DOCTORAL T H E SIS Department of Computer Science, Electrical and Space Engineering Division of Embedded Internet Systems Lab Electromagnetic Modeling with ISSN 1402-1544 Modeling with Complex Dielectrics HartmanAndreas Electromagnetic ISBN 978-91-7790-302-4 (print) ISBN 978-91-7790-303-1 (pdf) Complex Dielectrics Luleå University of Technology 2019 A Partial Element Equivalent Circuit Approach Andreas Hartman Industrial Electronics Electromagnetic Modeling with Complex Dielectrics: A Partial Element Equivalent Circuit Approach Andreas Hartman Dept. of Computer Science and Electrical Engineering Lule˚aUniversity of Technology Lule˚a,Sweden Supervisors: Jonas Ekman, Jerker Delsing Printed by Luleå University of Technology, Graphic Production 2019 ISSN 1402-1544 ISBN 978-91-7790-302-4 (print) ISBN 978-91-7790-303-1 (pdf) Luleå 2019 www.ltu.se To my family iii iv Abstract 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 re- quirements 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 con- sidered. Specifically, the incorporation of dielectrics that exhibit loss, dispersion, and anisotropic properties into electromagnetic codes is addressed. The work has been exe- cuted within the partial element equivalent circuit (PEEC) method framework. First, a PEEC implementation that incorporates dispersive and lossy dielectrics, rep- resented by equivalent circuit models explicitly included in the PEEC equations, is devel- oped. 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 permittiv- ity 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 sub- strate. 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 con- sidered for the PEEC analysis of its impact on antennas. Dielectrics with temperature- dependent permittivity have been modeled with PEEC by standard approaches found in v 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 pro- vide 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 inter- val, 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. Veri- fication in both time and frequency domains indicates that the designed material closely resembles a distortionless material in the specified frequency interval. These results in- dicate 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 accu- racy and bandwidth, and the construction of such materials in practice could lead to new distortionless cable or material designs. vi Contents Part I 1 Chapter 1 { Thesis Introduction 3 1.1 Background . .3 1.2 Motivation . .4 1.3 Related Work . .6 1.4 Thesis Outline . .9 Chapter 2 { Electromagnetic Simulation and the Modeling of Ma- terials' Electromagnetic Properties 11 2.1 Maxwell's Equations . 11 2.2 Constitutive Relations for the Modeling of Materials in Maxwell's Equations 12 2.3 Dispersion and Loss . 16 2.4 Causality and Passivity . 17 2.5 Electromagnetic Mixtures . 19 2.6 Influence of Other Factors' on Permittivity . 21 2.7 Methods for Solving Maxwell's Equations . 23 Chapter 3 { The Partial Element Equivalent Circuit Method 29 3.1 The PEEC Method . 29 3.2 Dielectrics in the PEEC Method . 35 3.3 PEEC Circuit Equations . 46 Chapter 4 { Distortionless Propagation along Transmission Lines and Magneto-Dielectric Slabs 51 4.1 The Material Slab Setup and the Corresponding Transmission Line Model 51 4.2 The Heaviside Condition and Distortionless Propagation . 53 4.3 Approximation of the Heaviside Condition . 54 Chapter 5 { Thesis Summary 57 5.1 Contributions . 57 5.2 Conclusions . 60 5.3 Answers to the Research Questions . 61 5.4 Future Work . 63 References 65 vii Part II 77 Paper A 79 1 Introduction . 81 2 Modelling of Dispersive and Lossy Dielectrics . 82 3 Descriptor form of PEEC models to incorporate dispersive and lossy di- electrics . 86 4 Numerical examples . 89 5 Conclusions . 91 Paper B 93 1 Introduction . 95 2 The EFIE in an Anisotropic Dielectric Medium . 96 3 The PEEC cell for an Anisotropic Dielectric Volume Cell . 100 4 PEEC Matrix Model Equations for the Anisotropic Case . 103 5 Numerical Examples . 108 6 Conclusions . 110 Paper C 113 1 Introduction . 115 2 The Permittivity Model and Means to Model Temperature-Dependent Per- mittivity . 116 3 Temperature-dependent Permittivity . 117 4 Dielectric Mixing Rules . 118 5 The PEEC Method . 118 6 Numerical Examples . 119 7 Conclusions . 125 Paper D 129 1 Introduction . 131 2 Transmission Line Representation of a Slab and The Heaviside condition 133 3 Permittivity and Permeability Properties of Passive Materials . 135 4 Design Procedure for a Material to Approximate the Heaviside condition 136 5 Numerical Example . 140 6 Conclusions . 146 viii Acknowledgments This thesis has emerged through the support of several people to whom I would like to express my gratitude. First, I would like to thank my supervisors Jonas Ekman and Jerker Delsing for their guidance and support throughout this thesis project. I would also like to express my sincere gratitude to Prof. Giulio Antonini for his support and interest in the work, and his invaluable care to share his knowledge. I am also thankful for his hospitality during my visits to his research group in L'Aquila. In addition, I would like to thank my former supervisor Jonas Gustafsson for his help when I arrived to Lule˚a, and his support in the beginning of my studies. I would also like to thank the people at SRT, and personally Maria De Lauretis, the people at the SKF-UTC, and at SKF for their insights and help in the project, especially Defeng Lang for all interesting and fruitful discussions, and also Per-Erik Larsson for his support in the project. Next, I would like to acknowledge the financial support from SKF and the Arrowhead project. Finally, I would like to thank my family and friends who have always supported and believed in me. Lule˚a,February 2019 Andreas Hartman ix x Part I 1 2 Chapter 1 Thesis Introduction 1.1 Background Today, electromagnetic systems and devices play an important role in daily life. They form the basis of several industrial and business applications. Wireless communication systems are an integral part of the communication networks used to exchange information in business, personal and industrial settings, i.e., mobile networks and sensor networks. Technologies such as the Internet of Things (IoT) and wireless sensor networks (WSNs) are providing increasing interoperability among different devices, placing heavier require- ments on their