List of top Electronics and Communication Engineering Questions asked in GATE Electronics and Communication Engineering

Given that $ Z_0 = 50\Omega $, $ Z_L = (50 - j75)\Omega $, and $ P_i = 10 $ mW, find the power delivered to the load.

The frequency of occurrence of 8 symbols (a–h) is shown in the table below. A symbol is chosen and it is determined by asking a series of “yes/no” questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is (rounded off to two decimal places).

In the circuit below, the voltage $V_L$ is ______________ V (rounded off to two decimal places).}

In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of 1 MHz, the frequency of signal $Q_2$ in kHz, is ___________ (rounded off to the nearest integer).

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 $\mu$s. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is ____________ $\mu$s (rounded off to two decimal places).

In a semiconductor device, the Fermi-energy level is $0.35$ eV above the valence band energy. The effective density of states in the valence band at $T=300$ K is $1\times10^{19}\ \text{cm}^{-3}$. The thermal equilibrium hole concentration in silicon at $400$ K is ___________ $\times 10^{13}\ \text{cm}^{-3}$ (rounded off to two decimal places).
Given $kT$ at $300$ K is $0.026$ eV.

Let $X(t)$ be a white Gaussian noise with power spectral density $\dfrac{1}{2}$ W/Hz. If $X(t)$ is input to an LTI system with impulse response $e^{-t}u(t)$, the average power of the system output is ___________ W (rounded off to two decimal places).

Let $x_1(t) = u(t+1.5) - u(t-1.5)$ and $x_2(t)$ is shown in the figure below. For $y(t) = x_1(t) \ast x_2(t)$, the \[ \int_{-\infty}^{\infty} y(t) \, dt \] is ___________ (rounded off to the nearest integer).

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is \[ G(s) = \dfrac{k(s+z)^a}{s^b(s+p)^c}, \] where $k$, $z$, $p$, $a$, $b$, and $c$ are positive constants. The value of $(a+b+c)$ is ___________ (rounded off to the nearest integer).

In an extrinsic semiconductor, the hole concentration is given to be $1.5n_i$ where $n_i$ is the intrinsic carrier concentration of $1 \times 10^{10}$ $\text{cm}^{-3}$. The ratio of electron to hole mobility for equal hole and electron drift current is given as _____________ (rounded off to two decimal places).

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

The electric field of a plane electromagnetic wave is \[ E = \mathbf{a_x}\,C_{1x}\cos(\omega t - \beta z) + \mathbf{a_y}\,C_{1y}\cos(\omega t - \beta z + \theta)\ \text{V/m}. \] Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

The standing wave ratio on a $50\ \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive voltage minima is $30\ \text{cm}$ and the first minimum is located at $10\ \text{cm}$ from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance $R_m$ of the same line. The value of $R_m$ and $l_m$, respectively, are _____________

The S-parameters of a two port network is given as \[ [S] = \begin{bmatrix} S_{11} & S_{12} \\[2pt] S_{21} & S_{22} \end{bmatrix} \] with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1 = \beta l_1$ and $\theta_2 = \beta l_2$ are added to the input and output ports for measurement purposes, respectively. The S-parameters $[S']$ of the resultant two port network is

Let $x_1(t)$ and $x_2(t)$ be two band-limited signals having bandwidth $B = 4\pi \times 10^{3}$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample $y(t)$, is _____________

Let $x(t) = 10\cos(10.5Wt)$ be passed through an LTI system having impulse response \[ h(t) = \pi\left(\dfrac{\sin(Wt)}{\pi t}\right)^2 \cos(10Wt). \] The output of the system is _____________

Consider a discrete-time periodic signal with period $N=5$. Let the discrete-time Fourier series (DTFS) representation be \[ x[n] = \sum_{k=0}^{4} a_k e^{j\frac{2\pi kn}{5}}, \] where $a_0 = 1$, $a_1 = 3j$, $a_2 = 2j$, $a_3 = -2j$, and $a_4 = -3j$. The value of the sum \[ \sum_{n=0}^{4} x[n] \sin\left(\frac{4\pi n}{5}\right) \] is _____________

The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\dfrac{V_{out}}{V_s}$ is _____________

Let a frequency modulated (FM) signal \[ x(t) = A \cos\left(\omega_c t + k_f \int_{-\infty}^{t} m(\lambda) \, d\lambda \right), \] where $m(t)$ is a message signal of bandwidth $W$. It is passed through a non-linear system with output \[ y(t) = 2x(t) + 5(x(t))^2. \] Let $B_T$ denote the FM bandwidth. The minimum value of $\omega_c$ required to recover $x(t)$ from $y(t)$ is _____________

The switch $S_1$ was closed and $S_2$ was open for a long time. At $t=0$, switch $S_1$ is opened and $S_2$ is closed, simultaneously. The value of $i_c(0^+)$, in amperes, is _____________

In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as Y(s) = G$_1$(s)R(s) + G$_2$(s)D(s).
G$_1$(s) and G$_2$(s) are given by

A closed loop system is shown in the figure where $k > 0$ and $\alpha > 0$. The steady state error due to a ramp input $(R(s)=\alpha/s^{2})$ is _____________

In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of 0.7 V. $V_{IN}$ and $V_{OUT}$ are input and output voltages in volts. The transfer characteristic is _____________

The $\dfrac{V_{OUT}}{V_{IN}}$ of the circuit shown below is _____________

In the circuit shown below, switch S was closed for a long time. If the switch is opened at $t=0$, the maximum magnitude of the voltage $V_R$, in volts, is _____________ (rounded off to the nearest integer).