GATE 2025 EC – Question 43
The identical MOSFETs $M_1$ and $M_2$ in the circuit given below are ideal and biased in the saturation region. $M_1$ and $M_2$ have a transconductance $g_m$ of 5 mS.
The input signals (in Volts) are:
$V_1=2.5+0.01\sin\omega t$
$V_2=2.5-0.01\sin\omega t$
The output signal $V_3$ (in Volts) is ________.
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Correct answer: (D) $4-0.05\sin\omega t$
Explanation
The 2 mA tail current splits equally at DC, so each drain carries 1 mA and $V_3=5-1\text{ mA}\times1\text{ k}\Omega=4$ V. The signal is purely differential ($v_1=+0.01\sin\omega t$, $v_2=-0.01\sin\omega t$), so the source node stays at signal ground and $M_1$'s current changes by $g_mv_1=5\text{ mS}\times0.01\sin\omega t=0.05\sin\omega t$ mA. This reduces $V_3$ by $0.05\sin\omega t$ V, so $V_3=4-0.05\sin\omega t$.