Interconnects in high-speed VLSI circuits and systems exhibit transmission line effects. Due to the complex geometries of interconnections, coupling between various layers, and inhomogeneous insulating materials, these high-speed interconnects need to be modelled as nonuniform frequency dependent transmission lines. In this paper, we describe a method of simulating the transient response of nonuniform high-speed interconnects in its most general form, i.e. nonuniformly distributed, lossy, coupled, multiple lines with frequency-dependent parameters with linear and nonlinear terminations. Transmission line equations are formulated in the frequency domain as an initial value problem and solved using numerical integration. A new algorithm is proposed for overcoming the inherent initial value instability encountered in the solution of transmission line equations. The time domain response is obtained by Numerical Inversion of Laplace Transform (NILT). Nonlinear networks containing nonuniform high-speed interconnects are analyzed using the Piecewise Decomposition Technique. The accuracy and efficiency of the proposed method is illustrated by appropriate examples and comparisons with published results.>

A method based on numerical inversion of the Laplace transform for the transient analysis of nonuniform high-speed interconnects in LSI/VLSI circuits is described. The interconnects are treated as lossy multiconductor nonuniform frequency dependent transmission lines. An algorithm for overcoming the inherent initial value instability encountered while numerically integrating transmission line equations is described. The method is directly compatible with the piecewise decomposition technique (PDT) and can be extended to interconnect networks with nonlinear terminations. Further speed up can be achieved by using parallel processors. Examples and comparisons with published results are presented.>