CN105577355A - Voltage controlled memristor chaotic circuit based on second-order active band-pass filter - Google Patents

Voltage controlled memristor chaotic circuit based on second-order active band-pass filter Download PDF

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Publication number
CN105577355A
CN105577355A CN201510920521.3A CN201510920521A CN105577355A CN 105577355 A CN105577355 A CN 105577355A CN 201510920521 A CN201510920521 A CN 201510920521A CN 105577355 A CN105577355 A CN 105577355A
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China
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resistance
amplifier
voltage
electric capacity
pass filter
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CN201510920521.3A
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包伯成
蒋涛
王宁
姚凯文
钱辉
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Changzhou University
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Changzhou University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals

Abstract

The invention discloses a voltage controlled memristor chaotic circuit based on a second-order active band-pass filter. The chaotic circuit comprises a capacitor C1, a resistor R, the second-order active band-pass filter and an active voltage controlled memristor. The positive electrode end of the capacitor is connected with the input end (1 end) of the voltage controlled memristor. The negative end of the capacitor is connected with the output end (1' end) of the voltage controlled memristor. The right end of the resistor R is connected with the 1 end. The left end of the resistor R is connected with the input end (2 end) of the second-order active band-pass filter. The output end of the second-order active band-pass filter is marked as a 2' end. The 1' end and the 2' end are connected to the ground. Via the novel chaotic circuit, experimental observation is easy to carry out and development of a chaotic system is greatly promoted.

