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121
GATE ECE 2000 | Question 2.18
A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ ... $\omega_{o} \phi\left(\omega_{o}\right)_{1} \int_{-\infty}^{\omega_{\infty}} \phi(\lambda) d \lambda$
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122
GATE ECE 2000 | Question 2.19
A system described by the transfer function $\mathrm{H}(s)=\frac{1}{s^{3}+\alpha s^{2}+k s+3}$ is stable. The constraints on $\alpha$ and $k$ are $\alpha>0, \alpha k<3$ $\alpha>0, \alpha k>3$ $\alpha<0, \alpha k>0$ $\alpha>0, \alpha k<0$
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123
GATE ECE 2000 | Question 2.20
In an $\text{FM}$ system, a carrier of $100 \mathrm{MHz}$ is modulated by a sinusoidal signal of $5 \mathrm{kHz}$. The bandwidth by Carson's approximation is $1 \mathrm{MHz}$. If $y(t)=(\text { modulated waveform })^{3}$, then by using Carson's approximation, ... $1 \mathrm{MHz}, 15 \mathrm{kHz}$ $3 \mathrm{MHz}, 15 \mathrm{kHz}$ $1 \mathrm{MHz}, 5 \mathrm{kHz}$
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124
GATE ECE 2000 | Question 2.21
A uniform plane wave in air impinges at $45^{\circ}$ angle on a lossless dielectric material with dielectric constant $\varepsilon_{r}$. The transmitted wave propagates in a $30^{\circ}$ direction with respect to the normal. The value of $\varepsilon_{r}$ is $1.5$ $\sqrt{1.5}$ $2$ $\sqrt{2}$
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125
GATE ECE 2000 | Question 2.22
For an $8$feet $(2.4 \mathrm{~m})$ parabolic dish antenna operating at $4 \mathrm{GHz}$, the minimum distance required for far field measurement is closest to $7.5 \mathrm{~cm}$ $15 \mathrm{~cm}$ $15 \mathrm{~m}$ $150 \mathrm{~m}$
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126
GATE ECE 2000 | Question 2.23
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is $2 \mathrm{~dB}$ $5 \mathrm{~dB}$ $8 \mathrm{~dB}$ $12 \mathrm{~dB}$
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127
GATE ECE 2000 | Question 2.24
A rectangular waveguide has dimensions $1 \mathrm{~cm} \times 0.5 \mathrm{~cm}$. Its cut-off frequency is $5 \mathrm{GHz}$ $10 \mathrm{GHz}$ $15 \mathrm{GHz}$ $20 \mathrm{GHz}$
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128
GATE ECE 2000 | Question 2.25
Two coaxial cables $1$ and $2$ are filled with different dielectric constants $\varepsilon_{r 1}$ and $\varepsilon_{r 2}$ respectively. The ratio of the wavelengths in the two cables, $\left(\lambda_{1} / \lambda_{2}\right)$ ... $\varepsilon_{r 1} / \varepsilon_{r 2}$ $\varepsilon_{r 2} / \varepsilon_{r 1}$
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129
GATE ECE 2000 | Question 3
For the circuit in given figure, Find the Thevenin equivalent of the sub circuit faced by the capacitor across the terminals $a, b$. Find $v_{c}(t), t>0$, given $v_{c}(0)=0$. Find $i(t), t>0$
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130
GATE ECE 2000 | Question 4
For the given circuit, which is in steady state Find the frequency $\omega_{\mathrm{o}}$ at which the magnitude of the impedance across terminals $a, b$ reaches a maximum. Find the impedance across $a, b$ at the frequency $\omega_{0}$. If $v_{\mathrm{s}}(t)=\mathrm{V} \sin \left(\omega_{\mathrm{o}} t\right)$, find $i_{\mathrm{L}}(t), i_{\mathrm{R}}(t)$
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131
GATE ECE 2000 | Question 5
For the given circuit, write the state equations using $v_{c}$ and $i_{\mathrm{L}}$ as state variables.
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132
GATE ECE 2000 | Question 6
The network $\mathrm{N}$ in given figure consists only of two elements: a resistor of $1 \Omega$ and an inductor of $\text{L}$ Henry. A $5 \mathrm{~V}$ source is connected at the input at $t=0$ seconds. The inductor current is ... transfer function of the network. Find $\text{L}$, and draw the configuration of the network. Find the impulse response of the network.
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133
GATE ECE 2000 | Question 7
For the linear, time-invariant system whose block diagram is shown in figure with input $x(t)$ and output $y(t)$, Find the transfer function. For the step response of the system [i.e. find $y$ $(t)$ when $x(t)$ is a unit step function and the initial conditions are zero.] Find $y(t)$, if $x(t)$ is as shown in figure and the initial conditions are zero.
