Consider a dielectric $(c_r=4)$ filled waveguide $(a=5\mathrm{.}35mm$ and $b=2\mathrm{.}2mm).$ The recommended operating frequency band is $18$ GHz to $26\mathrm{.}5$ GHz $.$

$($a$)$ Calculate a value for the cutoff frequency $($in GHz $)$ for the $T{E}_{10}$ mode. $(25$ pts$)$

$($b$)$ Calculate a value for the wave impedance at a frequency of $21$ GHz $.(35$ pts$)$

$($c$)$ Calculate a value for the characteristic impedance of the waveguide $($powervoltage definition$)$ at a frequency of $21$ GHz $.(10$ pts $)$

$($d$)$ Calculate a value for the guided wavelength $($in mm$)$ at a frequency of $21$ GHz $.(30$ pts$)$