Question

An air-filled rectangular waveguide of interval dimensions a cm $\times$ b cm (a > b) has a cutoff frequency of 6 GHz for the dominant $T{E}_{10}$ mode. For the same waveguide, if the cutoff frequency of the $T{M}_{11}$ mode is 15 GHz, the cutoff frequency of the $T{E}_{01}$ mode in GHz is

• A. 13.75

Answer 1

The correct option is A 13.75
Given, $f_{c}T{E}_{10}$ mode is 6 GHz

$\Rightarrow \frac{C}{2a}=\frac{3\times {10}^{10}}{2\times a}=6\times {10}^9$

$\Rightarrow a=2.5cm$

Given $f_{c}forT{M}_{11}$ mode is 15 GHz

$\Rightarrow \frac{c}{2}\sqrt{\frac{1}{a^2}+\frac{1}{b^2}}=15\times {10}^9$

$\frac{3\times {10}^{10}}{2}\sqrt{\frac{1}{6.25}+\frac{1}{b^2}}=15\times {10}^9$

$\Rightarrow b=\frac{2.5}{\sqrt{5.25}}$

Now $f_{c}forT{E}_{01}$ mode is,

$f_c=\frac{C}{2b}=\frac{3\times {10}^{10}}{2.5}\sqrt{5.25}$

= 13.75 GHz