From Maxwell Garnett to Debye Model for Electromagnetic Simulation of Composite Dielectrics Part I: Random Spherical Inclusions

A semianalytical approach to obtain an equivalent Debye frequency dependence of effective permittivity for biphasic materials with random spherical inclusions from the well-known Maxwell Garnett (MG) mixing rule is proposed. Different combinations of frequency characteristics of mixture phases (host and inclusions) are considered: when at least one of the phases is frequency independent; lossy (with dc conductivity); or with a known single-term Debye frequency dependence. The equivalent Debye models approximate very well the frequency characteristics obtained directly from MG mixing rule. In some cases, there is an exact match between the two models, and a good approximation is achieved in the other cases and is quantified by the feature selective validation technique. The parameters of the derived equivalent Debye model can be employed in full-wave time-domain numerical electromagnetic codes and tools. This will allow for efficient wide-band modeling of complex electromagnetic structures containing composite materials with effective dielectric parameters obtained through MG mixing rule.