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GATE 2022 EC – Question 40

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

Consider an ideal long channel $n$MOSFET (enhancement-mode) with gate length $10\ \mu\text{m}$ and width $100\ \mu\text{m}$. The product of electron mobility ($\mu_n$) and oxide capacitance per unit area ($C_{ox}$) is $\mu_nC_{ox}=1\ \text{mA/V}^2$. The threshold voltage of the transistor is 1 V. For a gate-to-source voltage $V_{GS}=[2-\sin(2t)]$ V and drain-to-source voltage $V_{DS}=1$ V (substrate connected to the source), the maximum value of the drain-to-source current is ________.

  1. 40 mA
  2. 20 mA
  3. 15 mA
  4. 5 mA

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Correct answer: (C) 15 mA

Explanation

$V_{GS}$ varies between 1 V and 3 V, so the current is largest at $V_{GS}=3$ V, where $V_{GS}-V_T=2$ V. Since $V_{DS}=1$ V is less than 2 V, the device is in the triode region: $I_D=\mu_nC_{ox}\frac WL\left[(V_{GS}-V_T)V_{DS}-\frac{V_{DS}^2}{2}\right]=1\text{ mA}\times10\times(2-0.5)=15$ mA.