GATE Instrumentation

The RLC filter shown below acts as a _________.

A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a _________.

Given $x(t) = 4 \sin(15\pi t) + 7 \cos(4\pi t)$, where $t$ is in seconds. The fundamental period of $x(t)$ is ________ seconds.

Among the following, the differential equation(s) not representative of a linear dynamical system is/are ______. (i) $\frac{d^2x}{dt^2} + 2t \frac{dx}{dt} + x(t) = u(t)$ (ii) $(\fr...

The maximum signal to quantization noise ratio (SQNR) for a 16-bit analog-to-digital converter is approximately ________ dB.

The Kelvin double bridge is used to measure ________ valued resistances and has ________ resistors in its construction.

Active strain gauges are connected in a half-bridge configuration to measure strain in a cantilever element. When powered by a voltage source of 10 V, the voltage at the output of...

A glass pH electrode behaves linearly with an output change of 60 mV per unit change in pH. The measurement reference is set such that a solution of pH 6 produces an output of 60 m...

An analog speech signal contains signals from 200 Hz to 2400 Hz. It is sampled at 6 kHz and quantized with 512 levels for pulse code modulation (PCM). The bit rate will be ______ k...

The slope efficiency of a laser diode is 0.5 W/A, and the output optical power at a current of 100 mA is 30 mW. Assuming piece-wise linear characteristics of the laser diode, the t...

In a linear element, the measured current is 100 mA ± 2.5% and the measured voltage is 5 V ± 5%. Which of the following options show(s) the consumed power?

Which of the following statements is/are correct for a thermocouple?

A two-port network has z-parameters Z11 = Z22 = 10 Ω, and Z12 = Z21 = 5 Ω. The value of RL such that maximum power is transferred to RL is ________ Ω.

In the circuit shown below, the value of the output voltage V₀ is ____ V.

A signal x(t) is shown below. The plot of y(t) = 1 - x(4-t) is shown in ________.

In the table shown below, List-I are the system responses to input x(t) and List-II are the system properties. The correct matching is ______.

Given two signals: x(t) = u(t − 2) – u(t - 3), and y(t) = e^(-4t)u(t). If z(t) = x(t) * y(t), then Z(s) is _________.

A linear time invariant (LTI) system is described by: $\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -10 & -7 \end{bmatrix} \begin{bmatrix} x_1 \\...

In the circuit shown below, R is 1 kΩ and Rf is 10 kΩ. If Vin is 100 mV and the op-amps have supply voltages of ±15 V, then Vout is ________ V.

In the following active filter circuit with ideal op-amps, R is 1 kΩ, C is 1 µF, and Vin has an amplitude of 1 V at 1000 rad/s. The amplitude of Vout is _________ V.

The initial state of Q3Q2Q1Q0 in the digital circuit shown below is 1011. The new value of Q3Q2Q1Q0 after two rising edges of the clock (CLK) will be ________.

A closed Lissajous pattern observed on an oscilloscope in the X - Y mode has three horizontal tangencies and two vertical tangencies in steady state. If the signal-frequency on cha...

A parallel plate capacitive displacement sensor has a plate area of 2 cm². The air gap between the plates is decreased by 0.1 mm from an initial value of 0.5 mm. The percentage cha...

The emitted radiant energy from a piece of metal was measured using a pyrometer. The temperature was calculated to be 1000 °C, assuming a surface emissivity of 0.8. It was later fo...

An amplitude modulated voltage signal x(t) drives a load of 1 Ω. x(t) = K cos(300π t) + L cos(240π t) + L cos(360π t). If the efficiency is 60% and the carrier power is 50 W, the v...

Given a differential equation $\frac{d^2x}{dt^2} + x = 0$ with $x(0) \neq 0$. Which of the following statements is/are true?

Which of the following functions represent(s) the output of the CMOS logic-gate shown in the circuit below?

A single phase transformer has a rating of 10 kVA, 50 Hz, 1100 V/ 220 V. In an open circuit test with the high voltage side open, the following are obtained: * Voltage applied to t...

A linear time invariant (LTI) system has a transfer function $G(s) = \frac{10(s + 1)}{s(s^2 + 2s + 5)}$ The system is placed in unity negative feedback configuration. For a unit ra...

The system $G(s) = \frac{K}{(s+1)^4}$ has a gain margin of 20 dB. The value of K is ________. (rounded off to two decimal places)

In the phase-locked-loop circuit shown below, the output of the VCO is a digital square wave. If the input is a square wave at 10 kHz, the steady state frequency of the output is _...

A digital counter increments its count every 0.1 μs. The counter is used in an instrument to measure frequency. The counter is operated for one period of the input signal to the in...

A current carrying semiconductor of thickness 0.7 mm is placed in a transverse magnetic field. The measured Hall voltage is 0.9 mV and the current is 6 mA. If the Hall coefficient...

For a fiber Bragg grating-based sensor, the shift in the Bragg wavelength gives information about the value of the measurand. For a Bragg wavelength of 1550 nm and effective index...

A photodiode has a responsivity 0.8 A/W. If the input optical power to the photodiode is 2 mW, the power delivered to a 50 Ω load is ________ μW. (rounded off to the nearest intege...