Modeling-a-frequency-dependent-inductor-for-AC-swe

ModelingafrequencydependentinductorforACsweepanalysisPROBLEM:HowdoImodelafrequencydependentinductorforACsweepanalysis?SOLUTION:Theimpedanceofaninductoris:Z=L*swheres=j*2*PI*FrequencyInafrequencydependentinductor,theLintheaboveformulachangeswithfrequency.IfyouknowLasamathfunctionoffrequency,then:1.UseaGLAPLACEdevice.2.Connectthepositiveandnegativeinputstothepositiveandnegativeoutputs,respectively.3.Writethetransformexpressionas1/(L*s),whereLisreplacedbythedesiredmathformula,withfrequencyreplacedbyabs(s)/6.283185.Forexample,ifL=1/sqrt(Frequency),thenwritethetransformexpressionas:1/(1/sqrt(abs(s)/6.283185)*s)orsqrt(abs(s)/6.283185)/sIfyouhaveatableofinductancevaluesateachfrequency,then:1.UseaGFREQdevice.2.Connectthepositiveandnegativeinputstothepositiveandnegativeoutputs,respectively.3.Forthetableattribute,typethewordMAG,followedbyentriesforeachfrequency.4.Eachtableentryshouldbeintheform(frequency,Y,90);whereYisreplacedbythemanuallycalculatedvaluefor:1/(Lf*6.283185*frequency);Lfistheinductanceatthisfrequency.Forexample,iftheinductanceis1mHat10kHzand,1uHat100MegHz,then:TABLE=MAG(10k,0.0159155,90)(100Meg,0.00159155,90)Documentnumber:PSP02020Appliesto:PSpicever.AllCreatedon:17-APR-1998Lastmodified:8-JAN-2002Copyright©2005,CadenceDesignSystems,Inc.Allrightsreserved.ImplementingModelsinPSpiceNoteThemodelswerecreatedandverifiedinamodernhigh-frequencysimulationprogram(AWRMicrowaveOffice2002).TheresultsofidenticalmodelsinthestudentversionofPSPICEinsomecasesgavedifferentresults(upto3%differentZandL,anduptoa3°phaseangledifference).Thedifferenceswerenotduetoroundingofthemodeltablevaluesornumberofsimulationfrequencypoints.Sincethecomparedmodelswereidentical,wemustconcludethatthedifferencesresideinthesimulationsoftwareimplementation.Sincethedifferencesappeartobeinthesoftware,theycannotbeexplainedbyCoilcraftatthistime.Cautionisadvised.Themodelsarebasedonlyonsteady-stateACmeasurementsandanalysis.NoDCbiasortransientanalyseswereverified.TheGLaplaceelementisusedinPSPICEtodescribeafrequency-dependentimpedance.TheimpedanceisgivenbytheinverseoftheXFORM,orXFORM=1/Z(S).First,placeaGLaplaceelement(part)intothemodelcircuitschematicandconnectasshownintheschematicbelow.Next,edittheGLaplaceelementbydouble-clickingonthepartinyourschematic.ClickontheXFORM=1/Slineandeditthevalueinthevaluebox,asfollows:Forafrequency-dependentresistance(e.g.RVAR1,RVAR2)Note:ThisexampleusesRVAR1(=k1*sqrt(Frequency)).Inyourcircuit,substitutethenumericalvalueofk1giveninthemodeltableforthespecificmodelvalueyouareusing,intotheXFORMstatement.Z(S)=RVAR1=k1*sqrt(Frequency),whereFrequencyisindegreesSinceSisthefrequencyinradians,Frequencymustbeconvertedtodegrees.Theresultingfrequency-dependentresistancewillbeinOhmsunits.1/Z(S)=XFORM=1/(k1*sqrt(S/(2*3.14159265)))Forafrequency-dependentinductance(e.g.LVAR)Note:Inyourcircuit,substitutethenumericalvaluesofk3,k4,andk5giveninthemodeltableforthespecificmodelvalueyouareusing,intotheXFORMstatement.Z=S*LVAR=k3-(k4*LOG(k5*Frequency)),whereFrequencyisindegreesTheLOGfunctionusedhereisthenaturallogarithm(basee,notbase10).SinceSisthefrequencyinradians,Frequencymustbeconvertedtodegrees.SincetheinductanceisgiveninuHunits,theLVARexpressionisconvertedasshownbelow.1/Z=XFORM=1/(S*1e-6*(k3-(k4*LOG(k5*(S/(2*3.14159265))))))OthercircuitelementsPlaceandwiretheotherpartsofthemodelintheschematic.Ifthespecificmodelinductanceelementisafixedvalueinductor,usetheINDpartinsteadoftheGLaplacepart.Editthepartvaluestomatchthoseofthemodeltablevaluesforthespecificinductoryouaresimulating.Seetheexampleschematicandnetlistshownbelow.ExamplePSpiceschematicandnetlistInthecasewheretwoGLaplaceelementsareinseries,alarge-valuedresistancetoground(Rsim)wasaddedtopreventafloatingnodeerror.Thelarge-valuedresistance(R3)wasaddedtomeasurevoltageacrosstheentiremodel.Note:Makesuretosubstitutethespecificmodeltablevaluesforeachelement(part)oftheinductormodelintotheschematic.*ExampleSchematicsNetlist*R_R2$N_0002$N_00010.001V_V3$N_00020DC0VAC1vR_R3$N_0002010megR_Rsim0$N_000310megG_Rvar2$N_00010LAPLACE{V($N_0001,0)}{+1/(k2*sqrt(S/(2*3.14159265)))}R_R1$N_0004016000G_Lvar$N_00030LAPLACE{V($N_0003,0)}{+1/(S*1e-6*(k3-(k4*LOG(k5*(S/(2*3.14159265))))))}G_Rvar1$N_0001$N_0003LAPLACE{V($N_0001,$N_0003)}{+1/(k1*sqrt(S/(2*3.14159265)))}C_C$N_0001$N_0004.64pFToviewthespecificeffectivesimulationresultsIncludethefollowingMacrosinyourProbetraceanalysistoseefrequencyvs.inductance,impedance,phaseangle(indegrees),andQfactor:PI=3.14159265L=(IMG(V(R3:1)/I(R2))/(2*pi*FREQUENCY)Z=V(R3:1)/I(R2)ANG=(180/PI)*ARCTAN((IMG(V(R3:1)/I(R2)))/(R(V(R3:1)/I(R2))))QFACT=ABS((IMG(V(R3:1)/I(R2)))/(R(V(R3:1)/I(R2))))