电磁场与电磁波第17讲时谐场课件

FieldandWaveElectromagnetic电磁场与电磁波第17讲11.Faraday’sLawofElectromagneticInductionReview22.Maxwell’sEquations3.ElectromagneticBoundaryConditionsTheintegralformThedifferentialform

SignificanceFaraday’slaw(电磁感应定律)Ampere’scircuitallaw(全电流定律)Gauss’slaw(高斯定理)Noisolatedmagneticcharge(磁通连续性原理)34.PotentialFunctions5.WaveEquationsandTheirSolutions4Maxwell’sequationsandalltheequationsderivedfromthemsofarinthischapterholdforelectromagneticquantitieswithanarbitrarytime-dependence(时间任意相关).Theactualtypeoftimefunctionsthatthefieldquantitiesassumedependson(取决于)thesource(源)functions

andJ.Inengineering,oneofthe

mostimportant

casesoftime-varyingelectromagneticfieldsisthe

time-harmonic(sinusoidal)field(时谐场、正弦场).Inthistypeoffield,the

excitation

sourcevaries

sinusoidally

intimewith

a

singlefrequency(单一频率).In

alinearsystem(线性系统),asinusoidallyvarying

source

generates

fields

thatalsovarysinusoidallyintimeatallpointsinthesystem(正弦变化的源产生正弦变化的场).1)whatisTime-HarmonicFields3.Time-HarmonicFields52)讨论时谐场（正弦信号）的原因Whenfieldsareexaminedinthismanner,thereisnolossingeneralityas(a)Theyareeasytogenerate(b)anytime-varyingperiodicfunctioncanberepresentedbyaFourierseriesintermsofsinusoidalfunctions(c)theprincipleofsuperpositioncanbeappliedunderlinearconditions.Inotherwords,wecanobtainthecompleteresponseoftimevaryingperiodicfieldsbyusinglinearcombinationsofmonochromaticresponses（a）正弦信号容易产生，50Hz交流电，通信的载波都是正弦信号（b）从信号分析的角度来看，正弦信号是一种简单基本的信号。正弦信号进行各种运算（加减微分积分后仍为同频率正弦信号）（c）傅立叶分析：任意周期信号分解为不同频率的正弦之和（d）线性系统的叠加原理63.1

电路中的相量表达式Incircuittheory,youhavealreadyusedthephasornotation(相量)torepresentvoltagesandcurrentsvaryingsinusoidally

intime(1)Instantaneous(time-dependent)expressionofasinusoidalscalarquantity(瞬时值）三角函数表达式3Parameters:

angularfrequency:

amplitude:Im

phase：(2)

复数的表示xjyP（x,y）复平面上一点P7(3)正弦表达式和相量表达式的对应关系相量的模正弦量的幅值初位相复角频率是已知？频率相量乘以ejt，再取实部8EXAMPLE7-6P337-33893.2

Time-harmonicElectromagneticsFieldvectorsthatvarywithspacecoordinatesandaresinusoidalfunctionsoftimecansimilarlyberepresentedbyvectorphasors(矢量相量)thatdependonspacecoordinatesbutnotontime.Asanexample,wecanwriteatime-harmonicE

fieldreferringtocostaswhereE(x,y,z)isavectorphasor

(矢量相量)thatcontainsinformationondirection(方向),magnitude(振幅),andphase(相位).Phasorsare,ingeneral,complexquantities.weseethat,ifE(x,y,z,t)istoberepresentedbythevectorphasor

E(x,y,z),thenE(x,y,z,t)/tandE(x,y,z,t)dtwouldberepresentedby,respectively,vectorphasors

jE(x,y,z)

andE(x,y,z)/j.Higher-orderdifferentiationsandintegrationswithrespecttowouldberepresented,respectively,bymultiplicationsanddivisionsofthephasor

E(x,y,z)byhigherpowersofj.1011已知正弦电磁场的场与源的频率相同，因此可用复矢量形式表示麦克斯韦方程。考虑到正弦时间函数的时间导数为或因此，麦克斯韦第一方程可表示为上式对于任何时刻均成立，实部符号可以消去，即12瞬时值由相量值代替时间求导由jω代替Wenowwritetime-harmonicMaxwell’sequations(时谐麦克斯韦方程组)intermsofvectorfieldphasors(E,H)andsourcephasors(,J)inasimple(linear,isotropic,andhomogenous)mediumasfollows.13Thetime-harmonicwaveequations(时谐波动方程)forEandHbecome,respectively,Thetime-harmonicwaveequationsforscalarpotentialVandvectorpotentialAbecome,respectively,Letiscalledthewavenumber.14Then

Considerthetimedelayfactor,forasinusoidalfunctionitleadstoaphasedelayof.

Weobtain15ThecomplexLorentzconditionis

Thecomplexelectricandmagneticfieldscanbeexpressedintermsofthecomplexpotentialsas

163.3

source-free(无源)fieldsinsimplemediaInasimple,nonconducting(非导电)source-freemediumcharacterizedby=0,J=0,=0,thetime-harmonicMaxwell’sequationsbecome

17whicharehomogeneousvectorHelmholtz’sequations(齐次矢量亥姆霍兹方程).andwaveequationsforAandV

becomeThetime-harmonicwaveequationsforEandHbecome,respectively,Letiscalledthewavenumber.18Ifthesimplemediumisconducting(0)(导电介质),acurrentJ=Ewillflow,andtheequationshouldbechangedtowithTheotherthreeequationsinMaxwell’sequationareunchanged.Hence,allthepreviousequationsfornonconducting(非导电)mediawillapplytoconductingmediaifisreplacedbythecomplexpermittivity

c.Meanwhile,thereal(实数)

wavenumber

kinthehelmholtz’sequationsshouldbechangedtoacomplex(复数)

wavenumber:19Theratio’’/’

iscalledalosstangent(损耗正切)becauseitisameasureofthepowerlossinthemedium:Thequantityc

maybecalledthelossangle(损耗角).Amediumissaidtobeagoodconductor(良导体)if>>,andagoodinsulator(良绝缘体)if<<.Thus,amaterialmaybeagoodconductoratlowfrequencies(低频)butmayhavethepropertiesofalossydielectricatveryhighfrequencies(高频).201.Faraday’sLawofElectromagneticInductionReview212.Maxwell’sEquations3.ElectromagneticBoundaryConditionsTheintegralformThedifferentialform

SignificanceFaraday’slaw(电磁感应定律)Ampere’scircuitallaw(全电流定律)Gauss’slaw(高斯定理)Noisolatedmagneticcharge(磁通连续性原理)224.PotentialFunctions5.WaveEquationsandTheirSolutions236.Time-HarmonicFields相量的模正弦量的幅值初位相复角频率是已知？频率相量乘以ejt，再取实部24dx25P.7-7P34926P.7-13P35127梯度运算符合以下规则：C为常数散度运算规则旋度运算规则28P.7-25P3522930P.7-30P35331Theelectricfieldintensityinasource-freedielectric()regionisgivenas(V/m),whereangularfrequency，allareconstants.Find:Example.(1)Thephasorrepresentationofelectricfieldintens