On the excitation of a circular loop antenna by travelling-and standing-wave current distributions

Presented here is an exact formulation of the electric and magnetic (EM) fields radiated by a circular loop antenna, assuming both travelling- and standing-wave current distributions. By using a differential current element positioned in an azimuthal direction as the starting point, the paper systematically develops the EM fields radiated by the circular loop via a vector potential theory. This approach leads to a general integral representation for the radiation characteristics of the loop antenna where we completely evaluate the resulting expressions, when the excitations of the loop assume travelling- and standing-wave distribution forms. In addition, this paper briefly examines a method to generate approximately such current distributions by coupling the loop to a two- or four-wire transmission line. Furthermore, the paper discusses a graphical representation of the current distribution plotted as a function of frequency or loop size. From the field expressions determined, we derive generalized closed-form results for some important design parameters for the loop antenna. These parameters include the radial component of the Poynting vector, the total power radiated by the loop, the directivity, the radiation resistance, and the effective area and height of the antenna. When we specialize to the important case of uniform current excitation, the exact values of the parameters deduced from the general expressions, are summarized and exhibited in a comprehensive table. This table facilitates the computations of these important physical parameters. Further analysis involving small argument and asymptotic approximations in the residts for the travelling-wave current excitation leads to closed-form expressions in terms of tabulated functions. Numerical results presented, include the fields radiated by the loop when the standing-wave current excitation admits a Fourier series representation. The present approach via potential theory reveals that the fields can be calculated in any arbitrary direction : this is consistent with a previous observation of Knudsen (1951, 1953) who employed a different approach.