Recent questions in Network Solution Methods

The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\dfrac{Y(s)}{X(s)}$ is$H...

Consider a unity feedback system, as in the figure shown, with an integral compensator $\dfrac{K}{s}$ and open-loop transfer function$$G(s)=\dfrac{1}{s^{2}+3s+2}$$where $...

If the signal $x(t) = \large \frac{\sin(t)}{\pi t}$$*$$\large \frac{\sin(t)}{\pi t}$ with $*$ denoting the convolution operation, then $x(t)$ is equal to $\large\frac{\si...

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$\cos (200t) + 2\sin (500t)$...

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 ...

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...

The $z$-parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the two-port network shown is $\begin{bmatrix} 2 &-2\\-2 &2 \end{bmatrix} \\$...

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 ...

A second-order linear time-invariant system is described by the following state equations$$\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$$$$\frac{d}{dt}x_2(t)+x_2(t)=u(t)$$where $x_1(...

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as$$G(s)=\frac{K(s+2)}{s^2+2s+2}\;\...

The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i...

A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discrete-time filter with transfer function $G\left ( z\r...

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 a...

Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$?The solutions have neither maxima nor minima anywhere except at the bo...

Consider a two-port network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then $T^{-1} = T$$T^2 = T$Deter...

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2...

The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is$F(S) = \frac{1}{1+e^{-sT/2}} \\$$F(S) =\frac{1}{s(1+e^{-sT/2})} \\$$F(...

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’...

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...

The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s -2$. The number of zeroes in the right half of the $s$-plane is _________