Wireless communication systems have become an integral part of many complex systems in diverse areas of society, for the exchange of data in business and industrial settings. With the advent of Internet of Things (IoT) and wireless sensor network architectures, the tighter demands on interoperability between different devices are putting heavy requirements their ability to exchange data wirelessly among them reliably. However, many environments pose a challenging setting for a wireless communication system to operate within. Consequently, electromagnetic modeling could be used as a crucial part of the analysis and design of a wireless communication system in these environments.

In this thesis, means for the electromagnetic modeling of complex materials are considered. Specifically, the incorporation of dielectrics that exhibit loss, dispersion, and anisotropic properties into electromagnetic codes is addressed. The work has been executed within the partial element equivalent circuit (PEEC) method framework.

First, a PEEC implementation that incorporates dispersive and lossy dielectrics, represented by equivalent circuit models explicitly included in the PEEC equations, is developed. This provides a descriptor system form of the PEEC model that includes dielectrics with permittivities that can be represented as finite sums of Debye and Lorentz permittivity models and can be integrated by any time integration scheme of choice. Additionally, the description admits the application of model-order reduction techniques, reducing the model complexity of a large-scale PEEC model that consists of frequency-dispersive dielectrics.

Next, the incorporation of anisotropic dielectrics in PEEC simulations is considered. A PEEC cell for anisotropic dielectrics, with a general permittivity tensor, is derived. It turns out to be an extension of the standard dielectric PEEC cell for an isotropic dielectric by adding a voltage-dependent current source in parallel with the excess capacitance of the dielectric cell. A cross-coupling excess capacitance concept that defines the dependent current source for the anisotropic PEEC cell is defined and given for orthogonal PEEC meshes. As a result, the PEEC cell for an anisotropic dielectric is possible to extend to handle lossy and dispersive anisotropic dielectrics straightforwardly. The developed PEEC model has been applied to model a patch antenna mounted on an anisotropic substrate. The simulation results are in agreement with other simulation technique results. Consequently, the anisotropic model permits electromagnetic modeling of structures and devices that consist of a broader class of materials.

The modeling of dielectrics in different ambient temperature conditions is also considered for the PEEC analysis of its impact on antennas. Dielectrics with temperature dependent permittivity have been modeled with PEEC by standard approaches found in the literature. This has proved useful for frequency-domain simulations in PEEC. The utility has been demonstrated by investigating the impact due to temperature-dependent dielectrics on printed antennas. These types of investigations could provide valuable in-formation in the design of printed antennas in harsh environments.

Finally, the problem of designing magneto-dielectric materials that intrinsically provide distortionless propagation for TEM mode signals is investigated. The frequency dependent permittivity and permeability of a slab are related to the per-unit length (p.u.l.) parameters of a two-conductor transmission line. The p.u.l. parameters are specified to approximate the Heaviside condition in a specified and finite frequency interval, while simultaneously enforcing that the corresponding permittivity and permeability represent a passive material. Consequently, the passivity condition ensures the designed material is possible to realize in practice while the Heaviside condition secures that the material is distortionless. The design method has been employed to design a passive material that approximates the Heaviside condition in a narrow frequency interval. Verification in both time and frequency domains indicates that the designed material closely resembles a distortionless material in the specified frequency interval. These results indicate that an approximation of the Heaviside condition could be a potential aid in the design of distortionless materials for bandlimited applications. Further investigations on design method improvements, limitations on the approximation in terms of both accuracy and bandwidth, and the construction of such materials in practice could lead to new distortionless cable or material designs.