电磁场与电磁波第17讲时谐场概要

1、1,Field and Wave Electromagnetic 电磁场与电磁波,第17讲,2,1. Faradays Law of Electromagnetic Induction,Review,3,2. Maxwells Equations,3. Electromagnetic Boundary Conditions,4,4. Potential Functions,5. Wave Equations and Their Solutions,5,Maxwells equations and all the equations derived from them so far in thi

2、s chapter hold for electromagnetic quantities with an arbitrary time-dependence(时间任意相关). The actual type of time functions that the field quantities assume depends on(取决于) the source(源) functions and J. In engineering, one of the most important cases of time-varying electromagnetic fields is the tim

3、e-harmonic (sinusoidal) field(时谐场、正弦场). In this type of field ,the excitation source varies sinusoidally in time with a single frequency(单一频率). In a linear system(线性系统), a sinusoidally varying source generates fields that also vary sinusoidally in time at all points in the system(正弦变化的源产生正弦变化的场).,1)

4、 what is Time-Harmonic Fields,3. Time-Harmonic Fields,6,2) 讨论时谐场（正弦信号）的原因,When fields are examined in this manner,there is no loss in generality as (a) They are easy to generate (b) any time-varying periodic function can be represented by a Fourier series in terms of sinusoidal functions (c) the pri

5、nciple of superposition can be applied under linear conditions. In other words, we can obtain the complete response of time varying periodic fields by using linear combinations of monochromatic responses,（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

6、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,7,3.1 电路中的相量表达式,In circuit theory, you have already used the phasor notation(相量) to represent voltages and currents varying sinusoidally in time,(1) Instantaneous (time-dependent) expression of a sinusoidal scalar quantity(瞬时值）三角函数表达式,3 Parameters: angular freque

7、ncy: amplitude: Im phase：,(2) 复数的表示,8,(3) 正弦表达式和相量表达式的对应关系,9,EXAMPLE 7-6 P337-338,10,3.2 Time-harmonic Electromagnetics,Field vectors that vary with space coordinates and are sinusoidal functions of time can similarly be represented by vector phasors(矢量相量) that depend on space coordinates but not on

8、 time. As an example, we can write a time-harmonic E field referring to cost as,where E(x, y, z) is a vector phasor (矢量相量) that contains information on direction(方向), magnitude(振幅), and phase(相位). Phasors are, in general, complex quantities. we see that, if E(x, y, z, t) is to be represented by the

9、vector phasor E(x, y, z) , then E(x, y, z, t)/t and E(x, y, z, t)dt would be represented by, respectively, vector phasors jE(x, y, z) and E(x, y, z)/j. Higher-order differentiations and integrations with respect to would be represented, respectively, by multiplications and divisions of the phasor E(

10、x, y, z) by higher powers of j.,11,12,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,13,瞬时值由相量值代替 时间求导由j代替,We now write time-harmonic Maxwells equations (时谐麦克斯韦方程组) in terms of vector field phasors (E, H) and source phasors (, J) in a simple (linear, is

11、otropic, and homogenous) medium as follows.,14,The time-harmonic wave equations(时谐波动方程) for E and H become, respectively,The time-harmonic wave equations for scalar potential V and vector potential A become, respectively,Let,is called the wavenumber.,15,Then,Consider the time delay factor , for a si

12、nusoidal function it leads to a phase delay of .,We obtain,16,The complex Lorentz condition is,The complex electric and magnetic fields can be expressed in terms of the complex potentials as,17,3.3 source-free(无源) fields in simple media,In a simple, nonconducting(非导电) source-free medium characterize

13、d by =0, J=0, =0, the time-harmonic Maxwells equations become,18,which are homogeneous vector Helmholtzs equations(齐次矢量亥姆霍兹方程). and wave equations for A and V become,The time-harmonic wave equations for E and H become, respectively,Let,is called the wavenumber.,19,If the simple medium is conducting

14、(0)(导电介质), a current J=E will flow, and the equation should be changed to,with,The other three equations in Maxwells equation are unchanged. Hence, all the previous equations for nonconducting(非导电) media will apply to conducting media if is replaced by the complex permittivity c . Meanwhile, the rea

15、l(实数) wavenumber k in the helmholtzs equations should be changed to a complex(复数) wavenumber:,20,The ratio / is called a loss tangent(损耗正切) because it is a measure of the power loss in the medium:,The quantity c may be called the loss angle(损耗角). A medium is said to be a good conductor(良导体) if , and

16、 a good insulator(良绝缘体) if . Thus, a material may be a good conductor at low frequencies(低频) but may have the properties of a lossy dielectric at very high frequencies(高频).,21,1. Faradays Law of Electromagnetic Induction,Review,22,2. Maxwells Equations,3. Electromagnetic Boundary Conditions,23,4. Po

17、tential Functions,5. Wave Equations and Their Solutions,24,6. Time-Harmonic Fields,25,26,P.7-7P349,27,P.7-13 P351,28,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,29,P.7-25 P352,30,31,P.7-30 P353,32,The electric field intensity in a source-free dielectric( ) region is given as (V/m),where angular frequency ，all ar

18、e constants. Find:,Example.,(1) The phasor representation of electric field intensity,(V/m),(2) The phasor representation of magnetic field intensity,33,(4) the average power density,(5) the instantaneous power density,or Poynting vector,34,Let us consider a source-free dielectric medium having permittivity magn