Modeling of DistributedRLCInterconnect and Transmission Line via Closed Forms and Recursive Algorithms

Abstract

This paper presents the closed forms of the state-space models and the recursive algorithms of the transfer function models for fast and accurate modeling of the distributed RLC interconnect and transmission lines, which may be evenly or unevenly distributed. Considered models include the distributed RLC interconnect lines with or without external source and load connection. The effective closed forms and recursive algorithms do not involve any matrix inverse, LU matrix factorization, or matrix multiplication, thus reducing the computation complexity dramatically. Especially, the computation complexity of the closed forms for any evenly or unevenly distributed RLC interconnect line circuits is only O(1) or ( ), respectively, in sense of the scalar multiplication times, where of the system order. The features of new recursive algorithms are two recursive s-polynomials and the low computation complexity. Examples illustrate the new methods in both time and frequency domains. Comparing with the PSpice, the new methods can dramatically reduce the runtime of the time responses and the Bode plots by 25% -98.5% in the examples. The results can be applied to the RLC interconnect analysis and model reduction as a key to new approach.

Frequency Response of Transmission Lines with Unevenly Distributed Properties with Application to Railway Safety Monitoring

“…The electrical properties at one subsection can be different from the others, which imitates a transmission line with unevenly distributed properties. The transmission line model and its approximated counterpart, the circuit network model, are shown in Figures 1 and 2, and are similar to the networks constructed in [7], [10], [11].…”