The GATE Grind

GATE 2017 EC – Question 50

Analog Circuits · BJT and MOSFET Amplifiers · 2 marks · Numerical answer

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage $V_{tn} = 1$ V and its transconductance parameter $\mu_n C_{ox}\left(\frac{W}{L}\right) = 1\ mA/V^2$. Neglect channel length modulation and body bias effects. Under these conditions, the drain current $I_D$ in mA is ________.

$V_{DD} = 8$ V feeds a $1\ \text{k}\Omega$ drain resistor $R_D$ and a gate divider of $R_1 = 3\ \text{M}\Omega$ (to $V_{DD}$) and $R_2 = 5\ \text{M}\Omega$ (to ground). The source has a $1\ \text{k}\Omega$ resistor $R_S$ to ground.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 2

Explanation

The gate voltage is $V_G = 8 \times \frac{5}{3 + 5} = 5$ V. With $I_D$ in mA and $R_S = 1\ \text{k}\Omega$, $V_{GS} = 5 - I_D$. The saturation current is $I_D = \frac{1}{2}(1)(V_{GS} - 1)^2 = \frac{1}{2}(4 - I_D)^2$. This gives $I_D^2 - 10I_D + 16 = 0$, so $I_D = 2$ or 8. The value 8 would make $V_{GS}$ negative, so $I_D = 2$ mA.