Semi-analytical Computation of the Magnetic Field from IPT Coils of Complex Shape

A number of coils used in Inductive Power Transfer come in shapes which include straight sections and circular arcs. While the magnetic field from straight conductors or fully circular conductors can be computed with analytical or semi-analytical formulas found in the literature, similar formulas have not been available for circular arcs, leaving Finite Element Analysis as the final resort for designers. The derivation of such formulas is presented, with which fast mapping of the magnetic field can be achieved, as well as optimization procedures. Essentially, the formulas can be used to map the field from coils of any complex shape, since any shape consists of straight segments and arcs. The validity of the formulas has been verified by experimental measurements.