Computation of Geometric Mean Distance through Monte Carlo Simulation to Predict Inductance of Circular Coil with Arbitrary Cross-Section

The calculation of inductance is of paramount importance in various electromagnetic systems utilizing coils. Numerous research efforts have focused on calculating the self-inductance of coils, often providing formulas for approximating the inductance of coils with specific shapes. The self-inductance of a circular coil can be calculated directly using the geometric mean distance (GMD), but GMD calculations have rarely been studied except for simple cross-sections such as circles or squares. This paper introduces a method employing modified Monte Carlo simulation to obtain GMD based on the aspect ratio of arbitrary shapes. The proposed approach is applied to calculate the self-inductance of a circular coil with a complex cross-section.