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521
GATE ECE 1999 | Question 1.18
A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ is a real and even function of $\omega$ a imaginary and odd function of $\omega$ an imaginary and even function of $\omega$ a real and odd function of $\omega$
A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ isa real and even function of $\omega$a imaginary and o...
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GATE ECE 1999 | Question 1.19
The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by \[ y(t)=(1 / 100) \cos \left(100 t-10^{-6}\right) \cos \left(10^{6} t-1.56\right) \] The group ... $t_{g}=10^{8}, t_{p}=1.56 \times 10^{-6}$ $t_{g}=10^{8}, t_{p}=1.56$
The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this i...
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GATE ECE 1999 | Question 1.20
A modulated signal is given by, \[ s(t)=m_{1}(t) \cos \left(2 \pi f_{c} t\right)+m_{2}(t) \sin \left(2 \pi f_{c} t\right) \] where the baseband signal $m_{1}(t)$ and $m_{2}(t)$ have bandwidths of $10 \; \mathrm{kHz}$ and $15 \; \mathrm{kHz}$, respectively. The bandwidth of the modulated signal, in $\mathrm{kHz}$, is $10$ $15$ $25$ $30$
A modulated signal is given by,\[s(t)=m_{1}(t) \cos \left(2 \pi f_{c} t\right)+m_{2}(t) \sin \left(2 \pi f_{c} t\right)\]where the baseband signal $m_{1}(t)$ and $m_{2}(t...
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GATE ECE 1999 | Question 1.21
A modulated signal is given by \[s(t)=e^{-a t} \cos \left[\left(\omega_{c}+\Delta \omega\right) t\right] u(t),\] where $a, \omega_{c}$ and $\Delta \omega$ are positive constants, and $\omega_{c} \gg \Delta \omega$. The complex envelope of $s(t)$ is given by ... $\exp (j \Delta \omega t) \cdot u(t)$ $\left.\exp \left[j \omega_{c}+\Delta \omega\right) t\right]$
A modulated signal is given by\[s(t)=e^{-a t} \cos \left[\left(\omega_{c}+\Delta \omega\right) t\right] u(t),\]where $a, \omega_{c}$ and $\Delta \omega$ are positive cons...
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GATE ECE 1999 | Question 1.22
An electric field on a plane is described by its potential \[\mathrm{V}=20\left(r^{-1}+r^{-2}\right)\] where $r$ is the distance from the source. The field is due to a monopole a dipole both a monopole and a dipole a quadrupole
An electric field on a plane is described by its potential\[\mathrm{V}=20\left(r^{-1}+r^{-2}\right)\]where $r$ is the distance from the source. The field is due toa monop...
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GATE ECE 1999 | Question 1.23
Assuming perfect conductors of a transmission line, pure $\text{TEM}$ propagation is $\text{NOT}$ possible in coaxial cable air-filled cylindrical waveguide parallel twin-wire line in air semi-infinite parallel plate wave guide
Assuming perfect conductors of a transmission line, pure $\text{TEM}$ propagation is $\text{NOT}$ possible incoaxial cableair-filled cylindrical waveguideparallel twin-wi...
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GATE ECE 1999 | Question 1.24
Indicate which one of the following will $\text{NOT}$ exist in a rectangular resonant cavity. $\mathrm{TE}_{110}$ $\mathrm{TE}_{011}$ $\mathrm{TM}_{110}$ $\mathrm{TM}_{111}$
Indicate which one of the following will $\text{NOT}$ exist in a rectangular resonant cavity.$\mathrm{TE}_{110}$$\mathrm{TE}_{011}$$\mathrm{TM}_{110}$$\mathrm{TM}_{111}$
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GATE ECE 1999 | Question 1.25
Identify which one of the following will $\text{NOT}$ satisfy the wave equation. $50 \; e^{f(\omega t-3 z)}$ $\sin [\omega(10 z+5 t)]$ $\cos \left(y^{2}+5 t\right)$ $\sin (x) \cos (t)$
Identify which one of the following will $\text{NOT}$ satisfy the wave equation.$50 \; e^{f(\omega t-3 z)}$$\sin [\omega(10 z+5 t)]$$\cos \left(y^{2}+5 t\right)$$\sin (x)...
