GATE EE 2017 Question Paper (11-Feb-2017) (Shift 1)

Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, $H\left(1\right)=\frac{5}{4}$. The poles of H(z) are $p_k=\frac{1}{\sqrt{2}}\exp \left(j\frac{\left(2k-1\right)}{4}\pi \right)$ for k = 1, 2, 3, 4. The zeros of H(z) are all at z = 0. Let g[n] = jⁿh[n]. The value of g[8] equals __________. (Give the answer up to three decimal places.)

The circuit shown in the figure uses matched transistors with a thermal voltage V${}_T$ = 25 mV. The base currents of the transistors are negligible. The value of the resistance R in kΩ that is required to provide 1 μA bias current for the differential amplifier block shown is ___________. (Give the answer up to one decimal place.)

The figure below shows an uncontrolled diode bridge rectifier supplied from a 220 V, 50 Hz, 1-phase ac source. The load draws a constant current I₀ = 14 A. The conduction angle of the diode D₁ in degrees (rounded off to two decimal places) is ________.

The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu and 0.1 pu respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _________(assume fault impedance to be zero). (Give the answer up to one decimal place.)

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sin δ, where δ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of δ, as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is P${}_{max}$ sin δ, the value of P${}_{max}$, in pu is ______. (Give the answer up to three decimal places.)