Question

Antenna Theory

A small circular loop with circumference C < 1/20 is used as a receiving antenna. A uniformplane wave traveling along the x-axis and toward the positive (+).x direction (as shown in the

figure), whose electric field is given by

\mathbf{E}_{w}^{i}=\left(\hat{q}_{y}+2 \hat{q}_{z}\right) e^{-j k x}

is incident upon the antenna. Determine the

(a) polarization of the incident wave. Justify your answer.

(b) axial ratio of the polarization ellipse of the incident wave.

(c) polarization of the loop antenna toward the x-axis.

(d) polarization loss factor (dimensionless and in dB).

(e) maximum power at 1 GHz that can be delivered to a load connected to the antenna,E.if the power density of the above incident wave is 5 m watts/cm². Assume no other losses

\text { Hint: } \hat{\mathbf{a}}_{\phi}=-\hat{\mathbf{a}}_{x} \sin \phi+\hat{a}_{y} \cos \phi


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