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GATE ECE 1999 | Question 2.1
The Fourier series representation of an impules train denoted by \[s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text { is given by }\] $\frac{1}{\mathrm{~T}_{0}} \sum_{n=-\infty}^{\infty} \exp -\frac{j 2 \pi n t}{\mathrm{~T}_{0}}$ ... $\frac{1}{\mathrm{~T}_{0}} \sum_{u=-\infty}^{\infty} \exp \frac{j 2 \pi n t}{\mathrm{~T}_{0}}$
The Fourier series representation of an impules train denoted by\[s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text { is given by }\]$\frac{1}{\mathrm{~T}...
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GATE ECE 1999 | Question 2.2
The Thevenin equivalent voltage $\mathrm{V}_{\mathrm{TH}}$ appearing between the terminals $A$ and $B$ of the network shown in the given figure is given by $j 16(3-j 4)$ $j 16(3+j 4)$ $16(3+j 4)$ $16(3-j 4)$
The Thevenin equivalent voltage $\mathrm{V}_{\mathrm{TH}}$ appearing between the terminals $A$ and $B$ of the network shown in the given figure is given by$j 16(3-j 4)$$j...
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GATE ECE 1999 | Question 2.3
The value of $R$ (in ohms) required for maximum power transfer in the network shown in the given figure $2$ $4$ $8$ $16$
The value of $R$ (in ohms) required for maximum power transfer in the network shown in the given figure$2$$4$$8$$16$
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GATE ECE 1999 | Question 2.4
A Delta-connected network with its Wye-equivalent is shown in the given figure is. The resistances $R_{1}, R_{2}$ and $R_{3}$ (in ohms) are respectively $1.5,3$ and $9$ $3,9$ and $1.5$ $9,3$ and $1.5$ $3,1.5$ and $9$
A Delta-connected network with its Wye-equivalent is shown in the given figure is. The resistances $R_{1}, R_{2}$ and $R_{3}$ (in ohms) are respectively$1.5,3$ and $9$$3,...
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GATE ECE 1999 | Question 2.5
An $n$-channel $\text{JEFT}$ has $\mathrm{I}_{\mathrm{DSS}}=2 \mathrm{~mA}$ and $\mathrm{V}_{p}=-4 \mathrm{~V}$. Its transconductance $\mathrm{gm}$ (in milliohm) for an applied gate-to-source voltage $\mathrm{V}_{\mathrm{GS}}$ of $-2 \mathrm{~V}$ is $0.25$ $0.5$ $0.75$ $1.0$
An $n$-channel $\text{JEFT}$ has $\mathrm{I}_{\mathrm{DSS}}=2 \mathrm{~mA}$ and $\mathrm{V}_{p}=-4 \mathrm{~V}$. Its transconductance $\mathrm{gm}$ (in milliohm) for an a...
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GATE ECE 1999 | Question 2.6
An $\text{npn}$ transistor (with $\mathrm{C}=0.3 \; \mathrm{pF}$ ) has a unity gain cutoff frequency $f_{\mathrm{T}}$ of $400 \; \mathrm{MHz}$ at a $\text{dc}$ bias current $I_{c}=1 \mathrm{~mA}$. The value of its $C_{\mu}$ (in $\mathrm{~pF}$ ) is approximately $\left(\mathrm{V}_{\mathrm{T}}=26 \; \mathrm{mV}\right)$ $15$ $30$ $50$ $96$
An $\text{npn}$ transistor (with $\mathrm{C}=0.3 \; \mathrm{pF}$ ) has a unity gain cutoff frequency $f_{\mathrm{T}}$ of $400 \; \mathrm{MHz}$ at a $\text{dc}$ bias curre...
