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1161
GATE ECE 1996 | Question 1.13
The total number of memory accesses involved (inclusive of the $op$ – code fetch) when an $8085$ processor executes the instruction $\text{LDA}$ $2003$ is $1$ $2$ $3$ $4$
The total number of memory accesses involved (inclusive of the $op$ – code fetch) when an $8085$ processor executes the instruction $\text{LDA}$ $2003$ is$1$$2$$3$$4$
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1162
GATE ECE 1996 | Question 1.14
The trigonometric Fourier series of an even function of time does not have the $d c$ term cosine terms sine terms odd harmonic terms
The trigonometric Fourier series of an even function of time does not have the$d c$ termcosine termssine termsodd harmonic terms
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1163
GATE ECE 1996 | Question 1.15
The Fourier transform of a real-valued time signal has odd symmetry even symmetry conjugate symmetry no symmetry
The Fourier transform of a real-valued time signal hasodd symmetryeven symmetryconjugate symmetryno symmetry
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1164
GATE ECE 1996 | Question 1.16
A rectangular pulse of duration $T$ is applied to a filter matched to this input. The output of the filter is a rectangular pulse of duration $T$ rectangular pulse of duration $2 \mathrm{~T}$ triangular pulse sine function
A rectangular pulse of duration $T$ is applied to a filter matched to this input. The output of the filter is arectangular pulse of duration $T$rectangular pulse of durat...
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1165
GATE ECE 1996 | Question 1.17
The image channel rejection in a superheterodyne receiver comes from $\text{IF}$ stages only $\text{RF}$ stages only detector and $\text{RF}$ stages only detector $\text{RF}$, and $\text{IF}$ stages
The image channel rejection in a superheterodyne receiver comes from$\text{IF}$ stages only$\text{RF}$ stages onlydetector and $\text{RF}$ stages onlydetector $\text{RF}$...
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1166
GATE ECE 1996 | Question 1.18
The capacitance per unit length and the characteristic impedance of a lossless transmission line are $\mathrm{C}$ and $\mathrm{Zo}$ respectively. The velocity of a travelling wave on the transmission line $Z_{0} C$ $\frac{1}{\mathrm{Z}_{\mathrm{o}} \mathrm{C}}$ $\frac{Z_{0}}{C}$ $\frac{\mathrm{C}}{\mathrm{Z}_{0}}$
The capacitance per unit length and the characteristic impedance of a lossless transmission line are $\mathrm{C}$ and $\mathrm{Zo}$ respectively. The velocity of a travel...
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1167
GATE ECE 1996 | Question 1.19
A transverse electromagnetic wave with circular polarisation is received by a dipole antenna. Due to polarisation mismatch, the power transfer efficiency from the wave to the antenna is reduced to about $50 \%$ $35.3 \%$ $25 \%$ $0 \%$
A transverse electromagnetic wave with circular polarisation is received by a dipole antenna. Due to polarisation mismatch, the power transfer efficiency from the wave to...
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1168
GATE ECE 1996 | Question 1.20
A metal sphere with $1 \mathrm{~m}$ radius and a surface charge density of $10 \; \mathrm{Coulombs / m}^{2}$ is enclosed in a cube of $10 \mathrm{~m}$ side. The total outward electric displacement normal to the surface of the cube is $40 \pi$ Coulombs $10 \pi$ Coulombs $5 \pi$ Couloms None of these
A metal sphere with $1 \mathrm{~m}$ radius and a surface charge density of $10 \; \mathrm{Coulombs / m}^{2}$ is enclosed in a cube of $10 \mathrm{~m}$ side. The total out...
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1169
GATE ECE 1996 | Question 1.21
In the circuit shown in the given figure $\mathrm{N}$ is a finite gain amplifier with a gain of $k$, a very large input impedance, and a very low output impedance. The input impedance of the feedback amplifier with the feedback impedance $\mathrm{Z}$ connected as shown will be $\mathrm{Z}\left(1-\frac{1}{k}\right)$ $Z(1-k)$ $\frac{\mathrm{Z}}{(k-1)}$ $\frac{Z}{(1-k)}$
In the circuit shown in the given figure $\mathrm{N}$ is a finite gain amplifier with a gain of $k$, a very large input impedance, and a very low output impedance. The in...
