Kimmo Kärkkäinen

Effective permittivity of mixtures: numerical validation by the FDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional (2-D) dielectric mixture is calculated by FDTD simulations of such a sample in a TEM waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits. Calculated permittivity distribution is also compared with theoretical mixture models. No model seems to be able to predict the simulated behavior over the whole range of volume fraction.

Analysis of a three-dimensional dielectric mixture with finite difference method

The present paper reports the results of a numerical analysis of electric fields in random dielectric materials. The effective permittivity of a three-dimensional (3D) dielectric mixture is calculated by the finite difference method. The results show the distribution of the effective permittivity of a mixture with different random inclusion positionings. New empirical mixing models are created as least squares approximations to fit the collection of numerical results. The calculated permittivity distribution is also compared with theoretical mixture models, showing that in case of clustered inclusions, the Bruggeman model is quite reasonable. On the other hand, if the inclusions in the mixture are separate, the results are closer to the Maxwell-Garnett model.

Numerical testing of dielectric mixing rules by FDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of the mixture is calculated by FDTD simulations of such a sample in a TEM-waveguide. The mixture consists of a homogeneous free space background in which circular cylinders are embedded in random positions. Clustering of the inclusions is allowed. The choice of two-dimensional spheres allows us to make much more use of the numerical capacity than what would be the case in three-dimensional inclusions. Various dielectric contrasts are studied from permittivity ratio 2 to 50. Numerical results are compared with classical mixing rules, and they show moderate agreement with the Bruggeman rule rather than the Maxwell Garnett approach. However, another key finding of this paper is that obtained mixing results are not symmetric with respect to inclusions and background. This makes the exact validity of the symmetric Bruggeman formula questionable.

On the Estimation of SAR and Compliance Distance Related to RF Exposure From Mobile Communication Base Station Antennas

In this paper, maximum specific absorption rate (SAR) estimation formulas for RF main beam exposure from mobile communication base station antennas are proposed. The formulas, given for both whole-body SAR and localized SAR, are heuristic in nature and valid for a class of common base station antennas. The formulas were developed based on a number of physical observations and are supported by results from an extensive literature survey together with supplementary measurements and numerical simulations of typical exposure situations. Using exposure limits, the proposed SAR estimation formulas can be converted to formulas for estimating compliance distance.

Two-dimensional extension of a novel FDTD technique for modeling dispersive lossy bi-isotropic media using the auxiliary differential equation method

This letter describes a two-dimensional (2-D) extension of a recently developed finite-difference time-domain (FDTD) scheme to model wave propagation in bi-isotropic media. To our knowledge this method is the only one successfully generalized to modeling transient microwave signals in general lossy dispersive bi-isotropic media. The new 2-D cell built and computational procedure of the FDTD algorithm developed is described. Condon and Lorentz dispersion models have been included for modeling the frequency dependence of the medium parameters and the auxiliary differential equation (ADE) method is considered to deal with dispersion in order to avoid defining complex back-stored numbers to compute the convolutions recursively. Finally the oblique incidence of a wave on a chiral medium and the propagation in a general lossy bi-isotropic medium have been successfully simulated.

Limits for the effective permittivity of mixtures: numerical validation by the FDTD method

Reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional dielectric mixture is calculated by FDTD simulations of such a sample in a TEM-waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits.

Effective permittivity of a random mixture with spherical inclusions

The paper reports the results of a numerical analysis of electric field in random dielectric materials. The effective permittivity of a three-dimensional mixture is calculated by the finite difference method. The studied mixture is a two-component mixture with a homogeneous background in which spheres of another material are embedded in random positions. A new technique to derive difference equations in the neighborhood of material interfaces is considered. Hundreds of mixture samples with different random inclusion distributions are analysed to get a good insight into average characteristics of the mixture material. The calculated permittivity distributions are also compared with well-known theoretical models such as Maxwell Garnett and Bruggeman models.