CN105227293A - A kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator - Google Patents

A kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator Download PDF

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CN105227293A
CN105227293A CN201510580159.XA CN201510580159A CN105227293A CN 105227293 A CN105227293 A CN 105227293A CN 201510580159 A CN201510580159 A CN 201510580159A CN 105227293 A CN105227293 A CN 105227293A
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resistance
wien
electric capacity
bridge oscillator
noninductive
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包伯成
王宁
徐权
王将
陈墨
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Changzhou University
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Changzhou University
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Abstract

The invention discloses a kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator, comprise wien-bridge oscillator, electric capacity C 1, resistance R, simplify Cai Shi diode R n; Wherein electric capacity C 1be connected in parallel with the two ends simplifying Cai Shi diode (being denoted as 1,1 ' end); 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 wien-bridge oscillator (being denoted as 2 ends), and the output and 2 ' of wien-bridge oscillator is held and is connected; 1 ' end, 2 ' end ground connection.The present invention adopts one-level operational amplifier to achieve a kind of Cai Shi diode of simplification, thus achieves a kind of only containing noninductive, the simple and easy Chua's chaotic circuit of two operational amplifiers.The chaos circuit proposed can produce the complex nonlinear phenomenons such as cycles limit ring, chaos attractor, the attractor that coexists, twin double scroll chaos, twin limit cycle.Become the simplest noninductive Chua's chaotic circuit of a class, larger progradation is played in the development for chaos system.

