Exact Expressions for the Total Radiated Power, Radiation Resistance, and Directivity of an Arbitrary Size Uniform Current Elliptical Loop Antenna

This communication presents complete derivations of exact analytical expressions for the total radiated power, radiation resistance, and directivity corresponding to an elliptical loop antenna of arbitrary size with a uniform current distribution. Known results for the important special case of the far-zone electric fields radiated by an arbitrary size uniform current elliptical loop antenna serve as a starting point in the development. These field expressions are then utilized to derive an advantageous form of an exact expansion for the total radiated power and associated radiation resistance. This derivation is carried out in an elegant and complete manner by invoking properties of generalized hypergeometric functions as well as gamma and beta functions. Finally, a convenient expansion is presented that can be used to obtain a series of useful approximations for the directivity by including an appropriate number of higher-order terms, e.g., which are valid for loops of increasing size.