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

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 \(\_\_\_\_\).

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 \(\_\_\_\_\).

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 \(\_\_\_\_\).

Which of the following statements is/are true for a BJT with respect to its DC current gain \(\beta\)?

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?

The information bit sequence \(\{1 \, 1 \, 1 \, 0 \, 1 \, 0 \, 1 \, 0 \, 1\}\) is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is \(C(x) = x^4 + x + 1\). The encoded sequence of bits 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 \(\_\_\_\_\).

A satellite attitude control system, as shown below, has a plant with transfer function: \[ G(s) = \frac{1}{s^2}, \] cascaded with a compensator: \[ C(s) = \frac{K(s + \alpha)}{s + 4}, \] \vspace{0.5cm} \begin{center} \includegraphics[width=8cm]{38.png} \end{center} 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 \(\_\_\_\_\).

A 4-bit priority encoder has inputs \( D_3, D_2, D_1, \) and \( D_0 \) in descending order of priority. The two-bit output \( AB \) is generated as 00, 01, 10, and 11 corresponding to inputs \( D_3, D_2, D_1, \) and \( D_0 \), respectively. The Boolean expression of the output bit \( B \) is \(\_\_\_\_\).

Consider the Earth to be a perfect sphere of radius \(R\). Then the surface area of the region, enclosed by the \(60^\circ N\) latitude circle, that contains the north pole in its interior is \(\_\_\_\_\).

A uniform plane wave with electric field: \[ \vec{E}(x) = A_y \hat{a}_y e^{-\frac{j2\pi x}{3}} \, {V/m}, \] is traveling in the air (relative permittivity, \(\epsilon_r = 1\), and relative permeability, \(\mu_r = 1\)) in the \(+x\) direction. It is incident normally on an ideal electric conductor (conductivity, \(\sigma = \infty\)) at \(x = 0\). The position of the first null of the total magnetic field in the air (measured from \(x = 0\), in meters) is \(\_\_\_\_\).

In the circuit given below, the switch \(S\) was kept open for a sufficiently long time and is closed at time \(t = 0\). The time constant (in seconds) of the circuit for \(t>0\) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{32.png} \end{center}

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is \(\_\_\_\_\).

A digital communication system transmits through a noiseless bandlimited channel \([-W, W]\). The received signal \(z(t)\) at the output of the receiving filter is given by: \[ z(t) = \sum_n b[n] x(t - nT), \] where \(b[n]\) are the symbols and \(x(t)\) is the overall system response to a single symbol. The received signal is sampled at \(t = mT\). The Fourier transform of \(x(t)\) is \(X(f)\). The Nyquist condition that \(X(f)\) must satisfy for zero intersymbol interference at the receiver is: