III. a$)$ Assuming that $=200$ for all transistors, and using the bias currents obtained in the test question II$,$ determine $r_{}$ for transistors $Q_1$ through $Q_6.$ b$)$ Determine the differential input impedance of the second differential amplifier and $Q_4).$ c$)$ Draw the small $-$ signal equivalent circuit for the first differential amplifier, including the input impedance of the second stage. Use the $r_{}-$ model for the transistors. d$)$ Assume that the input is a pure differential signal $($i$.$e$.,v_1=\frac{v_{id}}{2}$ and $v_2=-\frac{v_{id}}{2}).$ Determine the differential voltage gain magnitude of the first stage. The gain is the differential output voltage divided by the differential input voltage.