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

The current ${\mathrm{i}}_{\mathrm{b}}$ through the base of a silicon npn transistor is $1+0.1cos(10000\pi \mathrm{t})\mathrm{mA}$.

At $300\mathrm{K}$, the ${\mathrm{r}}_{\pi }$ in the small signal model of the transistor is



Take Boltzmann's constant as k = 1.38064852 × 10⁻²³ m² kg s⁻² K⁻¹

The power spectral density of a real process $\mathrm{X}(\mathrm{t})$ for positive frequencies is as shown below. The value of $\mathrm{E}\left[{\mathrm{X}}^2\left(\mathrm{t}\right)\right]$ and $\mathrm{E}\left[\mathrm{X}\left(\mathrm{t}\right)\right]$ is:

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

A plane wave propagating in air with $\vec{E}=\left(8{\hat{a}}_x+6{\hat{a}}_y+5{\hat{a}}_z\right)e^{j\left(\omega t+3x-4y\right)}\frac{V}{m}$ is incident on a perfectly conducting slab positioned at x ≤ 0. The $\vec{E}$ field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, travelling along the positive xdirection, is given by$\vec{E}=10\left({\hat{a}}_y+j{\hat{a}}_z\right)e^{-j25x}$ The frequency and polarization of the wave, respectively, are: