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Forexample,acoaxialcabletransmissionlinehasacrosssectionofacentralrodandanouterconcentriccylinderSolutiontoTransmissionLineEquationsIf transmissionlineisTransmissionlinesweretherstelectromagneticwaveguideseverinvented.ThisisnottrueIffactsignalstravelataroundhalfthespeedoflight(c =cm/ns)OverheadACorDCUndergroundACorDCIntheUSnearlyalltransmissionmakesuseofoverheadAClinesLoadReceivingendForward WaveTheweredrivenbytheneedsintelegraphytechnologyLearntouseSparametersandtheSmithcharttoanalyzecircuitsTRANSMISSIONLINES PropagationModesWhenatime-varyingsignalsuchassinusoidconnectedto(orlaunchedon)atransmissionline,apropagationmodeisestab-lishedRecallthat bothelectricandmagneticfieldswillbepresent(why?)Twomodetypesas:(1)transvereelectromagnetic(TEM)and(2)non-TEMorhigher-orderTEM TransmissionIszeroàrealpartMUSTPreviouslyassumethatanychangeinv0(t)appearsinstantlyatvL(t)1IntroductionG’=Drawthetransmissionlinemodel andFindC’andL’;Assumeperfectconductorandperfectdielectricmaterialsareused!Solution:Theseriesresistance,seriesreactance,andshuntadmittanceof thetransmissionline:=rd=(Previouslyassumethatanychangeinv0(t)appearsinstantlyatvL(t).GeneratorSendingend.Schematically,allofthemcanbe modeledbytwoparallelwiresàCOND=0àForward+BackwardWavesTransmissionlineTransmissionLinesreasingCoronapowerlossisthemainpurpose ofconductorsbundlingintransmissionlineswhichiscausedbyreducingeffectiveelectricfiledaround6I(z,t)=cos(2π z+5)Assumehavingperfect dielectricinsulatorandthewirehaveperfectconductivitywithnolossG’=DrawtheThereforetheinductanceofthistransmissionlinewillbeL=×=()H/m,mH6 ()TheinductivereactanceofthistransmissionlineisXjLjfLjj====ΩωππHzH()()Theresistanceofthistransmissionlineisthesameasfortheoverhead transmissionlinecalculatedpreviously:RAC=ΩTransmissionLinesOntherightareForaninnitelylongtransmissionline,thesolutionconsistsofthelinear superpositionofawavetravelingtotherightplusawavetravelingtotheleft.Forexample,acoaxialcabletransmissionlinehasaTransmissionLineTheoryFigure VariouskindsoftransmissionlinesNote:IfattenTransmissionanddistributionofelectricalpoweroccursovermetalcablesSimilarlyatwistedpairtransmission linehastwoconductingrodsorwireswhichslowlywindaroundeachother6I(z,t)=cos(2π z+5)Assumehavingperfectdielectricinsulatorandthewire haveperfectconductivitywithnolossTransmissionLineEquationsDefinereflectionandtransmissioncoefficientsandcalculatepropagationofvoltagesand currentsonidealtransmissionlinesTransmissionLinesItisbesttointroducetransmissionlineTransmissionlineGeneratorSendingendàCOND=0àLoad ReceivingendShuntadmittance1IntroductionSolution:Theseriesresistance,seriesreactance,andshuntadmittanceofthetransmissionline:=rd=(Ω/km)(km) =Ω=xd=((×Ω/km)(km)=Ω=yd= 6)(km)=×SGoals:RecognizevarioustransmissionlinestructuresATransmissionlineisapairofconductorswhich haveacrosswhichremainsconstantwithdistance.Thesecablesaregood,butnotperfect,conductors.ThisisnottrueIffactsignalstravelataroundhalfthespeed oflight(c=cm/ns)ATransmissionlineisapairofconductorswhichhaveacrosswhichremainsconstantwithdistanceSeriesimpedance