Many amplifiers are designed to be simultaneously conjugate$-$matched at both ports when used between $50$ source and load impedances. Suppose that you have obtained such an amplifier, and that the specifications for the amplifier state that the power gain of the unit is $20$ dB in a $50$ system. Furthermore, the specifications state that the reverse isolation of the amplifier is $23$ dB in a $50$ system. Reverse isolation is the power attenuation of the amplifier when the amplifier is driven at the output port and the load is connected to the input port. $($Reverse isolation of $23$ dB means that the reverse power gain of the amplifier is $-23$ dB$.)($a$)$ What are S$11$ and S$22($Zo $=50)$ for the amplifier? $($b$)$ Is this amplifier unconditionally stable? Justify your answer. $($c$)$ Suppose that the amplifier is used between a $400$ source and a $50$ load. The power available from the source is Pavs $=10$ dBm$.$ Find the power delivered to the load. Express your result in dBm$.($d$)$ Suppose that the system of part c$.$ is modified by adding a lossless impedance matching network between the output of the $2-$port and the $50$ load. Find the power delivered to the load. Express your result in dBm$.($e$)$ Suppose that two of these amplifiers are cascaded, and used between a $400$ source with Pavs $=10$ dBm and a $50$ load. Find the power delivered to the load. Express your result in dBm$.$