In this article, we present two methods for calculation of the inductance of toroidal inductor wound by rectangular cross-sectional wire, considering that the current density is inversely proportional to the circular coil radius. The first method is to simplify the helical toroidal coil into a thick-walled toroidal, and based on Grover’s toroidal inductor formula, the inductance is obtained by calculation the magnetic flux and the calculation method is simple, but the applicability is poor. The second method is to simplify the helical toroidal coil into a collection of self-closing circular coils, the calculation method is complex but has high accuracy, and the mutual inductance between the circular coils is calculated by the filament method based on the adjusted Grover’s mutual inductance of circular coils with inclined axes. We verify the adjusted Grover’s mutual inductance of filamentary circular coils with inclined axes and the mutual inductance between inclined circular coils with a rectangular cross section. Finally, we compared and analyzed the results calculated by the two methods proposed in this article and the results calculated by the finite element method.

中文翻译：

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矩形截面线绕环形电感的计算电感

在本文中，考虑到电流密度与圆形线圈半径成反比，我们提出了两种计算矩形截面线绕环形电感器电感的方法。第一种方法是将螺旋形环形线圈简化为厚壁环形，根据格罗弗的环形电感公式，通过计算磁通量得到电感量，计算方法简单，但适用性较差。第二种方法是将螺旋环形线圈简化为一组自闭合的圆形线圈，计算方法复杂但精度高，圆形线圈之间的互感是根据调整后的格罗弗互感通过灯丝法计算出来的。具有倾斜轴的圆形线圈的电感。我们验证了经过调整的具有倾斜轴的丝状圆形线圈的 Grover 互感和具有矩形横截面的倾斜圆形线圈之间的互感。最后，我们对本文提出的两种方法的计算结果和有限元方法的计算结果进行了对比分析。