A fractional-order multifunctional n -step honeycomb RLC circuit network
Frontiers of IT & EE(2017)
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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Key words
Honeycomb network, Equivalent transformation, Fractional differential equation, Impedance characteristics, O441.1, TN711.3
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