一种分析微带线随机参数敏感性的多项式混沌展开方法
发布时间：2019-01-04 19:50
【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]:Aiming at the influence of random uncertainty of material and structure parameters on transmission performance in transmission line processing, a polynomial chaotic (PC) expansion method is proposed to calculate the transmission line telegram equation with random coefficients. By using the chaotic basis function of orthogonal polynomials, the random equivalent lumped parameters, transmission line voltage and current responses in the transmission line telegram equation are first expanded. Secondly, by using the Galerkin method, the Telegraph equation problem with random coefficients is transformed into the deterministic expansion equations of the orthogonal polynomial expansion coefficients of voltage and current, and the expansion coefficients of voltage and current can be calculated by combining the boundary conditions of transmission lines. The mean, variance and probability density distributions of voltage, current and transfer function are obtained. The simulation results of random parameter microstrip transmission line show that the transmission performance of the microstrip line is greatly influenced by the width of the conduction band at low frequency and the transmission performance by the dielectric constant at high frequency. At the same time, the PC expansion method has higher computational efficiency than the traditional Monte Carlo (MC) method, and the computational time is only about 1 / 500 of that of the MC method.
【作者单位】： 西安交通大学电子与信息工程学院;
【基金】：国家自然科学基金资助项目(61471293)
【分类号】：TN817
[Abstract]:Aiming at the influence of random uncertainty of material and structure parameters on transmission performance in transmission line processing, a polynomial chaotic (PC) expansion method is proposed to calculate the transmission line telegram equation with random coefficients. By using the chaotic basis function of orthogonal polynomials, the random equivalent lumped parameters, transmission line voltage and current responses in the transmission line telegram equation are first expanded. Secondly, by using the Galerkin method, the Telegraph equation problem with random coefficients is transformed into the deterministic expansion equations of the orthogonal polynomial expansion coefficients of voltage and current, and the expansion coefficients of voltage and current can be calculated by combining the boundary conditions of transmission lines. The mean, variance and probability density distributions of voltage, current and transfer function are obtained. The simulation results of random parameter microstrip transmission line show that the transmission performance of the microstrip line is greatly influenced by the width of the conduction band at low frequency and the transmission performance by the dielectric constant at high frequency. At the same time, the PC expansion method has higher computational efficiency than the traditional Monte Carlo (MC) method, and the computational time is only about 1 / 500 of that of the MC method.
【作者单位】： 西安交通大学电子与信息工程学院;
【基金】：国家自然科学基金资助项目(61471293)
【分类号】：TN817
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