GATE 2024 EC – Question 64
An NMOS transistor operating in the linear region has $I_{DS}$ of 5 μA at $V_{DS}$ of 0.1 V. Keeping $V_{GS}$ constant, the $V_{DS}$ is increased to 1.5 V.
Given that $\mu_nC_{ox}\dfrac WL=50$ μA/V$^2$, the transconductance at the new operating point (in μA/V, rounded off to two decimal places) is ______.
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Correct answer: 52.24 to 52.76
Explanation
In the linear region $I_{DS}=\mu_nC_{ox}\frac WL\left[(V_{GS}-V_T)V_{DS}-\frac{V_{DS}^2}{2}\right]$. So $5=50[0.1V_{ov}-0.005]$, giving $V_{ov}=V_{GS}-V_T=1.05$ V. At $V_{DS}=1.5$ V $>V_{ov}$ the device is in saturation, where $g_m=\mu_nC_{ox}\frac WL V_{ov}=50\times1.05=52.50$ μA/V.