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

Abstract

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 $\times n$ ${RL}_{\alpha }C_{\beta }$ 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 $\omega $ , the number of circuit units $n$ , fractional order $\alpha $ for inductance, fractional order $\beta $ 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.

Keywords

• 3D fractional order circuit
• circuit networks
• impedance characteristics