Frequency-Dependent Resistance of Litz-Wire Square Solenoid Coils and Quality Factor Optimization for Wireless Power Transfer

In order to achieve the highest efficiency of wireless power transfer (WPT) systems, the quality factor of the resonant coil should be as high as possible. Due to the skin effect and the proximity effect, the coil resistance increases with the increase in the frequency. The highest quality factor exists for the optimal frequency together with the corresponding frequency-dependent inductor resistance. This paper employs the Biot-Savart law to calculate the magnetic field strength, which results in the proximity-effect resistance in single-layer litz-wire square solenoid coils without a magnetic core. A strand-number coefficient is introduced to reflect the influence of the strand number inside the wire bundle on the proximity-effect resistance. The coefficient is obtained through simple inductor resistance measurements for various numbers of litz-wire strands. The optimal frequency for the highest quality factor is derived based on the resistance evaluation. Several prototype coils were manufactured to verify the resistance analysis. Two 50 cm × 50 cm square coils were employed to construct a WPT prototype. The maximum dc-dc efficiency of this WPT was about 75% at 100-cm distance.