New exact solution procedure for the near fields of the general thin circular loop antenna

An analytical method is presented which gives the various fields, including the scalar potential, of a general circular loop antenna in cylindrical coordinates in terms of six separate series. Three of the series are elementary and the other three involve Legendre functions of the second kind and half-integral order. The results obtained are compared with direct numerical integration and with two far-field formulae; the standard textbook expression and what appears to be a new formula which gives more accurate results. The series solution is more robust than numerical integration for the higher Fourier terms of the general solution close to the loop. The solution has also been compared with the solution of Werner, and it agrees exactly. The solution presented here gives better convergence close to the loop, whereas Werner´s solution is better far from the loop. Sample calculations are given for the axisymmetric case.