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GATE 2017 EC (EC2) – Question 64

Electromagnetics · Waveguides and Optical Fibers · 2 marks · Multiple choice

Air-filled rectangular waveguides with dimensions a=2.29 cm and b=1.02 cm are intended for radar. They must operate only in the dominant TE10 mode, at least 25% above its cutoff and no higher than 95% of the next higher cutoff. The allowable frequency f is

  1. $8.19\ \mathrm{GHz}\le f\le13.1\ \mathrm{GHz}$
  2. $8.19\ \mathrm{GHz}\le f\le12.45\ \mathrm{GHz}$
  3. $6.55\ \mathrm{GHz}\le f\le13.1\ \mathrm{GHz}$
  4. $1.64\ \mathrm{GHz}\le f\le10.24\ \mathrm{GHz}$

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Correct answer: (B) $8.19\ \mathrm{GHz}\le f\le12.45\ \mathrm{GHz}$

Explanation

For the dominant mode, $f_{c10}=c/(2a)=3\times10^8/[2(0.0229)]=6.5502$ GHz. Its 25% margin requires $f\ge1.25f_{c10}=8.1878$ GHz.

The next candidates are TE20 at $c/a=13.1004$ GHz and TE01 at $c/(2b)=14.7059$ GHz. TE20 is lower, so the upper operating limit is $0.95(13.1004)=12.4454$ GHz.

The rounded range is **8.19–12.45 GHz, B**.

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