Fig1 Fig1 withimpedanceinvertersusingtheconventionalbandstoptransformationforacertainstopbandbandwidthFrom Fig1 theimpedancefunctionofanyofthelumpedbandstopresonatorscanbeexpressedintermsoftheL ID: 823087
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Fig.1depictsalumpedelementlowpassprotot
Fig.1depictsalumpedelementlowpassprototypethatrealisesÞnite-frequencytransmissionzerosduetotheseriesparallelLCbranches.Thisprototypeisthentrans-formedtothatofFig.1(withimpedanceinverters)usingtheconventionalbandstoptransformationforacertainstop-bandbandwidth.FromFig.1theimpedancefunctionofanyofthelumpedbandstopresonatorscanbeexpressedintermsoftheLaplacevariable,Thetransmissionzerosofthefundamentalstopbandarefoundfrom(1)asfollows2vrp
tan1
tan1...In(3)and(4),isequalto))wheretheangularfrequencyatwhichthestubsoftheprototypeareonequarter-wavelengthlong.Thus,totransformaSðpv3oiLiCiþpvoiÞS2þjð2vrv2oiLiCiþ2vrÞSþpvFig.3.TheinterestingfeatureisthatthelocationoftheÞrstpairofspuriousstopbandsisafunctionofthecommensuratefrequency,,andthusbyspecifyingaslargeaspossible,itisfeasibletohaveawidespurious-freeuppe
rpassband.TheInstitutionofEngineeringan
rpassband.TheInstitutionofEngineeringandTechnology2007doi:10.1049/iet-map:20060147PaperÞrstreceived29thJuneandinrevisedform19thNovember2006W.M.FathelbabiswiththeDepartmentofElectricalandComputerEngineering,SouthDakotaSchoolofMinesandTechnology,RapidCity,SD57701-3995,USAM.B.SteeriswiththeDepartmentofElectricalandComputerEngineering,NorthCarolinaStateUniversity,Raleigh,NC27695-7911,USAE-mail:wfathelbab@ieee.orgIETMicrow.AntennasPropag.,2007,,(2),pp
.523Ð526Authorized licensed use limite
.523Ð526Authorized licensed use limited to: North Carolina State University. Downloaded on February 2, 2009 at 13:54 from IEEE Xplore. Restrictions apply.Authorized licensed use limited to: North Carolina State University. Downloaded on February 2, 2009 at 13:54 from IEEE Xplore. Restrictions apply.Authorized licensed use limited to: North Carolina State University. Downloaded on February 2, 2009 at 13:54 from IEEE Xplore. Restrictions apply