Homogenization for Analysis of Magnetic Devices
摘要
This chapter describes homogenization methods for electromagnetic field analysis of magnetic devices. The homogenization method replaces the microstructure such as soft laminated steel sheet, magnetic composite core, multi-turn coil, and litz wire with a uniform material with equivalent electromagnetic property. This avoids fine discretization and greatly reduces the computing cost. This chapter first introduces complex permeability, which describes the proximity effect in simple geometries, such as cylinders and spheres. It then introduces the homogenization methods based on the extended Ollendorff formula and complex permeability as well as the unit cell approach. The Dowell method, which has been widely used in the analysis of AC resistance and eddy current losses in multiturn coils in magnetic devices, is also discussed. It is shown that the homogenization and Dowell methods give the consistent results for the AC resistance under the above conditions, while the former gives accurate results even when this condition does not hold. Finally, the modeling of the multiturn coils is described, taking into account the displacement currents due to the parasitic capacitance.