This paper presents a 3-D partial element equivalent circuit (PEEC) model of linear magnetic materials under the quasi-static hypothesis. Rigorous analytical formulas are proposed for integrals accounting for flux density due to both current and magnetization densities for Manhattan-type discretizations. Such closed-form formulas remove the singularities exhibited by existing formulas and completely avoid numerical integration. The resulting model preserves the circuit interpretation of standard PEEC models and, thus, can be easily integrated in a SPICE-like circuit solver. Numerical results are presented showing that the proposed closed formulas outperform the numerical schemes and guarantee an excellent agreement with existing results available in the literature.

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems.

This paper presents a novel partial element equivalent circuit formulation to handle 3-D non-linear problems. Since the displacement currents are taken into account, the proposed formulation is not restricted to low-frequency applications, although the propagation delays are neglected. The non-linear problem is solved by means of the Newton-Raphson algorithm. Special care is taken in order to analytically compute the Jacobian of the problem. Furthermore, an adaptive setting of the time step is adopted in the transient analysis allowing to maintain the size of the time step as large as possible while preserving the accuracy. Computed results for a closed magnetic circuit and the testing electromagnetic analysis methods workshop problem 10 are reported.

The solution of mixed electromagnetic/circuit problems is important for the electromagnetic compatibility/signal integrity/power integrity system designs. The ever-increasing frequency content of signals and decrease of geometrical features requires the 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, to be used for the analysis and design of high-speed circuits. Very large systems of equations are often produced and their efficient solution can be extremely challenging. In this paper, we propose a new frequency-domain PEEC solver which is based on the adaptive cross approximation and singular value decomposition. Taking advantage of the rank deficiency of the dense partial inductance and coefficient of potential matrices, a multiscale block decomposition is adopted to explicitly compute the inverse of the admittance matrix of the PEEC circuit. The proposed approach provides both speedup and memory storage saving, while preserving the accuracy. The efficiency of the proposed method is demonstrated through its application to the PEEC modeling of typical interconnect problems.

A new formulation of the partial element equivalent circuit (PEEC) method is presented, which is well suited to be combined with compression and matrix–vector product acceleration techniques. In particular, taking advantage of the rank‐deficiency of the magnetic and electric field couplings, the adaptive cross approximation (ACA) technique is firstly, adopted to compress PEEC interaction matrices, namely partial inductances and coefficients of potential matrices. Differently from the use of ACA in conjunction with the method of moments, in this study, magnetic and electric field couplings are kept distinct, thus allowing to efficiently compress both magnetic and electric field interaction matrices. Secondly, the compressed matrices are used to accelerate the transient analysis of PEEC circuits. Indeed, Kirchoff voltage and current laws are enforced to PEEC circuits so that matrix–vector products involving the interaction matrices can be significantly accelerated in virtue of their compression, thus leading to very good speed‐ups when using iterative solvers like the generalised method of residuals algorithm. Numerical results demonstrate the validity, accuracy and performance of the proposed approach in terms of both memory usage saving and transient analysis speed‐up.

This paper describes the approach developed to model the current return networks installed aboard aircrafts having parts made in composite materials. The surface partial element equivalent circuit (PEEC) method is adopted for its high-fidelity modeling capabilities, and its accuracy in the low-frequency region, which is of interest for the characterization of the return networks. State of the art of PEEC modeling is implemented in order to allow real-life aircrafts to be modeled. A special complex mock-up has been realized and measured. The numerical results are compared with measurements to assess their adequacy.