GATE EC Circuit Analysis questions

The open-loop transfer function of a unity-feedback control system is $$G(s)= \frac{K}{s^2+5s+5}$$. The value of $K$ at the breakaway point of the feedback contol system’s root-locus plot is _________

The open-loop transfer function of a unity feedback control system is given by $$G(s)= \frac{K}{s(s+2)}$$. For the peak overshoot of the closed-loop system to a unit step input to be $10 \%$, the value of $K$ is _________

The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________

The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. The steady state magnitude of the capacitor voltage $V_{c}$ (in volts) is ______

In the RLC circuit shown in the figure, the input voltage is given by $$v_i(t) = 2\cos (200t) + 4\sin (500t).$$ The output voltage $v_o(t)$ is

The diodes $D1$ and $D2$ in the figure are ideal and the capacitors are identical. The product $RC$ is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage $V_o$(in volt) at the steady state is _______

Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\;\Omega$ resistor suddenly burns out, resulting in an open circuit. The current $i(t)$ (in ampere) at $t=0^+$ is _______

The $z$-parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the two-port network shown is

In the circuit shown in the figure, transistor $M1$ is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation $\lambda$ to be zero,the small signal input pole frequency (in $kHz$) is _________

In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ____________.

In the network shown in the figure, all resistors are identical with $R = 300 \Omega$. The resistance $R_{ab}$ (in $\Omega$) of the network is __________.

The damping ratio of a series RLC circuit can be expressed as

In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.

In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.

A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is $G_c(s)=\frac{s+2}{s+4}$, the value of $RC$ is ___________.

The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is

The voltage $(ܸV_{C})$ across the capacitor (in Volts) in the network shown is ______.

In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.

Let the signal ݂$f(t) = 0$ outside the interval $[T_{1},T_{2}]$, where ܶ$T_{1}$ and ܶ$T_{2}$ are finite. Furthermore, $\mid f(t) \mid < \infty$. The region of convergence (RoC) of the signal’s bilateral Laplace transform $F(s)$ is

By performing cascading and/or summing/differencing operations using transfer function blocks $G_{1}(s )$ and $G_{2}(s),$ one CANNOT realize a transfer function of the form