Principle and Application of Frequency-Domain Characteristic Analysis of Fractional-Order Memristor

Scaling fractional-order memristor circuit is important for realizing a fractional-order memristor. However, the effective operating-frequency range, operation order, and fractional-order memristance of the scaling fractional-order memristor circuit have not been studied thoroughly; that is, the fractional-order memristance in the effective operating-frequency range has not been calculated quantitatively. The fractional-order memristance is a similar and equally important concept as memristance, memcapacitance, and meminductance. In this paper, the frequency-domain characteristic-analysis principle of the fractional-order memristor is proposed based on the order- and F-frequency characteristic functions. The reasons for selecting the order- and F-frequency characteristic functions are explained. Subsequently, the correctness of the frequency-domain characteristic analysis using the order- and F-frequency characteristic functions is verified from multiple perspectives. Finally, the principle of the frequency-domain characteristic analysis is applied to the recently realized chain-scaling fractional-order memristor circuit. The results of this study indicate that the principle of the frequency-domain characteristic analysis of the fractional-order memristor can successfully calculate the fractional-order memristance of the chain-scaling fractional-order memristor circuit. The proposed principle of frequency-domain characteristic analysis can also be applied to mem-elements, such as memristors, memcapacitors, and meminductors. The main contribution of this study is the principle of the frequency-domain characteristic analysis of the fractional-order memristor based on the order- and F-frequency characteristic functions.