GATE2019 EC: 55
In the circuit shown, $V_{1}=0$ and $V_{2}=V_{dd}.$ The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of $I_{out}$ is _________ $mA$ (rounded off to $1$ decimal place).
edited Dec 26, 2019 in Others by Lakshman Patel RJIT (190 points)
numerical-answers
In the circuit shown, the threshold voltages of the $pMOS\:\: (|V_{tp}|)$ and $nMOS\:\: (V_{tn})$ transistors are both equal to $1\:V.$ All the transistors have the same output resistance $r_{ds}$ of $6\:M\Omega.$ The other parameters ... unit area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is ______ (rounded off to $1$ decimal place).
A CMOS inverter, designed to have a mid-point voltage $V_{1}$ equal to half of $V_{dd}.$ as shown in the figure, has the following parameters: $V_{dd}=3V$ $\mu_{n} C_{ox}=100\: \mu A/V^{2}; V_{tn}=0.7\:V $ for $\text{nMOS}$ ... ration of $\left(\frac{W}{L}\right)_{n}$ to $\left(\frac{W}{L}\right)_{p}$ is equal to _______ (rounded off to $3$ decimal places).
In the circuit shown. $V_{s}$ is a $10\:V$ square wave of period, $T=4\: ms$ with $R=500\: \Omega$ and $C= 10\:\mu F.$ The capacitor is initially uncharged at $t=0,$ and the diode is assumed to be ideal. The voltage across the capacitor $(V_{c})$ at $3\:ms$ is equal to _____ volts (rounded off to one decimal place)
A rectangular waveguide of width $w$ and height $h$ has cut-off frequencies for $TE_{10}$ and $TE_{11}$ modes in the ration $1:2$ . The aspect ratio $w/h$, rounded off to two decimal places , is _______.
Consider a long-channel MOSFET with a channel length $1\:\mu m$ and width $10\: \mu m.$ The device parameters are acceptor concentration $N_{A}=5 \times 10^{16}\: cm^{-3},$ electron mobility $\mu_{n}=800\: cm^{2}/V-s,$ ... $mA$ (rounded off to two decimal places.). $[\varepsilon_{0}=8.854 \times 10^{-14}F/cm, \varepsilon_{si} =11.9]$
In an ideal $pn$ junction with an ideality factor of $1$ at $T=300\:K,$ the magnitude of the reverse-bias voltage required to reach $75\%$ of its reverse saturation current, rounded off to $2$ decimal places, is ______ $mV.$ $[k=1.38 \times 10^{-23} JK^{-1}, h=6.625 \times 10^{-34} J-s, q=1.602 \times 10^{-19}C]$
A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surface has a $100\: nm$ of loss-less Silicon dioxide layer that reflects one-fourth of the ... the bandgap is $0.66\: eV,$ the thickness of the Germanium layer, rounded off to $3$ decimal places, is ________ $\mu m.$
A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is independent of ... the probability of error $Pr[ \hat{X} \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is _________.
A voice signal $m(t)$ is in the frequency range $5\:kHz$ to $15\:kHz$. The signal is amplitude-modulated to generated an AM signal $f(t)=A\left(1+m(t)\right)\cos 2\pi f_{c}t,$ where $f_{c}=600\: kHz.$ The AM signal $f(t)$ ... bits required for the encoding. The rate, in Megabits per second (rounded off to $2$ decimal places), of the resulting stream of coded bits is ________ Mbps.
Let a random process $Y(t)$ be described as $Y(t)=h(t) \ast X(t)+Z(t),$ where $X(t)$ is a white noise process with power spectral density $S_{x}(f)=5$W/Hz. The filter $h(t)$ has a magnitude response given by $ \mid H(f) \mid =0.5$ ... , with power spectral density as shown in the figure. The power in $Y(t),$ in watts, is equal to _________ $W$ (rounded off to two decimal places).
Let $h[n]$ be a length - $7$ discrete-time finite impulse response filter, given by $h[0]=4, \quad h[1]=3,\quad h[2]=2,\quad h[3]=1,$ $\quad h[-1]=-3, \quad h[-2]=-2, \quad h[-3]=-1,$ and $h[n]$ is zero for $|n|\geq4.$ ... $g[n],$ respectively. For the filter that minimizes $E(h,g),$ the value of $10g[-1]+g[1],$ rounded off to $2$ decimal places, is __________.
Consider the homogenous ordinary differential equation $x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$ with $y(x)$ as a general solution. Given that $y(1)=1 \quad \text{and} \quad y(2)=14$ the value of $y(1.5),$ rounded off to two decimal places, is________.
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).
The $\text{RC}$ circuit shown below has a variable resistance $R(t)$ given by the following expression: $R(t)=R_{0}\left(1-\frac{t}{T}\right) \text{for} \:\: 0 \leq t < T$ where $R_{0}=1\: \Omega,$ and $C=1\:F.$ ... at time $t=0$ is $1\: A,$ then the current $I(t)$, in amperes, at time $t=T/2$ is __________ (rounded off to $2$ decimal places).
In the circuits shown the threshold voltage of each $\text{nMOS}$ transistor is $0.6\:V.$ Ignoring the effect of channel length modulation and body bias. the values of $\text{Vout}1$ and $\text{Vout} 2,$ respectively, in volts, are $1.8$ and $1.2$ $2.4$ and $2.4$ $1.8$ and $2.4$ $2.4$ and $1.2$
The state transition diagram for the circuit shown is
In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are $20\:V$ and $60\:mA$, respectively. The values of $R_{1}$ and $R_{L}$ are $200\: \Omega$ and $1\:k\Omega,$ respectively. What is the range of $V_{i}$ that will maintain the Zener diode in the 'on' state? $22\: V$ to $34\: V$ $24\: V$ to $36\: V$ $18\: V$ to $24\: V$ $20\: V$ to $28\: V$
Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the system, and $y(t)$ is its output. Let $B=[0\quad0\quad1]^{T}$ ... $A=\begin{bmatrix} 0&1&0\\ 0&0&1\\-3&-2&-1 \\\end{bmatrix} \text{and} \quad C=\begin{bmatrix} 0&0&1 \end{bmatrix}$
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 $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
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 steady-state value $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
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 $\sin(1000\: t)+ \cos(1000\: t)$ $2 \sin(1000\: t) +2 \cos(1000\: t)$ $3 \sin(1000\: t) + \cos(1000\: t)$ $\sin(1000\: t) +3 \cos(1000\: t)$
It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form $x[n]= c_{1}exp\left(-\dfrac{j\pi n}{2}\right)+c_{2}\left(\dfrac{j\pi n}{2}\right),$ where $c_{1}$ and $c_{2}$ ... $n$, when $x[n]$ is as given above ? $a=1,b=1$ $a=0,b=-1$ $a=-1,b=1$ $a=0,b=1$
Consider a six-point decimation-in-time Fast Fourier Transform $(FFT)$ algorithm, for which the signal-flow graph corresponding to $X[1]$ is shown in the figure. Let $W_{6}=exp\left(-\:\dfrac{j2\pi}{6}\right).$ In the figure, what should be the values of the coefficients $a_{1},a_{2},a_{3}$ in terms ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
Consider the line integral $\int_{c} (xdy-ydx)$ the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $R$ shown in the figure below. The region $R$ is the area enclosed by the union of a $2 \times 3$ rectangle and ... -circle of radius $1$. The line integral evaluates to $6+ \dfrac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$
The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$ is $k(\omega)= (1/c) \sqrt{\omega^{2}-\omega_{\circ}^{2}}$ where the speed of light $c= 2 \times 10^{8}\: m/s$ and $\omega_{\circ}$ ... $2 \times 10^{8}\: m/s$ $3 \times 10^{8}\: m/s$ $4.5 \times 10^{8}\: m/s$
Two identical copper wires $W1$ and $W2$ placed in parallel as shown in the figure, carry currents $I$ and $2I$, respectively, in opposite directions. If the two wires are separated by a distance of $4r$, then the magnitude of the magnetic field $\overrightarrow{B}$ between the wires at a distance $r$ ... $\frac{5\mu_{0}I}{6\pi r}$ $\frac{\mu_{0}^{2}I^{2}}{2\pi r^{2}}$
The quantum efficiency $(\eta)$ and responsivity $(R)$ at wavelength $\lambda \:(\text{in}\: \mu m)$ in a p-i-n photodetector are related by $R= \frac{\eta \times \lambda}{1.24}$ $R= \frac{\lambda}{\eta \times 1.24}$ $R= \frac{1.24 \times\lambda}{\eta}$ $R= \frac{1.24}{\eta \times \lambda}$
A single bit, equally likely to be $0$ and $1$, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density $N_{0}/2.$ Binary signaling with $0 \mapsto p(t),$ and $1 \mapsto q(t),$ is used for the transmission, along with an optimal ... $E$ would we obtain the $\textbf{same}$ bit-error probability $P_{b}$? $0$ $1$ $2$ $3$
Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $ \mid f'(x) \mid \leq 2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[-2,2]?$ $f(x)\leq \frac{1}{2} \mid x+1 \mid$ $f(x)\leq 2 \mid x+1 \mid $ $f(x)\leq \frac{1}{2} \mid x \mid$ $f(x)\leq 2 \mid x \mid$
In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is $12\:kHz$. The frequency of the signal at $Q_{2}$ is _______ kHz.
In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50\: \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place).
Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ________ $\%.$
The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the $PM$ signal $\varphi(t)=\cos(2\pi f_{c}t+ k\:\: m(t)).$ The time $t$ on the $x-$ axis in the figure is in milliseconds. If the carrier ... the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _________ (rounded off to $2$ decimal places).
Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundamental time period, in seconds, is __________.
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by $F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.
The value of the integral $\int_{0}^{\pi} \int_{y}^{\pi}\dfrac{\sin x}{x}dx\: dy ,$ is equal to __________.
If $X$ and $Y$ are random variables such that $E\left[2X+Y\right]=0$ and $E\left[X+2Y\right]=33$, then $E\left[X\right]+E\left[Y\right]=$___________.
The number of distinct eigenvalues of the matrix $A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$ is equal to ____________.
The value of the contour integral $\frac{1}{2\pi j} \oint\left(z+\frac{1}{z}\right)^{2}dz$ evaluated over the unit circle $\mid z \mid=1$ is_______.
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