A universal equivalent circuit of a floating fractional-order memory element

Abstract

The present invention specifically relates to a universal equivalent circuit of a floating 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, and has a simple structure. Without changing the circuit topology, by changing the element types of the first impedance element (3), the second impedance element (5), the third impedance element (1), the fourth impedance element (6) and the fifth impedance element (8), any grounded type fractional-order memory element can be converted into any floating type fractional-order memory element, and has strong universality; after applying an excitation voltage signal v(t) between terminal A and terminal B, the universal equivalent circuit of the floating type fractional-order memory element can ensure that the current i1(t) of terminal A and the current i2(t) of terminal B are equal. When in use, the terminal A and the terminal B of the universal equivalent circuit of the floating type fractional-order memory element can be arbitrarily connected with elements in other circuits, and has high flexibility.

Description

Technical Field

[0001] The present invention belongs to the technical field of equivalent circuits of memory elements, and specifically relates to a universal equivalent circuit of a floating-ground fractional-order memory element. Background Art

[0002] In 2009, based on memristors, Professor Cai Shaotang and Ventra et al. proposed the concepts of memcapacitors and memductors, and called them memory elements (Ventra MD, Pershin YV, Chua L O. Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors [J]. Proceedings of the IEEE, 2009, 97 (10): 1717-1724.), where memristors represent the relationship between magnetic flux and charge, memcapacitors represent the relationship between the integral of charge and magnetic flux, and memductors represent the relationship between the integral of magnetic flux and charge. Due to the limitations of the harsh experimental environment and sophisticated nanotechnology, only memristors have been successfully prepared, but commercial production has not been achieved, and memcapacitors and memductors have not yet been prepared. Therefore, in order to facilitate the analysis and study of the characteristics of memory elements and their related applications by a large number of scientific researchers, designing equivalent circuits to realize different memory elements has become a convenient and efficient method.

[0003] In 2013, Yang Ru and others invented the patented technology of "A two-terminal active equivalent circuit of magnetically controlled memristor" (CN103297026A); in 2016, Wang Guangyi and others invented the patented technology of "An equivalent circuit of magnetically controlled memristor" (CN105373677A); in 2018, Gan Zhaohui and others successively invented the patented technologies of "An equivalent circuit of fractional-order memristor" (CN108319797A), "An equivalent circuit of fractional-order memristor (CN108334700A)" and "An equivalent circuit of fractional-order memristor" (CN108509704A); in 2019, Yuan Fang and others invented the patented technology of "Quadratic curve memristor equivalent analog circuit" (CN109885858A). These equivalent circuits are all single-type memory elements realized by using a large number of operational amplifiers and resistors and capacitors, with complex circuits and inflexible use. Therefore, realizing an equivalent circuit with a simple circuit structure and capable of completing the conversion between memory elements has become a new hotspot in current research.

[0004] XYWang et al. (Wang XY, Fitch AL, Iu HHC, et al. Design of amemcapacitor emulator based on a memristor [J]. Physics Letters A, 2012, 376 (4): 394-399.) designed an LDR memristor equivalent circuit, and then obtained the memcapacitor circuit based on the conversion relationship between the memristor and the memcapacitor. Liang Yan et al. (Liang Yan, Yu Dongsheng, Chen Hao. A new memsensor equivalent model based on analog circuits [J]. Acta Physica Sinica, 2013, 62 (15): 158501-1-158501-10.) established a memristor equivalent circuit model based on the controllability of the resistance of the photoresistor, and then obtained the memsensor equivalent circuit based on the conversion relationship between the memristor and the memsensor. Wu Mengwen et al. (Wu Mengwen, Gan Zhaohui, Wu Yuxin. A memristor model based on voltage-controlled memristor [J]. Microelectronics and Computers, 2015, 000(011): 166-171.) designed an equivalent circuit that converts a memristor into a memristor based on the linear conversion relationship between memristors and memristors. These equivalent circuits only realize one conversion relationship between memory elements, and the converted memory elements are all grounded, which has great limitations in circuit applications.

