvolutionoperation 26

PAGE 41

ontheinputsignal.Optimalmemorylength(tapsoftheWiener lter)canbefound toobtaintheminimummean-squareerror(MSE). ToobservethePAs'performanceinarealisticsituation,digital lymodulatedsignalsandmulti-sinesignalsareusedinPAmeasurementsandchara cterization,such astheworkreportedin[38],[39],and[40].Auto-regressionmo vingaverage(ARMA) modelsarederivedfromthesemeasurements,whichcanbegenera lizedinEquation2.22: A ( q ) y ( t )= q n k B ( q ) C ( q ) u ( t )+ D ( q ) F ( q ) e ( t )(2.22) whereuandyareinput/outputsignals;A,B,C,D,Farepolynomia lfunctions; qisthedelayoperator.Themodeltreportedin[38]iswithi ntheorderof96%. [39]alsopointsoutthatdierentmodulatedstimulusmayresul tindierentorder ofmemorylength.Forexample,11thordernonlinearARMAmode lissucient forbinaryphaseshiftkeying(BPSK)modulation,while23rdor derisrequiredfor minimumshiftkeying(MSK)toobtainsimilaraccuracy. In[35,33]theauthorsgaveadetaildescriptionandanalysiso fthetwo-tone measurementprocedureutilizedforPAmodeling.Athree-box modelwasdeveloped basedontheobtaineddataset.Generallyspeaking,thismodelc anbetreatedasan improvedversionofPozaandSalehmodel. CarvalhoandPedro[41]studiedtheoriginfortheasymmetricI MDperformance observedinpowerampliers.Adescribingfunctioncombinedwi thsmall-signalmodel wasusedtomodelthelarge-signalIMDperformance.Kuetal[42 ]emphasizedon theeectofthefrequencyspacingoftheinputtonesontheIMD performance.A two-dimensionaltransferfunction(frequencytonespacingan dinputsignalpower level)wasdevelopedtocharacterizethelongtimeconstantm emoryeects.Apar27

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Figure2.12Illustrationoftheparallelwienermodel[42]. allelWienermodelwascreatedbasedonthefrequencydepende nttransferfunction. Figure2.12illustratesthemodelstructure. Maziere[43]constructedanewmemorymodelbycharacterizin gtherelationship betweentheinputandoutputenvelopeinformation.Themode lwasbasedonthe nonlineardierentialequationshowninEquation2.23.Only rstorderapproximationwasusedinthepaper. ~ y ( t )= f NL (~ x ( t ) ; d ~ x ( t ) dt ; d 2 ~ x ( t ) d 2 t ; ; d n ~ x ( t ) d n t )(2.23) Itturnsoutthatthersttimederivativeoftheinputsignalx( t)isthe\keyparameterforthecharacterizationofthenonlinearslowdynamics, includinggroupdelay, thermaldependenceandspuriousmodulationofbiaspoint"[4 3].Throughthetime derivative,theprevioussamplesaretakenintoaccountinth emodel,thuscapturing the\memory"eects.Thisapproachisquitesimilartothetime domainstate-space modelingtechniquereportedin[44]and[45],inwhichnonli nearordinarydierential equationsareformalizedtodescribetherelationshipbetwee ntheterminalcurrents andvoltages. 28

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Weakly nonlinear circuit x(t) y(t) Figure2.13IllustrationoftheVolterra-seriesbasednonline armodel. Thememorymodelsintroducedabovecharacterizethefreque ncy-dependentpropertiesofPAsusinglinearlter(s)andseparateitfromthememor ylessnonlinearpart. Volterra-seriesbasedmodels,ontheotherhand,takeadieren trouteandtreatthe memoryandmemorylesspropertiestogether[46],asshowninFi gure2.13. ThebasicformoftheVolterraseriesis: y ( t )= 1 X n =0 H n [ x ( t )](2.24) where H n [ x ( t )]= Z 1 1 Z 1 1 h n ( 1 ; 2 ; ; n ) x ( t 1 ) x ( t 2 ) x ( t n ) d 1 d 2 d n (2.25) h n ( 1 ; 2 ; ; n )issocalled n th orderVolterrakernel.Thiscanbeconsideredasan n th -orderimpulseresponse[2].ItscorrespondingFouriertransfor misgivenby: H n ( 1 ;! 2 ; ;! n )= Z 1 1 Z 1 1 h n ( 1 ; 2 ; ; n ) e j ( 1 1 + 2 2 + + n n ) d 1 d 2 d n (2.26) Therefore,Volterra-seriesPAmodelingistondthe n th orderkernelInfact, the1storderkernelcanbeconsideredasthelineargainoftheP A,whilethe3rd, 5thorderkernelsdescribethecorrespondingIMproducts.Thus, theoutputsignal issimplyasummationofallthecontributingitems.Sincethen th kernelhastime constants,ifmodeledproperly,itcanrepresentthememoryee cts.Thelimitationof 29

PAGE 44

theVolterraseriesmodelingtechniqueisthatitisonlysuita bleforweaklynonlinear devices.Whenusedtodescribethehardnonlinearperformances, itwillrequirevery highordermodelwhichmakesthekerneldeterminationproce ssdicultandtedious. Large-signalscatteringfunctionmodelhasbeenproposed[47, 48,49].Thebasic ideaistoextendthesmall-signalS-parameterconceptintono nlinearregionthrough nonlineardescribingfunctions.Elaboratemeasurementsystems weredevelopedto testpoweramplierordevicesandextractthemodel.InChapt er4,thisconceptwill bestudiedindetail. Besidesallthemodelingmethodsreviewedabove,therearesti llseveralother techniques,suchasdynamicneuralnetworkandnonlineartime seriesthatapproach theproblemfromthetimedomain,anddescribingfunctioninf requencydomain,as summarizedin[1]and[3].2.4Proposedresearchtopics Inlastsection,currentstateofartmemorylessandmemorymodel ingtechniques havebeenreviewed.Althoughwithalltheadvancesinthisare a,stilltherearesome questionsthathaven'tbeenansweredcorrectly. Generally,abehavioralmodelwillbeusedinasimulationschem aticwithprecedingandfollowingblocks(e.g.inputoroutputmatchingn etworks)topredictthe systemperformance.Therefore,itisvitalforthebehavioral modeltobeabletodetect automaticallythesourceandloadimpedancesandadjustitsre sponseaccordingly. Ithasbeenwidelyacknowledgedthattheperformanceofpowe rampliersis signicantlyaectedbythesourceandloadimpedancestheyar eembeddedin.This eectiscalledsource-pullingorload-pulling.Therearespe cialmeasurementsetups thatarededicatedtocapturetheseeects,suchastheloadpull measurementsystems providedbyMauryMicrowave[50]andFocusMicrowave[51]. 30

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However,mostofthebehavioralmodelsdiscussedsofardon'tprovi dethiscapability(exceptthelarge-signalscatteringfunctionmodel sandthemodelshaving small-signalS-parameterblocks).Inmostcases,theloadeectso nthenonlinearities arenotstudiedornotemphasized. Therefore,howcanwecreateanonlinearbehavioralmodelth atcanaddressthe limitationmentionedabove?Whatmeasurementsshouldbetake nforcreatingsuch abehavioralmodel?Thesearethemainquestionsthisdissertati onwilltrytoanswer inthefollowingchapters.2.5Conclusion Inthischapter,anextensiveliteraturereviewhasbeenprese ntedonthecurrentresearchstatusofbehavioralmodelingforpoweramplie rs/devices.Modeling techniquescoveredincludemathematicalmemorylessmodels, lter-basedtwo-box andthree-boxmemorymodels,Volterraseriesbasedmemorymode lsandlarge-signal scatteringfunctionmodels.Tworesearchtopicshavebeenprop osedthatareaimed tosolvetwoaspectsofthelimitationsofcurrentmodelingtec hniques. Therstresearchtopicisonbehavioralmodelingofload-rela tednonlinearitiesof powerampliersbasedonloadpullmeasurements.Thesecondtopi cisonintegration ofmemoryeectmodelingwiththeloadpullbehavioralmodel topredictthememory eectundervariousloadconditions.Theultimategoalistod evelopabehavioral modelingtechniqueorprocedurethatcaneasilygeneratebeh avioralmodelsforpower ampliersordevicethatarebasedonloadpullmeasurementsfo rsystemsimulations andarereadyforpracticalnon-50ohmapplications. 31

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CHAPTER3 ADVANCEDLOADPULLMEASUREMENTS 3.1Introduction Loadpullmeasurementhasbeenwidelyusedincharacterizatio nofdevicesand components.Itprovidesvaluableinsightaboutthedeviceper formanceunderdierent source/loadconditionsanddierentpowerlevels.Thisisver yimportantinformation forpoweramplierdesigners.Traditionalloadpullmeasureme ntsincludeone-tone andtwo-tonemeasurements,generatingmeasureddatasetsforga incompression,3rd interceptpoint(IP3),poweraddedeciency(PAE)andadjace ntchannelpowerratio (ACPR).Athermalimagingloadpullmeasurementhasalsobeend escribedin[52]. However,withtheadvanceddevelopmentinthebasebandalgori thmsaswellas themoreandmorecomplexmodulationtechniques,thetraditi onalmetricslikeP1dB andIP3obtainedthroughone-toneortwo-tonestimulicannot predictthesystem performancecompletely,because: thenonlinearphaseperformanceisnotcharacterizedproper ly; thetestingsignalsdon'trerecttherealisticcomplexmodulat edRFsignals.The performanceofatransistoriscloselyrelatedtothestimulussig nal[53]. Twoloadpullmeasurementproceduresaredevelopedtoaddress thesetwolimitations.BothmeasurementproceduresarebasedontheAutomatedTe stSystem(ATS) fromMauryMicrowave.Section3.2presentsanAM-PMloadpullm easurementproceduredevelopedusingtheAgilent's8719Dvectornetworkana lyzer.Althoughthe 32

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AM-PMloadpullmeasurementprocedureisavailablethroughsom ecommercialmeasurementsystems(e.g,Maury'sATSsystem),itisnotasaroutinep rocedureas thegaincompressionmeasurementis.Therefore,inSection3.2, thedetailanalysis andinstructionaregivenonhowtomakethismeasurement.Exam plemeasurement resultsaregivenoutforanMaxim2373lownoiseampliersample andaFujitsu L-bandGaAsFETpowerdevicesample. Section3.3presentsadigitaldemodulationloadpullmeasure mentprocedurebased ontheAgilent89610vectorsignalanalyzer(VSA).Thisnewmeasur ementprocedure providesthehardwaredesignersthecapabilitytostudythesyst emperformance(such aserrorvectormagnitude(EVM))directlyinloadpullmeasure ment.ExamplemeasurementresultsaregivenforIntersil3984poweramplierand FujitsuL-bandGaAs LDMOSdevice.Partoftheresultshasbeendocumentedin[54].3.2AM-PMloadpullmeasurementprocedure3.2.1Introduction Highspectraleciencyanddataratecanbeachievedthroughad vanceddigital modulationtechniqueslike16Quadratureamplitudemodula tion(QAM)or64QAM, whichapplybothamplitudeandphasemodulation.Thenonline aramplitude(AMAM)andphase(AM-PM)compressionofanamplier,therefore,dete rioratesthe modulationquality.Forexample,Parkreportsthesimulated AM-AMandAM-PM eectsonACPRwithrespecttothepowerback-oconsideration [55].Thesetwo nonlineareectshavebeenstudiedextensivelyandaccuratel ymodelledin50ohm condition,e.g.[13][18]and[19]. TheloadpullAM-AMmeasurementshavebeenwidelyappliedtoeva luatethe performanceofpowerampliersanddevices[56],[57].Howev er,theAM-PMper33

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formanceunderloadpullconditionshasn'tbeengivenenough attentionsofar.Part ofthereasonisthatthephasecompressiondoesn'tdeterioratele gacysystemperformancesignicantlyasgaincompressiondoes.Alsothemodulati ontechniques usedwerenotverycomplex.Thisphasecompressioncannotbeigno redanymorefor moderncomplexmodulationtechniques,whichapplycloserpha sedistancebetween symbolpoints. Therefore,inthisstudyameasurementprocedureisdeveloped tocharacterizethe loadimpedance'seectsonthephasecompressionofthenonline aramplier.The developedAM-PMloadpullmeasurementprocedureisbasedonthe Agilent8719D VNAandtheMauryAutomatedTestSystem(ATS).3.2.2IntroductionofatypicalVNAstructureandprocessin gsteps Beforestartingthediscussionofthedevelopedmeasurementsystem ,let'sreview thesystemstructureandthedataprocessingstepsofatypicalVNA.Thi sreview willhelpunderstandhowthemeasurementprocedureisdesigned .Figure3.1shows thesystemdiagramoftheAgilent8719DVNA[58].Althoughonlythe8 719DVNA isdiscussedinthispaper,asimilarprocedurecanbedevelopedf orotherkindsof VNAs,aswell. AtypicalVNAiscomposedoffourparts:thesynthesizedsource,testse t,vector receiversanddisplaydevice[58].Aphaselockloop(PLL)circ uitisusedtosynchronizethesourceandthereceiverstomaketheS-parameter ratiomeasurements. ThetestsetisusedtoseparatethesignalintoR,AandBchannels.A/R representsthe S 11 or S 22 rerectioncoecientmeasurement,whileB/Rforthe S 21 or S 12 transmissionmeasurement. Figure3.2illustratesthedataprocessingalgorithmusedinthe 8719DVNA.The sampledsignalisrstconvertedtodigitalsignalthroughtheADC andltered.If 34

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RAB Phase Lock TestDUT Synthesized Source Set ReceiverDisplay Figure3.1SystemdiagramofHP8719D. ratiomeasurementsaredesired,like S 11 ,theRATIOcalculationwillbeperformedon thesampledsignals;otherwisetheinputsignalwillbekeptconsta ntandpassedto thenextstage.Afteranaveragingprocess,thedataisstoredina\ RAW"arrayfor furthercorrectionusingthecalibrationerrorarraysobtai nedthroughthecalibration process.Thenthecorrecteddataarrayswillbeformattedinth edesiredformatand displayedonthescreen. FILTER DIGITAL ADC RATIO CORRECTION SAMPLER/IF AVERAGING SWEEP/SWEEP RAW DATA ARRAY CORRECTION ERROR ARRAY DATA MATH TRACE ARRAY MEMORY ERROR CORRECTION ARRAY FORMAT AUX IN R B A Figure3.2DataprocessingrowdiagramoftheHP8719DVNA. 3.2.3AM-PMmeasurementthroughvectorreceiversetup TomeasureAM-PM,onecaneithermeasurethesweptpower S 21 orusetheVNA asavectorreceiverandmeasuretheabsolutevectorvalueofth eB2.Fortherst method,theinputpowerlevelissweptandthe S 21 iscollectedateachpowerlevel. 35

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Thecompressionpropertycanbederivedbysettingthe S 21 obtainedatthelowest inputpowerlevelasthereferenceandcomparingtheother S 21 valuestoit.By comparingtheamplitudeofthe S 21 s,onegetstheAM-AM;comparingthephase, onegetstheAM-PMmeasurements. Theadvantageofthepowerswept S 21 methodisthattheprocedureisbuilt-in andthemeasurementisstraightforward.Thedataprocessingisa lsoconvenient. However,thismethodisnotrexiblebecauseitisbundledtothe internalsource.If itisusedtogetherwithotherinstrumentsinaloadpullmeasure ment,theintegration willbetroublesomesinceextraswitchesmayberequired. Thevectorreceivermethodcanovercometheseshortcomings.By inspectingthe dataprocessingstepsgivenoutabove,onenoticesthatVNAscongu redasavector receiverperformtheabsolutevectormeasurementsoftheinco mingsignalstoA/B/R ports.Thesampledincomingsignalisacomplexvalue.Iftheinp utpowersweeps, themeasuredresultwillbeanarrayofcomplexvalues.TheAM-PMi nformationis containedinthisRAWdataarray,infact.Insteadofgoingthr oughalltheratioand correctionprocessing,theRAWdataarraycanbeuseddirectlyt ogettheresults. Asforthecalibrationconsideration,themagnitudeoftheresu ltcanbecorrected throughreceivercalibrationproceduretoremovethepossibl edistortioncausedby thesystemhardware.Thephasecanbecalibratedinsimilarwayas well. Therearesomeextrahardwaresetupstepsrequired.TheVNAneedst obe synchronizedwiththeexternalsynthesizer.Itneedstoknowwh ichport(vector receiver)theincomingsignalissentto.Thefrequencyofthei ncomingsignalcannot beswept,otherwisethesynchronizationwillbelost. Acustom8719DVNAdriverwasdevelopedtosupportextractionand analysis oftheRAWdataarrays.ThemeasurementsystemdiagramisshowninF igure3.3. TheincidentsignaliscoupledtotheRINportwhilethererect edandtransmitted 36

