# Solved Problems-14

Problem-14
1. Show that for a rectangular waveguide, the dominant mode exhibits a minimum attenuation due to conductor loss at a certain frequency. Find that frequency in terms of the cut-off frequency of the mode.
2. If , find the frequency for minimum attenuation.
3. For a square waveguide, show that attenuation  is minimum for TE10 mode when .
Solution
(a) For a TE10 mode rectangular wave, the attenuation constant is given as,

Substituting the value of the surface resistance , we have,

where  is constant.

For the attenuation constant to be minimum,

Solving this equation and taking only the positive root, we get,

This is the frequency corresponding to the minimum attenuation due to conductor loss.

(b) If a = 3b, we have,

(c) For square waveguide, a = b, so that we get,