中英文翻译高耦合系数层叠结构片上变压器的频率无关等效电路.docx
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中英文翻译高耦合系数层叠结构片上变压器的频率无关等效电路.docx
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中英文翻译高耦合系数层叠结构片上变压器的频率无关等效电路
中英文翻译高耦合系数层叠结构片上变压器的频率无关等效电路
--k
XiaJun,WangZhigong,andLiWei
(InstituteofRF-&OE-ICs,SoutheastUniversity,Nanjing210096,China)
Anew22Πlumpedelementequivalentcircuitmodelforhigh-kstacked
on-chiptransformersisproposed.Themodelparametersareextractedwithhigh
precision,mainlybasedonanalyticalmethods.Thedevelopedmodelenablesfast
andaccuratetimedomaintransientanalysisandnoiseanalysisinRFICsimulation
sinceallelementsinthemodelarefrequencyindependent.Thevalidityofthe
proposedmodelhasbeendemonstratedbyafabricatedmonolithicstackedt
ransformerinTSMC’s0.13ummixed-signal(MS)/RFCMOSprocess.
high-k;stackedon-chiptransformer;frequency-independent;
equivalentcircuit
2570
TN432A0253-4177(2008)08-1461-04
Recently,monolithictransformershavebeenwidelyemployedasimportant
elementstoenhancetheperformanceofmanykindsofRFblocks,includinglow
noiseamplifiers(LNA),voltage-controlledoscillators(VCO),andpower
amplifiers(PA)[1~3].Therearethreedifferenton-chiptransformer
realizations,namely,thetapped,theinterleaved,andthestacked[4].The
stackedcanprovidethehighestcouplingfactor(k)andthebestareaefficiency,buthasalowerself-resonancefrequency(SRF).Asanessential
toolforcircuitdesign,accurateequivalentcircuitmodelsoftrans-
formers,usinglumpedRLCelements,efficientlycharacterizetheirelectrical
performancesforcircuitsimulation.Severalmodelsofstackedtransformerhave
1
beenpresentedinthepastdecade[4,5].However,currentmodelsare
frequency-dependentbecausesomeelementsinthemodelsdependonfrequency.
Itisdifficulttoincorporatefrequency-dependentelementsinSPICE-type
simulators[6].Inaddition,frequency-dependentmodelsarenotcompatible
withtimedomaintransientanalysis.Thus,itisimportanttoinvestigatea
frequency-independentmodelforstackedtransformers.Inthispaper,the
on-chiphigh-kstackedtransformerisintroduced.Then,alumpedelement
frequency-independentmodelwithhighaccuracyispresented.Astackedtrans-
formerisrealizedinTSMC’s0.13μmRF/MSCMOSprocess.TheS-parameteroftherealizedtransformerismeasuredwithanAgilentE8363BVNA.Themeasured
resultsagreewellwiththemodelingparameters.
-k
Figure1showsastackedstructuremonolithictransformer.Itusesmultiple
metallayersandexploitsbothverticalandlateralmagneticcouplingtoprovide
thehighestcouplingfactor(k)andthebestareaefficiency.Thekfactorcan
reach0.9ormore,andtheoccupiedchipareacanbereducedsignificantly.The
maindrawbackofthisstructureisthehighport-to-portcapacitance,and
consequentlyalowerSRF.But,thelowSRFcanbeimprovedbyincreasingthe
oxidethicknessbetweenspiralsinmodernsilicon-basedmulti-metal-level
processes.Inpractice,thiscanbeimplementedbyselectingpropermetallevels.
Thekfactormustbedecreasedwhentheoxidethicknessisincreased.However,
thechangeofportparasiticcapacitanceismuchmoresensitivethanthek
factor[4].Therefore,decreasingthekfactorisusuallyacceptablewhentheoxidethicknessisincreasedtoimprovetheSRF.
2
Fig.1Stackedstructuremonolithictransformer
Fig.2Frequency-independentequivalentcircuitforastackedon-chip
transformerinwhichallmutualinductancesarenotshown
Theelectricalperformanceofatransformercanbecharacterizedby
frequencydomainnetworkparameters,suchastheS-,Y-,orZ-parameters.Yetanequivalentcircuitisin-dispensableforcircuitdesignduetothefactthat
thefrequencydomainnetworkparameterscannotbeemployedinthetimedomain
simulationornoiseanalysis.Moreover,asmentionedabove,theequivalent
circuitshouldbefrequency-independent.Theproposedequivalentcircuitfor
astackedon-chiptransformerissketchedinFig.2.Thereareanumberofelements
inthecircuitmodel,andtheirphysicalmeaningsandhowtoextracttheirvalues
accordingtothedevice’sgeometricdimensionswillbepresentedindetail.
