Mutual Inductance Calculation for Planar Square and Hexagonal Coils

Abstract

In this paper, we have derived the formula for calculating the mutual inductance between filaments of arbitrary position and square and hexagonal coils. Mutual inductance is an important factor in calculating the exact inductance value of the coils. The studies show that the mutual inductance depends on many factors, such as the type and thickness of the conductors, the distance between the conductors, and the geometric shape. When factors such as the number of turns and the number of sides increase for polygonal shapes, the calculation of inductance becomes more complex. The formulas for square and hexagonal coils are established as a function of the number of turns, the side length of the outermost polygon, and the distance between the coils. We believe that the proposed method is simple, straightforward, accurate, and practical for engineering applications that use inductance calculations. The values of mutual inductance calculated by the proposed method were checked using Grover's formulas, Neumann integral, and COMSOL.