Question

The interior of a $\frac{20}{3}cm\times \frac{20}{4}cm$ rectangular waveguide is completely filled with a dielectric of ${ϵ}_r=4$, Waves of free space wave lengths shorter than_________ can be propagated in the $T{E}_{11}$ mode.

• A. 8

Answer 1

The correct option is A 8
$V=\frac{1}{\sqrt{\mu ϵ}}=\frac{1}{{\mu }_0{ϵ}_0{ϵ}_r}$

$=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}\times \frac{1}{\sqrt{{ϵ}_r}}$

$v=\frac{3\times {10}^8}{\sqrt{4}}$

=1.5 $\times$ ${10}^{8}m/sec$

m = n = 1

$f_c=\frac{V}{2\pi }\sqrt{{\left(\frac{n\pi }{a}\right)}^2{\left(\frac{n\pi }{b}\right)}^2}$

$=\frac{1.5\times {10}^8}{2}\sqrt{{\left(\frac{3}{20}\right)}^2+{\left(\frac{4}{20}\right)}^2}\times {10}^2$

$f_c=\frac{7.5\times {10}^9}{20}\times 5=1.875\times {10}^{9}Hz$

${\lambda }_c=\frac{v}{f_c}=\frac{1.5\times {10}^8}{1.875\times {10}^9}=8cm$

So, waves of free space Wavelength shorter than 8cm can be propagated.

${\lambda }_c=8cm$