Electromagnetic Modeling Using the Partial Element Equivalent Circuit Method Jonas Ekman EISLAB Dept. of Computer Science and Electrical Engineering Lule˚a University of Technology Lule˚a, Sweden Supervisor: Prof. Jerker Delsing ii To my parents Kjell and Gunilla Ekman iv Abstract This thesis presents contributions within the field of numerical simulations of electro- magnetic properties using the Partial Element Equivalent Circuit (PEEC) method. Numerical simulations of electromagnetic properties are of high industrial interest. The two major fields of use are to ensure compliance with electromagnetic compati- bility (EMC) regulations and to verify functionality in electronic designs. International EMC regulations bounds companies that develop or assemble electric products to market products that are electromagnetic compatible with other products in their environment. Failure to comply with regulations can result in products withdrawal and fines. To avoid incompatibility, numerical simulations can be used to improve EMC characteristics in the development and assembly stage in a cost efficient way. Functionality of today's compact high-performance electronic systems can be affected by unwanted internal electromag- netic effects. The result can be degradation of performance, malfunction, and product damage. Numerical simulations are used to predict electromagnetic effects at the design phase, thus minimizing the need for post-production actions delaying product releases and increasing product cost. At the Embedded Internet System Laboratory (EISLAB), Lule˚a University of Tech- nology, a project concerning numerical simulations of electromagnetic properties in elec- tric systems using the PEEC method is in progress. This thesis focuses on the devel- opment of the PEEC method for practical use, thus demanding optimal performance of the basic sections within a PEEC based electromagnetic solver in terms of speed and ac- curacy. In the PEEC method, the two most demanding sections are the partial element calculations and the solution of the final equation system. The latter problem is a pure mathematical problem with continuous progress while the partial coefficient calculations require further research. This thesis proposes several techniques for efficient partial element calculations. First, a discretization strategy is used for one-layer structures to enable the use of fast analytic formulas and the resulting simplified PEEC models are solved using a freeware version of SPICE, exemplifying the accessibility of the PEEC method. Second, a fast multi- function method is proposed in which different order of numerical integration is used, in the calculation of the partial elements, depending on a predefined coupling factor. Third, the fast multi-function method is further developed and compared to a fast multipole method applied to partial element calculations. Fourth, the calculation of the three- dimensional node coefficients of potential is addressed and three novel approaches are presented and evaluated in terms of speed and accuracy. The thesis includes a paper dealing with nonorthogonal PEEC models. This model extension allows the use of nonorthogonal volume and surface cells in the discretization of v vi objects. This facilitates the modeling of realistic complex structures, improves accuracy by reducing the use of staircase-approximations, and reduces the number of cells in the PEEC model discretizations. The nonorthogonal formulation excludes the use of analyt- ical formulas thus make topical the use of fast multi-function- and multipole-methods. The fundamentals of the PEEC method makes free-space radiation analysis compu- tationally efficient. Radiated field characterization is important in EMC processes and therefore of great interest. One paper in this thesis explore different possibilities to use PEEC model simulations to determine the electric field emissions from objects. vii Contents Chapter 1 - Thesis Introduction 1 1.1 Background . 2 1.2 Motivation . 5 1.3 Thesis Outline . 6 Chapter 2 - Introduction to EM Simulation Techniques 7 2.1 Introduction . 8 2.2 Finite Difference Method, FDM . 12 2.3 Finite Element Method, FEM . 14 2.4 Method of Moments, MoM . 16 2.5 Partial Element Equivalent Circuit Method, PEEC . 18 Chapter 3 - The Partial Element Equivalent Circuit (PEEC) Method 21 3.1 Background . 22 3.2 Basic PEEC Theory . 22 3.3 Practical EM Modeling Using the PEEC Method . 36 Chapter 4 - Thesis Summary 63 4.1 Summary of Contributions . 63 4.2 Conclusions . 66 4.3 Future Development of the PEEC Method . 66 Paper A 79 1 Introduction . 81 2 Derivation of the PEEC Model . 82 3 Simplified PEEC Models . 84 4 Equations for Partial Element Calculations . 85 5 Experiments . 88 6 Conclusions . 91 Paper B 95 1 Introduction . 