Analysis of VLSI multiconductor systems by bi-level waveform relaxation

Abstract

A novel algorithm to compute the transient response of a coupled, dispersive multiconductor system terminated in nonlinear loads such as transistors is developed. The characterization of the multiconductor system is obtained from a full-wave analysis based on the spectral domain approach, and it is suitable for circuit simulation. The transient response of such a system is computed by a bi-level waveform relaxation method. The solution process consists of two steps. One is to obtain a time domain solution at the input and output interfaces by local waveform relaxation, and the second is to transform the waveforms into the frequency domain and obtain the necessary updates for the next global relaxation step. The method allows the interconnects to be separated from the rest of the system so that both the nonlinear termination circuit and the multiconductor system can be analyzed in the most efficient way. The method has been applied to multiconductor systems terminated in MOS, ECL (emitter coupled logic), and GaAs transistors and it is shown that reflections and couplings can create logic errors in the system. The program that implements the algorithm is written in C.