$1.(15$p$)$

A Coplanar Waveguide Line with Signal width equal to $20$ um and Signal$-$to$-$Ground width equal to $\backslash (30$ u m $\backslash )$ is built on Alumina substrate $(\backslash (\backslash$varepsilon$=8\mathrm{.}8,\backslash$overline$\{\backslash$mu r$=1,\backslash$sigma$=0\}\backslash ))$ with $\backslash (\backslash$mathrm$\{$Z$\}\_\{0\}=74\mathrm{.}65\backslash$Omega $\backslash ).$ It is used for the feeding of a Parallel$-$Plate Waveguide filled with Alumina and plate$-$distance equal to $1\mathrm{.}2$ mm $.$ The walls of the parallel$-$plate waveguide can be assumed to be perfect conductors. This topology is a part of a satellite transponder operated at $12$ GHz $.$

$($a$)$By calculating the standing$-$wave ratio, determine whether it is a good transition. Would it be a good transition at $100$ GHz and why??

$($b$)$ If under matched conditions the CPW feeding line would deliver $5$ Watts to the load, how much power does it deliver to the load without any matching?

$($c$)$ Design a single$-$section matching transformer. Assuming that it is going to be fabricated on Alumina substrate, determine its physical length and its characteristic impedance. Give an approximate expression for the reflection coefficient bandwidth for a maximum tolerable Reflection Coefficient value of $0\mathrm{.}1.$ Do you consider this bandwidth to be sufficient for satellite applications?