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Solved Problems-15

Problem-15
Evaluate the ratio of the area of a circular waveguide to that of a rectangular one if both are to have the same cut-off frequency for dominant mode.
Solution
Let r be radius of the circular waveguide and a be the larger dimension of the rectangular waveguide.
 
We understand that the dominant mode in a circular waveguide is TE11 mode. For this mode, the cut-off frequency is given as,
 
Description: 42994.png
 
For TE10 mode rectangular waveguide, the cut-off frequency is given as,
 
Description: 42986.png
 
Since both will have the same cut-off frequency, we get,
 
or, Description: 42978.png
 
The area of the circular waveguide is, Description: 42968.png
 
For standard rectangular waveguide a : b = 2 : 1, so that the area of the rectangular waveguide is, Description: 42960.png.
 
Description: 42952.png
 





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