Efficient Calculation of Non-Orthogonal Partial Elements for the PEEC Method

Abstract

For various electrical interconnect and EMC problems, the Partial Element Equivalent Circuit (PEEC) method has proven to be a valid and fast solution method of the electrical field integral equation in the time as well as the frequency domain. Therefore, PEEC has become a multi-purpose full-wave method, especially suited for the solution of combined circuit and EM problems, as found, for instance, on printed circuit board layouts, power electronics devices or EMC filters. Recent research introduced various extensions to the basic PEEC approach, for example a nonorthogonal cell geometry formulation. This work presents a fast, flexible and accurate computational method for determining the matrix entries of partial inductances and the coefficients of potential for general non-orthogonal PEEC cell geometries. The presented computation method utilizes analytical filament formulas to reduce the integration order and therefore to reduce computation time. The validity, accuracy and speed of the proposed method is compared with a standard integration routine on example cell geometries where the numeric results of the new method show improved accuracy, coming along with reduced computation time.

Performance Analysis of Parallel Non-Orthogonal Peec-Based Solver for Emc Applications

“…The process of computing partial elements in non-orthogonal models is rigorous and heavy due to the multiple integrations in (5) and (6). Here, a numerical approach using Legendre-Gaussian quadrature is used for the evaluation.…”

“…If the dot-product of the edge vectors will be less than a small constant e.g., 10 −9 , then the edges will be orthogonal to each other. Partial elements calculations for non-orthogonal structures are carried out using numerical routines, while for orthogonal structures analytical routines are invoked [6]. It should be noted that in PEECs, very high accuracy for near and self terms for the partial elements are needed while for far coefficients/couplings the same level of the accuracy is not needed [26].…”

“…Although partial element calculations are quite fast for orthogonal models, it usually takes much longer time for non-orthogonal structures due to multiple folded integrals in the Equations (5) and (6). The time taken to calculate these values, are highly dependent to the value of LGO, as stated in Section 2.1.…”

“…Additionally, extending the PEEC-method to be able to handle non-orthogonal structures by taking advantage of parallel computer systems will provide the possibility to perform EMC analysis on real world problems with complex structures. Further, recent research has extended the basic PEEC-method to handle non-orthogonal cell geometries [6][7][8] which allows direct modelling of geometrically complex geometries. Unlike for orthogonal structures, partial elements can not be calculated using fast analytical formulations.…”

A Generic Matrix Method to Model the Magnetics of Multi-Coil Air-Cored Inductive Power Transfer Systems

“…Typically, coil optimization and magnetic parameter estimation (L 1 , L 2 , M, k) are performed relying on electromagnetic (EM) field solvers and/or combing with evolutionary algorithms [4,5]. In other work, numerical techniques (solving look-up tables (book of Grover [6]), solving Bessel functions [7], solving elliptical integrals [8]) and partial element equivalent circuit (PEEC) solvers [9,10] are used to achieve the same. In Grover's book, there are available closed-form expressions for self-inductance of a number of polygonal shapes.…”