Modeling a transmission interconnect by optimal number of lumped sections

The growing demand for high-speed interconnects in VLSI circuits has turned a high impetus for their accurate modeling. The classical uniform transmission line theory based on distributed RLC circuit model has several limitations as far as CAD practices are concerned. Distributed models are being replaced with reduced-order lumped models for efficient simulation and design applications. The present literature is replete with numerous reduced-order models and macro-models. These models are developed based on an approximating criterion either in time or frequency domain with the aim of reducing computational complexity. We introduce a technique to find the optimum number of lumped sections for approximating a transmission interconnect of a given length and rise-time. This is done by first considering the simple well- known relationship between the primary constants of the line and the image parameters of each individual section viewed as a linear two-port network. Next, the sensitivity of this relationship as a function of frequency is used to develop a formula for the least number of sections needed. This method is further compared with the existing frequency domain based macro-models. Since the final formulas turn out to be simpler, they have excellent use in CAD applications.