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121
GATE ECE 2000 | Question 1.14
The amplitude modulated wave form $s(t)=A_{c}\left[1+K_{a} m(t)\right] \cos \omega_{c} t$ is fed to an ideal envelope detector. The maximum magnitude of $\mathrm{K}_{0} m(t)$ is greater than $1$ ... $\mathrm{A}_{c}\left[1+\mathrm{K}_{a} m(t)\right]^{2}$
The amplitude modulated wave form $s(t)=A_{c}\left[1+K_{a} m(t)\right] \cos \omega_{c} t$ is fed to an ideal envelope detector. The maximum magnitude of $\mathrm{K}_{0} m...
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GATE ECE 2023 | Question: 18
The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ is Note: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$ $\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$ $\frac{e^{-\frac{\omega^{2}}{4}}}{2 \sqrt{\pi}}$ $\sqrt{\pi} e^{-\frac{\omega^{2}}{4}}$ $\sqrt{\pi} e^{-\frac{\omega^{2}}{2}}$
The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ isNote: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$$\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$$\frac{e^{-\frac{\o...
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May 20, 2023
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GATE ECE 2022 | Question: 14
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current $\text{(in Amperes)}$ through the resistor is $2\sin (t+\pi/2).$ The displacement current $\text{(in Amperes)}$ through the capacitor is ______________. $2 \sin (t)$ $2 \sin (t + \pi)$ $2 \sin(t + \pi/2)$ $0$
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current $\text{(in Amperes)}$ through the resistor is $2\sin (t+\pi...
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124
GATE ECE 2023 | Question: 15
The open loop transfer function of a unity negative feedback system is $G(s)=\frac{k}{s\left(1+s T_1\right)\left(1+s T_2\right)}$, where $k, T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in $\text{rad/s,}$ is $\frac{1}{\sqrt{T_1 T_2}}$ $\frac{1}{T_1 T_2}$ $\frac{1}{T_1 \sqrt{T_2}}$ $\frac{1}{T_2 \sqrt{T_1}}$
The open loop transfer function of a unity negative feedback system is $G(s)=\frac{k}{s\left(1+s T_1\right)\left(1+s T_2\right)}$, where $k, T_1$ and $T_2$ are positive c...
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125
GATE ECE 2023 | Question: 20
For a real signal, which of the following is/are valid power spectral density/densities? $\text{S}_X(\omega)=\frac{2}{9+\omega^2}$ $\text{S}_X(\omega)=e^{-\omega^2} \cos ^2 \omega$
For a real signal, which of the following is/are valid power spectral density/densities?$\text{S}_X(\omega)=\frac{2}{9+\omega^2}$$\text{S}_X(\omega)=e^{-\omega^2} \cos ^2...
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126
GATE ECE 2009 | Question: 12
If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is
If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is
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127
GATE ECE 2021 | Question: 25
The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.
The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum a...
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128
GATE ECE 2021 | Question: 18
Consider the circuit shown in the figure. The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.
Consider the circuit shown in the figure.The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.
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GATE ECE 2022 | Question: 25
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the raw (uncoded) data rate is ____________ mega-bits per second (rounded off to one decimal place).
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the ...
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130
GATE ECE 1997 | Question 1.1
The current $i_4$ in the circuit of the figure is equal to $12 \mathrm{~A}$ $-12 \mathrm{~A}$ $4 \mathrm{~A}$ None of these
The current $i_4$ in the circuit of the figure is equal to$12 \mathrm{~A}$$-12 \mathrm{~A}$$4 \mathrm{~A}$None of these
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131
GATE ECE 2022 | Question: 11
Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure. Note that the Nyquist contour has been ... of the closed-loop transfer function in the closed right-half of the complex plane is ________________. $0$ $1$ $2$ $3$
Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer func...
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132
GATE ECE 2004 | Question: 89
A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non magnetic, dielectric material with $\varepsilon>\varepsilon_{0}$. Maxima and minima are observed when the electric field is measured in front of the slab. The maximum electric ... $60 \; \pi \Omega$ $600 \; \pi \Omega$ $24 \; \pi \Omega$
A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non magnetic, dielectric material with $\varepsilon>\varepsilon_...
