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1721
GATE ECE 1991 | Question 1.4
Two two-port networks are connected in cascade. The combination is to be represented as a single two-port network. The parameters of the network are obtained by multiplying the individual $z$-parameter matrix $h$-parameter matrix $y$-parameter matrix $\text{ABCD}$ parameter matrix
Two two-port networks are connected in cascade. The combination is to be represented as a single two-port network. The parameters of the network are obtained by multiplyi...
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1722
GATE ECE 1991 | Question 1.5
The pole-zero pattern of a certain filter is shown in the figure below. The filter must be of the following type. low pass high pass all pass band pass
The pole-zero pattern of a certain filter is shown in the figure below. The filter must be of the following type.low passhigh passall passband pass
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1723
GATE ECE 1991 | Question 1.6
The necessary and sufficient condition for a rational function of $\mathrm{s}$. $\mathrm{T}(\mathrm{s})$ to be driving point impedance of an $\text{RC}$ network is that all poles and zeros should be simple and lie on the negative axis in the $s$-plane ... $s$-plane simple and lie on the positive real axis of the $s$-plane
The necessary and sufficient condition for a rational function of $\mathrm{s}$. $\mathrm{T}(\mathrm{s})$ to be driving point impedance of an $\text{RC}$ network is that a...
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1724
GATE ECE 1991 | Question 1.7
In the signal flow graph of Figure, the gain $c / r$ will be $\frac{11}{9}$ $\frac{22}{15}$ $\frac{24}{23}$ $\frac{44}{23}$
In the signal flow graph of Figure, the gain $c / r$ will be$\frac{11}{9}$$\frac{22}{15}$$\frac{24}{23}$$\frac{44}{23}$
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1725
GATE ECE 1991 | Question 1.8
A second order system has a transfer function given by $ G(s)=\frac{25}{s^2+8 s+25} $ If the system, initially at rest is subjected to a unit step input at $\mathrm{t}=0$, the second peak in response will occur at $\pi \mathrm{sec}$ $\frac{\pi}{3}$ sec $\frac{2 \pi}{3} \sec$ $\frac{\pi}{2}$ sec
A second order system has a transfer function given by$$ G(s)=\frac{25}{s^2+8 s+25} $$If the system, initially at rest is subjected to a unit step input at $\mathrm{t}=0$...
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1726
GATE ECE 1991 | Question 1.9
The open loop transfer function of a feedback control system is: $ G(s) H(s)=\frac{1}{(s+1)^3} $ The gain margin of the system is: $2$ $4$ $8$ $16$
The open loop transfer function of a feedback control system is:$$ G(s) H(s)=\frac{1}{(s+1)^3} $$The gain margin of the system is:$2$$4$$8$$16$
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1727
GATE ECE 1991 | Question 1.10
A unity feedback control system has the open loop transfer function $ G(s)=\frac{4(1+2 s)}{s^2(s+2)} $ If the input to the system is a unit ramp, the steady state error will be $0$ $0.5$ $2$ $\textsf{infinity}$
A unity feedback control system has the open loop transfer function$$ G(s)=\frac{4(1+2 s)}{s^2(s+2)} $$If the input to the system is a unit ramp, the steady state error w...
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1728
GATE ECE 1991 | Question 1.11
The characteristic equation of a feedback control system is given by $ s^3+5 s^2+(K+6) s+K=0 $ Where $K>0$ is a scalar variable parameter. In the root loci diagram of the system the asymptotes of the root locus for large values of $\mathrm{K}$ meet at a point in the $s$-plane whose coordinates are $(-3,0)$ $(-2,0)$ $(-1,0)$ $(2,0)$
The characteristic equation of a feedback control system is given by$$ s^3+5 s^2+(K+6) s+K=0 $$Where $K>0$ is a scalar variable parameter. In the root loci diagram of the...
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1729
GATE ECE 1991 | Question 1.12
A linear second order single input continuous time system is described by the following set of differential equations ... and $u(t)$ is the control variable. The system is: controllable and stable controllable but unstable uncontrollable and unstable uncontrollable and stable
A linear second order single input continuous time system is described by the following set of differential equations$$ \begin{aligned} &x_1(t)=-2 x_1(t)+4 x_2(t) \\ &x_2...
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1730
GATE ECE 1991 | Question 1.13
A linear time-invariant discrete-time system is described by the vector matrix difference equation $ x(k+1)=F \underline{X}(k)+G \underline{u}(k) $ Where $\underline{X}(k)$ is the state vector, $F$ is an $n \times n$ constant matrix, $G$ is a $(n \times r)$ ... by inverse $Z$-transform of $ZI - F$ $(Z I-F) Z$ $(Z I-F)^{-1} G$ $(Z I-F)^{-1} Z$
A linear time-invariant discrete-time system is described by the vector matrix difference equation $$ x(k+1)=F \underline{X}(k)+G \underline{u}(k) $$Where $\underline{X}(...
