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Stability and Passivity Analysis, Application of Vector Fitting in RLC Equivalent Circuit Synthesi

机译：稳定性和无源性分析，矢量拟合在RLC等效电路综合中的应用

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摘要

Vector Fitting (VF) is one of the most well-known techniques in calculating a rational approximation based on given frequency responses, and VF has been used in modeling different electrical systems. This thesis focuses on three main areas. First, the VF algorithm will be studied in depth regarding its advantages, weaknesses and strengths. Second, the implementation of the VF algorithm using python scripting language, and validation of the performance and the functionality of VF in python through numerical examples; this includes the original VF and the relaxed VF. Third, the analysis of the stability and the passivity of the results of each numerical example that is generated by VF. Semi-Analytic and Cellular method is used to analyze the stability and the passivity of each RLC circuit branch, while the Hamiltonian Matrix method is used to verify the passivity of the network. Also, one of applications of VF discussed in this thesis is using VF to approximate poles and residues for Scattering (S-) and Admittance (Y-) parameters of a two-port network to synthesize the RLC circuit based on the approximated poles and residues.;The results show that the VF method has demonstrated accurate approximation with very small error between actual frequency response and fitted frequency response. The relaxed VF (RVF) method produces a more accurate approximation when the values of responses are small compared to non-relaxed VF. The VF feature to enforce stability is confirmed and its result is in agreement with the result from stability theory analysis, the real part of all poles is less than zero. Passivity analysis shows that even though there might be no passivity at one or more RLRC circuit branches in the network, the network could still be passive. Also, ability of the VF algorithm to detect unstable systems is investigated and verified. Finally, the frequency responses of S-parameters of synthesized equivalent RLC circuits, which are approximated by VF, are well matched against the given tabulated frequency responses.
机译：矢量拟合（VF）是基于给定频率响应计算有理近似值的最著名技术之一，并且VF已用于对不同的电气系统进行建模。本论文集中在三个主要领域。首先，将对VF算法的优点，缺点和优点进行深入研究。其次，使用python脚本语言实现VF算法，并通过数值示例验证python中VF的性能和功能；这包括原始VF和松弛VF。第三，分析由VF生成的每个数值示例的结果的稳定性和无源性。半解析和蜂窝方法用于分析每个RLC电路分支的稳定性和无源性，而哈密顿矩阵方法则用于验证网络的无源性。另外，本文讨论的VF的应用之一是使用VF近似两极网络的散射（S-）和导纳（Y-）参数的极点和残留物，以基于近似的极点和残留物合成RLC电路结果表明，VF方法已经证明了精确的近似值，并且实际频率响应和拟合频率响应之间的误差很小。与非松弛VF相比，当响应值较小时，松弛VF（RVF）方法可产生更准确的近似值。确认了增强稳定性的VF特征，其结果与稳定性理论分析的结果一致，所有极点的实部均小于零。无源性分析表明，即使网络中的一个或多个RLRC电路分支处可能没有无源性，网络也可能是无源的。此外，还研究并验证了VF算法检测不稳定系统的能力。最后，由VF近似的合成等效RLC电路的S参数的频率响应与给定的列表频率响应完全匹配。

著录项

  • 作者

    Nguyen, Tao Duy.;

  • 作者单位

    University of Idaho.;

  • 授予单位 University of Idaho.;
  • 学科 Electrical engineering.
  • 学位 M.S.
  • 年度 2016
  • 页码 116 p.
  • 总页数 116
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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