From Maxwell Garnett to Debye Model for Electromagnetic Simulation of Composite Dielectrics—Part II: Random Cylindrical Inclusions

A mixing rule in the theory of composites is intended to describe an inhomogeneous composite medium containing inclusions of one or several types in a host matrix as an equivalent homogeneous medium. The Maxwell Garnett mixing rule is widely used to describe effective electromagnetic properties (permittivity and permeability) of composites, in particular, biphasic materials, containing inclusions of canonical shapes (spherical, cylindrical, or ellipsoidal). This paper presents a procedure for deriving an equivalent Debye model that approximates the geometry-based Maxwell Garnett model for randomly distributed cylindrical inclusions. The derived Debye model makes the equivalent dielectric material suitable for any time-domain electromagnetic simulations.