8×n阶矩形网络的等效电阻和电容及2个猜想  

Equivalent Resistance and Capacitance of 8×n-rectangular Network and Two Conjectures of m×n-rectangular Network

作　　者：谭志中[1] 陈翠萍[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《河北师范大学学报（自然科学版）》2013年第6期579-586,共8页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11104151);南通大学自然科学研究项目(11Z054)

摘　　要：采用网络分析方法,建立了四元矩阵方程模型,构造了矩阵变换方法,给出了等效电阻公式,并给出了其无穷网络的等效电阻公式.根据电容参数与电阻参数之间存在的反比映射关系,给出了8×n阶矩形电容网络的等效电容公式.根据已经得到的一些矩形网络等效电阻公式的结构特征,提出了任意m×n阶矩形网络的等效电阻和等效电容公式猜想.在对比研究中发现了一个三角函数恒等式.A quaternion matrix equation and the method of matrix transformations in terms of the network analysis were built. A brief equivalent resistance formula is proposed. Meanwhile,a equivalent resistance of infinite networks is given. Considering the inverse mapping relation between capacitance and resistance parameters,the equivalent capacitance formula is given for the 8 × n-rectangular capacitance network. Two conjectures of the equivalent resistance and capacitance formulas for the random m × n-rectangular network are proposed according to the architectural feature of a series of formulas of equivalent resistance which have been achieved before. By comparison in this paper,a new trigonometric identity is obtained.

关 键 词：8×n阶矩形网络 等效电阻 等效电容 矩阵方程 矩阵变换 猜想 

分 类 号：O441[理学—电磁学]