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signalsaresampledthroughtheinputandoutputcouplers.Thesa mpledsignalat Port2isstoredinRAWdataarray.TheAM-PMinformationcanbee xtractedfrom theRAWdataarraybycomparingthephaseofthecomplexdataar raytotherst valueinthearray(correspondingtosmall-signalphase). R IN R OUT VNA 12 Tuner Source Tuner Load PowerMeter DUT EXT REF IN EXT REF OUT Figure3.3AM-PMloadpullmeasurementsystemdiagram. Theextrasetupstepsregardingtothe8719DVNAaregivenbelowfo rthepurpose ofcompleteness.Thesequenceofthepanelbuttonstobepressedis givenoutfor eachstep. System-InstrumentMode-TunedReceiver(settheVNAinvectorrec eiver mode); Menu-CWFreq-settheCWfrequencyofinterest; Meas-InputPorts-B(channelBisusedtosamplethesignal); Meas-Testport-2(testport2isselectedasthesamplingport). 3.2.4ExampleAM-PMresults TwoDUTsweremeasuredusingthisdevelopedAM-PMloadpullsystem.O ne deviceisaMaxim2373lownoiseamplier(LNA)sample;theotheri sanFLL120MK highpowerGaAsFETsamplefromFujitsu.Firstofall,thevalidit yofthedeveloped 37

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systemshouldbecheckedagainsttheVNA.Figure3.4showsthecompari sonof themeasuredAM-PMandAM-AMdatasetsfortheLNAsampleunder50ohmconditionfromthetwomethods.Obviously,theresultobtained usingtheloadpull systempresentsgoodagreementwiththeHP8719Dresultatsmallsign allevels.The discrepancyatthehighpowerlevelsisbecauseofthesignican tharmonicsignals generated. -15 -10 -5 0 5 0.5 1 1.5 2 2.5 3 Pin (dBm)Gain (dB) -15 -10 -5 0 5 0 2 4 6 8 10 12 14 16 18 20 Phase Compression (degree) Loadpull systemVNA Figure3.4ComparisonofmeasuredAM-AMandAM-PMresultsfromtheVNA and theloadpullsystemfortheLNAsampleat900MHz. Figure3.5presentsanexampleAM-PMloadpullmeasurementresul t.TheAMPMcompressionismeasuredatsixloadimpedances.Fordierentlo adimpedances, thecharacteristicsofthegaincompressionandthephasecompre ssionchangedramatically.Atloadpointsthatcausehighgaincompression,the phasecompressionis alsosignicantlydierentfromthemildcompressedcases. Similarobservationcanbemadefromthemeasuredresultsforth eGaAsFET devicesampleat2.14GHz.AsshowninFigure3.6,atloadpointswh erethedevice showslowergaincompression,italsohassmoothAM-PMcurves.Onthe otherhand, loadpointsassociatedwithhighgaincompressioncausesignican tphasecompression 38

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-30 -20 -10 0 10 -5 0 5 10 15 20 Pin (dBm)Gain (dB) 0.91078<33.97180.90842<41.40750.90779<48.62190.78575<44.14710.019031<122.9469 -30 -20 -10 0 10 -100 -80 -60 -40 -20 0 20 40 Pin (dBm)Phase Compression (degree) 0.91078<33.97180.90842<41.40750.90779<48.62190.78575<44.14710.019031<122.9469 Figure3.5AM-AMandAM-PMloadpullmeasurementresultsat900MHzf orthe LNAsample.evenatlowpowerlevels.Sinceconjugateloadcauseshigherga in,itsuggeststhatthe AM-PMcompressionwillbehighneartheconjugateloadareaonth esmithchart. 10 15 20 25 30 35 40 -2 0 2 4 6 8 10 12 14 Pin (dBm)Gain (dB) 0.022317<117.08170.26221<-92.70180.91884<-148.23810.78769<-147.0403 10 15 20 25 30 35 40 -5 0 5 10 15 Pin (dBm)Phase Compression (degree) 0.022317<117.08170.26221<-92.70180.91884<-148.23810.78769<-147.0403 Figure3.6AM-AMandAM-PMloadpullmeasurementresultsat2.14GHz forthe highpowerGaAsFETsample. Fromthemodelingviewpoint,thisadditionalinformationsu ggeststhatthenonlinearmodelforampliersshouldbeabletoadjustitsgainand phasecompression propertieswithrespecttodierentloadconditions. 39

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3.3DigitalDemodulationloadpullmeasurementprocedure Inthissection,weintroduceaninnovativedigitaldemodula tionloadpullmeasurementprocedurethatdirectlycharacterizessystemperforman ceofapowertransistor (oramplier)undervarioustestconditions,togetherwithth etraditionalnonlinear metrics,e.g.gaincompressionandintermodulationdistortion (IMD).Thekeyparameterunderstudyinthissectionistheerrorvectormagnitu de(EVM). 3.3.1DenitionandmeasurementofEVM EVMisametricthatquantiesthequalityofdigitalmodulate dsignals.Itisdenedasthemagnitudeofthephasordierencesbetweenanidea lreferencesignaland themeasuredtransmittedsignalafterithasbeencompensatedin timing,amplitude, frequency,phaseanddcoset[59].Itcanbecomputed(3.1): EVM RMS = vuuuuut N P i =1 j S ideal ( i ) S meas ( i )) j 2 N P i =1 j S ideal ( i ) j 2 (3.1) where S ideal ( i )and S meas ( i )arethe i th normalizedidealcomplexreferenceconstellationpointandthemeasuredsymbolrespectively[60].Bec auseitchangescontinuouslyduringeverysymboltransition,EVMisdenedasthero ot-mean-square (RMS)valueoftheerrorvectorovertime. Somestudieshavealreadybeenreportedtosuccessfullypredict theEVMbased onone-tone[61][62][63]ortwo-tonedistortion[64]ofpowe rampliers.However, mostoftheworkdealseitherwithamatched50ohmconditionor providesonlythe simulationresultswithrespecttotheloadtuning.Thisnewmea surementprocedure, asdemonstratedinthefollowingsections,providesamuchmore realisticandcomplete 40

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viewoftheperformanceoftheDUT,includingmeasurementvali dationofbothpower andsource/loadimpacts. BeforeproceedingtothediscussionoftheEVMloadpullmeasureme nt,let'sreviewhowatypicalEVMmeasurementisdone.Fig.3.7illustrates themeasurement diagram[65].TheinputRFsignalisrstdown-convertedtothe lowintermediate frequency(IF)sothattheADCcansampleitadequatelyanddownconvertitto basebandforfurtherprocessing.TheLOisnotdirectlyphase-lo ckedtotheincoming signal(unliketheVNAratiomeasurement),therefore,itwillin troducesomefrequencyoset.Thefrequencyosetwillbetranslatedintoaphase rotationinthe timedomainandcanbeestimatedandcompensatedthroughadigi talprocessing algorithm.Infact,frequencyosetisoneofthemeasurementc apabilitiesofaVSA. RF IN ADCDEMOD I/Q REF I/Q MEAS. I/Q EVM Results MOD S Estimated Bitstream Figure3.7EVMmeasurementdiagram. Basedonthesampleddatastream,theidealconstellationpoints arerecoveredby rstdemodulatingtheincomingstreamandthenre-modulating theobtaineddigits. TheRMSEVMiscomputedthroughaveragingalltheframesusedin themeasurement.TomaketheRMSEVMaccurate,alargenumberofframesare required,e.g. 802.11aWLANspecication[66]requiresatleast20frames.3.3.2Measurementsystemandcalibrationconsideration TheEVMloadpullmeasurementsystemisdevelopedbasedontheAutom atic TunerSystem(ATS)fromMauryMicrowaveandthe89610AVector SignalAna41

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lyzer(VSA)fromAgilentTechnologies.Fig.3.8showstheintegra tedsystemsetup. TheATScontrolsalltheinstrumentsinthemeasurementsysteman dcoordinates themeasurementprocedure.Thedigitaldemodulationmeasure mentisperformedby theVSA.Anin-houseprogramisdevelopedtoaccesstheVSAmeasureme ntresults throughthecommonobjectmodel(COM)APIinterface.Theprog ramcanautomaticallyadjusttheinputrangesetupfortheVSAsothattheinpu tsignalcanbe sampledandevaluatedatproperlevelstoobtaintheoptimalm easurementresults. TheRMSEVMisaveragedoverseveralreadingsandthencollecte dbytheprogram andportedtoATSforcontouranalysis. Source Tuner Supply Bias DUT Load Tuner Controller Tuner VSA Meter Power Pre Amp GPIB Bus Source ESG Figure3.8Illustrationofthedigitaldemodulationloadpul lmeasurementsystem. AsthedigitallymodulatedRFsignalpassesthroughthemeasureme ntsystem, someerrorswillbeintroduced,mainlyduetothedistortione ectsofthedriver amplierprecedingtheDUTandthedown-converter.Thedistor tionofthedownconvertercanbeminimizedbyadjustingthestepattenuator.Ho wever,thedistortion causedbythedriveramplierisdiculttoseparate.ThesystemE VM(actingasthe EVMnoiseroorforthemeasurementsystem)shouldbeevaluatedbefo reperforming furthermeasurementstomakesurethedriveramplierislinea renough. 42

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ThiscanbedonebypluggingaTHRUbetweenthesourceandloadtu nersand measuringtheEVMassociatedwiththeTHRU.AratEVMcurveacrossthep ower rangeofinterestindicatesalinearsystem.Otherwise,additio nalcareshouldbe takenregardtomeasuredresultsclosetotheEVMnoiseroorindica tedbythethru measurement. Fig.3.9comparesthesystemEVMandthatassociatedwiththeDUT.Ob viously fromthisgure,wecantellthatthesystempresentssignicantn onlinearitiesdueto thedriveramplier.Thedistortionofthedriveramplierdo minatesatthelowand midpowerrangeuntilthenonlinearpoweramplierstartsdom inating. 0 5 10 15 20 25 30 0 2 4 6 8 10 12 14 16 Pin (dBm)EVM (%)Comparison of EVM with/without the DUT System EVMMeas. EVM Figure3.9ComparisonofthesystemEVMandmeasuredEVMoftheDUT. Fig.3.10demonstratessimilarphenomenonfortheACPRmeasure ments.Ascan beseen,theACPRappearedatlowinputpowerlevels(upto17dB m)ismainlythe contributionofthethenonlineardriveramplier. Fig.3.11comparesthemeasurementsystemEVMandtheDUTEVMforalo w poweramplier.Inthismeasurementsetup,thereisnorequire mentforadriver amplier.Therefore,thesystemshowslittledistortion;thesyst emEVMisquiterat 43

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0 10 20 30 40 -45 -40 -35 -30 -25 -20 -15 Comparison of the System and the DUT APCR Pin (dBm)ACPR (dBc) DUT ACPRSystem ACPR Figure3.10ComparisonofthesystemACPRandmeasuredACPRofthe DUT. acrossthewholepowerrange.Thisresultagainemphasizesthei mportanceoflinear driveramplierforaccurateEVMmeasurements.3.3.3ExampleloadpullEVMmeasurementresults Inthissection,theloadpullEVMmeasurementdatasetsfortwode vicesare demonstrated.TherstdeviceunderstudyisahighpowerGaAsFET samplefrom Fujitsu.Thetypicaloutputpowerat1dBcompressionpointis40 dBmwithagain of10dB.ThePAEisaround40%[67].Theloadrelatedgainandph asecompression propertieshavebeenshowninFig.3.6. TheFETwasstudiedat2.14GHzusinganOFDMmodulatedsignaltoex plore itscapabilitytohandlemulti-carriersignalswhichhavehi ghpeak-to-averagepower ratio(PAPR).HighPAPRsignalsposehighrequirementsontheline arityofpower ampliers. Fig.3.12comparesthetransducergain(GT)andEVMperformanc einanexample sourcepullmeasurement.Theloadissetatconjugatematchandt heinputpoweris 44

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-30 -25 -20 -15 -10 -5 0 5 0 5 10 15 20 Pin (dBm)EVM (%) DUT EVMSYS EVM Figure3.11ComparisonofthesystemandDUTEVM. setat22dBm.SimilarcomparisonisshowninFig.3.13foraloadp ullmeasurement. Inbothcase,thetestsignalwasa64carrierOFDMmodulatedsigna l. Typically,thegoalofthesourcetuningistogetthebestgaino utoftheDUT, whiletheloadtuningoptimizesthetotaloutputpower.Ifam ulti-carriersignal passesthroughtheDUTwithhighgain,thechanceismuchhigherf orthepeaksof thesignalgettingdistortedduetothelimitedpowerhandling capabilityoftheDUT. Ontheotherhand,bytuningtheloadtoobtainthemaximumout putpower, thesignalisallowedtoswingtothelargestextentpossible,whic hprovidesthebest signaldelity.Therefore,wemightexpecttheEVMperformanc etodegradewhen thesourceimpedanceapproachestheconjugatematch,andbet terEVMperformance forloadimpedanceoptimizingtheoutputpower.Thispointi sdemonstratedinFig. 3.12andFig.3.13. Fig.3.14presentsabetterillustrationofthesource/loadinr uence.Showninthe gurearetwoEVMsurfaces.Thelowersurfaceisforthesourcepull ingmeasurement. ComparingtoFig.3.12andFig.3.13,onecanseethattheEVMdeg radessignicantly 45

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Sourcepull transducer gain and EVM contours 2.7882.7882.7884.94094.94094.94097.09387.09387.09389.24679.246711.399611.3996 GTEVM Figure3.12TransducergainandEVMcontoursforexamplesource pullmeasurement. The L is-0.72827-j*0.40883.Theoptimal S fortheGTis-0.67904-j*0.60152.The maximumGTis10.75dB.ThemaximumEVM(13.75%)appearsat S of-0.68003j*0.58930. 46

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Loadpull transducer and EVM contours -0.431081.83861.83861.83861.83864.10834.10834.10834.10836.37816.37816.37818.64788.64788.6478 12.840113.673513.673514.50714.50714.50714.50715.340515.340516.1739 GTEVM Figure3.13TransducergainandEVMcontoursforexampleloadp ullmeasurement. The S is-0.67904-j*0.60152.Theoptimal L fortheGTis-0.72827-j*0.40883. ThemaximumGTis10.87dB.ThemaximumEVM(16.86%)appearsat L of -0.7890+j*0.2966. -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 0 2 4 6 8 10 12 14 16 18 EVM (%) Sourcepull,load at 50 ohm. Loadpull, source at conjugate point Figure3.14Sourcepull/loadpullEVMmeasurements;Pinissetat 22dBm. 47

