The figure above shows a MOS Differential Amplifier with the drain resistors R_D implemented using diode-connected PMOS transistors, Q3 and Q4. Let Q1 and Q2 be matched, and Q3 and Q4 be matched.
a) Find the differential half-circuit and use it to derive an expression for A_d in terms of gm1,2, gm3,3, ro1,2, and ro3,4.
b) Neglecting the effect of the output resistances ro, find A_d in terms of u_n, u_p, (W/L)1,2, and (W/L)3,4.
c) If u_n = 4 u_p and all four transistors have the same channel length, find the (W1,2/W3,4) that results in A_d = 10 V/V.