AsshowninFig.2,basedontheladdercircuitrepresentation,a2Πequivalentcircuitmodelisbuilttocapturethedistributedcharacteristics
ofthemonolithictransformer.First,theDCcurrentisuniformlydistributed
insidetheprimaryandsecondaryconductors,andcanbecharacterizedbyRsiandLsi(i=1,2,3,4)inserieswithmutualinductancesdenotedbyMij(notshowninFig.2)betweeneachtwoselfinductances(Lsi,Lsj,i,j=1,2,3,4,i 3 pushtheACcurrenttothemetalsurface,whichresultsinafrequencydependent lossandinductanceinthemetalconductor.Unlessfrequencydependent componentsareemployed,asimpleRLseries(RsiandLsi)branchcannotmodelthiseffect.Therefore,anadditionalRLladder(RpiandLpi)inparalleltotheRsi(i=1,2,3,4)andtwelvemutualinductancesMpij(notshowninFig.2either)betweenLsiandLpj(i,j=1,2,3,4,i? j)areintroducedtomodelthefrequencydependentlossandinductance.Therearetwokindsof parasiticcapacitancesthatleadtothestackedon-chiptransformer’slowerSRF.Onecomesfromhorizontalelectricfieldandtheotherisduetothevertical electricfield.ThecapacitanceCKi(i=1,2,3,4)representsthecoupling betweentheadjacentmetaltracksoftheprimaryorsecondarycoilsofthe transformer,respectively.Thehorizontalelectricfieldcouplingcontributes tothosecapac-itances.Theoverlapcapacitanceduetoverticalelectricfield couplingbetweenprimaryandsecondarycoilscanberepresentedbyCOVi(i=1? 7).TheotherpartofverticalcapacitancesisCpandCs,whichrepresenttheoverlapcapacitancebetweenthespiralandunderpassmetallines.Thelossy capacitivecouplingbetweenthesecondaryofthestackedtransformerand conductivesubstratecanbemodeledbythreeRCsubcircuits{Coxi,RSUBi,CSUBi,i=1,2,3}. Intheproposedmodel,themostimportantaspectistheextractionofmodel parameters.Theparametersextractionstepsinthispaperaremainlybasedon analyticmethods.Thecomponentsoftheladdersubcircuits,Lsi,Rsi,Lpi,Rpi(i=1,2,3,4)canbecalculated by[8]: Rpi=KRRsi,Lpi=KLLsi (1) Rsi=(1+1/KR)Rdci (2) Lsi=Ldci/[1+KL(1+KR)-2](3) 4 whereKLandKRaretwointroducedcoefficientsacquiredbyfittingoptimization. RdciandLdciaretheDCresistanceandinductanceoftheithspiral,respectively.Rdciisequaltotheproductofthemetalsheetresistanceand theaspectofthemetalline(totalmetallength/metalwidth).Ldcicanbecalculatedbyananalyticalequation[5].Thetransformermutualinductances Mij(i,j=1,2,3,4,i Imag(Zij)/ω,whereZijaretheelementsoftheZ-parametermatrix,which isconvertedfromthemeasuredS-parametermatrix,whileωshouldbelow(inthispaper,ω=2π×100MHz).Calculatingtheproximityeffectmutual inductancesMpij(i,j=1,2,3,4,i? j)byananalyticalformulais difficult.Mpijisobtainedalsobyfittingiteration.However,thevariables tobefittedcanbereducedtofourusingasymmetriclayout.Thelateralcoupling capacitanceCKi(i=1,2,3,4)canbeobtainedbyGupta’sfringingcapacitance curvesforcoplanarrectangularcoupledbars[9].Thetotaloverlapcapacitance betweenprimaryandsecondarycoils,COV,canbeestimatedbyAε/tOX+PCPS,whereεandtOXaretheoxidedielectricconstantandthicknessbetween primaryandsecondary,respectively.Aistheareaofthespirals,andPisthelengthoftheshorteroftheprimaryorsecondary.CPSisthe per-unit-lengthspecificcapacitancewhosevalueisobtainedalsobyGupta’sfringingcapacitancecurves.TheCOVi(i=1? 7)isequalto1/8COVfori? 4and1/4COVfori=4.CPandCScanbeevaluatedapproximatelybythe commonlyusedparallelplatecapacitorformula.Thecomponentsrelatedtothe capacitivecouplingbetweensubstrateandthesecondary,{Coxi,RSUBi,CSUBi,i=1,2,3}canbedeterminedbyaseriesofanalyticalformulasderivedbyHuo etal.[10]withtheknowledgeoftransformerlayoutandprocesstechnology. 5 Fig.3Micrographoftheimplementedtransformer Fordemonstration,astackedmonolithictransformerhasbeenfabricated inTSMC’s0113μmRF/MSCMOSprocess.Figure3showsthemicrographofthe implementedtransformer.Theouterdiametersofboththeprimaryandsecondary are300μmandthewidthofmetallineis10μm.Thespacingofadjacentmetal linesis2μmandtheturnsoftheprimaryandsecondaryarefour.The S-parametersoftheimplementedtransformerhavebeenmeasuredupto5GHzby anAgilentE8363BVNA.Theextractedequivalentcircuitparametersofthe transformerareasfollows: Lsi=314nH,Lpi=113nH,Mij=311nH(wheresubscripti,j=1,2,3,4,i substratecomponentsare: COX1=91.5fF,COX2=109.4fF,COX3=200.9fF;CSUB1=13.7fF,CSUB2=15.9fF,CSUB3=29.5fF;RSUB1=771.0Ω,RSUB2=663.4Ω,RSUB3=340.8Ω.Figures4and5showcomparisonsbetweenthemod
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