Hybrid electromagnetic modeling of noise interactions in packaged electronics based on the partial-element equivalent-circuit formulation

Abstract

The partial-element equivalent-circuit (PEEC) method is used to develop a flexible, hierarchical electromagnetic modeling and simulation environment for the analysis of noise generation and signal degradation mechanisms in packaged electronic components and systems. The circuitoriented approach used by the method for the development of the numerical approximation of the electric-field integral equation leads to SPICE-compatible, yet fully dynamic, discrete approximation of the electromagnetic problem. Contrary to other full-wave formulations, the proposed method has the important attribute of lending itself to a very systematic and physical model complexity reduction on the basis of the electrical size of the various portions of the system. Thus, a hybrid electromagnetic modeling and simulation environment is established for the analysis of complex structures which exhibit large variation in electrical size over their volume, using a combination of lumpedcircuit elements, transmission lines, as well as three-dimensional (3-D) distributed electromagnetic models. These models may or may not account for retardation, depending on the electrical size of the part of the structure that is being modeled. These special attributes of the proposed electromagnetic-simulation environment are demonstrated through several examples from its application to the modeling of noise interactions in generic interconnect and package geometries.

Nonorthogonal PEEC formulation for time- and frequency-domain EM and circuit modeling

“…Starting from (2.4) with the externally applied electric field set to zero, and substituting for and from (2.7) and (2.9), respectively. For more details, please see any one of the PEEC papers, e.g., [36], [14], [20], [37]. A derivation of the PEEC model with the rectangular, finite dielectrics is given in [13].…”

“…Early work, where mostly explicit numerical integration methods are employed is summarized in [54]. Since then, several researchers have shown that much more stable solutions can be obtained with implicit numerical integration methods, e.g., [55], [14], [56], [57]. This implies that today, the stable transient analysis of large structures can be accomplished efficiently.…”

Partial Element Equivalent Circuit models in the solution of the electric field integral equation

“…Among all EM methods, the Partial Element Equivalent Circuit (PEEC) method [4] has been found particularly useful for modeling PCBs and interconnects. The PEEC method uses a circuit interpretation of the Electric Field Integral Equation (EFIE) [6], thus being especially suitable to problems involving both electromagnetic fields and circuits [2,4,7]. Nonlinear circuit devices such as drivers and receivers are usually connected to PEEC equivalent circuits using a time domain circuit simulator (e.g.…”

Parameterized model order reduction with guaranteed passivity for PEEC Circuit analysis

“…With respect to other EM methods, it is worth pointing out its capability to provide a circuit interpretation of the EFIE equation, thus allowing to handle complex problems involving both circuits and electromagnetic fields [2], [7], [15]- [17]. In what follows, we describe a quasistatic PEEC formulation [2] that approximates the full-wave PEEC approach [15].…”

“…These EM methods usually results in very large systems of equations which are often prohibitively expensive to solve and model order reduction (MOR) techniques are therefore needed to reduce the resulting high model complexity and computational cost of the simulations [4], [5]. The Partial Element Equivalent Circuit (PEEC) method has gained increasing popularity among electromagnetic compatibility engineers, since it is able to transform the EM system under examination into a passive RLC equivalent circuit [2], [6], [7]. Nonlinear circuit devices, such as drivers and receivers, are usually connected with PEEC equivalent circuits using a time domain circuit simulator (e.g.…”