一种用于分析高速VLSI中频变互连线瞬态响应的精细积分算法

A Precise Integration Algorithm for Transient Simulation of Interconnects in High-Speed VLSI

本文利用精细积分法求解高速VLSI中频变参数互连线的瞬态响应 .首先 ,从频域传输线方程出发 ,利用反拉氏变换将其转化为含有卷积项的时域方程 ,经过空间坐标离散后 ,再采用精细积分法进行求解 .与以往的空间离散方法相比较 ,提出采用电压和电流空间间隔取点的方法 ,减小了截断误差 .在计算常微分方程组中的非齐次项时 ,采用递归计算代替传统数值卷积大大提高了计算的效率 .该方法对于耦合传输线无须进行解耦 ,在处理非均匀频变传输线时也非常方便 .数值实验结果表明 ,该算法稳定性好 ,计算精度高 .

The precise integration method is employed to analyze the transient response of frequency-dependent interconnects.This method starts from frequency-domain telegrapher's equations and the time-domain equations including convolutions are obtained by inverse Laplace transform.After the discretization with respect to the space coordinate(x),the spatial derivatives are eliminated and replaced by finite differences,and then,the precise integration method is used.The truncation error is efficiently decreased by interlacing the voltage and current nodes along the x-axis.This is in contrast to the classical methods where the samples of both voltages and currents are taken at the same points.In addition,traditional numerical convolution is replaced by recursion algorithm in the computation of inhomogeneous items in the ordinary differential equations,such that the computational efficiency rises greatly.This method needs not decouple the telegrapher's equations for multiconductor transmission lines,and is also suitable to nonuniform coupled transmission lines.Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.