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GATE ECE 2021 | Question: 10
Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure. Assuming $\left | V_{\text{IN}} \right |\ll \left | V_{\text{CC}} \right |$ and $\left | V_{\text{REF}} \right |\ll \left | V_{\text{CC}} \right | $, the condition at which $V_{\text{OUT}}$ equals ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure.Assuming $\left | V_{\text{IN}} \right |\ll \left | V_{\text{CC}} \right |$ and $\left | V_{\text{RE...
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GATE ECE 2021 | Question: 7
The energy band diagram of a $\text{p-type}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in the figure. The valance band $E_{V}$ is sloped since doping is non-uniform along the bar. The difference ... bar is $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$
The energy band diagram of a $\text{p-type}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in th...
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GATE ECE 2023 | Question: 19
In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Continuous, periodic (b) Continuous, periodic (iii) Discrete, aperiodic (c) Discrete, aperiodic (iv) ...
In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic(a) Continuous, aperiod...
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GATE ECE 2022 | Question: 6
Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10} \; \text{cm}^{-3}.$ Electron and hole diffusion lengths are $2 \; \mu\text{m}$ ... $3.7 \times 10^{14} \; \text{cm}^{-3}$ $10^{3} \; \text{cm}^{-3}$
Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentrat...
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GATE ECE 2007 | Question: 22
Consider the function $f(x)=x^{2}-x-2$. The maximum value of $f(x)$ in the closed interval $[-4,4]$ is $18$ $10$ $-2.25$ indeterminate
Consider the function $f(x)=x^{2}-x-2$. The maximum value of $f(x)$ in the closed interval $[-4,4]$ is$18$$10$$-2.25$indeterminate
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GATE ECE 2021 | Question: 35
The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarter-wave line having a characteristic impedance $Z_1=75\:\Omega$ is connected to $Z_{L}$. Two stubs having ... the real part of $Z_{L}$ is $112.5\:\Omega$ $75.0\:\Omega$ $50.0\:\Omega$ $33.3\:\Omega$
The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarte...
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GATE ECE 2021 | Question: 33
The electrical system shown in the figure converts input source current $i_{s}(t)$ to output voltage $v_{o}(t)$ Current i $i_{L}(t)$ in the inductor and voltage $v_{c}(t)$ across the capacitor ... as well as completely observable completely state controllable but not observable completely observable but not state controllable neither state controllable nor observable
The electrical system shown in the figure converts input source current $i_{s}(t)$ to output voltage $v_{o}(t)$Current i $i_{L}(t)$ in the inductor and voltage $v_{c}(t)$...
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GATE ECE 2001 | Question: 1.12
For the ring oscillator shown in the figure, the propagation delay of each inverter is $100$ pico sec. What is the fundamental frequency of the oscillator output? $10 \; \mathrm{MHz}$ $100 \; \mathrm{MHz}$ $1 \; \mathrm{GHz}$ $2 \; \mathrm{GHz}$
For the ring oscillator shown in the figure, the propagation delay of each inverter is $100$ pico sec. What is the fundamental frequency of the oscillator output?$10 \; \...
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GATE ECE 1997 | Question 3.1
In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is $36$ Joules $16$ Joules $256$ Joules None of the above
In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is$36$ Joules$16$ Joules$256$ JoulesNone of the above...
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GATE ECE 2005 | Question: 32
Given the matrix $\left[\begin{array}{cc}-4 & 2 \\ 4 & 3\end{array}\right]$, the eigenvector is $\left[\begin{array}{l}3 \\ 2\end{array}\right]$ $\left[\begin{array}{l}4 \\ 3\end{array}\right]$ $\left[\begin{array}{c}2 \\ -1\end{array}\right]$ $\left[\begin{array}{c}-2 \\ 1\end{array}\right]$
Given the matrix $\left[\begin{array}{cc}-4 & 2 \\ 4 & 3\end{array}\right]$, the eigenvector is$\left[\begin{array}{l}3 \\ 2\end{array}\right]$$\left[\begin{array}{l}4 \\...