Description

Resistance chaos circuit recalled by a kind of voltage-controlled type based on second order active band pass filter
Technical field
The present invention relates to a kind of voltage-controlled type based on second order active band pass filter and recall resistance chaotic signal generating device, this device is based on second order active band pass filter form, by introducing novel imperfect active voltage-controlled type memristor, by resistance R and second order active band pass filter linear coupling after voltage-controlled type memristor shunt capacitance, achieve that one is novel recalls resistance chaos signal source.
Background technology
Recalling resistance (memristor), is the basic composition original paper of the realizing circuit describing electric charge (charge) and magnetic flux (magneticflux) relation.According to circuit basic variable combinatorial completeness principle, within 1971, the few Chinese bush cherry of Cai predicts the existence recalling resistance original paper theoretically, and set forth further in follow-up paper recall resistance fundamental characteristics, composition principle and application thereof, the Strukov in Hewlett-Packard (HP) company laboratory in 2008 etc. go up the realisation of reported first memristor at " nature ", and achievement in research has shocked the International Power electronic technology world.Start and recall resistance research boom.The appearance of nanometer memory resistor, is expected to realize non-volatile RAM.Further, based on the integrated level of random asccess memory recalling resistance, power consumption, the random asccess memory of read or write speed all than traditional is superior.In addition, recall the best way that resistance is the cynapse of hardware implementing artificial neural net, owing to recalling the non-linear nature of resistance, can chaos circuit be produced, thus also have a lot of application in secure communication.
Although memristor has been proved as the 4th kind of new circuit element, to have physics lesson realisation, but because technical difficulty is large, overall cost is high, memristor cannot reach commercial at short notice, makes researcher can't get this device from the market easily for every scientific research at present.Therefore, the discrete components such as resistance, electric capacity, operational amplifier, analog multiplier are utilized to realize various resistance analog circuit of recalling, or recall resistance circuit based on some broad sense of circuits built of special topological form, and multiplely recall sense and recall and hold equivalent electric circuit etc. recalling resistance equivalent electric circuit basis set up by transducer, significant contribution has been made in the research all for recalling resistance or recalling resistance system and expansive approach thereof.Propose herein a kind ofly to recall resistance chaos circuit based on second order active band pass filter, further expanded the way of realization recalling resistance simulator.
Summary of the invention
Technical problem to be solved by this invention is voltage-controlled type memristor, and realizes one based on second order active band pass filter and recall resistance chaos circuit.
For solving the problems of the technologies described above, the invention provides and a kind of realize a kind of voltage-controlled type based on second order active bandpass filtering and recall resistance chaos circuit, its structure is as follows:
Described main circuit comprises: electric capacity C 1, resistance R, second order active band pass filter, voltage-controlled type memristor W; Wherein electric capacity C 1anode be connected (being denoted as 1 end) with voltage-controlled type memristor input, electric capacity C 1negative terminal be connected (being denoted as 1 ' to hold) with the output of voltage-controlled type memristor; The right-hand member of resistance R is connected with 1 end, and the left end of resistance R is connected with the input of second order active band pass filter (being denoted as 2 ends), and the output of second order active band pass filter is designated as 2 ' end; 1 ' end, 2 ' end ground connection.
Second order active band pass filter comprises: operational amplifier U, resistance R 1, resistance R 2, resistance R 3, resistance R 4, electric capacity C 2, electric capacity C 3; Resistance R 1one termination g end, resistance R 1another termination d hold; Electric capacity C 3positive terminal connect the output of amplifier U, electric capacity C 3negative pole end connect c end; Electric capacity C 2positive terminal connect the electrode input end of amplifier U, electric capacity C 2negative pole end connect g end; Resistance R 2the in-phase input end of a termination amplifier U, resistance R 2the other end connect the output of amplifier U; Resistance R 3the inverting input of a termination amplifier U, resistance R 3the other end connect the output of amplifier U; Resistance R 4one end connect the inverting input of amplifier U, resistance R 4another termination d hold.
Active voltage-controlled type memristor comprises: voltage follower, integrator, multiplier, current inverters; Amplifier U ain-phase input end and multiplier M bone end be connected, amplifier U ainverting input and amplifier U aoutput be connected, amplifier U aoutput and resistance R aone end is connected; Amplifier U binverting input respectively with electric capacity C 0positive terminal and resistance R bone end be connected; Amplifier U bpositive input end grounding; Electric capacity C 0negative pole end and resistance R bother end computing meet amplifier U simultaneously boutput; Amplifier U boutput and multiplier M atwo inputs are connected simultaneously; Multiplier M aexport termination multiplier M banother input; Multiplier M boutput connecting resistance R c, resistance R canother termination amplifier U cinverting input through resistance R ereceive amplifier U coutput; Amplifier U cnormal phase input end is through resistance R dreceive amplifier U coutput.
The described voltage-controlled type based on second order active band pass filter recalls resistance chaos circuit main circuit as shown in Figure 1, and containing one of four states variable in circuit, they are the node voltage V of node a, c and e respectively 1, V 2, V 3with integrator output terminal voltage V in voltage-controlled type memristor 0.
Beneficial effect of the present invention is as follows:
Resistance chaos circuit recalled by a kind of voltage-controlled type based on second order active band pass filter of the present invention can produce double scroll chaos by regulating circuit parameter, become and novel recall resistance chaos circuit, the development for chaos system plays larger progradation.
Accompanying drawing explanation
In order to make content of the present invention be more likely to be clearly understood, below according to specific embodiments also by reference to the accompanying drawings, the present invention is further detailed explanation, wherein:
Fig. 1 recalls resistance chaos signal generator realizing circuit based on the voltage-controlled type of second order active band pass filter;
The imperfect active voltage-controlled type memristor realizing circuit of Fig. 2;
Fig. 3 recalls resistance chaos circuit at V when choosing canonical parameter 0(t)-V 3numerical simulation phase rail figure in (t) plane and experimental result;
Fig. 4 recalls resistance chaos circuit at V when choosing canonical parameter 1(t)-V 3numerical simulation phase rail figure in (t) plane and experimental result;
Fig. 5 recalls resistance chaos circuit at V when choosing canonical parameter 2(t)-V 3numerical simulation phase rail figure in (t) plane and experimental result;
Fig. 6 recalls resistance chaos circuit at V when choosing canonical parameter 1(t)-V 2numerical simulation phase rail figure in (t) plane and experimental result;
Fig. 7 is with parameter r 1at V when changing in 7 to 22 1(t)-V 3numerical simulation phase rail figure in (t) plane; Wherein (a) r 1=7, (b) r 1=7.6, (c) r 1=7.8, (d) r 1=8, (e) r 1=8.2, (f) r 1=8.2, (g) r 1=10.5, (h) r 1=12, (i) r 1=16.8, (j) r 1=22;
Fig. 8 is with parameter r 1at V when changing in 7 to 22 1(t)-V 3experimental result phase rail figure in (t) plane; Wherein (a) r 1=7, (b) r 1=7.6, (c) r 1=7.8, (d) r 1=8, (e) r 1=8.2, (f) r 1=8.2, (g) r 1=10.5, (h) r 1=12, (i) r 1=16.8, (j) r 1=22.
Embodiment
Mathematical modeling: a kind of voltage-controlled type based on second order active band pass filter of the present embodiment recalls resistance chaos signal generator circuits built as shown in Figure 1, supposes voltage and the electric current of v and i voltage-controlled type memristor input, V 0integrator U boutput voltage, the Mathematical Modeling of voltage-controlled type memristor can be described below:
i = W ( V 0 ) = ( - 1 R c + g a g b R c V 0 2 ) v C 0 dV 0 d t = f ( V 0 , v ) = - 1 R b V 0 - 1 R a v - - - ( 1 )
Wherein g aand g bmultiplier M aand M bparameter, above-mentioned Mathematical Modeling is consistent with the definition of broad sense memristor.
The design adopts model to be the operational amplifier of AD711KN, provides ± 15V operating voltage, wherein E satfor the saturation voltage of operational amplifier, E sat≈ 13V.
A kind of voltage-controlled type based on second order active band pass filter of the present embodiment recalls resistance chaos signal generator circuits built as shown in Figure 1, and the kinetic model of the chaos circuit that the present invention proposes can by the node voltage V of three nodes a, c and e 1, V 2, V 3with integrator output terminal voltage V in voltage-controlled type memristor 0be described below:
C 0 dV 0 d t = - 1 R b V 0 - 1 R a V 1 C 1 dV 1 d t = - 1 R V 1 + 1 R V 2 + ( 1 R c - g a b b R c V 0 2 ) V 1 C 2 dV 2 d t = - k R V 1 + k R ′ V 2 - 2 k + 1 ( k + 1 ) R 2 V 3 C 3 dV 3 d t = - k + 1 R V 1 + k + 1 R ′ V 2 - 2 R 2 V 3 - - - ( 2 )
Wherein, R'=RR 1/ (R+R 1), k=R 4/ R 3;
Foregoing circuit has 4 variablees and 14 circuit parameters, draws the Non-di-mensional equation of system by introducing 4 new variablees:
x = V 0 , y = V 1 , z = V 2 , w = V 3 , C 2 = C 3 = C , τ = t R C , u · = d u d τ ( u ≡ x , y , z , w ) , a = R C R a C 0 , b = R C R b C 0 , c 1 = R R c , c 2 = g a g b R R c , d = C C 1 , r 1 = R R 1 , r 2 = R R 2 - - - ( 3 )
Formula (2) is write as follows:
x · = - b x - a y y · = d ( c 1 - c 2 x 2 ) y - d ( y - z ) z · = - k y + k ( r 1 + 1 ) z - ( 2 k + 1 ) r 2 k + 1 w w · = - ( k + 1 ) y + ( k + 1 ) ( r 1 + 1 ) z - 2 r 2 w - - - ( 4 )
Numerical simulation: utilize MATLAB simulation Software Platform, can carry out Numerical Simulation Analysis to the system described by formula (4).Select Runge-Kutta (ODE45) algorithm to solve system equation, the phase rail figure that this recalls resistance chaos circuit state variable can be obtained.Permanent circuit parameter C 1=5nF, C 2=C 3=100nF, R a=30k Ω, R b=10k Ω, R c=1.4k Ω, R 1=150 Ω, R 2=10k Ω, R 3=1k Ω, R 4=50 Ω.When choosing R=1.5K Ω, the MATLAB numerical simulation phase rail figure of corresponding Different Plane is respectively as shown in Fig. 3,4,5,6.
Meanwhile, select the value of resistance R variable, numerical simulation can obtain the running status of circuit under different resistance values R.By the adjustment to resistance value R, this circuit can produce corresponding different complicated chaos scrollwork.Show thus, this circuit can produce different chaotic signals by regulating circuit parameter value, obtains the multiple chaotic behavior with complex dynamic characteristics, reaches a kind of feasible novel original intention recalling resistance chaos signal generator of invention.
Experimental verification: it is the four-quadrant multiplier of AD633JN that the design adopts model to be the operational amplifier of AD711KN and model, and provides ± 15V operating voltage.Resistance adopts accurate adjustable resistance, and electric capacity is leaded multilayer ceramic capacitor.Theory analysis and numerical simulation show, the self-excitation attractor that this circuit produces is insensitive to initial condition, when experimental circuit powers up, trigger at node " a " place, are easy to the state variable initial value required for realizing.
Adopt TektronixDPO3034 digital storage oscilloscope to catch measured waveform, the chaos attractor phase rail figure respectively in logarithm value emulation has carried out experimental verification, and experimental result is respectively as shown in Fig. 3, Fig. 4, Fig. 5, Fig. 6.
Comparing result can illustrate: resistance chaos circuit recalled by a kind of voltage-controlled type producing 2 self-excitation scroll chaotic attractors that the present invention realizes, the non-linear phenomena observed in experimental circuit and development law thereof and simulation result fit like a glove, can the correctness of proof theory analysis and numerical simulation.Therefore, resistance chaos signal generator recalled by a kind of voltage-controlled type based on second order active band pass filter that the present invention realizes, and its structure is simple, avoids inductance element, effectively prevent the impact of the endoparasitic equivalent series resistance of inductance element in physical circuit; And with voltage-controlled type memristor linear coupling, achieve a kind of novel chaos signal source.Integrated circuit can produce multiple different non-linear phenomena by regulating system parameter, that become a class novelty, feasible chaos signal generator.Believe that this invention will have larger progradation for the development of chaos system.
Above-described embodiment is only for example of the present invention is clearly described, and is not the restriction to embodiments of the present invention.For those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.Here exhaustive without the need to also giving all execution modes.