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1731
GATE ECE 1991 | Question 1.14
A silicon sample is uniformly doped with $10^{16}$ phosphorous atoms $/ \mathrm{cm}^3$ and $2 \times 10^{16}$ boron atoms $/ \mathrm{cm}^3$. If all the dopants are fully ionized, the material is $\mathrm{n}$ ... $2 \times 10^{16} / \mathrm{cm}^3$ $T_2$ will get damaged and $T_1$ will be safe
A silicon sample is uniformly doped with $10^{16}$ phosphorous atoms $/ \mathrm{cm}^3$ and $2 \times 10^{16}$ boron atoms $/ \mathrm{cm}^3$. If all the dopants are fully ...
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1732
GATE ECE 1991 | Question 1.15
An $n$-type silicon sample, having electron mobility $\mu_n=$ twice the hole mobility $\mu_p$, is subjected to a steady illumination such that the electron concentration doubles from its thermal equilibrium value. As a result, the conductivity of the sample increases by a factor of ...
An $n$-type silicon sample, having electron mobility $\mu_n=$ twice the hole mobility $\mu_p$, is subjected to a steady illumination such that the electron concentration ...
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1733
GATE ECE 1991 | Question 1.16
The small signal capacitances of an abrupt $P_1-n$ junction is $1 \mathrm{nF} / \mathrm{Cm}^2$ at zero bias. If the built in voltage is $1$ volt, the capacitance at a reverse bias voltage of $99$ volts is equal to $\ldots$
The small signal capacitances of an abrupt $P_1-n$ junction is $1 \mathrm{nF} / \mathrm{Cm}^2$ at zero bias. If the built in voltage is $1$ volt, the capacitance at a rev...
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1734
GATE ECE 1991 | Question 1.17
Referring to the figure. The switch $S$ is in position $1$ initially and steady state conditions exist from time $\mathrm{t}=0$ to $t=t_0$. The switch is suddenly thrown into position $2$. The current $1$ through the $10 \mathrm{~K}$ resistor as a function of ... $0$ , is .... (Give the sketch showing the magnitudes of the current at $t=0$, $t=t_0$ and $t=\infty$ )
Referring to the figure. The switch $S$ is in position $1$ initially and steady state conditions exist from time $\mathrm{t}=0$ to $t=t_0$. The switch is suddenly thrown ...
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1735
GATE ECE 1991 | Question 1.18
Discrete transistors $T_1$ and $T_2$ having maximum collector current rating of $0.75$ amps are connected in parallel as shown in the figure. This combination is treated as a single transistor to carry a total current of $1$ ampere, when biased with self bias ... will be safe $T_1$ will get damaged and $T_2$ will be safe $T_2$ will get damaged and $T_1$ will be safe
Discrete transistors $T_1$ and $T_2$ having maximum collector current rating of $0.75$ amps are connected in parallel as shown in the figure. This combination is treated ...
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1736
GATE ECE 1991 | Question 1.19
The built-in potential of the gate junction of a $n$-channel $\text{JFET}$ is $0.5$ volts. The drain current saturates at $V_{D S}=4.0$ volts when $V_{G S}=0$. The pinch off voltage is _________.
The built-in potential of the gate junction of a $n$-channel $\text{JFET}$ is $0.5$ volts. The drain current saturates at $V_{D S}=4.0$ volts when $V_{G S}=0$. The pinch ...
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1737
GATE ECE 1991 | Question 1.20
In figure, all transistors are identical and have a high value of beta. The voltage $V_{D C}$ is equal to _________.
In figure, all transistors are identical and have a high value of beta. The voltage $V_{D C}$ is equal to_________.
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1738
GATE ECE 1991 | Question 1.21
In figure, both transistors are identical and have a high value of beta. Take the $dc$ base-emitter voltage drop as $0.7$ volt and $\mathrm{KT} / \mathrm{q}=25 \; \mathrm{mV}$. The small signal low frequency voltage gain $\left(V_o / V_i\right)$ is equal to__________.
In figure, both transistors are identical and have a high value of beta. Take the $dc$ base-emitter voltage drop as $0.7$ volt and $\mathrm{KT} / \mathrm{q}=25 \; \mathrm...
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1739
GATE ECE 1991 | Question 1.22
In figure the input $V_1$ is a $100 \mathrm{~Hz}$ triangular wave having a peak to peak amplitude of 2 volts and an average value of zero volts. Given that the diode is ideal, the average value of the output $V_0$ is ___________.
