Modeling of planar coils for wireless power transfer systems including substrate effects

This paper presents an analytical model of the impedance between two coils supported by ferrite shield. The new model is not restricted to round coils and applies to more complex winding geometries, as specified by the Wireless Power Consortium. The mutual inductance is derived by solving Maxwell's equations and using Bessel function of the first kind. The model results are compared with experimental data as a function of the vertical displacement between the coils. In addition, a wireless power transfer system is modeled to calculate system efficiency by adopting the above coils impedance model. Experimental results run on 5W wireless power transfer system at several displacement steps are compared against simulation data.