[0005] Pershin et al. (Pershin YV, Ventra M D. Memristive circuits simulate memcapacitors and meminductors [J]. Electronics Letters, 2010, 46 (7): 517-518.) designed a conversion circuit that converts a memristor into a memcapacitor and a memsensor based on the conversion relationship between memristors and memcapacitors and memsensors. Although the equivalent circuit realizes the two conversions from memristors to memcapacitors and memsensors, the converted memory elements are still grounded. In 2013, Li Zhijun et al. invented the patented technology of "A floating memcapacitor and memsensor simulator based on memristors" (CN103531230A), which can convert grounded memristors into floating memcapacitors and memsensors. Zehra et al. (Zehra Gülru am Takran, Saba M, Ayten UE, et al. A New Universal Mutator Circuit for Memcapacitor and Meminductor Elements [J]. AEU-International Journal of Electronics and Communications, 2020, 119: 153180.) proposed a universal conversion circuit based on CBTA, and then used the circuit to convert a grounded memristor into a floating memcapacitor and meminductor.

[0006] The above-mentioned equivalent circuits for completing the conversion between memory elements are all imperfect, and only realize one or two conversions between memory elements, and do not realize arbitrary conversions between memory elements. Therefore, they are not universal, and only the conversions of integer-order memory elements are realized.

[0007] At present, there are relatively few studies on equivalent circuits for conversion between fractional-order memory elements. In 2016, Wu Yuxin used fractional-order memristors to construct equivalent circuits of fractional-order memristors and fractional-order memcapacitors (Wu Yuxin. Research on a fractional-order model of memristors and their applications [D]. [Master's thesis] Wuhan University of Science and Technology, 2016). This equivalent circuit only completed two conversions between fractional-order memory elements, which is also not universal, and the converted fractional-order memory element is still a grounded fractional-order memory element. Summary of the invention

[0008] The present invention aims to overcome the defects of the prior art and has the object of providing a universal equivalent circuit of a floating-type fractional-order memory element with a simple structure; the universal equivalent circuit can conveniently convert any grounded fractional-order memory element into any floating-type fractional-order memory element and has strong versatility and high flexibility.

[0009] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is:

[0010] The universal equivalent circuit of the floating type fractional-order memory element is composed of a third impedance element, a first current conveyor, a first impedance element, a second current conveyor, a second impedance element, a fourth impedance element, a fourth current conveyor, a fifth impedance element and a third current conveyor; 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.

[0011] The terminal A of the universal equivalent circuit of the floating-ground fractional-order memory element is connected to the terminal E1i of the first current transmitter, the terminal E1o of the first current transmitter is connected to the terminal Z11 of the first impedance element, the terminal E1- of the first current transmitter is connected to the terminal Z31 of the third impedance element, the terminal E1+ of the first current transmitter is connected to the terminal E4o of the fourth current transmitter, the terminal E4- of the fourth current transmitter is connected to the terminal Z52 of the fifth impedance element, the terminal E4i of the fourth current transmitter is connected to the terminal Z42 of the fourth impedance element, and the terminal E4+ of the fourth current transmitter is connected to the terminal E2o of the second current transmitter.

[0012] Terminal B of the universal equivalent circuit of the floating-type fractional-order memory element is connected to terminal E3i of the third current transmitter, terminal E3- of the third current transmitter is connected to terminal Z32 of the third impedance element, terminal E3o of the third current transmitter is connected to terminal E2+ of the second current transmitter, terminal E2- of the second current transmitter is connected to terminal Z12 of the first impedance element, and terminal E2i of the second current transmitter is connected to terminal Z21 of the second impedance element.

[0013] The terminal GND of the universal equivalent circuit of the floating-ground 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.

[0014] The first impedance element is one of a resistor, a capacitor and an inductor;

[0015] The third impedance element is one of a resistor, a capacitor and an inductor;

[0016] The second impedance element is one of a resistor, a capacitor, an inductor and a grounded fractional-order memory element;

[0017] The fourth impedance element is one of a resistor, a capacitor, an inductor and a grounded fractional-order memory element;

[0018] The fifth impedance element is one of a resistor, a capacitor, an inductor and a grounded fractional-order memory element;

[0019] The dimensions of the resistance, capacitance and inductance are Ω, F and H respectively.

[0020] The equivalent impedance Z between the terminal A of the universal equivalent circuit of the floating type fractional-order memory element and the terminal B of the universal equivalent circuit of the floating type fractional-order memory element AB (t) is:

[0021]

[0022] In formula (1): Z1 represents the impedance value of the first impedance element;

[0023] Z2 represents the impedance value of the second impedance element;

[0024] Z3 represents the impedance value of the third impedance element;

[0025] Z4 represents the impedance value of the fourth impedance element;

[0026] Z5 represents the impedance value of the fifth impedance element.

[0027] a) When any of the following conditions is met, the universal equivalent circuit of the floating fractional-order memory element is the equivalent circuit of the floating fractional-order memristor:

[0028] 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, Dimensionless.

