Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method
Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method
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DOI：
10.1016/j.jmmm.2019.03.078
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发表时间：
2019-08-01
影响因子：
2.7
通讯作者：
Korvink, Jan G.
中科院分区：
文献类型：
--
作者：
Poletkin, Kirill, V;Korvink, Jan G.
在这篇文章中，我们提出了一个新的分析公式，用于计算两个任意取向的圆形灯丝之间的互感，作为Grover（1944）和Babic等人（2010）分别在1944年和2010年报道的表达式的替代。该公式是通过Kalantarov-Zeitlin方法的推广推导出来的，该方法表明，圆形主灯丝和任何其他具有任意形状和相对于主灯丝的任何所需位置的副灯丝之间的互感的计算被简化为线积分。特别是，所获得的公式提供了一个解决方案的奇异性问题所产生的Grover和Babic公式的情况下，当平面的初级和次级圆形细丝是相互垂直的。卡兰塔罗夫-蔡特林方法的效率和灵活性使我们能够立即将所得结果的应用扩展到计算初级圆形灯丝及其在倾斜平面上的投影之间的互感的情况。新开发的公式已成功地验证了文献中提供的一些例子，并通过与FastHenry软件进行的计算结果的直接比较。
In this article, we present a new analytical formulation for calculation of the mutual inductance between two circular filaments arbitrarily oriented with respect to each other, as an alternative to Grover (1944) and Babic et al. (2010) expressions reported in 1944 and 2010, respectively. The formula is derived via a generalisation of the Kalantarov-Zeitlin method, which showed that the calculation of mutual inductance between a circular primary filament and any other secondary filament having an arbitrary shape and any desired position with respect to the primary filament is reduced to a line integral. In particular, the obtained formula provides a solution for the singularity issue arising in the Grover and Babic formulas for the case when the planes of the primary and secondary circular filaments are mutually perpendicular. The efficiency and flexibility of the Kalantarov-Zeitlin method allow us to extend immediately the application of the obtained result to a case of the calculation of the mutual inductance between a primary circular filament and its projection on a tilted plane. Newly developed formulas have been successfully validated through a number of examples available in the literature, and by a direct comparison with the results of calculation performed by the FastHenry software.