吳雄斌—無線電波傳播RadioWavePropagation無線電波傳播其次講電磁波介質提要電磁理論概要LC傳輸線上的波動方程例：電信號傳播速度Doppler頻移色散群速度電介質介電常數的微觀說明附：各向異性介質；常用介質類型Establishedin1873byJamesClerkMaxwellGeneralizedAmperecircuitlawFaraday’smagneticinductionlawGauss’lawforelectricfieldsGauss’lawformagneticfieldsE(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)MaxwellEquationsTheContinuityLawTheelectriccurrentandchargedensitiesatrareconserved.ThedivergenceofcurrentJfromaninfinitesimalvolumesurroundingrisequaltothedecreasingofelectricchargedensitywithtimet.連續性方程ConstitutiveRelationsThereareatotalof12scalarunknownsforthefourfieldvectorsE,H,BandD.ThetwoGauss’lawequationsinMaxwellEquationsarenotindependentones.Onlytwoofthemareindependent.Thusweneedsixmorescalarequations.Theyaretheconstitutiverelations.ForanisotropicmediumD=Ewhere=permittivity(=0

infreespace)B=Hwhere=permeability(=0

infreespace)ByisotropywemeanthatEisparalleltoDandHisparalleltoB本構關系（各向同性介質）ConstitutiveRelationsforFreeSpaceD=0EB=0Hwhere0

=

(1/36)10-98.8510-12farad/meter0=410-7henry/meter真空中的本構關系WaveEquationHelmholtzwaveequationThesimplestsolutiontakestheformThedispersionrelationprovidesanimportantconnectionbetweenthespatialfrequencykandthetemporalfrequency.k2=200波動方程TransverseEMWave橫波VectorAnalysisDivergencetheorem ThevolumeintegralofthedivergenceofthevectorfieldDisequaltothetotaloutwardfluxDthroughthesurfaceSenclosingthevolume.CurltheoremStokestheorem ThesurfaceintegralofthecurlofthevectorfieldHoveranopensurfaceSisequaltotheclosedlineintegralofthevectoralongthecontourenclosingtheopensurface.矢量分析BoundaryConditionsBoundaryConditionsforMovingBoundaries

邊界條件PolarizationVectorPAdielectricmaterialcanbedescribedbyafree-spacepartandapartthatisduetothematerialalone:D=E=0E+PThepolarizationPsymbolizestheelectricdipolemomentperunitvolumeofthedielectricmaterial.極化矢量MagnetizationVectorMAmagneticmaterialcanalsobedescribedbyafree-spacepartandapartcharacterizedbyamagnetizationvectorMsuchthat:

B=H=0H+0MAmediumisdiamagnetic(反磁性)if<0

andparamagnetic(順磁性)if>0.磁化矢量Ohm’sLawJc=E whichrelatesconductioncurrentJctotheelectricfieldEbytheconductivity.J=(+j)E

(includedisplacementcurrent)歐姆定律復數介電常數當介質中存在有傳導電流（有耗介質）時，通常用電導率（張量）來描述。全電流包含傳導電流Jc和位移電流Jd 在諧變狀況下可以寫成 式中復介電張量相當于把傳導電流等效為位移電流時的介電常數Polarization(極化)ThepolarizationofawaveisdefinedbythetimevariationofthetipoftheelectricfieldvectorEatafixedpointinspace. whereh,v,andthedirectionofpropagationaremutuallyperpendicularandthusformanorthogonalsystem.WeassumetheamplitudesAhandAvarebothpositive.LinearPolarizationv-h=2mv-h=(2m+1)EhoAyAxoAyAxEvEhEvCircularPolarizationv-h=/2v-h=-/2RighthandLefthandEhoAx=AyEvEhoAx=AyEvEllipticalPolarization v-h=/2v-h=-/2generalcase RighthandLefthandEhoEvEhoEvEhoEvPolarizationVariationsLetA=Av/Ahand=v-h

A0.512LC傳輸線上的波動方程耦合的LC振蕩器基本關系電壓滿足的波動方程電流滿足的波動方程電磁波vs機械波電壓vs電流阻抗電抗阻抗阻抗匹配傳播速度探討：信號在平行雙線上的傳播速度平行雙線感應系數的計算感應系數的計算電容的計算電容的計算平行雙線上的阻抗與波速光速能量功率多普勒頻移波源移動觀測者移動波源和觀測者同時移動運動方向不平行介質運動電磁波相對論意義下的多普勒頻移相對論意義下的多普勒頻移膨脹的宇宙膨脹的宇宙沖擊波突破音障馬赫錐色散（Dispersion）

Thedependenceofwavevelocityonfrequencyorwavelength.

