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

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

Black-box passive macromodeling in electronics: trends and open problems

Design and verification flows in the electronics industry are relying more and more on behavioral models of components, electrical interconnects, and subsystems. Such models are often derived from tabulated frequency responses obtained via direct measurements or through electromagnetic field solvers. Model extraction from this data involves a mix of system identification and approximation in the complex frequency domain. This problem becomes difficult or badly scalable due to the presence of passivity constraints, which must be enforced during model extraction. We review recent trends to deal with this complexity, and related open issues