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.