CN106856402A - A kind of voltage-controlled memristor simulator of modified - Google Patents
A kind of voltage-controlled memristor simulator of modified Download PDFInfo
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- CN106856402A CN106856402A CN201611201572.1A CN201611201572A CN106856402A CN 106856402 A CN106856402 A CN 106856402A CN 201611201572 A CN201611201572 A CN 201611201572A CN 106856402 A CN106856402 A CN 106856402A
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H11/00—Networks using active elements
- H03H11/46—One-port networks
Abstract
The invention discloses a kind of voltage-controlled memristor simulator of modified, including 2 operational amplifier UaAnd Ub, 2 multiplier M1And M2, 1 electric capacity C0, 3 resistance Ra、RbAnd Rc.First order operational amplifier UaVoltage follower circuit is constituted, for avoiding load effect；Second level operational amplifier UbWith resistance RaWith electric capacity C0An integrator circuit is connected and composed, integral operation, resistance R is realizedbDC voltage for avoiding integrator drifts about；Multiplier is used as the multiplying of voltage signal, finally in resistance RcTwo ends form voltage difference, flow through resistance RcElectric current be the electric current for flowing through memristor simulator.No current reverser of the present invention and without DC voltage drift, simple structure, it is easy to experimental observation can be applied to different chaos circuits and produce chaotic signals as a kind of new memristor simulator.
Description
Technical field
The present invention relates to a kind of voltage-controlled memristor simulator of modified, by operational amplifier, analog multiplier, electric capacity and resistance
Constituted Deng discrete component, realize a kind of novel broad sense memristor.
Background technology
Professor Cai Shaotang of Univ California-Berkeley is theoretically predicted except resistance, inductance and electricity within 1971
The 4th kind of basic circuit elements --- the presence of memristor held.2008, HP Lab researcher was based on metal and metal
Oxide successfully produces the physical device of memristor, and in famous magazine《Nature》On delivered this achievement, cause
Huge repercussion.Due to the unique nonlinear characteristic of memristor, it is set to have in the field such as nonlinear circuit and chaotic signal generation
Huge application prospect.But existing memristor physical device is either in technique, or be required in cost consumption compared with
High cost, this causes that it is difficult to obtain extensive use in a short time.Therefore, scientists are in research memory resistor physics realization
Meanwhile, it is also actively working to the researchs such as the equivalent circuit realization of new memristor Mathematical Modeling, numerical simulation, and memristor.
In recent years, in broad sense memristor (Generalized Memristor, GM) simulator realization in, scholars carry
The memristor simulator that such as single order diode bridge is realized, the memristor simulator that second order diode bridge is realized, based on photosensitive electricity are gone out
The broad sense memristor models such as the memristor simulator of (LDR), cubic non-linearity magnetic control memristor simulator are hindered, will in fact by equivalent circuit
Now and apply to engineering circuit, this causes that memristor simulator played an important role in the research such as chaos circuit.This hair
It is bright to propose a kind of novel single-end input voltage-controlled memristor simulator of modified, with no current reverser and without DC voltage drift
The characteristics of.
The content of the invention
The technical problems to be solved by the invention are to realize a kind of voltage-controlled memristor simulator of modified.
Technical scheme is as follows：
The voltage-controlled memristor simulator of modified is mainly comprised the following steps, and they are respectively：Voltage follower circuit,
Integrating circuit, mlultiplying circuit etc..
The voltage-controlled memristor simulator main circuit of modified includes：Operational amplifier UaAnd Ub, multiplier M1And M2, electric capacity
C0, resistance Ra、RbAnd Rc.The input of memristor simulator is designated as a ends, and input terminal voltage is designated as v, flows through the electricity of memristor simulator
Stream is designated as i, integrating capacitor C0Terminal voltage be designated as v0。
The voltage-controlled memristor simulator of modified realizes that circuit is as shown in Figure 1.Operational amplifier UaIn-phase input end connect
It is connected to memristor simulator input a ends；UaInverting input be connected to UaOutput end, be designated as b ends.Resistance RaLeft end connect
Connect b ends；RaRight-hand member concatenation operation amplifier UbInverting input, be designated as c ends.Resistance RbLeft end connection c ends；RbThe right side
Hold concatenation operation amplifier UbOutput end, be designated as d ends.Electric capacity C0Left end connection c ends；C0Right-hand member connection d ends.Simulation multiplies
Musical instruments used in a Buddhist or Taoist mass M1Two inputs be all connected with d ends；M1Output end be designated as e ends.Analog multiplier M2Input connection a ends；
M2Another input connection e ends；M2Output end be designated as f ends.Resistance RcUpper end connection a ends；RcLower end connection f ends.
Operational amplifier UbHomophase input termination " ".
Beneficial effects of the present invention are as follows：
The voltage-controlled memristor simulator of a kind of modified that the present invention is realized is a kind of new memristor simulator of single ended input, nothing
Electric current reverser and without DC voltage drift, structure is simpler, can be applied to different chaos circuits and produces chaotic signals, right
The application of memristor and memristor circuit will have huge help.
