Universal equivalent circuit of floating type fractional order memory element

文档序号：1889872 发布日期：2021-11-26 浏览：13次中文

阅读说明：本技术 一种浮地型分数阶记忆元件的通用等效电路 (Universal equivalent circuit of floating type fractional order memory element ) 是由尚涛甘朝晖余磊于 2021-08-26 设计创作，主要内容包括：本发明具体涉及一种浮地型分数阶记忆元件的通用等效电路。其技术方案是：浮地型分数阶记忆元件的通用等效电路由四个电流传输器和五个阻抗元件组成,结构简单,在不改变电路拓扑结构的情况下,通过改变第一阻抗元件(3)、第二阻抗元件(5)、第三阻抗元件(1)、第四阻抗元件(6)和第五阻抗元件(8)的元件类型,能将任意一种接地型分数阶记忆元件转换成任意一种浮地型分数阶记忆元件,通用性强；浮地型分数阶记忆元件的通用等效电路在端子A和端子B之间施加激励电压信号v(t)后,能够保证端子A的电流i-(1)(t)和端子B的电流i-(2)(t)相等,使用时浮地型分数阶记忆元件的通用等效电路的端子A和端子B都能与其他电路中的元件进行任意连接,灵活性高。(The invention relates to a general equivalent circuit of a floating ground type fractional order memory element. The technical scheme is as follows: the universal equivalent circuit of the floating type fractional order memory element is composed of four current transmitters and five impedance elements, is simple in structure, can convert any one grounding type fractional order memory element into any one floating type fractional order memory element by changing the element types of a first impedance element (3), a second impedance element (5), a third impedance element (1), a fourth impedance element (6) and a fifth impedance element (8) under the condition of not changing the topological structure of the circuit, and is strong in universality; the universal equivalent circuit of the floating type fractional order memory element can ensure the current i of the terminal A after applying an excitation voltage signal v (t) between the terminal A and the terminal B 1 (t) and the current i at the terminal B 2 And (t) is equal, and when the floating type fractional order memory element is used, the terminal A and the terminal B of the universal equivalent circuit of the floating type fractional order memory element can be randomly connected with elements in other circuits, so that the flexibility is high.)

1. A general equivalent circuit of a floating type fractional order memory element is characterized in that the general equivalent circuit of the floating type fractional order memory element is composed of a third impedance element (1), a first current transmitter (2), a first impedance element (3), a second current transmitter (4), a second impedance element (5), a fourth impedance element (6), a fourth current transmitter (7), a fifth impedance element (8) and a third current transmitter (9); the universal equivalent circuit of the floating type fractional order memory element is respectively provided with a terminal A of the universal equivalent circuit of the floating type fractional order memory element, a terminal B of the universal equivalent circuit of the floating type fractional order memory element and a terminal GND of the universal equivalent circuit of the floating type fractional order memory element;

the terminal A of the general equivalent circuit of the floating type fractional order memory element is connected with the terminal E1i of the first current conveyor (2), the terminal E1o of the first current conveyor (2) is connected with the terminal Z11 of the first impedance element (3), the terminal E1-of the first current conveyor (2) is connected with the terminal Z31 of the third impedance element (1), the terminal E1+ of the first current conveyor (2) is connected with the terminal E4o of the fourth current conveyor (7), the terminal E4-of the fourth current conveyor (7) is connected with the terminal Z52 of the fifth impedance element (8), the terminal E4i of the fourth current conveyor (7) is connected with the terminal Z42 of the fourth impedance element (6), the terminal E4+ of the fourth current conveyor (7) is connected with the terminal E2o of the second current conveyor (4);

the terminal B of the general equivalent circuit of the floating type fractional order memory element is connected with the terminal E3i of a third current transmitter (9), the terminal E3-of the third current transmitter (9) is connected with the terminal Z32 of a third impedance element (1), the terminal E3o of the third current transmitter (9) is connected with the terminal E2+ of a second current transmitter (4), the terminal E2-of the second current transmitter (4) is connected with the terminal Z12 of a first impedance element (3), and the terminal E2i of the second current transmitter (4) is connected with the terminal Z21 of a second impedance element (5);

the terminal GND of the general equivalent circuit of the floating type fractional order memory element is respectively connected with the terminal Z22 of the second impedance element (5), the terminal E3 of the third current transmitter (9), the terminal Z41 of the fourth impedance element (6) and the terminal Z51 of the fifth impedance element (8);

