Mutual Inductance Calculation Formula for Planar Square Coils

The mutual inductance calculation depends on the shape, size and position of the coils. The reciprocal inductance between the two filaments (thin wire) is used for the double-layer Neumann's formula. However, as the number of parts of these inductors will increase with the number of turns, calculating will be difficult and a complex situation will occur. Therefore, a general formula required depending on the number of turns, the length of the filament and the distance between the windings can be expressed mathematically. In this study, a general formula for square coil was obtained. The beginning of the formula is based on the Neumann method. Mutual inductance was calculated for two, three, four and five-turn square coils and a certain order was observed between the results. According to Neumann method, numerical calculations were made between two filaments. As a result, a simple formula has been created to allow easy calculation of complex calculations of filaments having a plurality of turns. Symbolic calculations were made with the Wolfram Mathematica program and the generalized formula was transferred to the Matlab programming language.