Stability, Causality, and Passivity in Electrical Interconnect Models

Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically.We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itsel

Analysis of crosstalk and field coupling to lossy MTL's in a SPICE environment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficienc

Transient simulation of lossy multiconductor interconnects

The transient simulation of electrically-long low-loss multiconductor interconnects is considered from a practical point of view. The importance of frequency dependent losses in these interconnects is discussed and a simple transmission line characterization procedure allowing for such losses is proposed. The characterization obtained yields simple and efficient interconnect models, that the user can include, without programming, in any simulator accepting differential operator

Compressed Passive Macromodeling

This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large scale is intended both in terms of number of electrical ports and required dynamic model order. For such structures, standard approaches based on rational approximation via vector fitting and passivity enforcement via model perturbation may fail because of excessive computational requirements, both in terms of memory size and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated singular value decomposition. Then we formulate a compressed rational fitting and passivity enforcement framework which is able to obtain speedup factors up to 2 and 3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed techniqu

Parametric macromodeling of lossy and dispersive multiconductor transmission lines

We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate orthonormal vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain