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不对称电路与丛电路模型和泛电路模型分析法

Asymmetric Circuit and Folding Circuit Models and Pan Circuit Models Analysis Method

  • 摘要: 复电路与凡电路(敆电路、卷电路和堃电路)都是对称电路(两相电路与差分电路、三相电路和四翼电路)的抽象模型,采用对称数系复数与凡数(敆数、卷数和堃数)分别表达分析与求解,而与对称电路结构形式相同但参数不同的不对称电路,则需要构建一套全新形式的抽象模型与相应的数学工具进行表达分析与求解。本文在全面梳理两相电路、差分电路、三相电路和四翼电路及其复电路模型、敆电路模型、卷电路模型和堃电路模型的基础上提出了不对称电路的丛电路模型和泛电路(怼电路、徽电路和堯电路)模型的概念,并基于对称数系复数、敆数、卷数和堃数构建非对称数系丛数、怼数、徽数和堯数,以此来表达分析与求解不对称电路,同时还给出了不对称电路的解算实例,以期呈现完整的不对称电路及其抽象模型的知识体系。

     

    Abstract: Both complex circuits and fan circuits(merged-circuit, roll-circuit, kun-circuit) are abstract models of symmetric circuits(two-phase circuit and differential circuit, three-phase circuit and four-wing circuit), expressed and analyzed using symmetric complex numbers and fan numbers(merged-numbers, roll-numbers, kun-numbers) respectively. However, asymmetric circuits with the same structural form but different parameters as symmetric circuits require the construction of a new form of abstract model and corresponding mathematical tools for expression, analysis, and solution. On the basis of a comprehensive review of two-phase circuits, differential circuits, three-phase circuits, and four wing circuits, as well as their complex circuit models, merged-circuit models, roll-circuit models, and kun-circuit models, this article proposes the concepts of folding circuit models and pan circuit(dui-circuit, hui-circuit, yao-circuit) models for asymmetric circuits. Based on symmetric number system complex numbers, merged-numbers, roll-numbers, and kun-numbers, asymmetric number system dui-numbers, hui-numbers, yao-numbers, and Yao numbers are constructed to express the analysis and solution of asymmetric circuits. At the same time, calculation examples of asymmetric circuits are also provided to present a complete knowledge system of asymmetric circuits and their abstract models.

     

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