GATE EC 2018 Question Paper (10-Feb-2018) (Shift 1)

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places), 0.5 seconds after closing the switch is ________.

A dc current of 26 μA flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, the diode has a junction capacitance of 0.5 nF. Its neutral region resistances can be neglected. Assume that the room temperature thermal equivalent voltage is 26 mV.



For ω = 2 × 10⁶ rad/s, the amplitude of the small-signal component of diode current (in μA, correct to one decimal place) is _______.

An op-amp based circuit is implemented as shown below.



In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node A, connected to the negative input of the op-amp as indicated in the figure is ________.

The input 4sinc(2t) is fed to a Hilbert transformer to obtain y(t), as shown in the figure below:



Here $\mathrm{sinc}\left(\mathrm{x}\right)=\frac{\sin \left(\pi \mathrm{x}\right)}{\pi \mathrm{x}}$ The value (accurate to two decimal places) $\underset{-\infty }{\overset{\infty }{\int }}{\left|\mathrm{y}\left(\mathrm{t}\right)\right|}^2\mathrm{dt}$ is ________.

A random variable 𝑋 takes values −0.5 and 0.5 with probabilities $\frac{1}{4}$ and $\frac{3}{4}$, respectively. The noisy observation of 𝑋 is 𝑌 = 𝑋 + 𝑍, where 𝑍 has a uniform probability density over the interval (−1, 1). 𝑋 and 𝑍 are independent. If the MAP rule-based detector outputs $\hat{X}$ as

X = ≤ft\{ {*20c - 0.5&{< α}\\ 0.5&{≥ α,} } .

then the value of 𝛼 (accurate to two decimal places) is _______.