一类分数阶多功能n阶蜂巢型RLC电路网络

周玲; 谭志中; 张庆华

doi:10.1631/FITEE.1601560

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一类分数阶多功能n阶蜂巢型RLC电路网络

常规文章 | Updated：2022-05-19

- 一类分数阶多功能n阶蜂巢型RLC电路网络
- A fractional-order multifunctional n-step honeycomb RLC circuit network
- 信息与电子工程前沿（英文） 2017年18卷第8期页码：1186-1196
- Affiliations：
  
  Department of Physics, Nantong University, Nantong 226019, China
  Department of Mathematics, Nantong University, Nantong 226019, China
- Author bio：
  
  [ "Ling ZHOU, E-mail: zl7103@163.com" ]
  Zhi-zhong TAN, E-mail: tanz@ntu.edu.cn
- Funds：
  
  Project supported by the Jiangsu Provincial Science Foundation (No. BK20161278)
- DOI：10.1631/FITEE.1601560
  中图分类号： O441.1;TN711.3
- 收稿：2016-10-18，
  
  修回：2017-;8-14，
  
  纸质出版：2017-08
- Accepted：
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周玲, 谭志中, 张庆华. 一类分数阶多功能n阶蜂巢型RLC电路网络[J]. 信息与电子工程前沿（英文）, 2017,18(8):1186-1196.

Ling ZHOU, Zhi-zhong TAN, Qing-hua ZHANG. A fractional-order multifunctional n-step honeycomb RLC circuit network[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(8): 1186-1196.
周玲, 谭志中, 张庆华. 一类分数阶多功能n阶蜂巢型RLC电路网络[J]. 信息与电子工程前沿（英文）, 2017,18(8):1186-1196. DOI： 10.1631/FITEE.1601560.

Ling ZHOU, Zhi-zhong TAN, Qing-hua ZHANG. A fractional-order multifunctional n-step honeycomb RLC circuit network[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(8): 1186-1196. DOI： 10.1631/FITEE.1601560.

摘要

研究了一类多功能

阶蜂巢型电阻网络模型，该问题一直未被解决。通过调节电路参数，该网络模型可以转化为含有多种功能的数个不同网络模型，例如一个规则的梯形网络、一个

阶三角形网络，等。我们导出了电阻网络的2个新的等效电阻公式，同时导出了LC网络的等效复阻抗公式，它们都属于分数阶范畴。首先，将一个复杂网络简化为一个简单的等效模型；其次，应用基尔霍夫定律，建立一个分式差分方程模型；再次，采用等效变换方法，给出非线性差分方程的通解。在实际应用中，获得了数个有趣的特殊结论。特别地，讨论分析了一个

阶LC复阻抗网络，发现了许多新的等效复阻抗特性。

Abstract

We investigate a multifunctional

-step honeycomb network which has not been studied before. By adjusting the circuit parameters

such a network can be transformed into several different networks with a variety of functions

such as a regular ladder network and a triangular network. We derive two new formulae for equivalent resistance in the resistor network and equivalent impedance in the LC network

which are in the fractional-order domain. First

we simplify the complex network into a simple equivalent model. Second

using Kirchhoff's laws

we establish a fractional difference equation. Third

we construct an equivalent transformation method to obtain a general solution for the nonlinear differential equation. In practical applications

several interesting special results are obtained. In particular

-step impedance LC network is discussed and many new characteristics of complex impedance have been found.

关键词

Keywords

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