The electric field of a uniform plane wave travelling along the negative z direction is given by:

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Question:

$E_{i}^{w}=(hat{x}+jhat{y})E_{o}e^{+jkz}=sqrt{2}hat{p}_{wave}E_{o}e^{+jkz}$

and is incident upon a receiving antenna placed at the orgin and whose radiated electric field, toward the incident wave, is given by

$E_{a}=(hat{x}+3jhat{y})E_{1}(rac{e^{-jkz}}{r})=sqrt{10}hat{p}_{Rx,and}E_{1}(rac{e^{-jkz}}{r})$

Determine the following:

(a) poarization of the incident wave, and why?

(b) If circular or elliptical, sense of rotation of the incident wave.

(c) Losses (dimensionless and in dB) due to polarizzation mismatch between the incident wave and the antenna, viz. compute $left | hat{p}_{wave}*(hat{p}_{Rx,ant})^{*} ight |.$ Note that dB value is evaluated using $A_{dB}=20logA$ , where A is associated with the fields (not power).