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1170
GATE ECE 1996 | Question 2.2
The inverse Laplace transform of the function $\frac{s+5}{(s+1)(s+3)}$ is $2 e^{-t}-e^{-3 t}$ $2 e^{-t}+e^{-3 t}$ $e^{-t}-2 e^{-3 t}$ $e^{-t}+e^{-3 t}$
The inverse Laplace transform of the function$\frac{s+5}{(s+1)(s+3)}$ is$2 e^{-t}-e^{-3 t}$$2 e^{-t}+e^{-3 t}$$e^{-t}-2 e^{-3 t}$$e^{-t}+e^{-3 t}$
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1171
GATE ECE 1996 | Question 2.3
The voltages $\mathrm{V}_{\mathrm{C} 1}, \mathrm{~V}_{\mathrm{C} 2}$, and $\mathrm{V}_{\mathrm{C} 3}$ across the capacitors in the circuit in the given figure, under steady state, are respectively. $80 \mathrm{~V}, 32 \mathrm{~V}, 48 \mathrm{~V}$ ... $20 \mathrm{~V}, 8 \mathrm{~V}, 12 \mathrm{~V}$ $20 \mathrm{~V}, 12 \mathrm{~V}, 8 \mathrm{~V}$
The voltages $\mathrm{V}_{\mathrm{C} 1}, \mathrm{~V}_{\mathrm{C} 2}$, and $\mathrm{V}_{\mathrm{C} 3}$ across the capacitors in the circuit in the given figure, under stea...
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1172
GATE ECE 1996 | Question 2.4
A uniform plane wave in air is normally incident on infinitely thick slab. If the refractive index of the glass slab is $1.5$, then the percentage of incident power that is reflected from the air-glass interface is $0 \%$ $4 \%$ $20 \%$ $100 \%$
A uniform plane wave in air is normally incident on infinitely thick slab. If the refractive index of the glass slab is $1.5$, then the percentage of incident power that ...
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1173
GATE ECE 1996 | Question 2.5
In a bipolar transistor at room temperature, if the emitter current is doubled the voltage across its base-emitter junction doubles halves increases by about $20 \; \mathrm{mV}$ decreases by about $20 \; \mathrm{mV}$
In a bipolar transistor at room temperature, if the emitter current is doubled the voltage across its base-emitter junctiondoubleshalvesincreases by about $20 \; \mathrm{...
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1174
GATE ECE 1996 | Question 2.6
An $\text{npn}$ transistor has a beta cut-off frequency $f \beta$ of $1 \; \mathrm{MHz}$, and common emitter short circuit low frequency current gain $\beta \mathrm{O}$ of $200$. It unity gain frequency $f \mathrm{T}$ and the alpha cut-off frequency $f \alpha$ ... $199 \;\mathrm{MHz}, 200 \; \mathrm{MHz}$ $201 \; \mathrm{MHz}, 200 \; \mathrm{MHz}$
An $\text{npn}$ transistor has a beta cut-off frequency $f \beta$ of $1 \; \mathrm{MHz}$, and common emitter short circuit low frequency current gain $\beta \mathrm{O}$ o...
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1175
GATE ECE 1996 | Question 2.7
A silicon $n$ $\text{MOSFET}$ has a threshold voltage of $1$ $\mathrm{V}$ and oxide thickness of $\mathrm{AO}$. $\left[\varepsilon_{r}\left(\mathrm{siO}_{2}\right)=3.9, \varepsilon_{\mathrm{o}}=8.854 \times 10^{-14} \mathrm{~F} / \mathrm{cm}\right.$ ... $5.4 \times 10^{11} / \mathrm{cm}^{2}, p$-type $5.4 \times 10^{11} / \mathrm{cm}^{2}, n$-type
A silicon $n$ $\text{MOSFET}$ has a threshold voltage of $1$ $\mathrm{V}$ and oxide thickness of $\mathrm{AO}$.$\left[\varepsilon_{r}\left(\mathrm{siO}_{2}\right)=3.9, \v...
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1176
GATE ECE 1996 | Question 2.8
A Darlington stage is shown in the figure is. If the transconductance of $Q_{1}$ is $g_{m 1}$ and $Q_{2}$ is $g_{m 2}$, then the overall transconductance $g_{m c}\left[\triangleq \frac{i_{c}^{c}}{v_{b c}^{c}}\right]$ is given by $g_{m 1}$ $0.5 \; g_{\text {m } 1}$ $g_{m 2}$ $0.5 \; g_{m 2}$
A Darlington stage is shown in the figure is. If the transconductance of $Q_{1}$ is $g_{m 1}$ and $Q_{2}$ is $g_{m 2}$, then the overall transconductance $g_{m c}\left[\t...
