电动力学第四章封闭空间(金属谐振腔)中的电磁波

第四讲在封闭空间中电磁波

——金属（理想导体）谐振腔

S11回波损耗，即有多少能量被反射回源端（Port1），这个值越小越好，一般S11< 0.1，即－20dB；S21插入损耗，也就是有多少能量被传输到目的端（Port2）了，这个值越大越好，理想值是1。

Boundary Conditions at the interface between ideal conductor, silver coatings （media 1）and dielectric media（media 2）, air in the cavity.

无源边界条件

Boundary conditions on the source-free surface

Conclusions:

()()

(

)()

212121210,,0

f

f n E E n D D n H H n B B σα⨯-=⋅-=⨯-=⋅-=r r r

r r r r r r r r r r 有源的边界条件

证明：两平行无穷大理想导体平板之间可以传播一种偏振的横电磁模（TEM Mode ）

TEM Wave: 0 and 0 over the space TE Wave: 0 and 0 over the space TM Wave: 0 and 0 over the space

z z z z z z E H E H E H ===≠≠=

√ TEM W ave 1: E z = 0, E x = 0, E y ≠ 0; H z = 0, H x ≠ 0, H y = 0 × TEM W ave 2: E z = 0, E x ≠ 0, E y = 0; H z = 0

Rectangular Metallic Cavity Resonators （矩形金属谐振腔）

2

()A A A A ∇⋅∇⨯=∇⨯∇⨯=∇∇⋅-∇r r r r

202

22

222222222,000

()001100j e E E H E j t t t E E E E E E E j t t t

E

E E j E E E t t t t

E E t

ρσρεμμσμρε

μμμεσσεμρμεμεερεμ====∂∂∂---∂∂∂∇-∇∂∂∂∂∇--=∇+∇-=∂∂∂⎡⎤∂∂∂∇⨯∇⨯=-∇⨯=-++⎢⎥∂∂∂⎣⎦=∇⨯∇⨯=∇∇⋅-∇=−−−−→∇⋅==−−−→∂∂∇-=⋅=∂∇r r

r r r r r r r r r r r r r r r r r r r r 2

2

22

0i t k E k E ωεμω-=−−∇+=−−→r r

00

22

222

22()

2222

2222

22000000

x x y i z t y z x x y y z z x x E e E e E e E y y k z e z k k E E E k E t

E e E e E e E E k E E k E E k E E k E ωωεμεμωεμ-=++==∂∇-=∇+=∂=++⇓⎧∇+=⎪∇+=−−−−−−−−−−−−−→∇+=⎨⎪∇+−=⎩

→r r r r r

r r r r r r r r r 简谐解）（腔内介质决定的分解成三个分量的标量方程

——矢量方程

现在要求解：

The resonant frequency

For a given cavity, resonance occurs only at certain frequencies. The particular frequency is called resonant frequency, and the corresponding wavelength is called the resonant wavelength.

The resonant frequency is the same for TM or TE modes (Cavity TM Mode to z, Cavity TE Mode to z), except that

the lowest-order TM is TM110 and the lowest-order in TE

is TE101.

few low-order modes in the cavity

1i

x

y z ωμ ⎪∂∂∂ ⎪ ⎪∂∂∂⎪⎝