Question

If Channel Length Modulation is present and gm is the transconductance of M1, what happens to the output resistance of for a fixed V2 in the following circuit?

(a) (1 + (gm * ro)) * Rs + ro

(b) (1 + (gm * ro)) * ro + Rs

(c) (ro + 2) * Rs

(d) (1 + (gm * ro)) * Rs

I have been asked this question in a national level competition.

The question is from MOSFET Amplifier with CS Configuration in portion FET Amplifiers of Analog Circuits

Answer 1

Right answer is (a) (1 + (gm * ro)) * Rs + ro

Explanation: By performing a small signal analysis of the following circuit, we find that the output impedance of the circuit is simply (1 + (gm * ro)) * Rs + ro. For doing this analysis, we have to short V1 and V2 to ground. Thereafter, we place a voltage source at the input node and measure current. The impedance measured will be the output impedance which is (1 + (gm * ro)) * Rs + ro.