RU2536424C1 - Chaotic vibration generator - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: chaotic vibration generator includes a resistive element, first and second bipolar element with capacitive resistance, a bipolar element with inductive resistance and a nonlinear current amplifier.

EFFECT: broader capabilities for electronic adjustment of parameters of the chaotic signal generated.

2 cl, 8 dwg

Description

The present invention relates to radio engineering and can be used as a source of chaotic electromagnetic waves.

A known generator of chaotic oscillations (AS Pikovsky, MI Rabinovich. A simple oscillator with stochastic behavior. Reports of the Academy of Sciences of the USSR, 1978, V.239, No. 2, p.302) containing a tunneling diode, the anode of which is connected to the first terminal of the resistor, the second terminal of which is connected to the first terminal of the inductance, the second terminal of which is connected to the first terminal of the device with a negative resistance, the second terminal of which is connected to the cathode of the tunnel diode, and parallel to the tunnel diode and the device with negative resistance cm respectively connected first and second capacitors.

Also known is a generator of chaotic oscillations (T. Matsumoto. Chaos in electrical circuits. TIIER, 1987, T.75, No. 8, p. 67-68, Fig. 1 and Fig. 6), containing a device with negative resistance, in parallel with which a first capacitor is included, the first terminal of which is connected to the first terminal of the resistor, the second terminal of which is connected to the first terminals of the inductive element and the second capacitor, the second terminals of which are connected to the second terminal of the first capacitor.

The disadvantage of these generators is the limited possibility of electronic tuning of the parameters of the generated chaotic signal.

The closest in technical essence to the claimed device is a chaotic oscillation generator (LO Chua, Guinian Lin. Intermittency in a piecewise-linear circuit // IEEE Transactions on Circuits and Systems, Vol. 38, N0.5, May 1991, p. 510, Fig. 1 (a)) containing a resistive element, the first output of which is connected to the first output of the bipolar element with inductive resistance, the second output of which is connected to the first output of the first bipolar element with capacitive resistance, the second output of which is connected to the first output of the second bipolar element with capacitance iem.

The disadvantage of this generator of chaotic oscillations is the limited range of electronic tuning of the parameters of the generated chaotic signal due to the insignificant possibility of changing the characteristics of the nonlinear element.

The aim of the invention is to expand the capabilities of electronic tuning parameters of the generated chaotic signal.

The purpose of the invention is achieved in that in a chaotic oscillator containing a resistive element, the first output of which is connected to the first output of the bipolar element with inductive resistance, the second output of which is connected to the first output of the first bipolar element with capacitive resistance, the second output of which is connected to the first output of the second a bipolar element with capacitive resistance, a nonlinear current amplifier is introduced, the first input terminal of which is connected to the second output of the resistive element, trans the output terminal of which is connected to the second terminal of the second bipolar element with capacitive resistance, the first terminal of which is connected to the second input terminal of the nonlinear current amplifier, the first and second output terminals of which are connected respectively to the first and second terminals of the first bipolar element with capacitive resistance, the transfer characteristic of nonlinear current amplifier is defined by the equation:

, $$i_{\mathrm{at}sx}\left(i_{\mathrm{at}x}\right)=b{i}_{\mathrm{at}x}+\frac{a-b}{2}\left(|\; |\; |i_{\mathrm{at}x}+I_{02}|\; |\; |-|\; |\; |i_{\mathrm{at}x}-I_{01}|\; |\; |-I_{02}+I_{01}\right)+I_{\mathrm{from}m}$$

,

where i _out (i _in ) is the output current flowing through the output terminals of the nonlinear current amplifier under the influence of the input current i _in flowing through the input terminals of the nonlinear current amplifier, a is the steepness of the average passing through the origin of the portion of the transfer characteristic, b is the steepness of the side sections of the transfer characteristic, I ₀₁ and I ₀₂ are the absolute values of the boundary currents between the middle and side sections of the transfer characteristic, I _cm is the bias current.

