HFSS和serenade滤波器设计.docx
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HFSS和serenade滤波器设计
EfficientDesignofChebychevBand-PassFilterswithAnsoftHFSSandSerenade
Tutorial
Dr.B.MayerandDr.M.H.Vogel
AnsoftCorporation
Contents
Abstract3
1.Introduction3
2.CircuitRepresentationoftheFilter5
3.RelationshipsbetweenCircuitComponentsandPhysicalDimensionsintheMicrowaveFilter10
4.InitialFilterDesigninHFSS14
5.CurveFittinginSerenade16
6.CorrectedFilterDesigninHFSS20
7.AdditionalInformationfromthe3DFieldSolver21
7a.EffectsofInternalLosses21
7b.Maximumpower-handlingcapability23
7c.MechanicalTolerances24
References25
AppendixADerivationoftheCircuit26
AppendixBThePhysicalMeaningsofKandQ43
Abstract
AnefficientmethodispresentedtodesigncoaxialChebychevband-passfilters.Themethodinvolvesa3Dfull-wavefieldsolver,AnsoftHFSS,teamingupwithacircuitsimulator,Serenade.Theauthorsshowhowforapracticalcase,a7-polebandpassfilterwitharippleofonly0.1dB,anaccuratedesignisobtainedinamatterofdays,asopposedtoweeksfortraditionalmethods.
Themethoddescribedisalsoapplicabletoevenmorechallengingdesignsofellipticfiltersandphaseequalizersrealizedindielectric,waveguideorcoaxialtechnology.
1Introduction
Inthispaper,wewilldescribeanefficientmethodtodesignafilter.Themethodinvolvesa3Dfull-wavefieldsolverteamingupwithacircuitsimulator.Thebasicideahasbeenexploredbyothers[1]butadifferentcircuitwasusedinthecircuitsimulator.WewillexplainourprocedurebypresentingindetailhowwedesignaChebychevbandpassfilterwiththefollowingspecifications:
Centerfrequency400MHz
Ripplebandwidth15MHz
Ripple0.1dB
Out-of-bandrejection24dBat390MHzandat410MHz
Inordertoachievetheout-of-bandrejection,wewillneedsevenpoles.
ThedesiredfiltercharacteristicisshowninFig.1.
Fig.1Desiredfiltercharacteristic
Asthebasicgeometryforthisfilterwehavechosenacavitywithsevencoaxialresonators,asshowninFig.2.Inthefigure,the“buckets”havebeendrawnaswireframesforclarity,toshowthatthecylindersdon’textendallthewaytothebottom.
Fig.2Basicfiltergeometry
Thisgeometryissymmetricalwithrespecttothecentralcylinder.Inthiskindoffilter,thewallsofthecavity,thelongcylinders,thebucketsunderthecylindersandthedisk-shapedobjectsnearthefirstandlastcylinderareallmadeofmetal.Thelongcylindersareconnectedtothetopofthecavity;thebucketsareconnectedtothebottomofthecavity.Cylindersandbucketsdon’ttouch.Thedisk-shapedobjectsnearthefirstandlastresonatorareconnectedtotheinputandoutputtransmissionlinesandprovidethenecessarycouplingtothesourceandtheload.Wewillcalltheseobjectsantennasinthisdocument.Theyarenearthefirstandlastcylinders,butnevertouchthem.Eachcylinder-bucketcombinationisaresonatingstructure.Atthisstage,withoutrestrictingourselves,wecanchoosemanydimensionsinthefilterrelativelyfreely.Wemakethefollowingchoices:
Cavitydimensions280x30x120mm
Resonatordiameter10mm
Buckets’innerdiameter12mm
Buckets’outerdiameter16mm
Buckets’height15mm
Antennas’diameter26mm
Antennas’thickness6mm
Sixdimensionsremain,andthesesixwillbecrucialinobtainingthedesiredfiltercharacteristic:
Thelengthofthefirstandlastresonatingcylinder(bothhaveequallength)
Thelengthofthefiveinteriorcylinders(allfivehaveequallength)
Thedistancebetweenanantennaanditsnearestcylinder
Threedistancesbetweenneighboringcylinders(rememberthefilterissymmetric)
Withtraditionalfilterdesignmethods,obtainingthecorrectdimensionsisatime-consumingtaskthatcommonlytakesseveralweeks.Filterdesignwithacircuitsimulator,ontheotherhand,isrelativelystraightforward.Filtertheoryprovidesthevaluesforthelumpedinductorsandcapacitorsthatareneededtoobtainthedesiredfiltercharacteristic.First,wewillshowhowtodesignacircuitthatnotonlyhasthedesiredfiltercharacteristic,butalsolendsitselftoimplementationwithmicrowavecomponents.Insuchacircuit,weuseseriesLandCforeachresonator,i.e.thecylinder-and-bucketcombinations,andimpedanceinvertorstorepresentthedistancesbetweenadjacentresonators.Second,wewillshowhowonecandeterminerelationshipsbetweencomponentsinthecircuitanddimensionsinthephysicalfilter.Third,wewillpresentaniterativeprocedurebetweentheelectromagneticfieldsolverandthecircuitsimulatortooptimizethedesign.Theprocedureconvergesveryquickly.
