A New Mathematical Expression for Mutual Inductance of Two Coupled Ring Coils

This study introduces an efficient method to determine the computation mathematical formula of mutual inductance (M) for a pair of ring coils. A design technique called Box-Behnken that based on the response surface methodology (RSM) was utilised to develop such a formula. The M was developed to be a function for the air-gap (d) between the coupled coils, coils dimensions, and misalignment parameters. Therefore, the introduced new formula is facilitating a ring coil design, and prediction of system behaviour in normal or misalignment conditions. The percentage impact of each parameter on the M was measured. It was found that M is mainly affected by d. Finally, the outcomes due to the new formula are in a line with the results obtained from the finite element modelling (FEM) simulation.