RU2625520C1 - Chaotic oscillator - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: chaotic oscillator contains a resistor, the first and the second bipolar elements with capacitive resistance, a two-pole element with inductive resistance, a device with negative resistance and a nonlinear impedance converter.

EFFECT: providing the possibility of adjusting the parameters of a chaotic signal.

3 cl, 11 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 (RF Patent No. 2379822, IPC Н03В 29/00), containing an operational amplifier, the negative feedback circuit of which contains a variable resistor and a first field-effect transistor, the input of which is connected to the output of the operational amplifier using the RC Wines circuit and with the input the second operational amplifier, the output of which is connected to the input of the nonlinear inertial converter, and the output of the nonlinear inertial converter is connected to the input of the field transistor, the nonlinear inertial conversion The body is made in the form of a second field-effect transistor with a low-pass filter as a load.

A generator of chaotic oscillations is also known (RF Patent 2549152, IPC Н03В 29/00, G06G 7/26), containing the first and second inductive elements, the first and second capacitors, the first and second resistors, a semiconductor voltage converter connected to its first output with a second output the second resistor, the first terminal of which is connected to the third terminal of the voltage converter, and the second terminal is connected to the first terminals of the second capacitor and the load resistance connected in parallel, connected by their second terminals to the four the fifth and fifth terminals of the semiconductor voltage converter, and with its first terminals with its sixth terminal, the second terminal of the semiconductor voltage converter is connected to the second terminal of the first capacitor and to the negative potential of the power source, the positive potential of which is connected through the first resistor and the first induction element connected in series with a first terminal of a semiconductor voltage converter and a first terminal of a first capacitor.

The disadvantage of these generators is the limited possibility of tuning the chaotic signal due to the insignificant possibility of changing the geometry of the chaotic attractor.

Closest to the technical nature of the claimed device is a chaotic oscillator (T. Matsumoto. Chaos in electrical circuits. TIIER, 1987, T. 75, No. 8, P. 67-68, Fig. 1 and Fig. 6), containing a resistor the first 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 device with negative resistance, the first terminal of the bipolar element with inductive resistance and the first terminal of the second bipolar element with capacitive otivleniem, a second terminal coupled to a second terminal of the bipolar element to the inductive reactance.

The disadvantage of this generator of chaotic oscillations is that it allows only a slight change in the configuration of the chaotic attractor, which limits the possibility of tuning the parameters of the generated chaotic signal.

The aim of the invention is to expand the ability to control parameters of a chaotic signal.

The purpose of the invention is achieved in that a chaotic oscillator containing a resistor, the first 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 device with negative resistance, the first output of the bipolar element with inductive resistance and the first output a second bipolar element with capacitance, a second terminal of which is connected to a second terminal of a bipolar element with inductive resistance , a nonlinear impedance converter is introduced, the first and second input terminals of which are connected respectively to the second terminal of the device with negative resistance and the second terminal of the bipolar element with inductive resistance, the first terminal of the resistor is connected to the first output terminal of the nonlinear impedance converter, the second output terminal of which is connected to the second terminal resistor, the transfer characteristic of the nonlinear impedance converter is such that the current flowing through the output terminals of the nonlinear the impedance converter is a unique function of the current flowing through the input terminals of the nonlinear impedance converter, the voltage at the first input terminal of the nonlinear impedance converter is equal to the voltage at the first output terminal of the nonlinear impedance converter, the voltage at the second input terminal of the nonlinear impedance converter is equal to the voltage at the second output terminal of the nonlinear converter impedance.

Moreover, the transfer characteristic of the nonlinear impedance converter is determined by the equation

where i _out (i _in ) is the current flowing through the output terminals of the nonlinear impedance converter under the action of the current i _in flowing through the input terminals of the nonlinear impedance converter, I ₀₁ and I ₀₂ are the absolute values of the boundary currents between the average passing through the origin, and the lateral sections of the transfer characteristic, and a , b1 and b2 are the material coefficients that determine the slope of the middle, first and second side segments of the transfer characteristic, respectively.

