List of top Questions asked in GATE Electronics and Communication Engineering

In the circuit shown, the \(n:1\) step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward-biased condition. If the input voltage (in Volts) is \(V_s(t) = 10\sin\omega t\) and the average value of load voltage \(V_L(t)\) (in Volts) is \(2.5/\pi\), the value of \(n\) is \(\_\_\_\_\). \begin{center} \includegraphics[width=5cm]{23.png} \end{center}
For the Boolean function: \[ F(A, B, C, D) = \Sigma m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15), \] the essential prime implicants are:
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}

A satellite attitude control system, as shown below, has a plant with transfer function:  $ G(s) = \frac{1}{s^2}, $ cascaded with a compensator:  $ C(s) = \frac{K(s + \alpha)}{s + 4}, $ where $ K $ and $ \alpha $ are positive real constants. In order for the closed-loop system to have poles at $ -1 \pm j\sqrt{3} $, the value of $ \alpha $ must be $\_\_\_\_\_$.

If ‘\(\rightarrow\)’ denotes increasing order of intensity, then the meaning of the words {charm} ---- {enamor} ------ {bewitch} is analogous to {bored} ----- _________ ---- {weary} . Which one of the given options is appropriate to fill the blank?

In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{62.png} \end{center}
The photocurrent of a PN junction diode solar cell is \(1 \, {mA}\). The voltage corresponding to its maximum power point is \(0.3 \, {V}\). If the thermal voltage is \(30 \, {mV}\), the reverse saturation current of the diode (in \({nA}\), rounded off to two decimal places) is \(\_\_\_\_\).
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 \(\_\_\_\_\).
An NMOS transistor operating in the linear region has \(I_{DS} = 5 \, \mu{A}\) at \(V_{DS} = 0.1 \, {V}\). Keeping \(V_{GS}\) constant, the \(V_{DS}\) is increased to \(1.5 \, {V}\). Given that: \[ \mu_n C_{ox} \frac{W}{L} = 50 \, \mu{A}/{V}^2, \] the transconductance at the new operating point (in \(\mu{A}/{V}\), 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}
Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of \(100 \, {nm}\), a fixed positive oxide charge of \(10^{-8} \, {C/cm}^2\) at the oxide-silicon interface, and a metal work function of \(4.6 \, {eV}\). Assume that the relative permittivity of the oxide is \(4\), and the absolute permittivity of free space is \(8.85 \times 10^{-14} \, {F/cm}\). If the flatband voltage is \(0 \, {V}\), the work function of the p-type silicon (in eV, rounded off to two decimal places) is \(\_\_\_\_\).
A lossless transmission line with characteristic impedance \(Z_0 = 50 \, \Omega\) is terminated with an unknown load. The magnitude of the reflection coefficient is \(|\Gamma| = 0.6\). As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in \(\Omega\)) is \(\_\_\_\_\).
Let \(X(t) = A \cos(2\pi f_0 t + \theta)\) be a random process, where amplitude \(A\) and phase \(\theta\) are independent of each other, and are uniformly distributed in the intervals \([-2, 2]\) and \([0, 2\pi]\), respectively. \(X(t)\) is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of \(X(t)\) is: \[ R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau), \] the signal-to-quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is \(\_\_\_\_\).
The radian frequency value(s) for which the discrete-time sinusoidal signal: \[ x[n] = A \cos(\Omega n + \pi/3) \] has a period of 40 is/are \(\_\_\_\_\).
Consider the matrix: \[ \begin{bmatrix} 1 & k
2 & 1 \end{bmatrix}, \] where \(k\) is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
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 \(\_\_\_\_\).
In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of \(R_1\) and the corresponding frequency of oscillation are \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{50.png} \end{center}
In the circuit shown below, the transistors \(M_1\) and \(M_2\) are biased in saturation. Their small signal transconductances are \(g_{m1}\) and \(g_{m2}\), respectively. Neglect body effect, channel length modulation, and intrinsic device capacitances. \begin{center} \includegraphics[width=6cm]{51.png} \end{center} Assuming that capacitor \(C_1\) is a short circuit for AC analysis, the exact magnitude of small signal voltage gain \(\left|\frac{v_{{out}}}{v_{{in}}}\right|\) is \(\_\_\_\_\).
Consider a system \(S\) represented in state space as: \[ \frac{dx}{dt} = \begin{bmatrix} 0 & -2
1 & -3 \end{bmatrix} x + \begin{bmatrix} 1
0 \end{bmatrix} r, \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix} x. \] Which of the state space representations given below has/have the same transfer function as that of \(S\)?
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?
The opamps in the circuit shown are ideal but have saturation voltages of \(\pm 10 \, {V}\). \begin{center} \includegraphics[width=10cm]{49.png} \end{center} Assume that the initial inductor current is \(0 \, {A}\). The input voltage (\(V_i\)) is a triangular signal with peak voltages of \(\pm 2 \, {V}\) and a time period of \(8 \, \mu {s}\). Which one of the following statements is true?
Which of the following statements is/are true for a BJT with respect to its DC current gain \(\beta\)?
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 full-scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is \(10 \, \mu {W}\). The effective number of bits (rounded off to the nearest integer) of the ADC is \(\_\_\_\_\).
Let \(z\) be a complex variable. If \(f(z) = \frac{\sin(\pi z){z^2 (z - 2)}\) and \(C\) is the circle in the complex plane with \(|z| = 3\), then:} \[ \oint_C f(z) \, dz \] is \(\_\_\_\_\).