GATE EC 2022 Question Paper (06-Feb-2022) (Shift 1)

Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2. The complete Nyquist plot of the transfer function G(s) is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ___________.

The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note that K is varied from 0 to ∞.

Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.

The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.

Statement I: The system is necessarily a pure delay system for inputs which are bandlimited to −α ≤ f ≤ α.

Statement II: For any wide-sense stationary input process with power spectral density S${}_X$ (f), the output power spectral density 𝑆${}_Y$ (f) obeys S${}_Y$ (f) = S${}_X$ (f) for −α ≤ f ≤ α. Which one of the following combinations is true?

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2 sin(t + π/2). The displacement current (in Amperes) through the capacitor is _________

Consider an FM broadcast that employs the pre-emphasis filter with frequency response

${\mathrm{H}}_{\mathrm{pe}}(\omega )=1+\frac{\mathrm{j}\omega }{{\omega }_0}$

where ω₀ = 10⁴ rad/sec.

For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of (R, C) values is/are ________.