GATE EC 2007 Electromagnetics Solution Q 4

GATE EC 2007 Electromagnetics Solution Q 4

An air-filled rectangular waveguide has in inner dimensions of 3 cm × 2 cm. The wave impedance of the TE20 mode of propagation in the waveguide at a frequency of 30 GHz is_____. ( free space impedance η0 = 377Ω )

a) 308\;\Omega

b) 355\;\Omega

c) 400\;\Omega

d) 461\;\Omega

Ans-(c)

Explanation

As\;TE_{20'}\;\;\;\lambda_C=a=3\times10^{-2}m \therefore f_c=\frac C{\lambda_C}=\frac{3\times10^8}{3\times10^{-2}}=10^{10}Hz \eta_{TE}=\frac\eta{\sqrt{1-\left({\displaystyle\frac{f_c}f}\right)^2}}=\frac{377}{\sqrt{1-\left({\displaystyle\frac{10^{10}}{3\times10^{10}}}\right)^2}} \therefore \eta_{TE}=400\Omega

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