GATE 2017 EC (EC2) – Question 48
Two n-channel MOSFETs T1 and T2 are identical except that T2 has twice the width of T1. Both operate in saturation, and T2 has twice the gate overdrive $(V_{GS}-V_{TH})$ of T1. If T1 has drain current $I_{D1}$ and transconductance $g_{m1}$, the corresponding T2 values are
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Correct answer: (B) $8I_{D1}$ and $4g_{m1}$
Explanation
In the saturation square-law model, $I_D=\tfrac12\mu_nC_{ox}(W/L)V_{ov}^2$. Doubling width and doubling overdrive multiplies current by $2(2^2)=8$.
Differentiating gives $g_m=\mu_nC_{ox}(W/L)V_{ov}$. Its scale factor is therefore $2(2)=4$.
Thus T2 has **$8I_{D1}$ and $4g_{m1}$**, option **B**.