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GATE 2022 IN – Question 47

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

The enhancement n-channel MOSFET shown is saturated with transconductance $g_m$. A low-frequency small-signal supply voltage $v_d$ causes output fluctuation $v_O$. Ignoring channel-length modulation, the small-signal gain $v_O/v_d$ is ______.

Diagram for GATE 2022 IN question 47
  1. $\dfrac{-g_mR_0}{1+g_mR_0}$
  2. $(g_mR_0+1)^{-1}$
  3. $\dfrac{-g_mR_0}{1+2g_mR_0}$
  4. $(g_mR_0/2+3/2)^{-1}$

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Show answer and explanation

Correct answer: (D) $(g_mR_0/2+3/2)^{-1}$

Explanation

No gate current flows, so its equal-resistor divider gives vg=vo/2. Output KCL is (vd−vo)/R0=vo/(2R0)+gmvo/2.

Therefore vd=vo(3/2+gmR0/2), yielding **vo/vd=(gmR0/2+3/2)⁻¹, D**.