GATE EC 2021 Question Paper (07-Feb-2021) (Shift 2)

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is 500 MHz.



Starting from the initial value of the flip-flop outputs Q₂Q₁Q₀ = 1 1 1 with D2 = 1, then the minimum number of triggering clock edges after which the flip-flop outputs Q₂Q₁Q₀ becomes 1 0 0 (in integer) is ______

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time t = 0.



Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is _______ A.

A unity feedback system that uses proportional-integral (PI) control is shown in the figure.



The stability of the overall system is controlled by tuning the PI control parameters K${}_P$ and K${}_I$. The maximum value of K${}_I$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is ________.

A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant 2 rad / volt. If the carrier signal is c(t) = 2cos(2π10⁶t). the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _______ Hz.

Consider a superheterodyne receiver tuned to 600 kHz. If the local oscillator feeds a 1000 kHz signal to the mixer, the image frequency (in integer) is _______ kHz.