the first impedance element (3) is one of a resistor, a capacitor and an inductor,

the third impedance element (1) is one of a resistor, a capacitor and an inductor,

the second impedance element (5) is one of a resistor, a capacitor, an inductor and a grounded fractional order memory element,

the fourth impedance element (6) is one of a resistor, a capacitor, an inductor and a grounded fractional order memory element,

the fifth impedance element (8) is one of a resistor, a capacitor, an inductor and a grounding fractional order memory element;

an equivalent impedance Z between the terminal A of the general equivalent circuit of the floating type fractional order memory element and the terminal B of the general equivalent circuit of the floating type fractional order memory element_AB(t) is:

in formula (1): z₁Representing the impedance value of the first impedance element (3),

Z₂representing the impedance value of the second impedance element (5),

Z₃representing the impedance value of the third impedance element (1),

Z₄representing the impedance value of the fourth impedance element (6),

Z₅represents the impedance value of the fifth impedance element (8);

a) when one of the following conditions is met, the general equivalent circuit of the floating type fractional order memory element is an equivalent circuit of a floating type fractional order memristor:

condition 1: the fifth impedance element (8) is of a grounded typeThe fractional order memristor comprises a first impedance element (3) which is one of a resistor, a capacitor and an inductor, a second impedance element (5) which is one of a resistor, a capacitor and an inductor, a third impedance element (1) which is one of a resistor, a capacitor and an inductor, a fourth impedance element (6) which is one of a resistor, a capacitor and an inductor,dimensionless;

condition 2: the second impedance element (5) is a grounding fractional order memory capacitor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fourth impedance element (6) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 3: the fourth impedance element (6) is a grounding fractional order memory capacitor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 4: the fifth impedance element (8) is a grounded fractional order memory inductor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, and the fourth impedance element (6) is one of a resistor, a capacitor and an inductorOne of a resistor, a capacitor and an inductor,is measured in the following dimension

b) When one of the following conditions is met, the general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of a floating type fractional order memory capacitor:

condition 1: the second impedance element (5) is a grounding fractional order memristor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fourth impedance element (6) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 2: the fourth impedance element (6) is a grounding fractional order memristor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 3: the fifth impedance element (8) is a grounding fractional order memcapacitor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor,the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fourth impedance element (6) is one of a resistor, a capacitor and an inductor,dimensionless;

condition 4: the second impedance element (5) is a grounding fractional order memory inductor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fourth impedance element (6) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 5: the fourth impedance element (6) is a grounding fractional order memory sensor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

c) When one of the following conditions is met, the general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of a floating type fractional order memory sensor:

condition 1: the fifth impedance element (8) is a grounding fractional order memristor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor, and the third impedance element (1) is one of a resistor, a capacitor and an inductorThe fourth impedance element (6) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 2: the second impedance element (5) is a grounding fractional order memory capacitor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fourth impedance element (6) is one of a resistor, a capacitor and an inductor, the fifth impedance element (8) is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 4: the fifth impedance element (8) is a grounding fractional order memory sensor, the first impedance element (3) is one of a resistor, a capacitor and an inductor, the second impedance element (5) is one of a resistor, a capacitor and an inductor, the third impedance element (1) is one of a resistor, a capacitor and an inductor, the fourth impedance element (6) is one of a resistor, a capacitor and an inductor,and no dimension is required.

Technical Field

The invention belongs to the technical field of equivalent circuits of memory elements. In particular to a general equivalent circuit of a floating type fractional order memory element.

Background

In 2009, based on Memristors, professor zeriana zeyland Ventra et al proposed the concept of memcapacitor and meminductor and called Memory Elements (Ventra M D, persin Y V, Chua L o. circuit Elements With Memory: memrisors, memcapagonists, and memmicroductors [ J ] Proceedings of the IEEE,2009,97(10): 1717-1724), where Memristors characterize the relationship of magnetic flux and charge, Memcapacitors characterize the relationship of integral of charge and magnetic flux, and Meminductors characterize the relationship of integral of magnetic flux and charge. Due to the limitation of severe experimental environment and precise nanotechnology, only the physical preparation of the memristor is successful at present, but the commercial production is not realized, and the physical preparation of the memristor and the memory inductor is not realized. Therefore, in order to facilitate the analysis and research of the characteristics of the memory elements and the related applications thereof by the wide scientific researchers, designing the equivalent circuit to realize different memory elements becomes a convenient and efficient method.

