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Hot questions in Network Solution Methods
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1
GATE ECE 2020 | Question: 37
Using the incremental low frequency small-signal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$
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2
GATE ECE 2020 | Question: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$
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GATE ECE 2020 | Question: 30
For the given circuit, which one of the following is correct state equation? ...
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4
GATE ECE 2020 | Question: 15
In the given circuit, the two-port network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.
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GATE ECE 2020 | Question: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle -96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle-23.63^{\circ}A$
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GATE ECE 2020 | Question: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.$ The value of $K$, for which the system is marginally stable, is ___________.
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GATE ECE 2020 | Question: 16
The current in the $\text{RL}$-circuit shown below is $i\left ( t \right )=10\cos\left ( 5t-\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.
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8
GATE ECE 2020 | Question: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
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9
GATE ECE 2020 | Question: 55
Consider the following closed loop control system where $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is $0.1$, then the value of $K$ is ______________.
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10
GATE ECE 2020 | Question: 49
A system with transfer function $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5 \cos3t$. The steady state output of the system is $\dfrac{1}{\sqrt{10}}\cos\left ( 3t-1.892 \right )$. The value of $a$ is _______.
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11
GATE ECE 2020 | Question: 53
The transfer function of a stable discrete-time $\text{LTI}$ system is $H\left ( z \right )=\dfrac{K\left ( z-\alpha \right )}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\mid \alpha \mid > 1$, for which the magnitude response of the system is constant over all frequencies, is ___________.
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12
GATE ECE 2019 | Question: 5
Let $Y(s)$ be the unit-step response of a causal system having a transfer function $G(s)= \dfrac{3-s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)$ $u(t)$
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13
GATE ECE 2019 | Question: 4
Consider the two-port resistive network shown in the figure. When an excitation of $5\: V$ is applied across Port $1$, and Port $2$ is shorted, the current through the short circuit at Port $2$ is measured to be $1\: A$ ... ), what is the current through the short circuit at Port $1?$ $0.5\: A$ $1\: A$ $2\: A$ $2.5\: A$
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14
GATE ECE 2019 | Question: 31
Consider a causal second-order system with the transfer function $G(s)=\dfrac{1}{1+2s+s^{2}}$ with a unit-step $R(s)=\dfrac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its ... value $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
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15
GATE ECE 2019 | Question: 30
In the circuit shown, if $v(t)=2 \sin(1000\: t)$ volts, $R=1\:k \Omega$ and $C=1\:\mu F,$ then the steady-state current $i(t)$, milliamperes (mA), is $\sin(1000\: t)+ \cos(1000\: t)$ $2 \sin(1000\: t) +2 \cos(1000\: t)$ $3 \sin(1000\: t) + \cos(1000\: t)$ $\sin(1000\: t) +3 \cos(1000\: t)$
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GATE ECE 2019 | Question: 32
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 $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
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17
GATE ECE 2019 | Question: 42
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 $K>0.$ The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal places).
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18
GATE ECE 2015 Set 2 | Question: 19
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 $G_{1}(s)G_{2}(s) \\$ $\dfrac{G_{1}(s)}{G_{2}(s)} \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)} + G_{2}(s)\right) \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)} - G_{2}(s)\right)$
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19
GATE ECE 2016 Set 3 | Question: 42
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 _________
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20
GATE ECE 2016 Set 3 | Question: 47
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 $x_1(t)$ and $x_2(t)$ are the two ... , then the system is controllable but not observable observable but not controllable both controllable and observable neither controllable nor observable
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21
GATE ECE 2015 Set 3 | Question: 31
The $ABCD$ parameters of the following $2$-port network are $\begin{bmatrix}3.5 + j2 & 20.5 \\ 20.5 & 3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}3.5 +j2 & 30.5 \\ 0.5&3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}10 &2+j0 \\2+j0 &10 \end{bmatrix} \\$ $\begin{bmatrix}7+j4 &0.5 \\ 30.5&7-j4 \end{bmatrix} $
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22
GATE ECE 2016 Set 3 | Question: 13
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 _______
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23
GATE ECE 2016 Set 3 | Question: 32
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 _______
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24
GATE ECE 2015 Set 3 | Question: 14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is a modulo-$5$ binary up counter a modulo-$6$ binary down counter a modulo-$5$ binary down counter a modulo-$6$ binary up counter
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25
GATE ECE 2015 Set 3 | Question: 6
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $a-b$ is _______.
