GATE ECE 2007
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GATE ECE

In a transconductance amplifier , it is desirable to have
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For the BJT circuit shown, assume that the $$\beta $$ of the transistor is very large and VBE = 0.7 V. The mode of oper
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For the Op-Amp circuit shown in the figure, V0 is
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In the Op-Amp circuit shown, assume that the diode current follows the equation I = Is exp (V/VT) . For Vi = 2V, Vo = V
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Consider the OP-Amp circuit shown in the figure. The transfer function $${V_o}\left( s \right)/{V_i}\left( s \right)$$ i
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Consider the OP-Amp circuit shown in the figure. If $${V_i} = {V_1}\,\,\sin \left( {\omega \tau + \phi } \right),$$ th
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A Hilbert transformer is a
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In delta modulation, the slope overload distortion can be reduced by
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In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 M
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The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off
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In a Direct sequence CDMA system the chip rate is $$1.2288\,\, \times \,\,{10^6}$$ chips per second. If the processing g
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During transmission over a certain binary communication channel, bit errors occurs independently with probability p. The
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An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of
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An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of
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If E denotes expectation, the variance of a random variable X is given by
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Two 4-ray signal constellations are shown. It is given that $${\phi _1}$$ and $${\phi _2}$$ constitute an orthonormal ba
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Two 4-ray signal constellations are shown. It is given that $${\phi _1}$$ and $${\phi _2}$$ constitute an orthonormal ba
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If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final v
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The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}
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A unity feedback control system has an open-loop transfer function $$$G\left(s\right)=\frac K{s\left(s^2+7s+12\right)}$$
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The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order
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If the closed-loop transfer function of a control system is given as T(s)=$${{s - 5} \over {(s + 2)(s + 3)}},$$ then it
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The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this
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A control system with a PD controller is shown in the figure. If the velocity error constant $${K_v} = 1000$$ and the d
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The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a
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The state space representation of a separately excited DC servo motor dynamics is given as $$$\left[ {\matrix{ {{{d\o
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Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t
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Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t
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X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represen
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The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is
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The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,}
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In the following circuit, X is given by
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For the circuit shown, the counter state (Q1 Q0) follows the sequence
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The circuit diagram of a standard TTL NOT gate is shown in the figure. When $${V_i}$$= 2.5V, the modes of operation of
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The following binary values were applied to the X and Y inputs of the NAND latch shown in the figure in the sequence ind
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In the digital-to-Analog converter circuit shown in the figure below, $${V_{R\,}}\, = \,10V$$ and $$R\, = \,10k\Omega $$
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In the digital-to-Analog converter circuit shown in the figure below, $${V_{R\,}}\, = \,10V$$ and $$R\, = \,10k\Omega $$
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A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $
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A load of 50 $$\Omega $$ is connected in shunt in a 2-wire transmission line of $$Z_0$$ = 50 $$\Omega $$ as shown in the
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The parallel branches of a 2-wire transmission line are terminated in 100 $$\Omega $$ and 200 $$\Omega $$ resistors as s
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If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current dens
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The $$\overrightarrow H $$ field (in A/m) of a plane wave propagating in free space is given by $$$\overrightarrow H
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An air-filled rectangular waveguide has inner dimensions of $$3\,cm\,\, \times \,\,2\,\,cm\,$$. The wave impedance of th
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The $$\mathop E\limits^ \to $$ field in a rectangular waveguide of inner dimensions $$a\,\, \times \,\,b$$ is given by
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A $$\lambda /2$$ dipole is kept horizontally at a height of $${\lambda _0}/2$$ above a perfectly conducting infinite gro
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In a p+n junction diode under reverse bias, the magnitude of electric field is maximum at
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A P+-N junction has a built-in potential of 0.8 V. The depletion layer width at a reverse bias of 1.2V is 2 µm. For a re
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The DC current gain ($$\beta$$) of a BJT is 50. Assuming that the emitter injection efficiency is 0.995, the base transp
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In the CMOS inverter circuit shown, if the transconductance parameters of the NMOS and PMOS transistors are Kn = Kp = μ
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$$\mathop {Lim}\limits_{\theta \to 0} {{\sin \left( {\theta /2} \right)} \over \theta }\,\,\,$$ is
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The following plot shows a function $$y$$ which varies linearly with $$x$$. The value of the integral $$\,\,{\rm I} = \i
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For the function $${e^{ - x}},$$ the linear approximation around $$x=2$$ is
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For $$\left| x \right| < < 1,\,\cot \,h\left( x \right)\,\,\,$$ can be approximated as
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Consider the function $$\,f\left( x \right) = {x^2} - x - 2.\,$$ The maximum value of $$f(x)$$ in the closed interval $$
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If $$E$$ denotes expectation, the variance of a random variable $$X$$ is given by
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An examination consists of two papers, paper $$1$$ and paper $$2.$$ The probability of failing in paper $$1$$ is $$0.3$$
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The solution of the differential equation $${k^2}{{{d^2}y} \over {d\,{x^2}}} = y - {y_2}\,\,$$ under the boundary condi
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The value of $$\oint\limits_C {{1 \over {\left( {1 + {z^2}} \right)}}} dz$$ where C is the contour $$\,\left| {z - {i \o
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The equation $${x^3} - {x^2} + 4x - 4 = 0\,\,$$ is to be solved using the Newton - Raphson method. If $$x=2$$ taken as t
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If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral $$\oint\limits_D {{
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An 8085 assembly language program is given below. Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH
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An 8085 assembly language program is given below. Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH
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An independent voltage source in series with an impedance Zs=Rs+jXs delivers a maximum average power to a load impedance
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For the circuit shown in the figure, the Thevenin voltage and resistance looking into X-Y are:
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In the circuit shown, VC is 0 volts at t = 0 sec. For t > 0, the capacitor current iC(t), where t is in seconds, is g
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The RC circuit shown in the figure is
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In the AC network shown in the figure, the phasor voltage VAB (in Volts) is:
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Two series resonant filters are as shown in the figure. Let the $$3$$-dB bandwidth of Filter $$1$$ be $${B_1}$$ and that
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If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s - 1} \right)}},$$ then its final
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A 5-point sequence x [n] is given as x$$\left[ { - 3} \right]$$ =1, x$$\left[ { - 2} \right]$$ =1, x$$\left[ { - 1} \ri
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The z-transform X (z) f a sequence x$$\left[ n \right]$$ is given by = $${{0.5} \over {1 - 2{z^{ - 1}}}}$$ . It is give
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The frequency response of a linear, time-invariant system is given by H(f) = $${5 \over {1 + j10\pi f}}$$. The step resp
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The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by
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A Hilbert transformer is a
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In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be:
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