Electromagnetic modeling using the partial element equivalent circuit method

Abstract: This thesis presents contributions within the field of numerical simulations of electromagnetic 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 compatibility (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 electromagnetic 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), Luleå University of Technology, a project concerning numerical simulations of electromagnetic properties in electric systems using the PEEC method is in progress. This thesis focuses on the development 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 accuracy. 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 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 analytical formulas thus make topical the use of fast multi-function- and multipole-methods. The fundamentals of the PEEC method makes free-space radiation analysis computationally 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.