规则RC分形分抗逼近电路的零极点分布

doi:10.3969/j.issn.0372-2112.2017.10.028

电子学报 ›› 2017, Vol. 45 ›› Issue (10): 2511-2520.DOI: 10.3969/j.issn.0372-2112.2017.10.028

规则RC分形分抗逼近电路的零极点分布

袁子^1,2, 袁晓^1,2

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

收稿日期:2014-11-17 修回日期:2015-11-03 出版日期:2017-10-25
- 作者简介:
- 袁子,男,1995年生于四川成都,毕业于成都七中,现就学于清华大学物理系.专业方向为凝聚态物理实验.E-mail:yuanz14@mails.tsinghua.edu.cn;袁晓,男,1964年生于四川中江,1998年毕业于电子科技大学电路与系统专业,工学博士.目前主要从事现代信号处理理论和应用(特别是分数阶数字滤波器理论与设计、分数阶微积分应用于图像信号和光电信号的分析与处理)、分数阶电路与系统理论(特别是分抗逼近电路的数学原理、分数阶电路设计、测试与应用)等研究.已公开发表学术论文一百余篇.E-mail:18608003303@wo.com.cn

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

YUAN Zi^1,2, YUAN Xiao^1,2

1. Department of Physics, Tsinghua University, Beijing 100084, China;
2. College of Electronic and Information, Sichuan University, Chengdu, Sichuan 610064, China

Received:2014-11-17 Revised:2015-11-03 Online:2017-10-25 Published:2017-10-25

摘要/Abstract

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.

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

Abstract: 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 review on fractal fractance approximation circuits is given and new concepts 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,2h-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.

Key words: fractional-order circuits and systems, fractance, iterating circuit, iterating matrix, polynomial roots

袁子, 袁晓. 规则RC分形分抗逼近电路的零极点分布[J]. 电子学报, 2017, 45(10): 2511-2520.

YUAN Zi, YUAN Xiao. On Zero-Pole Distribution of Regular RC Fractal Fractance Approximation Circuits[J]. Acta Electronica Sinica, 2017, 45(10): 2511-2520.

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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

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