Statistical analysis of electromagnetic radiation from random multi-conductor transmission lines
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摘要:
针对含随机参数的互连线缆电磁辐射计算问题，提出了一种基于混沌多项式展开和偶极子近似法的多导体传输线电磁辐射统计分析方法。利用正交多项式的性质对随机多导体传输线方程进行展开，结合边界条件求解得到传输线沿线电流，利用偶极子近似法和镜像法计算传输线电流引起的总辐射。仿真结果验证了所提方法的准确性，与传统的蒙特卡罗方法相比，计算效率得到大幅度提高。所提方法对于预测系统内含随机参数的线缆辐射场，评估线缆电磁辐射和检验系统性能指标，有一定的参考价值。
Abstract:In this paper, a statistical algorithm based on polynomial chaos expansion and dipole approximation for electromagnetic radiation calculation of interconnected cables with random parameters is proposed.In this method, orthogonal polynomials are used to expand the equation of the multi-conductor transmission line with random coefficients, the current along the transmission line is obtained by combining the boundary conditions, and then the electric dipole approximation and the mirror image method are used to calculate the total radiation caused by the current of the transmission line. Simulation results verify the accuracy of the proposed method, and the computational efficiency is greatly improved compared with the traditional Monte Carlo method. This method has certain reference value for predicting cable radiation field with random parameters, evaluating cable electromagnetic radiation and testing system performance index.
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图 3 三导体传输线系统辐射模型
Figure 3. Radiation model of three-conductor transmission line system
图 6 传输线辐射场概率密度对比
Figure 6. Probability density comparison of transmission line radiation field
图 7 线缆辐射场与国军标限值对比
Figure 7. Comparison diagram of cable radiation field and military limit value
表 1 Hermite正交多项式性质
Table 1. Properties of Hermite orthogonal polynomials
性质 描述 函数 函数Y，自变量ξ=[ξ1 ξ2 … ξn]T 展开 
正交基 Hermite正交多项式{ϕi(ξ)} 内积 
权重函数 
正交性 
展开系数 
平均 Y0 
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表 2 三个随机变量的Hermite正交多项式
Table 2. Hermite orthogonal polynomials of three random variables
序号i 阶数p 多项式ϕi 〈ϕi2〉 0 0 1 1 1 1 ξ1 1 2 1 ξ2 1 3 1 ξ3 1 4 2 ξ1ξ2 1 5 2 ξ1ξ3 1 6 2 ξ2ξ3 1 7 2 ξ12-1 2 8 2 ξ22-1 2 9 2 ξ32-1 2
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表 3 传输线辐射场计算效率对比
Table 3. Comparison of calculation efficiency of radiation field of transmission line
方法 计算时间/s 频点数 一阶多项式混沌-偶极子近似 27.42 100 蒙特卡罗-偶极子近似 9 340.26 100
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