Description

A kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator
Technical field
The present invention relates to a kind of noninductive chaotic signal generating device based on wien-bridge oscillator, this device has the topological structure of cai's circuit, adopt one-level operational amplifier to achieve a kind of Cai Shi diode of simplification, thus achieve a kind of only containing noninductive, the simple and easy cai's circuit of two operational amplifiers.Chaos circuit proposed by the invention can produce the complex nonlinear phenomenons such as cycles limit ring, chaos attractor, the attractor that coexists, twin double scroll chaos, twin limit cycle.
Background technology
The Analogical Electronics built by active nonlinear element and linear dynamic element easily realizes chaotic oscillation.In addition, consider that inductance element needs manual coiling usually, cause the circuit volume built comparatively large, be not easy to IC design, and be subject to the impact of the endoparasitic equivalent series resistance of inductance element, should avoid using inductance element in physical circuit as far as possible.Therefore, propose a kind of noninductive cai's circuit based on wien-bridge oscillator herein, and adopt one-level operational amplification circuit to achieve simplification Cai Shi diode, simplify circuit further, construct a kind of only containing the noninductive chaos signal generator of two operational amplifiers.
Summary of the invention
Technical problem to be solved by this invention simplifies Cai Shi diode, and realize a kind of only containing the noninductive chaos signal generator of two amplifiers based on wien-bridge oscillator.
For solving the problems of the technologies described above, the invention provides a kind of noninductive chaos signal generator based on wien-bridge oscillator, its structure is as follows:
Described main circuit comprises: wien-bridge oscillator, electric capacity C 1, resistance R, simplify Cai Shi diode R n; Wherein electric capacity C 1be connected in parallel with the two ends simplifying Cai Shi diode (being denoted as 1,1 ' end); 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 wien-bridge oscillator (being denoted as 2 ends), and the output and 2 ' of wien-bridge oscillator is held and is connected; 1 ' end, 2 ' end ground connection.
Wien-bridge oscillator comprises: operational amplifier U 2, resistance R 1, resistance R 2, resistance R 3, resistance R 4, electric capacity C 2with electric capacity C 3; Electric capacity C 2positive terminal connect 2 ends, electric capacity C 2negative pole end connect 2 ' end; Resistance R 1with electric capacity C 2in parallel; Operational amplifier U 2output respectively with resistance R 2and R 3one end be connected; Resistance R 2the other end connect electric capacity C 3positive terminal, electric capacity C 3negative pole end connect amplifier U 2in-phase input end, and U 2in-phase input end connect 2 ends; Resistance R 3other end concatenation operation amplifier U 2inverting input; Resistance R 4one end connect U 2inverting input, resistance R 4other end ground connection.
Simplify Cai Shi diode to comprise: operational amplifier U 1, resistance R a, resistance R b, resistance R c; The in-phase input end of operational amplifier and inverting input respectively with resistance R bwith resistance R cone end be connected; The output of operational amplifier respectively with resistance R bwith resistance R cthe other end be connected; Resistance R aone end be connected with the negative input of operational amplifier, another termination 1 ' hold.
As shown in Figure 1, containing three dynamic elements in circuit, corresponding three state variables are respectively electric capacity C to the described noninductive chaos circuit main circuit based on wien-bridge oscillator 1both end voltage v 1, electric capacity C 2both end voltage v 2, electric capacity C 3both end voltage v 3.
Beneficial effect of the present invention is as follows:
A kind of noninductive chaos circuit based on wien-bridge oscillator of the present invention can produce by regulating circuit parameter single scroll chaotic attractor that two scrollwork and fork coexist, become the simplest noninductive Chua's chaotic circuit of a class, larger progradation is played in the development for chaos system.
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 is the noninductive simplification Cai Shi chaos signal generator realizing circuit based on wien-bridge oscillator;
Fig. 2 is wien-bridge oscillator realizing circuit;
Fig. 3 is only containing the simplification Cai Shi diode realizing circuit of an operational amplifier;
Fig. 4 is the v simplifying Cai Shi diode n– i n(Voltammetric Relation);
Fig. 5 is state variable v 1(t), v 2(t) time domain waveform numerical simulation figure;
Fig. 6 is the noninductive simplification cai's circuit v based on wien-bridge oscillator 1(t)-v 2numerical simulation phase rail figure in (t) plane and experimental result (R=1.6k Ω);
Fig. 7 is the noninductive simplification cai's circuit v based on wien-bridge oscillator 1(t)-v 3numerical simulation phase rail figure in (t) plane and experimental result (R=1.6k Ω);
Fig. 8 for circuit parameter R change corresponding to v 1(t) bifurcation graphs;
Fig. 9 is the Lyapunov exponential spectrum changed with circuit parameter R;
Figure 10 is when choosing R=1.4k Ω based on the noninductive simplification cai's circuit of wien-bridge oscillator, v 1(t)-v 2the numerical simulation phase rail figure of (t) and experimental result (cycle 2 coexist limit cycle);
Figure 11 is when choosing R=1.5k Ω based on the noninductive simplification cai's circuit of wien-bridge oscillator, v 1(t)-v 2the numerical simulation phase rail figure of (t) and experimental result (coexist chaos attractor);
Figure 12 is when choosing R=1.8k Ω based on the noninductive simplification cai's circuit of wien-bridge oscillator, v 1(t)-v 2the numerical simulation phase rail figure of (t) and experimental result (twin double scroll chaos);
Figure 13 is when choosing R=1.95k Ω based on the noninductive simplification cai's circuit of wien-bridge oscillator, v 1(t)-v 2the numerical simulation phase rail figure of (t) and experimental result (cycle 2 twin limit cycle);
Figure 14 is when choosing R=2k Ω based on the noninductive simplification cai's circuit of wien-bridge oscillator, v 1(t)-v 2the numerical simulation phase rail figure of (t) and experiment phase rail figure (double scroll chaos);
Figure 15 is when choosing R=2.2k Ω based on the noninductive simplification cai's circuit of wien-bridge oscillator, v 1(t)-v 2the numerical simulation phase rail figure of (t) and experiment phase rail figure (cycle 2 coexist limit cycle).
Embodiment
Mathematical modeling: a kind of noninductive simplification Cai Shi chaos signal generator circuits built based on wien-bridge oscillator of the present embodiment as shown in Figure 1, and is carried out circuit analysis according to Fig. 1 and can be shown that this chaos signal generator can be described below:
dv 1 d t = - v 1 RC 1 + v 2 RC 1 - h ( v 1 ) C 1 dv 2 d t = v 1 RC 2 + ( k R 2 - 1 R - 1 R 1 ) v 2 C 2 - v 3 R 2 C 2 dv 3 d t = kv 2 R 2 C 2 - v 3 R 2 C 3 - - - ( 1 )
Wherein, k is the feedback oscillator of wien-bridge oscillator, k=R 3/ R 4; H (v 1) represent simplification Cai Shi diode R npiecewise linear function.
Simplify the circuit structure diagram of Cai Shi diode as shown in Figure 3.According to Cai Shi diode R nterminal voltage v n(be equal to electric capacity C 1both end voltage v 1) and flow through current i n, its voltage-current characteristic relational expression is as follows:
i N = h ( v N ) = G b v N + 1 2 ( G a - G b ) ( | v N + B p | - | v N - B p | ) - - - ( 2 )
Wherein,
G a = - 1 R a , G b = 1 R b , B p = R a R a + R b E s a t - - - ( 3 )
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, works as R b=R ctime, obtain G a=-714.29 μ S, G b=250 μ S, B p=3.37V.
Based on differential equation group formula (1), select the value of resistance R variable, be depicted in the v that variable element R changes 1t the bifurcation graphs of () as shown in Figure 8.First corresponding states initial guess of Fig. 8 is v 1(0)=1mV, v 2(0)=0V, v 3(0) second corresponding states initial guess of=0V, Fig. 8 is v 1(0)=– 1mV, v 2(0)=0V, v 3(0)=0V.Be positioned at adjustable range 1.2k Ω ~ 2.2k Ω at circuit parameter R, there is cycles limit ring, chaotic oscillation in this circuit, coexist the advanced dynamic behaviors such as Bifurcation Patterns.It should be noted that, under different initial value, noninductive simplification cai's circuit based on wien-bridge oscillator can produce different cycles the cycles limit ring that coexists, coexist chaos attractor, twin double scroll chaos, the complex nonlinear phenomenons such as the twin cycles limit ring of different cycles, and than classical cai's circuit, there is larger parameter adjustable range.
Meanwhile, selection circuit parameter R value is variable, and 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 complex nonlinear phenomenon.Show thus, this circuit can produce different chaotic signals by regulating circuit parameter value, obtains the multiple chaotic signal with complex dynamic characteristics, reaches the original intention of inventing a kind of noninductive, simple and easy, feasible chaos signal generator.
The one that the present invention realizes is based on wien-bridge oscillator noninductive simplification Cai Shi chaos signal generator, and its structure is simple, achieving without helping to change, effectively prevent the impact of the endoparasitic equivalent series resistance of inductance element in physical circuit; And make circuit more simple by simplifying Cai Shi diode and be easy to realize.Be totally by wien-bridge oscillator and simplification Cai Shi diode linear coupling, achieve a kind of easy noninductive Cai Shi chaos signal source.Different non-linear phenomenas can be produced, that become a class novelty, feasible chaos signal generator by regulating circuit parameter.Believe that this invention will have larger progradation for the development of chaos circuit.
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., based on the noninductive chaos circuit only containing two amplifiers of wien-bridge oscillator, it is characterized in that: comprise wien-bridge oscillator, electric capacity C 1, resistance R, simplify Cai Shi diode R n; Wherein electric capacity C 1be connected in parallel with the two ends simplifying Cai Shi diode (being denoted as 1,1 ' end); 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 wien-bridge oscillator (being denoted as 2 ends), and the output and 2 ' of wien-bridge oscillator is held and is connected; 1 ' end, 2 ' end ground connection.
2. a kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator according to claim 1, is characterized in that: described wien-bridge oscillator comprises operational amplifier U 2, resistance R 1, resistance R 2, resistance R 3, resistance R 4, electric capacity C 2with electric capacity C 3; Electric capacity C 2positive terminal connect 2 ends, electric capacity C 2negative pole end connect 2 ' end; Resistance R 1with electric capacity C 2in parallel; Operational amplifier U 2output respectively with resistance R 2and R 3one end be connected; Resistance R 2the other end connect electric capacity C 3positive terminal, electric capacity C 3negative pole end connect amplifier U 2in-phase input end, and U 2in-phase input end connect 2 ends; Resistance R 3other end concatenation operation amplifier U 2inverting input; Resistance R 4one end connect U 2inverting input, resistance R 4other end ground connection.
3. a kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator according to claim 1, is characterized in that: described simplification Cai Shi diode comprises operational amplifier U 1, resistance R a, resistance R b, resistance R c; The in-phase input end of operational amplifier and inverting input respectively with resistance R bwith resistance R cone end be connected; The output of operational amplifier respectively with resistance R bwith resistance R cthe other end be connected; Resistance R aone end be connected with the negative input of operational amplifier, another termination 1 ' hold.
4. a kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator according to claim 1 or 2 or 3, is characterized in that: containing three state variables, be respectively electric capacity C 1both end voltage v 1, electric capacity C 2both end voltage v 2, electric capacity C 3both end voltage v 3.
CN201510580159.XA 2015-09-13 2015-09-13 A kind of noninductive chaos circuit only containing two amplifiers based on wien-bridge oscillator Pending CN105227293A (en)

