LinearityofX-bandClass-BPowerAmplifiersinaDigitalPolarTransmitterNarisiWang,NestorD.Lopez,VahidYousefzadeh,JohnHoversten,DraganMaksimovicandZoyaPopovicDepartmentofElectricalandComputerEngineeringUniversityofColorado,Boulder,Colorado80309,USAAbstract-Thispaperdiscussesthelinearityofaclass-EX-bandPAinadigitalpolartransmitter.ThePAisnonlinearsinceitiscompressedby2.2dBwhenachievinga59%PAEat10GHz.Load-pullisperformedunderatwo4onetestandtheresultingoptimalefficiencyimpedanceisfoundtobeover30%differentfromthesingle4oneload-pull.Inadditionstandardtwo4oneload-pullmeasurementsindicatethattheimpedanceformaxP0utcoincidewithworstnonlinearity(IMD).Surprisingly,inthetwo4onepolarload-pull,impedanceformaxP0utdifferssignificantlyfromtheimpedancecorrespondingtoworstIMD.Therefore,underpolarmodulationadifferentmatchingcircuitshouldbedesignedforoptimallinearityandefficiency.ThePAispartofadigitalpolartransmitterwhichenableslinearizationincludingphasepredistortion,withIMDlevelsover11dBlowerthaninthestandardtwo4onetest.Load-pullperformedonthepolarclass-EPAshowsthatthelevelofintermodulationproductsvariesfordifferentsignalsinputintothePA.IndexTerms-Envelopeeliminationandrestoration,polarmodulation,envelopeamplifier,class-EamplifierI.INTRODUCTIONM/[ODERNcommunicationsystemsareforcedtocontin-uallyimprovetheirspectralefficiencyinanefforttoachievehigherbitratesinlimitedbandwidth.ThisimprovementistypicallymanifestedasacomplexschemeinwhichbothamplitudeandphaseoftheRFcarrieraremodulatedatahighrateandoverawidedynamicrange.Suchmodulatedsignalsdemandverylinearpoweramplifiers,whichareoperatedtypicallyinclassAorbacked-offclassABmodes.TheselinearoperatingmodeslimittheefficiencyofthePAtoaround30%.Anumberofresearchershaveinvestigatedsupply-modulatingtechniquesthatcansimultaneouslyprovidehighefficiencyandgoodlinearity,andmostnotableexamplesareEnvelopeEliminationandRestoration(EER),polarmodulationanddynamicbiasing[1]-{4].Thesetypesoftransmittersaremorecomplex,andthetotaltransmitterefficiencydependsonboththePAandthesupplymodulatingcircuitefficiency.Inthispaper,weexaminethelinearityofaultra-nonlinearhigh-efficiencyswitched-modePAinadigitalpolartransmitter.TheRFcarrierisat10GHz,whichisahigherfrequencythanmostcurrentcommercialcommunicationsystems,butisacommonfrequencyinotherapplications,suchasradar.Atcarrierfrequenciesabove2GHz,thecircuitparasiticsanddevicenonlinearitiesaremorepronouncedanddifficulttomodel.Theclass-EX-bandPAusedinthisstudyhasbeendemonstratedinatwo-stageefficientPA[5]anditslinearityLinerassistedsAitchirgiplifierFig.1.BlockdiagramofapolarsystemwithFPGAdigitalcontrol.TheRFPAisaclass-E1O-GHzMESFETamplifier.TheenvelopesignalissplitintoalowfrequencycomponentwhichcontrolsaDC-DCconverterandahighfrequencycomponentwhichprovidesadditionalenvelopeACvariations.Phasevariationisachievewithadigitallycontrolledphaseshifter.Fig.2.Pout(solidline)andPAE(dashedline)load-pullcontoursforMESFETAFM04P2(Alphaindustries).Theclass-Eimpedance(27.2+j31.4Q)isindicatedwith'x'.andEERoperationwereinvestigatedin[6].Theclass-EmodeofoperationlendsitselfnaturallytoEERandpolartransmitterarchitectures.Itcanbeshown,e.g.in[5],thattheoutputvoltageintoafixedresistive(RL)loadisproportionaltothesupplyvoltage(VDD):Vout=±(26.fs*CoRERLVDD(1)whereREistherealpartoftheoptimalimpedancepresentedtothedeviceforclass-Eswitchedmodeoperation,fsistheoperatingfrequencywhichisalsotheswitchingfrequency,andC0utistheoutputcapacitanceoftheactivedevice.Inaddition,1-4244-0688-9/07/$20.00C2007IEEE10832010EO-19.5dB-18dBcE-0--1-0.