[0029] Condition 2: The second impedance element is a grounded fractional-order memristor, the first impedance element is a resistor, a capacitor, or an inductor, the third impedance element is a resistor, a capacitor, or an inductor, the fourth impedance element is a resistor, a capacitor, or an inductor, and the fifth impedance element is a resistor, a capacitor, or an inductor. The dimension of

[0030] Condition 3: The fourth impedance element is a grounded fractional-order memcapporat, 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 fifth impedance element is one of a resistor, a capacitor, and an inductor. The dimension of

[0031] Condition 4: 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. The dimension of

[0032] b) Whenever any of the following conditions is met, the universal equivalent circuit of the floating fractional-order memory element is the equivalent circuit of the floating fractional-order memristor:

[0033] Condition 1: the second impedance element is a grounded 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, and the fifth impedance element is one of a resistor, a capacitor, and an inductor, The dimension of

[0034] Condition 2: the fourth 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 fifth impedance element is one of a resistor, a capacitor, and an inductor. The dimension of

[0035] Condition 3: The fifth impedance element is a grounded fractional-order memcapporat, 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. Dimensionless.

[0036] Condition 4: the second impedance element is a grounded 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, and the fifth impedance element is one of a resistor, a capacitor, and an inductor. The dimension of

[0037] Condition 5: The fourth 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 fifth impedance element is one of a resistor, a capacitor, and an inductor. The dimension of

[0038] c) When any of the following conditions is met, the universal equivalent circuit of the floating fractional-order memory element is the equivalent circuit of the floating fractional-order memsensor:

[0039] 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, The dimension of

[0040] Condition 2: The second impedance element is a grounded fractional-order memristor, the first impedance element is a resistor, a capacitor, or an inductor, the third impedance element is a resistor, a capacitor, or an inductor, the fourth impedance element is a resistor, a capacitor, or an inductor, and the fifth impedance element is a resistor, a capacitor, or an inductor. The dimension of

[0041] Condition 3: The fourth impedance element is a grounded fractional-order memcapporat, 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 fifth impedance element is one of a resistor, a capacitor, and an inductor. The dimension of

[0042] Condition 4: 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. Dimensionless.

[0043] Due to the adoption of the above technical solution, the present invention has the following positive effects compared with the prior art:

[0044] 1. After applying an excitation voltage v(t) between terminal A and terminal B, the present invention can ensure that the current i1(t) of terminal A and the current i2(t) of terminal B are equal.

[0045] 2. The present invention uses only four current transmitters and five impedance elements, and has a simple structure and is easy to implement.

[0046] 3. The present invention can convert any grounded memory element into any floating memory element by simply 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 without changing the circuit topology. The conversion is convenient and the versatility is strong.

[0047] 4. The present invention can replace actual fractional-order memristors, fractional-order memcapacitors and fractional-order memsensors to conduct relevant characteristic analysis and application research.

[0048] 5. The present invention adopts a floating ground form, which can be arbitrarily connected with components in other circuits without restriction and has high flexibility.

[0049] Therefore, the present invention has a simple structure and is easy to implement. The obtained universal equivalent circuit of the floating type fractional-order memory element can conveniently convert any grounded type fractional-order memory element into any floating type fractional-order memory element, and has strong versatility and high flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A structural schematic diagram of the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods, which does not limit the protection scope of the present invention.

[0052] For the convenience of description, the marks involved in this specific implementation are first described uniformly as follows:

[0053] i1(t) represents the current at terminal A of the universal equivalent circuit of the floating-type fractional-order memory element;

[0054] i2(t) represents the current at terminal B of the universal equivalent circuit of the floating-type fractional-order memory element;

[0055] i3(t) represents the current at the terminal E1 − of the first current conveyor 2 and the current at the terminal E3 − of the third current conveyor 9;

[0056] Z1 represents the impedance value of the first impedance element 3;

[0057] Z2 represents the impedance value of the second impedance element 5;

[0058] Z3 represents the impedance value of the third impedance element 1;

[0059] Z4 represents the impedance value of the fourth impedance element 6;

[0060] Z5 represents the impedance value of the fifth impedance element 8;

[0061] V E1+ represents the voltage value of the terminal E1+ of the first current conveyor 2;

[0062] V E1- represents the voltage value of the terminal E1- of the first current conveyor 2;

[0063] V E1i represents the voltage value of the terminal E2i of the first current conveyor 2;

[0064] V E1o represents the voltage value of the terminal E1o of the first current conveyor 2;