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aroundthehighgainregiononthesourceSmithchart.TheEVMlo adcontouris relativelysmoother.Thismightbenotaperfectwaytoevalua tethesourceor load-pulleectontheEVMorotherparameters.Abetterwayist oevaluatethese parametersunderconstantoutputpowerlevels. Fig.3.15showsanloadtuningexampletoobtaintheimprovedE VM.Twosets ofsweptpowerEVMmeasurementsarecompared.Inonecase,theloa distunedto obtaintheoptimumGT,whileintheothercase,theloadistune dforbetterEVM. Thesourceiskeptatconjugatematchingpoint.ThetunedEVMis about2.5-3.5% betterthantheformercase,with0.5dBlossofgain. 0 5 10 15 20 25 30 15 20 25 30 35 Pout (dBm) 0 5 10 15 20 25 30 0 2 4 6 8 10 12 14 16 + Optimal GT case o Optimal EVM case Pin (dBm)EVM (%)Two load conditions: optimal GT and optimal EVM Figure3.15ImprovementoftheEVMperformancebytuningthel oad. TheseconddevicestudiedisanIntersil3984WLANpoweramplier sample.Traditionalone-toneandtwo-toneloadpullmeasurementsarepe rformedrst,followed bytheEVMloadpullmeasurements.Thepoweramplierisstudieda t2.45GHz. Figure3.16comparesthetransducergaincontourswiththeEVM contoursat constantoutputpowerlevels.Theoutputpoweris15dBmin(a)a nd18dBmin (b).Similaritycanbefoundforthistwocontours.Noticethat theoptimalload 48

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impedancesforthesetwomeritsaredierent,whichmeanstra deoscanbemade basedondierentapplicationrequirements. TheACPRcontoursandtheEVMcontoursarecomparedinFigure3 .17.Both measurementswereobtainedusingthe54MbpsOFDMmodulatedsig nal.Themeasurementresultsdemonstratethecloserelationshipbetweenthe twogure-of-merits. Theoptimalloadimpedancesforthesetwomeritsareveryclose toeachotherinboth cases. Similarly,theIP3andtheEVMcontoursarecomparedinFigure 3.18.Atlow outputpowerlevel(a),theoptimalloadimpedancesfortheI P3andEVMarevery close;forhighoutputpowerlevel(b),thedierencebecomesi gnicant.Therefore, insteadofresortingtotheIP3,engineerscanoptimizetheird esignsagainsttheEVM performance,whichwillprovidebettercorrelationbetwee nthesimulationresultsand thesystemperformanceofthenalproducts.3.4Conclusion Inthischapter,twoloadpullmeasurementsarepresented.AnAMPMloadpull measurementsystemisintroducedwhichisbasedonAgilent8719Da ndMauryATS system.ItisshownthattheloadimpedancesaecttheAM-PMchara cteristicsignicantly.Theexamplemeasurementssuggestloadsthatareclo setoconjugateload impedancewillcausehigherAM-PMcompressionandthecharacter isticswillbemuch dierentfromothercases.Modelingengineersneedtobeaware ofthisfactandtake theloadintoaccount. Anewlydevelopeddigitaldemodulationloadpullmeasuremen tprocedureisdescribedthereafter.Theevaluationofthesystemlinearityisd iscussed.Theimportanceofthedriveramplierisemphasized.Examplemeasureme ntresultsaregiven, demonstratingthepossibletradeosbetweenthetraditional gure-of-meritsandthe 49

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GT: 16.8671 to 30.3085 dB, 10 steps EVM: 5.4102 to 16.4836%, 10 steps Constant Pout at 15 dBm (a) GT: 17.915 to 29.2604 dB, 10 steps EVM: 10.5791 to 15.8445%, 10 steps Constant Pout at 18 dBm (b) Figure3.16ComparisonoftheGTandEVMcontoursatconstantout putpower levelof15and18dBm. 50

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ACPR: -57.7069 to -39.3408 dBc, 10 steps EVM: 5.4102 to 16.4836%, 10 steps Constant Pout at 15 dBm (a) ACPR: -57.1581 to -33.4528 dBc, 10 steps EVM: 10.5791 to 15.8445%, 10 steps Constant Pout at 18 dBm (b) Figure3.17ComparisonoftheACPRandEVMcontoursatconstanto utputpower levelof15dBmand18dBm. 51

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IP3: 18.9019 to 31.0355 dBm, 10 steps EVM: 5.4102 to 16.4836%, 10 steps Constant Pout at 15 dBm (a) IP3: 22.6216 to 29.8459 dBm, 10 steps EVM: 10.5791 to 15.8445%, 10 steps Constant Pout at 18 dBm (b) Figure3.18ComparisonoftheIP3andEVMcontoursatconstantou tputpower levelof15dBmand18dBm. 52

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EVM.Thedesignersmightbeabletousethisinformationtoimpro vetheirdesigns bytuningloadimpedancestondthebetterperformancewith respecttotheEVM. Thispracticehelpsthedesignerscommunicatewithsystemengi neersusingcommon metricstocomeupwiththesystemspecication. 53

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CHAPTER4 LARGE-SIGNALSCATTERINGFUNCTIONMODELBASEDON LOADPULLMEASUREMENTDATASETS 4.1Introduction Small-signalScatteringparametersarewidelyusedinRFandm icrowaveengineeringtocharacterizelinearandmildlynonlineardevice sandcomponents.They canbethoughtofasasimplefrequencydomainbehavioralmode lforthenetwork studied,characterizingtherelationshipbetweenthein-goi ngandout-goingwaveformsatspecicfrequenciesoneatatime.Obviously,S-param etersdealwithlinear transferringrelationshipsonly,sincetheinputandoutputfr equenciesareidentical andnonewfrequenciesaregenerated.However,withtheadvan ceofmodernwireless communicationsystems,moreandmoredemandsaregeneratedfor nonlinearoperationofdevicesandamplierstogetbettertransmissionecie ncyandlesspower consumption.Thiscausesdistortioneects,suchasharmonicsan dspectralregrowth, asintroducedinChapter2.TheclassicalS-parametertheoryi snolongersuitable forthissituation. Large-signalscatteringfunctiontheoryisproposedtoaddress thislimitation.In general,thistheoryextendsthesmall-signaltheorytotakei ntoaccountnotonly thefundamental,butalsoharmonicsatdierentports.Thecon tributionofallthese spectralcomponentsisformulatedintononlinearfunctions, therefore,makingitpossibletocharacterizethenonlinearities.Aspecicmeasuremen tsystem,calleda 54

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large-signalnetworkanalyzer(LSNA),isrequiredtomeasurean dderivethistypeof large-signalbehavioralmodel. Thistheoryhasn'tbeenwidelyappliedduetothelimitedacce sstosuchspecialized (andcostly)systems.Therefore,onequestionisasked:isitpossibl etoderivepracticallyusefullarge-signalbehavioralmodelsusingmorewidely availablemeasurement systems(forthisstudy,theloadpullmeasurementsystem)? Thisisthemainresearchtopicpresentedinthischapter.Bycl oselystudying thelarge-signalscatteringfunctiontheory,theauthorcome stoaconclusionthat usefullarge-signalmodelscanbederivedfromtheloadpullme asurementsystem, althoughsomeadvancedmeasurementproceduresarerequired. Theprocedurefor derivingthebehavioralmodelwillbeexplainedandexample modelingresultswillbe demonstratedthatshowgoodperformance. Thisproposedmodelingtechniquealsoprovidesasolutiontofu llyutilizethe loadpullmeasurementdataset.Althoughtheloadpullmeasureme nthasbeenwidely appliedinpowerdevices(orampliers)characterizationan ddesign,derivationofan accuratebehavioralmodelfromthedatasetstillpresentsasah ugechallenge.Most ofthetime,theloadpullmeasurementdatasetsareonlyusedfor observationofthe optimalloadpointsorasavericationforthedevicemodeli ng.Therearesome commerciallyavailablesolutionsincurrentmicrowavecirc uitsimulationsoftware, suchastheAdvancedDesignSystem(ADS)[68]andtheMicrowaveOc e[69],to generatebehavioralmodelsfromthemeasurementdatasets,how ever,themodelhas limitations,aswillbepointedoutinthechapter.Themethod proposedinthechapter showsananalyticalwaytoexploitthedatasetsandpresentssign icantadvantages overtheexistingapproaches. Thetheoryofthelarge-signalscatteringfunctionisintrodu cedinSection4.2. Thelimitationsofthecurrentmodelingtechniquesareelab oratedinSection4.3.The 55

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detailderivationandoptimizationprocessoftheproposedme thodisthenpresented inSection4.4.Threeexamplemodelsareconstructed.Theirsi mulationresultsare comparedwithmeasurementresultsinSection4.5.Goodagreem entsobservedprove theeectivenessoftheproposedmodelingtechnique.4.2Introductionoflarge-signalscatteringfunctiontheo ry 4.2.1Small-signalnetworkanalysis AnN-portlinearnetworkcanbefullycharacterizedbycapturi ngtherelationship betweenthecurrentandvoltageateachport.Forexample,at woportnetworkas showninFigure4.1,canbefullydescribedthroughZ,Y,ABCDorSparameters. 1 transmission two-port I V I 12 2 V Figure4.1Twoportnetworkwiththevoltageandcurrentden ition. Forexample,theYparameterforthistwo-portnetworkisgiv eninEquation4.1: 264 i 1 i 2 375 = 264 y 11 y 12 y 21 y 22 375 264 v 1 v 2 375 (4.1) where i n and v n arethecurrentandvoltageatportn, y mn istheadmittancefromport ntoportmwithportmshorted.TheY-parametercanbedetermine dusingshort circuitedoutputs,i.e.the y mn canbedeterminedthroughEquation4.2byshorting 56

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theporti: y mn = i m v n v m =0 (4.2) Similarly,ZparameterisdenedinEquation4.3.Toobtaint heZ-parameter, opencircuitedoutputsarerequired,asindicatedinEquati on4.4. 264 v 1 v 2 375 = 264 z 11 z 12 z 21 z 22 375 264 i 1 i 2 375 (4.3) z mn = v m i n i m =0 (4.4) However,whendealingwithhighfrequencies,theseparameterd enitionisno longersuitable.First,theidealshortandopencircuitaredi culttoobtainathigh frequencies.Second,thevoltageandthecurrentaredicult tomeasureathigh frequencies.Therefore,thescatteringparameterisproposed tosolvetheseproblems. Theideaistomeasuretheincident,rerectedandtransmittedw aveformstocapture theperformanceofthenetworkstudied.Theingoingwave a andoutgoingwave b are denedas: a = v + Z 0 i p 2Re( Z 0 ) b = v Z 0 i p 2Re( Z 0 ) (4.5) where Z 0 isthereferenceimpedance. TheS-parameterisdenedinEquation4.6,asafunctionoffr equency f : 264 b 1 ( f ) b 2 ( f ) 375 = 264 s 11 ( f ) s 12 ( f ) s 21 ( f ) s 22 ( f ) 375 264 a 1 ( f ) a 2 ( f ) 375 (4.6) 57

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TheS-parametercanbedeterminedbyterminatingallotherp ortsinsteadofport jwithmatchedloadstoavoidrerectionandinterference. s ij ( f )= b i ( f ) a j ( f ) a i ( f )=0 (4.7) TheZ,YorS-parameterscanbeconsideredasbehavioralmodel s,sincetheydeal withonlytheportvariablesanddon'trequireinformationa bouttheinternalstructure ofthenetwork.Allthenetworkparametersetshaveoneimporta ntassumption,thatis thenetworkislinearandsuperpositionisvalid.Whenthenetw orkshowsnonlinear eects,typicallythroughthegenerationofnewfrequencies (harmonicsormixing products),theZ,YorS-parametersarenolongervalidandmor eadvancedmethods arerequiredtocharacterizethenetwork.4.2.2Theoryofthelarge-signalscatteringfunction Thelargesignalscatteringfunctionhasbeenproposedtoexten dtheapplicability ofthesmall-signal(linear)S-parameterconcept.Theideaof thelarge-signalSparameterwasinexistsince1997.Therearelotsofpublicatio nsonthisconcept,e.g. [47],[48],[70].Recently,anewbroadbandversionoftheori ginaltheorywaspresented [71],whichextendsthismodelingtechniquetoaddthefrequ encydimension. Asintroducedin[47]and[72],thelarge-signalscatteringfun ctioncanbeconsideredasalinearizationthatrelatestheincidentandrerect edwavecoecientsofa weaklynonlineartime-invariantdevice.\Weaklynonlinea r"meansthattheoutput signalsareastable,single-valued,andcontinuousfunctiono ftheinputsignalsaround thelarge-signaloperatingpoint[72].Italsohintsthatthesp ectralcomponentsin theoutputsignalsarelinearcombinationswithintegercoe cientsofthefrequencies attheinputport. 58

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Theinputandoutputvariablesaredenedinthefrequencydo mainasdepictedin Figure4.2: A ij denotesthecomplexnumberrepresentingthe j th spectralcomponent oftheincidentvoltagewaveatport\i"and B ij denotesinasimilarmannerthe scatteredvoltagewaves.Therelationshipbetweentheinputan doutputwavesignals canbedescribedbyEquation4.8,withallthespectralcompone ntsnormalizedto A 11 inphase. B ij = S ij (Re( A 11 ) ; Re( A 12 ) ; Im( A 12 ) ; ; Re( A 2 N ) ; Im( A 2 N ))(4.8) A2N DUT Port 1Port 2 A11A12A1N B12 B11B1N B21B22B2N A21A22 Figure4.2Theinputandoutputvariablesforatwo-portnetw orkusedinthelargesignalscatteringfunctionarecomposedofthefundamentalton esaswellastheharmonicsforboththeincidentandrerectedwaves[47]. The S ij iscalled\large-signalscatteringfunction".Itisacomplex multi-dimensional nonlinearfunction.Ifthereisonlyonelargetonepresentat theinputandallother harmonicsignalsarerelativelysmall,itispossibletosimplify (orlinearize)themultidimensionalnonlinearfunction S ij .Basedonthisassumption,thesuperposition principleholdsfortheharmonics,whichcanbeexpressedinEqu ation4.9[47],[71]: B ij ( j A 11 j )= X q X l =1 ; ;M S iq;jl ( j A 11 j ) P j l A ql + X q X l =1 ; ;M T iq;kl ( j A 11 j ) P j + l A ql (4.9) 59

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T p 1 ;k 1 =0(4.10) where P isthephaseof A 11 .Thisequationshowsthatthescatteredwave B ij the j th harmonicatport i ,isthesumofincidentwavesandtheirconjugatesof l th harmonicatport q incidentwaves.Theintroductionofthecomplexconjugate termsoftheincidentwavesistheconsequenceofthelineariz ationaroundthetimevaryingoperatingpointestablishedbythesinglelarge-ampli tudetoneintheabsence ofperturbation[71][72].Equation4.10isrequiredtoincl udethefundamentaltones inEquation4.9. S iq;jl and T iq;jl aredependentonthemagnitudeofthe A 11 that modelsthenonlinearperformanceoftheampliersordevice s. 4.2.3Creationofthelarge-signalscatteringfunctionmod el Thelarge-signalscatteringfunctionofadevicecanbederive dfrommeasurement resultsusingLSNA.ALSNA(sometimescalledvectornonlinearnetw orkanalyzer,or VNNA)iscomposedofthetestset,down-converter,digitizerandana lysissoftware, asshowninFigure4.3.Thesource1isasignalgeneratorthatcan generateCW signalsaswellasmodulatedsignals,ifrequired.Source2prov idestheperturbation signaltoport1or2throughtheswitch.Thissignalsimulatesthe smallperturbation signalpresentedinthemodel. Themeasurementsystemrequiresspecicmulti-tonephasecalibr ation,inadditiontothetraditionalVNAcalibration(suchastheSOLTorLRMc alibration)and absolutepowercalibration.Thephasecalibrationnormalize sallthefundamentaland harmonicspectralcomponentstothephaseof A 11 ,thedominanttoneattheport1. Toobtainthecoecientsinthelarge-signalbehavioralmode lforadevice,several measurementsarerequired.Let'suseanexampletoexplainthi sprocess.Ifweare interestedinthescatteredwave B 21 ,thefundamentaltoneatport2.Assumethis 60

