GATE ECE year:2019 PYQs & Answers — Page 6

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year:2019

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 6 of 7

The RC circuit shown below has a variable resistance

given by the following expression:

where

, and

. We are also given that

and the source voltage is

. If the current at time

is 1 A, then the current

, in amperes, at time

is __________ (rounded off to 2 decimal places).

Diagram for Electronics and Communication Engineering question 41

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Consider a unity feedback system, as in the figure shown, with an integral compensator

and open-loop transfer function

, where

. The positive value of

for which there are exactly two poles of the unity feedback system on the

axis is equal to ______ (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 42

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Consider the homogeneous ordinary differential equation

, with

as a general solution. Given that

and

, the value of

, rounded off to two decimal places, is ______.

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Let

be a length-7 discrete-time finite impulse response filter, given by

, and

is zero for

. A length-3 finite impulse response approximation

has to be obtained such that

is minimized, where

and

are the discrete-time Fourier transforms of

and

, respectively. For the filter that minimizes

, the value of

, rounded off to 2 decimal places, is ______.

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Let a random process

be described as

, where

is a white noise process with power spectral density

. The filter

has a magnitude response given by

for

, and zero elsewhere.

is a stationary random process, uncorrelated with

, with power spectral density as shown in the figure. The power in

, in watts, is equal to ______ W (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 45

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A voice signal

is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal

, where

kHz. The AM signal

is to be digitized and archived. This is done by first sampling

at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using

bits, where

is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is ______ Mbps.

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A random variable

takes values

and

with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise

, so that the random variable at the channel output is

. The noise

is independent of

, and is uniformly distributed over the interval

. The receiver makes a decision

where the threshold

is chosen so as to minimize the probability of error

. The minimum probability of error, rounded off to 1 decimal place, is ______.

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A Germanium sample of dimensions

is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dioxide-Germanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is

and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is ______

Diagram for Electronics and Communication Engineering question 48

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In an ideal

junction with an ideality factor of 1 at

, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2 decimal places, is ______ mV. [

]

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Consider a long-channel MOSFET with a channel length 1

m and width 10

m. The device parameters are acceptor concentration

, electron mobility

, oxide capacitance/area

, threshold voltage

. The drain saturation current (

) for a gate voltage of 5 V is ______ mA (rounded off to two decimal places). [

]

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GATE ECE year:2019 PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50