蝶形电阻网络圆周边界任意端口间等效电阻的计算

Equivalent Resistance Between Arbitrary Ports on the Circle Boundary in the Butterfly Resistance Network

本文将电路理论中的网孔分析法与递归变换法相结合,给出了一种求解蝶形电阻网络圆周边界任意端口间等效电阻的简捷方法。计算过程中,首先基于网孔分析法建立了非线性的差分方程组,随后利用矩阵变换方法,将非线性差分方程组转化为线性的差分方程组。此外,本文将一般外加单一电流源求等效电阻的策略推广为外加多个电流源,由此获得的等效电阻解析表达式可适用于计算任意端口的等效电阻。

This paper proposes a simple method for equivalent resistance between arbitrary ports on the circle boundary in the butterfly resistance network by the mesh analysis in circuit theory and the recursion-transforrnation in combination mathematics. During the calculations, nonlinear difference equations are firstly built based on mesh analysis, and then matrix transformation is used to transform the nonlinear difference equations to linear equations. Furthermore, singlet current source is extended to multiple current sources to solve equivalent resistance, the obtained analytic expressions apply to the equivalent resistance between arbitrary ports.