Analytical Expression of the Mirror Coefficient by Joint Analytical Calculation Method

To address the universal challenge that the mirror coefficient (MC) cannot be analytically expressed, the joint analytical calculation (JAC) method is initially proposed in this article. Selecting the magnetic vector potential (MVP) as a uniform analytical target, the JAC method constructs a bridge, linking the truncated region eigenfunction expansion (TREE) method and the mirror method. Furthermore, an analytical expression of MC is derived based on the uniqueness principle of the magnetic field. The JAC method comprehensively reflects the effect of magnetic medium parameters, coil parameters, and field point coordinates on MC. Furthermore, the double TREE method is proposed to further improve the analytical accuracy of MVP. The experiment indicates that the analytical error of MVP is shrunk by a maximum of 3.16%. Then, magnetic flux density (MFD) is solved according to the analytical expressions of MC. The experiment shows that the JAC method and the mirror method have a maximum error of 4.08% and 27.99% for calculating MFD, respectively.