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1177
GATE ECE 1996 | Question 2.9
Value of $R$ in the oscillator circuit shown in the given figure, so chosen that it just oscillates at an angular frequency of $\omega$. The value of $\omega$ and the required value of $R$ ... $10^{5} \; \mathrm{rad} / \mathrm{sec}, 10^{5} \; \Omega$
Value of $R$ in the oscillator circuit shown in the given figure, so chosen that it just oscillates at an angular frequency of $\omega$. The value of $\omega$ and the req...
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1178
GATE ECE 1996 | Question 2.10
A Zener diode in the circuit shown in the figure is has a knee current of $5 \mathrm{~mA}$, and a maximum allowed power dissipation of $300 \mathrm{~mW}$. What are the minimum and maximum load currents that can be drawn safely from the circuit, keeping the output voltage ... $10 \mathrm{~mA}, 55 \mathrm{~mA}$ $60 \mathrm{~mA}, 180 \mathrm{~mA}$
A Zener diode in the circuit shown in the figure is has a knee current of $5 \mathrm{~mA}$, and a maximum allowed power dissipation of $300 \mathrm{~mW}$. What are the mi...
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1179
GATE ECE 1996 | Question 2.11
A dynamic $\text{RAM}$ cell which hold $5 \mathrm{~V}$ has to be refreshed every $20 \mathrm{~m}$ secs, so that the stored voltage does not fall by more than $0.5 \mathrm{~V}$. If the cell has a constant discharge current of $0.1 \; \mathrm{pA}$, the storage capacitance ... $4 \times 10^{-9} \mathrm{~F}$ $4 \times 10^{-12} \mathrm{~F}$ $4 \times 10^{-15} \mathrm{~F}$
A dynamic $\text{RAM}$ cell which hold $5 \mathrm{~V}$ has to be refreshed every $20 \mathrm{~m}$ secs, so that the stored voltage does not fall by more than $0.5 \mathrm...
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1180
GATE ECE 1996 | Question 2.12
A $10$ - bit $\text{ADC}$ with a full scale output voltage of $10.24 \mathrm{~V}$ is designed to have $\mathrm{a} \pm \mathrm{LSB} / 2$ accuracy. If the $\mathrm{ADC}$ is calibrated at $25^{\circ} \mathrm{C}$ ... $\pm 800 \; \mu \; \mathrm{V} /{ }^{\circ} \mathrm{C}$
A $10$ - bit $\text{ADC}$ with a full scale output voltage of $10.24 \mathrm{~V}$ is designed to have $\mathrm{a} \pm \mathrm{LSB} / 2$ accuracy. If the $\mathrm{ADC}$ is...
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1181
GATE ECE 1996 | Question 2.13
A memory system of size $26 \mathrm{~K}$ bytes is required to be designed using memory chips which have $12$ address lines and $4$ data lines each. The number of such chips required to design the memory system is $2$ $4$ $8$ $16$
A memory system of size $26 \mathrm{~K}$ bytes is required to be designed using memory chips which have $12$ address lines and $4$ data lines each. The number of such chi...
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1182
GATE ECE 1996 | Question 2.14
The following sequence of instructions are executed by an $8085$ microprocessor: $\begin{matrix} 1000 &LXI & SP &27 \; FF \\ 1000 &CALL & & 1006\\ 1006 &POP \; H & & \end{matrix}$ ... $\mathrm{SP}=27 \; \mathrm{FF}, \mathrm{HL}=1006$ $\mathrm{SP}=27 \; \mathrm{FD}, \mathrm{HL}=1006$
The following sequence of instructions are executed by an $8085$ microprocessor:$\begin{matrix}1000 &LXI & SP &27 \; FF \\ 1000 &CALL & & 1006\\ 1006 &POP \; H & & \...
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1183
GATE ECE 1996 | Question 2.15
The number of bits in a binary $\mathrm{PCM}$ system is increased from $n$ to $n+1$. As a result, the signal to quantization noise ratio will improve by a factor $\frac{n+1}{n}$ $2^{(n+1) / n}$ $2^{2(n+1) / n}$ which is independent of $n$
The number of bits in a binary $\mathrm{PCM}$ system is increased from $n$ to $n+1$. As a result, the signal to quantization noise ratio will improve by a factor$\frac{n+...
