GATE 2006 Electronics & Communication

$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to

The unit impulse response of a system is: $$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit step input is equal to

A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its corresponding 3-bit binary code. For example, the base-5 nu...

The input impedance (Z i ) and the output impedance (Z o ) of an ideal transconductance (voltage controlled current source) amplifier are

The unit-step response of a system starting from rest is given by $$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm t\geq0$$$The transfer function...

The open-loop transfer function of a unity-gain feedback control system is given by $$G(s) = {K \over {(s + 1)(s + 2)}},$$ the gain margin of the system in dB is given by

Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$ The 3-dB bandwidths of their freq...

A two-port network is represented by ABCD parameters given by $$\left[ {\matrix{ {{V_1}} \cr {{I_1}} \cr } } \right] = \,\left[ {\matrix{ A & B \cr C & D \cr } } \right]\,\left[ {\...

The eigen values and the correspondinng eigen vectors of a $$2 \times 2$$ matrix are given by Eigen value $${\lambda _1} = 8$$ $${\lambda _2} = 4$$ Eigen vector $${V_1} = \left[ {\...

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ The value of 'a', so that the system has a phase-margin equal t...

An n-channel depletion MOSFET has following two points on its I D - V GS curve: (i)V GS = 0 at I d = 12 mA and (ii)V GS = -6 Volts at Z o =$$\infty $$ Which of the following Q-poin...

A linear system is described by the following state equation $$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),A = \left[ {\matrix{ 0 & 1 \cr...

For the function of a complex variable w = lnz (where w = u + jv and z = x + jy) the u = constant lines get mapped in the z-plane as

For the matrix $$\left[ {\matrix{ 4 & 2 \cr 2 & 4 \cr } } \right].$$ The eigen value corresponding to the eigen vector $$\left[ {\matrix{ {101} \cr {101} \cr } } \right]$$ is

Consider the function $$f(t)$$ having laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}},\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0.$$ The...

The value of the counter integral $$$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,positive\,sense\,is$$$

The electric field of an electromagnetic wave propagating in the positive z-direction is given by $$$E = {\widehat a_x}\sin \left( {\omega t - \beta z} \right) + {\widehat a_y}\sin...

The following question refer to wide sense stationary stochastic process: It is desired to generate a stochastic process (as voltage process) with power spectral density $$$S\left(...

A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source enc...

A mast antenna consisting of a 50 meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at frequency of 600 kHz. The radiation resistance...

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function) x(t) = 125t(u(t) - u (t - 1) + (250 - 1...

A medium of relative permittivityb $${\varepsilon _r} = 2$$ forms an interface with free-space. A point source of electromagnetic energy is located in the medium at a depth of $$1$...

The following question refer to wide sense stationary stochastic process: The parameters of the system obtained in Q. 12 would be

Let $$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}^ * p\left( t \right)$$ where $$ * $$ denotes convolution and...

Following is the segment of a 8085 assembly Language program: LXI SP, EFFF H CALL 3000 H 3000H: LXI H, 3CF4H PUSH PSW SPHL POP PSW RET On completion of RET execution, the contents...

A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period t s = 0.03 msec. The samp...

The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain margin of the system in dB is equal to

Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the

When a plane wave traveling in free-space is incident normally on a medium having $${\varepsilon _r} = 4.0,$$ the fraction of power transmitted into the medium is given by

A rectangular waveguide having $$T{E_{10}}$$ mode as dominant mode is having a cutoff frequency of 18 GHz for the $$T{E_{30}}$$ mode. The inner broad-wall dimension of the rectangu...

A transmission line is feeding 1 Watt of power to a horn antenna having gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna...

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$. With the value of "a" set for phase-margin of $$\pi $$/4, the...

For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are (i) $$y=0$$ for $$x=0$$ and (ii) $$y=0$$ for $$x=a$$ The form of non-zero solu...

The transfer function of a phase-lead compensator is given by $${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$ where T > 0. The maximum phase-shift provided by such a compesator is

The rank of the matrix $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr } } \right]$$ is

A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The...

The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {{{\sin \,\,2\,\pi \,1000\,t)} \...

If the region of convergence of $${x_1}\left[ n \right]$$ + $${x_2}\left[ n \right]$$ is 1/3< $$\left| {z\,} \right|$$<2/3, then the region of convergence of $${x_1}\left[ n \right...

The Dirac delta function $$\delta (t)$$ is defined as

The concentration of minority carriers in an extrinsic semiconductor under equilibrium is:

An n-channel depletion MOSFET has following two points on its I D − V GS curve: (i) V GS = 0 at I D = 12 mA and (ii) V GS = - 6 Volts at I D = 0 Which of the following Q-points wil...

Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0$$...

A low-pass filter having a frequency response $$H(j\omega )$$ = $$A(\omega ){e^{j\Phi (\omega )}}$$, does not product any phase distortion if

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\delta (t - 0.5x{{10}^{ - 4}}k)} $$...

Let x(t) $$ \leftrightarrow $$ X($$(j\omega )$$ BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3) in terms of X($$(j\omega )$$ is given as

As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$

Let g(t) = p(t) * p(t), where * denotes convolution and p(t) = u(t) - (t-1) with u(t) being the unit step function. The impulse response of filter matched to the singal s(t) = g(t)...

A solution for the differential equation $$\mathop x\limits^. $$(t) + 2 x (t) = $$\delta (t)$$ with intial condition $$x({0^ - }) = 0$$ is

$$\nabla \times \nabla \times P$$, where P is a vector, is equal to

The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (here W is...