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SRC 1 IF DIGITIZER PC TESTSET LO SRC2 Figure4.3FunctionalblockoftheLSNA. wavevariableisdeterminedbytheinputlargesignaltone A 11 atonespecicpower levelandthespectralcomponentsatport2,including A 21 A 22 and A 23 .The B 21 canbewritteninEquation4.11: B 21 = S 21 ; 11 A 11 + S 22 ; 11 A 21 + T 22 ; 11 A 21 P 2 + S 22 ; 12 A 22 P 1 + T 22 ; 12 A 22 P 3 + S 22 ; 13 A 23 P 2 + T 22 ; 13 A 23 P 4 (4.11) Thereare7unknowncoecientsforthisspecicpowerlevelan dfrequency.Since superpositionholds,asthetheoryassumes,the7coecientscanbe obtainedthrough threemeasurements: measurementwithonlythelarge-signal A 11 present; 61

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twomeasurementswiththesmall-signalperturbation A 21 atdierentphase relativetothe A 11 ; twomeasurementswiththesmall-signalperturbation A 22 atdierentphase relativetothe A 11 ; twomeasurementswiththesmall-signalperturbation A 23 atdierentphase relativetothe A 11 ; Bycombiningallthesemeasurementdatasetsandapplyingaleast -square-errort, the7coecientscanbedeterminedthereafter.Bysweepingth eamplitudeofthe A 11 wewillgetatableforthe7coecientscorrespondingtoeachi nputsignalamplitude. Theneitheralook-up-table(LUT)modeloranttingfunction (e.g.ANNmodel) canbeusedtoimplementthelarge-signalmodelincommercialm icrowavesimulation softwaretosimulatethedeviceperformance. Ifonlythefundamentalfrequencyisconsideredinthelargesignalmodel,thatis theharmonicspectralcomponentsdon'tappearinthemodel,t helarge-signalmodel isreducedtosocalledthe\Hot"S22method[49].Equation4.12 illustratesthis model: B 2 = S 21 ( j A 1 j ) A 1 + S 22 ( j A 1 j ) A 2 + T 22 ( j A 1 j ) P 2 A 2 (4.12) Aspointedoutin[48],themeasurementsareactuallyacombina tionofpassive andactive(harmonic)loadpullmeasurements,sincethesecondsy nthesizerinjects signalstotheDUTstosimulatethevariationintheload.Thisan alogysuggests thepossibilitytoapproximatelycreatethelarge-signalmode lfromageneralloadpull measurementdataset. 62

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4.3Currentloadpull-basedmodelingtechniqueandtheirli mitations Thereareseveralexistingtechniquestoutilizetheloadpull datasetformodeling purposes[73],[74]and[75].Somecommercialmicrowavesimul ationsoftware packagesprovidethecapabilitiestoreadtheloadpulldata lesintothesimulatorfor linearornonlinearsimulation[68]and[69]. Generallythesetechniquescanbegroupedintotwocategorie s:le-basedmodeling andanalyticalmodeling.Asthenamehints,thele-basedtechn iquesprovidea solutiontodirectlyaccesstheloadpulldatalethroughsomei ndexingdesigntond outthedeviceperformanceaccordingtoasetofrules.[68],[6 9],[73]and[74] belongtothiscategory. Carlson[74]describedanovelmethodtointegratetheloadpul ldatasetinmicrowavesimulationsoftwareforoptimizationoftheloadcond itionfordierentgoals (e.g.outputpowerorIP3).Insteadofsweepingtheamplitudea ndphaseofthe rerectioncoecientoftheload L ,theauthorproposedtosweeptheresistanceand capacitancebasedontheobservationofthesmall-signalS22seen attheoutputport oftheDUT.Thismethodcancapturethefrequencyeectthroug hthecapacitance, whichmakesthedataprocessingeasier.However,thismethodhas itslimitationin thatitonlyprovidesawaytoobservetheloadpulldataleand ndtheoptimal loadpointsforspecicgoals.Itdoesn'tprovideausablebehavi oralmodelforgeneral simulationpurposes. Olahetal[73]introducedasystematicmethodtocreatebehavi oralmodelsbased ontheloadpulldatale.Themethodhasthreesteps: scattereddatainterpolation:triangulationisusedtogener ateasetoftriangular mesh;thecontoursareplottedbytraversingthesetriangularp atches; 63

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convertthetriangulatedscattereddatatoagrid(regularor uniformdata)for easyusageinsimulators; calculatetheincidentandscatteringwavesasfunctionsofl oadimpedances usingthegriddeddatasets;theresultsarestoredinaleforacce ssduring simulation. Thelimitationaboutthismethodisthatitrequiresthestora geoflargedatales; alotoftheinformationmightberedundant.Forexample,whe ntheinputsignal levelislow,asimplesmall-signalS-parametermodelisenough topredictthegain atvariousloads.However,thismethodwouldutilizethestored B 1 and B 2 forevery possibleload,whichwillrequirealargedatale.Theextensiv eleaccessoperation makesthismethodinecient. Anotherlimitationofthismethodisthatthele-basedmodelr equiresalarge numberoftestingloadpointstobeabletointerpolateorextr apolatesmoothlyon theSmithchart.Figure4.4illustratesthisproblem.Ascanob served,thele-based modeldoesn'textrapolatetheoutputpowercontoursproperl y.Analyticmodelsare abletoovercomethisproblem,aswillbedemonstratedinthee xamplesinSection4.5. [75]isanexampleoftheuseofanalyticmethodstomodelthelo adpullperformanceofadevice.ByexpandingthelinearS-parameterthrou ghanonlinear S 21 function,themodelwasabletopredictthegaincompressione ects.Thisisoften called\large-S21"method.Thistechniqueprovidesasimple solutiontopredictthe nonlinearperformanceoftheDUTbasedontheloadpullmeasurem ents.However, thelarge-S21modelhaslimitedaccuracyinpredictingtheg ain/phasecompression andintermodulationperformanceatdierentloadconditio ns. Duetothelimitationofthecurrentmodelingtechniquesbase dontheloadpull measurementdatasets,anewapproachisproposedtoaddresstheli mitations.The 64

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Pout comparison (Pin at -30 dBm): file-based model vs. measurement File-based ModelMeasurement Figure4.4Theinterpolationandextrapolationproblemwit hthele-basedmodel. Thisisduetotheinsucienttestingpoints.However,aswillbesh owninlater sections,analyticmodelshavebetterperformanceininterpo lationandextrapolation. newmodelingtechniqueexploitsthelarge-signalscattering functiontheoryandderivestherelationshipbetweentheincidentandscatteringwa vesthroughtheloadpull measurementdatasets.Thedetailanalysisisgiveninthefollow ingsection. 4.4Behavioralmodelbasedonloadpullgainandphasecompre ssionmeasurements Apowerampliercanbetreatedasatwo-portnetwork,asshown inFigure4.5.A typicalone-toneloadpullmeasurementgivesinformationab outthesourceimpedance (orrerectioncoecient, S ),loadimpedances(orrerectioncoecient, L ),theinput power( P in ),themeasureddeliveredpower( P out ). Forsimplicity,supposethedeviceisunilateral(i.e. S 12 =0),theinputimpedance oftheport1canbeexpressedasEquation4.13.Thisconstrainca nberemovedif 65

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I DUT E S Z S 1 V 1 G S G IN G OUT G L Z L V 2 I 2 Figure4.5Diagramofatwo-portnetworkwithavoltagesource of E s andsource impedanceof Z S .Theloadimpedanceis Z L theinputportrerectedpoweriscapturedintheloadpullmea surement. Z in = Z 0 1+ IN 1 IN = Z 0 1+ S 11 1 S 11 (4.13) Basedonthegiveninformation,thevoltageandcurrentatpor t1canbecalculated throughthefollowingsteps: Z S = Z 0 1+ S 1 S (4.14) P in = E 2 S 8 Re ( Z S ) (4.15) E S = p 8 Re ( Z S ) P in (4.16) V 1 = E S Z in Z in + Z S (4.17) I 1 = V 1 Z in (4.18) 66

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Therefore,theincidentandrerectedwaveformsatport1are calculatedas: A 1 = V 1 + I 1 Z 0 p 2 Re ( Z 0 ) = V 1 M 1 (4.19) B 1 = V 1 I 1 Z 0 p 2 Re ( Z 0 ) = A 1 S 11 (4.20) M 1 = Z 0 + Z in Z in p 2 Re ( Z 0 ) (4.21) Theincidentandrerectedwaveformsatport2arecharacteri zedbasedonthe large-signalscatteringfunctiontheory,asshowninEquation 4.22andEquation4.23. Thephaseofthe A 11 P ,isabsorbedintothe T 22 coecient. B 2 = S 21 A 1 + S 22 A 2 + T 22 A 2 (4.22) A 2 = B 2 L (4.23) CombiningEquation4.22and4.23gives: B 2 = S 21 A 1 + S 22 B 2 L + T 22 B 2 L (4.24) Equation4.24isanimplicitexpressionfor B 2 ;itcanbefurthertransformedto anexplicitfunctiontosimplifythemodelgeneration.Assume S 21 S 22 and T 22 are representedas: S 21 = c 1 +j c 2 S 22 = c 3 +j c 4 T 22 = c 5 +j c 6 67

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where c i ;i =1 ; ; 6areunknownstobedetermined. Suppose B 2 = B 2 r +j B 2 i and A 1 = A 1 r +j A 1 i B 2 r and B 2 i aretherealand imaginarypartsof B 2 respectively. A 1 i and A 1 i aretherealandimaginarypartsof A 1 respectively.Equation4.24canberewrittenas: ( c 1 +j c 2 ) A 1 +( k 1 +j k 2 ) B 2 +( m 1 +j m 2 ) B 2 =0(4.25) where k 1 +j k 2 =( c 3 +j c 4 ) L 1(4.26) m 1 +j m 2 =( c 5 +j c 6 ) P 2 L (4.27) Arrangetherealandimaginarypartandwecanget: 264 c 1 A 1 r c 2 A 1 i c 1 A 1 i + c 2 A 1 r 375 + 264 k 1 + m 1 k 2 + m 2 k 2 + m 2 k 1 m 1 375 264 B 2 r B 2 i 375 =0(4.28) Bysolvingthelinearfunction4.28,therealandimaginarypa rtof B 2 canbe derivedas: 264 B 2 r B 2 i 375 = 1 D 264 ( k 1 + k 2 m 1 m 2 ) c 1 ( k 1 + k 2 + m 1 m 2 ) c 2 ( k 1 k 2 + m 1 m 2 ) c 1 ( k 1 + k 2 + m 1 + m 2 ) c 2 375 264 A 1 r A 1 i 375 (4.29) where D = k 2 1 k 2 2 m 21 + m 22 Obviously,inordertoobtainthe B 2 r and B 2 i ,themeasurementsforboththe magnitudeandphasearerequired.Thisiswhyitisimportantt oobtaintheloadpull AM-PMdatasets.TheloadpullAM-AMmeasurementsprovidetheoptim ization 68

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criteriaforthemagnitude,whiletheloadpullAM-PMmeasurem entssetuptherule forthephaseoptimization. Themagnitudecanbederivedfromthedeliveredoutputpower .Theoutput poweratport2isdeterminedbythe A 2 and B 2 through: P out = 1 2 ( j B 2 j 2 j A 2 j 2 ) = 1 2 j B 2 j 2 (1 j L j 2 )(4.30) Sincetheoutputpowerisknownthroughthemeasurement,the B 2 canbeexpressedas: j B 2 j = s 2 P out 1 j 2L j (4.31) Optimizationprocesscanbeappliedtoobtainthe6unknownco ecients c 1 to c 6 Theleast-mean-square(LMS)errorsforthemagnitudeandphase canberepresented byEquation4.4and4.4. err mag = X n (( B 2 2 r + B 2 2 i ) ( 1 1 j L j 2 P out )) 2 n (4.32) err phase = X n (( A 2+ B 2 A 1+ B 1 ) AM-PM) n (4.33) where n isthenumberofloadpointsusedintheoptimizationprocess.AMPM isthephasecompressiondataobtainedthroughtheloadpullAM-P Mmeasurement. Itisthephasedierencebetweenthevoltagesattheinputand outputports.The 69

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Optimize Measurements Loadpull Model Formulation Data Preparation and Simulations Loadpull Meet the Criteria? Save and exit YES NO Coefficients Figure4.6TherowchartoftheMatlabprogramcreatedforthe behavioralmodel optimizationbasedontheloadpullAM-AMandAM-PMdatasets.inputandoutputvoltagesarethesumoftheincidentandrerec tedwavesattheport respectively. TheanalysisgivenabovehasbeenimplementedinaMatlabprog ram[76].Figure4.6demonstratestheproceduretogeneratethebehaviora lmodelbasedonthe loadpulldatasets.Noticethattheloadpulldatasetscancomefr omeitherthemeasurementsorfromsimulations,dependingontheapplicationsofth ismodelingtechnique. 4.5Experimentalresult1:measurement-basedbehavioralm odel Todemonstratethemodelingtechniqueproposedinprevioussec tion,threeexamplemodelsarecreatedandcomparedwithexistingtechniques. Thethreeexamples arechosensothattheyshowtwotypesofapplicationsofthisbeh avioralmodeling technique.Thersttwoexamplemodelsarecreatedbasedonmea surementresults, showinganecientwaytointegratemeasurementresultsintode sign.Thethirdex70

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Figure4.7IllustrationoftheMAXIM2373LNAsample. ampleisbasedonthesimulationresults,whichwillleadtodecre mentincomputing complexityandthereforethesimulationtime.4.5.1ExamplemodelofapackagedRFICLNA TherstexamplecomponentusedisanMAX2373lownoiseamplier(L NA). Figure4.7showsthiscomponent.Thiscomponentwascharacte rizedat900MHz. Loadpullgainandphasecompressionmeasurementswereperforme d.Twotoneloadpullmeasurementswereperformedaswell.TheMatlabmodelin gprogramwasused toprocessthemeasurementdatalesandgeneratethemodelcoe cientsthrough theunconstraintnonlinearoptimizationprocedure.Inaddi tion,ale-basedmodelis createdforcharacterizingthe3rdorderintermodulationp roducts. ThemodelwasimplementedinADS2004Ausingthefrequencydoma indened device(FDD).Theadvantageofusingthisdeviceisthatitpro videstheabilityto denethebehaviorofindividualfrequencycomponentssepar ately.Themodelonlyrequirestwosetupparameters:thefundamentalfrequency(RFfr eq),andthefrequency spacing(fspacing).Foronetonesimulation,thefspacingisseta t0.Therefore,the modelrequiresminimuminteractionfromtheusersandmakesi teasyforusage. 71

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-30 -25 -20 -15 -10 -5 0 5 2 3 4 5 Pin (dBm)Gain (dB) -30 -25 -20 -15 -10 -5 0 5 -10 0 10 20 Pin (dBm)Ph. Compress. (degree) Meas.Beh. Model Meas.Beh. Model Figure4.8Comparisonofthemeasuredandsimulatedgainandpha secompression at50ohm. Themeasurementconditionissummarizedinthefollowing: Frequency:900MHz; Inputpower:-30dBmto5dBm; Twotonefrequencyspacing:100KHz; AGCBias:1.3875V; Vccbias:2.775V. Figure4.8comparesthemeasuredandsimulatedgainandphaseco mpression performanceofthisLNAat50ohmcondition.Themodelpredict sthecompression propertycorrectly. Figure4.9showsthesimulatedoutputpowercontourscompared withthemeasuredresult.Theinputpowerislowat-30dBm.Goodagreementi sobserved.In fact,thelargesignalmodelreducestosmall-signalS-paramet ermodelwhentheinputsignalislowenough.Thevariationoftheoutputpowerwit hrespecttotheload 72

