Electronics and Communication Gate 2016 Set-1 Questions with Answer

Ques 14 GATE 2016 SET-1

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1. Assuming a binary symmetric channel with crossover probability p=0.1, the average probability of error is

Ques 15 GATE 2016 SET-1

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t)=s(t)+n(t) where n(t) is additive white Gaussian noise with power spectral density N₀/2. The received signal is passed through a filter with impulse response h(t). Let E_s and E_h denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter (SNR_max), which of the following holds?

Ques 16 GATE 2016 SET-1

What is the voltage V_out in the following circuit?

Ques 17 GATE 2016 SET-1

Which one of the following is a property of the solutions to the Laplace equation: ∇²f=0?

Ques 18 GATE 2016 SET-1

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m², -4 nC/m² and ρ_s, respectively. The value of ρ_s (in nC/m²) required to ensure that the electric flux density D=0 at radius 10 m is

Ques 19 GATE 2016 SET-1

The propagation constant of a lossy transmission line is (2+j5) m^-1 and its characteristic impedance is (50+j0)Ω at ω=10⁶ rad s^-1. The values of the line constants L, C, R, G are, respectively,

Ques 20 GATE 2016 SET-1

The current density in a medium is given by J=400sinθ/(2π(r²+4))â_r Am^-2. The total current and the average current density flowing through the portion of a spherical surface r=0.8 m, π/12≤θ≤π/4, 0≤φ≤2π are given, respectively, by

Ques 21 GATE 2016 SET-1

An antenna pointing in a certain direction has a noise temperature of 50 K. The ambient temperature is 290 K. The antenna is connected to a pre-amplifier that has a noise figure of 2 dB and an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise temperature T_e for the amplifier and the noise power P_ao at the output of the preamplifier, respectively, are

Ques 22 GATE 2016 SET-1

Two lossless X-band horn antennas are separated by a distance of 200λ. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are 0.15 and 0.18, respectively. The maximum directivities of the transmitting and receiving antennas (over the isotropic antenna) are 18 dB and 22 dB, respectively. Assuming that the input power in the lossless transmission line connected to the antenna is 2 W, and that the antennas are perfectly aligned and polarization matched, the power (in mW) delivered to the load at the receiver is

Ques 23 GATE 2016 SET-1

The electric field of a uniform plane wave travelling along the negative z direction is given by the following equation: E_wⁱ=(â_x+jâ_y)E₀e^jkz. This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation: E_a=(â_x+2â_y)E₁(1/r)e^-jkr. The polarization of the incident wave, the polarization of the antenna and losses due to the polarization mismatch are, respectively,

Ques 24 GATE 2016 SET-1

The far-zone power density radiated by a helical antenna is approximated as: W_rad≈W_average≈â_rC₀(1/r²)cos⁴θ. The radiated power density is symmetrical with respect to φ and exists only in the upper hemisphere: 0≤θ≤π/2; 0≤φ≤2π; C₀ is a constant. The power radiated by the antenna (in watts) and the maximum directivity of the antenna, respectively, are

Ques 25 GATE 2016 SET-1

Consider the constant current source shown in the figure below. Let β represent the current gain of the transistor. The load current I₀ through R_L is

Ques 26 GATE 2016 SET-1

The following signal V_i of peak voltage 8 V is applied to the non-inverting terminal of an ideal opamp. The transistor has V_BE=0.7 V and β=100. V_LED=1.5 V, V_CC=10 V and -V_CC=-10 V.