Claims (4)

1. a resistance chaos circuit recalled by the voltage-controlled type based on second order active band pass filter, it is characterized in that: comprise electric capacity C 1, resistance R, second order active band pass filter, voltage-controlled type memristor W; Wherein electric capacity C 1positive terminal be connected (being denoted as 1 end) with voltage-controlled type memristor input, electric capacity C 1negative pole end be connected (being denoted as 1 ' to hold) with the output of voltage-controlled type memristor; The right-hand member of resistance R is connected with 1 end, and the left end of resistance R is connected with the input of second order active band pass filter (being denoted as 2 ends), and the output of second order active band pass filter is designated as 2 ' end; 1 ' end, 2 ' end ground connection.
2. resistance chaos circuit recalled by a kind of voltage-controlled type based on second order active band pass filter according to claim 1, it is characterized in that: described second order active band pass filter comprises operational amplifier U, resistance R 1, resistance R 2, resistance R 3, resistance R 4, electric capacity C 2, electric capacity C 3; Resistance R 1one termination g end, resistance R 1another termination d hold; Electric capacity C 3positive terminal connect the output of amplifier U, electric capacity C 3negative pole end connect c end; Electric capacity C 2positive terminal connect the in-phase input end of amplifier U, electric capacity C 2negative pole end connect g end; Resistance R 2the in-phase input end of a termination amplifier U, resistance R 2the other end connect the output of amplifier U; Resistance R 3the inverting input of a termination amplifier U, resistance R 3the other end connect the output of amplifier U; Resistance R 4one end connect the inverting input of amplifier U, resistance R 4another termination d hold.
3. resistance chaos circuit recalled by a kind of voltage-controlled type based on second order active band pass filter according to claim 1, it is characterized in that: described voltage-controlled type memristor comprises: voltage follower, integrator, multiplier, current inverters; Amplifier U ain-phase input end and multiplier M bone end be connected, amplifier U ainverting input and amplifier U aoutput be connected, amplifier U aoutput and resistance R aone end is connected; Amplifier U binverting input respectively with electric capacity C 0positive terminal and resistance R bone end be connected; Amplifier U bpositive input end grounding; Electric capacity C 0negative pole end and resistance R bother end computing meet amplifier U simultaneously boutput; Amplifier U boutput and multiplier M atwo inputs are connected simultaneously; Multiplier M aexport termination multiplier M banother input; Multiplier M boutput connecting resistance R c, resistance R canother termination amplifier U cinverting input through resistance R ereceive amplifier U coutput; Amplifier U cnormal phase input end is through resistance R dreceive amplifier U coutput.
4. the noninductive chaos circuit of resistance recalled by a kind of voltage-controlled type based on second order active band pass filter according to claim 1 or 2 or 3, it is characterized in that: containing one of four states variable, is respectively electric capacity C 0both end voltage v 0, electric capacity C 1both end voltage v 1, electric capacity C 2both end voltage v 2, electric capacity C 3both end voltage v 3.
CN201510920521.3A 2015-12-12 2015-12-12 Voltage controlled memristor chaotic circuit based on second-order active band-pass filter Pending CN105577355A (en)

