Question

An airfilled rectangular waveguide of dimensions a = 4 cm, b=2 cm transports energy in the dominant mode at a rate of 2 mW.If the frequency of operation is 10GHz, the peak value of the electric field in the waveguide is

Answer 1

Dominant mode is $T{E}_{10}(\because a>b)$

Given f=10GHz

$f_c=\frac{c}{2a}=\frac{3\times {10}^{10}}{2\times 4}=3.75\text{GHz}$

${\eta }_{TE}=\frac{n_0}{\sqrt{1-{\left(\frac{f_c}{f}\right)}^2}}=\frac{377}{\sqrt{1-{\left(\frac{3.75}{10}\right)}^2}}=406.7\Omega$

$p_{avg}=\frac{E_0^{2}ab}{4\eta }\Rightarrow E_0^2=\frac{p_{avg}4\eta }{ab}\Rightarrow E_0=\sqrt{\frac{p_{avg}4\eta }{ab}}$

$=\sqrt{\frac{2\times {10}^{-3}\times 4\times 405.7}{4\times 2\times {10}^4}}=63.7V/m$