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首页> 外文期刊>Magnetics, IEEE Transactions on >Improvement of Self-Inductance Calculations for Circular Coils of Rectangular Cross Section
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Improvement of Self-Inductance Calculations for Circular Coils of Rectangular Cross Section

机译：矩形截面圆形线圈自感计算的改进

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摘要

In this paper, an improvement for calculating the self-inductance of circular coils of rectangular cross section is presented. An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral without the exponential factor is solved to a closed form which consists of the complete elliptic integrals of the first and second kind and generalized hypergeometric functions. Due to this method, the main difficulties of the numerical evaluations of the inductance expression are overcome. Excellent agreement with published method is confirmed by the numerical comparisons and the calculations can be accelerated to several tens to hundreds of times depending on the shape factors of the coils. Similar expressions of the special cases (thin-wall solenoids and disk coils) are also given and compared with previous methods. Furthermore, the asymptotic behaviors of the special coils which tend to be a circular ring are obtained and numerically validated.
机译：本文提出了一种改进的矩形截面圆形线圈自感计算方法。应用基本函数的积分替换电感表达式中被积分的Bessel和Struve函数，将没有指数因子的不正确积分项求解为一个封闭形式，该形式由第一和第二个椭圆的完整积分组成种类和广义超几何函数。由于该方法，克服了电感表达式的数值评估的主要困难。数值比较证实了与已公开方法的极佳一致性，并且根据线圈的形状因子，计算可以加速数十到数百倍。还给出了特殊情况（薄壁螺线管和磁盘线圈）的类似表达式，并将其与以前的方法进行了比较。此外，获得了倾向于为圆环的特殊线圈的渐近特性，并进行了数值验证。

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