CN103295628A - Double-end active equivalent circuit of charge-control memristor - Google Patents

Double-end active equivalent circuit of charge-control memristor Download PDF

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CN103295628A
CN103295628A CN2013101485024A CN201310148502A CN103295628A CN 103295628 A CN103295628 A CN 103295628A CN 2013101485024 A CN2013101485024 A CN 2013101485024A CN 201310148502 A CN201310148502 A CN 201310148502A CN 103295628 A CN103295628 A CN 103295628A
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resistance
subtracter
memristor
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CN103295628B (en
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杨汝
李斌华
刘佐濂
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Guangzhou University
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Abstract

A double-end active equivalent circuit of a charge-control memristor is disclosed by the invention, and comprises a resistor R1, a resistor R2, a resistor R3, a first voltage follower, a second voltage follower, a first subtracter, a first adder, a second subtracter, a second adder, a third subtracter, an integrator, a divider, a fourth subtracter and a voltage source Uref. The current flowing through the active memristor is controlled by a feedback, the resistor R1, R2 and R3 in serial connection are used to divide voltage, and the currents flowing through the resistor R1 and the resistor R3 are controlled by respectively adding the feedback between the resistor R1 and R2, and between the resistor R2 and R3. The feedback is realized by an operational circuit based on the U-I characteristic of the memristor, and the U-I curve is made to accord with electrical characteristics of the memristor. Because the double-end active equivalent circuit is realized without control of a variable resistor, the control precision is high; and because the double ends are definite and mathematic concept is clear, the double-end active equivalent circuit can be used with other elements in serial or parallel connection by being accessed into a circuit, and the memristor with the double-end active equivalent circuit is a practical active memristor.

