Distributed-Element Modelling For Spiral Resonators Used In Wireless Power Transfer

In this paper, a circuit model for the printed circular spiral resonators based on the piece electrical equivalent circuit is presented. Lumped circuit elements such as inductors, resistors, and mutual inductances are calculated using the conventional formulae for circular loops, whereas the mutual capacitances are calculated by a numerical algorithm. These capacitances are renormalized by scaling factors derived from a simulation-based library of the self-resonant frequency of the spiral resonators. It is shown that involving minuscule effects such as mutual capacitances of nonadjacent turns causes a more accurate estimation of the current distribution and high-frequency characteristics of the resonator. Finally, a closed-form formula for estimating the capacitor values is extracted by curve fitting leading to a decrease in analysis time. The proposed model predicts the input impedance, quality factor, and current distribution along the resonator in agreement with the results generated by full-wave simulation and experimental results.