[0065] V E2+ represents the voltage value of the terminal E2+ of the second current conveyor 4;

[0066] V E2- represents the voltage value of the terminal E2- of the second current conveyor 4;

[0067] V E2i represents the voltage value of the terminal E2i of the second current conveyor 4;

[0068] V E2o represents the voltage value of the terminal E2o of the second current conveyor 4;

[0069] V E3+ represents the voltage value of the terminal E3+ of the third current conveyor 9;

[0070] V E3- represents the voltage value of the terminal E3- of the third current conveyor 9;

[0071] V E3i represents the voltage value of the terminal E3i of the third current conveyor 9;

[0072] V E3o represents the voltage value of the terminal E3o of the third current conveyor 9;

[0073] V E4+ represents the voltage value of the terminal E4+ of the fourth current conveyor 7;

[0074] V E4- represents the voltage value of the terminal E4- of the fourth current conveyor 7;

[0075] V E4i represents the voltage value of the terminal E4i of the fourth current conveyor 7;

[0076] V E4orepresents the voltage value of the terminal E4o of the fourth current conveyor 7;

[0077] Z AB (t) represents the equivalent impedance between terminal A of the universal equivalent circuit of the floating-type fractional-order memory element and terminal B of the universal equivalent circuit of the floating-type fractional-order memory element.

[0078] Example 1

[0079] A universal equivalent circuit of a floating fractional-order memory element. Figure 1 As shown, the universal equivalent circuit of the floating type fractional-order memory element is composed of a third impedance element 1, a first current conveyor 2, a first impedance element 3, a second current conveyor 4, a second impedance element 5, a fourth impedance element 6, a fourth current conveyor 7, a fifth impedance element 8, and a third current conveyor 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.

[0080] Terminal A of the universal equivalent circuit of the floating-ground fractional-order memory element is connected to terminal E1i of the first current conveyor 2, terminal E1o of the first current conveyor 2 is connected to terminal Z11 of the first impedance element 3, terminal E1- of the first current conveyor 2 is connected to terminal Z31 of the third impedance element 1, terminal E1+ of the first current conveyor 2 is connected to terminal E4o of the fourth current conveyor 7, terminal E4- of the fourth current conveyor 7 is connected to terminal Z52 of the fifth impedance element 8, terminal E4i of the fourth current conveyor 7 is connected to terminal Z42 of the fourth impedance element 6, and terminal E4+ of the fourth current conveyor 7 is connected to terminal E2o of the second current conveyor 4.

[0081] Terminal B of the universal equivalent circuit of the floating-ground fractional-order memory element is connected to terminal E3i of the third current conveyor 9, terminal E3- of the third current conveyor 9 is connected to terminal Z32 of the third impedance element 1, terminal E3o of the third current conveyor 9 is connected to terminal E2+ of the second current conveyor 4, terminal E2- of the second current conveyor 4 is connected to terminal Z12 of the first impedance element 3, and terminal E2i of the second current conveyor 4 is connected to terminal Z21 of the second impedance element 5.

[0082] The terminal GND of the universal equivalent circuit of the floating-ground 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.

[0083] In this embodiment, an excitation voltage signal v(t) is applied between a terminal A of the universal equivalent circuit of the floating type fractional-order memory element and a terminal B of the universal equivalent circuit of the floating type fractional-order memory element.

[0084] From the transmission characteristics of the current conveyor, it can be seen that the current of the terminal E1i of the first current conveyor 2 is equal to the current of the terminal E1- of the first current conveyor 2. Since the terminal A of the universal equivalent circuit of the floating-type fractional-order memory element is connected to the terminal E1i of the first current conveyor 2, therefore:

[0085] i1(t)=i3(t) (1)

[0086] It can be seen from the transmission characteristics of the current conveyor that the current of the terminal E3i of the third current conveyor 9 is equal to the current of the terminal E3- of the third current conveyor 9. Since the terminal B of the universal equivalent circuit of the floating-type fractional-order memory element is connected to the terminal E3i of the third current conveyor 9, therefore:

[0087] i2(t)=i3(t) (2)

[0088] From equations (1) and (2), it can be seen that the currents at terminals A and B of the universal equivalent circuit of the floating-ground fractional-order memory element are equal, that is:

[0089] i1(t)=i2(t) (3)

[0090] The voltage value of the terminal E1- of the first current conveyor 2 is:

[0091] V E1- =i3(t)·Z3+V E3- (4)

[0092] It can be seen from the transmission characteristics of the current conveyor that 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, therefore:

