List of top Networks, Signals and Systems Questions asked in GATE Electronics and Communication Engineering

A non-degenerate n-type semiconductor has \(5\%\) neutral dopant atoms. Its Fermi level is located at \(0.25 \, {eV}\) below the conduction band (\(E_C\)) and the donor energy level (\(E_D\)) has a degeneracy of \(2\). Assuming the thermal voltage to be \(20 \, {mV}\), the difference between \(E_C\) and \(E_D\) (in \({eV}\), rounded off to two decimal places) is \(\_\_\_\_\).

For the two-port network shown below, the value of the \(Y_{21}\) parameter (in Siemens) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{60.png} \end{center}

The relationship between any \(N\)-length sequence \(x[n]\) and its corresponding \(N\)-point discrete Fourier transform \(X[k]\) is defined as: \[ X[k] = \mathcal{F}\{x[n]\}. \] Another sequence \(y[n]\) is formed as: \[ y[n] = \mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}. \] For the sequence \(x[n] = \{1, 2, 1, 3\}\), the value of \(y[0]\) is \(\_\_\_\_\).

Let \(F_1, F_2,\) and \(F_3\) be functions of \((x, y, z)\). Suppose that for every given pair of points \(A\) and \(B\) in space, the line integral: \[ \int_C \left(F_1 dx + F_2 dy + F_3 dz\right) \] evaluates to the same value along any path \(C\) that starts at \(A\) and ends at \(B\). Then which of the following is/are true?

A source transmits a symbol \(s\), taken from \(\{-4, 0, 4\}\) with equal probability, over an additive white Gaussian noise channel. The received noisy symbol \(r\) is given by \(r = s + w\), where the noise \(w\) is zero mean with variance 4 and is independent of \(s\). Using: \[ Q(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{t^2}{2}} dt, \] the optimum symbol error probability is \(\_\_\_\_\).

A continuous-time signal \(x(t) = 2 \cos(8\pi t + \pi/3)\) is sampled at a rate of 15 Hz. The sampled signal \(x_s(t)\) when passed through an LTI system with impulse response: \[ h(t) = \frac{\sin(2\pi t)}{\pi t} \cos(38\pi t - \pi/2), \] produces an output \(x_0(t)\). The expression for \(x_0(t)\) is \(\_\_\_\_\).

Consider a unity negative feedback control system with forward path gain: \[ G(s) = \frac{K}{(s+1)(s+2)(s+3)}. \] \vspace{0.5cm} \begin{center} \includegraphics[width=8cm]{37.png} \end{center} The impulse response of the closed-loop system decays faster than \(e^{-t}\) if \(\_\_\_\_\).

In the given circuit, the current \(I_x\) (in mA) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{31.png} \end{center}

As shown in the circuit, the initial voltage across the capacitor is \(10 \, {V}\), with the switch being open. The switch is then closed at \(t = 0\). The total energy dissipated in the ideal Zener diode \((V_Z = 5 \, {V})\) after the switch is closed (in mJ, rounded off to three decimal places) is \(\_\_\_\_\). \begin{center} \includegraphics[width=6cm]{35.png} \end{center}

Let \(\rho(x, y, z, t)\) and \(\mathbf{u}(x, y, z, t)\) represent density and velocity, respectively, at a point \((x, y, z)\) and time \(t\). Assume \(\frac{\partial \rho}{\partial t}\) is continuous. Let \(V\) be an arbitrary volume in space enclosed by the closed surface \(S\), and \(\mathbf{\hat{n}}\) be the outward unit normal of \(S\). Which of the following equations is/are equivalent to: \[ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = 0? \]

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is \(\_\_\_\_\).

A white Gaussian noise \(w(t)\) with zero mean and power spectral density \(\frac{N_0}{2}\), when applied to a first-order RC low-pass filter produces an output \(n(t)\). At a particular time \(t = t_k\), the variance of the random variable \(n(t_k)\) is:

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (\(T\)) dependence of free electron concentration (\(n\))?

In the feedback control system shown in the figure below, \[ G(s) = \frac{6}{s(s+1)(s+2)}. \] \vspace{0.5cm} \begin{center} \includegraphics[width=10cm]{13.png} \end{center} \(R(s)\), \(Y(s)\), and \(E(s)\) are the Laplace transforms of \(r(t)\), \(y(t)\), and \(e(t)\), respectively. If the input \(r(t)\) is a unit step function, then:

Let \(\hat{i}\) and \(\hat{j}\) be the unit vectors along \(x\) and \(y\) axes, respectively, and let \(A\) be a positive constant. Which one of the following statements is true for the vector fields: \[ \vec{F_1} = A(\hat{i}y + \hat{j}x) \quad {and} \quad \vec{F_2} = A(\hat{i}y - \hat{j}x)? \]