Convergence of transverse waveform relaxation for the electrical analysis of very wide transmission line buses

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 $(k \ll 1)$. 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 $(\approx 3)$ GaussJacobi iterations are sufficient for convergence to the exact solution.

Original languageBritish English
Article number5166597
Pages (from-to)1150-1161
Number of pages12
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume28
Issue number8
DOIs
StatePublished - Aug 2009

Keywords

  • Circuit simulation
  • Coupled transmission lines
  • On-chip buses
  • Very large scale integration (VLSI)
  • Waveform relaxation (WR)

Fingerprint

Dive into the research topics of 'Convergence of transverse waveform relaxation for the electrical analysis of very wide transmission line buses'. Together they form a unique fingerprint.

Cite this