射频电路设计基础课件

1射频电路设计基础1射频电路设计基础3B.RFMicrowaveFilters3B.RFMicrowaveFilters1.0BasicFilterTheory1.0BasicFilterTheoryIntroductionAnidealfilterisalinear2-portnetworkthatprovidesperfecttransmissionofsignalforfrequenciesinacertainpassbandregion,infiniteattenuationforfrequenciesinthestopbandregion,andalinearphaseresponseinthepassband(toreducesignaldistortion).Thegoaloffilterdesignistoapproximatetheidealrequirementswithinacceptabletolerancewithcircuitsorsystemsconsistingofrealcomponents.IntroductionAnidealfilterisCategorizationofFiltersLowpassfilter(LPF),highpassfilter(HPF),bandpassfilter(BPF),bandstopfilter(BSF),arbitrarytype,etc.Ineachcategory,thefiltercanbefurtherdividedintoactiveandpassivetypes.Inanactivefilter,therecanbeamplificationofthesignalpowerinthepassbandregion;apassivefilterdonotprovidepoweramplificationinthepassband.Filtersusedinelectronicscanbeconstructedfromresistors,inductors,capacitors,transmissionlinesections,andresonatingstructures(e.g.,piezoelectriccrystal,SurfaceAcousticWave(SAW)devices,mechanicalresonators,etc.).Anactivefiltermaycontainatransistor,FET,

andanop-amp.FilterLPFBPFHPFActivePassiveActivePassiveCategorizationofFiltersLowpFilterFrequencyResponseFrequencyresponseimpliesthebehaviorofthefilterwithrespecttosteady-statesinusoidalexcitation(e.g.,energizingthefilterwithasinevoltageorcurrentsourceandobservingitsoutput).Therearevariousapproachestodisplayingthefrequencyresponse:TransferfunctionH()(thetraditionalapproach)AttenuationfactorA()S-parameters,e.g.,s21()Others,suchasABCDparameters,etc.FilterFrequencyResponseFrequFilterFrequencyResponse(cont’d)Lowpassfilter(passive)

FilterH()V1()V2()ZLcA()/dB0c31020304050(1.1b)(1.1a)c|H()|1TransferfunctionArg(H())ComplexvalueRealvalueFilterFrequencyResponse(conFilterFrequencyResponse(cont’d)Lowpassfilter(passive)continued...Fortheimpedancematchedsystem,usings21toobservethefilterresponseismoreconvenient,asthiscanbeeasilymeasuredusingavectornetworkanalyzer(VNA).ZcZcZcTransmissionlineisoptionalc20log|s21()|0dBArg(s21())FilterZcZcZcVsa1b2ComplexvalueFilterFrequencyResponse(conLowpassfilter(passive)continued...FilterFrequencyResponse(cont’d)A()/dB0c31020304050

FilterH()V1()V2()ZLPassbandStopbandTransitionbandCut-offfrequency(3dB)Lowpassfilter(passive)contHighpassfilter(passive)FilterFrequencyResponse(cont’d)A()/dB0c31020304050c|H()|1TransferfunctionStopbandPassbandHighpassfilter(passive)FiltFilterFrequencyResponse(cont’d) Bandpassfilter(passive) BandstopfilterA()/dB401330201002o1|H()|1Transferfunction2oA()/dB401330201002o1|H()|1Transferfunction2oFilterFrequencyResponse(conBasicFilterSynthesisApproachesImageParameterMethod.ZoZoZoZoZoFilterZoH1()

H2()

Hn()