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GATE ECE 1999 | Question 2.7
An amplifier has an open-loop gain of $100$, an input impedance of $1 \; \mathrm{k \Omega}$, and an output impedance of $100 \; \Omega$. A feedback network with a feedback factor of $0.99$ is connected to the amplifier in a voltage series feedback mode. The new input and ... and $10 \; k \Omega$ $100 \; \Omega$ and $1 \; \Omega$ $100 \; k \Omega$ and $1 \; k\Omega$
An amplifier has an open-loop gain of $100$, an input impedance of $1 \; \mathrm{k \Omega}$, and an output impedance of $100 \; \Omega$. A feedback network with a feedbac...
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GATE ECE 1999 | Question 2.8
A $\text{dc}$ power supply has a no-load voltage if $30 \mathrm{~V}$, and a full-load voltage of $25 \mathrm{~V}$ at a full - load current of $1 \mathrm{~A}$. Its output resistance and load regulation, respectively, are $5\; \Omega\; \mathrm{and} \;20\%$ $25 \;\Omega\; \mathrm{and} \;20 \%$ $5 \;\Omega\; \mathrm{and} \;16.7 \%$ $25\; \Omega \;\mathrm{and}\; 16.7 \%$
A $\text{dc}$ power supply has a no-load voltage if $30 \mathrm{~V}$, and a full-load voltage of $25 \mathrm{~V}$ at a full - load current of $1 \mathrm{~A}$. Its output ...
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GATE ECE 1999 | Question 2.9
An amplifier is assumed to have a single-pole high-frequency transfer function. The rise time of its output response to a step function input is $35\;\text{nsec}$. The upper $-3 \; d B$ frequency (in $\text{MHz}$) for the amplifier to a sinusoidal input is approximately at $4.55$ $10$ $20$ $28.6$
An amplifier is assumed to have a single-pole high-frequency transfer function. The rise time of its output response to a step function input is $35\;\text{nsec}$. The up...
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GATE ECE 1999 | Question 2.10
The minimized form of the logical expression $(\bar{A} \bar{B} \bar{C}+\bar{A} B \bar{C}+\bar{A} B C+A B \bar{C})$ is $\overline{\mathrm{A}} \overline{\mathrm{C}}+\mathrm{B} \overline{\mathrm{C}}+\overline{\mathrm{A}} \mathrm{B}$ ... $\mathrm{A} \overline{\mathrm{C}}+\overline{\mathrm{B}} \mathrm{C}+A \overline{\mathrm{B}}$
The minimized form of the logical expression $(\bar{A} \bar{B} \bar{C}+\bar{A} B \bar{C}+\bar{A} B C+A B \bar{C})$ is$\overline{\mathrm{A}} \overline{\mathrm{C}}+\mathrm{...
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GATE ECE 1999 | Question 2.11
For a binary half-subtractor having two inputs $\text{A}$ and $\text{B}$, the correct set of logical expressions for the outputs $\text{D}$ ( = $\text{A}$ minus $\text{B}$ ) and $\text{X}(=$ ... $\mathrm{D}=\mathrm{AB}+\overline{\mathrm{A}} \overline{\mathrm{B}}, \mathrm{X}=\mathrm{A} \overline{\mathrm{B}}$
For a binary half-subtractor having two inputs $\text{A}$ and $\text{B}$, the correct set of logical expressions for the outputs $\text{D}$ ( = $\text{A}$ minus $\text{B}...
