Oldham RC链分抗逼近电路零极点精确求解
Precise solutions of zero pole of oldham RC chain fractance approximation circuits
作者：易舟(四川大学电子信息学院)；袁晓(四川大学电子信息学院)；陶磊(四川大学电子信息学院)；刘盼盼(四川大学电子信息学院)
Author：YI Zhou(College of Electronics and Information Engineering, Sichuan University)；YUAN Xiao(College of Electronics and Information Engineering, Sichuan University)；TAO Lei(College of Electronics and Information Engineering, Sichuan University)；LIU Pan Pan(College of Electronics and Information Engineering, Sichuan University)
收稿日期：2014-12-28 年卷（期）页码：2015,52(6):1255-1261
期刊名称：四川大学学报: 自然科学版
Journal Name：Journal of Sichuan University (Natural Science Edition)
关键字：分数阶微积分； 电路与系统； 零极点； 迭代矩阵； 阻抗； 多项式的根
Key words：Fractional order calculus； Circuits and systems； Zero pole； Iterative matrix； Impedance； Polynomial roots
基金项目：成都市科技计划项目（12DXYB255JH 002）
中文摘要
根据Oldham RC链分抗逼近电路的电路特征与数学特征，采用理论推导和MATLAB编程两种方法实现四类Oldham RC链分抗逼近电路的零极点的求解．针对Oldham RC链的规则级联结构特点，由简化电路求出传输矩阵、迭代矩阵，并求出阻抗函数的一般数学表达式．使用特征值分解法和Hamilton—Cayley展开法求出迭代矩阵幂而获得各类Oldham RC链分抗的简洁数学表达式，并给出特殊初始阻抗情形下各类Oldham RC链分抗的零极点的解析解．利用MATLAB中的“solve”和“roots”函数编程实现任意简单初始阻抗下零极点的数值求解．验根结果表明，实现了电路零极点的精确求解．
英文摘要
Based on the circuit features and mathematical characteristics of Oldham RC chain fractance approximation circuits，the ways of theoretical deduction and programming on MATLAB are used to solve the zero pole of these circuits．According to the characteristics of the regular cascade structure of the Oldham RC chain，the transfer matrix and iterative matrix are obtained by the simplified circuits，and then the general mathematical expression of the impedance function is achieved．The iterating matrix power is calculated and the simple mathematical expression of various Oldham RC chain fractance is derived by using the methods of eigenvalue decomposition and Hamilton Cayley expansion．Analytical solutions of zero pole for four kinds of Oldham RC chain fractance are given with special initial impedance．Two functions，“solve” and “roots” in MATLAB，are adopted to find numerical solutions under simple initial impedance．The test of roots shows that，the accurate solutions of zero pole for Oldham RC chain fractance are realized．
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