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26
GATE ECE 2015 Set 3 | Question: 46
The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steady-state position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.
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27
GATE ECE 2016 Set 1 | Question: 30
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is $F(S) = \frac{1}{1+e^{-sT/2}} \\$ $F(S) =\frac{1}{s(1+e^{-sT/2})} \\$ $F(S) = \frac{1}{s(1-e^{-sT})} \\$ $F(S) = \frac{1}{1-e^{-sT}}$
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28
GATE ECE 2015 Set 2 | Question: 17
Let the signal ݂$f(t) = 0$ outside the interval $[T_{1},T_{2}]$, where ܶ$T_{1}$ and ܶ$T_{2}$ are finite. Furthermore, $\mid f(t) \mid < \infty$ ... ݆$j\Omega$ axis a parallel strip not containing the ݆$j\Omega$ axis the entire $s$- plane a half plane containing the ݆$j\Omega$ axis
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29
GATE ECE 2015 Set 2 | Question: 48
The transfer function of a mass-spring-damper system is given by $G(S) = \dfrac{1}{Ms^{2}+Bs+K}$ ... The unit step response of the system approaches a steady state value of ________.
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30
GATE ECE 2015 Set 2 | Question: 1
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 $\dfrac{a-b}{s} \\$ $\dfrac{e^{s}(a-b)}{s} \\$ $\dfrac{e^{-as}-e^{-bs}}{s} \\$ $\dfrac{e^{s(a-b)}}{s}$
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31
GATE ECE 2015 Set 2 | Question: 45
Let $x(t) = \alpha s(t) + s(-t)$ with $s(t) = \beta e^{-4t}u(t),$ where $u(t)$ is unit step function. If the bilateral Laplace transform of $x(t)$ is $X(s) = \dfrac{16}{s^{2} – 16}\:\: -4 < Re\{s\}<4;$ then the value of $\beta$ is ______.
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32
GATE ECE 2016 Set 3 | Question: 7
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 $\large\frac{\sin(t)}{\pi t}$ $\large\frac{\sin(2t)}{2\pi t}$ $\large\frac{2\sin(t)}{\pi t}$ $\bigg(\frac{\sin(t)}{\pi t}\bigg)^2$
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GATE ECE 2016 Set 3 | Question: 9
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 $\cos (200t) + 2\sin (500t)$ $2\cos (200t) + 4\sin (500t)$ $\sin (200t) + 2\cos (500t)$ $2\sin (200t) + 4\cos (500t)$
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34
GATE ECE 2015 Set 2 | Question: 7
In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.
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35
GATE ECE 2016 Set 1 | Question: 46
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 _________
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36
GATE ECE 2015 Set 1 | Question: 32
In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.
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37
GATE ECE 2015 Set 3 | Question: 21
The transfer function of a first-order controller is given as $G_{C}(s) = \dfrac{K(s+a)}{s+b}$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is $a<b$ $a>b$ $K<ab$ $K>ab$
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38
GATE ECE 2016 Set 2 | Question: 32
A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ ... sampled at $2$ $Hz$, is identical at the sampling instants to the impulse response of the discrete time-filter. The value of $k$ is _________
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39
GATE ECE 2016 Set 1 | Question: 4
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 boundaries. The solutions are not separable in the coordinates. The solutions are not continuous. The solutions are not dependent on the boundary conditions.
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40
GATE ECE 2016 Set 3 | Question: 34
The $z$-parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the two-port network shown is $\begin{bmatrix} 2 &-2\\-2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 2 &2\\2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 9 &-3\\6 &9 \end{bmatrix} \\$ $\begin{bmatrix} 9 &3\\6 &9 \end{bmatrix}$
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