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GATE ECE 1999 | Question 2.12
The ripple counter shown in the given figure is works as a $\bmod -3$ up counter $\bmod -5$ up counter $\bmod - 3$ down counter $\bmod - 5$ down counter
The ripple counter shown in the given figure is works as a$\bmod -3$ up counter$\bmod -5$ up counter$\bmod - 3$ down counter$\bmod - 5$ down counter
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GATE ECE 1999 | Question 2.13
If $\text{CS}=\text{A}_{15} \; \text{ A}_{14} \; \text{A}_{13}$ is used as the chip select logic of a $4 \; \text{K RAM}$ in an $8085$ system, then its memory range will be $3000 \; \mathrm{H}-3 \; \mathrm{FFF \; H}$ ... $6000 \; \mathrm{H}-6 \; \mathrm{FFF} \; \mathrm{H} \; \text{and} \; 7000 \; \mathrm{H}-7 \; \mathrm{FFF \; H}$
If $\text{CS}=\text{A}_{15} \; \text{ A}_{14} \; \text{A}_{13}$ is used as the chip select logic of a $4 \; \text{K RAM}$ in an $8085$ system, then its memory range will ...
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GATE ECE 1999 | Question 2.14
If the closed-loop transfer function $T(s)$ of a unity negative feedback system is given by \[ \mathrm{T}(\mathrm{s})=\frac{a_{n -1} \mathrm{~s}+a_{n}}{\mathrm{~s}^{n}+n_{1} s^{n-1}+\ldots+a_{n-1} s+a_{n}} \] then the steady state error for a unit ramp input is $\frac{a_{n}}{a_{n-1}}$ $\frac{a_{n}}{a_{n-2}}$ $\frac{a_{n-2}}{a_{n-2}}$ zero
If the closed-loop transfer function $T(s)$ of a unity negative feedback system is given by\[\mathrm{T}(\mathrm{s})=\frac{a_{n -1} \mathrm{~s}+a_{n}}{\mathrm{~s}^{n}+n_{1...
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GATE ECE 1999 | Question 2.15
Consider the points $s_{1}=-3+j 4$ and $s_{2}=-3-j 2$ in the $s$-plane. Then, for a system with the open-loop Transfer function \[G(s) H(s)=\frac{K}{(s+1)^{4}}\] $s_{1}$ is on the root locus,but not $s_{2}$ $s_{2}$ is on the root locus, but not $s_{1}$ both $s_{1}$ and $s_{2}$ are on the root locus neither $s_{1}$ nor $s_{2}$ is on the root locus.
Consider the points $s_{1}=-3+j 4$ and $s_{2}=-3-j 2$ in the $s$-plane. Then, for a system with the open-loop Transfer function\[G(s) H(s)=\frac{K}{(s+1)^{4}}\]$s_{1}$ is...
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GATE ECE 1999 | Question 2.16
For the system described by the state equation \[ x=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0.5 & 1 & 2 \end{array}\right] x+\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right] u \] If the control signal $u$ ... $x+v$, then the eigenvalues of the closed-loop system will be $0,-1,-2$ $0,-1,-3$ $-1,-1,-2$ $0,-1,-1$
For the system described by the state equation\[x=\left[\begin{array}{ccc}0 & 1 & 0 \\0 & 0 & 1 \\0.5 & 1 & 2\end{array}\right] x+\left[\begin{array}{l}0 \\0 \\1\end{arra...
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GATE ECE 1999 | Question 2.17
The $z$-transform of a signal is given by \[C(z)=\frac{1 z^{-1}\left(1-z^{-4}\right)}{4\left(1-z^{-1}\right)^{2}}\] Its final value is $1 / 4$ zero $1.0$ infinity
The $z$-transform of a signal is given by\[C(z)=\frac{1 z^{-1}\left(1-z^{-4}\right)}{4\left(1-z^{-1}\right)^{2}}\]Its final value is$1 / 4$zero$1.0$infinity
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GATE ECE 1999 | Question 2.18
The Nyquist sampling frequency (in $\mathrm{Hz}$ ) of a signal given by $6 \times 10^{4} \sin c^{2}(400 t)^{*} 10^{6} \sin c^{3}(100 t)$ is $200$ $300$ $500$ $1000$
The Nyquist sampling frequency (in $\mathrm{Hz}$ ) of a signal given by$6 \times 10^{4} \sin c^{2}(400 t)^{*} 10^{6} \sin c^{3}(100 t)$ is$200$$300$$500$$1000$
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GATE ECE 1999 | Question 2.19
The peak-to-peak input to an $8$-bit $\text{PCM}$ coder is $2$ volts. The signal power-to-quantization noise power ratio (in $d\text{B}$) for an input of $0.5 \cos \left(\omega_{m} t\right)$ is $47.8$ $49.8$ $95.6$ $99.6$
The peak-to-peak input to an $8$-bit $\text{PCM}$ coder is $2$ volts. The signal power-to-quantization noise power ratio (in $d\text{B}$) for an input of $0.5 \cos \left(...
