GATE EC 2016 Question Paper (31-Jan-2016) (Shift 1)

In the circuit shown in the figure, the magnitude of the current (in amperes) through R2 is ________.

A continuous-time filter with transfer function $\mathrm{H}\left(\mathrm{s}\right)=\frac{2\mathrm{s}+6}{{\mathrm{s}}^2+6\mathrm{s}+8}$ is converted to a discretetime filter with transfer function $\mathrm{G}\left(\mathrm{z}\right)=\frac{2{\mathrm{z}}^2-0.5032\mathrm{z}}{{\mathrm{z}}^2-0.5032\mathrm{z}+\mathrm{k}}$ so that the impulse response of the continuous-time filter, sampled at $2\mathrm{Hz}$, is identical at the sampling instants to the impulse response of the discrete time filter. The value of $\mathrm{k}$ is ________

The Discrete Fourier Transform (DFT) of the 4-point sequence

$\mathrm{x}[\mathrm{n}]=\{\mathrm{x}[0],\mathrm{x}[1],\mathrm{x}[2],\mathrm{x}[3]\}=\{3,2,3,4\}$ is

$\mathrm{X}[\mathrm{k}]=\{\mathrm{X}[0],\mathrm{X}[1],\mathrm{X}[2],\mathrm{X}[3]\}=\{12,2j,0,-2j\}$.

If ${\mathrm{X}}_1[\mathrm{k}]$ is the DFT of the 12-point sequence ${\mathrm{x}}_1[\mathrm{n}]=\{3,0,0,2,0,0,3,0,0,4,0,0\}$, the value of $\left|\frac{{\mathrm{X}}_1\left[8\right]}{{{\mathrm{X}}_1\left[11\right]}_{}}\right|$ is ________

The switch S in the circuit shown has been closed for a long time.

It is opened at time t = 0 and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop.

The steady-state magnitude of the capacitor voltage V${}_c$ (in Volts) is ________.

A voltage ${\mathrm{V}}_{\mathrm{G}}$ is applied across a MOS capacitor with metal gate and p-type silicon substrate at $\mathrm{T}=300\mathrm{K}$. The inversion carrier density (in number of carriers per unit area) for ${\mathrm{V}}_{\mathrm{G}}=0.8\mathrm{V}$ is $2\times 10^{11}\mathrm{c}{\mathrm{m}}^{-2}$. For ${\mathrm{V}}_{\mathrm{G}}=1.3\mathrm{V}$, the inversion carrier density is $4\times 10^{11}\mathrm{c}{\mathrm{m}}^{-2}$. What is the value of the inversion carrier density for ${\mathrm{V}}_{\mathrm{G}}=1.8\mathrm{V}$?