2CircuitRepresentationoftheFilter
Inordertodesignanorder-sevenband-passfilteraround400MHzwitha0.1dBripple,filtertheorytellsustostartwithanorder-sevenlow-passfilter,normalizedto1radian/s.Thenormalizedfilteristohavea0.1dBripple,likethedesiredbandpassfilter.Thesourceandloadimpedancesofthenormalizedlowpassfilterarenormalizedto1Ohm.ThiscircuitisshowninFig.3anditscharacteristicinFig.4.Filtertheoryprovidesuswiththevaluesfortheinductorsandthecapacitors,denotedbyg1throughg7inthefigure.Thesevaluesareinourcase
g1=g7=1.1812H
g3=g5=2.0967H
g2=g6=1.4228F
g4=1.5734F.
Fig.3Normalizedlow-passfiltercircuit,startingpointfordesignprocedure
Fig.4Filtercharacteristicforthenormalizedlow-passfilterinFig.3
Thestep-by-stepprocedurefromthisnormalizedlow-passfiltercircuittothefinalband-passfiltercircuitispresentedindetailinAppendixA.Here,weshowanoutlineofthemajorsteps.
Animportantstepisthereplacementofshuntcapacitorsbyseriesinductorsandimpedanceinverters.Basically,animpedanceinvertertransformsimpedancesinthesamewayasaquarter-wave-lengthtransmissionline,butindependentoffrequency.TheresultingcircuitisshowninFig.5.Thisisstillanormalizedlow-passfilterwiththesamecharacteristicasthecircuitinFig.3.Thereasonforthischangeisthatatmicrowavefrequenciesitisoftenimpossibletorealizetheladdercircuitconsistingofseriesinductorsandshuntcapacitors.Dependingonthebasicstructureeitherserieselementsorshuntelementsareeasilyrealizablebutoftennotbothinthesamestructure.Takingadvantageofimpedanceinverters,itispossibletotransformshuntcapacitorsintoseriesinductors.Inthephysicalfiltertheseimpedanceinverterswillberealizedbycouplingsbetweenthecoaxialresonators.
Fig.5Normalizedlow-passfilterwithoutshuntcapacitors
Followingastandardprocedure,wetakethefollowingstepstoderivethedesiredband-passfiltermodel:
(1)De-normalizethelow-passcut-offangularfrequencyfrom1rad/stobwrad/s.
(2)Transformthelow-passfiltertoaband-passfilterwitharelativebandwidthofbwandacenterangularfrequencyof1rad/sbyinsertinga1Fcapacitorinserieswithevery1Hinductor.
(3)De-normalizethecenterfrequencyto400MHzbychoosing
L=1/(2×π×4E8)HandC=1/(2×π×4E8)F.
(4)De-normalizetheportimpedancesfrom1Ohmtotheusual50Ohmbyintroducingimpedanceinvertersattheinputandoutputwithcouplingcoefficientsof√50.
(5)Introducefinitequalityfactorstotheindividualresonatorsbyaddingaseriesresistortoeachresonator.
(6)Introduceindividualresonantfrequenciestothefirstandlastresonatorstobeabletobeabletotakethefrequencyshiftduetothecouplingantennasintoaccount.
(7)AddahomogeneoustransmissionlineoflengthZULbetweenfilterinput/outputandport1/port2tobeabletoadjustthephaseduetotheconnectors.
ThisgivesusthefiltershowninFig.6.TheprocedureoutlinedaboveispresentedinmoredetailinAppendixA.
Fig.6Finalfiltercircuit,representingthedesiredbandpassfilter
Inthiscircuit,everyLCpairresonatesat400MHz.FurtherK12,K23,K34andQLhavebeendefinedas
(1)
and
(2)
wherebwistherelativebandwidthandgiistheithgvaluefromfiltertheory.
Noticethat,sincethegvaluesareknownfromfiltertheory,westillknowthevaluesoftheallthecomponentsinthecircuit,eventhroughthecomponentshavechangedconsiderablyintheprocess.
Filtertheory[2]tellsusthatKi,i+1andQLhaveimportantphysicalmeanings.Ki,i+1isknownasthecouplingconstantbetweenadjacentresonators.Ifwehavejusttworesonatorsinthecavity,withaverylightcouplingtothesourceandtheload,thentherelationbetweencouplingconstantK12andresonantfrequenciesf1andf2isgivenby
K12=2(f2-f1)/(f2+f1).(3)
QLisknownastheloadedQofthecircuit.Ifwehavejustoneresonatorinthecavity,coupledtosourceandload,therelationbetweenQL,resonantfrequencyfRand3-dBbandwidthBW3dBisgivenby
QL=fR/BW3dB(4)
Inthenextsection,wewilllinkthecomponentsofthiscircuittodimensionsinthephysicalgeometryofthefilter.
3RelationshipsBetweenCircuitComponentsandPhysicalDimensionsintheMicrowaveFilter
Asexplainedintheprevioussection,everyLCpairresonatesat400MHz.Inthemicrowavefilter,wemustchoosethelengthofeachresonatorsuchthatitresonatesat400MHz.Thatwilldeterminethelengthofeachofthem.
Further,Ki,i+1(i=1,2,3)arethecouplingcoefficientsbetweenadjacentresonators.Therefore,thesethreecoefficientsarerelatedtothedistancesbetweenadjacentresonators.
Finally,QListheloadedQofthecircuit.Therefore,inanotherwiselosslesscircuit,itisdirectlyrelatedtothedistancebetweenthefi