In order to obtain increased temperature stability, the non-linear current amplifier contains a voltage amplifier, the inverting input of which is connected to the first input terminal of the non-linear current amplifier and the first terminal of the first resistor, the second terminal of which is connected to the output of the first current generator, the emitter of the first transistor and the first terminal of the non-linear resistive element, the second terminal of which is connected to the second input terminal of a nonlinear current amplifier and a common bus, the collector of the first transistor is connected to the input the current mirror mirror, the output terminal of which is connected to the output of the sixth current generator and the first output terminal of a non-linear current amplifier, the non-inverting input of the voltage amplifier is connected to the second output terminal of the non-linear current amplifier and a common bus, the first terminal of the non-linear resistive element is connected to the first terminal of the second resistor, the second the output of which is connected to the second output of the nonlinear resistive element and the base and collector of the second transistor, the emitter of which is connected to the base of the third transistor and the collector of the fourth transistor, the emitter of which is connected to the output of the second current generator and the first output of the third resistor, the second output of which is connected to the output of the third current generator and the emitter of the fifth transistor, the base of which is connected to the output of the fourth current generator and the emitter of the third transistor, the collector of which is connected to the first the power bus and the collector of the sixth transistor, the emitter of which is connected to the base of the fourth transistor and the output of the fifth current generator, the collector of the fifth transistor is connected inen with the base of the sixth transistor and the emitter of the seventh transistor, the base and collector of which is connected to the first output of the nonlinear resistive element, the input terminal of the current mirror is connected to the base and collector of the eighth transistor and the base of the ninth transistor, the emitter of the eighth transistor is connected to the collector of the tenth transistor, with the first power bus and the emitter of the eleventh transistor, the base and collector of which are connected to the base of the tenth transistor and the emitter of the ninth transistor, collect p is connected to the output terminal of the current mirror, the common bus of the first, second, third, fourth, fifth and sixth current generators are connected to the second power supply bus.

The inventive generator of chaotic oscillations is illustrated in figure 1, which shows its electrical circuit diagram, figure 2, which shows the distribution of currents and voltages in the circuit of the generator during its operation, figure 3, which shows the dimensionless transfer characteristic of a nonlinear current amplifier, fig .4, which shows the electrical diagram of the practical implementation of the chaotic oscillation generator, Figs. 5 and 6, which show examples of the projection of a dimensionless strange attractor onto the (x, y) plane, and Figs. 7 and 8, on which x shows examples of the dependence of the dimensionless variable y on time.

The chaotic oscillator contains the first 1 and second 2 bipolar elements with capacitive resistance, a bipolar element with inductive resistance 3, a resistive element 4 and a non-linear current amplifier 5, a non-linear current amplifier contains a voltage amplifier 6, a non-linear resistive element 7, a current mirror 8, a first resistor 9, the first transistor 10, the first 11 and sixth 12 current generators, the non-linear resistive element contains the second 13 and third 14 resistors, the second 15, third 16, fourth 17, fifth 18, sixth 19 and seventh 20 transistor , Second 21, third 22, fourth 23 and fifth 24 current generator, a current mirror 25 comprises the eighth, ninth, 26, 27, the tenth and eleventh transistors 28.

We write the equations describing the dynamics of this generator, assuming the input resistance and output conductivity of the nonlinear current amplifier to be negligible, (see figure 2):

; $$i_{C\mathrm{one}}=C_{\mathrm{one}}\frac{d{u}_{C\mathrm{one}}}{dt}=i_{\mathrm{at}sx}\left(i_{\mathrm{at}x}\right)-i_L$$

;

; $${\mathrm{<figure-callout\; id="2"\; label="i\; C"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">i\; </figure-callout>}}_C=C_2\frac{d{u}_{C2}}{dt}=i_L-i_{\mathrm{at}x}$$

;

$$i_L=L\frac{d{i}_L}{dt}=u_{C\mathrm{one}}-{\mathrm{<figure-callout\; id="2"\; label="u\; C"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_C;\text{(one)}$$

, $$i_{\mathrm{at}x}=\frac{u_{C2}}{R}$$

,

where C ₁ is the capacitance of the first bipolar element with capacitance 1; C ₂ - the capacity of the second bipolar element with capacitance 2; L is the inductance of a bipolar element with inductive resistance 3; u _C1 and i _C1 - voltage at the first bipolar element with capacitance 1 and the current flowing through it, respectively; u _C2 and i _C2 - voltage at the second bipolar element with capacitance 2 and the current flowing through it, respectively; u _L and i _L - voltage on a bipolar element with inductive resistance 3 and the current flowing through it, respectively; R is the resistance of the resistive element 4.

