电磁场与电磁波第25讲矩形波导的传播特性课件.ppt

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1、ElectromagneticFieldandWave电磁场与电磁波第25讲1作业情况1班：人合计：人情况:2Review1.GeneralWaveBehaviorsalongUniformGuidingStructures34Maintopic1.RectangularWaveguides51.RectangularWaveguidesSelecttherectangularcoordinatesystemandletthebroadsidebeplacedalongthex-axis,thenarrowsidealongthey-axis,andthepropag

2、atingdirectionbealongthez-axis.azyxb,ForTMwaves,Hz=0,andaccordingtothemethodoflongitudinalfields,thecomponentEzshouldfirstbesolved,andfromwhichtheothercomponentscanbederived.Thez-componentoftheelectricfieldintensitycanbewrittenas1.1TMwaves6ItsatisfiesthefollowingscalarHelmholtzequatio

3、n,i.e.Inordertosolvetheaboveequation,themethodofseparationofvariablesisused.LetWeobtainwhereX"denotesthesecondderivativeofXwithrespecttox,andY"denotesthesecondderivativeofYwithrespecttoy.7Theonlywaytheequationcanbesatisfiedisthatbothtermsontheleftsideareconstants.Nowletwherekxandkyareca

4、lledtheseparationconstants,andtheycanbefoundbyusingtheboundaryconditions.Obviously8wherealltheconstantsC1,C2,C3,C4,andkx,ky,dependontheboundaryconditions.Thetwoequationsaresecondorderordinarydifferentialequations,andthegeneralsolutions,arerespectivelyThez-componentoftheelectricfieldinte

5、nsitycanbewrittenasBoundaryconditions:azyxb,910Andallthefieldcomponentsarewhere11Thecutoffofaparticularmodeistheconditionthatmakesvanish.FortheTMmnmodethecutofffrequencyisAlternatively,wemaywriteWherecisthecutoffwavelength.12(a)Thephaseoftheelectromagneticwaveisrelatedtothevariablez

6、only,whiletheamplitudetothevariablesxandy.Hence,atravelingwaveisformedinthez-direction,andastandingwaveisinthex-directionandy-direction.(b)Theplanez=0isawavefront.Becausetheamplitudeisrelatedtoxandy,theTMwaveisanon-uniformplanewave.(c)Ifmorniszero,then(forTMwave),andallcomponentswillbez

7、ero.Thusthemandnarenon-zerointegrals,andtheyhaveclearphysicalmeanings.Thevalueofmstandsforthenumberofhalf-cyclevariationsofthefieldsalongthebroadside,whilendenotesthatforthenarrowside.(d)Sincemandnaremulti-valued,thepatternofthefieldhasmultipleforms,alsocalledmultiplemodes.Apai