A two-level waveform relaxation approach for fast transient simulation of long high-speed interconnects

Abstract

This paper presents a waveform relaxation approach for efficient transient simulation of fully-coupled high-speed channels of medium to large electrical length. The channel is first described via a passive Delayed Rational Macromodel, which is suitably identified from tabulated scattering data. The structure of the macromodel is then exploited to setup a two-level iterative relaxation scheme for the solution of terminal voltage and current waveforms. Numerical results show that the proposed scheme outperforms standard SPICE-based solvers at no loss of accuracy.

Fast iterative simulation of high-speed channels via frequency-dependent over-relaxation

“…The possibly nonlinear terminations are cast as nonlinear discrete-time macromodels using the M log approach [6]. Using the same transient scattering waves as port variables, we can express driver and receiver characteristics in explicit form, as detailed in [5]. The resulting transient simulation problem requires the solution of system…”

“…The proposed Waveform Relaxation scheme is one possible method for performing this inversion. As discussed in [5], [14], we perform a twolevel decoupling. First, the channel operator ℋ is split into its (block-) diagonal part , including direct transmission and reflection coefficients of each independent channel, and remainder , including all coupling terms between adjacent channels.…”

“…In [5], a new approach for fast channel simulation based on Waveform Relaxation (WR) was presented. This method is based on macromodels for drivers/receivers [6], and channel [7].…”

“…A fixed-point iteration is then established for solving the transient analysis within a Waveform Relaxation framework [8]- [13]. This method combines the advantage of SPICE-level accuracy with a fast runtime, as discussed in [5].…”

“…This work builds on previous formulations [5], [14] and constructs a new iterative scheme based on a frequency-dependent over-relaxation. The main novel contribution of this paper is the possibility of optimize separately and independently each spectral component of the solution, by maximizing the corresponding frequency-dependent convergence rate.…”