Electronics and Communication Gate 2014 Set-2 Questions with Answer

Ques 1 GATE 2014 SET-2

The diode in the circuit shown has V_on = 0.7 Volts but is ideal otherwise. If V_i = 5 sin(ωt)Volts, the minimum and maximum values of V_o (in Volts) are, respectively,

Ques 2 GATE 2014 SET-2

The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is

Ques 3 GATE 2014 SET-2

In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are A_cm and A_d, respectively. If the resistance R_E is increased, then

Ques 4 GATE 2014 SET-2

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain A_v0, input resistance R_in, and output resistance R_o for A1 and A2 are as follows:
A1: A_v0 = 10, R_in = 10 kΩ, R_o = 1 kΩ.
A2: A_v0 = 5, R_in = 5 kΩ, R_o = 200 Ω.
The approximate overall voltage gain v_out/v_in is __________.

Ques 5 GATE 2014 SET-2

The input to a 1-bit quantizer is a random variable X with pdf f_X(x) = 2e^-2x for x ≥ 0 and f_X(x) = 0 for x < 0. For outputs to be of equal probability, the quantizer threshold should be _____.

Ques 6 GATE 2014 SET-2

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s₁(t) = α cos 2πf₁t and s₂(t) = α cos 2πf₂t, where α = 4 mV. Assume an AWGN channel with two-sided noise power spectral density N₀/2 = 0.5 × 10^-12 W/Hz. Using an optimal receiver and the relation Q(v) = (1/√(2π)) ∫_v^∞ e^-u2/2 du, the bit error probability for a data rate of 500 kbps is

Ques 7 GATE 2014 SET-2

The power spectral density of a real stationary random process X(t) is given by
S_X(f) = (1/W) for |f| ≤ W
S_X(f) = 0 for |f| > W.
The value of the expectation E[π X(t) X(t - 1/(4W))] is_________.

Ques 8 GATE 2014 SET-2

In the figure, M(f) is the Fourier transform of the message signal m(t) where A = 100 Hz and B = 40 Hz. Given v(t) = cos(2πf_ct) and w(t) = cos(2π(f_c + A)t), where f_c > A. The cutoff frequencies of both the filters are f_c. The bandwidth of the signal at the output of the modulator (in Hz) is _____.

Ques 9 GATE 2014 SET-2

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by
C = W log₂ (1 + P/(σ²W)) bits per second (bps), where W is the channel bandwidth, P is the average power received and σ² is the one-sided power spectral density of the AWGN.
For a fixed P/σ² = 1000, the channel capacity (in kbps) with infinite bandwidth (W → ∞) is approximately

Ques 10 GATE 2014 SET-2

Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index (μ) when the maximum and minimum values of the envelope, respectively, are 3 V and 1 V, is ________.

Ques 11 GATE 2014 SET-2

An unforced linear time invariant (LTI) system is represented by

Ques 12 GATE 2014 SET-2

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.

Ques 13 GATE 2014 SET-2

Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is