Question

Consider an air-filled rectanular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. At 10 GHz operating frequency, The value of the propagation constant (per meter) of the corresponding propagating mode is

• A. 158

Answer 1

The correct option is A 158
Operation frequency = 10 GHz

Cutoff frequency for $T{E}_{10},f_c=\frac{c}{2a}$

$f_c=\frac{3\times {10}^8}{2\times 2.286\times {10}^{-2}}$

= 6.57 GHz

Next mode $T{E}_{20}$ has $f_c$ = 13 GHz

10 GHz operates only in dominant mode.

$\gamma =\sqrt{{\left(\frac{m\pi }{a}\right)}^2-{\omega }^2\mu ϵ}$

$=\sqrt{{\left(\frac{\pi }{a}\right)}^2-\frac{(2\pi f{)}^2}{(3\times {10}^8{)}^2}}$

$=\pi \sqrt{{\left(\frac{1}{2.286\times {10}^{-2}}\right)}^2-{\left(\frac{2\times 10\times {10}^9}{3\times {10}^8}\right)}^2}$

$=j158\left(m^{-1}\right)$