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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 Description: 43126.png, find the frequency for minimum attenuation.
  3. For a square waveguide, show that attenuation Description: 43119.png is minimum for TE10 mode when Description: 43111.png.
Solution
(a) For a TE10 mode rectangular wave, the attenuation constant is given as,
Description: 43101.png
 
Substituting the value of the surface resistance Description: 43090.png, we have,
 
Description: 43083.png
 
where Description: 43074.png is constant.
 
For the attenuation constant to be minimum,
 
Description: 43066.png
Description: 43058.png
 
 
Solving this equation and taking only the positive root, we get,
 
Description: 43048.png
 
Description: 43040.png
 
This is the frequency corresponding to the minimum attenuation due to conductor loss.

(b) If a = 3b, we have,
 
Description: 43031.png
Description: 43024.png
 
(c) For square waveguide, a = b, so that we get,
Description: 43015.png
Description: 43006.png
 





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