Question

If g is the transconductance and r is the resistance due to channel length modulation – what is the total voltage gain if both M2 and M3 has channel length modulation?

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

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

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

(d) R/ ((1/g ) + R) * g *R * R *2g

The question was asked in final exam.

My doubt is from MOSFET Amplifier with CD Configuration topic in portion FET Amplifiers of Analog Circuits

Answer 1

Correct answer is (b) R/ ((1/g + R) * g * (R || r) * R/ ((1/g || r) + R)

Explanation: 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). The second stage has a gain of g * (R || r)  while the final stage has a gain of R/ ((1/g || r) + R)- the effect of r is simply due to channel length modulation. After multiplying the gains, we get R/ ((1/g + R) * g * (R || r) * R/ ((1/g || r) + R).