Three-dimensional magnetic field modeling for coupling calculation between air-cored rectangular coils

A semianalytical model is derived for the description of the three-dimensional magnetic field of an array of air-cored rectangular coils. The model describes the magnetic field with Fourier series and is obtained by solving the Maxwell equations using a combination of the magnetic vector and scalar potential. The model avoids the necessity of finite element analysis and allows three-dimensional analysis between air-cored rectangular coils in contactless energy transfer systems. As an example, the model is used to calculate the magnetic coupling between an array of primary and one secondary air-cored coil.