ZoZoConsiderafiltertobeacascadeoflinear2-portnetworks.Synthesizeorrealizeeach2-portnetwork,sothatthecombineeffectgivestherequiredfrequencyresponse.The‘image’impedanceseenattheinputandoutputofeachnetworkismaintained.ThecombinedresponseResponseofasinglenetworkBasicFilterSynthesisApproacBasicFilterSynthesisApproaches(cont’d)InsertionLossMethod.FilterZoZoUsetheRCLMcircuitsynthesistheoremtocomeupwitharesistiveterminatedLCnetworkthatcanproducetheapproximateresponse.ZoIdealApproximatewithrationalpolynomialfunction|H()|WecanalsouseAttenuationFactoror|s21|forthis.Approximateidealfilterresponsewithpolynomialfunction:BasicFilterSynthesisApproacOurScopeOnlyconcentrateonpassiveLCandstriplinefilters.FiltersynthesisusingtheInsertionLossMethod(ILM).TheImageParameterMethod(IPM)ismoreefficientandsuitableforsimplefilterdesigns,buthasthedisadvantagethatarbitraryfrequencyresponsecannotbeincorporatedintothedesign.OurScopeOnlyconcentrateonp2.0PassiveLCFilterSynthesisUsingtheInsertionLossMethod2.0PassiveLCFilterSynthesiInsertionLossMethod(ILM)Theinsertionlossmethod(ILM)enablesasystematicwaytodesignandsynthesizeafilterwithvariousfrequencyresponses.TheILMmethodalsoenablesafilterperformancetobeimprovedinastraightforwardmanner,attheexpenseofa‘higherorder’filter.Arationalpolynomialfunctionisusedtoapproximatetheideal|H()|,A(),or|s21()|.Phaseinformationistotallyignored.Ignoringphasesimplifiestheactualsynthesismethod.AnLCnetworkisthenderivedwhichwillproducethisapproximatedresponse.TheattenuationA()canbecastintopowerattenuationratio,calledthePowerLossRatio,PLR,whichisrelatedtoA()2.InsertionLossMethod(ILM)TheMoreonILMThereisahistoricalreasonwhyphaseinformationisignored.Originalfiltersynthesismethodsaredevelopedinthe1920s–60s,forvoicecommunication.Thehumanearisinsensitivetophasedistortion,thusonlythemagnituderesponse(e.g.,|H()|,A())isconsidered.Modernfiltersynthesiscanoptimizeacircuittomeetbothmagnitudeandphaserequirements.Thisisusuallydoneusingcomputeroptimizationprocedureswith‘goalfunctions’.ExtraMoreonILMThereisahistoricPowerLossRatio(PLR)PLRlarge,highattenuationPLRcloseto1,lowattenuationForexample,alowpassfilterresponseisshownbelow:ZLVsLossless2-portnetwork1ZsPAPinPLPLR(f)LowpassfilterPLRf10LowattenuationHighattenuationfc(2.1a)PowerLossRatio(PLR)PLRlargPLRands21Intermsofincidentandreflectedwaves,assumingZL=Zs=ZC.ZcVsLossless2-portnetworkZcPAPinPLa1b1b2(2.1b)PLRands21IntermsofincidenPLRfortheLowPassFilter(LPF)Since|1()|2isanevenfunctionof,itcanbewrittenintermsof2as:PLRcanbeexpressedas:VarioustypesofpolynomialfunctionincanbeusedforP().TherequirementisthatP()musteitherbeanoddorevenfunction.Amongtheclassicalpolynomialfunctionsare:MaximallyflatorButterworthfunctionsEqualrippleorChebyshevfunctionsEllipticfunctionMany,manymore(2.2)(2.3a)(2.3b)ThisisalsoknownasCharacteristicPolynomialThecharacteristicsweneedfrom[P()]2forLPF:[P()]20for<c[P()]2>>1for>>cPLRfortheLowPassFilter(LCharacteristicPolynomialFunctionsMaximallyflatorButterworth:EqualrippleorChebyshev:Besselorlinearphase:N=orderoftheCharacteristicPolynomialP()(2.4a)(2.4b)(2.4c)CharacteristicPolynomialFuncExamplesofPLRfortheLowPassFilterPLRofthelowpassfilterusing4thorderpolynomialfunctions(N=4)–Butterworth,Chebyshev(ripplefactor=1),andBessel.Normalizedtoc=1rad/s,k=1.ButterworthChebyshevBesselPLRIdealIfweconvertintodB,thisrippleisequalto3dBk=1ExamplesofPLRfortheLowPaExamplesofPLRfortheLowPassFilter(cont’d)PLRofthelowpassfilterusingtheButterworthcharacteristicpolynomial,normalizedtoc=1rad/s,k=1.N=2N=6N=4N=5N=3N=7Conclusion:Thetypeofpolynomialfunctionandtheorderdeterminetheattenuationrateinthestopband.ExamplesofPLRfortheLowPaCharacteristicsofLowPassFiltersUsingVariousPolynomialFunctionsButterworth:Moderatelylinearphaseresponse,slowcutoff,smoothattenuationinthepassband.Chebyshev:Badphaseresponse,rapidcutoffforasimilarorder,containsrippleinthepassband.MayhaveimpedancemismatchforNeven.Bessel:Goodphaseresponse,linear.Veryslowcutoff.Smoothamplituderesponseinthepassband.CharacteristicsofLowPassFiLowPassPrototypeDesignAlosslesslinear,passive,reciprocalnetworkthatcanproducetheinsertionlossprofileforthelowpassfilteristheLCladdernetwork.ManyresearchershavetabulatedthevaluesfortheLandCforthelowpassfilterwithcut-offfrequencyc

