HFSS和serenade滤波器设计.docx

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