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134
GATE ECE 2000 | Question 8
A certain linear, time-invariant system has the state and output representation shown below: \[ \left(\begin{array}{l} \dot{x}_{1} \\ \dot{x}_{2} \end{array}\right)=\left(\begin{array}{rr} -2 & 1 \\ 0 & -3 \end{array}\right)\left(\begin{array}{l} x_{1} \ ... conditions $x_{1}\left(0_{+}\right)$and $x_{2}\left(0_{+}\right)$such that $y(t)=A e^{-2 t}$ for $t>0$.
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135
GATE ECE 2000 | Question 9
The block diagram of a feedback system is shown in the figure. Find the closed loop transfer function. Find the minimum value of $G$ for which the step response of the system would exhibit an overshoot, as shown in figure. For G equal to twice this minimum value, find the time period $T$ indicated in the figure.
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136
GATE ECE 2000 | Question 10
(a) For given figure, Plot $v_{o}$ under steady state conditions, with and without $C$. Assume that the diode is ideal. (b) Design a circuit using two ideal diodes, one resistor and two voltage sources that would convert the input voltage of figure is to the output voltage of fourth figure. The resistor value need not be specified.
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137
GATE ECE 2000 | Question 11
For the amplifier of given figure, $I_{C}=1.3 \mathrm{~mA}$, $R_{C}=2 \mathrm{k} \Omega, R_{\mathrm{C}}=500 \Omega, \mathrm{V}_{\mathrm{T}}=\mathrm{T} / q=26 \mathrm{mV}, \beta=100$ ... the approximate $\mathrm{A}_{v}$, if $\mathrm{C}_{c}$ is removed ? What will $v_{o}$ be if $\mathrm{C}_{b}$ is short circuited?
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138
GATE ECE 2000 | Question 12
For a feedback amplifier, the open loop transfer function has three poles at $100 k \mathrm{rad} / \mathrm{s}, 1 \mathrm{M} \mathrm{rad} / \mathrm{s}$ and $10 \mathrm{M} \mathrm{rad} / \mathrm{s}$. The low frequency open loop gain is $1000$ and the feedback factor $(\beta)$ is $1$. Use Bode plots to determine the phase margin of the amplifier. Is the amplifier stable?
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139
GATE ECE 2000 | Question 13
The figure shows a common base amplifier. (a) Write expressions for the time-constants associated with the capacitors, $C_{B}$ and $C_{S}$. (b) What is the approximate lower cut-off frequency of the amplifier?
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140
GATE ECE 2000 | Question 14
For the $\text{CMOS}$ monostable multivibrator of given figure, $\mathrm{R}=50 \mathrm{~kW}, \mathrm{C}=0.01 \mu \mathrm{F}, \mathrm{V}_{\mathrm{DD}}=5 \mathrm{~V}$, and the CMOS NOR gates have a threshold voltage $\left(V_{T}\right)$ ... $v_{\mathrm{R}}(t)$, for $t>0$. Find the time period of the output pulse.
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141
GATE ECE 2000 | Question 15
The operating conditions $(O N=1, O F F=0)$ of three pumps $(x, y, z)$ are to be monitored. $x=1$ implies that pump $X$ is on. It is required that the indicator $\text{(LED)}$ on the panel should glow when a majority of the pumps fail. Enter the logical ... $1 \mathrm{~V}$. Assume that $P$ can source or $\sin k 10 \mathrm{~mA}$ and a $5 \mathrm{~V}$ supply is available.
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142
GATE ECE 2000 | Question 16
A one-bit full adder is to be implemented using $8$-to-$1$ multiplexers $\text{(MUX)}$. Write the truth table for sum $\text{(S)}$ and carry to the next stage $\left(\mathrm{C}_{\mathrm{N}}\right)$ in terms of the two bits $\text{(A, B)}$ and carry from the ... $(000,001,010$, ... etc.). Implement $\text{S}$ and $\text{C}_{N}$ using $8$-to-$1$ multiplexers.
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143
GATE ECE 2000 | Question 17
(a) The program and machine code for an $8085$ ... $2000 \mathrm{H}$ (c) Write an instruction which takes the minimum possible time to clear the accumulator of the $8085$.
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144
GATE ECE 2000 | Question 18
A bandlimited signal $x(t)$ with $a^{\prime}$ spectrum $X(f)$ as shown in first figure is processed as shown in second figure is $\mu(t)$ ... Fourier Transform of $p(t)$. Obtain and sketch the spectrum of $x_{s}(t)$. Obtain and sketch the spectrum of $y(t)$.
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GATE ECE 2000 | Question 19
Zero mean white Gaussian noise with a two-sided power spectral density of $4 \mathrm{~W} / \mathrm{kHz}$ is passed through an ideal lowpass filter with a cut-off frequency of $2 \mathrm{kHz}$ and a passband gain of $1$, to produce the noise ... $n\left(t_{1}\right) n\left(t_{2}\right)$ has the most negative expected value and obtain this most negative expected value.