[0093] V E3- =V E3+ =0 (5)

[0094] Substituting formula (5) into formula (4), we can get:

[0095] V E1- =i3(t)·Z3 (6)

[0096] From the transmission characteristics of the current conveyor, it can be seen that the voltage of the terminal E1- of the first current conveyor 2 is equal to the voltage of the terminal E1+ of the first current conveyor 2, and the voltage of the terminal E4o of the fourth current conveyor 7 is equal to the voltage of the terminal E4i of the fourth current conveyor 7. Since the terminal E1+ of the first current conveyor 2 and the terminal E4o of the fourth current conveyor 7 are connected, therefore:

[0097] V E1- =V E1+ =V E4o =V E4i (7)

[0098] Substituting formula (7) into formula (6), we can get:

[0099] V E4i =i3(t)·Z3 (8)

[0100] It can be seen from the transmission characteristics of the current conveyor that 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. Therefore, the voltage at the terminal E4- of the fourth current conveyor 7 is:

[0101]

[0102] It can be seen from the transmission characteristics of the current conveyor that the voltage of the terminal E2i of the second current conveyor 4 is equal to the voltage of the terminal E2o of the second current conveyor 4, and the voltage of the terminal E4+ of the fourth current conveyor 7 is equal to the voltage of the terminal E4- of the fourth current conveyor 7. Since the terminal E2o of the second current conveyor 4 is connected to the terminal E4+ of the fourth current conveyor 7, the voltage of the terminal E2i of the second current conveyor 4 is:

[0103]

[0104] From the transmission characteristics of the current conveyor, it can be seen that 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, therefore:

[0105]

[0106] It can be seen from the transmission characteristics of the current conveyor that the voltage of the terminal E3i of the third current conveyor 9 is equal to the voltage of the terminal E3o of the third current conveyor 9, and the voltage of the terminal E2+ of the second current conveyor 4 is equal to the voltage of the terminal E2- of the second current conveyor 4. Since the terminal E2+ of the second current conveyor 4 is connected to the terminal E3o of the third current conveyor 9, therefore:

[0107] V E2- =V E2+ =VE3o =V E3i (12)

[0108] From the transmission characteristics of the current conveyor, it can be seen that 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, therefore:

[0109] V E1o =V E1i (13)

[0110] Substituting equation (12) and equation (13) into equation (10), we can obtain:

[0111]

[0112] Therefore, the equivalent impedance between terminal A of the universal equivalent circuit of the floating type fractional-order memory element and terminal B of the universal equivalent circuit of the floating type fractional-order memory element is:

[0113]

[0114] In this embodiment, the specific types of the five impedance elements are:

[0115] The fifth impedance element 8 is a grounded fractional-order memristor, and the memristance value of the grounded fractional-order memristor is R m (t);

[0116] The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0117] The second impedance element 5 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0118] The third impedance element 1 is a capacitor 1, and the capacitance value of the capacitor 1 is C1;

[0119] The fourth impedance element 6 is a capacitor 2 , and the capacitance value of the capacitor 2 is C2 .

[0120] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0121] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, and its memristance value R' m (t) is:

[0122]

[0123] Example 2

[0124] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0125] In this embodiment, the specific types of the five impedance elements are:

[0126] The second impedance element 5 is a grounded fractional-order memcapacitor, and the memcapacitance value of the grounded fractional-order memcapacitor is C m (t);

[0127] The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0128] The third impedance element 1 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0129] The fourth impedance element 6 is a resistor 3, and the resistance value of the resistor 3 is R3;

[0130] The fifth impedance element 8 is a capacitor, and the capacitance value of the capacitor is C.

[0131] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0132] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristance value R' m (t) is:

[0133]

[0134] Example 3

[0135] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0136] In this embodiment, the specific types of the five impedance elements are:

[0137] The fourth impedance element 6 is a grounded fractional-order memcapacitor, and the memcapacitance value of the grounded fractional-order memcapacitor is C m (t);

[0138] The first impedance element 3 is a resistor, and the resistance value of the resistor is R;

[0139] The second impedance element 5 is an inductor 1, and the resistance value of the inductor 1 is L1;

[0140] The third impedance element 1 is an inductor 2, and the resistance value of the inductor 2 is L2;

[0141] The fifth impedance element 8 is a capacitor, and the capacitance value of the capacitor is C.

