变量分离法在传输线瞬态分析中的应用

A Variable-Separation Method for Transient Analysis of Transmission Lines

提出一种用于分析高速集成电路系统中互连线的瞬态响应的变量分离法 该方法利用Chebyshev展开式逼近传输线电压和电流变量 ,使时、空变量分离 ,化偏微分方程为常微分方程 ,由此建立了分析传输线的时域模型 介绍方法的基本原理 ,分析实际应用中的精度和误差 ,并给出相应的等步长技术的应用 ,最后给出几个实例 结果表明 ,本方法模型简便实用、计算效率和精度良好 ,方法适用面广 ,不仅适用于多导体传输线系统 。

The variable separation method is proposed to analyze transient response of interconnecting system in high speed integrated circuit. This method approximates voltage and current variables of transmission lines by using the Chebyshev expansion directly. Thus the temporal and spatial variables are separated and the partial differential equations are reduced to the ordinary ones. The time domain model in analyzing transmission line is also established. The basic principle of this method is introduced and the accuracy and error are analyzed. In addition, the application of equal step length technology is given. At last, some illustrative examples are provided. It proves that the model of this method is simple, practical, efficient and of high accuracy. What's more, it is applicable to not only the multi conductor transmission lines systems, but also the nonuniform transmission ones.