GATE EC 2012 Question Paper (12-Feb-2012) (Shift 2)

The source of a silicon (nᵢ= 10¹⁰ per cm³) n-channel MOS transistor has an area of 1 sq μm and a depth of 1 μm. If the dopant density in the source is 10¹⁹/cm³, the number of holes in the source region with the above volume is approximately,

A BPSK schemes operating over an AWGN channel with noise spectral density ${\mathrm{N}}_{\mathrm{o}}/2$ uses equiprobable signals ${\mathrm{s}}_1\left(\mathrm{t}\right)=\sqrt{\frac{2E}{\mathrm{T}}}\sin \left({\omega }_{\mathrm{c}}\mathrm{t}\right)$ and ${\mathrm{s}}_2\left(\mathrm{t}\right)=-\sqrt{\frac{2E}{\mathrm{T}}}\sin \left({\omega }_{\mathrm{c}}\mathrm{t}\right)$ over the symbol interval, $(0,\mathrm{T})$. If the local oscillator in a coherent receiver is ahead in phase by $45^{\circ }$ with respect to the received signal, the probability of error in the resulting system is:

A transmission line with a characteristic impedance of 100 Ω is used to match a 50 Ω section to a 200 Ω section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately:

The input x(t) and output y(t) of a system are related as $y(t)={\int }_{-\infty }^{t}x(\tau )cos(3\tau )d\tau .$ The system is

The feedback system shown below oscillates at 2 rads/sec. when