Approximations to the radiation resistance and directivity of circular-loop antennas

The purpose of this article is to derive approximate formulas for the radiation resistance (R), and the directivity (D) of circular loop antennas. It is shown that simple approximations to the Bessel functions can be employed, to accurately model the oscillatory behavior of the Bessel function integral for both small and intermediate-sized loop antennas. Furthermore, when these approximations are combined with the usual asymptotic contributions to the integral in the case of a large input parameter ka (a=loop radius, a=2/spl pi///spl lambda/) accurate and relatively simple results for R and D can be secured for all loop sizes. Numerical results can, if necessary, be obtained using a simple pocket calculator.>