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Pout comparison (Pin at -30 dBm): behaviroal model vs. measurement BEH. ModelMeasurement Figure4.9Thesimulatedoutputpowercontoursarecomparedw iththemeasurements.Theinputpowerisat-30dBm.canbecharacterizedthroughthesmall-signalS-parameter.D etailedanalysiscanbe foundin[77].Comparedwiththele-basedmodel,obviouslyth eanalyticmodel providesmuchbetterinterpolationandextrapolationchar acteristics. However,thesmall-signalS-parametercannotpredictaccurat elynonlineareects associatedwithlargeinputsignal.Thesimplelarge-S21modelp rovideslimitedpredictionaccuracy,comparedwiththeproposedmodel,asshowni nFigure4.10.In thisgure,themeasuredoutputpowercontouratinputsignalo f-5dBmiscompared withthelarge-signalmodelin(a)andthemodelbasedonthelar ge-S21techniquein (b).Bylookingat(a),onecanseethattheproposedbehavioral modeldoesadecent jobinpredictingthechangeintheloadimpedanceforoptima loutputpowerperformance.However,thesimplelarge-S21modelingtechniqueassume sthecompression propertiesatallloadpointsarethesame.Thisexplainswhyt helarge-S21model behavesdierentfromtheproposedlarge-signalmodel. Sinceonlythefundamentaltoneisconsideredinthemodelgen eration,itscapabilitytopredicttheintermodulationproductsislimite d.Therefore,ale-based 73

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BEH. ModelMeasurement Better prediction of the optimal load impedance (a) Large-S21 ModelMeasurement The large-S21 model cannot predict the optimal load impedance correctly. (b) Figure4.10Comparisonofsimulatedandmeasuredoutputpowerc ontours.Thenew modelandthelarge-S21modelarecomparedsidebyside,showing theimprovement ofthenewmodeltopredictthechangingoptimalloadimpedan ce. Table4.1Listofthe6exampleloadrerectioncoecientsusedt otesttheLNA model. (a) 0.56723+j*0.03630 (b) 0.36904+j*0.40569 (c) 0.75532+j*0.50893 (d) 0.77211+j*0.16110 (e) 0.17539+j*0.76875 (f) 0.30559-j*0.57057 modelisimplementedforpredictionofthe3rdorderintermo dulationproducts.A contourinterpolationalgorithmisutilizedduringthegen erationofthedatale. Figure4.11illustratesthecomparisonofthemeasuredandsimul atedIP3.The inputpoweris-20dBm.Ascanbeseen,thebehavioralmodeldoes agoodjob predictingtheIP3performanceoveradenedregion. Sixloadimpedancesarechosenasexamplestotestthelarge-sig nalmodel.The simulatedfundamentaltoneandthe3rdorderintermodulatio nproductarecompared withthemeasurementresults.Thererectioncoecientsofthe6 exampleloadsare listedinTable4.1andplottedinSmithChart,asshowninFigur e4.12.Theload examplesarechosentospreadovertheSmithChart. Thesimulatedresultsarecomparedwithcorrespondingmeasurem entdatasets inFigure4.13.Goodagreementscanbeobservedforallcases.Also givenout 74

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15.3839 13.6338 11.8836 10.1335 15.8015 13.9914 12.1813 10.3711 BEH. ModelMeasurement Figure4.11ComparisonofthemeasuredandsimulatedIP3usingth elarge-signal behavioralmodel. a b c d e f Figure4.12Illustrationofthesixloadimpedanceexampleson theSmithChart.The sixloadsspreadinalargearea,showingtherobustnessofthismod eltopredictthe nonlineareectinawideloadrange. 75

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arethesimulatedresultsobtainedfromthelarge-S21model.T helarge-S21model presentsgoodperformanceforlimitedsetofloadpoints,suchas at(a),(d),(e), and(f).However,at(b)and(c)thesimulationresultsshowsigni cantdiscrepancies. Therefore,thenewlarge-signalbehavioralmodelprovidesb etterperformanceagainst thelarge-S21behavioralmodel. Figure4.14showstheerrorsinthesimulatedfundamentaltone atdierentloads. Ascanbeseen,thenewmodelhasmuchlesserrorscomparedwithth elarge-S21 model.Similarly,Figure4.15illustratestheerrorsinthesi mulatedIM3atdierent loads.Again,thenewmodelhasbetterperformancecomparedwi ththelarge-S21 model. 76

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-25 -20 -15 -10 -5 0 5 -20 -10 0 10 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -100 -50 0 Pin (dBm)IM3 (dBm) Meas.Large-S21 ModelNew Beh. Model Meas.Large-S21 ModelNew Beh. Model -25 -20 -15 -10 -5 0 5 -20 -10 0 10 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -80 -60 -40 -20 0 Pin (dBm)IM3 (dBm) Meas.Large-S21 ModelNew Beh. Model Meas.Large-S21 ModelNew Beh. Model (a)0.56723+j*0.03630(b)0.36904+j*0.40569 -25 -20 -15 -10 -5 0 5 -15 -10 -5 0 5 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -80 -60 -40 -20 0 Pin (dBm)IM3 (dBm) Meas.Large-S21 ModelNew Beh. Model Meas.Large-S21 ModelNew Beh. Model -25 -20 -15 -10 -5 0 5 -20 -10 0 10 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -100 -50 0 Pin (dBm)IM3 (dBm) Meas.Large-S21 ModelNew Beh. Model Meas.Large-S21 ModelNew Beh. Model (c)0.75532+j*0.50893(d)0.77211+j*0.16110 -25 -20 -15 -10 -5 0 5 -20 -10 0 10 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -100 -50 0 Pin (dBm)IM3 (dBm) Meas.Large-S21 ModelNew Beh. Model Meas.Large-S21 ModelNew Beh. Model -25 -20 -15 -10 -5 0 5 -30 -20 -10 0 10 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -100 -50 0 Pin (dBm)IM3 (dBm) Meas.Large-S21 ModelNew Beh. Model Meas.Large-S21 ModelNew Beh. Model (e)0.17539+j*0.76875(f)0.30559-j*0.57057 Figure4.13ComparisonofthemeasuredandsimulatedPoutandIM 3at6load impedances. 77

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-25 -20 -15 -10 -5 0 5 -4 -2 0 2 4 6 Pin (dBm)Error (dB) Figure4.14Theerrorsofthesimulatedfundamentaltoneat6l oadsareplotted. Thebluecurvesrepresenttheerrorsassociatedwiththenewlyd evelopedmodel;the redcurvesrepresenttheerrorsassociatedwiththelarge-S21m odel.Thenewmodel presentsbetterperformance,comparedwiththelarge-S21mo del. -25 -20 -15 -10 -5 0 5 -15 -10 -5 0 5 10 Pin (dBm)Error (dB) Figure4.15Theerrorsofthesimulated3rdorderintermodula tionproductat6loads areplotted.Thebluecurvesrepresenttheerrorsassociatedwi ththenewlydeveloped model;theredcurvesrepresenttheerrorsassociatedwiththel arge-S21model.The newmodelpresentsbetterperformance,comparedwiththelar ge-S21model. 78

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Figure4.16IllustrationoftheISL3984powerampliersample 4.5.2ExamplemodelofaPAsample ThesecondexamplecomponentusedisanIntersilpoweramplier (ISL3984). Figure4.16showsthetestedISL3984powerampliersample.Loa dpullgainand phasecompressionmeasurementswereperformedonthispoweramp liersampleat 2450MHz.Themeasurementconditionissummarizedbelow: Frequency:2450MHz; Inputpower:-20dBmto0dBm; Twotonefrequencyspacing:100KHz; Bias:3.3V. Toverifytheperformanceofthebehavioralmodel,asweptpow erharmonicsimulationisdonein50ohmcondition,i.e.thesourceandloadimp edancesareat50ohm. Thesimulatedgainandphasecompressioncurvesarecomparedtot hemeasureddata inFigure4.17.Goodagreementcanbeseeninthegure. 79

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-20 -15 -10 -5 0 5 18 20 22 24 26 Pin (dBm)Gain (dB) -20 -15 -10 -5 0 5 -6 -4 -2 0 2 Pin (dBm)Phase Compression (degree) HP8719D MeasBEH. ModelATS Meas. HP8719D Meas.BEH. ModelATS Meas. Figure4.17Comparisonofthesimulatedandmeasuredgainandph asecompression in50ohm. Figure4.18comparesthesimulatedandmeasuredoutputpowerc ontoursatinput powerlevelof-20dBm.Thesourceimpedanceissettobeconjuga telymatched.The S is0 : 34051+j 0 : 58271.Ascanbeseen,thetwodatasetsagreeverywell. SimilartotheLNAmodel,ale-basedmodeliscreatedforthesim ulationofIM3. Figure4.19comparesthesimulatedandmeasuredIM3contoursa tinputpowerlevel of-20dBm.Thele-basedmodelpredictsthe3rdorderintermo dulationproduct accuratelyundervariousloadconditions. Sixloadimpedancesarechosenasexamplestotestthelarge-sig nalmodel.The simulatedfundamentaltoneandthe3rdorderintermodulatio nproductarecompared withthemeasurementresults.Thererectioncoecientsofthe6 exampleloadsare listedinTable4.2andplottedinSmithChart,asshowninFigur e4.20.Theload examplesarechosentospreadovertheSmithChart. Thesimulatedresultsarecomparedwithcorrespondingmeasurem entdatasetsin Figure4.21.Goodagreementscanbeobservedbetweenthesimul atedresultsfrom theproposedmodelandthemeasurements.Alsogivenoutarethesimu latedresults 80

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Pout comparison (Pin at -20 dBm): behvairoal model vs. measurement BEH. ModelMeasurement Figure4.18Comparisonofthesimulatedoutputpowercontourw iththemeasured dataset. IM3 comparison (Pin at -20 dBm): behvairoal model vs. measurement BEH. ModelMeasurement Figure4.19ComparisonofthesimulatedIM3contourusingthebe havioralmodel withthemeasureddataset.Table4.2Listofthe6exampleloadrerectioncoecientsusedt otestthePAmodel. (a) 0.62561+j*0.39360 (b) -0.36966+j*0.09652 (c) 0.19215+j*0.33529 (d) 0.87741+j*0.07210 (e) 0.61180+j*0.627895 (f) 0.52078-j*0.53337 81

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a b c d e f a b c d e f Figure4.20Illustrationofthesixloadimpedanceexamplesuse dtotestthebehavioral modeldevelopedfortheISL3984ontheSmithChart.Thesixloa dsspreadinalarge area,showingtherobustnessofthismodeltopredictthenonlin eareectinawide loadrange.obtainedfromthelarge-S21model.Thelarge-S21modelprese ntsgoodperformance forlimitedsetofloadpoints,suchasat(a),(b),(d),and(e).Ho wever,at(c)and (f)thesimulationresultsshowsignicantdiscrepancies.Theref ore,thenewlargesignalbehavioralmodelprovidesbetterperformanceagainst thelarge-S21behavioral model. Figure4.22showstheerrorsinthesimulatedfundamentaltone atdierentloads. Ascanbeseen,thenewmodelhasmuchlesserrorscomparedwithth elarge-S21 model.Similarly,Figure4.23illustratestheerrorsinthesi mulatedIM3atdierent loads.Again,thenewmodelhasbetterperformancecomparedwi ththelarge-S21 model. Throughthecomparisonresultsillustratedfromthetwoexampl emodels,the validityofthemodelhasbeenproved.Thebehavioralmodeld erivedfromtheloadpull gainandphasecompressionmeasurementscanpredicttheperform anceoftheDUT undervariousloadconditionsandinputpowerlevelsaccura telytosomeextent. 82

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-25 -20 -15 -10 -5 0 5 5 10 15 20 25 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -60 -40 -20 0 20 Pin (dBm)IM3 (dBm) Meas.New Beh. ModelLarge-S21 Model Meas.New Beh. ModelLarge-S21 Model -25 -20 -15 -10 -5 0 5 5 10 15 20 25 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -60 -40 -20 0 20 Pin (dBm)IM3 (dBm) Meas.New Beh. ModelLarge-S21 Model Meas.New Beh. ModelLarge-S21 Model (a)0.62561+j*0.39360(b)-0.36966+j*0.09652 -25 -20 -15 -10 -5 0 5 5 10 15 20 25 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -60 -40 -20 0 20 Pin (dBm)IM3 (dBm) Meas.New Beh. ModelLarge-S21 Model Meas.New Beh. ModelLarge-S21 Model -25 -20 -15 -10 -5 0 5 0 5 10 15 20 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -60 -40 -20 0 Pin (dBm)IM3 (dBm) Meas.New Beh. ModelLarge-S21 Model Meas.New Beh. ModelLarge-S21 Model (c)0.19215+j*0.33529(d)0.87741+j*0.07210 -25 -20 -15 -10 -5 0 5 0 5 10 15 20 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -60 -40 -20 0 20 Pin (dBm)IM3 (dBm) Meas.New Beh. ModelLarge-S21 Model Meas.New Beh. ModelLarge-S21 Model -25 -20 -15 -10 -5 0 5 5 10 15 20 25 Pin (dBm)Pout (dB) -25 -20 -15 -10 -5 0 5 -60 -40 -20 0 20 Pin (dBm)IM3 (dBm) Meas.New Beh. ModelLarge-S21 Model Meas.New Beh. ModelLarge-S21 Model (e)0.61180+j*0.62789(f)0.52078-j*0.53337 Figure4.21ComparisonofthemeasuredandsimulatedPoutandIM 3at6load impedances. 83

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-25 -20 -15 -10 -5 0 5 -1 -0.5 0 0.5 1 1.5 2 2.5 Pin (dBm)Error (dB) Figure4.22Theerrorsofthesimulatedfundamentaltoneat6l oadsareplotted. Thebluecurvesrepresenttheerrorsassociatedwiththenewlyd evelopedmodel;the redcurvesrepresenttheerrorsassociatedwiththelarge-S21m odel.Thenewmodel presentsbetterperformance,comparedwiththelarge-S21mo del. -25 -20 -15 -10 -5 0 5 -8 -6 -4 -2 0 2 4 6 8 Pin (dBm)Error (dB) Figure4.23Theerrorsofthesimulated3rdorderintermodula tionproductat6loads areplotted.Thebluecurvesrepresenttheerrorsassociatedwi ththenewlydeveloped model;theredcurvesrepresenttheerrorsassociatedwiththel arge-S21model.The newmodelpresentsbetterperformance,comparedwiththelar ge-S21model. 84

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Thismeasurement-basedbehavioralmodelingtechniqueisalso demonstratedas simplesolutiontointegratetheloadpullmeasurementdatasets withcommercialCAE softwares.Theresultedmodelprovidestheinvaluableinsights fordesignerstostudy nonlinearcomponentsatsystemlevelswithoutlosingmuchaccu racy. 4.6Experimentalresult2:simulation-basedbehavioralmo del Wehavediscussedthemeasurement-basedbehavioralmodelingapp roachinprevioussection.Thesecondbehavioralmodelingexamplewillde monstratetheprocess toderiveaabstractmodelbasedonthesimulationdatasets.Anequi valentcircuit modelforthe30WattsCreeUGF21030LDMOSpowertransistorisuse dtocreate thesimulationdatasets.ThiscircuitmodelwasdevelopedbyMo delithics[78]. Thismodelwassimulatedat2.17GHzundersweptpowerandvariou sloadconditions.ThesimulatedAM-AMandAM-PMdatasetswereusedtocreatet helargesignalbehavioralmodel.Thesimulationsetupforgeneratingt hetestdatasetsis givenbelow: Frequency:2170MHz; Inputpower:0dBmto35dBm; Twotonefrequencyspacing:100KHz; Bias:Vgsis4VandVdsis25V(biasedfordeepClassABamplier). Figure4.24comparesthesimulatedresultsfromthebehaviora lmodelandthe circuitmodelforthegainandphasecompression.Goodagreemen tsareachievedfor the50ohmcase. Figure4.25andFigure4.26showthedeliveredpowersimulated underloadpull conditions,attwoinputpowerlevels(10dBmand30dBm).Theso urcererect 85

