A First-Order Model of the Multiple-Feed Toroidal Magneto-Dielectric Antenna

A model of the input impedance of the toroidal permeable antenna, which is the dual of the conventional metal loop antenna, is derived, starting from Schelkunoff's transmission line description of the loop antenna instead of the electrically small limit model. This antenna operates in both the monopole mode and circularly polarized dipole mode and is constructed from a torus of high permeability material. Since the ultimate goal is to obtain an impedance model from which to derive the best matching network; the input impedance is expressed in a form that has a frequency independent resistor terminating a reactive network which is called the Darlington form. Because such a circuit mimics closely the input impedance of the dipole modes of the spherical mode expansion, it is a much better model of the antennas as we go beyond the electrically small limit. The feed loop contribution is explicitly accounted for and the results are compared with fullwave simulations of a typical toroidal antenna operating in both monopole and circularly polarized dipole modes which show a good agreement well beyond the electrically small limit.