电磁场与电磁波第24讲导波的一般特性

1Stripline带状线Two-wireline双导线Rectangularwaveguide矩形波导Microstripline微带线Dielectricwaveguide,Fiberoptic介质波导光纤Coaxialline同轴线Circularwaveguide圆波导2SystemsWavetypesEMshieldingWavebandTwo-wirelineTEMwavPoor>3mCoaxiallineTEMwaveGood>10cmStriplineTEMwavePoorCentimeterMicrostriplineQuasi-TEMwavePoorCentimeterRectangularwaveguideTEorTMwaveGoodCentimeterMillimeterCircularwaveguideTEorTMwaveGoodCentimeterMillimeterFiberopticTEorTMwavePoorOpticalwaveThemainpropertiesofseveralwaveguidingsystems3MaintopicWaveguidesandCavityResonators1.GeneralWaveBehaviorsalongUniformGuidingStructures4Forharmonictimedependencewithanangularfrequency,thedependenceonzandtforallfieldcomponentscanbedescribedbytheexponentialfactor

Supposethewaveguidingsystemis

infinitely

long,andletitbeplacedalongthe

z-axis

andthepropagatingdirectionbealongthepositivez-directionwithapropagationconstant=+jthatisyettobedetermined.Asanexample,foracosinereferencewemaywritetheinstantaneousexpressionfortheEfieldinCartesiancoordinatesas5Theelectricandmagneticfieldintensitiesinthecharge-freedielectricregioninsidesatisfythefollowinghomogeneousvectorHelmholtz’sequations:Thethree-dimensionalLaplacianoperator2maybebrokenintotwoparts:2u1u2forthecross-sectionalcorrdinatesand2zforthelongitudinalcoordinate.ForwaveguideswitharectangularcrosssectionweuseCartesiancoordinates:then6Ex0

,Ey0

,Hx0

,Hy0

canbecalled

thetransversecomponents横向场量

andEz0,Hz

0canbecalled

thelongitudinalcomponents纵向场量.

Basedonthe

boundaryconditions

ofthewaveguidingsystemandbyusingthemethodof

separationofvariables,wecanfindthesolutionsfortheseequations.7

FromMaxwell’sequations,wecanfindtherelationshipsbetweenthe

x-component

orthe

y-component

andthe

z-component

as8Where.

Theserelationshipsarecalledtherepresentationofthe

transverse

componentsbythe

longitudinal

components.Supposedthelongitudinalcomponentsareknown,wecanobtainWe

onlyneedtosolvethescalarHelmholtzequationforthe

longitudinal

components,andthenfrom

therelationships

betweenthetransversecomponentsandthelongitudinalcomponents

alltransversecomponents

canbederived.9

Inthesameway,incylindricalcoordinatesthe

z-componentcanbeexpressedintermsofthe

r-componentand

–componentas10ItisconvenienttoclassifythepropagatingwavesinauniformwaveguideintothreetypesaccordingtowhetherEzorHz

exists.1.Transverseelectromagnetic(TEM)waves.Thesearewavesthatcontainneither

Ez

nor

Hz.WeencounteredTEMwavesinChapter8whenwediscussedplanewavesandinChapter9onwavesalongtransmissionlines.2.TransverseMagnetic(TM)waves.Thesearewavesthatcontainanonzero

Ez

butHz=0.3.Transverseelectric(TE)waves.

ThesearewavesthatcontainanonzeroHz

butEz

=0.Thepropagationcharacteristicsofthevarioustypesofwavesaredifferent;theywillbediscussedinsubsequentsubsections.111.1transverseelectromagneticwavesTEM(Ez=0,Hz=0)wavesexistonlywhenItfollowsthatthevelocityofpropagation(phasevelocity)forTEMwavesis12WecanobtaintheratiobetweenEx0andHy0,whichiscalledthewaveimpedance.WecanobtaintheratiobetweenEy0andHx013WecanobtainthefollowingformulaforaTEMwavepropagatinginthe+z-direction:TEM

wavescannotexistinasingle-conductorhollow单导体波导(ordielectric-filled)waveguideofanyshape.1.2transversemagneticwavesTM(Ez0,Hz=0)14ForTMwaveswesetHz=0toobtainItconvenienttowriteintroducethewaveimpedance15ThefollowingrelationbetweentheelectricandmagneticfieldintensitiesholdsforTMwave:Inthefollowingsectionswewillalsodiscoverthattheeigenvaluesofthevariouswaveguideproblemsarerealnumber实数.WehaveThevaluesofhforwhichasolutionofequationexistsarecalledthecharacteristicvaluesoreigenvaluesoftheboundary-valueproblem.特征值或本征值Twodistinctrangesofthevaluesforthepropagationconstantarenoted,thedividingpointbeing=0,where两个截然不同的区域16Thetwodistinctrangesofcanbedefinedintermsoftheratio(f/fc)2ascomparedtounity.a)(f/fc)2>1,orf>fc.Inthisrange,2>handisimaginary.WehaveThefrequency,fc,atwhich=0iscalledacutofffrequency截止频率.Thevalueoffc

foraparticularmodeinawaveguidedependsontheeigenvalueofthismode.Wecanwriteas17Itisapropagatingmodewithaphaseconstant

:Thecorrespondingwavelengthintheguideiswhereisthewavelengthofaplanewavewithafrequencyfinanunboundeddielectricmediumcharacterizedbyand,anduisthevelocityoflightinthemedium.Equationcanberearrangedtogiveasimplerelationconnecting,theguidewavelengthg,andthecutoffwavelengthc=u/fc18ThephasevelocityofthepropagatingwaveintheguideisThephasevelocitywithinawaveguideisalwayshigherthanthatinanunboundedmediumandiffrequency-dependent.Hencesingle-conductorwaveguidearedispersive色散

transmissionsystems,althoughanunboundedlosslessdielectricmediumisnondispersive.ThegroupvelocityforapropagatingwaveinawaveguideisThus,Thewaveimpedanceis19b)(f/fc)2<1,orf<fc.Inthisrange,2<handisreal.WehaveWhichis,infact,anattenuationconstant.Sinceallfieldcomponentsdiminishesrapidlywithzandissaidtobeevanescent.Therefore,awaveguideexhibitsthepropertyofahigh-passfilter.Foragivenmode,onlywaveswithafrequencyhigherthanthecutofffrequency

ofthemodecanpropagateintheguide.只有频率高于模式的截止频率的波，才可能在波导内传播。ThewaveimpedanceisThus,thewaveimpedanceofevanescent

TM迅衰模modesatfrequenciesbelowcutoffispurelyreactive纯电抗性,indicatingthatthereisnopower

flowassociatedwithevanescentwaves.201.3transverseelectricwave