Brief description of the drawings
In order that present disclosure is more likely to be clearly understood, below according to specific embodiment and with reference to accompanying drawing,
The present invention is further detailed explanation, wherein：
The voltage-controlled memristor simulator of Fig. 1 modifieds realizes circuit and memristor graphical diagram；
Fig. 2 ideal magnetic control memristor simulators realize circuit；
Fig. 3 fixes VmVolt-ampere (v-i) coefficient values analogous diagram of memristor simulator when=400mV, frequency f change；
Fig. 4 fixes f=800Hz, amplitude VmVolt-ampere (v-i) coefficient values analogous diagram of memristor simulator during change；
Fig. 5 fixes VmVolt-ampere (v-i) relationship experiments proof diagram of memristor simulator when=400mV, frequency f change；
Fig. 6 fixes f=800Hz, amplitude VmVolt-ampere (v-i) relationship experiments proof diagram of memristor simulator during change.
Specific embodiment
Mathematical modeling：Magnetic control (voltage-controlled) memristor model of one smooth continuous cubic non-linearity function description is represented by
In formula, a and b are constant.For recalling for magnetic control (voltage-controlled) memristor is led, i.e.,
A kind of voltage-controlled memristor simulator of modified of the present embodiment builds as shown in Figure 1.Mainly to existing reason shown in Fig. 2
Think that magnetic control memristor simulator has made 2 points of improvement：1) by original resistance "-R realized by electric current reverserc" directly replace with electricity
Resistance " Rc", simplify circuit structure；2) parallel resistance " R in integrating capacitorb", it is to avoid the DC voltage drift of integrator.
First, in order to avoid load effect, input a signal into end a and be connected to operational amplifier UaThe voltage follow electricity of composition
Road, the voltage of output end b is designated as vb, then have vb=v.
Second level operational amplifier UbWith resistance RaWith electric capacity C0An integrator circuit is connected and composed, integral operation is realized,
Resistance RbFor avoiding integrator DC voltage from drifting about.Integrating capacitor C0Terminal voltage v0Can be stated with following relation
Due to operational amplifier UbHomophase input termination " ", so UbInverting input " virtual earth ", by kirchhoff
There is following relation in voltage law (KVL) and current law (KCL), the electric current for flowing through c points
i1=i2+i3 (4)
I.e.
State equation can be written as
Voltage v0Through multiplier M1After making square operation, M1The voltage of output end e is
Wherein, g1It is multiplier M1Variable scale factor, g herein1=1.
E point voltages veWith a point voltage v through multiplier M2After making multiplying, M2The voltage of Ausgang is
Wherein, g2It is multiplier M2Variable scale factor, g herein2=0.1.
At this moment, in resistance RcTwo ends form voltage difference, then flow through RcElectric current i be
Wherein, W (v0) it is to recall to lead value
Can be obtained by formula (2) and formula (10)
So, the model described by formula (6) and formula (9) meets the model of memristor.
Numerical simulation：Using MATLAB simulation Software Platforms, the model as described by formula (6) and formula (9) can be carried out
Numerical Simulation Analysis.Selection Runge-Kutta (ODE45) algorithm is solved to system equation, can obtain the volt-ampere of this memristor simulator
(v-i) relation phase rail figure.It is v=V when input stimulus source is chosenmSin (2 π ft), circuit parameter is C0=5nF, Ra=5k Ω, Rb
=50k Ω, Rc=120 Ω, g1=1, g2=0.1.Fixed Vm=400mV, when frequency f is respectively 500Hz, 1kHz and 5kHz, recalls
Volt-ampere (v-i) the coefficient values simulation result for hindering simulator is as shown in Figure 3.Fixed f=800Hz, amplitude VmRespectively 0.3V,
During 0.4V and 0.5V, volt-ampere (v-i) coefficient values simulation result of memristor simulator is as shown in Figure 4.
Be can be seen that by Fig. 2 and Fig. 3：1) under the driving of bipolarity periodic signal, the memristor simulator is in v-i planes
One tight hysteresis curve shunk in origin, and response is the cycle；2) since critical frequency, magnetic hysteresis secondary lobe area is with excitation
The increase of frequency and dull reduce；3) as frequency increases, final tight hysteresis curve is punctured into a monotropic function.Meet memristor
Three substantive characteristics of element.
Experimental verification：The voltage-controlled memristor simulator of the cubic non-linearity according to Fig. 1, the design uses model AD711KN
Operational amplifier and model AD633JN analog multiplier, and provide ± 15V operating voltages, electric capacity is ROHS, electricity
It is accurate adjustable resistance to hinder.Pumping signal needed for being produced using signal source Tektronix AFG 3102C, digital oscilloscope
Tektronix TDS 3034C are observed and are recorded experimental result.The corresponding experimental results of Fig. 3 and Fig. 4 are respectively such as Fig. 5 and Fig. 6 institutes
Show.Contrast further demonstrate correctness of the invention and feasibility it can be found that both results are basically identical.
