B. Wang, S.-G. Wang, and B. Yuan
Model simplification, VLSI interconnect, RC distributed circuit, modelling, closed-form, algorithm
The advance of high-speed deep-submicron VLSI technology requires chip interconnect and packaging to be modelled by distributed circuits, eventually resulting in large scale linear circuits to be analyzed. This paper presents closed-forms of the state space model and recursive algorithms of the transfer function for even-distributed RC interconnect and its even-length-order (ELO) simplification models. They reveal the characteristics of the ELO models and their relationship to the accurate original model, further lead to a model simplification. The closed-forms with a computation complexity O(1) avoid very large dimension matrix inverse or LU decomposition, and are easy for evaluating a model and its performance. The ELO models are simulated in both time and frequency domains via the closed-forms and recursive algorithms. The results show that extremely high-order RC interconnects can be accurately approximated only by a tenth or higher ELO model. However, when the source and load ports are included, the whole model may be approximated by a low-order ELO model. The results may be applied to VLSI interconnect model reduction and design.
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