无线系统的微波与射频设计5

MicrowaveandRFDesignofWirelessSystemsChapter5FilterDr.ZhangYonghongFiltersareusedtocontrolthefrequencyresponse.Functions:①allowingtransmissionatfrequencywithinthepassbandofthefilter.②attenuationwithinthestopbandofthefilter.Classificationsbyresponse:Low-Pass,high-pass,bandpass,bandstopLPFHPFBPFBSFApplication:Inreceivers①rejectionsignalsoutsidetheoperatingband.②attenuatingundesiredmixerproducts.③SettingtheIFbandwidthofthereceiver.Intransmitters①tocontrolthespuriousresponseofupconvertingmixers.②toselectthedesiredsidebands.③tolimitthebandwidthoftheradiatedsignal.§5.1FilterDesignbytheInsertionLossMethod§5.2FilterScalingandTransformation§5.3Low-passandhigh-passusingTransmissionlinestub§5.4Stepped-Impedancelow-passFilters§5.5BandpassFiltersusingTransmissionLineResponse§5.1FilterDesignbytheInsertionLossMethodIdealfiltershaveZeroinsertionlossinthepassband;Infiniteattenuationinthestopband;Linearphaseresponseinthepassband.Compromisesmustbemade.Theinsertionlossmethodallowahighdegreeofcontroloverthepassbandandstopbandamplitudeandphasecharacteristics.1.CharacterizationbyPowerLossRatio2.MaximallyFlatLow–passFilterprototype.3.Equal–RippleLow–passFilterprototype.3.Equal–RippleLow–passFilterprototype1.CharacterizationbyPowerLossRatio2.MaximallyFlatLow–passFilterprototypeMaximallyflatresponse(Butterworth)Equal-rippleresponse(Chebyshev)LinearphaseresponseLow-passFilterPrototype1.CharacterizationbyPowerLossRatioPowerLossratio:211inLRLoadPPPLRPdBILlg10Becauseofthecausalpropertiesofnetworks,2isanevenfunctionof,Therefore,writing2asapolynomialin22222NMM221NMPLRMaximallyflatresponse(Butterworth)NcLRkP221WhereNistheorderofthefiltercisthecutofffrequencyPassband:c0Thepowerlossratioatthebandedgec:21kIFk=1,thenPLR=3dBcForNcLRkP22Equal-rippleresponse(Chebyshev)WhereTN(x)isaChebyshevpolynomicaloforderN.Therippleofamplitudeinthepassbandis1+k2.221LRNCPkTNCLRkP2224cForLinearphaseresponse:NCPA21ThegroupdelayNCNPAdd2121→amaximallyflatfunction.Low-passFilterPrototype①normalizedintermsofimpedanceandfrequency.②simplifiesthedesignoffiltersforarbitraryfrequency,impedanceandtype(BPF,BSP,LPF,HPF).BeginningwithashuntcapacitorBeginningwithaseriesinductor③IF11,NgtheloadismatchedIF,11NgtheprototyperealizesImpedancetransformer.Feature:①alloftheelementvaluesfortheladder–typecircuitsisnormalized.②theelementvaluesaredifferentaccordingtodifferentresponse.Process:Filterspecifications→Low-passprototypedesign→scallingandconversion→Impedance2.MaximallyFlatLow–passFilterprototype,FromthefilterPrototype.1,,inKKNZhLCg11ininZZ'22121,,11NLRkKNPhLCgkSolvingtheequation,kkCL,willbeknown.11Ng3.Equal–RippleLow–passFilterprototypeForfilterprototype,221NLRTkP001NforNoddTforNeven1,',NkkLRgCLhPNisodd,011ggNNiseven,11Ngimpedancetransformer.§5.2FilterScalingandTransformation1．ImpedanceScalingandFrequencyScaling(forLPF)2．Low-passtoHigh-pass3．BandpassTransformation1.ImpedanceScalingandFrequencyScaling(forLPF)ZXZRRBYYLZXCYBCSeriesinductorscKKcKKRCCLRL0'0'Shuntcapacitors:''0,0sLLRRRRREXAMPLE5.2,page162.c00c1c1002.Low-passtoHigh-passTransformationThenegativesignisneededtoconvertCLandLC'1KKCKCjLjjXKCKLC1''1KKCKLjCjjBKCKCL1'3.BandpassTransformation110002100021001012Fractionbandwidthofthepassband2101002'00'001KKKkKKjLLjXLjjjLjC'0KKLLKKLC0'0KKLC0KKCCBandStopTransformation§5.3Low-passandhigh-passusingTransmissionlinestubAtMW:①lumpedelementsareavailableonlyforalimitedfrequencyrange.②Thevalveoflumpedelementistoosmalltoberealizedatmicrowave.③Theelectricaldistancebetweenfiltercomponentsisnotnegligible.④Openorshorttransmissionlinestubcanbeusedasreactiveelements.How?Foundation:jLtgBlLjjXLjCtgBlCjjBC1tgl1.Richard’sTransformationTheRichard’s-transformationhasthesamecutofffrequencywiththelow-passfilterprototype.Atthefrequencyawayfromc,theimpedanceofthestubswillnolongermatchtheoriginallumped-elementimpedance.Sodosethefilterresponse.2.Kuroda’sIdentitiesItuseredundanttransmissionlinesectionstoachieveamorepracticalmicrowavefilter.Function:①Physicallyseparatetransmissionlinestubs.②Transformseriesstubsintoshuntstubs,orviceversa.③ChangeimpracticalcharacteristicImpedancesintomorerealizableones.1221ZZn8lat1orCExample5.4page172①Theseriesstubwouldbedifficulttoimplementinmicrostripform.②Theredundantelementsdonotaffectfilterperformancesincetheyarematchedtothesourceandloadimpedance.③Thepassbandcharacteristicareverysimilar.④Thedistributedelementfilterhasamuchsharpcutoffresponse.⑤Thedistributedelementfilterhasaperiodicresponse.⑥SimilarprocedurescanbeusedforLPFandBSF,notusefulforHPFandBPF.lowfrequency§5.4Stepped-Impedancelow-passFilters0hLRlZatC0lCZlRatChi-Zandlow-ZLPFExample5.5page176Feature:①easytodesign.②takeuples