In 2013, Yang Ru et al invented a double-end active equivalent circuit (CN103297026A) patent technology of a magnetic control memristor; in 2016, the Wang Guangxi et al invented "an equivalent circuit of magnetic control memory container" (CN105373677A) patent technology; in 2018, the patent technologies of 'an equivalent circuit of a fractional order memristor' (CN108319797A), 'an equivalent circuit of a fractional order memcapacitor (CN 108334700A)' and 'an equivalent circuit of a fractional order meminductor' (CN108509704A) were invented by Ganhui et al in turn; in 2019, Yuan Fang et al invented a patent technology of a quadratic curve memory sensor equivalent analog circuit (CN 109885858A). These equivalent circuits are single type memory devices implemented by using a large number of operational amplifiers and resistance-capacitance devices, and the circuits are complex and not flexible enough. Therefore, it is a new focus of current research to realize an equivalent circuit with a simple circuit structure and capable of completing the conversion between memory elements.

An LDR memristor equivalent circuit is designed by the people of X, Y, Wang, et al (Wang X Y, Fitch A L, Iu H C, et al, design of a memcapacitor based on a memrisor [ J ]. Physics Letters A,2012,376(4):394 and 399.), and then a memcapacitor circuit is obtained according to the conversion relation between the memristor and the memcapacitor. A memristor equivalent circuit model is established by utilizing the controllability of the resistance value of a photoresistor by a novel memristor equivalent model [ J ] reported in physics, 2013,62(15):158501-1-158501-10 ] based on an analog circuit, and then the memristor equivalent circuit is obtained according to the conversion relation between the memristor and the memristor. Wu Meng Wen et al (Wu Meng Wen, Ganhui, Wu Yuxin. a memristor-based memcapacitor model [ J ] microelectronics and computer, 2015,000(011):166 + 171.) designed an equivalent circuit for converting the memristor into the memcapacitor according to the linear conversion relationship between the memristor and the memcapacitor. These equivalent circuits only realize a conversion relationship between the memory elements, and the converted memory elements are all grounded memory elements, which has great limitation in circuit application.

Pershin et al (Pershin Y V, Ventra M D. Memritic circuits synergistic reactors and memducors [ J ]. Electronics Letters,2010,46(7):517 and 518.) design a conversion circuit for converting a memristor into a memcapacitor and a meminductor according to the conversion relationship of the memristor, the memcapacitor and the meminductor. Although the equivalent circuit realizes two conversions from a memristor to a memristor and to a memristor, the converted memory element is still in a grounding type. In 2013, Li Shi Jun et al invented a patent technology of a memristor-based floating memory container and memory sensor simulator (CN103531230A), which can convert a grounded memristor into a floating memory container and a floating memory sensor. Zehra et al (Zehra Gulru am Takran, Saba M, Ayten U E, et al. A New Universal Multi Circuit for Memcapacitor and memducor Elements [ J ]. AEU-International Journal of Electronics and Communications,2020,119:153180.) propose a CBTA-based Universal conversion Circuit that is then used to convert a grounded memristor to a floating memristor Memcapacitor and memristor.

The above equivalent circuits for completing the conversion between the memory elements are all imperfect, only one or two types of conversion between the memory elements are realized, and arbitrary conversion between the memory elements is not realized, so that the equivalent circuits are not universal and conversion between the memory elements of integer order is realized.

Currently, there is relatively little research on the equivalent circuit for switching between fractional order memory elements. In 2016, wuyuxin uses a fractional order memristor to respectively construct an equivalent circuit of a fractional order memristor and a fractional order memristor capacitor (wuyuxin, a fractional order model of the memristor and application research thereof [ D ] [ master thesis ] university of wuhan science and technology, 2016), the equivalent circuit only completes two conversions between fractional order memory elements, and the equivalent circuit also has no universality, and the conversion results in the fractional order memory elements which are still grounded.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a general equivalent circuit of a floating type fractional order memory element with a simple structure; the universal equivalent circuit can conveniently convert any one grounding fractional order memory element into any one floating fractional order memory element, and has strong universality and high flexibility.