In figure the input $V_1$ is a $100 \mathrm{~Hz}$ triangular wave having a peak to peak amplitude of 2 volts and an average value of zero volts. Given that the diode is i...
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1740
GATE ECE 1991 | Question 1.23
In figure, the $n$-channel $\text{MOSFETs}$ are identical and their current voltage characteristics are given by the following expressions: For $V_{D S}, I_D=\left[\left(V_{G S}-1\right) V_{D S}-\frac{V^2 D S}{2}\right] m A$ ... and $I_0$ is the drain current. The current $I_{D C}$ flowing through the transistor ' $\mathrm{M}$ ' is equal to__________.
In figure, the $n$-channel $\text{MOSFETs}$ are identical and their current voltage characteristics are given by the following expressions:For $V_{D S}, I_D=\left[\left(V...
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1741
GATE ECE 1991 | Question 1.24
In order that the circuit of Figure works properly as differentiator, it should be modified to ________ (draw the modified circuit)
In order that the circuit of Figure works properly as differentiator, it should be modified to ________ (draw the modified circuit)
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1742
GATE ECE 1991 | Question 1.25
Two non-inverting amplifiers, one having a unity gain and the other having a gain of twenty are made using identical operational amplifiers. As a compared to the unity gain amplifier, the amplifier with gain twenty has less negative feedback greater input impedance less bandwidth none of the above
Two non-inverting amplifiers, one having a unity gain and the other having a gain of twenty are made using identical operational amplifiers. As a compared to the unity ga...
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1743
GATE ECE 1991 | Question 1.26
Two dimensional addressing of $256 \times 8$ bit $\text{ROM}$ using to $1$ selectors requires ________ (how many?) $\text{NAND}$ gates.
Two dimensional addressing of $256 \times 8$ bit $\text{ROM}$ using to $1$ selectors requires ________ (how many?) $\text{NAND}$ gates.
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1744
GATE ECE 1991 | Question 1.27
The $\textsf{CMOS}$ equivalent of the following $\textsf{nMOS}$ gate (in figure) is___________ (draw the circuit).
The $\textsf{CMOS}$ equivalent of the following $\textsf{nMOS}$ gate (in figure) is___________ (draw the circuit).
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1745
GATE ECE 1991 | Question 1.28
In figure, the Boolean expression for the output in terms of inputs $A, B$ and $C$ when the clock $\textsf{'CK'}$ is high, is given by __________.
In figure, the Boolean expression for the output in terms of inputs $A, B$ and $C$ when the clock $\textsf{'CK'}$ is high, is given by __________.
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1746
GATE ECE 1991 | Question 1.29
An $\text{S-R FLIP-FLOP}$ can be converted into a $\textsf{T FLIP FLOP}$ by connecting __________ to $\mathrm{Q}$ and ___________ to $\mathrm{Q}$.
An $\text{S-R FLIP-FLOP}$ can be converted into a $\textsf{T FLIP FLOP}$ by connecting __________ to $\mathrm{Q}$ and ___________ to $\mathrm{Q}$.
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1747
GATE ECE 1991 | Question 1.30
A bit stored in a $\text{FAMOS}$ device can be erased by _____________.
A bit stored in a $\text{FAMOS}$ device can be erased by _____________.
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1748
GATE ECE 1991 | Question 1.31
A signal has frequency components from $300 \mathrm{~Hz}$ to $1.8 \; \mathrm{KHz}$. The minimum possible rate at which the signal has to be sampled is ___________.
A signal has frequency components from $300 \mathrm{~Hz}$ to $1.8 \; \mathrm{KHz}$. The minimum possible rate at which the signal has to be sampled is ___________.
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1749
GATE ECE 1991 | Question 1.32
A sequential multiplexer is connected as shown in figure. Each time the multiplexer receives the clock, it switches to the next channel (From $6$ it goes to $1$). If the input signals are $A=5 \cos 2 \pi\left(4 \times 10^3 t\right)$ ... $D=4 \cos 2 \pi\left(1.7 \times 10^3 t\right)$ he minimum clock frequency should be _________ $\mathrm{KHz}$.
A sequential multiplexer is connected as shown in figure. Each time the multiplexer receives the clock, it switches to the next channel (From $6$ it goes to $1$). If the ...
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1750
GATE ECE 1991 | Question 1.33
For the signal constellation shown in figure below, the type of modulation is ___________.
For the signal constellation shown in figure below, the type of modulation is ___________.
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1751
GATE ECE 1991 | Question 1.34
Two resistors $R_1$ and $R_2$ (in ohms) at temperatures $T_1$ and $T_2 K$ respectively, are connected in series. Their equivalent noise temperatures is ___________ $K$.
