电介质电容器LC传输线色散关系波速.ppt

吴雄斌无线电波传播,RadioWavePropagation,无线电波传播第二讲电磁波介质,提要,电磁理论概要LC传输线上的波动方程例：电信号传播速度Doppler频移色散群速度电介质介电常数的微观解释附：各向异性介质；常用介质类型,Establishedin1873byJamesClerkMaxwellGeneralizedAmperecircuitlawFaradaysmagneticinductionlawGausslawforelectricfieldsGausslawformagneticfieldsE(r,t)=electricfieldstrength(volts/m)B(r,t)=magneticfluxdensity(webers/m2)H(r,t)=magneticfieldstrength(amperes/m)D(r,t)=electricdisplacement(coulombs/m2)J(r,t)=electriccurrentdensity(amperes/m2)(r,t)=electricchargedensity(coulombs/m3),MaxwellEquations,TheContinuityLaw,Theelectriccurrentandchargedensitiesatrareconserved.ThedivergenceofcurrentJfromaninfinitesimalvolumesurroundingrisequaltothedecreasingofelectricchargedensitywithtimet.,连续性方程,ConstitutiveRelations,Thereareatotalof12scalarunknownsforthefourfieldvectorsE,H,BandD.ThetwoGausslawequationsinMaxwellEquationsarenotindependentones.Onlytwoofthemareindependent.Thusweneedsixmorescalarequations.Theyaretheconstitutiverelations.ForanisotropicmediumD=Ewhere=permittivity(=0infreespace)B=Hwhere=permeability(=0infreespace)ByisotropywemeanthatEisparalleltoDandHisparalleltoB,本构关系,（各向同性介质）,ConstitutiveRelationsforFreeSpace,D=0EB=0Hwhere0=(1/36)10-98.8510-12farad/meter0=410-7henry/meter,真空中的本构关系,WaveEquation,HelmholtzwaveequationThesimplestsolutiontakestheformThedispersionrelationprovidesanimportantconnectionbetweenthespatialfrequencykandthetemporalfrequency.k2=200,波动方程,TransverseEMWave,横波,VectorAnalysis,DivergencetheoremThevolumeintegralofthedivergenceofthevectorfieldDisequaltothetotaloutwardfluxDthroughthesurfaceSenclosingthevolume.CurltheoremStokestheoremThesurfaceintegralofthecurlofthevectorfieldHoveranopensurfaceSisequaltotheclosedlineintegralofthevectoralongthecontourenclosingtheopensurface.,矢量分析,BoundaryConditions,BoundaryConditionsforMovingBoundaries,边界条件,PolarizationVectorP,Adielectricmaterialcanbedescribedbyafree-spacepartandapartthatisduetothematerialalone:D=E=0E+PThepolarizationPsymbolizestheelectricdipolemomentperunitvolumeofthedielectricmaterial.,极化矢量,MagnetizationVectorM,Amagneticmaterialcanalsobedescribedbyafree-spacepartandapartcharacterizedbyamagnetizationvectorMsuchthat:B=H=0H+0MAmediumisdiamagnetic(反磁性)if0.,磁化矢量,OhmsLaw,Jc=EwhichrelatesconductioncurrentJctotheelectricfieldEbytheconductivity.J=(+j)E(includedisplacementcurrent),欧姆定律,复数介电常数,当介质中存在有传导电流（有耗介质）时，通常用电导率（张量）来描述。全电流包含传导电流Jc和位移电流Jd在谐变情况下可以写成式中复介电张量相当于把传导电流等效为位移电流时的介电常数,Polarization(极化),ThepolarizationofawaveisdefinedbythetimevariationofthetipoftheelectricfieldvectorEatafixedpointinspace.whereh,v,andthedirectionofpropagationaremutuallyperpendicularandthusformanorthogonalsystem.WeassumetheamplitudesAhandAvarebothpositive.,LinearPolarization,v-h=2mv-h=(2m+1),Eh,o,Ay,Ax,o,Ay,Ax,Ev,Eh,Ev,CircularPolarization,v-h=/2v-h=-/2RighthandLefthand,Eh,o,Ax=Ay,Ev,Eh,o,Ax=Ay,Ev,EllipticalPolarization,v-h=/2v-h=-/2generalcaseRighthandLefthand,Eh