In order to achieve the purpose, the invention adopts the technical scheme that:

the general equivalent circuit of the floating type fractional order memory element consists of a third impedance element, a first current transmitter, a first impedance element, a second current transmitter, a second impedance element, a fourth current transmitter, a fifth impedance element and a third current transmitter; the general equivalent circuit of the floating type fractional order memory element is respectively provided with a terminal A of the general equivalent circuit of the floating type fractional order memory element, a terminal B of the general equivalent circuit of the floating type fractional order memory element and a terminal GND of the general equivalent circuit of the floating type fractional order memory element.

The terminal A of the universal equivalent circuit of the floating type fractional order memory element is connected with the terminal E1i of the first current conveyor, the terminal E1o of the first current conveyor is connected with the terminal Z11 of the first impedance element, the terminal E1-of the first current conveyor is connected with the terminal Z31 of the third impedance element, the terminal E1+ of the first current conveyor is connected with the terminal E4o of the fourth current conveyor, the terminal E4-of the fourth current conveyor is connected with the terminal Z52 of the fifth impedance element, the terminal E4i of the fourth current conveyor is connected with the terminal Z42 of the fourth impedance element, and the terminal E4+ of the fourth current conveyor is connected with the terminal E2o of the second current conveyor.

The terminal B of the universal equivalent circuit of the floating type fractional order memory element is connected with the terminal E3i of a third current conveyor, the terminal E3-of the third current conveyor is connected with the terminal Z32 of a third impedance element, the terminal E3o of the third current conveyor is connected with the terminal E2+ of a second current conveyor, the terminal E2-of the second current conveyor is connected with the terminal Z12 of a first impedance element, and the terminal E2i of the second current conveyor is connected with the terminal Z21 of a second impedance element.

The terminal GND of the common equivalent circuit of the floating type fractional order memory element is connected to the terminal Z22 of the second impedance element, the terminal E3+ of the third current conveyor, the terminal Z41 of the fourth impedance element, and the terminal Z51 of the fifth impedance element, respectively.

The first impedance element is one of a resistor, a capacitor and an inductor;

the third impedance element is one of a resistor, a capacitor and an inductor;

the second impedance element is one of a resistor, a capacitor, an inductor and a grounding fractional order memory element;

the fourth impedance element is one of a resistor, a capacitor, an inductor and a grounding fractional order memory element;

the fifth impedance element is one of a resistor, a capacitor, an inductor and a grounding fractional order memory element;

the corresponding dimensions of the resistor, the capacitor and the inductor are omega, F and H in sequence.

An equivalent impedance Z between the terminal A of the general equivalent circuit of the floating type fractional order memory element and the terminal B of the general equivalent circuit of the floating type fractional order memory element_AB(t) is:

in formula (1): z₁Representing an impedance value of the first impedance element;

Z₂representing a resistance value of the second resistance element;

Z₃representing the impedance value of the third impedance element;

Z₄representing the impedance value of the fourth impedance element;

Z₅representing the impedance value of the fifth impedance element.

a) When one of the following conditions is met, the general equivalent circuit of the floating type fractional order memory element is an equivalent circuit of a floating type fractional order memristor:

condition 1: the fifth impedance element is a grounding fractional order memristor, the first impedance element is one of a resistor, a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor,and no dimension is required.

Condition 2: the second impedance element is a grounded fractional order memcapacitor, the first impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor, the fifth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 3: the fourth impedance element is a grounded fractional order memcapacitor, the first impedance element is one of a resistor, a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fifth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 4: the fifth impedance element is a grounded fractional order memory inductor, the first impedance element is a resistor,One of a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

condition 1: the second impedance element is a grounding fractional order memristor, the first impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor, the fifth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 2: the fourth impedance element is a grounding fractional order memristor, the first impedance element is one of a resistor, a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fifth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 3: the fifth impedance element is a grounded fractional order memcapacitor, the first impedance element is one of a resistor, a capacitor and an inductor,the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor,and no dimension is required.

