Empirical Closed-Form Analysis for Inductance and Coupling Coefficient Calculation for Ferrite-Based Matched Inductive Charging Systems

Knowledge of the self-inductance and coupling coefficients of coils used in inductive wireless charging systems is essential for system level optimization and design of power electronic circuits. The traditional approach for computing these inductances relies on FEM simulations. Depending on the size of the design search space, this tends to be a computationally intensive approach. This paper presents a framework for performing empirical analyses on ferrite based coil designs. Approximate close-form expressions for commonly used coil designs, namely the rectangular and DD coils are developed. Four basic degrees of freedom are taken into consideration - the coil length and width, the copper area fill factor and the air gap between the coils in a matched system. The closed form inductance expressions presented in this paper match the corresponding FEM results and achieve an RMS error of less than 3% over the chosen design space.