一种分析微带线随机参数敏感性的多项式混沌展开方法

A Polynomial Chaos Expansion Method for Sensitivity Analysis of Microstrip Transmission Lines with Stochastic Parameters

针对传输线加工中材料及结构参数随机不确定性对传输性能影响的问题,提出了一种计算随机系数传输线电报方程的多项式混沌(PC)展开方法。利用正交多项式混沌基函数,该方法首先将传输线电报方程中的随机等效集总参数、传输线电压及电流响应进行展开;其次利用Galerkin法,将随机系数的电报方程问题转化为关于电压、电流正交多项式展开系数的确定性扩阶方程组问题,并结合传输线边界条件可计算电压、电流的展开系数,进而获得电压、电流及传递函数的均值、方差和概率密度分布。随机参数微带传输线的仿真结果表明:低频时导带宽度对微带线的传输性能影响较大,高频时介电常数对其传输性能影响较大;在满足计算精度要求的同时,PC展开方法具有比传统蒙特卡罗(MC)方法更高的计算效率,计算耗时仅约为MC方法的1/500。

A method based on polynomial chaos （PC） expansion is proposed to calculate the response of transmission lines with uncertain parameters, such as variability in the substrate material and conductor geometry introduced in manufacturing processes. The stochastic per-unit-length lumped equivalent parameters of the transmission line, as well as the stochastic voltage and current responses for the transmission line, are expanded in terms of a series of orthogonal polynomial chaos basis functions, and all these stochastic variables are substituted into telegraph equations with random parameters. Then Galerkin＇s method is used to transform the telegraph equations into a set of augmented equations with the expansion coefficients of voltage and current as variables. The expansion coefficients are then obtained by solving the augmented equations combined with source and load conditions. Moreover, the statistical properties, such as the means, variance and probability density distribution of the voltage and current responses and transfer functions, are obtained. Simulation results of the microstrip transmission lines show that the conductor width has a greater impact on the performance of the microstrip transmission line at lower frequencies, while the dielectric constant has a greater effect on transmission performance at higher frequencies. In addition, the computational cost of the proposed method is lower, and its simulation time is about 0. 2% of the Monte Carlo method.