Modeling Planar Fluxgate Structures

Planar fluxgate structures have been the focus of multiple experimental studies. However, theoretical treatises are still limited to the classical models that describe 3D structures. In this paper we derive an effective fluxgate equation for planar systems, dealing with strong stray fields and direct coupling, and show the stability and applicability of the Vacquier implementation. To support the theoretical model, FEM simulations are performed that also provide means of layouting planar fluxgates by pure magnetostatic simulation.