矩形波导中的TE10波及例题讲解(双语)

TE01 TE20
TM11

0

a

TE10 2a

The cutoff wavelength of the TE10 wave is 2a, and that of TE20 wave is a.
The left figure gives the distribution of c the cutoff wavelength 截止波长 for a
3. Characterization of Electromagnetic Waves in Rectangular Waveguides

Since kc2



k

2



k

2 z

,

or

k

2 z

k 2 kc2, if

k

kc , then

kz

0

. This means

that the propagation of the wave is cut off, and kc is called the cutoff

the

From k 2π , we can find the cutoff propagation constant kc

cutoff as

wavelength c

corresponding

c



2π kc



2


Baidu Nhomakorabea
m a

2





n b

2

The cutoff frequency or the cutoff wavelength is related to the dimensions of the waveguide a, b and the integers m, n . For a given size of waveguide, different modes have different cutoff frequencies and cutoff wavelengths. A mode of higher order has a higher cutoff frequency 截止频率 , or a shorter cutoff wavelength 截止波长 .

TE10 wave is usually used, and it is called the dominant mode 主模 of the rectangular waveguide 矩形波导 .

In practice, we usually takea 2b to realize the transmission of

wave propagating along the positive z-direction.
If f fc , kz is an imaginary number, then ejkzz

kz
e



fc f

2 1

which states that this time-varying electromagnetic field is not

transmitted, but is an evanescent field.

For a given mode and in a given size waveguidef,c is the lowest frequency of the mode to be transmitted. In view of this, the waveguide acts like a high-pass filter.
waveguide with a 2b .

If c , then the corresponding mode will be cut off. From the figure we see that if 2a , all modes will be cut off.

TE01 TE20
TM11

propagation constant.

kc2



k

2 x



k

2 y

kc2





mπ a

2





nπ b

2

Fromk 2πf , we can find the cutoff frequency fc corresponding to the cutoff propagation constant kc , as given by

0

a

TE10 2a

Cutoff area

Ifa 2a , then only TE10 wave
exists, while all other modes are cut off . If a , then the other modes will be supported.
Hence, if the operating wavelength c 工作波长 satisfies the inequality
a 2a

Then the transmission of a single mode is realized, and the TE10 wave is the single mode to be transmitted.
The transmission of a single mode 单模传输 wave is necessary in practice since it is helpful for coupling energy into or out of the waveguide.

the single mode TE10 in the frequency band 频a带 2a

.

To support the TE10 mode the sizes of the rectangular waveguide

should satisfy the following inequality

2



a





b



2

The lower limit for the narrow side depends on the transmitted

fc



kc 2π



2

1



m a

2





n b

2

The propagation constant kz can be expressed as

kz k

1

fc f

2



k











1 jk

fc f

2

,

fc f

2

1,

f fc f fc

if f fc ,k z is a real number, and the factor e jkzz stands for the