Condition 4: the second impedance element is a grounding fractional order memory inductor, the first impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor, the fifth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

Condition 5: the fourth impedance element is a grounding fractional order memory inductor, the first impedance element is one of a resistor, a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fifth impedance element is one of a resistor, a capacitor and an inductor,is measured in the following dimension

condition 1: the fifth impedance element is a grounded fractional order memristor, the first impedance element is one of a resistor, a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, and the fourth impedance element is one of a resistor, a capacitor and an inductor,One of the inductors is used as a reference,is measured in the following dimension

Condition 4: the fifth impedance element is a grounding fractional order memory inductor, the first impedance element is one of a resistor, a capacitor and an inductor, the second impedance element is one of a resistor, a capacitor and an inductor, the third impedance element is one of a resistor, a capacitor and an inductor, the fourth impedance element is one of a resistor, a capacitor and an inductor,and no dimension is required.

Due to the adoption of the technical scheme, compared with the prior art, the invention has the following positive effects:

1. the invention can ensure the current i of the terminal A after applying the exciting voltage v (t) between the terminal A and the terminal B₁(t) and the current i at the terminal B₂(t) are equal.

2. The invention only uses four current transmitters and five impedance elements, has simple structure and is easy to realize.

3. According to the invention, under the condition of not changing a circuit topological structure, any one grounding memory element can be converted into any one floating memory element only by changing the element types of the first impedance element, the second impedance element, the third impedance element, the fourth impedance element and the fifth impedance element, so that the conversion is convenient and the universality is strong.

4. The method can replace an actual fractional order memristor, a fractional order memory container and a fractional order memory sensor to perform related characteristic analysis and application research.

5. The invention adopts a floating terrain mode, can be randomly connected with elements in other circuits, is not limited and has high flexibility.

Therefore, the structure of the invention is simple and easy to realize, the obtained universal equivalent circuit of the floating-ground type fractional order memory element can conveniently convert any one grounding type fractional order memory element into any one floating-ground type fractional order memory element, and the invention has strong universality and high flexibility.

Drawings

FIG. 1 is a schematic diagram of a structure of the present invention.

Detailed Description

The invention is further described with reference to the following figures and detailed description, without limiting the scope of the invention.

For convenience of description, the following reference numerals in the present embodiment are used together:

i₁(t) represents the current at terminal a of the universal equivalent circuit of the floating-type fractional order memory element;

i₂(t) indicating a floating type fractional order memoryThe current of terminal B of the universal equivalent circuit of the element;

i₃(t) represents the current at terminal E1-of the first current conveyor 2 and the current at terminal E3-of the third current conveyor 9;

Z₁represents the impedance value of the first impedance element 3;

Z₂represents the impedance value of the second impedance element 5;

Z₃represents the impedance value of the third impedance element 1;

Z₄represents the impedance value of the fourth impedance element 6;

Z₅represents the impedance value of the fifth impedance element 8;

V_E1+represents the voltage value of terminal E1+ of the first current conveyor 2;

V_E1-represents the voltage value of terminal E1-of the first current conveyor 2;

V_E1irepresents the voltage value of terminal E2i of the first current conveyor 2;

V_E1orepresents the voltage value of the terminal E1o of the first current conveyor 2;

V_E2+represents the value of the voltage at terminal E2+ of the second current conveyor 4;

V_E2-represents the value of the voltage at terminal E2-of the second current conveyor 4;

V_E2irepresents the value of the voltage at terminal E2i of the second current conveyor 4;

V_E2orepresents the value of the voltage at terminal E2o of the second current conveyor 4;

V_E3+represents the voltage value of terminal E3+ of the third current conveyor 9;

V_E3-represents the voltage value of terminal E3-of the third current conveyor 9;

V_E3irepresents the voltage value of terminal E3i of the third current conveyor 9;

V_E3orepresents the voltage value of terminal E3o of the third current conveyor 9;

V_E4+a voltage value representing the terminal E4+ of the fourth current conveyor 7;

V_E4-represents the voltage value of terminal E4-of the fourth current conveyor 7;

V_E4irepresents the voltage value of terminal E4i of the fourth current conveyor 7;

V_E4orepresents the voltage value of terminal E4o of the fourth current conveyor 7;

Z_AB(t) represents the equivalent impedance between the terminal A of the common equivalent circuit of the floating type fractional order memory element and the terminal B of the common equivalent circuit of the floating type fractional order memory element.

