In the design and production of electrical and electronic devices and circuits, it is desirable to have a calculation formula for obtaining exact inductance values, which are generally fundamental for coils. In this paper, a formula that can be applied to the exact calculations of the self-inductance of arbitrary-shaped single-layer coils is presented, and its application to the several types of coils that are technologically valuable is reported. Specifically, the formula employs a new coefficient corresponding to the Nagaoka coefficient and the shape function determined by the coil. Moreover, it realizes a versatile and convenient inductance calculation method. In addition, as the formula is derived via an analytical method, it has the advantage that it can be calculated with a short-time numerical integration. As examples of the application of the formula, rhombic, race-track, elliptic, and regular polygonal coils were discussed, and the process and result of deriving the shape function and new coefficient for each coil were presented. Furthermore, regarding the calculation formula for regular polygonal coils, we made a regular pentagonal coil and conducted an experiment, and the validity of the calculation formula was confirmed. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

中文翻译：

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任意形状单层线圈的自感计算公式的应用（正多边形线圈的形状函数推导和电感计算）

在电气和电子设备和电路的设计和生产中，希望有一个计算公式来获得精确的电感值，这通常是线圈的基础。本文提出了一个可用于精确计算任意形状单层线圈自感的公式，并报告了其在几种具有技术价值的线圈中的应用。具体而言，该公式采用了与长冈系数和由线圈确定的形状函数相对应的新系数。此外，它实现了一种通用且方便的电感计算方法。此外，由于公式是通过解析方法导出的，它具有可以用短时间数值积分计算的优点。作为公式应用的例子，讨论了菱形线圈、跑道线圈、椭圆线圈和正多边形线圈，并给出了每个线圈的形状函数和新系数的推导过程和结果。此外，关于正多边形线圈的计算公式，我们制作了正五角线圈并进行了实验，证实了计算公式的有效性。© 2022 日本电气工程师学会。由 Wiley Periodicals LLC 出版。验证了计算公式的有效性。© 2022 日本电气工程师学会。由 Wiley Periodicals LLC 出版。验证了计算公式的有效性。© 2022 日本电气工程师学会。由 Wiley Periodicals LLC 出版。