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1184
GATE ECE 1996 | Question 2.16
The autocorrelation function of an energy signal has no symmetry conjugate symmetry odd symmetry even symmetry
The autocorrelation function of an energy signal hasno symmetryconjugate symmetryodd symmetryeven symmetry
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1185
GATE ECE 1996 | Question 2.17
An $\text{FM}$ signal with a modulation index $9$ is applied to a frequency tripler. The modulation index in the output signal will be $0$ $3$ $9$ $27$
An $\text{FM}$ signal with a modulation index $9$ is applied to a frequency tripler. The modulation index in the output signal will be$0$$3$$9$$27$
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1186
GATE ECE 1996 | Question 2.18
The critical frequency of an ionospheric layer is $10 \; \mathrm{MHz}$. What is the maximum launching angle from the horizon for which $20 \; \mathrm{MHz}$ wave will be reflected by the layer? $0^{\circ}$ $30^{\circ}$ $45^{\circ}$ $90^{\circ}$
The critical frequency of an ionospheric layer is $10 \; \mathrm{MHz}$. What is the maximum launching angle from the horizon for which $20 \; \mathrm{MHz}$ wave will be r...
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1187
GATE ECE 1996 | Question 2.19
A $1 \mathrm{~km}$ long microwave link uses two antennas each having $30 \mathrm{~dB}$ gain. If the power transmitted by one antenna is $1 \mathrm{~W}$ at $3 \; \mathrm{GHz}$, the power received by the other antenna is approximately $98.6 \; \mu \mathrm{W}$ $76.8 \; \mu \mathrm{W}$ $63.4 \; \mu \mathrm{W}$ $55.2 \; \mu W$
A $1 \mathrm{~km}$ long microwave link uses two antennas each having $30 \mathrm{~dB}$ gain. If the power transmitted by one antenna is $1 \mathrm{~W}$ at $3 \; \mathrm{G...
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1188
GATE ECE 1996 | Question 2.20
Some unknown material has a conductivity of $10^{6} \; \mathrm{mho} / \mathrm{m}$ and a permeability of $4 \pi \times 10^{-7} \; \mathrm{H} / \mathrm{m}$. The skin depth for the material at $1 \; \mathrm{GHz}$ is $15.9 \; \mu \mathrm{m}$ $20.9 \; \mu \mathrm{m}$ $25.9 \; \mu \mathrm{m}$ $30.9 \; \mu \mathrm{m}$
Some unknown material has a conductivity of $10^{6} \; \mathrm{mho} / \mathrm{m}$ and a permeability of $4 \pi \times 10^{-7} \; \mathrm{H} / \mathrm{m}$. The skin depth ...
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1189
GATE ECE 1996 | Question 3.1
In the circuit shown in the figure is $(a)-(c)$, assuming initial voltage and capacitors and currents through the inductors to be zero at the time of switching $(t=0)$, then at anytime $t>0$. Current increases ... time Current decreases monotonically with time Current remains constant at $V/R$ Current first increases then decreases No current can ever flow
In the circuit shown in the figure is $(a)-(c)$, assuming initial voltage and capacitors and currents through the inductors to be zero at the time of switching $(t=0)$, t...
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1190
GATE ECE 1996 | Question 3.2
(a) Cascade amplifier (b) Differential (c) Darlington pair does not provide current gain is a wideband amplifier amplifier has very low input common-emitter impedance and very amplifier high current gain has very high input impedance and very high current gain provides high common mode voltage rejection
(a) Cascade amplifier(b) Differential(c) Darlington pairdoes not provide current gainis a wideband amplifier amplifierhas very low input common-emitter impedance and very...
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1191
GATE ECE 1996 | Question 3.3
(a) A shift register (b) A multiplexer (c) A decoder can for code conversion can be used to generate memory can be used chip select for parallel-to-serial be used conversion as a many-to-one switch for analog-to-digital conversion
(a) A shift register(b) A multiplexer(c) A decoder canfor code conversion can be usedto generate memory can be used chip selectfor parallel-to-serial be used conversionas...