, $$\frac{{\text{du}}_{\text{C2}}}{\text{dt}}$$

, и $$\frac{d{i}_L}{dt}$$

, получим следующую систему дифференциальных уравнений:By solving equations (1) with respect to $$\frac{d{u}_{C\mathrm{one}}}{dt}$$

, $$\frac{{\text{du}}_{\text{C2}}}{\text{dt}}$$

, and $$\frac{d{i}_L}{dt}$$

, we obtain the following system of differential equations:

$$\{\begin{array}{l}\frac{d{u}_{C\mathrm{one}}}{dt}=\frac{i_{\mathrm{at}sx}\left(\frac{u_{\mathrm{FROM}2}}{R}\right)-i_L}{C{}_{\mathrm{one}}};\\ \frac{d{u}_{C2}}{dt}=\frac{i_L-\frac{U_{C2}}{\mathrm{<figure-callout\; id="2"\; label="R\; C"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">R\; </figure-callout>}}}{C_{}};\text{(2)}\\ \frac{{\text{di}}_{\text{L}}}{\text{dt}}=\frac{u_{C\mathrm{one}}-u_{C2}}{L}.\end{array}$$

, $$y=\frac{u_{C2}}{R{I}_0}$$

, $$z=\frac{i_L}{I_0}$$

, где $$I_0=\sqrt{I_{01}{I}_{02}}$$

, и безразмерное время $$\tau =\frac{t}{R{C}_2}$$

, представим полученные уравнения в безразмерном виде:Introducing dimensionless variables $$x=\frac{u_{C\mathrm{one}}}{R{I}_0}$$

, $$y=\frac{u_{C2}}{R{I}_0}$$

, $$z=\frac{i_L}{I_0}$$

where $${\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000028.png,00000030.png"\; state="\{\{state\}\}">I</figure-callout>}}_0=\sqrt{I_{01}{I}_{02}}$$

, and dimensionless time $$\tau =\frac{\mathrm{<figure-callout\; id="2"\; label="t\; R\; C"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">t\; </figure-callout>}}{R{C}_{}}$$

, we present the obtained equations in a dimensionless form:

$$\{\begin{array}{l}\frac{dx}{d\tau }=A\left[f\left(y\right)-z\right];\\ \frac{dy}{d\tau }=z-y;\text{(3)}\\ \frac{\text{dz}}{\text{d}\tau }=B\left(x-y\right),\end{array}$$

- безразмерная передаточная характеристика нелинейного усилителя тока $$g=\frac{I_{см}}{I_0}$$

; $$d=\sqrt{\frac{I_{02}}{I_{01}}}$$

; $$A=\frac{C_2}{C_1}$$

; $$B=\frac{C_2{R}^2}{L}$$

.Where $$f\left(y\right)=\frac{i\left(\frac{u_{C2}}{R}\right)}{{\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000028.png,00000030.png"\; state="\{\{state\}\}">I</figure-callout>}}_0}=by+\frac{a-b}{2}\left(|\; |\; |x+d|\; |\; |-|\; |\; |x-\frac{\mathrm{one}}{d}|\; |\; |-d+\frac{\mathrm{one}}{d}\right)+g$$

- dimensionless transfer characteristic of a nonlinear current amplifier $$g=\frac{I_{\mathrm{from}\mathrm{<figure-callout\; id="0"\; label="m\; I"\; filenames="00000028.png,00000030.png"\; state="\{\{state\}\}">m\; </figure-callout>}}}{I_{}}$$

; $$d=\sqrt{\frac{I_{02}}{I_{01}}}$$

; $$A=\frac{C_2}{C_{\mathrm{one}}}$$

; $$B=\frac{C_2{R}^2}{L}$$

.

