电磁场与电磁波第17讲时谐场

v dl
(V)
'
d dt
S
v B
v dS
d dt
(V)
2
2. Maxwell’s Equations
The integral form
The differential form
ÑC
v E
v dl v
v
S
v B
t v
v dS
v D
d
dt v
ÑC H dl S (J t ) dS
vv
Ñ S D dS Q
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 time-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).
v E
v B
v H
v J
t v D
t
v
D
vv
Ñ S B dS 0
v B 0
Significance
Faraday’s law(电磁感应定律)
Ampere’s circuital law(全电流定律)
Gauss’s law(高斯定理)
No isolated magnetic charge(磁通连续 性原理)
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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 principle 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
amplitude: Im
phase：
(2) 复数的表示
代数表达式：A x jy;
Field and Wave Electromagnetic 电磁场与电磁波
第17讲
Review
1. Faraday’s Law of Electromagnetic Induction
d (V)
dt
ÑC (uv
vv B) dl
(V)
蜒C Ev
'
v dl
t
S
v B
v dS
C
(uv
v B)
(1) Instantaneous (time-dependent) expression of a sinusoidal scalar
quantity(瞬时值）三角函数表达式 交变电动势： (t) m cos(t )
3 Parameters:
angular frequency:
交变电压：u(t) Um cos(t u ) 交变电流：i(t) Im cos(t i )
3. Electromagnetic Boundary Conditions
vv aˆn2 (E1 E2 ) 0
vv aˆn2 (B1 B2 ) 0
vv
vv v
aˆn2 (D1 D2 ) S aˆn2 (H1 H2 ) JS
3
4. Potential Functions
v
v 2E
（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
6
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
2E t 2ຫໍສະໝຸດ vvB A
uv
J 1
t
v E
v A
t
2 V
v H
v A
v 2H t 2
V t
v J
v 2 A
v 2A t 2
v
J
2V 2V t2
5. Wave Equations and Their Solutions
V (R,t) 1
4π
R R'
R R'
R',t
u
V
R R'
dV
A(R,t)
J R',t
u
4π V
R R'
dV
4
3. Time-Harmonic Fields
1) what is Time-Harmonic Fields
Maxwell’s equations and all the equations derived from them so far in this chapter hold for electromagnetic quantities with an arbitrary timedependence(时间任意相关). The actual type of time functions that the