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 voltage gain for only M2?

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

(b) g * {(1 + gr)* R + R} || 4R

(c) g * {(1 + gr)* R + 3R} || 4R

(d) g * {(1 + 2gr)* R + R} || 4R

I have been asked this question by my college professor while I was bunking the class.

My question is taken from MOSFET Amplifier with CD Configuration in chapter FET Amplifiers of Analog Circuits

Answer 1

Correct choice is (a) g * {(1 + gr)* (R || 1/g || r) + (R || 1/g || r)} || R

The explanation is: The voltage gain for M2 will be due to a CG stage. M2 has channel length modulation and is degenerated by (R || 1/g || r). Thus the output impedance rises to {(1 + gr)* (R || 1/g || r) + (R || 1/g || r)} ||R and hence the gain for only M2 is g * {(1 + gr)* (R || 1/g || r) + (R || 1/g || r)} || R.