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146
GATE ECE 2000 | Question 20
Given $\mathrm{E}=10 e^{-f(4 x-k y)} \mathrm{V} / \mathrm{m}$ in free space: Write all the four Maxwell's equations in free space. Find $\nabla \times E$. Find $\mathrm{H}$.
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147
GATE ECE 2000 | Question 21
The three regions shown in figure are all lossless and non-magnetic. Find. Wave impedance in mediums $2$ and $3$. $d$ such that medium $2$ acts as a quarter wave $(\lambda / 4)$ transformer. Reflection coefficient $(\Gamma)$ and voltage standing wave ratio $\text{(VSWR)}$ at the interface of the mediums $1$ and $2$, when $d=\lambda / 4$.
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148
GATE ECE 2000 | Question 22
Design a lossless impedance matching network shown in figure to transform $Z_{L}=10+$ $j 10 \Omega$ to $Z_{\text {in }}=50 \Omega$. Find the values of $\text{L, C}$ and quality factor $(\mathrm{Q})$ of the circuit at $f=1 \mathrm{GHz}$.
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149
GATE ECE 1999 | Question 1.1
Identify which of the following is $\text{NOT}$ a true of the graph shown in the given figure is $begh$ $adfg$ $defg$ $aegh$
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150
GATE ECE 1999 | Question 1.2
The $z$-transform $\mathrm{F}(z)$ of the function $f(n \mathrm{~T})=a^{\prime \prime}$ is $\frac{z}{z-a^{\mathrm{T}}}$ $\frac{z}{z+a^{\mathrm{T}}}$ $\frac{\mathrm{z}}{\mathrm{z}-\mathrm{a}^{-\mathrm{T}}}$ $\frac{z}{z+a^{-T}}$
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151
GATE ECE 1999 | Question 1.3
If $[f(t)]=\mathrm{F}(s)$, then $[f(t-\mathrm{T})]$ is equal to $e^{s \mathrm{~T}} \mathrm{~F}(s)$ $e^{-s \mathrm{~T}} \mathrm{~F}(s)$ $\frac{\mathrm{F}(s)}{1-e^{s T}}$ $\frac{\mathrm{F}(s)}{1-e^{-\mathrm{sT}}}$
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152
GATE ECE 1999 | Question 1.4
A $2$-port network is shown in the given figure. The parameter $h_{21}$ for this network can be given by $-1 / 2$ $+1 / 2$ $-3 / 2$ $+3 / 2$
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GATE ECE 1999 | Question 1.5
The early effect in a bipolar junction transistor is caused by fast turn-on fast turn-off large collector-base reverse bias large emitter-base forward bias
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154
GATE ECE 1999 | Question 1.6
The first dominant pole encountered in the frequency response of a compensated $\text{op - amp}$ is approximately at $5 \mathrm{~Hz}$ $10 \mathrm{kHz}$ $1 \mathrm{MHz}$ $100 \mathrm{MHz}$
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GATE ECE 1999 | Question 1.7
Negative feedback in an amplifier reduces gain increases frequency and phase distortions reduces bandwidth increases noise
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GATE ECE 1999 | Question 1.8
In the cascade amplifier shown in the given figure, if the common - emitter stage $\left(Q_{1}\right)$ has a transconductance $\mathrm{gm}_{1}$, and the common base stage $\left(Q_{2}\right)$ has a transconductance $\mathrm{gm}_{2^{\prime}}$ ... the cascade amplifier is $g_{m 1}$ $g_{m 2}$ $\frac{g_{m 1} 1}{2}$ $\frac{g_{m 2}}{2}$
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GATE ECE 1999 | Question 1.9
Crossover distortion behaviour is characteristic of Class $\text{A}$ output stage Class $\text{B}$ output stage Class $\mathrm{AB}$ output stage Common - base output stage
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GATE ECE 1999 | Question 1.10
The logical expresion $y=\mathrm{A}+\overline{\mathrm{A}} \mathrm{B} $ is equivalent to $y=\mathrm{AB}$ $y=\overline{\mathrm{A}} \mathrm{B}$ $y=\bar{A}+\mathrm{B}$ $y=\mathrm{A}+\mathrm{B}$
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GATE ECE 1999 | Question 1.11
A Darlington emitter - follower circuit is sometimes used in the output stage of a $\text{TTL}$ gate in order to increase its $\mathrm{I}_{\mathrm{OL}}$ reduce its $\mathrm{I}_{\mathrm{OH}}$ increase its speed of operation reduce power dissipation
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GATE ECE 1999 | Question 1.12
Commercially available $\text{ECL}$ gears use two ground lines and one negative supply in order to reduce power dissipation increase fan-out reduce loading effect eliminate the effect of power line glitches or the biasing circuit
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