Exact Expressions for the Far-Zone Electromagnetic Fields Radiated by Thin Elliptical Loop Antennas of Arbitrary Size

Circular loop antennas have received considerable attention over the years due to their wide range of practical applications. However, in comparison, surprisingly little research work has been devoted to the study of elliptical loop antennas, which provide designers with an additional degree of freedom to control their radiation properties. Here, a complete set of analytical expressions is derived for the vector potential and corresponding far-zone electromagnetic fields of a thin elliptical loop antenna of an arbitrary size based on a general Fourier cosine series representation of the current distribution. Furthermore, several important special cases of the general theory are considered including elliptical loop antennas with a constant and a cosinusoidal current distribution. It is also shown that for the special case when the lengths of the semimajor and semiminor axes are equivalent, the general expressions for the far-zone electromagnetic fields will reduce to well-known results for a circular loop. Finally, some example radiation pattern plots for elliptical loop antennas are generated using the exact theoretical expressions derived in this paper.