Completely Analytical Model of Inductance for Circular Coils With Bilateral Finite Magnetic Cores and Al Plates in WPT Systems

Circular coils are essential components in wireless power transfer (WPT) systems. While some research has focused on analytical inductance calculations, a completely analytical model (CAM) for circular coils with finite magnetic cores and aluminum (Al) plates is lacking. This article addresses this gap by introducing a CAM using the truncated region eigenfunction expansion (TREE) method. The model comprises two variants: the coaxial complete analytical model (CCAM) and the noncoaxial complete analytical model (NCCAM). In the CCAM, the width of cores (w(core)) is considered by using a truncation region (TR). Additionally, an effective technique is proposed to separate expansion coefficients related to Al plate width (w(Al)) and eigenvalues by assuming w(Al)) equals TR, which is valid when (w(Al)) >= 1.2w(core) in practical applications. The CCAM encompasses all design parameters. Meanwhile, the NCCAM is applied to evaluate the fluctuation of mutual inductance (MI) when horizontal misalignment (HM) occurs. By assuming an extension of core width to TR, the NCCAM incorporates an equivalent relative permeability (ERP). Real-time ERP is extracted from the CCAM model when the self-inductance (SI) changes. Experiment shows that the analytical results of inductance have an error of 5.12% or less, regardless of alignment between the transfer and pickup sides.