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0 5 10 15 20 25 30 35 0 5 10 15 Pin (dBm)gain (dB)AM-AM and AM-PM comparison: Behavioral model vs. Circuit model Beh. modelCircuit model 0 5 10 15 20 25 30 35 -55 -50 -45 -40 Pin (dBm)AM-PM (degree) Beh. modelCircuit model Figure4.24Comparisonofthesimulatedgainandphasecompressio nunder50ohm condition:behavioralmodelvs.circuitmodel.coecientissetat 0 : 55244 j 0 : 23757.Forthesmallinputpowerlevel(10dBm), thebehavioralmodelpresentsalmostidenticalperformancea sthecircuitmodel. Evenathighpowerlevels(e.g.30dBm),thebehavioralmodel stilldoesagoodjob topredictthedriftintheoptimalloadimpedancefortheout putpower. Asoneexampletodemonstratetheimportancetohavetheloadpu llAM-PM informationinthemodelcreation,twobehavioralmodelswe recreated,oneoptimized withtheAM-PMinformationandonewithout. Figure4.27comparestheIM3contourssimulatedbythebehavi oralmodelswith andwithouttheAM-PMinformation.Theresultsareobtainedth roughEnvelope simulationofthebehavioralmodel.Obviously,theloadpullAM -PMinformation doeshelpthelarge-signalmodeltodoabetterjobtopredictt heintermodulation performance.Thiscomparisonprovestheimportanceofhavin gtheloadpullinformationforcreatingalarge-signalbehavioralmodelbasedonl oadpullmeasurements. Noticethatnotliketheprevioustwoexamplemodels,theIM3pr edictionheredoesn't dependonle-basedmodels. 86

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Pout comparison (Pin at 10 dBm): behvairoal model vs. circuit model BEH. Model CIR. Model Figure4.25ComparisonofthesimulatedPoutcontoursfromthe behavioralmodel andthecircuitmodelatconstantPinof10dBm. Pout comparison (Pin at 30 dBm): behvairoal model vs. circuit model BEH. Model CIR. Model Figure4.26ComparisonofthesimulatedPoutcontoursfromthe behavioralmodel andthecircuitmodelatconstantPinof30dBm. 87

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IM3 Comparison for two different behavioral models Without LP AM-PM With LP AM-PM Figure4.27ComparisonofthesimulatedIM3contoursfrombeha vioralmodels:one optimizedwithloadpullAM-PMinformationandonewithout. Figure4.28comparesthesimulatedIM3contoursfromthebeha vioralmodel(with theAM-PMinformation)andthecircuitmodel.Ingeneral,the modelpredictsthe trendoftheIM3performance.However,sinceonlythefundamen taltoneisutilized inthemodelgeneration,itsabilitytopredicttheIM3islim ited.Togetbetterresults fortheintermodulationproducts,eitherle-basedmodelcan beusedoradditional loadpullharmonicmeasurementswillhelp. Figure4.29evaluatestheperformanceofthebehavioralmod elundertwotone stimuliagainstthatofthecircuitmodel.Theinputpowerisset tosweepinthe simulation.Again,bothbehavioralmodelsareevaluated.High levelagreementscan beobservedforthesimulateddatasetsfrombothmodels. Noticethedierencebetweenthetwobehavioralmodels.Themo delwithoutthe AM-PMinformationpredictsafalsesweetspotintheIM3curve.Th isisavoided throughincludingtheAM-PMinformationinthemodelgenerat ionprocess. 88

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IM3 comparison (Pin at 10 dBm): behaviroal model vs. circuit model BEH. Model CIR. Model Figure4.28ComparisonofthesimulatedIM3contoursfromtheb ehavioraland circuitmodels. 0 5 10 15 20 25 30 0 10 20 30 40 Behavioral Model and Circuit Model Performance Comparison Pin (dBm)Pfund (dBm) circuit modelbeh. model 1beh. model 2 0 5 10 15 20 25 30 -60 -40 -20 0 20 40 Pin (dBm)IM3 (dBm) circuit modelbeh. model 1beh. model 2 Figure4.29ComparisonofthesimulatedIM3fromthecircuitmo delandthebehavioralmodels.Behavioralmodel1iscreatedwiththeloadpull AM-PMinformation, whilebehavioralmodel2isn't.ThesimulatedIM3Behavioralm odel2showsafake sweetspot,showingtheimportancetohavetheloadpullAM-PMinf ormationinthe modelgenerationprocess.The L isat 0 : 80213 j 0 : 08629. 89

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. Table4.3Simulationtimecomparison:behavioralmodelvs.ci rcuitmodel.Loadpull harmonicbalancesimulationatthreeinputpowerlevelsispe rformedforthistest. Type 10dBm 20dBm 30dBm BEH.Model 2.55sec 2.66sec 2.89sec CIR.Model 3.08sec 3.95sec 4.05sec Oneadvantageusingbehavioralmodelsinsteadofcircuitmode lsisthatbehavioral modelsrequirelesssimulationtime.Thiswillbecomeimporta ntwhensimulatinga completedesignsystem,whichusuallycontainsdozensoftransist orsormore. Table4.6comparesthesimulationtimeusingthebehavioralmo delandthecircuit model.Theloadpullharmonicbalancesimulationfor100load pointsisperformed atthreedierentinputpowerlevels:10dBm,20dBmand30dBm. Thistest wasperformedonaworkstationwithaPentium-4CPUand1GBmem ory.The behavioralmodelrequireslesssimulationtime,especiallyat highpowerlevels,ascan beobservedfromthetable.4.7Conclusion Inthischapter,abehavioralmodelingtechniqueispresente dthatisbaseddirectlyontheloadpullgainandphasecompressionmeasurements.D evelopedfrom thelarge-signalscatteringfunctiontheory,thistechnique showsthepossibilityto generatethelarge-signalscatteringfunctionmodelusingtra ditionalloadpullmeasurementsystems.Thelarge-signalscatteringfunctiontheoryis presentedandthe analogybetweentheLSNAandtheloadpullmeasurementsystemsis drawn.Adetailanalysisofthemodelgenerationprocessisgivenout.Thr eeexamplebehavioral modelsarecreatedtodemonstratethecapabilityofthisnewt echnique.Twoofthem arebasedonmeasurements,whileoneisbasedonthesimulationdat asetfroma equivalentcircuitmodel.Thesemodelsarestudiedfromdier entaspects,including 90

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theonetoneloadpullandpowersweptsimulation,twotoneload pullandpowerswept simulation.Goodagreementsareobservedbetweenthemodelsim ulatedresultsand measurements,showingthestrongcapabilityofthismodelingte chnique. 91

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CHAPTER5 MEMORYEFFECTMODELINGOFPOWERAMPLIFIERSIN LOADPULLCONDITIONS 5.1Introduction Thememoryeectinapoweramplierexhibitsitselfeitherin thefrequency domainasasymmetricspectrum,ortimedomainasthedynamicAMAMandAMPMbehavior.Thiseectiscausedbyseveralissues,includinginp utandoutputtuned network,lowfrequencydispersion,electrothermalinteract ionsandbiascircuitry[3], [4].Thememoryeectbehavioralmodelingofpoweramplier softendealswith timedomainsamples,typicallyobtainedthroughvectorsignal analyzers(VSAs)or microwavetransitionanalyzers(MTAs)[39][79].Thereasontost udythetestsignal intimedomainisthatthememoryeectscanbeobservedeasilyi ntimedomain throughthedynamicAM-AMandAM-PMnonlinearphenomena. Figure5.1showsatypicaltimedomainmeasurementsetup.Theba sebandI/Q signalisgeneratedthroughthePCsoftwareanddownloadedtot hearbitrarywaveformgenerator(AWG).Thesignalgeneratoracceptsthemodul atedsignalfromthe AWGandup-convertsittothedesiredfrequency.Themodulate dsignalisusedto drivetheDUT;theoutputsignalisdown-convertedandsampledt hroughthevector signalgenerator(VSA).TheinputsignaltotheDUTcanbeobtained bydirectly applyingtheinputsignaltotheVSAinputport.Similaroperat ions,suchasdownconversionandsampling,willbeperformedontheinputsignal. Theinputandoutput 92

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samplesshouldbealignedintimesothatthecorrectinput-outp utresponsecanbe derived. I & Q DAC LO Signal Analyzer AWG DACDAC Signal Generator RF Switch DUT BOX Q I LO o 90 Figure5.1Examplemeasurementsetuptoobtainthetime-domai ntestsignal[79]. Oncetheinputandoutputsamplesareobtained,themodelingp roblemisreduced tomatchingtheinputsamplestotheoutputsamplesthroughela boratemathematical expressions.Thishasbeenstudiedextensivelyindigitalsignalp rocessingarea[80] [81],althoughmostlythebasebandengineersdealwithlinear processing.Byadding nonlinearblocksintheprocessingalgorithms,abehavioralmo delcanbecreatedthat capturesboththememoryanddistortioneectsoftheamplie runderstudy. Lotsofmodelingtechniqueshavebeenreportedtocharacter izethememoryeect ofapoweramplier[34,79,82,83,84,85].Generallyspeakin g,thesemodeling techniquescanbegroupedintotwocategories: two-boxorthree-boxmodelingtechniques[34][82]and[85] thatseparatethe linearmemoryeectfromthenonlinearbehaviorandtreatth emdierentmathematically;typically,look-up-tableorpolynomialsareu sedtomodelthenonlineargainandphasecompression,whilelinearlteringfunct ionsareusedto tthelinearmemoryeect; 93

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integratednonlinearmodelingtechniques[79],[83]and[8 4],whichexploitthe capabilitiesofmulti-tappolynomialordynamicneuralnet workstructuresto modelboththememoryeectandthenonlineargainandcompre ssionbehavior. 5.1.1Filteringmodelingofmemoryeects Tosimplythemodelingproblemsofthenonlinearampliers,th etwo-boxorthreeboxmodelstructuresareproposedthatarecomposedofthelinea rdynamictime invariantsystemsandstaticnonlinearsystem,e.g[39],[34]and [85].Successful resultshavebeenreportedbyusingthesetechniques.Forexampl e,themethod proposedin[82]adoptsatwo-boxmodelingstructurethathasa linearniteimpulse ltering(FIR)blockandanonlinearfunctionblock.Themod eldiagramisshown inFigure5.2.TheoutputsignalfromtheFIRblockisgiveninE quation5.1.This outputsignalofthismemorymodelcanbeexpressedinEquation5 .2. u(n) LinearFilter AM/PM LUT AM/AM and |x(n)| ComplexMultiplier x(n) Gq Gi x(n) y(n) Figure5.2Modeldiagramcombininglinearlteringandnonl inearLUTsections[82]. x ( n )= M X i =0 a i u ( n i )(5.1) y ( n )=( G i + jG q ) x ( n )= Gx ( n )(5.2) 94

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where x ( n )and y ( n )arethediscrete-timeinputandoutputsamples;the G i and G q aretheoutputofthenonlinearblock.Mrepresentsthememory spandetermining howmanypastsamplesareutilizedtopredictthecurrentoutpu tsample. Generally,themodelingprocessutilizingthetwo-boxorthr ee-boxstructureinvolvestwosteps.Therststepinvolvesde-embeddingthestaticn onlinearityfromthe datasamples.Thesecondstepistoidentifythecoecientsofthe lteringfunction throughoptimization.5.1.2Neuralnetworkmodelingofmemoryeects Severalneuralnetworkstructuresarereportedtomodelthem emoryeects.One commonfeatureofthereportedworksisthatallofthemutili zedelayedtapsto modelthememoryeects.Thedelayedtapsarebasicallyawayto combinethe currentandpastvaluestopredictthecurrentoutput.Ingene ral,theoutputsignal canbedescribedbyEquation5.3: y ( n )= f ANN [ y ( n 1) ;y ( n 2) ; ;y ( n p ) ;x ( n ) ;x ( n 1) ; ;x ( n q )](5.3) where x ( n )and y ( n )arethediscrete-timeinputandoutputsamples;pandqstand forthememoryspansfortheinputandoutputsamples. f ANN isanonlinearneural networkfunction. Isakssonetal[79]proposedusingdelayed-tapradialbasisfuncti onneuralnetwork (RBFNN)tomodelthedynamicAM-AMandAM-PMdistortion.TheRBFNNmodelcanbeadjustedthroughthenumberofneurons(M)intheh iddenlayerand thenumberofdelaytaps(L)totthetrainingseries.Itisshown inthepaper thatthistypeofneuralnetworkhasbetterperformancethan theone-tapparallel Hammersteinmodel. 95

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Fullyrecurrentneuralnetwork(FRNN)isanothertypeofdynam icneuralnetworkshavingthecapabilityoflearningandthenrepresentin gtheinput-outputbehaviorofsystems.Luongvinhetal[83]usethisnetworkstructure tomodelthe memoryeectsofanamplier.Byusingglobalfeedback(feedi ngtheoutputback totheinput),andlocalinterconnectionsinFRNN(connectin gtheneuronsinthe hiddenlayers),theabilityofthenetworktomodelnonlinear dynamicsofsystemscan beenhanced.Inthereportedwork[83],aWCDMAsignalisusedas thetrainingsignal.Athree-layerFRNNof10delaytapsand10hiddenneuronsa ndtanhactivation functionisconstructed. Atimedelayneuralnetwork(TDNN)isproposedbyAhmedetal[86]t omodel thememoryeectofthePA.Theperformanceoftheneuralnetwo rkmodelsutilizing unityandnon-unitytimedelaytapsarecompared.Itisshownt hatnon-unitydelay tapswillgivebetterresults. Woodetal[87]discussesamodelingmethodthatcombinesthepol ynomialbased \SystemAmplier"modelinADSthatmodelsonefrequencyAM-AMand AM-PM propertiesandaANNtomodelthedynamicpropertiesoftheampl ierundertest. TheANNistraineduponthedierencebetweentheoutputsignals oftheSystem Amplierandtheamplierundertest,overtherangeofthefreq uenciesandpower levels.Thedynamicalvariablesthatareusedaretimedelaysi ntheportvoltages. 5.2Limitationofcurrentmodelingtechniquesandproposed solution Whenweconsiderusingabehavioralmodelinasimulation,oneof theimportant featureisthatthemodelneedstoprovidethecapabilitytoa djustitsperformance accordingtotheenvironmentitisembeddedin.Inthisstudy, thesourceandload impedancesarethemainfactorsthatthemodelshouldbeablet oadjustperformance 96

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to.Ifweapplythiscriteriatothetechniquesdiscussedabove, wewillndthe limitationofthesemodelingtechniques. Themodelingtechniquesdiscussedabovedealwithpowerampli ersoperatingin onespecicloadimpedance,mostlikely50ohmcondition.When theloadcondition changes,thegainandphasecompressionpropertiesoftheampli ermightchangeas well.However,themodelingtechniquesdiscussedabovedon'tpr ovidethecapability topredictthischange.Thislimitstheapplicabilityofthe semodelsinrealworld designwork,inwhichthedesignengineerstendtooptimizethe irproductsthrough carefulloadpullanalysisandmatchingnetworksdesign. Animprovedbehavioralmodelisproposedinthischaptertoadd ressthislimitation.Thisimprovedmodelisbasicallyatwo-boxmodelthat combinestheloadawarelarge-signalscatteringfunctionbehavioralmodeland thelinearlteringfunctionmodel.AsshowninChapter4,thelarge-signalscatteringfu nctionmodelis capableofpredictingtheloadpullgainandphasecompression. Therefore,itisan excellentcandidate.FIRlteringfunctionisutilizedtoc haracterizethelinearmemoryeect,similarto[82].Theproposedmodelisillustratedin Figure.5.3.The mathematicalexpressionofthismodelisgiveninEquation5.4 FIR FILTER x(t) y(t) G(|x(t)|,ZL)*exp(j*Phase(|x(t)|,ZL) g(t) LoadPull Gain/Phase Model Figure5.3Diagramoftheproposedmemoryeectmodelwiththe load-related nonlineargain/compressioncharacterizationfeatureinteg rated. y ( t )=FIR( x ( t )) G ( j x ( t ) j ;Z L )exp j( x ( t ) ;Z L ) (5.4) 97