Description

The active equivalent electrical circuit of a kind of both-end of lotus control memristor
Technical field
The present invention relates to a kind of essential electronic element, be specifically related to the active equivalent electrical circuit of a kind of both-end of lotus control memristor.
Background technology
The concept of memristor (Memristor) is proposed in 1971 by the few Chinese bush cherry of Cai, gain the name in its resistance to the dependence by electric weight, be considered to the 4th basic circuit elements outside resistance, electric capacity and the inductance.To characteristic time memory of resistance it is had broad application prospects in model analysis, tandem circuit design, circuit devcie design with to the various fields such as emulation of organic memory behavior.
Owing to lack the support of experiment, memristor after being suggested twenties in the period of, though correlation theory has development not cause enough concerns.
A kind of nanometer both-end resistance with memory function had been found in the HP laboratory in 2008, and its electrical specification conforms to the memristor characteristic of Cai Shaotang prediction, thereby had confirmed the existence of memristor.
The memristor that the HP laboratory is found is a kind of nanoscale components and parts, manufactures the comparison difficulty, also almost can't buy this components and parts in the market.Therefore, the method for studying this memristor at present is to mainly contain: 1. build active memristor, namely by FEEDBACK CONTROL variable resistor (as photoresistance, digital regulation resistance), make variable resistor present the electrical specification of memristor.The shortcoming of this research method is the electrical specification that variable-resistance shortcoming can restrict memristor, and affected by environment big such as photoresistance, the change in resistance of digital regulation resistance is not continuous.2. set up realistic model.The shortcoming of this research method is that the variable resistor in the realistic model is Utopian, can only realize in emulation, may realize in actual experiment hardly.3. realize the electrical specification of memristor by logical circuit, computing circuit.From present document, this active memristor does not have clear and definite both-end definition, but namely can not be equivalent to the both-end element in the place in circuit fully, such as connecting with other element.
Summary of the invention
The objective of the invention is to overcome above-mentioned the deficiencies in the prior art, a kind of equivalent electrical circuit of active memristor is provided.The present invention does not use variable resistor, thereby overcome the influence that variable-resistance shortcoming causes active memristor, simultaneously, circuit structure of the present invention, clear and definite both-end definition and mathematical concept are arranged, in experiment, realize easily, can be used as the characteristic research of active memristor and directly use as the memristor components and parts.
For realizing above purpose, the technical scheme that the present invention has taked is:
The active equivalent electrical circuit of a kind of both-end of lotus control memristor, it comprises: resistance R 1, resistance R 2, resistance R 3, first voltage follower, second voltage follower, first subtracter, first adder, second subtracter, second adder, the 3rd subtracter, enlargement factor are integrator, divider, the 4th subtracter and the voltage source U of K Ref
Described resistance R 1, resistance R 2, resistance R 3 are connected successively, and the two ends of resistance R 1 are labeled as side a and b respectively, and the two ends of resistance R 3 are labeled as C end and D end respectively, and wherein the B end is the common port of resistance R 1 and resistance R 2, and the C end is the common port of resistance R 3 and resistance R 2;
Described A end is connected in the input end of second voltage follower, and described D end is connected in the input end of first voltage follower; The positive input terminal of first subtracter is connected to the output terminal of first voltage follower, and the negative input end of first subtracter is connected to the output terminal of second voltage follower; The negative input end of described the 3rd subtracter is connected in the output terminal of second voltage follower, and its positive input terminal is connected to the B end; The input end of described integrator is connected to the output terminal of the 3rd subtracter; The positive and negative input end of described the 4th subtracter is connected to voltage source U RefOutput terminal and the output terminal of integrator; The molecule input end of described divider is connected to the output terminal of first subtracter, and its denominator input end is connected to the output terminal of the 4th subtracter; One input end of described second adder is connected to the output terminal of second voltage follower, and another input end is connected to the output terminal of divider, and its output terminal is connected to the B end; The positive and negative input end of second subtracter is connected to the output terminal of first subtracter and the output terminal of divider respectively; One input end of described first adder is connected to the output terminal of second voltage follower, and its another input end is connected to the output terminal of second subtracter, and its output terminal is connected to the C end.
The resistance of described resistance R 3 and resistance R 1 equates.
