Fig1Fig1withimpedanceinvertersusingtheconventionalbandstoptransformationforacertainstopbandbandwidthFromFig1theimpedancefunctionofanyofthelumpedbandstopresonatorscanbeexpressedintermsoftheLaplacevari ID: 879022
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1 Fig.1 depictsalumpedelementlowpassprotot
Fig.1 depictsalumpedelementlowpassprototypethatrealisesÞnite-frequencytransmissionzerosduetotheseriesparallelLCbranches.Thisprototypeisthentrans-formedtothatof Fig.1 (withimpedanceinverters)usingtheconventionalbandstoptransformationforacertainstop-bandbandwidth.From Fig.1 theimpedancefunctionofanyofthelumpedbandstopresonatorscanbeexpressedintermsoftheLaplacevariable, Thetransmissionzerosofthefundamentalstopbandarefoundfrom(1)asfollows 2vrp
2 tan1
tan1 ...In(3)and(4),isequalto))wheretheangularfrequencyatwhichthestubsoftheprototypeareonequarter-wavelengthlong.Thus,totransforma Sðpv3oiLiCiþpvoiÞS2þjð2vrv2oiLiCiþ2vrÞSþpv Fig.3 .TheinterestingfeatureisthatthelocationoftheÞrstpairofspuriousstopbandsisafunctionofthecommensuratefrequency,,andthusbyspecifyingaslargeaspossible,itisfeasibletohaveawidespurious-freeuppe
3 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
4 .523Ð526 Authorized licensed use limite
.523Ð526 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. Authorized licensed use limited to: North Carolina State University. Downloaded on February 2, 2009 at 13:54 from IEEE Xplore. Restrictions apply