Finite-Width Magnetic Mirror Models of Mono and Dual Coils for Wireless Electric Vehicles

Improved magnetic mirror models (IM³) for mono and dual coils with a finite width and infinite permeability are proposed in this paper. By introducing a mirror current, which is located at the same distance from a source current but with a smaller magnitude than the source current, the magnetic flux density of the mono and dual coils can be determined in a closed form. The ratio of the mirror current and source current is identified as a function of the width of the core plate and the distance between the source current and core plate, as rigorously derived from finite-element method simulations. Applying the proposed IM³ to the mono and dual coils used for wireless electric vehicles, the magnetic flux density over an open core plate is analyzed and its maximum points on the plate are found, which is crucial in the design of the coils to avoid local magnetic saturation. Furthermore, the magnetic flux density when a pick-up core plate is positioned over a primary core plate is also analyzed by introducing successive mirror currents. The proposed magnetic mirror models were extensively verified by experiments as well as site tests, showing quite promising practical usefulness.