A single shunt open$-$circuit $($OC$)$ stub is to be used to match a load impedance $($ZL$)$to a $50$ system impedance. $$ Refer to the schematic below captured from ADS.$$The main goal of this set of problems is to determine the length of the stub $($parameter $\text{'}$E$\text{'}$ of TL$2$ in the schematic$)$ as well as the distance between the load and the connection point of the stub $($parameter $\text{'}$E$\text{'}$ of TL$1$ in the schematic$).($Notice that these quantities have been left blank in the schematic captured from ADS.$)$

The load impedance consists of a parallel RL $($R $=100$ ohms and L $=3\mathrm{.}9$ nH$).$ Assume a frequency of $3\mathrm{.}8$ GHz$.$

First, let's find the real and imaginary parts of the load admittance.$$ Begin by evaluating the real part of YL$.$ Type your answer in milli$-$siemens $($mS$)$ to two places after the decimal.

Hint: YL$=1$R$1+$j$2$fC$1=$GL$+$jBL$=1$ZL