A Simple Calculation Method Using a Numerical Table of Shape Coefficient for Self-Inductance of Single-Layer Regular Polygonal Coils

For the self-inductance of single-layer regular polygonal coils, an exact formula already exists. However, obtaining the exact value requires cumbersome and skillful work for numerical integration, as the formula involves a double infinite integral. If a simpler, faster and highly accurate calculation method for determining the inductance value could be found, its utility in coil design would be extremely high. In this technical note, we introduce a new “shape coefficient” and tabulate its exact values, similar to the Nagaoka coefficient. Then using shape coefficients read from the numerical table, we have proposed a simplified calculation method that quickly determines inductance through basic arithmetic operations. We have also verified the validity and usefulness of this simplified calculation method by applying it to three types of coils (equilateral triangle, regular pentagon and regular hexagon). Ultimately, by utilizing the shape coefficient determined by the coil specifications, it is possible to easily obtain accurate inductance values.