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where x ( t )and y ( t )areinputandoutputtimedomainsamples;FIR()isthelinear lter; G ()and()arethenonlineargainandphasecompressionmodels. Theadvantagesofthismodelingtechniqueincludes: Comparedtothetraditionalmemoryeectmodelingtechniqu es(asdiscussed inSection1),thisnewtechniquecanadjusttheAM-AMandAM-PMno nlinearfunctionscorrespondingtotheloadconditions;thismode lprovidesbetter performanceinsituationswheretheloadimpedancechanges; Comparedtothecontinuous-wave(CW)loadpullAM-AMandAM-PMmo del, thisnewmodelprovidesextracapabilitythroughthelinear blocktopredictthe frequencyresponseofthepoweramplierwhenawidebandmodul atedsignal isapplied. ThismodeldiagramisquitesimilartothemodelproposedbyAsbec ketal.[88], whousedanadditionalparametertocharacterizethedynamic eectsassociated withtime-varyingparameters,suchassupplyvoltageorinstant aneoustemperature. Thedierencehereisthattheadditionalparameterinthisn ewmodelistheload impedance,thatisusedtoadjusttheperformanceofthenonlin earblock. Oneimportantassumptionforthismodelingstructureisthatth elinearmemory eectisindependentoftheloadconditions.Theextractedme moryeectsfrom dierenttime-domainmeasuredsamplesatdierentloadimped ancesshouldremain thesame. Thelinearmemoryeectwasconceivedtosolvetheproblemwit hthememoryless narrow-bandmodelssuchastheAM-AMandAM-PMmodels.Theproblem appears whentheinputsignalbandwidthislargeenoughcomparedtoth esystembandwidth, thataCWrepresentationofthesystemisnolongervalid[3]. 98

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Therefore,thelinearmemoryeectrepresentstheresidualli nearfrequencyresponseofthesystemthatcannotbecharacterizedbythenonlinea rAM-AMand AM-PMmodels.Conceptually,itisresultedfromthefrequencyr esponseoftheinputandoutputtuningnetwork.Sincethesenetworksarelinea ringeneral,thesource andloadimpedanceswon'tchangetheirbehavior.Intheprop osedmodel,thelinear blockwillremainconstantregardlessofthesourceorloadcond itions. 5.3Experimentalresults Todemonstratetheeectivenessoftheproposedmodel,anexamp lemodelis developed.Duetothecurrentlimitationofthemeasurementc apabilities,theexample modelisderivedfromthesimulationresultsofanequivalentc ircuittransistormodel. Specically,thesameCree30WattsLDMOSmodeldiscussedprevio uslyinChapter 4isusedinthisstudy. A54MbpsWLANOFDMsignalisusedasthestimulustodrivethepower device. ThesimulationschematicisshowninFigure5.4.Thesimulationse tupislistedbelow: RFcarrierfrequency:2.17GHz; RFpower:20dBm; Vgs(gatevoltage):4V; Vds(drainvoltage):25V; TimeStep:20ps; StopTime:80us; ThedynamicAM-AMandAM-PMarecalculatedthroughEquation5.5 and5.6, usingthetimedomaininputandoutputsamples. y ( t )and x ( t )arecomplexinput 99

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Figure5.4Simulationschematicsetup:WLAN54MbpsOFDMsourcei sused. andoutputtimesamples,respectively.Duetothememoryeect, thegainandphase compressionwilldemonstratedynamicbehaviorundermodulate dstimuli,whichis showninFigure5.5. AM AM = y ( t ) x ( t ) (5.5) AM PM = y ( t ) x ( t ) (5.6) Figure5.5comparesthedynamicandstaticAM-AMandAM-PMperfor mances. By\static",wemeantheAM-AMandAM-PMobtainedunderCWstimuli. The dynamicsshownintheAM-AMandAM-PMobtainedundermodulatedsig nalstimuli isanevidenceofthememoryeect. ThelineareectisextractedbysubtractingthenonlinearAMAMandAM-PM fromthedynamiccurves.Figure5.6showstheextractedlinear memoryeect. 100

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-30 -20 -10 0 10 20 30 0 10 20 30 Pin (dBm)AM-AM (dB) DynamicStatic -30 -20 -10 0 10 20 30 -150 -100 -50 0 50 Pin (dBm)AM-PM (degree) DynamicStatic Figure5.5ComparisonofstaticanddynamicAM-AMandAM-PMeects. 54Mbps WLANsignalisusedinthemodulationsimulationsetup. -30 -20 -10 0 10 20 30 -10 0 10 20 Pin (dBm)AM-AM (dB) -30 -20 -10 0 10 20 30 -100 -50 0 50 Pin (dBm)AM-PM (degree) Figure5.6ExtractedlinearmemoryeectfromthedynamicAMAMandAM-PM eect. 101

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Tovalidateourassumptionoftheindependenceofthelinearme moryontheload impedances,severalloadimpedancesarechosenandthesimulate dresultsarecomparedwitheachother.Figure5.7comparesthelinearmemory eectsextractedat threedierentloadconditions.Theextractedmemoryeects atthesecasesdemonstrateconsistentbehavior.Thesamecomparisonhasbeendoneatse veralotherload conditions;similarresultswereobserved.Thisconsistencyprov esthevalidityofthe assumptiontosomeextent. -30 -20 -10 0 10 20 30 -15 -10 -5 0 5 10 Pin (dBm)AM-AM (dB) ZL=50ZL=25+j*2.5ZL=70-j*30 -30 -20 -10 0 10 20 30 -200 -100 0 100 200 Pin (dBm)Phase (degree) ZL=50ZL=25+j*2.5ZL=70-j*30 Figure5.7Thememoryeectbehavesindependentlyontheloa dimpedances. Thelimitationofthetraditionalmemoryeectmodelingtec hniquesworkingina loadpullconditionwillbedemonstratedinFigure5.8andFig ure5.9.Supposeweare interestedintheperformanceofanpoweramplierattwoload impedances.Thetwo loadscausedierentnonlinearCWAM-AMandAM-PMeects.Iftheno nlinear blockwithinthemodeldiagramcannotdetecttheloadcondit ionandalwaysuses thesamenonlinearfunctiontoextractthelineareect,itis verypossiblethatthe extractedresultwon'tbelinearandwillshowsomeresidualnonl inearity.Figure5.8 illustratesthiseect. 102

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-30 -20 -10 0 10 20 30 0 10 20 30 Pin (dBm)AM-AM (dB) -30 -20 -10 0 10 20 30 -10 0 10 20 Pin (dBm) Extracted AM-AM (dB) DynamicStatic Figure5.8BadextractionofthelinearAM-AMandAM-PMdistortio n. Thenonlinearblockinthemodelisthemaincontributiontot hespectralregrowth. Therefore,ifthenonlinearblockdoesn'trerecttheactualAM -AMandAM-PM performance,thepredictedspectrumregrowthmightbesigni cantdierentfromthe desiredone,ascanbeseeninFigure5.9.Twosimulatedoutputspe ctrumsfrom behavioralmodelsarecomparedwiththesimulatedresultfrom thecircuitmodel. OneofthetwobehavioralmodelsutilizesthecorrectAM-AMand AM-PMfunctions whiletheotherutilizestheAM-AMandAM-PMcorrespondingtoadi erentload condition.Thesignicantdierencebetweenthe\badpredic tion"andthecircuit modelsimulatedresultiscausedbythenonlinearmodeling. AbehavioralmodelbasedonthesimulationdatasetsoftheLDMOS modelis developed.Thenonlinearblockisthesamemodelasusedinchap ter4,whichis alarge-signalscatteringfunctionmodelderivedfromtheloa dpullgainandphase compressionsimulation.Thelinearmemoryeectischaracteri zedbya5-tapFIR lter.Thecoecientsarettedtotheextractedlinearmemo ryeect.Themodelis implementedinADSusingtheFDDcomponent. 103

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-4 -2 0 2 4 x 10 7 -30 -20 -10 0 10 20 30 40 FrequencyPower Specturm Magnitude (dB) CIR. ModelNew BEH. Model (a) -4 -2 0 2 4 x 10 7 -30 -20 -10 0 10 20 30 40 FrequencyPower Specturm Magnitude (dB) CIR. ModelOriginal BEH. Model (b) Figure5.9IllustrationofinruenceofnonlinearAM-AMandAM-PM compression ontheoutputspectrum.In(a),thenewmodelcanadjustitsnonl inearAM-AMand AM-PMmodeltoadapttotheloadconditionandpredictthespect rumcorrectly.In (b)thetraditionaltwo-boxmodelcannotpredictthespectru mcorrectlybecauseits nonlinearmodelisdevelopedfor50ohm.Thesimulatedloadim pedanceis67.0+j* 93.8ohm. TodemonstratethelimitationoftheCWloadpullmodelpredic tingthedynamics oftheAM-AMandAM-PMperformance,Figure5.10comparesthesimu altedresults fromthenewbehavioralmodelwiththelinearblockandtheCW loadpullmodel.As canbeseen,thedynamiceectofthecircuitmodeliscaptured throughtheaddition ofthelinearblock,whichisnotpredictedbytheCWmodel. Figure5.11comparesthepredictedmemoryeectfromthelin earlteringblock withtheextracteddata.The5-tapmodelparameterislistedi nTable5.3. Table5.1Theoptimized5-tapFIRcoecients. B1 B2 B3 B4 B5 0.8787 0.0744 0.1144 -0.1027 0.0343 Figure5.12comparesthesimulatedoutputsignalfromthebeha vioralmodelwith thatofthecircuitmodel.Themodulatedsignalisa54MbpsWLAN signal(which uses64QAMmodulation).Thetwodatasetspresentgoodagreement 104

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-20 -10 0 10 20 30 -10 0 10 20 30 40 simulated Pout vs. Pin Pin (dBm)Pout (dBm) CIR. ModelBEH. Model with linear blockBEH. Model without linear block Figure5.10Illustrationoftheeectofthelinearblock.Bya ddingthelinearblockto thenonlinearmodel,thenewmodelcanpredictthedynamicssh ownintheAM-AM andAM-PMperformance.ThisisnotcapturedbytheCWloadpull model. -40 -30 -20 -10 0 10 20 30 -20 0 20 40 Pin (dBm)AM-AM (dB) CIR. ModelBEH. Model -40 -30 -20 -10 0 10 20 30 -200 -100 0 100 200 Pin (dBm)AM-PM (dB) CIR. ModelBEH. Model Figure5.11Comparisonofthesimulatedlinearmemoryeect:c ircuitmodelvs. behavioralmodel. 105

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-30 -20 -10 0 10 20 30 -10 0 10 20 30 40 Pin (dBm)Pout (dBm) CIR. ModelBEH. Model Figure5.12Comparisonofthesimulatedoutputpower:behavio ralmodelvs.circuit model.54MbpsWLANsignalisusedastheinputsignal. Toexplorethecapabilityofthisbehavioralmodeltohandle dierentmodulated signals,a6MbpsWLANsignal(QPSKmodulated)isusedastheinputsi gnalinthe simulation.Figure5.13comparestheresultsandveriesthat thebehavioralmodel canhandledierentmodulatedsignals. Figure5.14showsthecomparisonoftheoutputspectrumsobtain edfromthe behavioralmodelandthecircuitmodel.Theoutputspectrums fromtwomodels areverysimilar.Thisisexpectedbecausethesimulatedtimesam plesfromthetwo modelsagreetoeachotherverywellandthatthespectrumisob tainedthrough Fourieranalysisofthetimedomainsignal. TheACPRassociatedwiththeupperandlowersidebandissimulate dforthree loadimpedances,i.e.67.0+j*93.8ohm,50ohmand5ohm.Table 5.2andTable5.3 comparethesimulatedlowerandupperACPRofthecircuitmode lwiththatofthe behavioralmodel.Theaverageinputpowerissetat20dBm.The loadis67.0 +j*93.8ohm.Thenewlyproposedmodelpresentsbetterperform anceagainst thetraditionaltwo-boxmodel,sincethetraditionaltwo-bo xmodelcannotadaptits 106

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-20 -10 0 10 20 30 -10 0 10 20 30 40 Pin (dBm)Pout (dBm) CIR. ModelBEH. Model Figure5.13Vericationofthebehavioralmodelwitha6MBps WLANsignal.The simulatedoutputsignalsfrombothbehavioralmodelandcircu itmodelmatchvery well. -4 -2 0 2 4 x 10 7 -30 -20 -10 0 10 20 30 40 FrequencyPower Specturm Magnitude (dB) CIR. ModelBEH. Model Figure5.14Comparisonofthesimulatedandmeasuredoutputspec trumofthe examplepoweramplier. 107

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performancewithrespecttotheloadconditions.Comparedtot heCWloadpull model,thenewmodelhasbetterprediction,duetotheadditi onofthelinearblock. Table5.2ComparisonofthesimulatedACPRforlowersideband(6 7.0+j*93.8ohm). Averageinputpowerissetat20dBm. LowerSideband Dierence Circuitmodel -34.477 Loadpulltwo-boxbeh.model -33.516 0.961 Traditionaltwo-boxbeh.model -37.003 2.526 CWloadpullbeh.model -33.241 1.236 Table5.3ComparisonofthesimulatedACPRforuppersideband(6 7.0+j*93.8ohm). Averageinputpowerissetat20dBm. UpperSideband Dierence Circuitmodel -33.639 Loadpulltwo-boxbeh.model -33.215 0.324 Traditionaltwo-boxbeh.model -35.682 2.043 CWloadpullbeh.model -32.72 0.919 Table5.4andTable5.5comparethesimulatedlowerandupperA CPRofthe circuitmodelwiththatofthebehavioralmodel.Theloadis5 0ohm.Forthiscase, thetraditionalandthenewtwo-boxloadpullmodelhavethesa meperformance, becausethenonlinearblocksinbothmodelscharacterizethe AM-AMandAM-PM at50ohmverywell.Table5.4ComparisonofthesimulatedACPRforlowersideband(5 0ohm).Average inputpowerissetat20dBm. LowerSideband Dierence Circuitmodel -37.513 Loadpulltwo-boxbeh.model -37.003 0.51 Traditionaltwo-boxbeh.model -37.003 0.51 CWloadpullbeh.model -36.610 0.903 108

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Table5.5ComparisonofthesimulatedACPRforuppersideband(5 0ohm).Average inputpowerissetat20dBm. UpperSideband Dierence Circuitmodel -35.188 Loadpulltwo-boxbeh.model -35.682 0.494 Traditionaltwo-boxbeh.model -35.682 0.494 CWloadpullbeh.model -36.17 0.982 TheupperandlowerACPRsimulatedfromdierentmodelsat5oh mloadare comparedinTable5.6andTable5.7.Ascanbeseen,thenewmodel predictsthe ACPRbetterthantheothertwobehavioralmodels.Table5.6ComparisonofthesimulatedACPRforlowersideband(5 ohm).Average inputpowerissetat20dBm. LowerSideband Dierence Circuitmodel -33.573 Loadpulltwo-boxbeh.model -32.805 0.767 Traditionaltwo-boxbeh.model -37.003 3.43 CWloadpullbeh.model -32.423 1.15 Table5.7ComparisonofthesimulatedACPRforuppersideband(5 ohm).Average inputpowerissetat20dBm. UpperSideband Dierence Circuitmodel -32.489 Loadpulltwo-boxbeh.model -32.073 0.416 Traditionaltwo-boxbeh.model -35.682 3.193 CWloadpullbeh.model -31.767 0.722 5.4Conclusion Inthischapter,weproposedanewbehavioralmodeltocharact erizethememory eectinloadpullconditions.Thisnewmodelcombinestheloa d-awarelarge-signal scatteringfunctionmodeldevelopedinChapter4withalinea rlteringblock.This modelhasthesametwo-boxstructureassomeofthetraditionalm odelingtechniques 109

