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Solved Problems-9

Problem-9
The cross section of a rectangular waveguide is 20 cm × 5 cm. If it is filled with air, find the first six lowest order modes which will propagate through the waveguide and their cut-off frequencies.
Solution
Here, a = 20 cm, b = 5 cm.
 
The cut-off frequency is given as,
 
Description: 43866.png
 
We know that for TEmnp modes, any two indices have to be nonzero; whereas for TMmnp modes, all the indices have to be nonzero. Since a > b, the lowest-order mode will be TE10. Next higher order modes will be TE20TE30TE40TE01TE11 and TM11.
 
The corresponding cut-off frequencies are given as follows.
 
Description: 43858.png
 
Hence, the first six lowest-order modes with their cut-off frequencies are given in this table.
 
Mode Resonant Frequency (GHz)
TE10 0.75
TE20 1.5
TE30 2.25
TE40 3
TE01 3
TE11 and TM11 3.092





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