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1、IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.46,NO.4,APRIL1998343AUnifiedApproachtotheDesign,Measurement,andTuningofCoupled-ResonatorFiltersJohnB.NessAbstractÐTheconceptofcouplingcoefficientshasbeenaheretoincludedirectlysettingthecouplingvaluesaswellveryusefuloneinthedesigno
2、fsmall-to-moderatebandwidthastheresonantfrequencyandªrealtimeºadjustmentformicrowavefilters.Itisshowninthispaperthatthegroupdelaytheeffectsoffrequencypullingoftheresonantfrequency.oftheinputreflectioncoefficientsofsequentiallytunedresonatorsSettingthecouplingvaluesarisesfromthesimp
3、lerelationshipcontainsalltheinformationnecessarytodesignandtunefilters,andthatthegroup-delayvalueatthecenterfrequencyofthefilterbetweenthecouplingandgroupdelayofthereflectedsignal.canbewrittenquitesimplyintermsofthelow-passprototypeTherelevantequationsarederivedinthispaperandconfirm
4、edvalues,theLCelementsofabandpassstructure,andthecouplingbymeasuredresultsonfiltersandbycomparisonwithothercoefficientsoftheinvertercoupledfilter.Thisprovidesaneasytechniques.methodtomeasurethekeyelementsofafilter,whichisconfirmedbyresultspresentedinthispaper.Itisalsosuggestedthatsin
5、cethegroupdelayofthereflectioncoefficient(i.e.,thetimeII.THEORYtakenforenergytogetinandoutofthecoupledresonators)isThestandardapproachtofilterdesignusinglow-passeasilymeasured,itisausefulconceptualalternativetocouplingbandpassinvertercoupledresonatorsisshowninFig.1.concepts.Thenome
6、nclatureusedfollowsconvention.Thecouplingbe-IndexTermsÐCoupling,filters,groupdelay,resonators.tweentheconnectinglinesandtheinputandoutputresonators,referredtoastheexternalor,andthecouplingbetweenI.INTRODUCTIONresonatorsarereadilyspecifiedintermsoftheprototypevaluesandtherelativeba
7、ndwidth.OncethesecouplingHEDESIGNofmicrowavefiltersisbasedonvaluesaresetandtheresonatorsalltunedtothecenterTwell-establishedtechniqueswithperhapsthefrequency,theinvertercoupledfilterwillhavethefrequencylowpass±bandpass±invertercoupled-resonatorprocessbeingresponsepredictedbythetra
8、nsformedlow-passprototypethemostcommondesignmet