Dielectricdispersion,thedependenceofthepermittivityofadielectricmaterialonthefrequencyofanappliedelectricfield.脈沖傳播過程中色散的影響

群速度（GroupVelocity）波包波包的傳播'波包的傳播群速度已知電磁波在等離子體中的色散關系為2(k)=p2+c2k2 其中p2=Ne2/(0m) 某一個脈沖星向空間發出短而窄的電磁脈沖，測得其中兩個脈沖的頻率分別為：1=2563MHz,2=3833MHz 假定星際電離氫氣體的電子密度N=105m-3，引起這種現象的緣由是該氣體的色散，問：(a)哪個頻率的脈沖先到？(b)假如接收到兩種脈沖的時間間隔是0.367s，估計脈沖星到地球的距離。研習問題：估計脈沖星到地球的距離電介質電容器LC傳輸線色散關系波速課后作業（上述脈沖星到地球距離問題）

3.63.163.17附1：AnisotropicMedia(各向異性介質)TheconstitutiverelationsforanisotropicmediaareusuallywrittenasD=Ewhere=permittivitytensorB=

Hwhere=permeabilitytensorEisnolongerparalleltoD,andHisnolongerparalleltoB.electricallyanisotropic:tensorandscalermagneticallyanisotropic:scalerandtensorBothelectricallyandmagneticallyanisotropic:bothofandaretensors群傳播與相傳播方向的夾角(P86~87)基波前子波前OMNCM'N'波包nrnpAB2CrystalsCrystalsaredescribedingeneralbysymmetricpermittivitytensorswhichcanbetransformedintoadiagonalmatrix.Thethreecoordinateaxesarereferredtoastheprincipalaxesofthecrystal.x=y=z-isotropicUniaxialcrystal:zistheopticalaxisx

y

z-biaxialcrystalBianisotropicMediaIsotropicoranisotropicmediabecomepolarizedwhenplacedinanelectricfieldandbecomemagnetizedwhenplacedinamagneticfield.Abianisotropicmediumprovidesthecross-couplingbetweentheelectricandmagneticfields:D=E+

Hwhere

andaretensorsB=

E+

Hwhere

andaretensorsWhenplacedinanelectricoramagneticfield,abianisotropicmediumbecomesbothpolarizedandmagnetized.Almostanymediumbecomesbianisotropicwhenitisinmotion.Thebianisotropicdescriptionofmaterialhasfundamentalimportancefromthepointofviewofrelativity.Theconstitutiverelationsareform-invariantwhentheyarewritteninbianisotropicform.(Theprincipleofrelativitypostulatesthatallphysicallawsofnaturemustbecharacterizedbymathematicalequationsthatareform-invariantfromoneobservertotheother.)BiisotropicMediaThegyratorelement(微波回轉元件)possessesconstitutiverelationsoftheform D=E+HB=E+Hwhere,and

arescalers and2/isnearlyequalto1.Chiralmedia(手征介質)havethefollowingconstitutiverelations: where

isthechiralparameter.附2：宏觀介質類型按介質的宏觀電磁特性劃分，傳播信道大致可分為7種類型1勻整各向同性無耗介質介質的電磁參數、為實常數，電磁波以恒速沿直線傳播；由點源輻射的能量隨距離r沿球面擴散，則觀測點在t時刻的瞬時電場為 即場的幅度反比于r，而相位延遲正比于r。2勻整有耗介質介質的、為復常數，傳播常數，沿波矢量方向r處的瞬時電場為 即照舊以恒速v=/沿直線傳播，但由于損耗而產生幅度沿路徑的指數衰減。損耗一般源于介質分子（例如對流層中的氧氣與水汽分子及電離層中的帶電粒子）對電子運動能量的阻尼吸取，并消耗于焦耳熱和再輻射。3勻整色散介質介質效應表現為在電磁場作用下的介質極化和磁化，當場量頻率超過確定數值時，由于帶電粒子的質量有限而可能使效應建立的速度跟不上場的變更，因而介質電磁參數、與頻率有關，傳播常數與ω不為線性關系，則介質稱為時間色散的。當電磁場在介