At high frequency, power losses of a winding due to eddy currents becomes significant. Moreover, the skin and proximity AC resistances are influenced by the width of printed circuit board (PCB) conductors and distance between the adjacent tracks which causes many difficulties to design windings with lowest AC resistances. To clarify this phenomenon, this paper focuses on modeling the influence of skin and proximity effects on AC resistance of planar PCB winding, thereby providing guidelines to reduce the winding AC resistance. An approximate electromagnetic calculation method is proposed and it shows that when the winding proximity AC to DC ratio $\left(F_{proximity}\right)$ is equal to $\frac{1}{3}$ the AC on DC ratio caused by skin effect $\left(F_{skin}\right)$ , the winding is optimized and it has lowest AC resistance. 3-D finite element simulations of 3, 7 and 10-Turn windings, which are divided into 3 groups with the same footprint, are presented to investigate the lowest AC resistance when the track width varies from 3 mm to 5 mm and the frequency range is up to 700 kHz. In order to verify the theoretical analysis and simulation results, an experiment with 3 simulated groups, (9 prototypes in total) is built and has a very good fit with simulation results. Experimental results show that at the optimal width, the AC resistance of the windings can be reduced up to $16.5\%$ in the frequency range from 200 kHz to 700 kHz.

中文翻译：

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优化实心PCB绕组的交流电阻

在高频下，由于涡电流而引起的绕组功率损耗变得很大。此外，皮肤和接近AC电阻受印刷电路板（PCB）导体的宽度和相邻走线之间的距离的影响，这给设计具有最低AC电阻的绕组带来了许多困难。为了澄清这种现象，本文着重于建模趋肤效应和邻近效应对平面PCB绕组交流电阻的影响，从而为降低绕组交流电阻提供了指导。提出了一种近似的电磁计算方法，该方法表明当绕组接近交直流比时。 $（F_{p\mathrm{[R}ØX\mathrm{一世}米\mathrm{一世}Ťÿ}）$ 等于 $\frac{\mathrm{1个}}{3}$ 皮肤效应引起的交流对直流比率 $（F_{sķ\mathrm{一世}ñ}）$ ，绕组经过优化，具有最低的交流电阻。提出了3、7和10匝绕组的3-D有限元仿真，该仿真分为3组且具有相同的占位面积，以研究磁道宽度从3 mm到5 mm以及频率范围变化时的最低交流电阻高达700 kHz。为了验证理论分析和仿真结果，建立了一个包含3个仿真组的实验（共9个原型），并且与仿真结果非常吻合。实验结果表明，在最佳宽度下，绕组的交流电阻可以降低到 $16.5％$ 在200 kHz至700 kHz的频率范围内。