基于波形松弛迭代的大规模多导体线缆高频耦合广义传输线模型

Classical transmission line model is suitable for analyzing of electromagnetic field coupling to multi-conductor lines in the case that wavelength is much larger than the transverse dimension of lines. It is hard to be applied in the analysis of high frequency electromagnetic field such as high power microwave coupling to multi-conductor lines. The generalized transmission line model takes into account the high frequency coupling effect while keeping a relatively simple expression. However, the existing generalized multi-conductor transmission lines model mainly contains two problems: one is that most of the generalized multi-conductor transmission lines models are based on frequency domain and can not handle the nonlinear load problem; the other is the low computational efficiency in the case that transmission line contains large scale conductors. For that, this project intends to research the generalized multi-conductor transmission lines model based on waveform relaxation iteration. Based on waveform relaxation iteration technique, the interaction effects between lines are equivalent to the virtual equivalent sources along the lines, thus the high frequency electromagnetic field-to-multi-conductor lines coupling problem is simplified to the high frequency electromagnetic field-to-single lines coupling problem with the additional interaction effects. The solving method would be investigated. The most suitable method for generalized multi-conductor transmission lines model to represent the frequency dependent parameters in time domain is investigated. In this way, the time domain generalized multi-conductor transmission lines model is established. At last, the convergence of the high frequency coupling model is researched, and the model is validated experimentally. The proposed model can not only handle the nonlinear load and frequency-dependent parameters at the same time but also has a high computational efficiency in the case that transmission line contains large scale conductors. The achievements of this project can provide the foundation for analyzing of intentional electromagnetic interference (IEMI) effect of the electronic and electrical systems.

经典传输线模型适用于波长远大于线缆间横向尺寸的多导体线缆电磁场耦合分析场合，难以满足近年来高功率微波等高频场的耦合分析需求。广义传输线模型能够处理高频耦合问题，又保持了较为简洁的形式。但是，现有的广义传输线模型还存在着两个问题：其一是针对于多导体线缆的广义传输线模型大多基于频域，难以处理非线性负载问题；其二是在大规模线缆情况下计算效率较低。为此，本项目拟研究基于波形松弛迭代的时域广义多导体传输线模型。项目采用将线缆间互耦效应等效为线缆上沿线分布的虚拟等效源的方法，将多导体线缆高频耦合问题简化为单根线缆高频耦合问题叠加互耦效应，研究其求解方法；研究适用于广义传输线模型的频变参数时域表征方法，建立时域广义多导体传输线模型；研究模型的收敛性并开展试验验证。所提出的模型既可以同时考虑非线性负载和频变参数，又能够高效处理大规模线缆的高频耦合问题。本项目的成果将为电子电气系统IEMI效应研究提供基础。

多导体线缆广泛存在于集成电路等电子系统或电气系统中，是现代电子电气系统的重要组成部分。瞬态电磁场能够耦合在多导体线缆上并感应出高幅值的瞬态电压和电流，对于电子电气系统具有严重威胁。由于随着电子电气系统所面临的电磁干扰（Electromagnetic Interference，EMI）频率越来越高，若仍然采用经典传输线耦合模型开展建模分析就会导致较大的计算误差。因此，本项目为了准确地对多导体高频耦合响应开展研究，创新地提出了基于渐近理论的多导体高频电磁场耦合模型，首先利用细线近似理论和经典传输线理论对导体进行区域划分，实现了导体渐进区域的解析表达式求解，然后将导体终端区域产生的高频效应，用散射系数与反射系数进行量化表示，结合渐近理论等效思想，得到电流随长度变化的表达式，并利用最小二乘拟合短线电流响应，求出任意长度下的耦合电流响应，考虑到不同情况下的导体数量和地面电气参数，引入模态变换和矩阵运算，该耦合模型能够求解有损地面上方任意数量导体的高频耦合电流响应，并通过对地面阻抗公式的修正，将该耦合模型的精度进一步提高。上述多导体高频电磁场耦合模型与基于麦克斯韦方程组的全波数值计算方法相比，其所需计算机资源将大大减少，尤其在导体长度远超过导体高度时，该模型能以极高的效率有效地计算导体的耦合响应。本项目所提出的多导体高频电磁场耦合模型，能够为进一步开展EMI对电子电气系统耦合效应研究提供基础。