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Efficient generation of compact symbolic network functions in a nested rational form
International Journal of Circuit Theory and Applications ( IF 1.8 ) Pub Date : 2020-05-24 , DOI: 10.1002/cta.2789 Vladimir Filaretov 1 , Konstantin Gorshkov 2
International Journal of Circuit Theory and Applications ( IF 1.8 ) Pub Date : 2020-05-24 , DOI: 10.1002/cta.2789 Vladimir Filaretov 1 , Konstantin Gorshkov 2
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This paper presents the extension of generalized parameter extraction method for direct circuit function generation in a fully symbolic form of rational expressions or a nested s‐expanded polynomial. The new formula for implicit extraction of parameters that allows effective factoring by grouping of determinants of circuits containing any linear models of active elements, such as controlled sources, nullors, and pathological mirrors, is proposed. The concept of nullor with parameter is used for implicit extraction. The rules of optimal selection of parameters for extraction are presented. The proposed algorithm of symbolic analysis is implemented in the CirSym program, which is available online. The paper discusses the results of automatic analysis of several large active circuits, as well as determinants of matrixes and passive topologies, in terms of compact size and minimization of the number of arithmetic operations. Experimental results demonstrate that the expressions of determinants derived by CirSym are more compact than the results of the factorization algorithms of commercial computer algebra systems. The comparison with several other symbolic analysis algorithms shows that CirSym is the only available program that provides the exact calculation of the symbolic function of large circuits in the s‐expanded form with every coefficient being a compact‐nested expression.
中文翻译：
嵌套有理形式的紧凑符号网络函数的高效生成
本文提出了以完全符号形式的有理表达式或嵌套s形式生成直流电路功能的广义参数提取方法的扩展扩展多项式。提出了用于参数隐式提取的新公式，该公式可通过对包含活动元素的任何线性模型（例如受控源，归零和病理镜）的电路的行列式进行分组来进行有效分解。带参数的nullor的概念用于隐式提取。提出了提取参数的最佳选择规则。拟议的符号分析算法在CirSym程序中实现，该程序可在线获得。本文讨论了几种大型有源电路的自动分析结果，以及矩阵和无源拓扑的行列式，包括紧凑的尺寸和最少的算术运算次数。实验结果表明，与商用计算机代数系统的分解算法结果相比，CirSym导出的行列式的表达式更为紧凑。与其他几种符号分析算法的比较表明，CirSym是唯一可提供精确计算大型电路符号功能的程序。s展开形式，每个系数都是紧缩表达式。
更新日期：2020-05-24
中文翻译：
嵌套有理形式的紧凑符号网络函数的高效生成
本文提出了以完全符号形式的有理表达式或嵌套s形式生成直流电路功能的广义参数提取方法的扩展扩展多项式。提出了用于参数隐式提取的新公式，该公式可通过对包含活动元素的任何线性模型（例如受控源，归零和病理镜）的电路的行列式进行分组来进行有效分解。带参数的nullor的概念用于隐式提取。提出了提取参数的最佳选择规则。拟议的符号分析算法在CirSym程序中实现，该程序可在线获得。本文讨论了几种大型有源电路的自动分析结果，以及矩阵和无源拓扑的行列式，包括紧凑的尺寸和最少的算术运算次数。实验结果表明，与商用计算机代数系统的分解算法结果相比，CirSym导出的行列式的表达式更为紧凑。与其他几种符号分析算法的比较表明，CirSym是唯一可提供精确计算大型电路符号功能的程序。s展开形式，每个系数都是紧缩表达式。
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