# 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
We understand that the dominant mode in a circular waveguide is
For
Since both will have the same cut-off frequency, we get,
or,
The area of the circular waveguide is,
For standard rectangular waveguide

*r*be radius of the circular waveguide and*a*be the larger dimension of the rectangular waveguide.*TE*_{11}mode. For this mode, the cut-off frequency is given as,*TE*_{10}mode rectangular waveguide, the cut-off frequency is given as,*a : b*= 2 : 1, so that the area of the rectangular waveguide is, .