规则RC分形分抗逼近电路的零极点分布  

On Zero-Pole Distribution of Regular RC Fractal Fractance Approximation Circuits

作　　者：袁子 袁晓[2] 

机构地区：[1]清华大学物理系,北京100084 [2]四川大学电子信息学院,四川成都610064

出　　处：《电子学报》2017年第10期2511-2520,共10页Acta Electronica Sinica

摘　　要：从电路结构特性与数学表示特征两方面,考察与探讨经典的规则RC分形分抗逼近电路的阻抗函数之零极点解析求解与数值求解理论与方法.首先简要介绍经典分形分抗逼近电路并引入迭代电路、迭代函数、迭代矩阵等新概念.通过特征值分解或Hamilton-Cayley展开,求出迭代矩阵幂而获得某些经典(比如Oldham分形链、Carlson分形格、B型、2h型等)分形分抗的阻抗函数之简洁数学解析表达式.最后给出分抗逼近电路零极点的解析求解法与有效数值求解法及其解结果并进行理论与实践验证.The principal purpose of this paper is to investigate and probe the theories and methods of analytical solution and valid numerical solution for the zero-poles of the classical regular RC fractal fractance approximation circuits considering both the circuit structure specialities and mathematic representation characteristics. A brief survey and reviewon fractal fractance approximation circuits is given and newconcepts of iterating circuit,iterating function,and iterating matrix etc are introduced. Finding the iterating matrix power by means of eigenvalue decomposition method or Hamilton-Cayley expansion,a simple expression of the analytical solution is derived for the normalized impedance function of some classical（ such as the Oldham fractal chain,the Carlson fractal lattice,H-type,2 h-type etc） fractal fractance approximation circuits.An analytical solution and a valid numerical solution for the zeros and poles of some classical fractal fractance approximation circuit are presented. The solutions are tested in both theory and simulation experiments.

关 键 词：分数阶电路与系统 分抗 迭代电路 迭代矩阵 多项式的根 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]