Abstract：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.
罗垚, 陈柏超. 空心矩形截面圆柱线圈自感计算的新方法[J]. 电工技术学报, 2012, 27(6): 1-5.
Luo Yao, Chen Baichao. New Method for Self-Inductance Calculations of Air-Core Circular Coils with Rectangular Cross-Sections. Transactions of China Electrotechnical Society, 2012, 27(6): 1-5.
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2012, Vol. 27 
