Abstract-Electromagnetic solvers based on the partial element equivalent circuit (PEEC) approach have proven to be well suited for the solution of combined circuit and EM problems. The inclusion of all types of Spice circuit elements is possible. Due to this, the approach has been used in many different tools. Most of these solvers have been based on a rectangular or Manhattan representation of the geometries. In this paper, we systematically extend the PEEC formulation to nonorthogonal geometries since many practical EM problems require a more general formulation. Importantly, the model given in this paper is consistent with the classical PEEC model for rectangular geometries. Some examples illustrating the application of the approach are given for both the time and frequency domain.Index Terms-Circuit modeling, partial element equivalent circuit (PEEC) method , full-wave analysis.

Cables, printed circuit boards, and VLSI interconnects are commonly modeled as multiconductor transmission lines. Models of electrically long transmission lines are memory and time consuming. In this paper, a robust and efficient algorithm for the generation of a delay-based model is presented. The impedance representation via the open-end matrix Z is analyzed. In particular, the rational formulation of Z in terms of poles and residues is exploited for both lossless and lossy cases. The delays of the lines are identified, and explicitly incorporated into the model. A model order reduction of the system is automatically performed, since only a limited number of poles and residues are included in the rational part of the model, whereas the high-frequency behavior is captured by means of closed expressions that account for the delays. The proposed method is applied to two relevant examples and validated through the comparison with reference methods. The time-domain solver is found to be more accurate and significantly faster than the one obtained from a pure-rational model.

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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.

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