GATE EC 2014 Question Paper (15-Feb-2014) (Shift 1)

Let $Q\left(b\sqrt{\gamma }\right)$ be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density N₀/2. The parameter γ is a function of bit energy and noise power spectral density. A system with two independent and identical AWGN channels with noise power spectral density N₀/2 is shown in the figure. The BPSK demodulator receives the sum of outputs of both channels.



If the BER of this system is Q(𝑏√𝛾), then the value of b is _______

A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let L be the number of tosses to get this first ‘Head’. The entropy H(L) in bits is _________.

In spherical coordinates, let â${}_{\theta }$, â${}_{\text{ϕ}}$ denote unit vectors along the θ, ϕ directions.

$E=\frac{100}{r}\sin \theta \cos \left(\omega t-\beta r\right){\hat{a}}_{\theta }V/m$

$H=\frac{0.265}{r}\sin \theta \cos \left(\omega t-\beta r\right){\hat{a}}_{\varphi }\frac{A}{m}$

Represents the electric and magnetic field components of the EM wave at large distance r from a dipole antenna, in free space, the average power (W) crossing the hemispherical shell located at r = 1 km, 0 ≤ θ ≤ π/2 is _______

For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of spacing between the plates by a factor of two results in

The input impedance of a $\frac{\lambda }{8}$ section of a lossless transmission line of characteristic impedance 50 Ω is found to be real when the other end is terminated by a load Z${}_L$ (= R + jX)Ω. If X is 30Ω, the value of R (in Ω) is ______