=1rad/s,thatworkswiththesourceandloadimpedanceZs=ZL=1.ThislowpassfilterisknownastheLowPassPrototype(LPP).AstheorderNofthepolynomialPincreases,therequiredelementalsoincreases.Theno.ofelements=N.L1=g2L2=g4C1=g1C2=g3RL=gN+11L1=g1L2=g3C1=g2C2=g4RL=gN+1g0=1DualofeachotherLowPassPrototypeDesignAlosLowPassPrototypeDesign(cont’d)TheLPPisthe‘buildingblock’fromwhichrealfiltersmaybeconstructed.Varioustransformationsmaybeusedtoconvertitintoahighpass,bandpass,orotherfilterofarbitrarycenterfrequencyandbandwidth.ThefollowingslidesshowsomesampletablesfordesigningLPPforButterworthandChebyshevamplituderesponseofPLR.LowPassPrototypeDesign(conTablefortheButterworthLPPDesignSeeExample2.1inthefollowingslidesonhowtheconstantvaluesg1,g2,g3,…etc.,areobtained.TablefortheButterworthLPPTablefortheChebyshevLPPDesignRipplefactor20log10=0.5dBRipplefactor20log10=3.0dBTablefortheChebyshevLPPDeTablefortheMaximally-FlatTimeDelayLPPDesignTablefortheMaximally-FlatTExample2.1:FindingtheConstantsfortheLPPDesignandThusThereforewecancomputethepowerlossratioas:[P()]2RRVsCLRjLRVs1/jCV1Considerasimplecaseofa2ndorderlowpassfilter:ExtraExample2.1:FindingtheConst30ExtraPLRcanbewrittenintermsofpolynomialof2:ForButterworthresponsewithk=1,c=1:(E1.1)(E1.2)Comparingequations(E1.1)and(E1.2):SettingR=1fortheLowPassPrototype(LPP):(E1.3)(E1.4)Thusfromequation(E1.4):Using(E1.3)ComparethisresultwithN=2inthetableforthe

