A load has an impedance $Z=75+\jmath 15 \Omega$.
(a) What is the load reflection coefficient, $\Gamma_{L}$, if the system reference impedance is $75 \Omega ?$
(b) Design a shorted stub at the load that will make the impedance of the load plus the stub, call this $Z_{1}$, be purely real; that is, the reflection coefficient of the effective load, $\Gamma_{1}$ has zero phase. Choose a stub characteristic impedance of $75 \Omega$. At this stage do an electrical design only. ( This require complete electrical information, e.g. the electrical length of the stub.)
(c) Following on from
(b), now design a quarter-wave transformer between the source and the stub that will present $50 \Omega$ at the input. (The design must include the characteristic impedance of the transmission line and its electrical length. Thus the structure is a $\lambda / 4$ transformer, a stub, and the load.)
(d) Now convert the electrical design into a physical design at $1 \mathrm{GHz}$ using microstrip technology with substrate thickness $h=$ $0.5 \mathrm{~mm}$ and relative permittivity $\varepsilon_{r}=10$ You must design the widths and lengths of the stub and the quarter-wave transformer.