GATE 2016 EC – Question 64
The electric field of a uniform plane wave travelling along the negative $z$ direction is given by the following equation:
$$\vec{E}_w^i = (\hat{a}_x + j\hat{a}_y)E_0 e^{jkz}$$
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:
$$\vec{E}_a = (\hat{a}_x + 2\hat{a}_y)E_I \frac{1}{r}e^{-jkr}$$
The polarization of the incident wave, the polarization of the antenna and losses due to the polarization mismatch are, respectively,
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Show answer and explanation
Correct answer: (C) Circular (clockwise), Linear, -3dB
Explanation
The incident field has equal $x$ and $y$ components that are 90° out of phase, so it is circularly polarized. The antenna field has $x$ and $y$ components in phase, with ratio $1:2$, so it is linearly polarized. For a circularly polarized wave received by a linearly polarized antenna, half the power is received no matter how the antenna is oriented. This is a loss of 3 dB. The sense of rotation (clockwise or anticlockwise) depends on the viewing convention, which is why the official key accepts both options C and D.