LPPButterworthresponse.Thisdirect‘bruteforce’approachcanbeextendedtoN=3,4,5…Example2.1:FindingtheConstantsfortheLPPDesign(cont’d)ExtraPLRcanbewritteninter31Example2.1:VerificationExtraExample2.1:VerificationExtraExample2.1:Verification(cont’d)Extra–3dBat160mHz(milliHertz!!),whichisequivalentto1rad/sPowerlossratioversusfrequencyExample2.1:Verification(conImpedanceDenormalizationandFrequencyTransformationofLPPOncetheLPPfilterisdesigned,thecut-offfrequencyccanbetransformedtootherfrequencies.FurthermoretheLPPcanbemappedtootherfiltertypessuchashighpass,bandpass,andbandstop.ThisfrequencyscalingandtransformationentailschangingthevalueandconfigurationoftheelementsoftheLPP.Finallytheimpedancepresentedbythefilterattheoperatingfrequencycanalsobescaled,fromunitytoothervalues;thisiscalledimpedancedenormalization.LetZobethenewsystemimpedancevalue.ThefollowingslidesummarizesthevarioustransformationfromtheLPPfilter.ImpedanceDenormalizationandImpedanceDenormalizationandFrequencyTransformationofLPP(cont’d)LPPtoLowPassLPPtoHighPassLPPtoBandpassLPPtoBandstopNotethattheinductoralwaysmultiplieswithZowhilethecapacitordivideswithZo(2.5a)(2.5b)LCCenterfrequencyFractionalbandwidthImpedanceDenormalizationandSummaryofPassiveLCFilterDesignFlowUsingtheILMMethodStep1:Fromtherequirements,determinetheorderandtypeofapproximationfunctionstouse.Insertionloss(dB)inthepassband?Attenuation(dB)inthestopband?Cut-offrate(dB/decade)inthetransitionband?Tolerableripple?Linearityofphase?Step2:Designanormalizedlowpassprototype(LPP)usingtheLandCelements.L1=g2L2=g4C1=g1C2=g3RL=gN+11|H()|011SummaryofPassiveLCFilterDSummaryofPassiveFilterDesignFlowUsingtheILMMethod(cont’d)Step3:Performfrequencyscaling,anddenormalizetheimpedance.Step4:Choosesuitablelumpedcomponents,ortransformthelumpedcircuitdesignintodistributedrealization.|H()|011250Vs15.916pF0.1414pF79.58nH0.7072nH0.7072nH15.916pF50RLAllusesthemicrostripstriplinecircuitSummaryofPassiveFilterDesiFiltervs.ImpedanceTransformationNetworkIfwepondercarefully,thesharpobserverwillnoticethatthefiltercanbeconsideredasaclassofimpedancetransformationnetwork.Inthepassband,theloadismatchedtothesourcenetwork,muchlikeafilter.Inthestopband,theloadimpedanceishighlymismatchedfromthesourceimpedance.However,theproceduredescribedhereonlyappliestothecasewhenbothloadandsourceimpedanceareequalandreal.ExtraFiltervs.ImpedanceTransformExample2.2A:LPFDesign–ButterworthResponseDesigna4thorderButterworthlowpassfilter,Rs=RL=50,

fc=1.5GHz.L1=0.7654HL2=1.8478HC1=1.8478FC2=0.7654FRL=1g0=1L1=4.061nHL2=9.803nHC1=3.921pFC2=1.624pFRL=50

g0=1/50Steps1&2:LPPStep3:FrequencyscalingandimpedancedenormalizationExample2.2A:LPFDesign–ButDesigna4thorderChebyshevlowpassfilter,0.5dBripplefactor,Rs=50,fc=1.5GHz.Example2.2B:LPFDesign–ChebyshevResponseL1=1.6703HL2=2.3661HC1=1.1926FC2=0.8419FRL=1.9841g0=1L1=8.861nHL2=12.55nHC1=2.531pFC2=1.787pFRL=99.2g0=1/50Steps1&2:LPPStep3:FrequencyscalingandimpedancedenormalizationDesigna4thorderChebyshevlExample2.2(cont’d)ChebyshevButterworth|s21|Rippleisroughly0.5dBArg(s21)ChebyshevButterworthBetterphaselinearityforButterworthLPFinthepassbandComputersimulationresultusingACanalysis(ADS2003C)Note:EquationusedinDataDisplayofADS2003Ctoobtainacontinuousphasedisplaywiththebuilt-infunctionphase().Example2.2(cont’d)ChebyshevBExample2.3:BPFDesignDesignabandpassfilterwithButterworth(maximallyflat)response.N=3Centerfrequencyfo=1.5GHz3dBBandwidth=200MHzorf1=1.4GHz,f2=

1.6GHzImpedance=50ΩExample2.3:BPFDesignDesignExample2.3(cont’d)Fromtable,designthelowpassprototype(LPP)for3rdorderButterworthresponse,c=1.Zo=1g1

1.000Fg3

1.000Fg2

2.000Hg412<0oSimulatedresultusingPSpiceVoltageacrossg4Steps1&2:LPPExample2.3(cont’d)FromtableExample2.3(cont’d)LPPtobandpasstransformationImpedancedenormalization50Vs15.916pF0.1414pF79.58nH0.7072nH0.7072nH15.916pF50RLStep3:FrequencyscalingandimpedancedenormalizationExample2.3(cont’d)LPPtobanExample2.3(cont’d)SimulatedresultusingPSpice:VoltageacrossRLExample2.3(cont’d)SimulatedAllPassFilterThereisalsoanotherclassoffilterknownastheAllPassFilter(APF).Thistypeoffilterdoesnotproduceanyattenuationinthemagnituderesponse,butprovidesphaseresponseinthebandofinterest.APFisoftenusedinconjunctionwithLPF,BPF,HPF,etc.,tocompensateforphasedistortion.ExtraZoBPFAPFf0|H(f)|1fArg(H(f))ExampleoftheAPFresponsef|H(f)|10fArg(H(f))f0|H(f)|1fArg(H(f))LinearphaseinpassbandNonlinearphaseinpassbandAllPassFilterThereisalsoaExample2.4:PracticalRFBPFDesignUsingSMDDiscreteComponentsExample2.4:PracticalRFBPFExample2.4(cont’d)BPFsynthesisusingsynthesistoolE-synofADS2003CExample2.4(cont’d)BPFsyntheExample2.4(cont’d)|s21|/dBArg(s21)/degreeMeasuredSimulatedMeasurementisperformedwiththeAgilent8753ESVectorNetworkAnalyzer,usingFullOSLcalibrationExample2.4(cont’d)|s21|/dBAr3.0MicrowaveFilterRealizationUsingStriplineStructures3.0MicrowaveFilterRealizati3.1BasicApproach3.1BasicApproachFilterRealizationUsingDistributedCircuitElementsLumped-elementfilterrealizationusingsurfacemountedinductorsandcapacitorsgenerallyworkswellatlowerfrequencies(atUHF,say<3GHz).Athigherfrequencies,thepracticalinductorsandcapacitorslosestheirintrinsiccharacteristics.Also,alimitedrangeofcomponentvaluesisavailablefromthemanufacturer.Therefore,formicrowavefrequencies(>3GHz),thepassivefilterisusuallyrealizedusingdistributedcircuitelementssuchastransmissionlinesections.Herewewillfocusonstriplinemicrowavecircuits.FilterRealizationUsingDistrFilterRealizationUsingDistributedCircuitElements(cont’d)RecallinthestudyofTerminatedTransmissionLineCircuitthatalengthofterminatedTlinecanbeusedtoapproximateaninductorandacapacitor.ThisconceptformsthebasisoftransformingtheLCpassivefilterintodistributedcircuitelements.ZoZoZc,lLZc,lCZc,Zc,Zc,ZoZoFilterRealizationUsingDistrFilterRealizationUsingDistributedCircuitElements(cont’d)Thisapproachisonlyanapproximation.TherewillbedeviationbetweentheactualLCfilterresponseandthoseimplementedwithterminatedTline.Also,thefrequencyresponseofthedistributedcircuitfilterisperiodic.Otherissuesareshownbelow.Zc,Zc,Zc,ZoZoHowdoweimplementaseriesTlineconnection?(onlypracticalforcertainTlineconfiguration)Connectionofphysicallengthcannotbeignoredatthemicrowaveregion,comparabletoThussometheoremsareusedtofacilitatethetransformationoftheLCcircuitintostriplinemicrowavecircuits.ChiefamongthesearetheKuroda’sIdentities(SeeAppendix1)FilterRealizationUsingDistrMoreonApproximatingLandCwithTerminatedTline:Richard’sTransformationZc,lLZin(3.1.1a)Zc,lCZin(3.1.1b)ForLPPdesign,afurtherrequirementisthat:(3.1.1c)Wavelengthatcut-offfrequencyHere,insteadoffixingZcandtuningltoapproachanLorC,weallowZctobeavariabletoo.MoreonApproximatingLandCExample3.1:LPFDesignUsingStriplineDesigna3rdorderButterworthlowpassfilter,Rs=RL=50,

fc=1.5GHz.Steps1&2:LPPStep3:ConverttoTlinesZc=0.500Zc=1.0001Zc=1.0001Zo=1g1

1.000Hg3

1.000Hg2

2.000Fg41Length=c/8forallTlinesat=1rad/sExample3.1:LPFDesignUsingExample3.1(cont’d)Length=c/8forallTlinesat=1rad/sStep4:AddanextraTlineontheseriesconnectionandapplyKuroda’s2ndIdentity.Zc=0.500Zc=1.0001Zc=1.0001Zc=1.0Zc=1.0ExtraTlineExtraTlinen2Z1=2lZ2=1SimilaroperationisperformedhereYcExample3.1(cont’d)Length=Example3.1(cont’d)Zc=0.50011Zc=2.0Zc=2.0Zc=2.000Zc=2.000AfterapplyingKuroda’s2ndIdentityLength=c/8forallTlinesat=1rad/sSinceallTlineshavesimilarphysicallength,thisapproachtostriplinefilterimplementationisalsoknownasCommensurateLineApproach.Example3.1(cont’d)Zc=0.5001Example3.1(cont’d)Zc=255050Zc=100Zc=100Zc=100Zc=100Length=c/8forallTlinesatf=fc=1.5GHzZc/Ω/8@1.5GHz/mmW/mm5013.452.852512.778.0010014.230.61Microstriplineusingdouble-sidedFR4PCB(r=4.6,H=1.57mm)Step5:ImpedanceandfrequencydenormalizationHerewemultiplyallimpedancewithZo=50WecanworkoutthecorrectwidthWgiventheimpedance,dielectricconstant,andthickness.FromW/Hratio,theeffectivedielectricconstanteffcanbedetermined.Usethistogetherwithfrequencyat1.5GHztofindthewavelength.Example3.1(cont’d)Zc=25505Example3.1(cont’d)Step6:Thelayout(topview)Example3.1(cont’d)Step6:ThExample3.1(cont’d)SimulatedresultsExample3.1(cont’d)SimulatedConclusionsforSection3.1Furthertuningisneededtooptimizethefrequencyresponse.Themethodillustratedisgoodforthelowpassandbandstopfilterimplementation.Forhighpassandbandpass,otherapproachesareneeded.ConclusionsforSection3.1Fu3.2FurtherImplementations3.2FurtherImplementationsRealizationofLPFUsingtheStep-ImpedanceApproachArelativelyeasywaytoimplementLPFusingstriplinecomponents.UsingalternatingsectionsofhighandlowcharacteristicimpedanceTlinestoapproximatethealternatingLandCelementsinanLPF.Performanceofthisapproachismarginalasitisanapproximation,whereasharpcutoffisnotrequired.Asusual,bewareofparasiticpassbands!!!RealizationofLPFUsingtheSEquivalentCircuitofaTransmissionLineSectionZ11–Z12Z11–Z12Z12lZc(3.2.1a)(3.2.1b)(3.2.1c)IdeallosslessTlineT-networkequivalentcircuitPositivereactancePositivesusceptanceEquivalentCircuitofaTransmApproximationforHighandLowZCWhenl</2,theserieselementcanbethoughtofasaninductorandtheshuntelementcanbeconsideredacapacitor.Forl</4andZc=ZH>>1:Forl</4andZc=ZL

