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Oldham分形链与Liu-Kaplan分形链分抗的阻纳函数求解
Immittance functions solution of Oldham fractal Chain and Liu-Kaplan fractal chain fractance
投稿时间:2018-04-25  修订日期:2018-07-29
中文关键词:分数微积分  分形分抗  迭代电路  标度拓展  非正则标度方程
英文关键词:fractional calculus  fractal fractance  iterating circuit  scaling extension  irregular scaling equation
基金项目:
作者单位
高小龙 College of Electronic and Information EngineeringSichuan UniversityChengdu Sichuan 610065China 
袁 晓 College of Electronic and Information EngineeringSichuan UniversityChengdu Sichuan 610065China 
施卜椿 College of Electronic and Information EngineeringSichuan UniversityChengdu Sichuan 610065China 
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中文摘要:
      针对Oldham RC分形链类的电路特征,给定初始阻抗,采用3种方法理论推导Oldham分形链类阻抗函数解析表达式,并对比分析各求解方法。根据Oldham分形链分抗逼近电路的连分式表示和连分式三项递推公式,引入阻抗函数新的数学表示形式:连分式三项递推矩阵。通过分析Liu-Kaplan标度迭代电路和标度方程,推导出2种Liu-Kaplan分形链类阻抗函数的数学表示形式。通过理论验证和实验仿真对比不同分数阶下的阻抗函数表达式和频域特征与运算特征曲线。
英文摘要:
      Aiming for the circuit characteristics of the Oldham RC fractal chain, the analytical expressions of Oldham RC fractal chain impedance function are deduced by using three methods at given initial impedances. Then, the solution methods are compared and analyzed. According to the continued fractional representation of the approximation circuit of Oldham fractal chain fractance, and the three-term recurrence formula of continuous fraction, a new mathematical representation of impedance function is introduced: continuous fractional three-term recursion matrix. By analyzing the Liu-Kaplan scaling iteration circuit and the scaling equations, two mathematical representations of the impedance functions of Liu-Kaplan fractal chains are deduced. Theoretical and experimental simulations compare the impedance function expressions and frequency characteristics of different fractional orders.
引用本文:高小龙,袁 晓,施卜椿.Oldham分形链与Liu-Kaplan分形链分抗的阻纳函数求解[J].太赫兹科学与电子信息学报,2019,17(3):474~481
DOI:10.11805/TKYDA201903.0474
学科分类代码:
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