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A fractional-order multifunctional n-step honeycomb RLC circuit network

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Abstract

We investigate a multifunctional n-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, an n-step impedance LC network is discussed and many new characteristics of complex impedance have been found.

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Authors and Affiliations

  1. Department of Physics, Nantong University, Nantong, 226019, China

    Ling Zhou & Zhi-zhong Tan

  2. Department of Mathematics, Nantong University, Nantong, 226019, China

    Qing-hua Zhang

Authors
  1. Ling Zhou
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  2. Zhi-zhong Tan
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  3. Qing-hua Zhang
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Correspondence to Zhi-zhong Tan.

Additional information

Project supported by the Jiangsu Provincial Science Foundation (No. BK20161278)

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Zhou, L., Tan, Zz. & Zhang, Qh. A fractional-order multifunctional n-step honeycomb RLC circuit network. Frontiers Inf Technol Electronic Eng 18, 1186–1196 (2017). https://doi.org/10.1631/FITEE.1601560

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