基于等效变换对多边内星形电阻网络的研究

On Polygonal Internal Star Resistance Network Based on Equivalent Conversion

应用星形电路与多角形电路的等效互换以及构建等效条件法,对4边内星形电阻网络进行了等效分析,把它等效为目前最简单的四端网络.还分析了把5边内星形电阻网络等效为四端网络的情况.对这2个四端网络的4个端钮之间的等效电阻进行了计算.并用Multisim中的万用表对所计算电路的等效电阻以及与原电路对应的电阻进行了仿真测量,结论是理论计算与测量的结果相同.这项研究的目的是,用星形电路与多角形电路等效互换,结合构建等效条件法,扩展Y-△变换的应用,为解决与星形电路、多角形电路相关电路的等效变换问题提供可参考的实用分析方法.此方法适用于对无源多端网络的等效变换.

Using the equivalent conversion from star circuit to polygon circuit and equivalent condition constructing method,the quadrangle internal star resistance network has equivalently been analyzed.The quadrangle internal star resistance network is regarded equivalently as a currently simplest four-terminal network.The case that the pentagonal internal star resistance network is equivalently conversed to fourterminal network has been discussed.The equivalent resistances at 4 terminals for the pentagonal internal resistance network and four-terminal network have been calculated.The Multisim has been used to carry out a stimulatory measure for the calculated equivalent resistances and for the original circuit.The result shows that the theoretical calculation and the measurement are consistent.The purpose of this research is to expand the application of Y-△ conversion by equivalent conversion from star circuit to polygonal circuit and by equivalent condition constructing method,and to apply apractical and effective method for solving the equivalent conversion in star circuit and polygonal circuit.Such a method can also be used in the equivalent conversion for passive multi-terminal networks.