The method that the present invention realizes is the electric current that flows through active memristor by FEEDBACK CONTROL, resistance R 1, R2, the R3 dividing potential drop of 3 series connection have been used, add feedback between resistance R 1 and the resistance R 2 and control the electric current that flows through resistance R 1, add feedback between resistance R 2 and the resistance R 3 and control the electric current that flows through resistance R 3, add the feasible electric current I that flows through resistance R 1, R3 of voltage follower simultaneously 1, I 3Flow through the electric current at memristor two ends exactly.Feedback is the U-I characteristic according to memristor, realizes by computing circuit, makes it meet the electrical specification of memristor.
The present invention compared with prior art has following advantage: 1. do not realize by the control variable resistor, be not subjected to the influence of variable-resistance shortcoming, the control accuracy height; 2. not only can realize in emulation, and also can realize in actual experiment, be a kind of practicable active memristor; 3. both-end is clear and definite, and mathematical concept is clear, but uses with other element serial or parallel connection in the place in circuit.
Description of drawings
Fig. 1 is the structured flowchart of the active equivalent electrical circuit embodiment of a kind of both-end of lotus control memristor of the present invention;
Fig. 2 a is the passive memristor that the HP laboratory is found;
Fig. 2 b is the equivalent electrical circuit of active memristor among the embodiment of Fig. 1;
Fig. 3 is a kind of realization circuit theory diagrams of the embodiment of Fig. 1;
Fig. 4 is when Fig. 3 circuit is carried out emulation, after the two ends of active memristor apply sine wave, and the U-I family curve of this active memristor;
The figure that oscillograph is seen in Fig. 5 actual experiment.
Wherein: 2, voltage follower; 3, voltage follower; 4, subtracter; 5, totalizer; 6, subtracter; 7, totalizer; 8, subtracter; 9, integrator; 10, divider; 11, subtracter.
Embodiment
Below in conjunction with the drawings and specific embodiments content of the present invention is described in further details.
Embodiment:
Please refer to Fig. 1, the active equivalent electrical circuit of a kind of both-end of lotus control memristor, this equivalence circuit comprises that resistance R 1, resistance R 2, resistance R 3, voltage follower 2, voltage follower 3, subtracter 4, totalizer 5, subtracter 6, totalizer 7, subtracter 8, enlargement factor are integrator 9, divider 10, subtracter 11 and the voltage source U of K RefDescribed resistance R 1, resistance R 2, resistance R 3 are connected successively, the two ends of resistance R 1 are labeled as side a and b respectively, the two ends of resistance R 3 are labeled as C end and D end respectively, wherein the B end is the common port of resistance R 1 and resistance R 2, the C end is the common port of resistance R 3 and resistance R 2, and D end and A end have represented two ports (being respectively M end and N end) of the active memristor of equivalence respectively.The A end is connected in the input end of voltage follower 3, and the D end is connected in the input end of voltage follower 2; The positive input terminal of subtracter 4 is connected to the output terminal of voltage follower 2, and the negative input end of subtracter 4 is connected to the output terminal of voltage follower 3; The negative input end of described subtracter 8 is connected in the output terminal of voltage follower 3, and its positive input terminal is connected to the B end; The input end of described integrator 9 is connected to the output terminal of subtracter 8; The positive and negative input end of described subtracter 11 is connected to voltage source U RefOutput terminal and the output terminal of integrator 9; The molecule input end of described divider 10 is connected to the output terminal of subtracter 4, and its denominator input end is connected to the output terminal of subtracter 11; One input end of described totalizer 7 is connected to the output terminal of voltage follower 3, and another input end is connected to the output terminal of divider 10, and its output terminal is connected to the B end; The positive and negative input end of subtracter 6 is connected to the output terminal of subtracter 4 and the output terminal of divider 10 respectively; One input end of described totalizer 5 is connected to the output terminal of voltage follower 3, and its another input end is connected to the output terminal of subtracter 6, and its output terminal is connected to the C end.
The voltage that we define the A end is U A, the voltage of B end is U B, the voltage of C end is U C, the voltage of D end is U D, the voltage at M, N two ends is U i, the voltage of B end and A end is U 1, the voltage of D end and C end is U 3, the voltage of D end and A end is identical with the voltage at M, N two ends also to be U i, voltage source U RefOutput voltage be U Ref, so the output voltage=U of subtracter 8 B-U A=U 1, the output voltage=U of subtracter 4 D-U A=U i
By calculating as can be known: the output voltage of integrator 9=K ∫ U 1Dt(K is the enlargement factor of integrator 9), the output voltage=U of subtracter 11 Ref-K ∫ U 1Dt, the output voltage of divider 10
Figure BDA00003104916000041
The output voltage of totalizer 7 = U A + U i U ref - K ∫ U 1 dt = U B , The output voltage of subtracter 6 = U i - U i U ref - K ∫ U 1 dt , The output voltage of totalizer 5 = U A + U i - U i U ref - K ∫ U 1 dt = U C .
In above-mentioned formula
Figure BDA00003104916000045
Can push away the electric current of the resistance R 1 of flowing through i 1 = U B - U A R 1 = U i U ref R 1 - K R 1 ∫ U 1 dt = U i U ref R 1 - K R 1 R 1 ∫ U 1 R 1 dt = U i U ref R 1 - K R 1 R 1 ∫ i 1 dt - - - ( 1 )
Following formula (1) is the U-I characteristic of the active memristor of the present invention.
In conjunction with Fig. 2 a, the electronics mobile behavior complexity of passive memristor inside, the HP laboratory is derived at R after it is simplified ON＜＜R OFFThe resistance M of memristor with the pass of the electric charge q that flows through is under the condition:
