| Memristor,memcapacitor and meminductor are a class of nonlinear elements with memory characteristics,collectively referred to as memory elements.Memory elements are widely used in different fields due to their unique memory and non-linear characteristics.However,solid-state devices for memory elements are difficult to obtain,so constructing simpler,more efficient and accurate equivalent circuit models for memory elements instead of solid-state devices has become one of the hot topics of current research.The modeling of memory elements is the basis for their theoretical analysis and the design of applied circuits,and the fractional-order modeling of memory elements better reflects the memory characteristics of memory elements and enables the described memory elements to more closely approximate the characteristics of actual circuits.This thesis constructs a universal interface circuit that can implement three different types of fractional-order memory elements based on the theory of memory elements and the theory of fractional calculus.In addition,in order to explore the characteristics of fractional-order memory elements and their applications in nonlinear circuit systems more conveniently,Simulink & Simscape physical models of fractional-order memory elements are constructed,and new relaxation oscillator circuits are built based on the physical models of fractional-order memcapacitor and fractional-order memristor respectively,so that the oscillation frequency and duty cycle of the oscillator circuits can be more controllable.The main innovations and research contents of this thesis are summarized as follows:(1)In order to facilitate subsequent research on fractional-order memory elements,a universal floating equivalent circuit emulator of fractional-order memory elements(including fractional-order memristor,fractional-order memcapacitor,and fractional-order meminductor)composed of existing elements is proposed.With the overall structure of the circuit unchanged,the emulator can implement three different types of fractional-order memory element equivalent circuits by simply replacing two circuit elements(a resistor,a capacitor or an inductor)in the corresponding positions.The proposed circuit emulator utilizes fewer active and passive elements,which is not only low cost and easy to construct,but also provides convenience for subsequent application studies.In this thesis,the effectiveness and correctness of the proposed circuit emulators is verified by PSPICE simulation and PCB hardware experiments.(2)In order to study the characteristics and potential applications of fractional-order memory elements more conveniently,Simulink & Simscape physical models of fractional-order memory elements with electrical characteristics are built based on the theoretical basis of mathematical models of fractional-order memory elements,and new relaxation oscillator circuits are built based on the physical models of fractional-order memcapacitor and fractionalorder memristor,respectively.The effect of different orders on the dynamic characteristics of the nonlinear system of oscillator is also discussed and analyzed by Simscape physical simulation. |
