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I'm trying to calculate the cutoff frequency of an electrical conduit of 2 cm diameter. (Material of the conduit is not given)

The solution given is

Lowest mode TE11 mode \$\gamma = \sqrt{(\frac{1.84}{a})^2-\omega^2\mu \epsilon} = 0\$ at cutoff gives \$f_c = 87.8\text{ Ghz}\$

I tried using \$a = 0.02, \mu\text{ (free space)} = 4\pi \times 10^{-7}, \epsilon \text{ (free space)} = 8.85 \times 10^{-12}\$ to find \$f_c\$, but the value I got was 4.39 GHz, half of the given value.

What am I doing wrong here?

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1 Answer 1

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Umm. You are using a = 0.02 (diameter) instead of 0.01 (radius). Also fc = 8.78GHz, not 87.8.

\$f_c = \frac {1.8412 \cdot c}{2\pi a}\$

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