Design and Optimization of Unequal-Pitch Self-Resonant Helical Coils for High-Efficiency Mid-Range Wireless Power Transfer

In a wireless power transfer (WPT) system, the coil-to-coil transfer efficiency is significantly influenced by the performance of coupling coils. The self-resonant coil is widely employed for its excellent performance. Existing coil modeling methods suffer from significant errors or computational complexity, making them unsuitable for the design and optimization of coils. This article presents a modified analytical method for self-resonant coil modeling, with a specific focus on calculating the self-resonant frequency (SRF), ohmic resistance, and quality factor. First, considering the nonidentical current distribution along the self-resonant coil, a segmented filament model is formulated to calculate the SRF and current distribution. Furthermore, the uneven current density distribution on the wire's cross section is considered, and a modified segmented filament model is presented, where the current density is equated to a conduction current filament plus a pair of proximity current dipoles. The magnetic field arising from neighboring wires can, then, be calculated, enabling the determination of ohmic resistance and quality factor. Simulation and measurement results validate the accuracy of the modified model for both tightly and loosely wound coils. This model is employed to optimize the ohmic resistance and quality factor during the coil design process. To further enhance the quality factor across the entire operating frequency range, an unequal-pitch coil structure is proposed, along with a novel design guideline for coil optimization. Following this guideline, a 6.71 MHz unequal-pitch self-resonant coil is designed, fabricated, and measured. The coil-to-coil transfer efficiency reaches 95.8% and 82.7% at a transfer distance-to-coil diameter ratio of 1 (<inline-formula><tex-math notation="LaTeX">${{d}_{\text{TR}}} = 20{\rm{\ cm}}$</tex-math></inline-formula>) and 2 (<inline-formula><tex-math notation="LaTeX">${{d}_{\text{TR}}} = 40{\rm{\ cm}}$</tex-math></inline-formula>), respectively. Furthermore, an experimental prototype of a high-efficiency mid-range WPT system is constructed using the optimized coils. Specifically, the overall efficiency of the WPT system reaches 81.2% when <inline-formula><tex-math notation="LaTeX">${{d}_{\text{TR}}} = 20{\rm{\ cm}}$</tex-math></inline-formula> and 63.2% when <inline-formula><tex-math notation="LaTeX">${{d}_{\text{TR}}} = 40{\rm{\ cm}}$</tex-math></inline-formula>.