Question

If g is the transconductance, r is the resistance due to channel length modulation and if M2 and M1 has channel length modulation but M3 doesn’t, what is the total resistance at the drain of M2?

(a) {(1 + gr)* R + R} || 2R

(b) {(1 + gr)* 3R + 2R} || R

(c) {(1 + gr)* (R || 1/g || r) + (R || 1/g || r)} || R

(d) Infinite

The question was posed to me at a job interview.

The doubt is from MOSFET Amplifier with CD Configuration topic in chapter FET Amplifiers of Analog Circuits

Answer 1

Right choice is (c) {(1 + gr)* (R || 1/g || r) + (R || 1/g || r)} || R

Best explanation: The drain of M2 offers a resistance of {(1 + gr)* (R || 1/g || r) + (R || 1/g || r) due to channel length modulation and the degeneration resistance R || 1/g || r connected to the drain of M2. This comes in parallel to R connected to the source of M2. Hence the overall resistance becomes {(1 + gr)* (R || 1/g || r) + (R || 1/g || r).