Questions by go_editor / GO Electronics

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41

GATE ECE 2020 | Question: 31
A one-sided abrupt $pn$ junction diode has a depletion capacitance $C_{D}$ of $50$ $\text{pF}$ at a reverse bias of $0.2 V$. The plot of $1/C^{2}_{D}$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is ___________ $\times 10^{20}F^{-2}V^{-1}$. $-5.7$ $-3.8$ $-1.2$ $-0.4$

A one-sided abrupt $pn$ junction diode has a depletion capacitance $C_{D}$ of $50$ $\text{pF}$ at a reverse bias of $0.2 V$. The plot of $1/C^{2}_{D}$ versus the applied ...

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asked Feb 13, 2020

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42

GATE ECE 2020 | Question: 32
The band diagram of a $p$-type semiconductor with a band-gap of $1$ eV is shown. Using this semiconductor, a $\text{MOS}$ capacitor having $V_{TH}$ of $-0.16 V$, ${C}'_{ox}$ of $100\:nF/cm^{2}$ and a metal work function of $3.87 \: eV$ is fabricated. There is no ... $1.70\times 10^{-8}$ $0.52\times 10^{-8}$ $1.41\times 10^{-8}$ $0.93\times 10^{-8}$

The band diagram of a $p$-type semiconductor with a band-gap of $1$ eV is shown. Using this semiconductor, a $\text{MOS}$ capacitor having $V_{TH}$ of $-0.16 V$, ${C}'_{o...

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asked Feb 13, 2020

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43

GATE ECE 2020 | Question: 33
The base of an $\text{npn BJT T1}$ has a linear doping profile $N_{B}\left ( x \right )$ as shown below. The base of another $\text{npn BJT T2}$ has a uniform doping $N_{B}$ of $10^{17}cm^{-3}$. All other parameters are identical for both the ... $\text{T1}$. approximately $2.5$ times that of $\text{T1}$. approximately $0.7$ times that of $\text{T1}$.

The base of an $\text{npn BJT T1}$ has a linear doping profile $N_{B}\left ( x \right )$ as shown below. The base of another $\text{npn BJT T2}$ has a uniform doping $N_...

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asked Feb 13, 2020

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44

GATE ECE 2020 | Question: 34
A $pn$ junction solar cell of area $1.0\:cm^{2}$, illuminated uniformly with $100\:mW\:cm^{-2}$, has the following parameters: Efficiency $= 15\%$, open circuit voltage $= 0.7\:V$, fill factor $= 0.8$, and thickness $=200 \mu m$ ... $0.84\times 10^{19}.$ $5.57\times 10^{19}.$ $1.04\times 10^{19}.$ $83.60\times 10^{19}.$

A $pn$ junction solar cell of area $1.0\:cm^{2}$, illuminated uniformly with $100\:mW\:cm^{-2}$, has the following parameters: Efficiency $= 15\%$, open circuit voltage $...

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asked Feb 13, 2020

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45

GATE ECE 2020 | Question: 35
For the $\text{BJT}$ in the amplifier shown below, $V_{BE}=0.7V,\:kT/q=26\:mV$. Assume that $\text{BJT}$ output resistance $(r_{o})$ is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The ... The low frequency voltage gain $v_{o}/v_{i}$ of the amplifier is $-89.42$ $-128.21$ $-178.85$ $-256.42$

For the $\text{BJT}$ in the amplifier shown below, $V_{BE}=0.7V,\:kT/q=26\:mV$. Assume that $\text{BJT}$ output resistance $(r_{o})$ is very high and the base current is ...

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asked Feb 13, 2020

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46

GATE ECE 2020 | Question: 36
An enhancement $\text{MOSFET}$ of threshold voltage $3\:V$ is being used in the sample and hold circuit given below. Assume that the substrate of the $\text{MOS}$ device is connected to $-10\:V$. If the input voltage $V_{1}$ lies between $\pm 10\:V,$ the minimum and the maximum ... $\text{10 V and -10 V}$. $\text{13 V and -7 V}$. $\text{10 V and -13 V}$.

An enhancement $\text{MOSFET}$ of threshold voltage $3\:V$ is being used in the sample and hold circuit given below. Assume that the substrate of the $\text{MOS}$ device ...

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asked Feb 13, 2020

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47

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 $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$

Using the incremental low frequency small-signal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{d...

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asked Feb 13, 2020

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48

GATE ECE 2020 | Question: 38
$P, Q$, and $R$ are the decimal integers corresponding to the $4$-bit binary number $1100$ considered in signed magnitude, $1$’s complement, and $2$’s complement representations, respectively. The $6$-bit $2$’s complement representation of $(P+Q+R)$ is $110101$ $110010$ $111101$ $111001$

$P, Q$, and $R$ are the decimal integers corresponding to the $4$-bit binary number $1100$ considered in signed magnitude, $1$’s complement, and $2$’s complement repr...

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asked Feb 13, 2020

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49

GATE ECE 2020 | Question: 39
The state diagram of a sequence detector is shown below. State $S_{0}$ is the initial state of the sequence detector. If the output is $1$, then the sequence $01010$ is detected. the sequence $01011$ is detected. the sequence $01110$ is detected. the sequence $01001$ is detected.

The state diagram of a sequence detector is shown below. State $S_{0}$ is the initial state of the sequence detector. If the output is $1$, then the sequence $01010$ is d...

