GATE IN 2024 Question Paper (04-Feb-2024) (Shift 2)

A shielded cable with $C_{stray}=20$ pF and $R_{wire}=10$ Ω is used to connect the inductive sensors as shown in the figure. The RMS value of $V_{out}$ is ______________ V (rounded off to two decimal places).
Note: Assume all components are ideal, and sensors are not magnetically coupled.

In the figure shown, the diode current is given by $I_D=I_s{e}^{\frac{\alpha V_D}{T}}$. $V_D$ is the diode voltage in volts, $T$ is the absolute temperature in Kelvin, $\alpha =1.16\times 10^4$ K/V, and $I_s=10^{-15}$ A is the saturation current. The dc current source, opamp and the resistors are ideal, and are assumed to be temperature independent. The change in the output voltage $(V_{out})$ per Kelvin change in temperature is ______________ mV (rounded off to one decimal place).

An ADC has a full scale voltage of 1.4 V, resolution of 200 mV, and produces binary output data. The input signal of the ADC has a bandwidth of 500 MHz, and it samples the data at the Nyquist rate. The parallel data output is converted to a serial bit stream using a parallel-to-serial converter. The data rate at the output of the parallel-to-serial converter is ______________ Gbps (rounded off to nearest integer).

In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2$ ms is ______________ V (rounded off to one decimal place).

In the figure shown, $S_w$ is a switch whose position changes from 1 to 0 when $V_c$ changes from logic HIGH to LOW and vice versa. The bandwidth of the permanent magnet moving coil (PMMC) type voltmeter is 1 Hz. If $V_{sense}=2\sin (4000\pi t)$ V and $V_{ref}=4\sin (2000\pi t)$ V, the voltmeter reading is ______________ V (rounded off to nearest integer).
Note: Assume all components are ideal.