工艺参数随机扰动下的传输线建模与分析新方法

本文考虑集成电路制造过程中传输线制造工艺参数随机扰动对传输线传输性能的影响,建立了传输线的随机模型.结合精细积分算法与蒙特卡洛方法分析了该传输线随机模型的瞬态响应,通过对模型输出的正态性进行偏度-峰度检验给出了最差情况估计.对于正弦激励情况推导了无耗传输线相应随机微分方程解的一阶矩的解析形式,给出了二阶矩的数值计算方法,最后估计出输出信号振幅与相移的上下界.实验结果表明本文提出的传输线随机模型及其分析方法可以对传输线的性能进行有效的评估.

A New Stochastic Modeling and Analysis Method for Transmission Lines in the Presence of Random Process Variations

The random variations of technological parameters are always existent during manufacturing,which have a definite impact on transmission performance of transmission lines.Considering the impact,the stochastic model for transmission lines is proposed,and the precise integration algorithm is combined with Monte Carlo method to analyze the transient response of the stochastic model.Jarque-Bera test is made for the normality of the model's output and the worst-case estimation is given.In the case of sinusoidal excitation,lossless transmission lines are considered.The analytic form of first moment of the corresponding stochastic differential equation's solution is derived,and the numerical computation method for second moment is given,finally the upper and lower bound of the output signal's amplitude and phase shift is estimated.Experimental results demonstrate that the proposed stochastic model and the statistical analysis method can evaluate the transmission performance of transmission lines effectively.