Derivation of homogeneous permittivity of composite materials with aligned cylindrical inclusions for causal electromagnetic simulations

Abstract

The paper gives an analytical transition from the Maxwell Garnett model of a biphasic mixture (dielectric host and dielectric or conducting inclusions) to the parameters of a single- or double-term Debye representation of the material frequency response. The paper is focused on modeling biphasic mixtures containing cylindrical inclusions. This is practically important for engineering electromagnetic absorbing composite materials, for example, containing carbon fibers. The causal Debye representation is important for incorporation of a composite material in numerical electromagnetic codes, especially time-domain techniques, such as the finite-difference time-domain (FDTD) technique. The equations derived in this paper are different for different types of host and inclusion materials. The corresponding cases for the typical combinations of host and inclusion materials are considered, and examples are provided. The difference between the original Maxwell Garnett model and the derived Debye model is quantified for validating the proposed analytical derivation. It is demonstrated that in some cases the derived equivalent Debye model well approximates the frequency characteristics of the homogeneous model based on the MGA, and in some cases there is an exact match between Debye and Maxwell Garnett models.