The GATE Grind

GATE 2018 EC – Question 11

Analog Circuits · BJT and MOSFET Amplifiers · 1 mark · Multiple choice

Two identical nMOS transistors $M_1$ and $M_2$ are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. $V_{bias}$ and $V_D$ are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as $g_m=\frac{\partial i_D}{\partial v_{GS}}$ while the output resistance is $r_o=\frac{\partial v_{DS}}{\partial i_D}$, where $i_D$ is the current flowing into the drain of $M_2$. Let $g_{m1}$, $g_{m2}$ be the transconductances and $r_{o1}$, $r_{o2}$ be the output resistances of transistors $M_1$ and $M_2$, respectively.

Which of the following statements about estimates for $g_m$ and $r_o$ is correct?

Diagram for GATE 2018 EC question 11
  1. $g_m\approx g_{m1}\cdot g_{m2}\cdot r_{o2}$ and $r_o\approx r_{o1}+r_{o2}$
  2. $g_m\approx g_{m1}+g_{m2}$ and $r_o\approx r_{o1}+r_{o2}$
  3. $g_m\approx g_{m1}$ and $r_o\approx r_{o1}\cdot g_{m2}\cdot r_{o2}$
  4. $g_m\approx g_{m1}$ and $r_o\approx r_{o2}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $g_m\approx g_{m1}$ and $r_o\approx r_{o1}\cdot g_{m2}\cdot r_{o2}$

Explanation

This is a cascode. The same current flows through both devices, and it is controlled by the gate voltage of $M_1$, so $g_m\approx g_{m1}$. Looking into the drain of $M_2$, the source degeneration by $r_{o1}$ boosts the output resistance to about $r_{o1}\,g_{m2}\,r_{o2}$.