, $$b=-1-\frac{R1}{R2}$$

, $$I_{01}=\frac{R3}{R1}{I}_2$$

, $$I_{02}=\frac{R3}{R1}{I}_3$$

, I_см=I₄-I₁-I₃, где R1, R2, R3 - сопротивления соответственно первого 9, второго 13 и третьего 14, резисторов, I₁ - значение выходного тока первого генератора тока 11, I₂ - значение выходного тока второго генератора тока 21, I₃ - значение выходного тока третьего генератора тока 22, I₄ - значение выходного тока шестого генератора тока 12. Выходные токи первого 11 и шестого 12 генераторов тока устанавливаются в несколько раз большими выходных токов второго 21, третьего 22, четвертого 23 и пятого 24 генераторов тока: I₁=(2…5)I₂, I₁=(2…5)I₃, I₄=(2…5)I₂, I₄=(2…5)I₃, I₁=(2…5)I₅, I₄=(2…5)I₅, где I₅ - значение выходных токов четвертого 23 и пятого 24 генераторов тока.Non-linear current amplifier 5 in the circuit of figure 4 has the transfer characteristic shown in the claims, the parameters of which are equal to: $$a=\frac{R\mathrm{one}}{R3}-\mathrm{one}-\frac{R\mathrm{one}}{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">R</figure-callout>}2}$$

, $$b=-\mathrm{one}-\frac{R\mathrm{one}}{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">R</figure-callout>}2}$$

, $$I_{01}=\frac{R3}{R\mathrm{one}}{\mathrm{<figure-callout\; id="2"\; label="I"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">I</figure-callout>}}_2$$

, $$I_{02}=\frac{R3}{R\mathrm{one}}{\mathrm{<figure-callout\; id="3"\; label="I"\; filenames="00000027.png,00000029.png"\; state="\{\{state\}\}">I</figure-callout>}}_3$$

, I _cm = I ₄ -I ₁ -I ₃ , where R1, R2, R3 are the resistances of the first 9, second 13 and third 14, respectively, of the resistors, I ₁ is the value of the output current of the first current generator 11, I ₂ is the value of the output current the second current generator 21, I ₃ is the output current value of the third current generator 22, I ₄ is the output current value of the sixth current generator 12. The output currents of the first 11 and sixth 12 current generators are set several times higher than the output currents of the second 21, third 22, fourth 23 and fifth of 24 current generators: I ₁ = (2 ... 5) I ₂ , I ₁ = (2 ... 5) I ₃ , I ₄ = (2 ... 5) I ₂ , I ₄ = (2 ... 5) I ₃ , I ₁ = (2 ... 5) I ₅ , I ₄ = ( 2 ... 5) I ₅ , where I ₅ is the value of the output currents of the fourth 23 and fifth 24 current generators.

In system (3), there are irregular self-oscillations characterized by positive values of the highest characteristic Lyapunov exponent. For example, with a = 10, b = -2.1, d = 1, g = 0, A = 1, B = 0.7 ... 1.4, this figure is 0.12 ... 0.2, with a = 10, b = -2.1, d = 0.5, g = -1, A = 1, B = 0.5 ... 1.5 it is 0.05 ... 0.16, in particular with a = 10, b = -2.1, d = 1, g = 0, A = 1, B = 0.8 it is close to 0.16, with a = 10, b = -2.1, d = 0.5, g = -1, A = 1, B = 0.8, the senior characteristic Lyapunov exponent is approximately 0.06.

Therefore, for given values of the coefficients a, b, A, B, g, random oscillations are observed in the generator in Fig. 4.

Let R = 1 kOhm, R2 = 700 Ohm, C1 = 10 nF. Then, in the case A = 1, B = 0.8, a = 10, b = 2.1, d = 1, g = 0, chaotic oscillations in the circuit in Fig. 4 are observed at R1≈770 Ohm, R3≈62 Ohm, C2 = 10 nF , L≈12.5 mH. Putting I ₀₁ = I ₀₂ = I ₀ = 80 μA, we find that the output currents of the second and third current generators are I ₂ = I ₃ ≈1 mA, I _cm = 0; assuming I ₁ = 3 mA, we get I ₄ ≈4 mA; in this case, I ₅ ≈1 mA can be selected. In the case A = 1, B = 0.8, a = 10, b = -2.1, d = 0.5, g = -1, at I ₀ = 80 μA and, accordingly, I _cm = -80 μA, I ₀₁ = 160 μA , I ₀₂ = 40 μA, the output currents of the second and third current generators are equal to I ₂ ≈2 mA, I ₃ ≈0.5 mA, respectively; assuming I ₁ = 3 mA, we get I ₄ ≈3.58 mA; I ₅ ≈1 mA.

