2
a
b
2
The lower limit for the narrow side depends on the transmitted
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
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.
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
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.
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
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
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
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
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
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
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
the
From k 2π , we can find the cutoff propagation constant kc
cutoff as
wavelength ccorrespondi来自gc2π kc
2
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 .