M = R OFF - μ V R ON R OFF D 2 q - - - ( 2 )
Wherein, R ONAnd R OFFRepresent doped region and the resistance of doped region not respectively, D is the material TiO of memristor 2Total length, μ vBe the migration rate of particle, these parameters depend on material therefor, and when material has determined, these parameters have also just determined, can be considered constant.So can make E=R OFF, So (2) but in the formula relation abbreviation of resistance M and q be M=E – Fq, obviously resistance M is determined by electric charge q, so the passive memristor that the HP laboratory is found is a kind of lotus control memristor.
Its U-I closes i = U M = U E - Eq = U E - F ∫ idt - - - ( 3 )
Formula (1) formula and formula (3) above the contrast are as long as the formula of order (1) U RefR 1=E, KR 1R 1=F can satisfy the U-I relation of memristor, at this moment the i in (1) formula 1Satisfy the U-I relation of memristor.
Voltage follower plays buffer action, the feasible current i that flows through resistance R 1 1Equal to flow through the current i of this active memristor N end N, i.e. i N=i 1So current i of N end NSatisfy the U-I relation of memristor.
At the other end M of active memristor end, for resistance R 3, because U i=U D– U A, i.e. U D=U i+ U A, C end feedback makes U C = U A + U i - U i U ref -K∫ U 1 dt , So both end voltage of R3 U 3 = U D - U C = U i U ref - K ∫ U 1 dt .
As seen, when the both end voltage of resistance R 3 equates with the both end voltage of resistance R 1, even R 3=R 1, i is then arranged 3=i 1(i in the formula 3Be the electric current of the resistance R 3 of flowing through).Under the effect of voltage follower, i is arranged M=i 3, i.e. i M=i 3=i 1=i NSo current i of M end MSatisfy the U-I relation of memristor.
The electric current at two ends that is the equivalent electrical circuit of active memristor all satisfies the U-I relation of memristor, and the electric current that flows through two ends equates that these electric currents that equate represent that with i i=i is then arranged M=i 3=i 1=i N
The active schematic equivalent circuit of both-end is shown in Fig. 2 a and Fig. 2 b.M end and N end in M end among Fig. 2 b and the N end difference corresponding diagram 1; Flow through the i=i in the current i corresponding diagram 1 that M holds and N holds among Fig. 2 b M=i NThe active memristor of Fig. 1 description just can be represented with Fig. 2 b so, and the active memristor that obvious Fig. 2 b represents satisfies the U-I relation of memristor in the formula (3).Passive memristor among Fig. 2 a (as the memristor of HP laboratory discovery), its resistance M can represent that its U-I relation can be represented with (3) formula with formula (2).Definition by resistance
Figure BDA00003104916000054
As can be known, if the U-I relation of the voltage between two ports and the electric current that flows through these two ports has determined that its equivalent resistance has also just been determined so.If the respectively corresponding M end of X end and Y end and N end, Fig. 2 a has identical U-I relation with Fig. 2 b so, that is to say that Fig. 2 b is a kind of equivalent electrical circuit of Fig. 2 a.
Fig. 3 is the circuit of the theory diagram of Fig. 1 according to the present invention realization of building.Wherein, the voltage follower 2 in amplifier U11 and the peripheral circuit corresponding diagram 1 thereof, the voltage follower 3 in amplifier U12 and the peripheral circuit corresponding diagram 1 thereof, U RefVoltage source U in the corresponding diagram 1 Ref Subtracter 4 in amplifier U14 and the peripheral circuit corresponding diagram 1 thereof, subtracter 6 in amplifier U15 and the peripheral circuit corresponding diagram 1 thereof and the combination of totalizer 5, subtracter 8 in amplifier U16 and the peripheral circuit corresponding diagram 1 thereof, integrator 9 in amplifier U17 and the peripheral circuit corresponding diagram 1 thereof, subtracter 11 in amplifier U18 and the peripheral circuit corresponding diagram 1 thereof, the totalizer 7 in amplifier U19 and the peripheral circuit corresponding diagram 1 thereof, and do not describing in detail here for the annexation of circuit.
In each resistance value among Fig. 3 and the integrator 9 capacitance of capacitor C can be as required the passive memristor of equivalence adjust; In the present embodiment, each amplifier all can realize with chips such as LM741CN; Divider can be formed by multiplier such as AD633JN and amplifier, also can be with special divider chip.The supply voltage that each chip needs depends on the voltage that puts on active memristor two ends, and the voltage at two ends that puts on active memristor is more high, and the supply voltage that chip needs is just more high.The output voltage of integrator will have ceiling restriction, and this point can realize by limiting its supply voltage.The initial resistance of the equivalence of this active memristor depends on the initial voltage at the capacitor C two ends in the integrator.
When Fig. 3 circuit is carried out emulation, with ± the chip power supply of 12V (wherein the supply voltage of integrator be ± 4V), the initial voltage of capacitor C is-4V, it is 4V that the two ends of this active memristor are applied an amplitude, frequency is the sine wave of 1Hz, obtains its U-I family curve as shown in Figure 4.Also can see by oscillograph in the experiment, see Fig. 5.By Fig. 4 and Fig. 5 as seen, its U-I relation meets the electrical specification of memristor.
Above-listed detailed description is at the specifying of possible embodiments of the present invention, and this embodiment is not in order to limiting claim of the present invention, and the equivalence that all the present invention of disengaging do is implemented or change, all should be contained in the claim of this case.

