Impedance of thin-wire loop antennas

THE THIN-wire loop is one of the first antennas to receive theoretical consideration, having been discussed by Pocklington1 in 1897. Pocklington treated a closed loop excited by a plane wave; he obtained an exact solution for the current on the loop in the form of a Fourier series. More recently, Hallén2 considered a driven loop and obtained a solution, again in the form of a Fourier series, for the current and the impedance. However, Hallén pointed out that the coefficients of this series contained a singularity which made the series only quasiconvergent and hence useful only for loops small in comparison to a wave length. Moreover, the individual terms were complicated and their evaluation and a summation involved a somewhat difficult numerical task.