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Cited By (12)

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CN106357381A (en) * 2016-10-20 2017-01-25 常州大学 Three-order memory resistor chaotic signal generator realized based on two-order active band-pass filter
CN106533649A (en) * 2016-11-10 2017-03-22 常州大学 Third-order chaotic signal generator implemented based on memristor diode bridge
CN106603220A (en) * 2016-12-22 2017-04-26 常州大学 Three-order memristor active band-pass filter chaotic circuit
CN106911463A (en) * 2017-01-17 2017-06-30 常州大学 A kind of Cai Shi memristor chaos circuits based on active band-pass filter
CN107424647A (en) * 2017-08-03 2017-12-01 电子科技大学 A kind of phonetic storage and categorizing system based on memristor
CN109831289A (en) * 2019-01-21 2019-05-31 江苏理工学院 Three rank memristor Dendrolimus kikuchii chaotic oscillators
CN110535625A (en) * 2019-09-18 2019-12-03 常州大学 A kind of three element chaos signal generators based on memristor
US11456418B2 (en) 2020-09-10 2022-09-27 Rockwell Collins, Inc. System and device including memristor materials in parallel
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US11469373B2 (en) 2020-09-10 2022-10-11 Rockwell Collins, Inc. System and device including memristor material
US11631808B2 (en) 2020-12-07 2023-04-18 Rockwell Collins, Inc. System and device including memristor material
CN116011536A (en) * 2022-12-06 2023-04-25 常州大学 Nerve morphology circuit based on local active memristor

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Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106357381A (en) * 2016-10-20 2017-01-25 常州大学 Three-order memory resistor chaotic signal generator realized based on two-order active band-pass filter
CN106533649A (en) * 2016-11-10 2017-03-22 常州大学 Third-order chaotic signal generator implemented based on memristor diode bridge
CN106603220A (en) * 2016-12-22 2017-04-26 常州大学 Three-order memristor active band-pass filter chaotic circuit
CN106911463A (en) * 2017-01-17 2017-06-30 常州大学 A kind of Cai Shi memristor chaos circuits based on active band-pass filter
CN107424647B (en) * 2017-08-03 2020-08-04 电子科技大学 Voice storage and classification system based on memristor
CN107424647A (en) * 2017-08-03 2017-12-01 电子科技大学 A kind of phonetic storage and categorizing system based on memristor
CN109831289A (en) * 2019-01-21 2019-05-31 江苏理工学院 Three rank memristor Dendrolimus kikuchii chaotic oscillators
CN110535625A (en) * 2019-09-18 2019-12-03 常州大学 A kind of three element chaos signal generators based on memristor
US11456418B2 (en) 2020-09-10 2022-09-27 Rockwell Collins, Inc. System and device including memristor materials in parallel
US11469373B2 (en) 2020-09-10 2022-10-11 Rockwell Collins, Inc. System and device including memristor material
US11462267B2 (en) 2020-12-07 2022-10-04 Rockwell Collins, Inc. System and device including memristor material
US11631808B2 (en) 2020-12-07 2023-04-18 Rockwell Collins, Inc. System and device including memristor material
CN116011536A (en) * 2022-12-06 2023-04-25 常州大学 Nerve morphology circuit based on local active memristor
CN116011536B (en) * 2022-12-06 2024-01-23 常州大学 Nerve morphology circuit based on local active memristor

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Application publication date: 20160511