 GATE EC 1990 Electromagnetics Solution Q 3

# GATE EC 1990 Electromagnetics Solution Q 3

For a wave propagating in an air filled rectangular waveguide______.

a) Guided wavelength is never less than the free space wavelength.

b) Wave impedance is never less than the free space impedance.

c) Phase velocity is never less than the free space velocity.

d) TEM mode is possible if the dimensions of the waveguide are properly chosen.

Ans-(a) and (c)

Explanation

\lambda_g=\frac\lambda{\sqrt{1-\left({\displaystyle\frac{f_c}f}\right)^2}} \lambda_g>\lambda

So a is correct.

eta_{TE}=\frac{\eta_0}{1-e\sqrt{\left({\displaystyle\frac{f_c}f}\right)^2}} \eta_{TE}>\eta_0 \eta_{TM}=\eta_0\sqrt{1-\left(\frac{f_c}f\right)^2} \eta_{TM}<\eta_0

So b is not correct.

v_p=\frac c{\sqrt{1-\left({\displaystyle\frac{f_c}f}\right)^2}}

So phase velocity is greater than free space velocity. So c is correct. Become PRO At Electromagnetics Basics With Our 4 Ultimate Visual FREE E-Books On Coordinate Systems & Transformations

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