Implementation of Chain-Scaling Fractional-Order Memristors Using a Simple Circuit

Chain-scaling fractional-order memristors (fracmemristors) refers to the concept of implementing them in circuits. Despite its advantages, a few issues that require urgent attention remain, including the effect of input signals on its instantaneous valid frequency range, failure to find the corresponding time-domain electrical characteristic expression of the fracmemristor, and the use of several memristor emulators in circuit schematics. Accordingly, a simple circuit for implementing a chain-scaling fracmemristor (CSF) within a fixed valid frequency range is proposed in this paper. First, a CSF circuit configuration with a fixed valid frequency range is described. Subsequently, a simple circuit schematic of an incremental/decremental CSF is presented, and the corresponding time-domain electrical characteristic expressions of the fracmemristor are obtained. Finally, rich theoretical analysis results are obtained along with the CSF circuit implementation. The accuracy of the theoretical analysis is verified experimentally. In this study, we developed a method to achieve a CSF with a fixed valid frequency range through the replacement of all the capacitors with memcapacitors, which also facilitated the design of circuit schematics.