GATE EC 2018 Set 1 — Question 58
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Electromagnetics → Waveguides & Optical Fibers → Cutoff Frequency & Guide Wavelength
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Question
The cutoff frequency of mode of an air filled rectangular waveguide having inner dimensions is twice that of the dominant mode. When the waveguide is operated at a frequency which is 25% higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be 4 cm. The value of (in cm, correct to two decimal places) is _______.
Correct answer
0.7 to 0.8
Solution
The cutoff frequency for a mode in a rectangular waveguide is given by:
For the dominant mode: .
For the mode: .
Given .The operating frequency is .
The guide wavelength is related to the free-space wavelength by:
Given :
.
Since , we have .
For the dominant mode: .
For the mode: .
Given .The operating frequency is .
The guide wavelength is related to the free-space wavelength by:
Given :
.
Since , we have .
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