The Driving Point Impedance and Admittance of Thin, PEC Loops and Rings

Abstract

The driving point on the loop circumference is characterized by a broadband delta-function voltage source generator placed across an infinitesimal gap. This causes some divergence difficulties in the resulting Fourier series description of the current. Nevertheless, the Storer-Wu method generates a reasonably accurate modal function for the input impedance at the gap. From this function are derived all of the modal resonances, the fundamental loop resonances and the anti-resonances. The modal impedances have nearly the same form as series resonant circuits, and this insight is exploited to identify a circuit model for the loop where each mode is represented by an RLC circuit and the entire loop is represented by a combination of this infinite set of RLCs. This section also discusses the difficulties with this model while the rest of the volume relies on its accuracy. The chapter ends with a look at the sub-wavelength anti-resonance.