电路元件周期表——蔡氏周期表与新型记忆元件

Periodic table of circuit elements-Chua's periodic table and new memory elements

在介绍蔡氏周期表的基础上,给出已有电路元件(电阻、电容、电感、忆阻、忆容、忆感、分抗和分忆抗元等)在周期表中的位置。近年来,“分数阶忆阻”的概念开始逐渐出现在文献中,但其概念并不统一。本文将已有的分数阶忆阻及电路总结为4种,并确定对应的元件在蔡氏周期表中的位置。分数阶积分是表征有损记忆的有力工具,本文不仅给出电路元件禀赋关系统一表示式,还给出分数阶积分控制式记忆元件——电流分数阶积分控制式忆容(CFMC)、电压分数阶积分控制式忆容(VFMC)、电流分数阶积分控制式忆感(CFMI)、电压分数阶积分控制式忆感(VFMI)、电流分数阶积分控制式分忆抗(CFFM)、电压分数阶积分控制式分忆抗(VFFM)等的定义,并给出部分分数阶积分控制式记忆元件的运算结构图。

Based on the introduction of Chua's periodic table,the position of the existing circuit elements(resistor,capacitor,inductor,memristor,memcapacitor,meminductor,fractor and fracmemristor)in the periodic table are given.In recent years,the concept of Fractional Order Memristor(FOMR)has been developed,but the use of this name is not consistent.In this paper,the existing FOMR include circuit are summarized into four types,and the locations of the elements in Chua's periodic table are determined.Fractional integration is a powerful tool to represent memory loss.This paper not only gives the unified constitutive relation expressions for circuit elements,but also gives the definitions for fractional integral control type memory elements―Current Fractional integral controlled Memcapacitor(CFMC),Voltage Fractional integral controlled Memcapacitor(VFMC),Current Fractional integral controlled Meminductor(CFMI),Voltage Fractional integral controlled Meminductor(VFMI),and Current Fractional integral controlled Fracmemristor(CFFM),and Voltage Fractional integral controlled Fracmemristor(VFFM),etc.In addition,the operation structure diagrams of some fractional integral control memory elements are given,and their characteristic curves are analyzed theoretically.