Question

If M2 suffers from channel length modulation but M1 doesn’t, what is the voltage gain?

(a) 2gm1 * Rd || 1/gm2 * gm2 * Rd2

(b) 2gm1 * Rd || 1/gm2 * gm2 * 2Rd2

(c) gm1 * Rd || 12/gm2 * gm2 * Rd2

(d) gm1 * Rd || 1/gm2 || ro2 * gm2 * Rd2

The question was posed to me in a job interview.

My question is taken from MOSFET Amplifier with CG Configuration in section FET Amplifiers of Analog Circuits

Answer 1

Correct choice is (d) gm1 * Rd || 1/gm2 || ro2 * gm2 * Rd2

Easy explanation: The voltage gain due to M1 is gm1 * Rd || 1/gm2 || ro2 since we find that the drain of M1 is connected to the source of M2 and the impedance looking into the source of a MOSFET is 1/gm2 || ro2 due to the channel length modulation of M2. Now, the voltage gain due to the 2^nd CG stage is simply gm2*Rd2. Hence, the total voltage gain is a product of both the factors ie gm1 * Rd || 1/gm2 * gm2 * Rd2.