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

The \( Z \)-parameter matrix of a two-port network relates the port voltages and port currents as follows: \[ \begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = Z \begin{bmatrix} I_1 \\ I_2 \end{bmatrix} \] The \( Z \)-parameter matrix (with each entry in Ohms) of the network shown below is _________. 

Let \( G(s) = \frac{1}{10s^2} \) be the transfer function of a second-order system. A controller \( M(s) \) is connected to the system \( G(s) \) in the configuration shown below.

Consider the following statements.

• (i) There exists no controller of the form \( M(s) = \frac{K_I}{s} \), where \( K_I \) is a positive real number, such that the closed-loop system is stable.
• (ii) There exists at least one controller of the form \( M(s) = K_p + sK_D \), where \( K_p \) and \( K_D \) are positive real numbers, such that the closed-loop system is stable.

Which one of the following options is correct?

A 4-bit weighted-resistor DAC with inputs \( b_3, b_2, b_1, \) and \( b_0 \) (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bits are logic ‘1’ and open otherwise. When the input \( b_3b_2b_1b_0 \) changes from 1110 to 1101, the magnitude of the change in the output voltage \( V_o \) (in mV, rounded off to the nearest integer) is _________. 

The function \( y(t) \) satisfies \[ t^2 y''(t) - 2t y'(t) + 2y(t) = 0, \] where \( y'(t) \) and \( y''(t) \) denote the first and second derivatives of \( y(t) \), respectively. Given \( y'(0) = 1 \) and \( y'(1) = -1 \), the maximum value of \( y(t) \) over \( [0, 1] \) is _________ (rounded off to two decimal places).