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asked Feb 13, 2020

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50

GATE ECE 2020 | Question: 40
The characteristic equation of a system is $s^{3}+3s^{2}+\left ( K+2 \right )s+3K=0.$ In the root locus plot for the given system, as $K$ varies from $0$ to $\infty$, the break-away or break-in points(s) lie within $(-1, 0)$ $(-2, -1)$ $(-3, -2)$ $(-\infty, -3)$

The characteristic equation of a system is $$s^{3}+3s^{2}+\left ( K+2 \right )s+3K=0.$$ In the root locus plot for the given system, as $K$ varies from $0$ to $\infty$, t...

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asked Feb 13, 2020

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51

GATE ECE 2020 | Question: 41
The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $-3$ dB cut-off frequency of the circuit in Hz is $14.92$ $34.46$ $59.68$ $79.58$

The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $-3$ dB cut-off frequency of the circuit in Hz is$14.92$$34.46$$59.68$$79.5...

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asked Feb 13, 2020

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52

GATE ECE 2020 | Question: 42
For the modulated signal $x\left ( t \right )=m\left ( t \right )\cos\left ( 2\pi f_{c}t \right )$, the message signal $m\left ( t \right )=4\cos\left ( 1000\pi t \right )$ and the carrier frequency $f_{c}$ is $1\: MHz$. The signal $x(t)$ is passed ... $\cos\left ( 920\pi t \right )$ $\cos\left ( 1000\pi t \right )$ $\cos\left ( 540\pi t \right )$

For the modulated signal $x\left ( t \right )=m\left ( t \right )\cos\left ( 2\pi f_{c}t \right )$, the message signal $m\left ( t \right )=4\cos\left ( 1000\pi t \right ...

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asked Feb 13, 2020

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53

GATE ECE 2020 | Question: 43
For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A vertical infinitesimally small electric dipole $\left (\delta l \ll \lambda \right )$ ... field radiation pattern occurs at $\theta =60^{\circ}$, is $\lambda$ $0.5\lambda$ $0.25\lambda$ $0.75\lambda$

For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A...

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asked Feb 13, 2020

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54

GATE ECE 2020 | Question: 44
In the voltage regulator shown below, $V_{1}$ is the unregulated imput at $15\:V$. Assume $V_{BE}=0.7\:V$ and the base current is negligible for both the $\text{BJTs}$. If the regulated output $V_{O}$ is $9\:V$, the value of $R_{2}$ is ___________$\Omega$

In the voltage regulator shown below, $V_{1}$ is the unregulated imput at $15\:V$. Assume $V_{BE}=0.7\:V$ and the base current is negligible for both the $\text{BJTs}$. I...

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asked Feb 13, 2020

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55

GATE ECE 2020 | Question: 45
The magnetic field of a uniform plane wave in vacuum is given by $\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3x-y-z\right ).$ The value of $b$ is ___________.

The magnetic field of a uniform plane wave in vacuum is given by $$\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+...

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asked Feb 13, 2020

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56

GATE ECE 2020 | Question: 46
For a $2$-port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, is __________.

For a $2$-port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, i...

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asked Feb 13, 2020

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57

GATE ECE 2020 | Question: 47
$S_{PM}(t)$ and $S_{FM}(t)$ as defined below, are the phase modulated and the frequency modlated waveforms, respectively, corresponding to the message signal $m(t)$ ... $S_{PM}(t)$ and $S_{FM}(t)$ are same, then the value of the ratio $\dfrac{K_{p}}{K_{f}}$ is ________ seconds.

$S_{PM}(t)$ and $S_{FM}(t)$ as defined below, are the phase modulated and the frequency modlated waveforms, respectively, corresponding to the message signal $m(t)$ shown...

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asked Feb 13, 2020

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58

GATE ECE 2020 | Question: 48
In a digital communication system, a symbol $S$ randomly chosen from the set $\left \{ s_{1},s_{2},s_{3},s_{4} \right \}$ is transmitted. It is given that $s_{1}=-3,s_{2}=-1,s_{3}=+1$ and $s_{4}=+2$. The received ... decoding when the transmitted symbol $S=s_{i}$. The index $i$ for which the conditional symbol error probability $P_{i}$ is the highest is ___________.

In a digital communication system, a symbol $S$ randomly chosen from the set $\left \{ s_{1},s_{2},s_{3},s_{4} \right \}$ is transmitted. It is given that $s_{1}=-3,s_{2}...

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asked Feb 13, 2020

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59

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 _______.

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 ou...

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asked Feb 13, 2020

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60

GATE ECE 2020 | Question: 50
For the components in the sequential circuit shown below, $t_{pd}$ is the propagation delay, $t_{\text{setup}}$ is the setup-time, and $t_{\text{hold}}$ is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is _________$\text{MHz}$.

For the components in the sequential circuit shown below, $t_{pd}$ is the propagation delay, $t_{\text{setup}}$ is the setup-time, and $t_{\text{hold}}$ is the hold time....

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asked Feb 13, 2020

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61

GATE ECE 2020 | Question: 51
For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.

For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.

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asked Feb 13, 2020

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62

GATE ECE 2020 | Question: 52
$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (rounded off to two decimal places) is ____________

$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (round...

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asked Feb 13, 2020

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63

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 ___________.

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 nu...

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asked Feb 13, 2020

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64

GATE ECE 2020 | Question: 54
$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.

$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \r...

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asked Feb 13, 2020

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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 ______________.

Consider the following closed loop control systemwhere $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady s...

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asked Feb 13, 2020