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GATE ECE 1999 | Question 2.20
The input to a matched filter is given by $s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} \mathrm{sec} \\ & \text{otherwise} \end{array}$ The peak amplitude of the filter output is $10$ volts $5$ volts $10$ millivolts $5$ millivolts
The input to a matched filter is given by$s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} ...
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GATE ECE 1999 | Question 2.21
Four independent messages have bandwidths of $100 \mathrm{~Hz}, 200 \mathrm{~Hz}$, and $400 \mathrm{~Hz}$, respectively. Each is sampled at the Nyquist rate, and the samples are time division multiplexed ($\text{TDM}$) and transmitted. The transmitted sample rate (in $\mathrm{Hz}$ ) is $1600$ $800$ $400$ $200$
Four independent messages have bandwidths of $100 \mathrm{~Hz}, 200 \mathrm{~Hz}$, and $400 \mathrm{~Hz}$, respectively. Each is sampled at the Nyquist rate, and the samp...
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GATE ECE 1999 | Question 2.22
In a twin-wire transmission line in air, the adjacent voltage maxima are at $12.5 \mathrm{~cm}$ and $27.5 \mathrm{~cm}$. The operating frequency is $300 \; \mathrm{MHz}$ $1 \; \mathrm{GHz}$ $2 \; \mathrm{GHz}$ $6.28 \; \mathrm{GHz}$
In a twin-wire transmission line in air, the adjacent voltage maxima are at $12.5 \mathrm{~cm}$ and $27.5 \mathrm{~cm}$. The operating frequency is$300 \; \mathrm{MHz}$$1...
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GATE ECE 1999 | Question 2.23
A trasmitting antenna radiates $251 \mathrm{~W}$ isotropically. A receiving antenna, located $100 \mathrm{~m}$ away from the transmitting antenna, has an effective aperture of $500 \mathrm{~cm}^{2}$. The total received by the antenna is $10 \; \mu \mathrm{W}$ $1 \; \mu \mathrm{W}$ $20 \; \mu \mathrm{W}$ $100 \; \mu \mathrm{W}$
A trasmitting antenna radiates $251 \mathrm{~W}$ isotropically. A receiving antenna, located $100 \mathrm{~m}$ away from the transmitting antenna, has an effective apertu...
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GATE ECE 1999 | Question 2.24
In air, a lossless transmission line of length $50 \mathrm{~cm}$ with $\mathrm{L}=10 \; \mu \mathrm{H} / \mathrm{m}, \mathrm{C}=40 \; \mathrm{pF} / \mathrm{m}$ is operated at $25 \; \mathrm{MHz}$. Its electrical path length is $0.5$ meters $\lambda$ meters $\pi / 2$ radians $180$ degrees
In air, a lossless transmission line of length $50 \mathrm{~cm}$ with $\mathrm{L}=10 \; \mu \mathrm{H} / \mathrm{m}, \mathrm{C}=40 \; \mathrm{pF} / \mathrm{m}$ is operate...
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GATE ECE 1999 | Question 2.25
A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ ... $377$ $198.5 \angle 180^{\circ}$ $182.9 \angle 14^{\circ}$ $133.3$
A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ has its electric field given by $\overr...
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GATE ECE 1999 | Question: 3
In the circuit of the the switch '$\text{S}$' has remained open for a long time. The switch closes instantaneously at $t=0$ Find $V_{0}$ for $t \leq 0$ and as $t \rightarrow \infty$ Write an expression for $V_{0}$ as function of time for $0 \leq t \leq \infty$ Evaluate $\mathrm{V}_{0}$ at $t=25 \; \mu \mathrm{sec}$.