Figures 5 and 6 show examples of the projection of a chaotic attractor onto the (x, y) plane A = 1, B = 0.8, a = 10, b = -2.1, d = 1, g = 0 and with A = 1, B = 0.8, a = 10, b = -2.1, d = 0.5, g = -1, respectively. Figures 7 and 8 give corresponding examples of the dependence of the dimensionless variable y on time.

The advantage of the claimed generator of chaotic oscillations in comparison with the prototype is the ability to rebuild the parameters of chaotic oscillations by adjusting the position of the boundaries between the middle and side sections and changing the shift of the transfer characteristic of the nonlinear current amplifier, which allows you to modify the geometry of the strange attractor.

The increased temperature stability of the nonlinear current amplifier is due to the fact that its transfer characteristic is practically independent of the parameters of the transistors due to the mutual compensation of the emitter resistances of the transistors 15 and 17, 18 and 20 and the negligible effect on its parameters of the emitter resistances of the transistors 10, 16, 19, 25, 26, 27 and 28.

Claims (2)

1. A chaotic oscillation generator containing a resistive element, the first terminal of which is connected to the first terminal of the bipolar element with inductive resistance, the second terminal of which is connected to the first terminal of the first bipolar element with capacitive resistance, the second terminal of which is connected to the first terminal of the second bipolar element with capacitive resistance characterized in that a non-linear current amplifier is introduced into it, the first input terminal of which is connected to the second output of the resistive element, the first output which is connected to the second terminal of the second bipolar element with capacitive resistance, the first terminal of which is connected to the second input terminal of the non-linear current amplifier, the first and second output terminals of which are connected respectively to the first and second terminals of the first bipolar element with capacitive resistance, the transfer characteristic of the non-linear current amplifier defined by the equation:

where i _out (i _in ) is the output current flowing through the output terminals of the non-linear current amplifier under the influence of the input current i _in flowing through the input terminals of the non-linear current amplifier, a is the steepness of the average passing through the origin of the portion of the transfer characteristic, b is the steepness of the side sections of the transfer characteristic, I ₀₁ and I ₀₂ are the absolute values of the boundary currents between the middle and side sections of the transfer characteristic, I _cm is the bias current. 2. The chaotic oscillation generator according to claim 1, characterized in that the non-linear current amplifier comprises a voltage amplifier, the inverting input of which is connected to the first input terminal of the non-linear current amplifier and the first terminal of the first resistor, the second terminal of which is connected to the output of the first current generator, emitter of the first a transistor and a first terminal of a non-linear resistive element, the second terminal of which is connected to a second input terminal of a non-linear current amplifier and a common bus, the collector of the first transistor is connected to an input with the output of the current mirror, the output of which is connected to the output of the sixth current generator and the first output of the non-linear current amplifier, the non-inverting input of the voltage amplifier is connected to the second output of the non-linear current amplifier and a common bus, the first output of the non-linear resistive element is connected to the first output of the second resistor, the second terminal of which is connected to the second terminal of the nonlinear resistive element and the base and collector of the second transistor, the emitter of which is connected to the base of the third transistor ora and the collector of the fourth transistor, the emitter of which is connected to the output of the second current generator and the first output of the third resistor, the second output of which is connected to the output of the third current generator and the emitter of the fifth transistor, the base of which is connected to the output of the fourth current generator and the emitter of the third transistor, the collector of which is connected with the first power bus and the collector of the sixth transistor, the emitter of which is connected to the base of the fourth transistor and the output of the fifth current generator, the collector of the fifth transistor connected to the base of the sixth transistor and the emitter of the seventh transistor, the base and collector of which is connected to the first output of the nonlinear resistive element, the input terminal of the current mirror is connected to the base and collector of the eighth transistor and the base of the ninth transistor, the emitter of the eighth transistor is connected to the collector of the tenth transistor, with the first power bus and the emitter of the eleventh transistor, the base and collector of which is connected to the base of the tenth transistor and the emitter of the ninth transistor, count whose lecturer is connected to the output terminal of the current mirror, the common buses of the first, second, third, fourth, fifth and sixth current generators are connected to the second power bus.

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