空心矩形截面圆柱线圈自感计算的新方法

New Method for Self-Inductance Calculations of Air-Core Circular Coils with Rectangular Cross-Sections

对空心矩形截面圆柱线圈的自感的多重积分表达式进行了分析,指出了该积分难于处理的原因,并对此引入距离倒数的级数展开使被积函数变量去耦,使积分过程大为简化,并据此推出空心矩形截面圆柱线圈自感新的计算公式。特殊情形的单层线圈与盘式线圈的自感公式也一并给出。这些新公式包含Bessel函数、Struve函数、第一类和第二类完全椭圆积分。随后对本文提出的公式进行了数值计算并与已有文献中的结果进行了比较。数值结果表明,相较已有的公式而言,这些新的公式以足够简洁的形式给出高精度的计算结果,使空心矩形截面圆柱线圈以及单层圆柱线圈、圆盘线圈的自感计算效率与精度得以提高。

The expression of multi-dimensional integral for the self-inductance of air-core circular coils with rectangular cross-sections was analyzed and the difficulty of this integration procedure was pointed out, so the expansion of reciprocal distance was applied to decouple the integral variables and simplify the integration procedure greatly. Owing to the expansion method, new formulas for the self-inductance of air-core circular coils with rectangular cross-sections were obtained, the formulas of thin-wall solenoids and disk coils were also provided. The new formulas include Bessel functions, Struve functions and the complete elliptic integrals of the first and second kind. Then the numerical calculations were applied and the results were compared with those in the existing literatures The comparisons show that the can be calculated in high degree of accuracy with concise enough form, and the efficiency and accuracy of the calculation of air-core circular coils with rectangular cross sections can be improved.