Predicting of wideband electromagnetic responses of composites containing magnetic inclusions

Engineering of absorbing bulk and sheet composite materials, including nanocomposites, for various EMI applications, requires adequate prediction of frequency and concentration behavior of these composites. This paper proposes two simple analytical formulations for effective permittivity and permeability of magneto-dielectric composites as functions of frequency and concentration. The first new proposed mixing rule is based on the Ghosh-Fuchs theory, which gives good agreement with the measured permittivity and permeability for composites containing magnetic alloy powders. This approach employs the Bergman-Milton concept of spectral function. Herein, the spectral function typical for the Bruggeman effective medium theory, also known as the Bruggeman symmetric rule (BSR), is chosen. This spectral function is composed using two fitting parameters: an averaged shape factor of inclusions, and the percolation threshold. These fitting parameters are found from the concentration dependence of permittivity, and then they are used to retrieve frequency dependence of permeability. The proposed mixing law is valid for nearly spherical inclusions in the composite, e.g., crumbs. Another analytical model proposed in this work can be applied to predict effective permeability of composites containing magnetic inclusions. It is based on the Bruggeman asymmetric rule (BAR), which has been modified in such a way that it takes into account shape factors of magnetic inclusions, in particular, randomly oriented platelets.