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do.Thereasontoincludetheloaddependencyastheadditiona lfeaturetothe existingtwo-boxmodelingtechniqueistocapturetheload-r elatedgainandphase compressionvariation.Withoutthiscapability,thelinearm emoryeectmaynot beextractedcorrectly,asdemonstratedinFigure5.8.Alsowit houtthisload-aware capability,themodelisnotsuitableforsomeapplicationswh ereengineersmight experiencedierentloadconditionstooptimizetheirdesig ns. Anexamplebehavioralmodeliscreatedbasedonthesimulationr esultsofan LDMOScircuitmodel.Resultshavebeengiventodemonstrateth eimprovement ofthenewmodeloverthetraditionalmemorymodelsandtheCW loadpullmodel. Theperformanceofthenewmodeltopredicttheoutputsignals fromthepower deviceunderwidebandmodulatedsignals(WLAN)iscomparedtot hecircuitmodel performance.GoodpredictionoftheoutputspectrumsandACP Rsisobserved. Fromthesecomparisonresults,themodelshowspromiseforrealwor ldapplications. AprogramhasbeendevelopedinMatlabtoautomatethemodelg enerationprocess. 110

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CHAPTER6 CONCLUSIONSANDFUTURESTUDY 6.1Conclusions Behavioralmodelinghasreceivedsignicantinterestrecent ly.Thisisprimarily becauseofthechangesinthecurrentdesignpractices.Moreand moreengineerstend touseo-shelfICblocks,suchasLNAsandPAs,intheirdesignstosimpli fythe productstructure,minimizethediscretecomponents,reduced esigncomplexity,and cutthetimetomarket.Thisnewdesignmethodologygenerates signicantdemand foraccuratebehavioralmodelsfortheseblocks,sinceitisoft enthecasethatthe detailsofthecircuitareproprietaryandmodelsarenotpro videdalongwiththe devices.Powerampliersarethemaincomponentofinterestin thisdissertation. ThroughtheliteraturereviewgiveninChapter2,itisfound thatmostofthe reportedbehavioralmodelsarenotsuitableformanypractic alapplications.Oneof thespecicfeaturethatismissingisthecapabilitytoworkada ptivelyinaloadpull condition.Thepreviouslyproposedmodelsdealwithconstantl oadcondition(usually 50ohm)anddon'tprovidethecapabilitiestoadjustthemodel behaviorwithrespect tovaryingsourceandloadimpedances.Ontheotherhand,engin eerstendtostudy theseo-shelfcomponentsunderdierentloadconditionstoo ptimizetheirdesigns. Therefore,thereisagapbetweentheacademicresearchresult sandmanypractical applications. 111

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Large-signalscatteringfunctiontheoryprovidesanelegant solutiontothisproblembystudyingthenonlineareectsoftheamplierunderrea listicdrivingsignals. Specicinstrumentationshavebeendevelopedtogenerateth iskindofmodel.Since thelimitaccesstotheinstrument,thistheoryhasn'tbeenwide lyacceptedyet. Theprimaryfocusofthisdissertationistocomeupwithapract icalandlow-cost behavioralmodelingtechniquebasedonthewidelyavailable measurementsystems (inthisresearch,theloadpullmeasurementsystemsareofinter est).Themainfeature thatispursuedisthecapabilitytopredicttheloadpullperf ormancesofICblocks. Theproposedmodelingtechniqueisbasedonloadpullgainandp hasecompressionmeasurements.AM-AMmeasurementundervariousloadconditio nsisacommon routineincurrentloadpullmeasurementsystems.However,AM-PMl oadpullmeasurementhasn'treceivedasmuchattention.Itisfoundinthis dissertationthatthis informationisimportantforderivingaccuratebehavioral modelstopredictthenonlineareectsofpowerampliers.Byincorporatingthesetwom easurementdatasets inthemodelingprocess,itispossibletocreateabehavioralmod elthatcancapture theload-relatednonlinearitiesofapoweramplier. Threeexamplebehavioralmodelsaredevelopedusingthistec hnique.Therst twomodelsarederivedfromloadpullAM-AMandAM-PMmeasurement s.The performanceofthederivedmodelsarecomparedwithsimplela rge-S21models.Accordingtotheresults,thenewmodelsprovidebetterpredicti onofgaincompression atdierentloadconditionsthanthelarge-S21modelsdo.By applyingale-based model,themodelscanreproducetheintermodulationproduc ts.Thecapabilityof thelarge-S21modelspredictingtheIM3performanceis,howe ver,limited. Thethirdexamplemodelisgivenasademonstrationonhowtocr eateanabstract behavioralmodelfromacircuit-levelmodel.Theexamplemo delisderivedfrom thesimulatedloadpullAM-AMandAM-PMdatasets.Itisveriedunde rdierent 112

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conditions,including50ohmgainandphasecompression,one-to neloadpullandtwotoneloadpullsimulations.Theresultsshowgoodagreementsbet weenthesimulated datasetsfromthecircuit-levelmodelandtheabstractedbeha vioralmodel. Thesecondproblemthisdissertationtacklesistoimprovethel oadpullmodeldevelopedinChapter4toincludethememoryeectmodelingcap ability.Aspresented intheliteraturereview,thecurrentmemoryeectmodeling techniqueshaven'ttaken intoaccounttheload-relatedgainandphasecompressionperfo rmanceofapower amplier.Mostofthemodelscanonlyworkproperlyinoneload condition,typically 50ohm.Whentheloadischanged,itisverylikelythatthemod elswillfail. Toxtheproblem,onecansimplyaddaload-awarenonlinearmo del,likethe oneproposedinChapter4,andcombineitwiththelinearblock .Thenewmodel assumesthesametwo-boxstructure.Theresultedmodelcanberexi bleenoughto beappliedinvaryingloadsituations.Oneimportantassumption forthismodeling techniqueisthatthelinearmemoryeectisindependentont heloadconditions, whichisconrmedthroughthesimulationresultofanLDMOScir cuitmodel. AnexamplebehavioralmodelisderivedbasedonaLDMOScircuit modelsimulationresults.TheupperandlowerACPRsaresimulatedandcompar edwithdierent behavioralmodels.Accordingtotheexampleresults,theloadpu llmodelwiththe memoryeectcapturedshowsitsadvantageinpredictingthesp ectralregrowthand ACPR,comparedwiththetraditionaltwo-boxmodelaswellas theCWloadpull model.6.2Recommendationforfuturestudies Althoughtheproposedmodelingtechniquehassolvedsomeproble ms,thereare stilllotsofareasthatcanbeimproved. 113

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Firstofall,theproposedmodelingtechniqueisbasedontheloa dpullAM-AM andAM-PMmeasurements.Accordingtotheanalysisofthemodeling technique giveninChapter4,onlythefundamentaltonesattheinputan doutputportsofthe poweramplierunderstudyarecorrelatedthroughtheincide ntandscatteringwave variables.Noharmonicsaretakenintoaccountduringthemode lcreationprocess. Therefore,theresultedmodel,eventhoughbeingcapableofp redictingthecompressionpropertiescorrectly,cannotpredictthetimedomai ninputandoutputsignal correctly.Thetimedomainsignalpredictedbythemodelwill beaperfectsinusoidal signal.However,theactualtimedomainsignalsattheinputand outputportsare nolongersinusoidalsignalswhentheinputsignalishigh.Theya recomposedof multipleharmonics,dependingonhowhardthedeviceisdrive n. Oneapproachtore-createthedistortedtime-domainsignalis totakethehigher harmonicsintoaccountatboththeinputandoutputports,just likethelarge-signal scatteringfunctionmodelingtechniqueproposedin[47,71]. Harmonicloadpullmeasurementmaybeusefultowardsthisimprovement.Theimprovem entcomesatthe costofincreasingcomplexityinthemodelandtherequiredmea surements,whichalso makesthemodeldiculttobederivedandappliedinpractica lapplications. Thisharmonicloadpullmeasurementscanbedonethroughtrad itionalloadpull measurementsystemsorthroughtheLSNAsystem.TheLSNAsystem,inessen ce, isanactiveloadpullmeasurementsystem.Itoersintegratedc alibrationandmeasurementcapabilitiesthatarepowerfulandrexibletomeetd ierentrequirements. Italsoprovidespost-analysiscapabilitytoprocessthemeasure ddataanddisplayin appropriateformats.ByusingaLSNA,itwouldbeeasiertogetacom pletelargesignalscatteringfunctionmodel.Thedown-sideofthisapproa chisitshighcostand thereforelimitedaccessability. 114

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Theproposedloadpullmemorymodelhasbeenproventobeablet ogivebetter predictionofthepoweramplierperformanceunderdigital modulatedsignalsthan traditional.TheresultsgiveninChapter5arebasedonsimulat iondatasets.Theoreticallythememoryeectisindependentontheloadcondi tions.However,this hasn'tbeenveriedexperimentally,duetotheinstrumentlim itation.Atwoport vectorsignalanalyzerisrequiredtoverifythisstatementex perimentally.Themain purposetohavethisinstrumentistosampleandmeasuretheinput andoutputsignalsynchronously.Otherwise,somedigitalprocessingstepsarere quiredtoalignthe inputandoutputstreams. Twostepsareinvolvedinthemeasurementtostudytheloadeect onlinear memoryeect.Theinputandoutputsignalsofthepowerampli erunderstudy shouldbesampledandmeasuredsimultaneouslyatvariousloadcon ditions.The linearmemoryeectcanbeextractedbyremovingthenonline arAM-AMandAMPMeectsfromtheoutputsignalsamples.Foreachloadconditio n,thecorresponding AM-AMandAM-PMcompressioncurvesmeasuredusingtheCWsignalisusedintheextractionprocess.Theremainingsignalaftertheextra ctionisthelinear memoryeectfordierentloadconditions.Bycomparingthese signals,wecannd outwhethertheloadconditionswillhavesignicanteectso nthelinearmemory performance.Theexperimentalvericationoftheloadpull memorymodelwillbe anotherareaforthefuturestudy. Currentlytheproposedmemoryeectmodelhasatwo-boxstruct ure.However, accordingto[3],thetwo-boxstructurehaslimitationsinpr edictingthenonlinear memoryeect,orlong-termmemoryeect.Adynamicfeedback pathisrequiredto representthiseectattributedtoelectrothermaland/orbi ascircuitrydynamics.The limitationofthetwo-boxstructureisoneofthereasonforthe dierencesobserved betweentheACPRssimulatedfromthenewmodelandthecircuit model.Therefore, 115

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itwouldbeinterestingtoseehowtheadditionofthefeedbackp athintothemodel helpsimprovingthemodelperformance. 116

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REFERENCES [1]D.Root,J.Wood,andN.Tullaro,\Newtechniquesfornon-l inearbehavioral modelingofmicrowave/rficsfromsimulationandnonlinearm icrowavemeasurements,"in Proc.DesignAutomationConference,2003 ,June2003,pp.85{90. [2]P.WambacqandW.Sansen, DistortionAnalysisofAnalogIntegratedCircuits Boston,MA:KluwerAcademicPublishers,1998. [3]J.C.PedroandS.A.Maas,\Acomparativeoverviewofmicrow aveandwirelesspower-amplierbehaviroalmodelingapproaches," IEEETrans.Microwave TheoryTech. ,vol.53,pp.1150{1163,Apr.2005. [4]J.C.PedroandN.B.Carvalho, IntermodulationDistortioninMicrowaveand WirelessCircuits .Norwood,MA:ArtechHouse,2003. [5]J.S.Kenney,W.Woo,L.Ding,R.Raich,H.Ku,andG.T.Zhou, \Theimpact ofmemoryeectsonpredistortionlinearizationofRFpowera mpliers,"in Proc. ofthe8thInt.Symp.onMicrowaveandOpticalTechn. ,Montreal,Canada,June 2001,pp.189{193. [6]F.Launay,Y.Wang,andS.Toutain,\M-aryPSKsignalpowersp ectrumatthe outputofanonlinearpoweramplier,"in Proc.IEEEMTT-S ,vol.3,Seattle, WAUSA,June2002,pp.2197{2200. [7]H.LaiandY.Bar-Ness,\Minimumdistortionpowerpolynomialmo del(MDPPM)ofnonlinearpowerampliersanditsapplicationonanal ogpredistorters,"in Proc.IEEEVTC'99 ,vol.3,AmsterdamNetherlands,Sept.99,pp.1501{1505. [8]H.Songbai,L.Mingyu,D.Hongmin,andY.Juebang,\Analysisof CDMARF channelnonlineardistortion,"in Proc.IEEEComm.CircuitsandSystemsand WestSinoExpositions'02 ,vol.1,July2002,pp.474{477. [9]A.Springer,T.Frauscher,B.Adler,D.Pimingsdorfer,andR. Weigel,\Impact ofnonlinearampliersontheUMTSsystem,"vol.2,Sept.2000,p p.455{460. [10]Y.GuoandJ.Cavallaro,\Post-compensationofRFnon-line arityinmobile OFDMsystemsbyestimationofmemory-lesspolynomial,"in Proc.IEEEISCAS '02 ,vol.1,May2002,pp.26{29. 117

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ABOUTTHEAUTHOR JiangLiuobtainedhisBSEEatNanjingUniversityofPostsandTel ecommunicationsin1996andMSEEatUniversityofSouthFloridain2002.His researchfocuses ondevelopmentofadvancedRFandmicrowavemeasurementsystem sandnonlinear behavioralmodelingofRFandmicrowavecircuitsandsystems.


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Practical behavioral modeling technique of power amplifiers based on loadpull measurements
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ABSTRACT: Accurate linear and nonlinear models for devices and components are essential for successful RF/microwave computer aided engineering (CAE). The modeling techniques can be categorized in different levels based on the abstraction of the model as well as the application of the models at various design phases. This dissertation deals with behavioral modeling techniques for nonlinear RF components, especially amplifiers. There is an increasing demand for accurate behavioral models of RF and microwave components, or integrated circuit (IC) blocks used in wireless system designs. Accurate behavioral models help designers evaluate and select the appropriate components at simulation phase, thereby cutting development cost. However, there isnt a practical (or flexible) solution for accurate and effective behavioral model generation. This dissertation tries to tackle this problem. Power amplifiers and devices are the main components studied in this dissertation.The primary focus is on the characterization of the loadpull performance of power amplifiers and devices. Major contributions of this dissertation include development of advanced loadpull measurement procedures, large-signal load-aware behavioral model, and a load-aware behavioral model with memory-effect capabilities. There are two advanced loadpull measurements documented in this dissertation: the AM-PM loadpull measurement and the digital demodulation loadpull measurement. These two measurements may have been used internally by some research groups, however, according to the best knowledge of the author, they havent received much attention in the literature. This is the first published work on these two topics. It is shown in this work that the AM-PM performance can be strongly dependent on the load conditions. This property provides important information about the nonlinearities of power amplifiers and is used herein to create better behavioral models.This newly developed digital demodulation loadpull measurement procedure enables system designers to evaluate power amplifiers directly against digital communication system parameters such as error vector magnitude (EVM). Two example measurements are given to demonstrate the measurement system setup and the correlations between traditional nonlinear figure-of-merits and system metrics. A new behavioral modeling technique / procedure is developed based on loadpull AM-AM and AM-PM measurements. The large-signal scattering function theory is applied in the technique to formulate the model. The created model is able to automatically detect the load impedance and generate corresponding nonlinear properties. Three example models are presented to demonstrate the capability of this technique to predict accurately the output power contours, 50 ohm large-signal S21, and 3rd order intermodulation products (through additional file-based model).Finally, a modeling technique is demonstrated to enable predicting the linear memory effect within a varying load condition. The nonlinear block used in the traditional two-box model structure is replaced with the large-signal loadpull model mentioned above. By adding this new feature, the resulting model is able to predict the load-related AM-AM and AM-PM properties, which will improve the accuracy of ACPR prediction.
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Adviser: Lawrence P. Dunleavy.
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