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Solved Problems-7

Problem-7
In an air-filled rectangular waveguide, the cut-off frequency of a TE10 mode is 5 GHz, whereas that of TE01 mode is 2 GHz. Calculate
  1. The dimension of the guide
  2. The cut-off frequencies of the next three higher TE modes
  3. The cut-off frequency for TE11 mode if the guide is filled with a lossless material having εr = 2.25 and μr = 1
Solution
Here, Description: 65898.png

(a) Since the cut-off frequency is lowest in TE01 mode, this is the dominant mode. This implies that for the rectangular waveguide, b > a.
 
Now, for TE01 mode, the cut-off frequency is given as,
 
 
Description: 65910.png
 
Also, for TE10 mode, the cut off frequency is given as,
 
Description: 65920.png
 
So, the dimension of the rectangular waveguide is 3 cm × 7.5 cm.

(b) The cut-off frequency for TEmn mode is given as,
 
Description: 65927.png
 
Description: 65935.png
 
Next higher order modes will be TE02, TE11, TE03.
 
The corresponding cut-off frequencies are given as follows.
 
Description: 65945.png
 
(c) If the guide is filled with a lossless material having εr = 2.25 and μr = 1, the cut-off frequency for TE11 mode is,
 
Description: 65952.png
 
Description: 65959.png
 





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