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Finer feature sizes, increasing system complexity, and higher signal speeds have combined to make interconnect the dominant determinant of electronic circuit and system performance. These trends will continue into the foreseeable future, and new technologies that may be introduced will only add to them. Key components to interconnect analysis are efficient simulation of interconnect models, and macromodeling to make the modelsfit eficiently into existing simulation strategies. Asymptotic Waveform Evaluation (AWE) is an elegant and efficient solution to this problem. This paper illustrates the applicability of AWE to the analysis of MCM interconnect structures -from chip level through packaging, through thick or thin film interconnect and back again. I. OverviewAsymptotic Waveform Evaluation (AWE) [6] is a new method to efficiently analyze linear circuits. It employs a form of Pad6 approximation rather than numerical integration to approximate the behavior of linear circuits in either the time or frequency domains. AWE has been shown to be an efficient means to analyze large and complex interconnect circuits [8], with typical speedups of two or three orders magnitude over traditional simulators such as SPICE [3].AWE forms an approximate low order q pole model of a complex linear circuit by computing and matching its first 2q moments. The moments are the coefficients obtained from a Maclaurin series expansion of its impulse response H(s). In addition, AWE provides an efficient means to macromodel interconnect structures [2]. A multiport admittance matrix is constructed, where the port parameters are either represented by a moment expansion (in the frequency domain), or by a pole-residue model (in the time domain, typically). Such modeling capability allows efficient partitioning of large circuits. Fulther efficiency gains can be had as special solution techniques (that may not be applicable to the global circuit) can be applied to individual partitions [2], AWE efficiently handles distributed elements such as trans-151. This work is supported in part by DEC. IBM, Rockwell and SRC (Contract #91-DC-068).mission lines [ 11. Such lines can be lossless or lossy, coupled or non-coupled, and may include frequency dependent phenomena such as skin effect.Finally, AWE provides an efficient interface [7] to general purpose simulators such as SPICE. Such a capability is very important as nonlinear devices in interconnect drivers, load and pass gates can be simulated directly in a company's host simulator (with full nonlinear device models) -with AWE analyzing the linear portions of a circuit. For circuits dominated by interconnect, this methodology is typically at least an order of magnitude more efficient than SPICE. Thus AWE is an ideal technique to analyze large interconnect problems. It handles large interconnect problems in an integrated manner taking into account effects of both lossy and lossless interconnect, as well as the effect of nonlinear drivers and loads. II. Basic AlgorithmIn order to illustrate the basic princ...

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