Modeling of Mutual Coupling Between Planar Inductors in Wireless Power Applications

This paper presents a compact model of mutual inductance between two planar inductors, which is essential to design and optimize a wireless power transmission system. The tracks of the planar inductors are modeled as constant current carrying filaments, and the mutual inductance between individual filaments is determined by Neumann´s integral. The proposed model is derived by solving Neumann´s integral using a series expansion technique. This model can predict the mutual inductance at various axial and lateral displacements. Mutual coupling between planar inductors is computed by a 3-D electromagnetic (EM) solver, and the proposed model shows good agreement with these numerical results. Different types of planar inductors were fabricated on a printed circuit board (PCB) or silicon wafer. Using these inductors, wireless power links were constructed for applications like implantable biomedical devices and contactless battery charging systems. Mutual inductance was measured for each of the cases, and the comparison shows that the proposed model can predict mutual coupling suitably.