NDLI: Convergence of Transverse Waveform Relaxation for the Electrical Analysis of Very Wide Transmission Line Buses

Content Provider	IEEE Xplore Digital Library
Author	Elfadel, I.M.
Copyright Year	1982
Abstract	In this paper, we study the convergence and approximation error of the transverse waveform relaxation (TWR) method for the analysis of very wide on-chip multiconductor transmission line systems. Significant notational simplicity is achieved in the analysis using a splitting framework for the per-unit-length matrix parameters of the transmission lines. This splitting enables us to show that the state-transition matrix of the coupled lines satisfies a linear Volterra integral equation of the second kind, whose solution is generated by the TWR method as a summable series of iterated kernels with decreasing norms. The upper bounds on these norms are proved to be O(k ^r/r ^!), where r is the number of iterations and k is a measure of the electromagnetic couplings between the lines. Very fast convergence is guaranteed in the case of weak coupling (k Lt 1). These favorable convergence properties are illustrated using a test suite of industrial very large scale integration global buses in a modern 65-nm CMOS process, where it is shown that few ( ap 3) Gauss-Jacobi iterations are sufficient for convergence to the exact solution.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	1150
Ending Page	1161
Page Count	12
File Size	1284659
File Format	PDF
ISSN	02780070
Volume Number	28
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Transmission lines Transmission line matrix methods Multiconductor transmission lines Approximation error System-on-a-chip Couplings Integral equations Kernel Upper bound waveform relaxation (WR) Circuit simulation coupled transmission lines on-chip buses very large scale integration (VLSI)
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

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