[0142] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0143] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristance value R' m (t) is:

[0144]

[0145] Example 4

[0146] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0147] In this embodiment, the specific types of the five impedance elements are:

[0148] The fifth impedance element 8 is a grounded fractional-order memristor, and the memristor value of the grounded fractional-order memristor is L m (t);

[0149] The first impedance element 3 is a resistor, and the resistance value of the resistor is R;

[0150] The second impedance element 5 is a capacitor 1, and the capacitance value of the capacitor 1 is C1;

[0151] The third impedance element 1 is capacitor 2, and the capacitance value of capacitor 2 is C2;

[0152] The fourth impedance element 6 is an inductor, and the inductance value of the inductor is L.

[0153] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0154] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristor value R' m (t) is:

[0155]

[0156] Example 5

[0157] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0158] In this embodiment, the specific types of the five impedance elements are:

[0159] The second impedance element 5 is a grounded fractional-order memristor, and the memristance value of the grounded fractional-order memristor is R m (t);

[0160] The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0161] The fourth impedance element 6 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0162] The fifth impedance element 8 is a resistor 3, and the resistance value of the resistor 3 is R3;

[0163] The third impedance element 1 is a capacitor, and the capacitance value of the capacitor is C.

[0164] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0165] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristor value C' m (t) is:

[0166]

[0167] Example 6

[0168] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0169] In this embodiment, the specific types of the five impedance elements are:

[0170] The fourth impedance element 6 is a grounded fractional-order memristor, and the memristance value of the grounded fractional-order memristor is R m (t);

[0171] The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0172] The second impedance element 5 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0173] The fifth impedance element 8 is a resistor 3, and the resistance value of the resistor 3 is R3;

[0174] The third impedance element 1 is a capacitor, and the capacitance value of the capacitor is C.

[0175] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0176] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristor value C' m (t) is:

[0177]

[0178] Example 7

[0179] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0180] In this embodiment, the specific types of the five impedance elements are:

[0181] The fifth impedance element 8 is a grounded fractional-order memcapacitor, and the memcapacitance value of the grounded fractional-order memcapacitor is C m (t);

[0182] The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0183] The second impedance element 5 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0184] The third impedance element 1 is a capacitor 1, and the capacitance value of the capacitor 1 is C1;

[0185] The fourth impedance element 6 is a capacitor 2 , and the capacitance value of the capacitor 2 is C2 .

[0186] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0187] At this time, this embodiment converts a grounded fractional-order memcapacitor into a floating fractional-order memcapacitor, and its memcapacitance value C' m (t) is:

[0188]

[0189] Example 8

[0190] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0191] In this embodiment, the specific types of the five impedance elements are:

[0192] The second impedance element 5 is a grounded fractional-order memristor, and the memristor value of the grounded fractional-order memristor is L m (t);

[0193] The first impedance element 3 is a capacitor, and the capacitance value of the capacitor is C;

[0194] The third impedance element 1 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0195] The fourth impedance element 6 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0196] The fifth impedance element 8 is an inductor, and the capacitance value of the inductor is L.

[0197] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0198] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristor value C' m (t) is:

[0199]

[0200] Example 9

[0201] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0202] In this embodiment, the specific types of the five impedance elements are:

[0203] The fourth impedance element 6 is a grounded fractional-order memristor, and the memristor value of the grounded fractional-order memristor is L m (t);

[0204] The first impedance element 3 is a capacitor, and the capacitance value of the capacitor is C;

[0205] The second impedance element 5 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0206] The third impedance element 1 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0207] The fifth impedance element 8 is an inductor, and the capacitance value of the inductor is L.

[0208] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memristor.

[0209] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, whose memristor value C' m (t) is:

[0210]

[0211] Example 10

[0212] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0213] In this embodiment, the specific types of the five impedance elements are:

[0214] The fifth impedance element 8 is a grounded fractional-order memristor, and the memristance value of the grounded fractional-order memristor is R m (t);

[0215] The first impedance element 3 is an inductor, and the inductance value of the inductor is L;

[0216] The second impedance element 5 is a resistor, and the resistance value of the resistor is R;

[0217] The third impedance element 1 is a capacitor 1, and the capacitance value of the capacitor 1 is C1;

[0218] The fourth impedance element 6 is a capacitor 2 , and the capacitance value of the capacitor 2 is C2 .

[0219] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memsensor.