97 2 Derivation of the PEEC Model . 98 3 Time Retardation . 100 4 Post-processing Equations . 100 5 Electric Field Sensor . 101 6 Experimental Setup . 102 7 Results . 102 8 Conclusions . 103 Paper C 107 1 Introduction . 109 2 The PEEC Method . 110 3 Integration Order Selection . 113 4 Validation and Refinements . 117 5 Conclusions . 119 Paper D 123 1 Introduction . 125 2 Nonorthogonal PEEC Model . 127 3 Evaluation of Circuit Elements . 134 4 General Circuit Solver Aspects . 135 5 Numerical Experiments . 137 6 Conclusions . 141 Paper E 149 1 Introduction . 151 2 FMM Basic Theory . 152 3 2-level FMM-based Computation of PEEC Parameters . 153 4 Multi-Function based Computation of PEEC Parameters . 156 5 PEEC Parameters Approximation Results . 157 6 Conclusions . 160 Paper F 163 1 Introduction . 165 2 The PEEC Method . 166 3 Reduction from Surface to PEEC Node Coefficients of Potential . 167 4 Circuit Equations for PEEC Problems . 170 5 Numerical Experiments . 171 6 Conclusions . 175 Preface This thesis summarizes my research and contributions within numerical simulations of electromagnetic properties using the PEEC method. The contributions focuses on the development of the PEEC method for practical use within research and development. The work has been performed at EISLAB, Lule˚a University of Technology, Sweden, between 1999 and 2003 under the supervision of Prof. Jerker Delsing. Funding was provided by the European Union's action in support of regional develop- ment, Lule˚a University of Technology faculty funds and personal grants from Ericsson's Research council. x Acknowledgements I would like to thank my supervisor Prof. Jerker Delsing for realizing the importance of this topic within electrical engineering and guiding me towards my Ph.D. It has been an interesting and rewarding journey. I spent most of the second part of my Ph.D. at the University of L'Aquila EMC Laboratory, Italy, and a short period at IBM T.J. Watson Research Center, N.Y. I would like to thank all people working there for taking me in and sharing their knowledge, especially Dr. Giulio Antonini, Prof. Antonio Orlandi and Dr. Albert E. Ruehli. Further I would like to thank Alessandra for her help and support, Antonio for his hospitality and Joris for helping me out at Yorktown. Among all the people that have helped me with my work I would like to give special thanks to Ak˚ e, Urban, and Jonny at LTU. Jonas Ekman, March 2003. xi xii Part I xiv Chapter 1 Thesis Introduction This chapter presents a fundamental problem description of the field of numerical simu- lation of electromagnetic properties followed by the thesis motivation. 1 2 Introduction 1.1 Background This thesis deals with the numerical modeling of electromagnetic (EM) properties using the Partial Element Equivalent Circuit (PEEC) method. Numerical modeling is widely used in, for example, product research and development, design of mechanical parts, and in the prediction of the weather forecast. The main reason for performing numerical simulation and modeling within research and industries is the possibility to test parts or products before production. For instance, mechanical parts can be tested for durability, water flow in piping systems can be verified, and ventilation in office spaces can be tuned. Numerical modeling of electromagnetic properties are used by, for example, the electronics industry to : 1. Ensure functionality of electric systems. The basic functions of large and complex electric systems must be verified using numerical simulations, i.e. circuit simulation software. For instance, the functionality of an amplifier in terms of amplification and bandwidth is traditionally verified using circuit simulation tools like SPICE. However, the fast development within the electronic industry and the trends in the society have emphasized the threat of electromagnetic interference (EMI) which is not accounted for in the traditional SPICE-like solvers. EMI is caused by unwanted EM energy penetrating and effecting electric components and/or systems. EMI may cause malfunction of electric systems, loss of data, and permanent damage in sensible equipment. It is possible to identify sources contributing to the increased EMI threat. They are: Increased performance. Increased performance (clock frequencies) of electric • systems is often generated by faster current- and voltage fluctuations within an electric system. This fast current- and voltage fluctuations can generate, in combination with the system geometry, radiated EM fields making the system a source of EM energy. Miniaturization. Miniaturization of electric components and systems reduces • separating distances and thereby increases internal capacitive and inductive couplings (parasitics). Plastic enclosures. The increased use of plastic, compared to