GATE 2005 Electronics & Communication

A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ is to be compensated to achieve the damping ratio $$\zeta = 0.5$$ and an undamped natural frequency, $${\omega _n}...

A linear system is equivalently represented by two sets of state equations. $$\mathop x\limits^ \bullet = \,\,{\rm A}X\,\, + BU$$ and $$\mathop W\limits^ \bullet = \,\,CW\,\, + DU....

Despite the presence of negative feedback, control systems still have problems of instability because the

A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively.

Decimal 43 in Hexadecimal and BCD number system is respectively

In the derivation of expression for peak percent overshoot,$$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\times100\%$$$ .Which one of the following conditions is NOT re...

A unity feedback system is given as,$$$G\left(s\right)=\frac{K\left(1-s\right)}{s\left(s+3\right)}$$$ indicate the correct root locus diagram.

The present output Q n of an edge triggered JK flip-flop is logic 0. If J=1, then Q n+1

A solution of the differential equation $${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$ is given by

The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptstyle {{x^2}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\sc...

The following differential equation has $$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} + 2 = x$$

The Dirac delta Function $$\delta \left( t \right)$$ is defined as

The open loop transfer function of a unity feedback system is given by g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ Based on the above results, the gain and phase mar...

The open loop transfer function of a unity feedback system is given by G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ The gain and phase crossover frequencies in rad/se...

A Silicon PN junction at a temperature of 20°C has a reverse saturation current of 10 pico-Amperes (pA). The reverse saturation current at 40°C for the same bias is approximately

The band gap of Silicon at room temperature is:

The cascode amplifier is a multistage configuration of

Consider an 8085 microprocessor system If in addition following code exists from 0109H onwards ORI 40H, ADD M What will be the result in the accumulator after the last instruction...

Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of $${10^{14}}$$ Hz in glass. Assume velocity of light is $$3\,\, \times \,{10^8}$$ m/s in...

Two identical and parallel dipole antennas are kept apart by a distance $$\lambda /4$$ of in the H-plane. They are fed with equal currents but the right most antenna has a phase sh...

Noise with uniform power spectral density of N 0 W/Hz is passed through a filter H(ω ) = 2exp (-jωt d ) followed by an ideal low pass filter of bandwidth B Hz. The output noise pow...

The magnetic field intensity vector of a plane wave is given by $$\overline H \left( {x,y,z,t} \right) = 10\,\sin \left( {50000t + 0.004x + 30} \right){\mathop a\limits^ \cap _y}$$...

Which one of the following does represent the electric field lines for the $$T{E_{02}}$$ mode in the cross-section of a hollow rectangular metallic waveguide?

Consider an 8085 microprocessor system The following program starts at locaton 0100H. LXI SP, 00FF LXI H, 0107 MVI A, 20H SUB M The contents of accumulator wnen the program counter...

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels. The quantization noise power for the quantization region b...

Characteristic impedance of a transmission line is 50$$\Omega $$. Input impedance of the open-circuited line is $${Z_{oc}} = 100\, + \,j\,\,150\Omega .$$ When the transmission line...

$$\nabla \times \left( {\nabla \times P} \right)\,\,$$ where $$P$$ is a vector is equal to

The Boolean expression for the truth table shown is A B C D 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0

Which one of the following polar diagrams corresponds to a lag network?

In a series $$RLC$$ circuit $$R = 2\,k\Omega ,\,\,\,L = \,1H$$ and $$C = \,1/400\,\mu F.$$ The resonant frequency is

A fair dice is rolled twice. The probability that an odd number will follow an even number is

The effect of current shunt feedback in an amplifier is to

Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 1} \cr 1 & { - 1} & 0 & 0 \cr 0 & 0 & 1 & { - 1} \cr } } \right]$$ then the value of $${\le...

Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is

Match the following and choose the correct combination Group $$-$$ $${\rm I}$$ $$E.$$ Newton $$-$$ Raphson method $$F.$$ Runge-Kutta method $$G.$$ Simpson's Rule $$H.$$ Gauss elimi...

If $$A = \left[ {\matrix{ 2 & { - 0.1} \cr 0 & 3 \cr } } \right]$$ and $${A^{ - 1}} = \left[ {\matrix{ {{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hb...

In what range should $$Re(s)$$ remain so that the laplace transform of the function $${e^{\left( {a + 2} \right)t + 5}}$$ exists?

A MOS capacitor made using p-type substrate is in the accumulation mode. The dominant charge in the channel is due to the presence of

The primary reason for the widespread use of Silicon in semiconductor device technology is

A silicon sample 'A' is doped with 10 18 atoms/cm 3 of Boron. Another sample 'B' of identical dimensions is doped with 10 18 atoms/cm 3 of Phosphorus. The ratio of electron to hole...

Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be defined.

A Silicon PN junction diode under reverse bias has depletion region of width 10 µm. The relative permittivity of Silicon, ɛ r = 11.7 and the permittivity of free space ɛ 0 = 8.854...

A signal x(n)$$ = \sin ({\omega _0}\,n + \phi )$$ is the input to a linear time-invariant system having a frequency response $$H({e^{j\omega }})$$.If the output of the system is $$...

Let x(n) = $${\left( {{1 \over 2}} \right)^n}$$ u(n), y(n) = $${x^2}$$, and Y ($$({e^{j\omega }})\,$$ be the Fourier transform of y(n). Then Y ($$({e^{jo}})$$ is

The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}} \right)^n}u( - n - 1)$$ must be

Match the following and choose the correct combination. GROUP 1 E- continuous and aperiodic signal F- continuous and periodic signal G- discrete and aperiodic signal H- discrete an...

For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by

The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}} \right)dx} $$ is

Which of the following can be impulse response of a causal system?

In what range should Re(s) remain so that the Laplace transform of the function e (a+2)t+5 exists?

The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: y(t) = 0.5 x $$(t - {t_d} + T) + \,x\,(t - {t_d}) + 0.5\,x(t - {t_d} - T)$...

Which of the following analog modulation scheme requires the minimum transmitted power and minimum channel bandwidth?

A device with input x(t) and output y(t) is characterized by: y(t) = x 2 (t). An FM signal with frequency deviation of 90 kHz and modulating signal bandwidth of 5 kHz is applied to...

A carrier is phase modulated (PM) with frequency deviation of 10 kHz by a single tone frequency of 1 kHz. If the single tone frequency is increased to 2 kHz, assuming that phase de...