Question

A parallel plate waveguide is to be designed so that only TEM modes can propagate in the frequency range 0<f<2 GHz. The dielectric material between the plates has ${\epsilon }_r=9,{\mu }_r=1.$The spacing 'd' allowed between the parallel plates of waveguide is

• A. d < 7.5 cm
• B. $d\le 2.5cm$
• C. $d\le 7.5cm$
• D. d < 2.5 cm

Answer 1

The correct option is D d < 2.5 cm

$f_{c_o,n}=\frac{nv}{2d}$
n = 1 has lowest cut off frequency.

$f_{c_o,1}=\frac{V}{2d}>2GHz$

$\Rightarrow v>4\times {10}^{9}d$

$\Rightarrow d<\frac{v}{4\times {10}^9}=\frac{3\times {10}^8}{\sqrt{9}\times 4\times {10}^9}m$

$\Rightarrow d<\frac{1}{40}m$

$ord<2.5cm$