Analysis of inductance calculation of coaxial circular filamentary coils, thin-wall solenoids, and disk coils using inverse hyperbolic functions

This study presents a method using inverse hyperbolic functions to calculate the mutual and self-inductance inductance of coaxial circular filamentary coils, thin-wall solenoids, disk coils, and coils with rectangular cross-section in air. A generalised expression is given for any combination of these coils, which only requires numerical integration with one variable. Singularities are fully analysed and methods to resolve the singularities are presented in this study. When calculating the self-inductance of a disk coil or a thin-wall solenoid, the proposed method involves an improper integral, and the accuracy of the proposed method is limited unless a quadrature rule applicable to improper integrals is applied. For other situations, results by the proposed method were compared with those in the literature, and they were in excellent agreement.