Example 1

A general equivalent circuit of a floating-ground fractional order memory device. As shown in fig. 1, the general equivalent circuit of the floating-ground fractional order memory element is composed of a third impedance element 1, a first current transmitter 2, a first impedance element 3, a second current transmitter 4, a second impedance element 5, a fourth impedance element 6, a fourth current transmitter 7, a fifth impedance element 8 and a third current transmitter 9; the general equivalent circuit of the floating type fractional order memory element is respectively provided with a terminal A of the general equivalent circuit of the floating type fractional order memory element, a terminal B of the general equivalent circuit of the floating type fractional order memory element and a terminal GND of the general equivalent circuit of the floating type fractional order memory element.

The terminal A of the universal equivalent circuit of the floating type fractional order memory element is connected with the terminal E1i of the first current conveyor 2, the terminal E1o of the first current conveyor 2 is connected with the terminal Z11 of the first impedance element 3, the terminal E1-of the first current conveyor 2 is connected with the terminal Z31 of the third impedance element 1, the terminal E1+ of the first current conveyor 2 is connected with the terminal E4o of the fourth current conveyor 7, the terminal E4-of the fourth current conveyor 7 is connected with the terminal Z52 of the fifth impedance element 8, the terminal E4i of the fourth current conveyor 7 is connected with the terminal Z42 of the fourth impedance element 6, and the terminal E4+ of the fourth current conveyor 7 is connected with the terminal E2o of the second current conveyor 4.

The terminal B of the general equivalent circuit of the floating type fractional order memory element is connected with the terminal E3i of the third current conveyor 9, the terminal E3-of the third current conveyor 9 is connected with the terminal Z32 of the third impedance element 1, the terminal E3o of the third current conveyor 9 is connected with the terminal E2+ of the second current conveyor 4, the terminal E2-of the second current conveyor 4 is connected with the terminal Z12 of the first impedance element 3, and the terminal E2i of the second current conveyor 4 is connected with the terminal Z21 of the second impedance element 5.

The terminal GND of the common equivalent circuit of the floating type fractional order memory element is connected to the terminal Z22 of the second impedance element 5, the terminal E3+ of the third current conveyor 9, the terminal Z41 of the fourth impedance element 6, and the terminal Z51 of the fifth impedance element 8, respectively.

In this embodiment, an excitation voltage signal v (t) is applied between the terminal a of the common equivalent circuit of the floating-type fractional order memory element and the terminal B of the common equivalent circuit of the floating-type fractional order memory element.

As is clear from the transmission characteristics of the current conveyor, the current at the terminal E1i of the first current conveyor 2 is equal to the current at the terminal E1-of the first current conveyor 2, and since the terminal a of the common equivalent circuit of the floating-type fractional order memory element is connected to the terminal E1i of the first current conveyor 2:

i₁(t)＝i₃(t) (1)

as is clear from the transmission characteristics of the current conveyor, the current at the terminal E3i of the third current conveyor 9 is equal to the current at the terminal E3-of the third current conveyor 9, and since the terminal B of the common equivalent circuit of the floating type fractional order memory element is connected to the terminal E3i of the third current conveyor 9:

i₂(t)＝i₃(t) (2)

as can be seen from equations (1) and (2), the currents at terminals a and B of the common equivalent circuit of the floating-type fractional order memory element are equal, that is:

i₁(t)＝i₂(t) (3)

the voltage value at terminal E1-of the first current conveyor 2 is:

V_E1-＝i₃(t)·Z₃+V_E3- (4)

from the transmission characteristics of the current conveyors, the voltage at the terminal E3-of the third current conveyor 9 is equal to the voltage at the terminal E3+ of the third current conveyor 9, so that:

V_E3-＝V_E3+＝0 (5)

by substituting formula (5) for formula (4), it is possible to obtain:

V_E1-＝i₃(t)·Z₃ (6)

as is apparent from the transmission characteristics of the current conveyors, the voltage at the terminal E1-of the first current conveyor 2 is equal to the voltage at the terminal E1+ of the first current conveyor 2, the voltage at the terminal E4o of the fourth current conveyor 7 is equal to the voltage at the terminal E4i of the fourth current conveyor 7, and since the terminal E1+ of the first current conveyor 2 and the terminal E4o of the fourth current conveyor 7 are connected, therefore:

V_E1-＝V_E1+＝V_E4o＝V_E4i (7)

when formula (7) is substituted into formula (6), it is possible to obtain:

V_E4i＝i₃(t)·Z₃ (8)

as is clear from the transmission characteristics of the current conveyor, the current at the terminal E4-of the fourth current conveyor 7 is equal to the current at the terminal E4i of the fourth current conveyor 7, and therefore the voltage at the terminal E4-of the fourth current conveyor 7 is:

from the transmission characteristics of the current conveyors, the voltage at the terminal E2i of the second current conveyor 4 is equal to the voltage at the terminal E2o of the second current conveyor 4, the voltage at the terminal E4+ of the fourth current conveyor 7 is equal to the voltage at the terminal E4-of the fourth current conveyor 7, and since the terminal E2o of the second current conveyor 4 is connected to the terminal E4+ of the fourth current conveyor 7, the voltage at the terminal E2i of the second current conveyor 4 is:

as is clear from the transmission characteristics of the current conveyor, the current at the terminal E2i of the second current conveyor 4 is equal to the current at the terminal E2-of the second current conveyor 4, and therefore:

as is apparent from the transmission characteristics of the current conveyors, the voltage at the terminal E3i of the third current conveyor 9 is equal to the voltage at the terminal E3o of the third current conveyor 9, the voltage at the terminal E2+ of the second current conveyor 4 is equal to the voltage at the terminal E2-of the second current conveyor 4, and since the terminal E2+ of the second current conveyor 4 is connected to the terminal E3o of the third current conveyor 9:

V_E2-＝V_E2+＝V_E3o＝V_E3i (12)

as is clear from the transmission characteristics of the current conveyors, the voltage at the terminal E1i of the first current conveyor 2 is equal to the voltage at the terminal E1o of the first current conveyor 2, and therefore:

V_E1o＝V_E1i (13)

by substituting formula (12) and formula (13) into formula (10), respectively, it is possible to obtain:

therefore, the equivalent impedance between the terminal a of the common equivalent circuit of the floating-type fractional order memory element and the terminal B of the common equivalent circuit of the floating-type fractional order memory element is:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fifth impedance element 8 is a grounded fractional order memristor, and the memristor value of the grounded fractional order memristor is R_m(t)；

The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The second impedance element 5 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The third impedance element 1 is a capacitor 1, and the capacitance of the capacitor 1 is C₁；

The fourth impedance element 6 is a capacitor 2, and the capacitance of the capacitor 2 is C₂。

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memristor.

At this time, the embodiment converts a grounded fractional order memristor into a floating fractional order memristor, of which the memristance R 'is recalled'_m(t) is:

example 2

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the second impedance element 5 is a grounded fractional order memcapacitor, and the memcapacitor value of the grounded fractional order memcapacitor is C_m(t)；

The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The third impedance element 1 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The fourth impedance element 6 is a resistor 3, and the resistance value of the resistor 3 is R₃；

The fifth impedance element 8 is a capacitor having a capacitance value C.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memristor.

At this time, the embodiment converts a grounded fractional order memcapacitor into a floating ground fractional order memristor, of which the memristor R 'is memred'_m(t) is:

example 3

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fourth impedance element 6 is a grounded fractional order memcapacitor, and the memcapacitor value of the grounded fractional order memcapacitor is C_m(t)；

The first impedance element 3 is a resistor, and the resistance value of the resistor is R;

the second impedance element 5 is an inductor 1, and the resistance value of the inductor 1 is L₁；

The third impedance element 1 is an inductor 2, and the resistance value of the inductor 2 is L₂；

The fifth impedance element 8 is a capacitor having a capacitance value C.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memristor.

At this time, the embodiment converts a grounded fractional order memcapacitor into a floating ground fractional order memristor, of which the memristor R 'is memred'_m(t) is:

example 4

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fifth impedance element 8 is a grounded fractional order memory inductor, and the memory inductance value of the grounded fractional order memory inductor is L_m(t)；

The first impedance element 3 is a resistor, and the resistance value of the resistor is R;

the second impedance element 5 is a capacitor 1, and the capacitance of the capacitor 1 is C₁；

The third impedance element 1 is a capacitor 2, and the capacitance of the capacitor 2 is C₂；

The fourth impedance element 6 is an inductor having an inductance value L.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memristor.

