Question

If g is the transconductance and r is the resistance due to channel length modulation – what is the total voltage gain if both M1 and M3 has channel length modulation?

(a) R / ((1/g || r) + R) * g * R * R / ((1/gm || r))

(b) R / ((1/g + 4R) * g * R / ((1/g || r) + 3R)

(c) R / ((1/g || r)) * g *R * R / ((1/g || r) + 2R)

(d) R / ((1/g) * R * R * g * 4g

This question was posed to me at a job interview.

I'm obligated to ask this question of MOSFET Amplifier with CD Configuration topic in chapter FET Amplifiers of Analog Circuits

Answer 1

Correct option is (a) R / ((1/g || r) + R) * g * R * R / ((1/gm || r))

The best I can explain: This is a cascade of a follower stage follower by a CS stage which precedes another follower stage. The gain due to each stage gets multiplied until we reach the output. For the first stage, the gain is R/ ((1/g || r) + R). The second stage has a gain of g * R while the final stage has a gain of R/ ((1/g || r) + R). The presence of r is due to channel length modulation. After multiplying the gains, we get R/ ((1/g || r) + R) * g * R * R / ((1/gm || r)).