Question

A parallel plate waveguide has 0.05m height and is filled with material having relative permitivity 2.4. The highest frequency over which there is single mode propogation is _______GHz.

Answer 1

The velocity in the material filling the waveguide
$v_1=\frac{c}{\sqrt{{\epsilon }_r}}=\frac{3\times {10}^8}{\sqrt{2.4}}=1.936\times {10}^{8}m/s$
The first mode which propogates on the parallel plate waveguide is TEM mode with zero cut-off frequency.
$\therefore$ The range over which single mode operation exists from 0 to $f_{C_1}$
$f_{C_1}=\frac{v_1}{2d}=\frac{1.936\times {10}^8}{2\times 0.05}=1.936GHz$