At this time, the embodiment converts a grounded fractional order memristor into a floating ground fractional order memristor, of which memristor R'_m(t) is:

example 5

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the second impedance element 5 is a grounded fractional order memristor, and the memristor value of the grounded fractional order memristor is R_m(t)；

The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The fourth impedance element 6 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The fifth impedance element 8 is a resistor 3, and the resistance value of the resistor 3 is R₃；

The third impedance element 1 is a capacitor having a capacitance value C.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory capacitor.

At this time, the embodiment converts a grounded fractional order memristor into a floating-ground fractional order memristor with a memristor capacitance value C'_m(t) is:

example 6

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fourth impedance element 6 is a grounded fractional order memristor, and the memristor value of the grounded fractional order memristor is R_m(t)；

The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The second impedance element 5 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The fifth impedance element 8 is a resistor 3, and the resistance value of the resistor 3 is R₃；

The third impedance element 1 is a capacitor having a capacitance value C.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory capacitor.

At this time, the embodiment converts a grounded fractional order memristor into a floating-ground fractional order memristor with a memristor capacitance value C'_m(t) is:

example 7

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fifth impedance element 8 is a grounded fractional order memcapacitor, and the memcapacitor value of the grounded fractional order memcapacitor is C_m(t)；

The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The second impedance element 5 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The third impedance element 1 is a capacitor 1, and the capacitance of the capacitor 1 is C₁；

The fourth impedance element 6 is a capacitor 2, and the capacitance of the capacitor 2 is C₂。

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory capacitor.

At this time, the embodiment converts a grounded fractional order memcapacitor into a floating fractional order memcapacitor with a memcapacitor value of C'_m(t) is:

example 8

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the second impedance element 5 is a grounded fractional order memory inductor with a memory inductance value L_m(t)；

The first impedance element 3 is a capacitor, and the capacitance value of the capacitor is C;

the third impedance element 1 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The fourth impedance element 6 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The fifth impedance element 8 is an inductor having a capacitance value L.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory capacitor.

At this time, the embodiment converts a grounding type fractional order memory sensor into a floating grounding type fractional order memory container with the memory content value C'_m(t) is:

example 9

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fourth impedance element 6 is a grounded fractional order memory inductor, and the memory inductance value of the grounded fractional order memory inductor is L_m(t)；

The first impedance element 3 is a capacitor, and the capacitance value of the capacitor is C;

the second impedance element 5 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The third impedance element 1 is a resistor 2, and the resistance value of the resistor 2 is R₂；

The fifth impedance element 8 is an inductor having a capacitance value L.

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory capacitor.

At this time, the embodiment converts a grounding type fractional order memory sensor into a floating grounding type fractional order memory container with the memory content value C'_m(t) is:

example 10

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the fifth impedance element 8 is a grounded fractional order memristor, and the memristor value of the grounded fractional order memristor is R_m(t)；

The first impedance element 3 is an inductor, and the inductance value of the inductor is L;

the second impedance element 5 is a resistor, and the resistance value of the resistor is R;

the third impedance element 1 is a capacitor 1, and the capacitance of the capacitor 1 is C₁；

The fourth impedance element 6 is a capacitor 2, and the capacitance of the capacitor 2 is C₂。

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory sensor.

At this time, the embodiment converts a grounded fractional order memristor into a floating fractional order memristor, the memristor is used for memorizing a sensing value L'_m(t) is:

example 11

A general equivalent circuit of a floating-ground fractional order memory device. The same as in example 1, except for the following specific kinds of 5 impedance elements:

in this embodiment, the specific types of the 5 impedance elements are respectively:

the second impedance element 5 is a grounded fractional order memcapacitor, and the memcapacitor value of the grounded fractional order memcapacitor is C_m(t)；

The first impedance element 3 is an inductor, and the inductance value of the inductor is L;

the third impedance element 1 is a capacitor, and the capacitance value of the capacitor is C;

the fourth impedance element 6 is a resistor 1, and the resistance value of the resistor 1 is R₁；

The fifth impedance element 8 is a resistor 2, and the resistance value of the resistor 2 is R₂。

The general equivalent circuit of the floating type fractional order memory element is the equivalent circuit of the floating type fractional order memory sensor.

At this time, the embodiment converts a grounded fractional order memcapacitor into a floating fractional order meminductor with a memory sensing value L'_m(t) is:

example 12