Calculations of Self- and Mutual Inductances for Racetrack Coils Using Equivalent Models

This article presents the calculations of self- and mutual inductances for thin racetrack coils using a novel approach. Approximate rectangular and diamond shape models for racetrack coils are used for the analysis with the same cross-sectional area and circumference as the racetrack coils. A 3-D analytical method using separation of variables method and Fourier series is developed for the magnetic fields analysis and calculation of self- and mutual inductances for thin racetrack coils. The analytical method utilizes magnetic vector potential with two components to solve Maxwell differential equations. Different racetrack coils with different dimensions are considered for the validation of analytical modeling for the inductance calculations. The inductance calculations of circular coils are also presented as special cases for racetrack coils. The approaches for the mutual inductance calculation of racetrack and circular coils could be utilized for wireless power transfer and charging applications.