,o,Ev,Eh,o,Ev,Eh,o,Ev,PolarizationVariations,LetA=Av/Ahand=v-h,A,0.5,1,2,LC传输线上的波动方程,耦合的LC振荡器,基本关系,电压满足的波动方程,电流满足的波动方程,电磁波vs机械波,电压vs电流,阻抗,电抗,阻抗,阻抗匹配,传播速度,讨论：信号在平行双线上的传播速度,平行双线,感应系数的计算,感应系数的计算,电容的计算,电容的计算,平行双线上的阻抗与波速,光速,能量,功率,多普勒频移,波源移动,观测者移动,波源和观测者同时移动,运动方向不平行,介质运动,电磁波,相对论意义下的多普勒频移,相对论意义下的多普勒频移,膨胀的宇宙,膨胀的宇宙,冲击波,突破音障,马赫锥,色散（Dispersion）Thedependenceofwavevelocityonfrequencyorwavelength.Dielectricdispersion,thedependenceofthepermittivityofadielectricmaterialonthefrequencyofanappliedelectricfield.,脉冲传播过程中色散的影响,群速度（GroupVelocity）,波包,波包的传播,波包的传播,群速度,已知电磁波在等离子体中的色散关系为2(k)=p2+c2k2其中p2=Ne2/(0m)某一个脉冲星向空间发出短而窄的电磁脉冲，测得其中两个脉冲的频率分别为：1=2563MHz,2=3833MHz假定星际电离氢气体的电子密度N=105m-3，引起这种现象的原因是该气体的色散，问：(a)哪个频率的脉冲先到？(b)如果接收到两种脉冲的时间间隔是0.367s，估计脉冲星到地球的距离。,研习问题：估计脉冲星到地球的距离,电介质,电容器,LC传输线,色散关系,波速,课后作业,（上述脉冲星到地球距离问题）3.63.163.17,附1：AnisotropicMedia(各向异性介质),TheconstitutiverelationsforanisotropicmediaareusuallywrittenasD=Ewhere=permittivitytensorB=Hwhere=permeabilitytensorEisnolongerparalleltoD,andHisnolongerparalleltoB.electricallyanisotropic:tensorandscalermagneticallyanisotropic:scalerandtensorBothelectricallyandmagneticallyanisotropic:bothofandaretensors,群传播与相传播方向的夹角(P8687),基波前,子波前,O,M,N,C,M,N,波包nr,np,A,B,2,Crystals,Crystalsaredescribedingeneralbysymmetricpermittivitytensorswhichcanbetransformedintoadiagonalmatrix.Thethreecoordinateaxesarereferredtoastheprincipalaxesofthecrystal.x=y=z-isotropicUniaxialcrystal:zistheopticalaxisxyz-biaxialcrystal,BianisotropicMedia,Isotropicoranisotropicmediabecomepolarizedwhenplacedinanelectricfieldandbecomemagnetizedwhenplacedinamagneticfield.Abianisotropicmediumprovidesthecross-couplingbetweentheelectricandmagneticfields:D=E+HwhereandaretensorsB=E+HwhereandaretensorsWhenplacedinanelectricoramagneticfield,abianisotropicmediumbecomesbothpolarizedandmagnetized.,Almostanymediumbecomesbianisotropicwhenitisinmotion.Thebianisotropicdescriptionofmaterialhasfundamentalimportancefromthepointofviewofrelativity.Theconstitutiverelationsareform-invariantwhentheyarewritteninbianisotropicform.(Theprincipleofrelativitypostulatesthatallphysicallawsofnaturemustbecharacterizedbymathematicalequationsthatareform-invariantfromoneobservertotheother.),BiisotropicMedia,Thegyratorelement(微波回转元件)possessesconstitutiverelationsoftheformD=E+HB=E+Hwhere,andarescalersand2/isnearlyequalto1.Chiralmedia(手征介质)havethefollowingconstitutiverelations:whereisthechiralparameter.,附2：宏观介质类型,按介质的宏观电磁特性划分，传播信道大致可分为7种类型1均匀各向同性无耗介质介质的电磁参数、为实常数，电磁波以恒速沿直线传播；由点源辐射的能量随距离r沿球面扩散，则观测点在t时刻的瞬时电场为即场的幅度反比于r，而相位延迟正比于r。,2均匀有耗介质介质的、为复常数，传播常数，沿波矢量方向r处的瞬时电场为即仍然以恒速v=/沿直线传播，但由于损耗而产生幅度沿路径的指数衰减。损耗一般源于介质分子（例如对流层中的氧气与水汽分子及电离层中的带电粒子）对电子运动能量的阻尼吸收，并消耗于焦耳热和再辐射。,3均匀色散介质介质效应表现为在电磁场作用下的介质极化和磁化，当场量频率超过一定数值时，由于带电粒子的质量有限而可能使效应建立的速度跟不上场的变化，因而介质电磁参数、与频率有关，传播常数与不为线性关系，则介质称为时间色散的。当电磁场在介质中的波长很短，即介质的传播常数k很大时，极化和磁化效应同外加电磁场不能视为局域对应，还与附近空间的场量有关，则介质称为空间色散的,4均匀各向异性介质从介质中的一点沿不同方向所测的介质特性不同，称为各向异性。各向异性介质有其特征方