GATE EC 2020 Question Paper (02-Feb-2020) (Shift 2)

For a 2-port network consisting of an ideal lossless transformer, the parameter S₂₁(rounded off to two decimal places)for a reference impedance of 10 Ω, is ________.

S${}_{PM}$ (t) and S${}_{FM}$ (t) as defined below, are the phase-modulated and the frequency-modulated waveforms, respectively, corresponding to the message signal m(t( shown in the figure.

$S_{PM}\left(t\right)=\cos \left(1000\pi t+K_{p}m\left(t\right)\right)$ and

$S_{FM}\left(t\right)=\cos \left(1000\pi t+K_f{\int }_{-\infty }^{t}m\left(\tau \right)d\tau \right)$

Where Kₚ is the phase deviation constant in radians/volt and K${}_f$ is the frequency deviation constant in radians/second/volt. If the highest instantaneous frequencies of S${}_{PM}$ (t) and S${}_{FM}$ (t) are the same, then the value of the ratio $\frac{K_p}{K_f}$ is ______ seconds.

In a digital communication system, a symbol S randomly chosen from the set (s₁, s₂, s₃, s₄) is transmitted. It is given that s₁ = -3, s₂ = -1, s₃ = +1 and s₄ = +2. The received symbol is Y = S + W. W is a zero-mean unit-variance Gaussian random variable and is independent of S. Pᵢ is the conditional probability of symbol error for the maximum likelihood (ML) decoding when the transmitted symbol S = sᵢ. The index i for which the conditional symbol error probability Pᵢ is the highest is

A system with transfer function $G\left(s\right)=\frac{1}{\left(s+1\right)\left(s+a\right)},a>0$ is subjected to an input 5 cos 3t. The steady-state output of the system is $\frac{1}{\sqrt{10}}\cos \left(3t-1.892\right)$. The value of a is

For the components in the sequential circuit shown below, t${}_{pd}$ is the propagation delay, t${}_{setup}$ is the setup time, and t${}_{hold}$ is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is ______ MHz.