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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. [ABSTRACT FROM AUTHOR]

Conventional calculation methods of air-core inductance utilized Neumann's equation for solenoidal coils and Fourier series for saddle coils. However, inductance formulas for arbitrarily shaped coils on a cylinder have not been well known. In this paper, mutual and self-inductances generated by any currents on a cylinder are expressed using Fourier-Bessel expansion of the vector potential. An experiment shows the validity of the proposed formulas. [ABSTRACT FROM AUTHOR]