Problem $3$: $(30$ points$)$

Consider the following circuit with active load. The current gain $$ for all transistors is $100.$ The $V_{bE(ON)}$ for $Q_1$ is $0\mathrm{.}67V,V_{AN}=120V$ and $V_{AP}=91\mathrm{.}8V.I_{Co}=0\mathrm{.}13mA.$

$($a$)$ Find the values of $I_{\text{R}\text{e}\text{f}}$ and $R_{E1}.$

$($b$)$ Calculate the output resistance $R_o$ of the current source.

$($c$)$ Assuming that all transistors are operating in the forward active mode, sketch the ac equivalent circuit for the amplifier using $R_0$ and find the voltage gain $Av=\frac{v_0}{V}$ in at no load.