Modeling and Optimization of MHz Self-resonant Planar Coil for Wireless Power Transfer

This paper presents a modeling and optimization framework for a high-frequency, self-resonant planar coil used in wireless power transfer (WPT) systems to maximize the coil’s quality factor (Q) and achieve high efficiency. While self-resonant planar coils inherently provide internal capacitance and enable compact, high-power operation, achieving high Q at MHz frequencies is challenging due to magnetic and conductor losses. To overcome this limitation, we develop a gradient-based optimization method using an equivalent circuit derived from closed-form expressions of inductance, capacitance, and series resistance based on an Archimedean spiral geometry. The optimized coil is driven by a class Φ2inverter, chosen for its single-switch architecture, which simplifies control and reduces device stress compared to conventional inverter topologies. A 24 cm-diameter copper-sheet prototype tested at 13.56 MHz achieved a measured Q > 700 and delivered 640 W over a 13 cm transfer distance with 95% coil-to-coil efficiency, validating the proposed design methodology for high-power MHz WPT applications.