GATE 2021 EC – Question 54
For the transistor $M_1$ in the circuit shown in the figure, $\mu_nC_{ox}=100\ \mu\text{A/V}^2$ and $(W/L)=10$, where $\mu_n$ is the mobility of electron, $C_{ox}$ is the oxide capacitance per unit area, $W$ is the width and $L$ is the length.
The channel length modulation coefficient is ignored. If the gate-to-source voltage $V_{GS}$ is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is ________ V.
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Show answer and explanation
Correct answer: 0.49 to 0.51
Explanation
Let $V_{OV}=V_{GS}-V_T$. In saturation $I_D=\frac12\mu_nC_{ox}\frac WL V_{OV}^2=0.5\times100\ \mu\text{A}\times10\times V_{OV}^2=0.5\ \text{mA}\cdot V_{OV}^2$. So $V_{DS}=3-20\text{k}\times I_D=3-10V_{OV}^2$. At the edge of saturation $V_{DS}=V_{OV}$, so $10V_{OV}^2+V_{OV}-3=0$ and $V_{OV}=0.5$ V. Hence $V_T=1-0.5=0.5$ V.