The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$$\overrightarrow E {}_w^i = \left( {{{\widehat a}_{_x}} + j{{\widehat a}_{_y}}} \right){E_0}{e^{jkz}}$$$

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:

$$${\overrightarrow E _{_a}} = \left( {{{\widehat a}_{_x}} + 2{{\widehat a}_{_y}}} \right){E_1}{1 \over r}{e^{ - jkr}}$$$

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

The propagation constant of a lossy transmission line is (2 + j5) $${m^{ - 1}}$$ and its characteristic impedance is (50 + j0) $$\Omega $$ at $$\omega = \,{10^6}\,rad\,{S^{ - 1}}$$. The values of the line constants L, C, R, G are, respectively,

An antenna pointing in a certain direction has a noise temperature of $$50K$$. The ambient temperature is $$290K$$. 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 $${T_e}$$ for the amplifier and the noise power $${P_{ao}}$$ at the output of the preamplifier, respectively, are

Two lossless X-band horn antennas are separated by a distance of $$200\lambda $$. 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 ________ .