# Electronics and Communication Engg - GATE 2012 Paper Solution

The current ib through the base of a silicon npn transistor is 1+0.1 cos(10000$\pi t$) mA. At 300 K, the r$\pi$ 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 is incident on a perfectly conducting slab positioned at $x\le 0$.The $\stackrel{\to }{E}$ 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 $\stackrel{\to }{E}=10\left({\stackrel{^}{a}}_{y}+j{\stackrel{^}{a}}_{z}\right){e}^{-j25x}$.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

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)$\Omega$ by a current $5\mathrm{cos}\left(100\pi t+100\right)A$ is

The unilateral Laplace transform of f (t) is $\frac{1}{{s}^{2}+s+1}$. The unilateral Laplace transform of t f (t) is

With initial condition $x\left(1\right)=0.5$ , the solution of the differential equation,

$t\frac{dx}{dt}+x=t$ 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 $\epsilon$ and decreases that of the second by $\epsilon$. 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 , the characteristic impedance of the cable is

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

$F\left(\theta \right)={\mathrm{cos}}^{4}\theta ;0\le \theta \le \mathrm{\pi }/2$

The directivity of the antenna is

If $x\left[n\right]={\left(1/3\right)}^{\left|n\right|}-{\left(1/2\right)}^{n}u\left[n\right]$, 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)=$\sum \left(2,3,4,5\right)$,the prime implicants are
G(s)=$\frac{\left({s}^{2}+9\right)\left(s+2\right)}{\left(s+1\right)\left(s+3\right)\left(s+4\right)}$
is excited by $\mathrm{sin}\left(\omega t\right)$. The steady-state output of the system is zero at