A New Mixing Rule for Predicting of Frequency-Dependent Material Parameters of Composites


A number of mixing rules are proposed in the literature to predict the dependence of effective material parameters of composites, the permittivity and permeability, on frequency and concentration. Alternatively to the mixing rules, properties of composites can be considered in terms of the Bergman-Milton theory (BMT), which employs the concept of the spectral function. All known mixing rules are particular cases of the BMT. Particularly, the Ghosh-Fuchs theory (GFT) has been proposed based on the BMT. The GFT is shown to agree well with measured material parameters of composites filled with ferromagnetic metal powders. However, the GFT is not convenient for use because of its complicated mathematical form. Herein, a simple analytic formulation of the GFT is proposed. The new mixing rule is based on the shape of the spectral function typical for the Bruggeman effective medium theory with the averaged depolarization factor of inclusions and the percolation thresholds introduced as fitting parameters. Since the permittivity and permeability of a composite are governed by the same mixing rule, these fitting parameters are found from the concentration dependence of permittivity of the composite for further use in the analysis of the frequency dependence of permeability. The proposed mixing law is valid for the case of nearly spherical shape of inclusions in the composite, e. g., stonelike inclusions.

Meeting Name

20th URSI International Symposium on Electromagnetic Theory (2010: Aug. 16-19, Berlin, Germany)


Electrical and Computer Engineering

Research Center/Lab(s)

Electromagnetic Compatibility (EMC) Laboratory

Keywords and Phrases

Concentration Dependence; Depolarization Factor; Effective Medium Theories; Ferromagnetic Metal; Fitting Parameters; Frequency Dependence; Frequency-Dependent; Fuchs Theory; Material Parameter; Mathematical Forms; Mixing Rules; Percolation Thresholds; Properties Of Composites; Spectral Function; Spherical Shape; Electric Fields; Electromagnetism; Magnetic Materials; Permittivity; Solvents; Spectroscopy; Mixing

International Standard Book Number (ISBN)

978-1424451555; 978-1424451548

Document Type

Article - Conference proceedings

Document Version


File Type





© 2010 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Aug 2010