Calculation Methodologies of Complex Permeability for Various Magnetic Materials

Abstract

In order to design power converters and wireless power systems using high-frequency magnetic materials, the magnetic characteristics for the inductors and transformers should be specified in detail w.r.t. the operating frequency. For investigating the complex permeability of the magnetic materials by simply test prototypes, the inductor model-based calculation methodologies for the complex permeability are suggested to find the core loss characteristics in this paper. Based on the measured results of the test voltage Ve, current Ie, and phase difference θe, which can be obtained simply by an oscilloscope and a function generator, the real and imaginary permeability can be calculated w.r.t. operating frequency by the suggested calculation methodologies. Such information for the real and imaginary permeability is important to determine the size of the magnetic components and to analyze the core loss. To identify the superiority of the high-frequency magnetic materials, three prototypes for a ferrite core, amorphous core, and nanocrystalline core have been built and verified by experiment. As a result, the ferrite core is superior to the other cores for core loss, and the nanocrystalline core is recommended for compact transformer applications. The proposed calculation for the complex (i.e., real and imaginary) permeability, which has not been revealed in the datasheets, provides a way to easily determine the parameters useful for industrial electronics engineers.