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GATE 2022 IN – Question 44

Analog Electronics · Diodes and transistor circuits · 2 marks · Multiple choice

The enhancement n-channel MOSFET in the small-signal circuit is saturated with transconductance $g_m$. Ignore channel-length modulation. The small-signal impedance looking into P is ______.

Diagram for GATE 2022 IN question 44
  1. $R_S\parallel R_L\parallel g_m^{-1}$
  2. $R_S\parallel g_m^{-1}$
  3. $(R_S+R_L)\parallel g_m^{-1}$
  4. $\dfrac{R_Lg_m}{1+R_Sg_m}(R_L\parallel g_m^{-1})$

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Correct answer: (B) $R_S\parallel g_m^{-1}$

Explanation

Apply source test voltage v. With gate grounded and ro infinite, the transistor contributes current gmv, equivalent to 1/gm to ground. This is parallel with RS. Drain RL does not affect that transconductance current when channel-length modulation is ignored.

Thus **RS||gm⁻¹, B**.