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

(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