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

The circuit shown in the figure is used to provide regulated voltage (5 V) across the 1 kΩ resistor. Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a minimum required Zener current, I${}_{Zmin}$ = 2 mA to its maximum allowable current. The input voltage V${}_I$ may vary by 5% from its nominal value of 6 V. The resistance of the diode in the breakdown region is negligible.



The value of R and the minimum required power dissipation rating of the diode, respectively, are

Let c(t) = A${}_c$ cos (2πf${}_c$ t) and m(t) = cos (2πf${}_m$ t). It is given that f${}_c$ ≫ 5f${}_m$. The signal c(t) + m(t) is applied to the input of a non-linear device, whose output vₒ(t) is related to the input vᵢ(t) as v₀(t) = avᵢ(t) + bvᵢ²(t) where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f${}_c$ and bandwidth 3 f${}_m$, to produce an amplitude modulated (AM) wave. If it is desired to have the side band power of the AM wave to be half of the carrier power, then a/b is

Consider a white Gaussian noise process N(𝑡) with two-sided power spectral density S${}_N$ (f) = 0.5 W/Hz as input to a filter with impulse response $0.5e^{-t^2/2}$ (𝑡 is in seconds) resulting in output Y(t). The power in Y(t), in watts, will be:

The state equation and the output equation of a control system are given below:

x = ≤ft[ {*20c - 4& - 1.5\\ 4&0 } ]+ ≤ft[ {*20c 2\\ 0 } ]\\ = ≤ft[ {*20c 1.5&0.625 } ]

The transfer function representation of the system is

Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red, green and blue diodes are V${}_R$, V${}_G$ and V${}_B$, respectively. Assume donor and acceptor doping to be the same (N${}_A$ and N${}_D$, respectively) in the p and n sides of all the three diodes.

Which one of the following relationships about the built-in voltages is TRUE?