List of top Analog Electronics Questions asked in GATE Electrical Engineering

Two passive two-port networks \( P \) and \( Q \) are connected as shown in the figure. The impedance matrix of network \( P \) is \( Z_P = \begin{bmatrix} 40 \, \Omega & 60 \, \Omega
80 \, \Omega & 100 \, \Omega \end{bmatrix} \). The admittance matrix of network \( Q \) is \( Y_Q = \begin{bmatrix} 5 \, S & -2.5 \, S
-2.5 \, S & 1 \, S \end{bmatrix} \). Let the ABCD matrix of the two-port network \( R \) in the figure be \( \begin{bmatrix} \alpha & \beta
\gamma & \delta \end{bmatrix} \). The value of \( \beta \) in \( \Omega \) is \_\_\_\_\_\_ (rounded off to 2 decimal places).
\includegraphics[width=0.5\linewidth]{48.png}

For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is \( 5 \, \text{mH} \) with their self-inductances being \( 125 \, \text{mH} \) and \( 1 \, \text{mH} \). The Thevenin's impedance \( Z_{th} \), between the terminals \( P \) and \( Q \) in \( \Omega \) is \_\_\_\_\_\_ (rounded off to 2 decimal places).
\includegraphics[width=0.5\linewidth]{49.png}

In the circuit shown, \( Z_1 = 50 \angle -90^\circ \, \Omega \) and \( Z_2 = 200 \angle -30^\circ \, \Omega \). It is supplied by a three-phase 400 V source with the phase sequence being R-Y-B. Assume the wattmeters \( W_1 \) and \( W_2 \) to be ideal. The magnitude of the difference between the readings of \( W_1 \) and \( W_2 \) in watts is \_\_\_\_\_\_ (rounded off to 2 decimal places).
\includegraphics[width=0.5\linewidth]{50.png}

Consider the complex function \( f(z) = \cos z + e^{z^2 \). The coefficient of \( z^5 \) in the Taylor series expansion of \( f(z) \) about the origin is \_\_\_\_\_ (rounded off to 1 decimal place).}

In the circuit, the present value of \( Z \) is 1. Neglecting the delay in the combinational circuit, the values of \( S \) and \( Z \), respectively, after the application of the clock will be:
\includegraphics[width=0.5\linewidth]{25.png}

To obtain the Boolean function \( F(X, Y) = XY + \overline{X \), the inputs \( P, Q, R, S \) in the figure should be:}
\includegraphics[width=0.5\linewidth]{26.png}

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step response of the original and the approximated systems are the same?
\includegraphics[width=0.5\linewidth]{22.2.png}

Simplified form of the Boolean function: \[ F(P, Q, R, S) = \overline{P}\overline{Q}R + \overline{P}QS + PQ\overline{R}S \] is:

The figure shows the single-line diagram of a 4-bus power network. Branches \( b_1, b_2, b_3 \), and \( b_4 \) have impedances \( 4z, z, 2z \), and \( 4z \) per-unit (pu), respectively, where \( z = r + jx \) with \( r>0 \) and \( x>0 \). The current drawn from each load bus (marked as arrows) is equal to \( 1 \, \text{pu} \), where \( I \neq 0 \). If the network is to operate with minimum loss, the branch that should be opened is:
\includegraphics[width=0.5\linewidth]{19.png}

For the block diagram shown in the figure, the transfer function \( \frac{C(s){R(s)} \) is:}
\includegraphics[width=0.5\linewidth]{20.png}

Consider the standard second-order system of the form: \[ \frac{\omega_n^2}{s^2 + 2\xi\omega_n s + \omega_n^2}, \] with the poles \(p\) and \(p^*\) having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below: System 1: \( \omega_n = 3 \, \text{rad/sec} \) and \( \theta = 60^\circ \). System 2: \( \omega_n = 1 \, \text{rad/sec} \) and \( \theta = 70^\circ \). Which one of the following statements is correct?
\includegraphics[width=0.5\linewidth]{22.png}

Which one of the following options represents possible voltage polarities in a single-phase two winding transformer? Here, \( V_p \) is the applied primary voltage, \( E_p \) is the induced primary voltage, \( V_s \) is the open circuit secondary voltage, and \( E_s \) is the induced secondary voltage.