-.-12O200~20-130-o-40-50-1-0.00.5OffsetFrequency(MHz)(a)(b)(c)Fig.3.(a)Singletonepowersweepforclass-EPAat10GHz,(b)two-oneoutputspectrumfor200kHzoffsetbetweentones(carrierfrequencyis10GHz),and(c)MESFETPoutandworstIMD3load-pullcontours.Class-Eimpedanceisindicatedwithan'x';forthisimpedancePAEis45%with+17.5dBmofPout.OptimumPAEof48%isobtainedfor22+j38Q,'o'with+17.5dBmofPout.WorstIMD3andmaximumPoutcontourscoincide.theoptimalefficiencyandoptimalloadimpedanceareideallynotaffectedbythebiasvariation,sincethetransistorcurrentandvoltageamplitudesonlychangewithbias,butnottheirtime-domainwaveformshapes.Thepowercantheoreticallyvaryfromzerotothemaximalavailablepower,butinpracticethelowestpowerislimitedbyfeedthrough,andthemaximalpowerisconstrainedbythepowerhandlingofthedevice.AsaresultofthePApropertydescribedbyEq.1,theoutputvoltageofaclass-EPAcanbevariedproportionallytovariationsinthesupplyvoltage,whichisrequiredforapolartransmitter,inwhichtheenvelopeofthemodulatedRFcarrieramplitude-modulatestheoutputvoltage,whilethephaseofthemodulatedsignalisdirectlyinputintothePAthroughthedrive(RFinput).ThisissimilartotheanalogEERtechnique[4],butcanbeimplementeddigitally,asshownwiththeschematicinFig.1.Thedigitally-controlleddrainbiasprovidesamplitudemodulationoftheoutputvoltagethroughaultra-efficientslowDC-DCconverterincombinationwithafastlessefficientlinearamplifierwhichprovidestheACportionofthesignalenvelope.ThesignalisgenerateddigitallyandconvertedfromIQtopolarform.Thedigitalcontrolofthebiasallowsallocationoftheamplitudemodulationbetweentheslowandfastcircuitsinordertooptimizeefficiencyfordifferentmodulatedsignals,possiblyadaptively.II.CLASS-EPAPERFORMANCEWITHASINGLEANDTwo-TONEINPUTPracticalclass-EPAshaveachieved96%drainefficiencyinthelowMHzrange[9],around90%atVHF[10]andashighas70%atX-band[5].In[6],class-EPAsareexaminedanditisshowntheycanbelinearizedtosomedegreeusingpolarmodulation.Theclass-EPAusedthroughoutthisworkwasdesignedusingdesignequationsasin[8]andload-pullcharacterizationofaGaAsMESFETat10GHz,showninFig.2.Thetheoret-icalclass-Eimpedancecalculatedfromtheoutputcapacitanceofthisdeviceis24.7+j28.4Q.ThemaximumPAEof59%at27.2+j31.4Qisobtainedfromload-pullmeasurements.P011t,gain,andriDforthePAare+19.9dBm,8.1dB,and64%respectivelywhenthePAiscompressedby2.2dB.Theinputimpedanceismatchedto8.2+j27.3Q.Fig.3ashowsaninputpowersweepfortheamplifierbiasedat4.1Vand10mA.Theoutputspectrumforatwo-onetestwhenthetonesareoffsetby200kHzandtheinputpoweris+1IdBm(optimumPAE)isshowninFig.3b.The200kHzbandwidthischosenasanexamplesinceitcorrespondstothebandwidthofanEDGEcommunicationsignal.TheupperandlowerIMD3levelsare-19.5dBcand-17.8dBc,respectively.ThePAEforthetwo-onetestwiththesametotalinputpowerdroppedto45%andtheoutputpowerdroppedto+17.5dBmindicatingagainreduction.Tounderstandthisdegradation,load-pullmeasurementsweretakenforatwo-onetestwiththesame200kHzoffset.Fig.3cshowsPo1ut(solidline)andworstIMD3contours(dashed-ine)fortheMESFETwith+11dBmofinputpower.It