Analytical Model of Inductance for the Magnetic Couplers Based on the Analytical Expressions of the Mirror Coefficients in WPT Systems

Facing wireless charging systems, this article proposes an innovative analytical model of self-inductance (SI) and mutual inductance (MI) for the magnetic couplers, using joint analytical calculation (JAC) method. The JAC method is extended to addresses the challenges of the construction of mirror model and the solution of mirror coefficient for source coils with bilateral finite ferrite cores. The influence of ferrite cores on inductance is divided into three parts, with each aspect being replaced by equivalent first, second, and third mirror coils. The constructed mirror model strictly satisfies the boundary value conditions at medium interfaces. Regardless of whether the magnetic couplers are perfectly aligned or not, mirror coefficients can be calculated by combining the double truncation region eigenfunction expansion method and the mirror method. After translating ferrite cores into air-core mirror coils, both SI and MI can be determined when horizontal and angular misalignments occur. Experimental verification confirms that the constructed model can accurately calculate SI and MI under various misalignment conditions.