In the circuit of the the switch '$\text{S}$' has remained open for a long time. The switch closes instantaneously at $t=0$Find $V_{0}$ for $t \leq 0$ and as $t \rightarr...
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GATE ECE 1999 | Question 4
For the network shown in the given figure is evaluate the current $I$ flowing through the $2 \; \Omega$ resistor using superposition theorem.
For the network shown in the given figure is evaluate the current $I$ flowing through the $2 \; \Omega$ resistor using superposition theorem.
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GATE ECE 1999 | Question 5
A coil with a quality factor $(Q)$ of $10$ is put in series with a capacitor $\mathrm{C}_{1}$ of $10 \; \mu \mathrm{F}$, and the combination is found to draw maximum current when a sinusoidal voltage of frequency $50 \mathrm{~Hz}$ is applied. ... $100 \mathrm{~Hz}$ if the applied voltage is $100 \mathrm{~V}(\mathrm{rms})$
A coil with a quality factor $(Q)$ of $10$ is put in series with a capacitor $\mathrm{C}_{1}$ of $10 \; \mu \mathrm{F}$, and the combination is found to draw maximum curr...
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GATE ECE 1999 | Question 6
A bipolar junction transistor amplifier circuit is shown in the figure is Assume that the current source $\text{I}_{\text {bias}}$ is ideal, and the transistor has vary large $b, r_{b}=0$, and $r_{0} \rightarrow \infty$. Determine the $\text{ac}$ small-signal ... $\left(R_{u}\right)$ of the circuit. Assume $V_{T}=26 \; \mathrm{mV}$
A bipolar junction transistor amplifier circuit is shown in the figure is Assume that the current source $\text{I}_{\text {bias}}$ is ideal, and the transistor has vary l...
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GATE ECE 1999 | Question 7
A $\text{JFET}$ having $\mu=50$ and $r_{d}=10 \mathrm{~K} \Omega$ is used in a common - source configuration as shown in the given figure. The $\text{JFET}$ capacitances are $C_{s^{s}}=5 \; pF$, $C_{g d}=2 \; p \mathrm{F}$ ... midband voltage gain $\left(\mathrm{V}_{0} / \mathrm{V}_{s}\right)$ and the upper $-3 \; d \mathrm{B}$ frequency of the circuit.
A $\text{JFET}$ having $\mu=50$ and $r_{d}=10 \mathrm{~K} \Omega$ is used in a common - source configuration as shown in the given figure. The $\text{JFET}$ capacitances ...
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GATE ECE 1999 | Question 8
Neatly sketch and label the $\text{dc}$ transfer characteristic (i.e., $\mathrm{V}_{0} v s . \mathrm{V}_{i n}$ ) of the circuit shown in the given figure as $V_{\text {in}}$ varies from $-2 \mathrm{~V}$ to $+2 \text{ V}.$ Assume ideal $\text{op-amp}$, and the diodes have a forward voltage of $0.6 \mathrm{~V}$ and zero incremental resistance.
Neatly sketch and label the $\text{dc}$ transfer characteristic (i.e., $\mathrm{V}_{0} v s . \mathrm{V}_{i n}$ ) of the circuit shown in the given figure as $V_{\text {in...
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560
GATE ECE 1999 | Question 9
A transistor $\mathrm{LC}$ oscillator circuit is shown in the given figure. Assume that the transistor has very high $\beta$ (so that you may neglect $r_{d}$ ). Derive an equation governing the circuit operation, and find the frequency of oscillation. Also, state the gain condition required for oscillation to start.
A transistor $\mathrm{LC}$ oscillator circuit is shown in the given figure. Assume that the transistor has very high $\beta$ (so that you may neglect $r_{d}$ ). Derive an...
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Sep 29, 2022
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gate1999-ec
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