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1192
GATE ECE 1996 | Question 3.4
(a) Capture effect is (b) Granular noise (c) Guard band is an $\text{AM}$ system a characteristics of an $\text{FM}$ system occurs in a $\text{DM}$ system required in a $\text{FDM}$ system a $\text{PCM}$ system a $\text{TDM}$ system
(a) Capture effect is (b) Granular noise(c) Guard band isan $\text{AM}$ system a characteristics ofan $\text{FM}$ system occurs ina $\text{DM}$ system required ina $\text...
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1193
GATE ECE 1996 | Question 3.5
(a) SSB Modulation (b) $\nabla \cdot \overline{\mathrm{B}}=0$ (c) Model dispersion Transmission line Hilbert transform Faraday's law Absence of magnetic monopoles Waveguides Phase-locked loop
(a) SSB Modulation(b) $\nabla \cdot \overline{\mathrm{B}}=0$(c) Model dispersionTransmission lineHilbert transformFaraday's lawAbsence of magnetic monopolesWaveguidesPhas...
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1194
GATE ECE 2006 | Question: 1
The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is $0$ $1$ $2$ $3$
The rank of the matrix $\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{array}\right]$ is$0$$1$$2$$3$
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1195
GATE ECE 2006 | Question: 2
$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to $\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$ $\nabla^{2} \text{P} +\nabla(\nabla \bullet \text{P})$ $\nabla^{2} \mathrm{P}+\nabla \times \mathrm{P}$ $\nabla(\nabla \bullet \mathrm{P})-\nabla^{2} \mathrm{P}$
$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to$\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$$\nabla^{2} \text{P...
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1196
GATE ECE 2006 | Question: 3
$\displaystyle{}\iint(\nabla \times \mathrm{P}) \bullet \mathrm{ds},$ where $\mathrm{P}$ is a vector, is equal to $\displaystyle{}\oint \text{P} \bullet d l$ $\displaystyle{}\oint \nabla \times \nabla \times \mathrm{P} \bullet d l$ $\displaystyle{}\oint \nabla \times \mathrm{P} \bullet d l$ $\displaystyle{}\iiint \nabla \bullet \mathrm{P} d v$
$\displaystyle{}\iint(\nabla \times \mathrm{P}) \bullet \mathrm{ds},$ where $\mathrm{P}$ is a vector, is equal to$\displaystyle{}\oint \text{P} \bullet d l$$\displaystyle...
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1197
GATE ECE 2006 | Question: 4
A probability density function is of the form $\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)$ The value of $\text{K}$ is $0.5$ $1$ $0.5 \alpha$ $\alpha$
A probability density function is of the form$\qquad p(x)=\mathrm{Ke}^{-\alpha|x|}, x \in(-\infty, \infty)$The value of $\text{K}$ is$0.5$$1$$0.5 \alpha$$\alpha$
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1198
GATE ECE 2006 | Question: 5
A solution for the differential equation $ \qquad \dot{x}(t)+2 x(t)=\delta(t)$ with initial condition $x(0-)=0$ is $e^{-2 t} \; u(t)$ $e^{2 t} \; u(t)$ $e^{-t} \; u(t)$ $e^{t} \; u(t)$
A solution for the differential equation$ \qquad \dot{x}(t)+2 x(t)=\delta(t)$with initial condition $x(0-)=0$ is$e^{-2 t} \; u(t)$$e^{2 t} \; u(t)$$e^{-t} \; u(t)$$e^{t} ...
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1199
GATE ECE 2006 | Question: 6
A low-pass filter having a frequency response $\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}$ does not produce any phase distortion, if $\mathrm{A}(\omega)=\mathrm{C}\omega^{2}, \phi(\omega)=k \omega^{3}$ ... $\mathrm{A}(\omega)=\mathrm{C}, \phi(\omega)=k \omega^{-1}$
A low-pass filter having a frequency response $\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}$ does not produce any phase distortion, if$\mathrm{A...
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1200
GATE ECE 2006 | Question: 7
The values of voltage $\left(\mathrm{V}_{\mathrm{D}}\right)$ across a tunnel-diode corresponding to peak and valley currents are $\text{V}_{\text{P}}$ and $\text{V}_{\text{V}}$ respectively. The range of tunnel-diode voltage $\text{V}_{\text{D}}$ for which the ... $\mathrm{V}_{\mathrm{D}} \geq \mathrm{V}_{\mathrm{V}}$
The values of voltage $\left(\mathrm{V}_{\mathrm{D}}\right)$ across a tunnel-diode corresponding to peak and valley currents are $\text{V}_{\text{P}}$ and $\text{V}_{\tex...
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