Design Of Mem-Elements Emulators

Mem-elements include memristor(MR), memcapacitor(MC) and meminductor(ML), which is an extension of the classical circuit theory. In 2008, the HP Lab found memristor, which has set off a research upsurge of mem-elements. However, the fabrication process of the memristor is complex and the experimental environment is strict, and enven the memcapacitor and the meminductor have not been able to find the corresponding object. So the study of these mem-elements is mainly dependent on the computer aided circuit analysis software, and the research of mem-elements emulators becomes an important issue.This paper comprehensively discussed the mem-elements constitutive equations, then try to design the mem-elements emulators( both grounding-type and floating-type). And then memristor-memcapacitor switching circuits and memristor-meminductor switching circuits are analyzed. Finally, memristor-based memcapacitor emulators and memristor-based meminductor emulators are obtained. Furthermore, this paper make a research on the fractional-order memristor, derive the fractional-order memristor’s mathematical equation, and get a general fractional-order memristor emulator. So that we can get a variety of fractional-order memristor emulator just need to enter the appropriate input parameters to it. It is very simple, convenient and quick. Taking 0.5-order and 0.9-order fractional memristor as representative to study the fractional-order memristor, then the fractional memristor’s input and output curves, state variables curves and memristance curves have been obtained. Finally, the memristor emulator was made by using the conventional circuit elements, and verified by simulation oscilloscope,proved the designs of the memristor simulator are correct.In a word, this paper has a wide range of theoretical significance and practical value for the research of mem-elements emulators.