GATE 2019 EC – Question 64

Analog Circuits · BJT and MOSFET Amplifiers · 2 marks · Numerical answer

In the circuit shown, the threshold voltages of the pMOS ($|V_{tp}|$) and nMOS ($V_{tn}$) transistors are both equal to 1 V. All the transistors have the same output resistance $r_{ds}$ of 6 M$\Omega$. The other parameters are listed below:

$\mu_nC_{ox}=60\ \mu\text{A/V}^2$; $\left(\frac WL\right)_{nMOS}=5$

$\mu_pC_{ox}=30\ \mu\text{A/V}^2$; $\left(\frac WL\right)_{pMOS}=10$

$\mu_n$ and $\mu_p$ are the carrier mobilities, and $C_{ox}$ is the oxide capacitance per unit area. Ignoring the effect of the channel length modulation and body bias, the gain of the circuit is ________ (rounded to 1 decimal place).

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Correct answer: 900

Explanation

The transconductance of the driver is $g_m=\mu C_{ox}\frac WL V_{ov}=300\ \mu\text{A/V}^2\times V_{ov}$ for both device types, which gives $g_m=300\ \mu$S at $V_{ov}=1$ V. The output resistance is $r_{ds}\|r_{ds}=3\ \text{M}\Omega$, so the gain magnitude is $g_m\times3\text{ M}\Omega=900$.