Two resistors $R_1$ and $R_2$ (in ohms) at temperatures $T_1$ and $T_2 K$ respectively, are connected in series. Their equivalent noise temperatures is ___________ $K$.
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1752
GATE ECE 1991 | Question 1.35
A binary source has symbol probabilities $0.8$ and $0.2$. If extension coding (blocks of $4$ symbols) is used. The lower and upper bounds on the average code word length are (a) lower _________. (b) higher ________.
A binary source has symbol probabilities $0.8$ and $0.2$. If extension coding (blocks of $4$ symbols) is used. The lower and upper bounds on the average code word length ...
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1753
GATE ECE 1991 | Question 1.36
In a reflex Klystron oscillator the maximum possible efficiency is $58 \%$ the frequency of oscillation varies linearly with the reflector voltage the power output varies continuously with reflector voltage the power output is maximum at fixed frequency.
In a reflex Klystron oscillatorthe maximum possible efficiency is $58 \%$the frequency of oscillation varies linearly with the reflector voltagethe power output varies co...
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1754
GATE ECE 1991 | Question 1.37
The input impedance of a short-circuited lossless transmission line quarter wave length is purely reactive purely resistive infinite dependent on the characteristic impedance of the line.
The input impedance of a short-circuited lossless transmission line quarter wave length ispurely reactivepurely resistiveinfinitedependent on the characteristic impedance...
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1755
GATE ECE 1991 | Question 1.38
The electric field component of a uniform plane electromagnetic wave propagating in the $Y$-direction in a lossless medium will satisfy the equation. $\frac{\partial^2 E_y}{\partial y^2}=\mu \in \frac{\partial^2 E_y}{\partial t^2}$ ... $\frac{\sqrt{E_x^2+E_z^2}}{\sqrt{H_x^2+H_z^2}}=\sqrt{\frac{\mu}{\epsilon}}$
The electric field component of a uniform plane electromagnetic wave propagating in the $Y$-direction in a lossless medium will satisfy the equation.$\frac{\partial^2 E_y...
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1756
GATE ECE 1991 | Question 1.39
A radio wave is incident on a layer of ionosphere at an angle of $30$ degree with the vertical. If the critical frequency is $1.2 \; \mathrm{MHz}$, the maximum usable frequency is $1.2 \; \mathrm{MHz}$ $2.4 \; \mathrm{MHz}$ $0.6 \; \mathrm{MHz}$ $1.386 \; \mathrm{MHz}$
A radio wave is incident on a layer of ionosphere at an angle of $30$ degree with the vertical. If the critical frequency is $1.2 \; \mathrm{MHz}$, the maximum usable fre...
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1757
GATE ECE 1991 | Question 1.40
In a broad side array of $20$ isotropic radiators, equally spaced at a distance of $\frac{\lambda}{2}$, the beam width between first nulls is $51.3$ degrees $11.46$ degrees $22.9$ degrees $102.6$ degrees
In a broad side array of $20$ isotropic radiators, equally spaced at a distance of $\frac{\lambda}{2}$, the beam width between first nulls is$51.3$ degrees$11.46$ degrees...
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1758
GATE ECE 1991 | Question 2
(a) Find the Laplace transform of the waveform $x(t)$ shown in figure. (b) The network shown in figure is initially under steady state condition with the switch in position $1$. The switch is moved from position $1$ to position $2$ at $t \neq$ 0 . Calculate the current $i(t)$ through $R_1$ after switching.
(a) Find the Laplace transform of the waveform $x(t)$ shown in figure.(b) The network shown in figure is initially under steady state condition with the switch in positio...
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1759
GATE ECE 1991 | Question 3
The open loop transfer function of a feedback control system incorporating a dead time element is given by $ G(s)=\frac{K e^{-T s}}{s(s+1)} $ Where $\mathrm{K}>0$, and $\mathrm{T}>0$ are variable scalar parameters. (a) For a ... $\omega_0$ is the smallest value of $\omega$ satisfying the equation $\omega=\cot \omega T$
The open loop transfer function of a feedback control system incorporating a dead time element is given by$$ G(s)=\frac{K e^{-T s}}{s(s+1)} $$Where $\mathrm{K}>0$, and $\...
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1760
GATE ECE 1991 | Question 4
The current $I$ in a forward biased $P^{+} N$ junction shown in figure (a) is entirely due to diffusion of holes from $x=0$ to $x=L$. The injected hole concentration distribution in the $m$ ... coefficient holes is $12 \mathrm{~cm}^2 / \mathrm{sec}$. (b) The velocity of holes in the $n$-region at $x=0$.
The current $I$ in a forward biased $P^{+} N$ junction shown in figure (a) is entirely due to diffusion of holes from $x=0$ to $x=L$. The injected hole concentration dist...
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