GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

The figure below shows a feedback amplifier constructed using an nMOS transistor. Assume that ${\mu }_n{C}_{ox}=1$ mA/V${}^2$, threshold voltage $V_T=1$ V and $W/L=2$. The bias voltage at the drain terminal is 4 V. The capacitors $C_{\infty }$ offer zero impedance at the signal frequency. The ratio $V_{out}/V_{in}$ is ________ (rounded off to two decimal places).

Consider the real-valued function $g(x)=\max \{(x\text{–}2{)}^2,-2x+7\}$,
where $x\in (-\infty ,\infty )$. The minimum value attained by $g(x)$ is ________ (rounded off to one decimal place).

A short-circuit test is conducted on a single-phase transformer by shorting its secondary. The frequency of input voltage is 1 kHz. The corresponding wattmeter reading, primary current and primary voltage are 8 W, 2 A and 6 V respectively. Assume that the no-load losses and the no-load currents are negligible, and the core has linear magnetic characteristics. Keeping the secondary shorted, the primary is connected to a 2 V (RMS), 1 kHz sinusoidal source in series with a $\frac{1}{2\pi \sqrt{5}}$ mF capacitor. The primary current (RMS) will be ________ A (rounded off to two decimal places).

The opamps in the circuit are ideal. The input signals are
$V_{S1}=3+0.10\sin (300t)$ V and $V_{S2}=-2+0.11\sin (300t)$ V.
The average value of the voltage $V_0$ is ________ V (rounded off to two decimal places).

In the circuit shown, the input voltage $V_{in}=100$ mV. The switch and the opamp are ideal. At time $t=0$, the initial charge stored in the 10 nF capacitor is 1 nC, with the polarity as indicated in the figure. The switch S is controlled using a 1 kHz square-wave voltage signal $V_s$ as shown. Whenever $V_s$ is ‘High', S is in position ‘1' and when $V_s$ is 'Low', S is in position '2'.
At $t=20$ ms, the magnitude of the voltage $V_o$ will be ________ mV (rounded off to the nearest integer).