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 t...Show MoreMetadata
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) Gauss–Jacobi iterations are sufficient for convergence to the exact solution.
Published in: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems ( Volume: 28, Issue: 8, August 2009)