GATE EC 2019 Question Paper (09-Feb-2019) (Shift 1)

Consider the signal f(t) = 1 + 2 cos(πt) + 3 sin$\left(\frac{2\pi }{3}t\right)+4\cos \left(\frac{\pi }{2}t+\frac{\pi }{4}\right)$, where t is in seconds. Its fundamental time period, in seconds, is __________.

The baseband signal m(t) shown in the figure is phase-modulated to generate the PM signal φ(t) = cos(2πf${}_c$ t + km(t)). The time t on the x-axis in the figure is in milliseconds. If the carrier frequency f${}_c$ = 50 kHz and k = 10π, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is __________ (rounded off to 2 decimal places).

Radiation resistance of a small dipole current element of length "l" at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is ____________ %.

In the circuit shown, Vₛis a square wave of period T with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and R₁ = R₂ = 50 Ω. The average value of V${}_L$ is ____ volts (rounded off to 1 decimal place).

In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz.The frequency of the signal at Q₂ is ____ kHz.