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Sep 22, 2022
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GATE ECE 2023 | Question: 22
In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).
In the circuit shown below, the current $i$ flowing through $200 \; \Omega$ resistor is___________ $\mathrm{mA}$ (rounded off to two decimal places).
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GATE ECE 2003 | Question: 11
Choose the correct match for input resistance of various amplifier configurations shown below ... $\text{CB-LO, CC-HI, CE-MO}$ $\text{CB-MO, CC-HI, CE-LO}$ $\text{CB-HI, CC-LO, CE-MO}$
Choose the correct match for input resistance of various amplifier configurations shown below$\begin{array}{ll}\text { Configuration } & \text { Input resistance } \\ \te...
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Sep 26, 2022
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GATE ECE 2006 | Question: 34
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by $8 e^{-0.004 t}$ Volts $8\left(1-e^{-0.004 t}\right)$ Volts $8 u(t)$ Volts $8$ Volts
In the figure shown, assume that all the capacitors are initially uncharged. If $\text{V}_i(t)=10 u(t)$ Volts, then $\text{V}_0(t)$ is given by$8 e^{-0.004 t}$ Volts$8\le...
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GATE ECE 1997 | Question 2.4
In a common emitter $\text{BJT}$ amplifier, the maximum usable supply voltage is limited by Avalanche breakdown of Base-Emitter junction Collector-Base breakdown voltage with emitter open $\left(\mathrm{BV}_{\mathrm{CBO}}\right)$ Collector-Emitter breakdown ... with base open $\left(\mathrm{BV}_{\mathrm{CBO}}\right)$ Zener breakdown voltage of the Emitter-Base junction
In a common emitter $\text{BJT}$ amplifier, the maximum usable supply voltage is limited byAvalanche breakdown of Base-Emitter junctionCollector-Base breakdown voltage wi...
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GATE ECE 2005 | Question: 83a
Statement for Linked Answer Questions 83a and 83b: Asymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels. If the probability density function is divided into three regions as shown in the figure, the value of a in the figure is $\frac{1}{3}$ $\frac{2}{3}$ $\frac{1}{2}$ $\frac{1}{4}$
Statement for Linked Answer Questions 83a and 83b:Asymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels.I...
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GATE ECE 2006 | Question: 40
A heavily doped $n$-type semiconductor has the following data Hole-electron mobility ratio : $0.4$ Doping concentration : $4.2 \times 10^{8} \; \mathrm{atoms/m}^{3}$ Intrinsic concentration : $1.5 \times 10^{4} \; \mathrm{atoms/m}^{3}$ The ... that of the intrinsic semiconductor of same material and at the same temperature is given by $0.00005$ $2,000$ $10,000$ $20,000$
A heavily doped $n$-type semiconductor has the following dataHole-electron mobility ratio : $0.4$Doping concentration : $4.2 \times 10^{8} \; \mathrm{atoms/m}^{3}$Intrins...
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GATE ECE 2021 | Question: 47
The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time ... maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is _______________ $A$.
The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is ass...
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GATE ECE 2022 | Question: 22
A simple closed path $C$ in the complex plane is shown in the figure. If $\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$ where $i = \sqrt{-1},$ then the value of $A$ is _________ (rounded off to two decimal places).
A simple closed path $C$ in the complex plane is shown in the figure. If$$\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$$where $i = \sqrt{-1},$ then the value of $...
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GATE ECE 2006 | Question: 33
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is $0.5 \mathrm{~A}$ $2.0 \mathrm{~A}$ $1.0 \mathrm{~A}$ $0.0 \mathrm{~A}$
A $2 \; \mathrm{mH}$ inductor with some initial current can be represented as shown below, where $s$ is the Laplace Transform variable. The value of initial current is$0...
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GATE ECE 2022 | Question: 13
The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure. Statement $\text{I}:$ The system is necessarily a pure delay system for inputs which are bandlimited to $ - \alpha \leq f \leq \alpha.$ Statement ... $\text{II}$ is correct Statement $\text{I}$ is incorrect, Statement $\text{II}$ is incorrect
The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure.Statement $\text{I}:$ The system is necessarily a pure delay system f...
