# Choosing R when designing CMOS Amplifier

I am trying to design a two stage amp like the one pictured above. I want the overall small-signal gain, |Av| = vo / vid = 240 V/V = (47.6 dB). I know in theory how to achieve this but am having trouble with the equations.

I know that: Vt0 = 0.7 V kn = 50 A/V^2 kp = 20 A/V^2 W/L = 100:1 for both NMOS and PMOS. The output conductance at a bias point of ID = 10 mA as 200 mhos for the NMOS device and 500 mhos for the PMOS device.

If needed I can also assume that: tox = 90 nm Nsub = 3.7*10^15 cm^-3

Due to a current mirror the current (Id) will be the same through the differential stage (M1-M4) and the PMOS common-source amp(M7). Transistor M8 provides bias current for M7 and functions as an active load on M7. I believe M5 and M6 act as a current source that keeps the current Io constant. RD7 and RD8 are used to venter the DC output at 0V. One or both will be zero for any calculation.

If I can get an equation for the gain through the differential amp (input: vid, output: between M2 and M4 going to M7) and an equation for the gain through M7 I can multiply them for the overall gain

What should I set R to in order to achieve an overall gain of