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In a passive macromodel for lossy, dispersive multiconductor transmission lines (MTL's) has been proposed. The macromodel uses a multiplicative approximation of the matrix exponential known as the Lie product. The circuit implementation of the macromodel is a cascade of elementary cells, each cell being the combination of a pure delay element and a lumped circuit representing the transmission line losses. Compared with passive rational macromodeling, the Lie product macromodel is capable of efficiently simulating long, low-loss MTL's while preserving passivity. In this paper, we build on the results of and use transmission line theory to derive a new time-domain error criterion for the Lie product macromodel. We also show how this criterion can be used to determine the minimum number of cells needed in the macromodel to guarantee that the magnitude of the time-domain error is below a given engineering tolerance.

In this note, three models are provided for the analysis of lossy transmission lines in support of the papers in the special session (IEEE 11th Topical Meeting on Electrical Performance of Electronic Packaging, 2002). The models are used for a one-to-one comparison between the transmission line transient analysis techniques presented in the papers in this session.

The rapid increase in operating speeds, density and complexity of modern integrated circuits has made interconnect analysis a requirement for all state-of-the-art circuit simulators. Recently, a passive closed-form optimal matrix-rational approximation based algorithm has been developed for macromodeling of lossy multiconductor transmission lines. This paper presents three case studies for optimal matrix rational approximation and provides a performance comparison with the conventional lumped discretization.

Today, it is well known that the exact modeling of lossy transmission lines for high performance systems is very important and challenging. In this paper, a transmission line modeling technique which is based on a method of characteristics approach is presented. The results from this work are compared to numerical experiments performed with the approach in (S. Grivet-Talocia et al., Digest of Electr-Perf. Electronic Packaging, vol. 11, 2002) presented in another talk in this session.

This paper describes the implementation of a macromodeling technique for lossy transmission lines with frequency-dependent data in the API framework of IBM's PowerSpice circuit solver. The technique is based on finding passive, low-pass, optimal matrix rational approximations of the line admittance matrix. This implementation is used to compare the accuracy and performance of these new passive transmission line macromodels with those of the generalized method of characteristics on the one hand and the matrix Pade approximation on the other.