Electronics and Communication Engg - GATE 2012 Paper Solution

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The current ib through the base of a silicon npn transistor is 1+0.1 cos(10000πt) mA. At 300 K, the rπ in the small signal model of the transistor is

The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X2(t)] and |E[X(t)]| , respectively, are

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

A plane wave propagating in air with E=8a^x+6a^y+5a^zejwt+3x-4y V/m is incident on a perfectly conducting slab positioned at x0.The E field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by E=10a^y+ja^ze-j25x.The frequency and polarization of the wave, respectively, are

Consider the given circuit.

In this circuit, the race around

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

The i-v characteristics of the diode in the circuit given below are

i=v-0.7500A,v0.7v0 A,v<0.7v

The current in the circuit is

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

The average power delivered to an impedance (4-j3)Ω by a current 5cos100πt+100A is

The unilateral Laplace transform of f (t) is 1s2+s+1. The unilateral Laplace transform of t f (t) is

With initial condition x(1)=0.5 , the solution of the differential equation,

tdxdt+x=t is

The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is

In the circuit shown

A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount ε and decreases that of the second by ε. After encoding, the entropy of the source

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given μ0=4π×10-7H/m, ε0=10-936πF/m, the characteristic impedance of the cable is

The radiation pattern of an antenna in spherical co-ordinates is given by

Fθ=cos4θ;0θπ/2

The directivity of the antenna is

If xn=1/3n-1/2nun, then the region of convergence (ROC) of its Z-transform in the Z-plane will be

In the sum of products function f(X,Y,Z)=2,3,4,5,the prime implicants are

A system with transfer function

G(s)=s2+9s+2s+1s+3s+4

is excited by sinωt. The steady-state output of the system is zero at

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