GATE EC 2008 Electromagnetics Solution Q 5

GATE EC 2008 Electromagnetics Solution Q 5

A rectangular waveguide of internal dimensions \left(a=4\;cm\;and\;b=3\;cm\right) is to be operated in TE11 mode. The minimum operating frequency is _.

a) 6.25 GHz

b) 6.0 GHz

c) 5.0 GHz

d) 3.75 GHz

Ans-(a)

Explanation

f_0=\frac C{2\pi}\sqrt{\left(\frac{m\pi}a\right)^2+\left(\frac{n\pi}b\right)^2} \begin{array}{l}For\;TE_{11}\;mode,\\f_0=\frac{3\times10^8}2\sqrt{\left(\frac1{0.04}\right)^2+\left(\frac1{0.03}\right)^2}\end{array} =\frac{3\times10^8}2\times\frac{0.05}{0.04\times0.03}=6.25\;GHz

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