[0220] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, and its memristance value L' m (t) is:

[0221]

[0222] Embodiment 11

[0223] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0224] In this embodiment, the specific types of the five impedance elements are:

[0225] The second impedance element 5 is a grounded fractional-order memcapacitor, and the memcapacitance value of the grounded fractional-order memcapacitor is C m (t);

[0226] The first impedance element 3 is an inductor, and the inductance value of the inductor is L;

[0227] The third impedance element 1 is a capacitor, and the capacitance value of the capacitor is C;

[0228] The fourth impedance element 6 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0229] The fifth impedance element 8 is a resistor 2 , and the resistance value of the resistor 2 is R2 .

[0230] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memsensor.

[0231] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, and its memristor value L' m (t) is:

[0232]

[0233] Example 12

[0234] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0235] In this embodiment, the specific types of the five impedance elements are:

[0236] The fourth impedance element 6 is a grounded fractional-order memcapacitor, and the memcapacitance value of the grounded fractional-order memcapacitor is C m (t);

[0237] The first impedance element 3 is an inductor, and the inductance value of the inductor is L;

[0238] The third impedance element 1 is a capacitor, and the capacitance value of the capacitor is C;

[0239] The second impedance element 5 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0240] The fifth impedance element 8 is a resistor 2 , and the resistance value of the resistor 2 is R2 .

[0241] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memsensor.

[0242] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, and its memristor value L' m (t) is:

[0243]

[0244] Embodiment 13

[0245] A universal equivalent circuit of a floating fractional-order memory element. Except for the specific types of the following five impedance elements, the rest is the same as in Example 1:

[0246] In this embodiment, the specific types of the five impedance elements are:

[0247] The fifth impedance element 8 is a grounded fractional-order memristor, and the memristor value of the grounded fractional-order memristor is L m (t);

[0248] The first impedance element 3 is a resistor 1, and the resistance value of the resistor 1 is R1;

[0249] The fourth impedance element 6 is a resistor 2, and the resistance value of the resistor 2 is R2;

[0250] The second impedance element 5 is a capacitor 1, and the capacitance value of the capacitor 1 is C1;

[0251] The third impedance element 1 is a capacitor 2, and the capacitance value of the capacitor 2 is C2.

[0252] Then the universal equivalent circuit of the floating-type fractional-order memory element is the equivalent circuit of the floating-type fractional-order memsensor.

[0253] At this time, this embodiment converts a grounded fractional-order memristor into a floating fractional-order memristor, and its memristance value L' m (t) is:

[0254]

[0255] Compared with the prior art, this specific implementation has the following positive effects:

[0256] 1. After applying an excitation voltage v(t) between terminal A and terminal B, this specific implementation can ensure that the current i1(t) at terminal A and the current i2(t) at terminal B are equal.

[0257] 2. This specific implementation uses only four current conveyors and five impedance elements, and has a simple structure and is easy to implement.

[0258] 3. In this specific embodiment, without changing the circuit topology, it is only necessary to change the element types of the first impedance element 3, the second impedance element 5, the third impedance element 1, the fourth impedance element 6 and the fifth impedance element 8, so that any grounded memory element can be converted into any floating memory element, which is convenient for conversion and has strong versatility.

[0259] 4. This specific implementation can replace actual fractional-order memristors, fractional-order memcapacitors and fractional-order memsensors to conduct relevant characteristic analysis and application research.

[0260] 5. This specific implementation adopts a floating ground form, which can be arbitrarily connected to components in other circuits without restrictions and has high flexibility.

[0261] Therefore, the present specific embodiment has a simple structure and is easy to implement. The obtained universal equivalent circuit of the floating-type fractional-order memory element can conveniently convert any grounded fractional-order memory element into any floating-type fractional-order memory element, and has strong versatility and high flexibility.

