GATE EC 2016 Question Paper (30-Jan-2016) (Shift 1)

The current density in a medium is given by

$\vec{\mathrm{J}}=\frac{400\sin \theta }{2\pi \left({\mathrm{r}}^2+4\right)}{\hat{\mathrm{a}}}_{\mathrm{r}}\mathrm{A}{\mathrm{m}}^{-2}$

The total current and the average current density flowing through the portion of a spherical surface $\mathrm{r}=0.8\mathrm{m},\frac{\pi }{12}\le \theta \le \frac{\pi }{4},0\le \varphi \le 2\pi$ are given, respectively, by

An antenna pointing in a certain direction has a noise temperature of 50 K. The ambient temperature is 290 K. The antenna is connected to a pre-amplifier that has a noise figure of 2 dB and an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise temperature Te for the amplifier and the noise power Pao at the output of the preamplifier, respectively, are

Two lossless X-band horn antennas are separated by a distance of 200λ. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are 0.15 and 0.18, respectively. The maximum directivities of the transmitting and receiving antennas (over the isotropic antenna) are 18 dB and 22 dB, respectively. Assuming that the input power in the lossless transmission line connected to the antenna is 2 W, and that the antennas are perfectly aligned and polarization matched, the power (in mW) delivered to the load at the receiver is ________.

The electric field of a uniform plane wave traveling along the negative z-direction is given by the following equation:

${\vec{\mathrm{E}}}_{\mathrm{w}}^{\mathrm{i}}=\left({\hat{\mathrm{a}}}_{\mathrm{x}}+\mathrm{j}{\hat{\mathrm{a}}}_{\mathrm{y}}\right){\mathrm{E}}_0{\mathrm{e}}^{\mathrm{jkz}}$

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation:

${\vec{\mathrm{E}}}_{\mathrm{a}}^{\mathrm{i}}=\left({\hat{\mathrm{a}}}_{\mathrm{x}}+{2\hat{\mathrm{a}}}_{\mathrm{y}}\right){\mathrm{E}}_{\mathrm{I}}\frac{1}{\mathrm{r}}{\mathrm{e}}^{-\mathrm{jkr}}$

The polarization of the incident wave, the polarization of the antenna, and losses due to the polarization mismatch are, respectively,

The far-zone power density radiated by a helical antenna is approximated as:

${\vec{\mathrm{W}}}_{\mathrm{rad}}={\vec{\mathrm{W}}}_{\mathrm{average}}\approx \widehat{{\mathrm{a}}_{\mathrm{r}}}{\mathrm{C}}_0\frac{1}{{\mathrm{r}}^2}{\cos }^4\theta$

The radiated power density is symmetrical with respect to φ and exists only in the upper

hemisphere: 0 ≤ 𝜃 ≤ 𝜋/2 ; 0 ≤ 𝜙 ≤ 2𝜋; 𝐶₀ is a constant. The power radiated by the antenna (in watts) and the maximum directivity of the antenna, respectively, are