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

doi:10.7652/xjtuxb201612019

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

更新时间：2025-07-09

- A Polynomial Chaos Expansion Method for Sensitivity Analysis of Microstrip Transmission Lines with Stochastic Parameters
- Vol. 50, Issue 12, Pages: 121-127(2016)
- 作者机构：
  
  西安交通大学电子与信息工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201612019
  CLC： TN811.2
- Online First：10 December 2016，
  
  Published：2016
- 稿件说明：
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A Polynomial Chaos Expansion Method for Sensitivity Analysis of Microstrip Transmission Lines with Stochastic Parameters[J]. 2016, 50(12): 121-127.
DOI：

A Polynomial Chaos Expansion Method for Sensitivity Analysis of Microstrip Transmission Lines with Stochastic Parameters[J]. 2016, 50(12): 121-127. DOI： 10.7652/xjtuxb201612019.

摘要

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。

Abstract

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.

关键词

Keywords

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