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 wideband modeling of complex electromagnetic structures containing composite materials with effective dielectric parameters obtained through MG mixing rule.


Electrical and Computer Engineering

Research Center/Lab(s)

Electromagnetic Compatibility (EMC) Laboratory

Keywords and Phrases

Biphasic Materials; Composite Dielectrics; DC Conductivity; Debye Frequencies; Debye Model; Debye Models; Dielectric Parameters; Effective Permittivity; Electromagnetic Simulation; Electromagnetic Structure; Frequency Characteristic; Frequency Independent; Frequency-Dependent; Maxwell-Garnett; Mixing Rules; Numerical Electromagnetic Codes; Semianalytical Approach; Spherical Inclusion; Time Domain; Wideband Modeling; Composite Materials; Computer Simulation; Dielectric Materials; Electromagnetism; Maxwell Equations; Phonons; Spheres; Superconducting Materials; Time Domain Analysis; Magnetic Materials; Composite Material; Frequency-Dependent Material; Spherical Inclusions

International Standard Serial Number (ISSN)

0018-9375; 1558-187X

Document Type

Article - Journal

Document Version


File Type





© 2011 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Nov 2011