On the Fractional-Order 3D △×nMemristor-LCCircuit Network Model

Long, Yan; Zhou, Rui; Zhang, Zhenduo; Chen, Diyi; Yao, Wei; Iu, Herbert Ho-Ching

doi:10.1080/15325008.2018.1471106

Cited by 2 publications

(2 citation statements)

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“…[17] established an equivalent transformation method to obtain the resistance and impedance of a type of n-step honeycomb RLC circuit network, and [18] proposed a 2×n fractional order electrical circuit network and calculated its equivalent impedances based on the mesh current method. While [19]- [22] introduced impedance characteristics by using the matrix transform method and the difference equation model in a fractional-order sense with different RLC models (2×n, ∇ × n, rectangular prism×n, ×n Memristor-LC).…”

Section: Introductionmentioning

confidence: 99%

“…The authors in [19]- [22] constructed the equivalent impedance formulas for arbitrary polygon RLC networks and made progress. With extensive research on 3D RLC networks, we naturally expand the polygon network to a 3D fractional order hexagon×n RL α C β (denoted as ×n RL α C β , similar to graphene)circuit network, as shown in Figure 1, which may lay the groundwork for further research on graphene networks, nonmetallic crystal structures or carbon nanotubes.…”

Section: Introductionmentioning

confidence: 99%

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A General Study on 3D Fractional Order Hexagon × n RL_ɑ C_β Circuit Network

Cui

Chen

et al. 2022

IEEE Access

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This paper studies the electrical conductivity of a conductive material with structures similar to graphene, which consists of three basic components. The influence of various factors on the electrical conductivity of the fractional order is also analyzed. Moreover, the new fundamentals of the hexagon×n RL α C β circuit network in the fractional domain are introduced, and the general laws are summarized. First, we derive three general formulas of the equivalent impedance (Z AD (n), Z BC (n), and Z AA (n)) of the circuit network by using the matrix transform method and the difference equation model in a special case. In addition, taking Z AA (n) as an example, we systematically investigate the effects of the seven system parameters (frequency ω, the number of circuit units n, fractional order α for inductance, fractional order β for capacitance, inductance L, capacitance C, and resistance R) on the impedance characteristics of the 3D fractional order circuit network. Specifically, interesting phenomena and laws are shown by visual figures.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%