Claims (2)

1. lotus is controlled the active equivalent electrical circuit of a kind of both-end of memristor, it is characterized in that it comprises: resistance R 1, resistance R 2, resistance R 3, first voltage follower (2), second voltage follower (3), first subtracter (4), first adder (5), second subtracter (6), second adder (7), the 3rd subtracter (8), enlargement factor are integrator (9), divider (10), the 4th subtracter (11) and the voltage source U of K Ref
Described resistance R 1, resistance R 2, resistance R 3 are connected successively, and the two ends of resistance R 1 are labeled as side a and b respectively, and the two ends of resistance R 3 are labeled as C end and D end respectively, and wherein the B end is the common port of resistance R 1 and resistance R 2, and the C end is the common port of resistance R 3 and resistance R 2;
Described A end is connected in the input end of second voltage follower (3), and described D end is connected in the input end of first voltage follower (2); The positive input terminal of first subtracter (4) is connected to the output terminal of first voltage follower (2), and the negative input end of first subtracter (4) is connected to the output terminal of second voltage follower (3); The negative input end of described the 3rd subtracter (8) is connected in the output terminal of second voltage follower (3), and its positive input terminal is connected to the B end; The input end of described integrator (9) is connected to the output terminal of the 3rd subtracter (8); The positive and negative input end of described the 4th subtracter (11) is connected to voltage source U RefOutput terminal and the output terminal of integrator (9); The molecule input end of described divider (10) is connected to the output terminal of first subtracter (4), and its denominator input end is connected to the output terminal of the 4th subtracter (11); One input end of described second adder (7) is connected to the output terminal of second voltage follower (3), and another input end is connected to the output terminal of divider (10), and its output terminal is connected to the B end; The positive and negative input end of second subtracter (6) is connected to the output terminal of first subtracter (4) and the output terminal of divider (10) respectively; One input end of described first adder (5) is connected to the output terminal of second voltage follower (3), and its another input end is connected to the output terminal of second subtracter (6), and its output terminal is connected to the C end.
2. the active equivalent electrical circuit of a kind of both-end of lotus control memristor according to claim 1 is characterized in that the resistance of described resistance R 3 and resistance R 1 equates.
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CN104134383A (en) * 2014-07-25 2014-11-05 华北电力大学（保定） Experimental device for simulating memory resistor element
CN104134383B (en) * 2014-07-25 2017-01-04 华北电力大学（保定） A kind of experimental provision for simulating memristor element
CN108172254A (en) * 2018-01-02 2018-06-15 深圳璞芯智能科技有限公司 A kind of Larger Dynamic range floats ground memristor equivalence element and non-linear controllable simulation resistance
CN108846215A (en) * 2018-06-21 2018-11-20 成都师范学院 A kind of extremely simple floating ground lotus control memristor circuit simulation model
CN108875204A (en) * 2018-06-15 2018-11-23 成都师范学院 Sensor circuit simulation model is recalled in a kind of extremely simple floating ground lotus control
CN109672516A (en) * 2017-10-13 2019-04-23 西华大学 A kind of lotus control memristor chaos circuit
CN111327286A (en) * 2020-03-05 2020-06-23 杭州电子科技大学 Mechanical load control memristor based on hardware integral control

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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104134383A (en) * 2014-07-25 2014-11-05 华北电力大学（保定） Experimental device for simulating memory resistor element
CN104134383B (en) * 2014-07-25 2017-01-04 华北电力大学（保定） A kind of experimental provision for simulating memristor element
CN109672516A (en) * 2017-10-13 2019-04-23 西华大学 A kind of lotus control memristor chaos circuit
CN108172254A (en) * 2018-01-02 2018-06-15 深圳璞芯智能科技有限公司 A kind of Larger Dynamic range floats ground memristor equivalence element and non-linear controllable simulation resistance
CN108172254B (en) * 2018-01-02 2020-12-11 深圳璞芯智能科技有限公司 Large-dynamic-range floating memristor equivalent element and nonlinear controllable analog resistor
CN108875204A (en) * 2018-06-15 2018-11-23 成都师范学院 Sensor circuit simulation model is recalled in a kind of extremely simple floating ground lotus control
CN108875204B (en) * 2018-06-15 2022-04-26 成都师范学院 Extremely simple floating ground load control memory sensor circuit simulation model
CN108846215A (en) * 2018-06-21 2018-11-20 成都师范学院 A kind of extremely simple floating ground lotus control memristor circuit simulation model
CN108846215B (en) * 2018-06-21 2022-04-26 成都师范学院 Extremely simple floating ground load control memristor circuit simulation model
CN111327286A (en) * 2020-03-05 2020-06-23 杭州电子科技大学 Mechanical load control memristor based on hardware integral control

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