Extended Theory on the Inductance Calculation of Planar Spiral Windings Including the Effect of Double-layer Electromagnetic Shield

Recent progress on wireless planar battery charging platform highlights a requirement that the platform must be shielded underneath so that the electromagnetic (EM) flux will not leak through the bottom of the charging platform. The presence of the EM shield will inevitably alter the flux distribution and thus the inductance of the planar windings. In this paper, a theory of calculating inductance of spiral windings is extended to determine the inductance of planar spiral windings shielded by a double-layer planar EM shield. With the generalized equations, the impedance of the planar spiral windings on double-layer shielding substrate and the optimal thickness of shielding materials can be calculated accurately without using time-consuming finite-element method. Therefore, the influence of the double-layer electromagnetic shield on the inductance of the planar spiral windings can be analyzed. Simulations and measurements have been carried out for several shielding plates with different permeability, conductivity and thickness. Both of the simulations and measurements of the winding inductance agree well with the extended theory.