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基于双曲函数的通用型荷控忆阻器电路等效模型分析

孙军伟 杨建领 刘鹏 王延峰

孙军伟, 杨建领, 刘鹏, 王延峰. 基于双曲函数的通用型荷控忆阻器电路等效模型分析[J]. 电子与信息学报, 2023, 45(2): 725-733. doi: 10.11999/JEIT211317
引用本文: 孙军伟, 杨建领, 刘鹏, 王延峰. 基于双曲函数的通用型荷控忆阻器电路等效模型分析[J]. 电子与信息学报, 2023, 45(2): 725-733. doi: 10.11999/JEIT211317
SUN Junwei, YANG Jianling, LIU Peng, WANG Yanfeng. Circuit Model Analysis of General Charge-controlled Memristor Based on Hyperbolic Functions[J]. Journal of Electronics & Information Technology, 2023, 45(2): 725-733. doi: 10.11999/JEIT211317
Citation: SUN Junwei, YANG Jianling, LIU Peng, WANG Yanfeng. Circuit Model Analysis of General Charge-controlled Memristor Based on Hyperbolic Functions[J]. Journal of Electronics & Information Technology, 2023, 45(2): 725-733. doi: 10.11999/JEIT211317

基于双曲函数的通用型荷控忆阻器电路等效模型分析

doi: 10.11999/JEIT211317
基金项目: 国家自然科学基金河南联合基金重点项目(U1804262),中原青年拔尖人才项目(ZYYCYU202012154),河南省教育厅科技创人才支持项目(20HASTIT027)
详细信息
    作者简介:

    孙军伟:男,副教授,研究方向为忆阻器模型及其电路实现

    杨建领:男,硕士生,研究方向为忆阻器模型及其电路实现

    刘鹏:男,讲师,研究方向为忆阻器模型及其电路实现

    王延峰:男,教授,研究方向为忆阻器模型及其电路实现

    通讯作者:

    孙军伟 junweisun@yeah.net

  • 中图分类号: TN601; TN751.2

Circuit Model Analysis of General Charge-controlled Memristor Based on Hyperbolic Functions

Funds: The Joint Funds of the National Natural Science Foundation of China (U1804262), The Zhongyuan Top Young Talents Program (ZYYCYU202012154), Henan Province University Science and Technology Innovation Talent Support Plan (20HASTIT027)
  • 摘要: 目前,忆阻器模拟器的研究主要集中在磁控忆阻器,对荷控忆阻器模拟器的研究不多,双曲函数型的荷控忆阻器模拟器也很少涉及。因此,该文提出一种基于双曲函数的通用型荷控忆阻器模拟器。模拟器通过电压-电流的相互转换电路,实现电路中电压和电流信号之间的相互转换,再通过电路中对应的电路模块对产生的信号进行计算,最终得到通用型双曲荷控忆阻器模型。模拟器能够实现双曲正弦、双曲余弦以及双曲正切函数对应的荷控忆阻器模型。通用型双曲函数荷控忆阻器模拟器对应的等效电路,主要由运算放大器、电阻、电容、三极管等基本元件组成。分析模拟器在不同幅值以及不同频率的输入信号下的伏安特性曲线,得出荷控忆阻器模拟器符合记忆元件的基本特性。该文提出的通用型双曲函数荷控忆阻器模型,对忆阻器模型的发展具有一定的参考意义。
  • 图  1  伏安特性曲线图

    图  2  通用双曲函数荷控忆阻器模型结构框图

    图  3  双曲荷控忆阻器模型电路图

    图  4  函数信号产生电路

    图  5  双曲正弦荷控忆阻器模型仿真图

    图  6  双曲余弦荷控忆阻器模型仿真图

    图  7  双曲正切荷控忆阻器模型仿真图

    表  1  双曲正弦荷控忆阻器数学模型和电路模型

    开关
    状态
    u1状态忆阻数学模型忆阻器电路模型
    S1断开
    S2闭合
    u1$ \ne $0$M(q) = a \cdot \sinh (b + cq) + {{p} }$$\begin{gathered} M(q) = \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_8} } }\frac{ {l{R_{39} } } }{ { {R_{38} } } }{R_5} \cdot \sinh \left[\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{16} } } }{u_1} \right.\\ \left. + \frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{15} } } }\rho q\right] + \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_9} } }{R_7} \\ \end{gathered}$
    S1闭合
    S2闭合
    u1$ = $0$M(q) = a \cdot \sinh (cq + d{q^2}) + {{p} }$$\begin{gathered} M(q) = \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_8} } }\frac{ {l{R_{39} } } }{ { {R_{38} } } }{R_5} \cdot \sinh \left[\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{15} } } }\rho q \right. \\ \left. + \frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{14} } } }{\rho ^2}{q^2}\right] + \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_9} } }{R_7} \\ \end{gathered}$
    S1闭合
    S2断开
    u1$ \ne $0$M(q) = a \cdot \sinh (b + d{q^2}) + {{p} }$$\begin{gathered} M(q) = \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_8} } }\frac{ {l{R_{39} } } }{ { {R_{38} } } }{R_5} \cdot \sinh \left[\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{16} } } }{u_1} \right. \\ \left. + \frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{14} } } }{\rho ^2}{q^2}\right] + \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_9} } }{R_7} \\ \end{gathered}$
    S1闭合
    S2闭合
    u1$ \ne $0$\begin{gathered} M(q) = a \cdot \sinh (b + cq + d{q^2}) \\ {\text{ } } + {{p} } \\ \end{gathered}$$\begin{gathered} M(q) = \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_8} } }\frac{ {l{R_{39} } } }{ { {R_{38} } } }{R_5} \cdot \sinh \left[\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{16} } } }{u_1} \right. \\ \left.\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{15} } } }\rho q{\text{ + } }\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{14} } } }{\rho ^2}{q^2}\right] + \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_9} } }{R_7} \\ \end{gathered}$
    下载: 导出CSV

