Combined simulation-based correction factors for reluctances of planar coil substrates

A method and a simplified analytical expression are presented for the calculation of the effective reluctance of a magnetic substrate underneath a planar coil as parameter in a simplified electromechanical network model. The investigated magnetic substrates have a toroid geometry with rectangular cross section, different thicknesses and permeabilities. The method is based on a combined simulation of the magnetic quantities where network parameters are determined by a Finite Element simulation. A network transformation allows the computation of partial inductances which are related to the reluctances. Depending on thickness and permeability the effective substrate reluctance differs from a geometrically based reluctance calculation, where an axisymmetric field distribution without axial component is assumed. From the almost linear relation between the reluctances a correction factor can be given. This factor allows the simplified calculation of the effective reluctance of a magnetic substrate underneath a planar coil.