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GATE 2020 EC – Question 47

Analog Circuits · BJT and MOSFET Amplifiers · 2 marks · Multiple choice

Using the incremental low frequency small-signal model of the MOS device, the Norton equivalent resistance of the following circuit is

Diagram for GATE 2020 EC question 47
  1. $r_{ds}+R+g_mr_{ds}R$
  2. $\dfrac{r_{ds}+R}{1+g_mr_{ds}}$
  3. $r_{ds}+\dfrac{1}{g_m}+R$
  4. $r_{ds}+R$

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Correct answer: (B) $\dfrac{r_{ds}+R}{1+g_mr_{ds}}$

Explanation

Apply a test voltage $v$ at the source with the gate grounded and the top of $R$ at ac ground. Then $v_{gs}=-v$ and the drain voltage is $v_d=-i_dR$. The drain current (drain to source) is $i_d=g_mv_{gs}+\frac{v_d-v}{r_{ds}}=-g_mv-\frac{i_dR+v}{r_{ds}}$, so $i_d\left(1+\frac{R}{r_{ds}}\right)=-v\left(g_m+\frac1{r_{ds}}\right)$ and $i_d=-v\frac{1+g_mr_{ds}}{r_{ds}+R}$. The current entering the source is $-i_d$, so $R_{eq}=\frac{v}{-i_d}=\frac{r_{ds}+R}{1+g_mr_{ds}}$.