    表  2  双曲余弦荷控忆阻器数学模型和电路模型

    开关
    状态
    u1状态忆阻数学模型忆阻器电路模型
    S1断开
    S2闭合
    u1$ \ne $0$M(q) = a'' \cdot \cosh (b'' + c''q) + {{p} }''$$ \begin{gathered} M(q) = \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_8}}}\frac{{g{R_{33}}}}{{{R_{32}}}}{R_5} \cdot \cosh \left[\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{16}}}}{u_1} \right.\\ \left. + \frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{15}}}}\rho q \right.] + \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_9}}}{R_7} \\ \end{gathered} $
    S1闭合
    S2闭合
    u1$ = $0$\begin{gathered} M(q) = a'' \cdot \cosh (c''q + d''{q^2}) + \\ {{ p} }'' \\ \end{gathered}$$ \begin{gathered} M(q) = \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_8}}}\frac{{{\text{g}}{R_{33}}}}{{{R_{32}}}}{R_5} \cdot \cosh \left.[\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{15}}}}\rho q \right. \\ \left. + \frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{14}}}}{\rho ^2}{q^2}\right] + \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_9}}}{R_7} \\ \end{gathered} $
    S1闭合
    S2断开
    u1$ \ne $0$M(q) = a'' \cdot \cosh (b'' + d''{q^2}) + {{p} }''$$\begin{gathered} M(q) = \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_8} } }\frac{ { {\text{g} }{R_{33} } } }{ { {R_{32} } } }{R_5} \cdot \cosh \left[\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{16} } } }{u_1} \right. \\ \left. + \frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{14} } } }{\rho ^2}{q^2}\right] + \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_9} } }{R_7} \\ \end{gathered}$
    S1闭合
    S2闭合
    u1$ \ne $0$\begin{gathered} M(q) = a'' \cdot \cosh (b'' + c''q + \\ {\text{ } }d''{q^2}) + {{p} }'' \\ \end{gathered}$$ \begin{gathered} M(q) = \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_8}}}\frac{{{\text{g}}{R_{33}}}}{{{R_{32}}}}{R_5} \cdot \cosh \left[\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{16}}}}{u_1} \right.\\ \left.\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{15}}}}\rho q{\text{ + }}\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{14}}}}{\rho ^2}{q^2}\right] + \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_9}}}{R_7} \\ \end{gathered} $
    下载: 导出CSV

    表  3  双曲正切荷控忆阻器数学模型和电路模型

    开关
    状态
    u1状态忆阻数学模型忆阻器电路模型
    S1断开
    S2闭合
    u1$ \ne $0$ M(q) = a''' \cdot \tanh (b''' + c'''q) $$ \begin{gathered} M(q) = \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_8}}}\frac{{l{R_{32}}{R_{39}}}}{{{\text{g}}{R_{33}}{R_{38}}}}z{R_5} \cdot \tanh \left[\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{16}}}}{u_1} \right. \\ \left. + \frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{15}}}}\rho q \right] \\ \end{gathered} $
    S1闭合
    S2闭合
    u1$ = $0$ M(q) = a''' \cdot \tanh (c'''q + d'''{q^2}) $$ \begin{gathered} M(q) = \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_8}}}\frac{{l{R_{32}}{R_{39}}}}{{{\text{g}}{R_{33}}{R_{38}}}}z{R_5} \cdot \tanh \left[\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{15}}}}\rho q \right.\\ \left. + \frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{14}}}}{\rho ^2}{q^2}\right] \\ \end{gathered} $
    S1闭合
    S2断开
    u1$ \ne $0$ M(q) = a''' \cdot \tanh (b''' + d'''{q^2}) $$ \begin{gathered} M(q) = \frac{{{R_{12}}}}{{{R_{11}}}}\frac{{{R_{10}}}}{{{R_8}}}\frac{{l{R_{32}}{R_{39}}}}{{{\text{g}}{R_{33}}{R_{38}}}}z{R_5} \cdot \tanh \left[\frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{16}}}}{u_1} \right. \\ \left. + \frac{{{R_{24}}}}{{\left( {{R_{23}} + {R_{24}}} \right){U_T}}}\frac{{{R_{19}}}}{{{R_{18}}}}\frac{{{R_{17}}}}{{{R_{14}}}}{\rho ^2}{q^2}\right] \\ \end{gathered} $
    S1闭合
    S2闭合
    u1$ \ne $0$ \begin{gathered} M(q) = a''' \cdot \tanh (b''' + c'''q + \\ {\text{ }}d'''{q^2}) \\ \end{gathered} $$\begin{gathered} M(q) = \frac{ { {R_{12} } } }{ { {R_{11} } } }\frac{ { {R_{10} } } }{ { {R_8} } }\frac{ {l{R_{32} }{R_{39} } } }{ { {\text{g} }{R_{33} }{R_{38} } } }z{R_5} \cdot \tanh \left[\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{16} } } }{u_1} \right. \\ \left.\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{15} } } }\rho q{\text{ + } }\frac{ { {R_{24} } } }{ {\left( { {R_{23} } + {R_{24} } } \right){U_T} } }\frac{ { {R_{19} } } }{ { {R_{18} } } }\frac{ { {R_{17} } } }{ { {R_{14} } } }{\rho ^2}{q^2}\right] \\ \end{gathered}$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-11-23
  • 修回日期:  2022-05-05
  • 录用日期:  2022-05-17
  • 网络出版日期:  2022-05-20
  • 刊出日期:  2023-02-07

目录

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    返回文章
    返回