A Mixing Rule for Predicting Frequency Dependence of Material Parameters in Magnetic Composites


A number of mixing rules are proposed in the literature to predict the dependence of effective material parameters (permittivity and permeability) of composites on frequency and concentration. However, the existing mixing rules for frequency dependence of permeability in magnetic composites typically do not provide satisfactory agreement with measured data. Herein, a simple mixing rule is proposed. Its derivation is based on the Bergman-Milton spectral theory. Both the Bruggeman effective medium theory and the Maxwell Garnett approximation are included as particular cases of the proposed mixing rule. The derived mixing rule is shown to predict accurately the frequency dependence of permeability in magnetic composites, which contain nearly spherical inclusions.


Electrical and Computer Engineering


Russian Foundation for Basic Research
National Science Foundation (U.S.). Industry/University Cooperative Research Centers Program


K. Rozanov acknowledges financial support of the study from the RFBR (Grant nos. 09-08-00158, 12-02-91193,12-02-91667, and 12-08-00664). M. Koledintseva and J. Drewniak acknowledge the support in part by a National Science Foundation Grant no. 0855878 through the I/UCRC program.

Keywords and Phrases

Effective Medium Theories; Frequency Dependence; Magnetic Composites; Material Parameter; Maxwell-Garnett; Measured Data; Mixing Rule; Mixing Rules; Spectral Theory; Spherical Inclusion; Composite Materials; Forecasting; Mechanical Permeability; Mixing; Composite Material; Microwave Magnetic; Permeability

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Article - Journal

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© 2012 Elsevier, All rights reserved.

Publication Date

01 Mar 2012