GATE 2014 EC (EC2) – Question 65
A rectangular waveguide has internal dimensions a × b, a > b. TE₁₁ cutoff is the arithmetic mean of TE₁₀ and TE₂₀ cutoffs. Given $a=\sqrt5$ cm, find b (cm).
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Correct answer: 1.9 to 2.1
Explanation
For a rectangular guide, $f_{c,mn}=(v/2)\sqrt{(m/a)^2+(n/b)^2}$. The mean of the TE₁₀ and TE₂₀ cutoffs is $3v/(4a)$. Equating TE₁₁ gives $1/a^2+1/b^2=9/(4a^2)$, so $b=2a/\sqrt5$. With $a=\sqrt5$ cm, **b = 2 cm**.