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GATE ECE 2024 | Question: 52
In the network shown below, maximum power is to be transferred to the load $R_{L}$. The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.
In the network shown below, maximum power is to be transferred to the load $R_{L}$.The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.
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GATE ECE 2022 | Question: 5
The Fourier transform $X(j \omega)$ of the signal $x(t) = \frac{t}{(1+t^{2})^{2}}$ is ______________. $\frac{\pi}{2j} \omega e^{– |\omega|}$ $\frac{\pi}{2} \omega e^{– |\omega|}$ $\frac{\pi}{2j}e^{– |\omega|}$ $\frac{\pi}{2}e^{– |\omega|}$
The Fourier transform $X(j \omega)$ of the signal$$x(t) = \frac{t}{(1+t^{2})^{2}}$$is ______________.$\frac{\pi}{2j} \omega e^{– |\omega|}$$\frac{\pi}{2} \omega e^{– ...
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GATE ECE 2021 | Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a wide-sense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________
The autocorrelation function $R_{X}\left ( \tau \right )$ of a wide-sense stationary random process $X(t)$ is shown in the figure.The average power of $X(t)$ is _________...
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GATE ECE 2022 | Question: 4
Consider the circuit shown in the figure. The current $I$ flowing through the $10 \; \Omega$ resistor is _____________. $1 \; \text{A}$ $0 \; \text{A}$ $0.1 \; \text{A}$ $ – 0.1 \; \text{A}$
Consider the circuit shown in the figure. The current $I$ flowing through the $10 \; \Omega$ resistor is _____________.$1 \; \text{A}$$0 \; \text{A}$$0.1 \; \text{A}$$ �...
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GATE ECE 2022 | Question: 24
An ideal $\text{MOS}$ capacitor (p-type semiconductor) is shown in the figure. The $\text{MOS}$ capacitor is under strong inversion with $V_{G} = 2 \; \text{V}.$ The corresponding inversion charge density $(Q_{IN})$ is $2.2 \; \mu \text{C /cm}^{2}.$ ... $Q_{IN}$ is ______________ $\mu \text{C/cm}^{2}$ (rounded off to one decimal place).
An ideal $\text{MOS}$ capacitor (p-type semiconductor) is shown in the figure. The $\text{MOS}$ capacitor is under strong inversion with $V_{G} = 2 \; \text{V}.$ The corr...
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GATE ECE 1997 | Question 1.11
The voltage $V$ in the figure is $10 \mathrm{~V}$ $15 \mathrm{~V}$ $5 \mathrm{~V}$ None of the above
The voltage $V$ in the figure is$10 \mathrm{~V}$$15 \mathrm{~V}$$5 \mathrm{~V}$None of the above
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GATE ECE 2024 | Question: 38
A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI system with impulse response \[ h(t)=\left(\frac{\sin 2 \pi t}{\pi t}\right) \cos (38 \pi t-\pi / 2) \] ... $15 \sin (38 \pi t-\pi / 3)$ $15 \cos (38 \pi t-\pi / 6)$ $15 \cos (38 \pi t+\pi / 6)$
A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI s...
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GATE ECE 2007 | Question: 39
In the CMOS inverter circuit shown, if the transconductance parameters of the NMOS and PMOS transistors are $k_{n}=k_{p}=\mu_{n} C_{o x} \dfrac{W_{n}}{L_{n}}=\mu_{p} C_{o x} \dfrac{W_{p}}{L_{p}}=40 \; \mu \mathrm{A} / \mathrm{V}^{2}$ and their threshold voltages ... the current $I$ is $0 \mathrm{~A}$ $25 \; \mu \mathrm{A}$ $45 \; \mu \mathrm{A}$ $90 \; \mu \mathrm{A}$
In the CMOS inverter circuit shown, if the transconductance parameters of the NMOS and PMOS transistors are $k_{n}=k_{p}=\mu_{n} C_{o x} \dfrac{W_{n}}{L_{n}}=\mu_{p} C_{o...
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