The present invention realize a kind of voltage-controlled memristor simulator of modified, no current reverser and without DC voltage drift, its
Structure is simpler, and is easy to physics realization, has reached a kind of original intention of new memristor simulator of invention.Believe that this invention will
There is larger help to the modeling of memristor simulator and the development of memristor circuit.
Above-described embodiment is not to implementation of the invention just for the sake of clearly demonstrating example of the present invention
The restriction of mode.For those of ordinary skill in the field, other can also be made not on the basis of the above description
With the change or variation of form.There is no need and unable to be exhaustive to all of implementation method.
Claims (4)
1. the voltage-controlled memristor simulator of a kind of modified, it is characterised in that：Including operational amplifier UaAnd Ub, multiplier M1And M2, electricity
Hold C0, resistance Ra、RbAnd RcDeng 8 discrete circuit elements.
2. the voltage-controlled memristor simulator of a kind of modified according to claim 1, it is characterised in that：First order operational amplifier
UaVoltage follower circuit is constituted, for avoiding load effect；Second level operational amplifier UbWith resistance RaWith electric capacity C0Connect and compose
One integrator, resistance RbDC voltage for avoiding integrator drifts about；Multiplier M1And M2Multiplication fortune as voltage signal
Calculate, resistance RcIt is load resistance.
3. the voltage-controlled memristor simulator of a kind of modified according to claim 1, it is characterised in that：The input of memristor simulator
End is designated as a ends, and input terminal voltage is designated as v, and the electric current for flowing through memristor simulator is designated as i, integrating capacitor C0Terminal voltage be designated as v0。
Operational amplifier UaIn-phase input end be connected to a ends；UaInverting input be connected to UaOutput end, be designated as b ends.Resistance
RaLeft end connection b ends；RaRight-hand member concatenation operation amplifier UbInverting input, be designated as c ends.Resistance RbLeft end connection c
End；RbRight-hand member concatenation operation amplifier UbOutput end, be designated as d ends.Electric capacity C0Left end connection c ends；C0Right-hand member connection d
End.Analog multiplier M1Two inputs be all connected with d ends；M1Output end be designated as e ends.Analog multiplier M2One input
End connection a ends；M2Another input connection e ends；M2Output end be designated as f ends.Resistance RcUpper end connection a ends；RcUnder
End connection f ends.Operational amplifier UbHomophase input termination " ".
4. the voltage-controlled memristor simulator of a kind of modified according to claim 1 or 2 or 3, it is characterised in that：Meet memristor unit
Three substantive characteristics of part, 1) under the driving of bipolarity periodic signal, the memristor simulator is in v-i planes for one in origin
The tight hysteresis curve for shrinking, and response is the cycle；2) since critical frequency, magnetic hysteresis secondary lobe area with driving frequency increase
And dull reduction；3) as frequency increases, final tight hysteresis curve is punctured into a monotropic function.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109670221A (en) * | 2018-12-06 | 2019-04-23 | 西安理工大学 | A kind of cubic non-linearity magnetic control memristor circuit being made of fractional order capacitor |
| CN109831289A (en) * | 2019-01-21 | 2019-05-31 | 江苏理工学院 | Three rank memristor Dendrolimus kikuchii chaotic oscillators |
| CN113054947A (en) * | 2021-03-15 | 2021-06-29 | 常州大学 | ReLU type memristor simulator |
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| US9019030B1 (en) * | 2014-09-18 | 2015-04-28 | King Fahd University Of Petroleum And Minerals | Memristor-based emulator for use in digital modulation |
| CN105530083A (en) * | 2015-12-17 | 2016-04-27 | 常州大学 | Voltage-controlled memristor chaotic circuit based on Wien bridge oscillator |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US9019030B1 (en) * | 2014-09-18 | 2015-04-28 | King Fahd University Of Petroleum And Minerals | Memristor-based emulator for use in digital modulation |
| CN105530083A (en) * | 2015-12-17 | 2016-04-27 | 常州大学 | Voltage-controlled memristor chaotic circuit based on Wien bridge oscillator |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109670221A (en) * | 2018-12-06 | 2019-04-23 | 西安理工大学 | A kind of cubic non-linearity magnetic control memristor circuit being made of fractional order capacitor |
| CN109670221B (en) * | 2018-12-06 | 2022-10-14 | 西安理工大学 | Cubic nonlinear magnetic control memristor circuit composed of fractional order capacitors |
| CN109831289A (en) * | 2019-01-21 | 2019-05-31 | 江苏理工学院 | Three rank memristor Dendrolimus kikuchii chaotic oscillators |
| CN113054947A (en) * | 2021-03-15 | 2021-06-29 | 常州大学 | ReLU type memristor simulator |
| CN113054947B (en) * | 2021-03-15 | 2023-09-22 | 常州大学 | ReLU type memristor simulator |
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Application publication date: 20170616 |