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CN106571906A (en) * 2016-11-10 2017-04-19 常州大学 Second-order non-autonomous signal generator realized based on Wien bridge oscillator
CN106656462A (en) * 2016-12-06 2017-05-10 常州大学 Non-inductive chaotic circuit realized through nonlinear coupling of Wien bridge oscillator and active band-pass filter
CN107124259A (en) * 2017-03-31 2017-09-01 常州大学 A kind of simple Dendrolimus kikuchii chaotic oscillator
CN108737066A (en) * 2018-07-30 2018-11-02 江苏理工学院 A kind of modified Chua's chaotic circuit

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CN103236918A (en) * 2013-01-31 2013-08-07 王少夫 Negative resistance equivalence method for Chua's chaotic circuits
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106571906A (en) * 2016-11-10 2017-04-19 常州大学 Second-order non-autonomous signal generator realized based on Wien bridge oscillator
CN106656462A (en) * 2016-12-06 2017-05-10 常州大学 Non-inductive chaotic circuit realized through nonlinear coupling of Wien bridge oscillator and active band-pass filter
CN107124259A (en) * 2017-03-31 2017-09-01 常州大学 A kind of simple Dendrolimus kikuchii chaotic oscillator
CN108737066A (en) * 2018-07-30 2018-11-02 江苏理工学院 A kind of modified Chua's chaotic circuit

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Application publication date: 20160106