Claims

1. A universal equivalent circuit of a floating fractional-order memory element, characterized in that The universal equivalent circuit of the floating type fractional-order memory element is composed of a third impedance element (1), a first current conveyor (2), a first impedance element (3), a second current conveyor (4), a second impedance element (5), a fourth impedance element (6), a fourth current conveyor (7), a fifth impedance element (8) and a third current conveyor (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 universal equivalent circuit of the floating-ground type fractional-order memory element is connected to the terminal E1i of the first current conveyor (2), the terminal E1o of the first current conveyor (2) is connected to the terminal Z11 of the first impedance element (3), the terminal E1- of the first current conveyor (2) is connected to the terminal Z31 of the third impedance element (1), the terminal E1+ of the first current conveyor (2) is connected to the terminal E4o of the fourth current conveyor (7), the terminal E4- of the fourth current conveyor (7) is connected to the terminal Z52 of the fifth impedance element (8), the terminal E4i of the fourth current conveyor (7) is connected to the terminal Z42 of the fourth impedance element (6), and the terminal E4+ of the fourth current conveyor (7) is connected to the terminal E2o of the second current conveyor (4); The terminal B of the universal equivalent circuit of the floating-ground fractional-order memory element is connected to the terminal E3i of the third current conveyor (9), the terminal E3- of the third current conveyor (9) is connected to the terminal Z32 of the third impedance element (1), the terminal E3o of the third current conveyor (9) is connected to the terminal E2+ of the second current conveyor (4), the terminal E2- of the second current conveyor (4) is connected to the terminal Z12 of the first impedance element (3), and the terminal E2i of the second current conveyor (4) is connected to the terminal Z21 of the second impedance element (5); The terminal GND of the universal equivalent circuit of the floating-ground fractional-order memory element is respectively 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); 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 grounded fractional-order memory element; The equivalent impedance Z between the terminal A of the universal equivalent circuit of the floating type fractional-order memory element and the terminal B of the universal equivalent circuit of the floating type fractional-order memory element AB (t) is: In formula (1): Z1 represents the impedance value of the first impedance element (3), Z2 represents the impedance value of the second impedance element (5), Z3 represents the impedance value of the third impedance element (1), Z4 represents the impedance value of the fourth impedance element (6), Z5 represents the impedance value of the fifth impedance element (8); a) When any of the following conditions is met, the universal equivalent circuit of the floating fractional-order memory element is the equivalent circuit of the floating fractional-order memristor: Condition 1: the fifth impedance element (8) is a grounded 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, and the fourth impedance element (6) is one of a resistor, a capacitor, and an inductor, dimensionless; Condition 2: The second impedance element (5) is a grounded fractional-order memcapacitor, the first impedance element (3) is a resistor, a capacitor, or an inductor, the third impedance element (1) is a resistor, a capacitor, or an inductor, the fourth impedance element (6) is a resistor, a capacitor, or an inductor, and the fifth impedance element (8) is a resistor, a capacitor, or an inductor. The dimension of Condition 3: The fourth impedance element (6) is a grounded fractional-order memcapacitor, the first impedance element (3) is a resistor, a capacitor, or an inductor, the second impedance element (5) is a resistor, a capacitor, or an inductor, the third impedance element (1) is a resistor, a capacitor, or an inductor, and the fifth impedance element (8) is a resistor, a capacitor, or an inductor. The dimension of Condition 4: The fifth impedance element (8) is a grounded 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, and the fourth impedance element (6) is one of a resistor, a capacitor, and an inductor, The dimension of b) Whenever any of the following conditions is met, the universal equivalent circuit of the floating fractional-order memory element is the equivalent circuit of the floating fractional-order memristor: Condition 1: the second impedance element (5) is a grounded 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, and the fifth impedance element (8) is one of a resistor, a capacitor, and an inductor, The dimension of Condition 2: the fourth impedance element (6) is a grounded 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, and the fifth impedance element (8) is one of a resistor, a capacitor, and an inductor, The dimension of Condition 3: The fifth impedance element (8) is a grounded 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, and 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 grounded 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, and the fifth impedance element (8) is one of a resistor, a capacitor, and an inductor, The dimension of Condition 5: The fourth impedance element (6) is a grounded 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, and the fifth impedance element (8) is one of a resistor, a capacitor, and an inductor, The dimension of c) When any of the following conditions is met, the universal equivalent circuit of the floating fractional-order memory element is the equivalent circuit of the floating fractional-order memsensor: Condition 1: the fifth impedance element (8) is a grounded 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, and the fourth impedance element (6) is one of a resistor, a capacitor, and an inductor, The dimension of Condition 2: The second impedance element (5) is a grounded fractional-order memcapacitor, the first impedance element (3) is a resistor, a capacitor, or an inductor, the third impedance element (1) is a resistor, a capacitor, or an inductor, the fourth impedance element (6) is a resistor, a capacitor, or an inductor, and the fifth impedance element (8) is a resistor, a capacitor, or an inductor. The dimension of Condition 3: The fourth impedance element (6) is a grounded fractional-order memcapacitor, the first impedance element (3) is a resistor, a capacitor, or an inductor, the second impedance element (5) is a resistor, a capacitor, or an inductor, the third impedance element (1) is a resistor, a capacitor, or an inductor, and the fifth impedance element (8) is a resistor, a capacitor, or an inductor. The dimension of Condition 4: The fifth impedance element (8) is a grounded 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, and the fourth impedance element (6) is one of a resistor, a capacitor, and an inductor, Dimensionless.

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