1:jX/2jBjX/2XZH

lBYLlWhenZc

1l</4WhenZc>>1l</4

Z11-Z12

Z11-Z12Z12ApproximationforHighandLowApproximationforHighandLowZC(cont’d)Notethatl</2impliesaphysicallyshortTline.ThusashortTlinewithhighZc(e.g.,ZH)approximatesaninductor.AshortTlinewithlowZc(e.g.,ZL)approximatesacapacitor.TheratioofZH/ZLshouldbeashighaspossible.Typicalvalues:ZH=100to150,ZL=10to15.(3.2.2a)(3.2.2b)ApproximationforHighandLowExample3.2:MappinganLPFCircuitintoaStepImpedanceTlineNetworkForinstance,considertheLPFDesignExample2.2A(Butterworth).Letususethemicrostripline.SinceamicrostripTlinewithlowZciswideandaTlinewithhighZcisnarrow,thetransformationfromcircuittophysicallayoutwouldbeasfollows:L1=4.061nHL2=9.803nHC1=3.921pFC2=1.624pFRL=50g0=1/50Example3.2:MappinganLPFCiExample3.2:PhysicalRealizationofLPFUsingthemicrostripline,withr=4.2,d=1.5mm:L1=4.061nH,L2=9.083nH,C1=3.921pF,C2=1.624pFExample3.2:PhysicalRealizatExample3.2:PhysicalRealizationofLPF(cont’d)l2l150Wline50Wlinel4l30.6mm15.0mm3.0mmTo50WLoadVerification:Neverthelesswestillproceedwiththeimple-mentation.Itwillbeseenthatthiswillaffecttheaccuracyofthe–3dBcut-offpointofthefilter.Example3.2:PhysicalRealizatExample3.2:StepImpedanceLPFSimulationwithADSSoftwareTransferringthemicrostriplinedesigntoADS:MicrostriplinemodelMicrostripstepjunctionmodelMicrostriplinesubstratemodelExample3.2:StepImpedanceLPExample3.2:StepImpedanceLPFSimulationwithADSSoftware(cont’d)Example3.2:StepImpedanceLPExample3.2:StepImpedanceLPFSimulationwithADSSoftware(cont’d)HoweverifweextentthestopfrequencyfortheS-parametersimulationto9GHz...Parasiticpassbands,artifactsduetousingtransmissionlinesExample3.2:StepImpedanceLPExample3.2:VerificationwithMeasurementThe–3dBpointisaround1.417GHz!TheactualLPFconstructedinyear2000.TheAgilent8720DVectorNetworkAnalyzerisusedtoperformtheS-parametermeasurement.Example3.2:VerificationwithExample3.3:RealizationofBPFUsingaCoupledMicrostripLineBasedontheBPFdesignofExample2.3:50Vs15.916pF0.1414pF79.58nH0.7072nH0.7072nH15.916pF50RLJ1–90oJ2–90oJ3–90oJ4–90oTlineAdmittanceinverterToRLTosourcenetworkSeeappendix(usingRichard’stransformationandKuroda’sidentities)Anarrayofcoupledmicrostriplineo=wavelengthatoSection1Section2Section3Section4AnequivalentcircuitmodelforcoupledTlineswithopencircuitattwoends.ExtraExample3.3:RealizationofBPExample3.3:RealizationofBPFUsingtheCoupledMicrostripLine(cont’d)Eachsectionofthecoupledstriplinecontainsthreeparameters:S,W,d.Theseparameterscanbedeterminedfromthevaluesoftheoddandevenmodeimpedances(Zoo&Zoe)ofeachcoupledline.ZooandZoeareinturndependonthe“gain”ofthecorrespondingadmittanceinverterJ.AndeachJnisgivenby:SWWdExtraFromExample2.3Example3.3:RealizationofBPExample3.3:RealizationofBPFUsingtheCoupledMicrostripLine(cont’d)Section1:Section2:Section3:Section4:Note:g1=1.0000g2=2.0000g3=1.0000g4=1.0000ExtraExample3.3:RealizationofBPExample3.3:RealizationofBPFUsingtheCoupledMicrostripLine(cont’d)Inthisexample,anedge-coupledmicrostriplineisusedtoimplementthecoupledtransmissionlinestructuresneededintheBPF.StriplinedoesnotsufferfromdispersionanditspropagationmodeispureTEMmode,howeveritismoredifficulttoimplementphysicallyduetothefactthatthetraceisburiedwithinthedielectric.Designequationsforcoupledmicrostriplineimplementedarewidelytabulated.HerewewilluseFR4(r=4.6,r=1.0)substratewith1.0mmdielectricthickness,and1ouncecopper(about36mthick)copperlaminate.Theconductivityofcopperisaround5.8107Siemens/meter.FurthermorewewillusetheLineCaltoolinAdvancedDesignSystemtoworkoutthedimensionsneededforthecoupledmicrostripline.ExtraExample3.3:RealizationofBPExample3.3:RealizationofBPFUsingtheCoupledMicrostripLine(cont’d)UsingtheLineCaltooltoworkoutthedimensionsforsections1and3.Electricallength(l),90oforquarterwavelength.ZoeZooZoVoltagecouplingfactorindBFixthefrequencyat1.5GHz,thecenterofpassbandStrategy:1)We‘tune’theWandSforthespecifiedZooandZoe.2)Thenwe‘tune’thelengthLtomeettheelectricallengthof/2(quarterwavelength)at1.5GHz.ExtraExample3.3:RealizationofBPExample3.3:RealizationofBPFUsingtheCoupledMicrostripLine(cont’d)UsingtheLineCaltooltoworkoutthedimensionsforsections2and4.ExtraExample3.3:RealizationofBPExample3.3:RealizationofBPFUsingtheCoupledMicrostripLine(cont’d)Alternativelywecanimplementourowndesigntool,asshownbelowimplementedonMicrosoftExcel.BasedondesignequationsfromGargR.,