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

A voice signal m(t) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal f(t) = A(1 + m(t)) cos 2πfct, where fc = 600 kHz. The AM signal f(t) is to be digitized and archived. This is done by first sampling f(t) 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 K bits, where K 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.

A random variable X takes values −1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise N is independent of X, and is uniformly distributed over the interval [−2 , 2]. The receiver makes a decision

x = ≤ft\{ {*20c - 1,~if~Y ≤ θ \\ + 1,if~Y > θ } .

where the threshold θ ∈ [−1,1] is chosen so as to minimize the probability of error Pr[X̂ ≠ X]. The minimum probability of error, rounded off to 1 decimal place, is_______.

A Germanium sample of dimensions 1 cm × 1 cm 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 3 × 10⁴cm⁻¹ and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is ______ μm.

In an ideal pn junction with an ideality factor of 1 at T=300 K, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2 decimal places is ____mV.

[k = 1.38 × 10⁻²³ JK⁻¹, h = 6.625 × 10⁻³⁴ J-s, q = 1.602 × 10⁻¹⁹C]

Consider a long-channel MOSFET with a channel length 1 μm and width 10 μm. The device parameters are acceptor concentration N${}_A$ = 5 × 1016 cm⁻³, electron mobility μₙ = 800 cm²/V-s, oxide capacitance/area Cₒₓ = 3.45 × 10⁻⁷ F/cm², threshold voltage V${}_T$ = 0.7 V. The drain saturation current (I${}_{Dsat}$) for a gate voltage of 5 V is _____mA (rounded off to two decimal places). [ε₀ = 8.854 × 10−¹⁴F/cm, ε${}_{Si}$ = 11.9]