Homogenized Permittivity of Composites With Aligned Cylindrical Inclusions for Causal Electromagnetic Simulations

Abstract

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 singleor 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.

A Spiral Shaped Slot as a Broad-Band Slotted Waveguide Antenna

“…There was excellent agreement between the simulated and measured S-parameters for the copper waveguide. The difference in S-parameters between the CFRP and copper waveguides are due to the insertion loss in the CFRP which is well described in [8,[18][19][20]. This resulted in the |S 21 | for the spiral shaped SWA in CFRP to be approximately 1 dB lower than that in the metallic waveguide throughout the band.…”

Evaluation of dielectric permittivity for homogeneous materials from transmittance requirements

“…The Debye parameters (ε sD , ε ∞D , τ D ) can be obtained graphically by looking at the real part and imaginary part of the ε eff_Approx obtained from (12); another way is to evaluate the limit of Re(ε eff_Approx ) for ω→0 and ω→∞ for extracting ε s and ε ∞ , respectively. [13]- [14]. The relaxation time τ D can be calculated from (18) [4].…”

“…The equivalent permittivity in Fig. 5 is obtained applying the Maxwell Garnett mixing rule, as described in [13]. The Debye parameters (ε sD , ε ∞D , τ D ) can be obtained graphically by looking at the real part and imaginary part of the ε eff_Approx obtained from (12); another way is to evaluate the limit of Re(ε eff_Approx ) for ω→0 and ω→∞ for extracting ε s and ε ∞ , respectively.…”

“…The synthesis assumes that the homogeneous material to be derived can be characterized by a permittivity described in terms of a first order Debye model [4], [6]- [7], as in (13).…”

Enhanced Electroactive Response of Unidirectional Elastomeric Composites with High‐Dielectric‐Constant Fibers

“…In (d), ε is presented as a function of fiber concentration for ADEPT composites at 1 kHz. The solid lines in (b)‐(d) serves as guides for the eye, whereas the solid line in (d) represents a nonlinear regression of the MGA developed for composites with cylindrical inclusions to the data.…”