A recasting of the effective parameters of composite mixtures into the language of artificial dielectrics

Effective medium theories (EMTs) along with percolation theory allow the characterization of the electromagnetic properties of binary composite mixtures at a frequency when the scale of a particle size allows the quasi-static limit approximation. These theories formulate an effective permittivity and permeability (ε^eff and μ^eff) to predict the expected electromagnetic response of binary composite mixtures of a scale size L much larger than the average homogeneous size ξ within the mixture (the correlation length of percolation theory). It can be shown that any physically realizable material's permittivity (i.e. a complex permittivity which is causal and analytic in the upper-half complex frequency plane) can be represented as a sum of series LRC circuits. From the effective permittivity described by EMTs (away from the percolation threshold) or percolation theory (near the percolation threshold), the corresponding distributed circuit models are formulated to recast the expected composite material electric response into a more familiar form. This corresponding circuit model describes the dominant contributions to the composites material response at any frequency in terms of the individual LRC circuit elements of the permittivity dispersion's model.