New AC resistance calculation of printed spiral coils for wireless power transfer

Wireless power transfer (WPT) is a promising technique for powering the Internet-of-Things devices. Printed spiral coils (PSCs) are commonly used in WPT because of their advantages of compact size and standardized fabrication. Under the demand of analytically optimizing the WPT system, like power transfer efficiency or power delivered to the load, an analytical resistance model is required. In this paper, the proximity-effect resistance is focused on. A formula is curve-fitted based on the data simulated from COMSOL Multiphysics and magnetic field calculation. The total AC resistance model which is the sum of skin-effect resistance and proximity-effect resistance is verified by HFSS simulation and measurement. Under the impact of inductance and parasitic capacitance, the comparison of the calculated, simulated, and measured real parts of Z-impedance shows that the difference between them is increased quickly when the operating frequency is higher than the frequency corresponding to the maximal quality factor of a PSC. A more accurate self-resonant frequency or capacitance model should be developed in the future work.