In order to improve the accuracy and stability of the transfer characteristic of the non-linear impedance converter, as well as the accuracy and stability of the equivalent negative resistance value of the device with negative resistance, the non-linear impedance converter contains a voltage amplifier, the non-inverting input of which is connected to the first input terminal of the non-linear impedance converter, the first output of the first resistor and the first conclusions of the first and second active four-terminal networks, the second conclusions of which are are dined by the second output of the first resistor, the first output of the second resistor and the output of the voltage amplifier, the inverting input of which is connected to the first output terminal of the nonlinear impedance converter, the second output of the second resistor, the output of the first current generator and the output of the current mirror, the input of which is connected to the third terminals of the first and second active four-terminal, the fourth conclusions of which are connected to the first power bus and the common bus of the current mirror, the common bus of the first current generator is connected to the second bus power supply, the second input and second output terminals of the nonlinear impedance converter are connected to a common bus, the device with negative resistance contains a third active four-terminal device, the first and third conclusions of which are connected to the first output of the device with negative resistance and the output of the second current generator, the common bus of which is connected to the first power bus and the common bus of the third current generator, the output of which is connected to the second and fourth terminals of the third active four-terminal network and the second terminal devices with negative resistance, each active four-terminal contains a first transistor, the base and collector of which are the corresponding first and third terminals of the active four-terminal, the second transistor, the base and collector of which are the corresponding second and fourth terminals of the active four-terminal, the emitter of the first transistor is connected to the collector of the third transistor and the base of the fourth transistor, the emitter of which is connected to the first terminal of the first four-terminal resistor and collector of the transistor, the base of which is connected to the second terminal of the first four-terminal resistor and the first terminal of the second four-terminal resistor, the second terminal of which is connected to the emitter of the fifth transistor, the base of the sixth transistor and the output of the first four-terminal current generator, the common bus of which is connected to the second power bus and the common bus of the second a four-terminal current generator, the output of which is connected to the base of the third transistor, the emitter of the seventh transistor and the first output of the third four-terminal resistor, the second terminal of which is connected to the base of the seventh transistor and the first terminal of the fourth resistor of the four-terminal, the second terminal of which is connected to the collector of the seventh transistor and the emitter of the eighth transistor, the base of which is connected to the emitter of the second transistor and the collector of the sixth transistor, the emitter of which is connected to the output of the third current generator of the four-terminal and the first output of the fifth four-terminal resistor, the second output of which is connected to the output of the fourth four-terminal current generator and the emitter of the third transistor, the collectors of the fourth and eighth transistors are connected to the first power bus, the common buses of the third and fourth current generators of the four-terminal are connected to the second power bus.

The inventive chaotic oscillator is illustrated in FIG. 1, which shows its electrical circuit diagram, FIG. 2, which shows the distribution of currents and voltages in the generator circuit during its operation, FIG. 3 and FIG. 4, which shows a schematic diagram of an electrical circuit of the practical implementation of the inventive generator; FIG. 5, which shows the transfer characteristic of a nonlinear impedance converter, FIG. 6, which shows an example of the projection of a chaotic attractor of a chaotic oscillation generator onto the (y, z) plane at a = -5, b1 = b2 = 3, d1 = d2-1, A = 2.5, B = 10, C = 3, FIG. . 7, which shows an example of the projection of a chaotic attractor of a chaotic oscillation generator onto the (y, z) plane at a = -5, b1 = -2, b2 = 6, d1 = 0.4, d2 = 1, A = 2, B = 10, C = 3, FIG. 8, which shows an example of the projection of a chaotic attractor of a chaotic oscillation generator onto the (y, z) plane at a = -5, b1 = -2, b2 = 3, d1 = 0.07, d2 = 1, A = -5, B = 10 FIG. 9, which shows an example of the time dependence of the variable y corresponding to the attractor in FIG. 6, FIG. 10, which shows an example of the time dependence of the variable y corresponding to the attractor in FIG. 7 and FIG. 11, which shows an example of the time dependence of the variable y corresponding to the attractor in FIG. 8.

The chaotic oscillator contains a resistor 1, the first 2 and second 3 bipolar elements with capacitive resistance, a bipolar element with inductive resistance 4, a device with negative resistance 5 and a non-linear impedance converter 6, a non-linear impedance converter contains a voltage amplifier 7, the first 8 and second 9 active four-terminal, first 10 and second 11 resistors, current mirror 12 and first current generator 13, a device with negative resistance 5 contains a third active four-terminal 14, in 15 and third 16 current generators, each active four-terminal network contains the first 17, second 18, third 19, fourth 20, fifth 21, sixth 22, seventh 23 and eighth 24 transistors, first 25, second 26, third 27, fourth 28 and fifth 29 four-terminal resistors, the first 30, second 31, third 32 and fourth 33 fourth-terminal current generators.

We write the equations describing the dynamics of the claimed generator (see Fig. 2):

where C1 and C2 are capacitances of the first 2 and second 3 bipolar elements with capacitance, respectively; L is the inductance of a bipolar element with inductive resistance 4; R is the resistance of the resistor 1; R _e - the absolute value of the equivalent negative resistance of the device with negative resistance 5; u _C1 and u _C2 - alternating voltages on the first 2 and second 3 bipolar elements with capacitance, respectively; i _C1 and i _C2 - alternating currents flowing in the circuits of the first 2 and second 3 bipolar elements with capacitance, respectively; u _L and i _L are the alternating voltage at the bipolar element with inductive resistance 4 and the alternating current flowing through it, respectively.

и

, получим следующую систему дифференциальных уравнений:By solving equations (1) with respect to

and

, we obtain the following system of differential equations:

,

,

и безразмерное время

, где I₀ - постоянный ток, представим полученные уравнения в безразмерном виде:Introducing dimensionless variables

,

,

and dimensionless time

, where I ₀ - direct current, we present the obtained equations in a dimensionless form:

Where

- безразмерная передаточная характеристика нелинейного преобразователя импеданса;

.

- dimensionless transfer characteristic of a nonlinear impedance converter;

.

где R1, R2 - сопротивления соответственно первого 10 и второго 11 резисторов; R3 и R4 - сопротивления пятых 29 резисторов четырехполюсника, входящих в состав соответственно первого 8 и второго 9 активных четырехполюсников; I1 - выходной ток четвертого 33 генератора тока четырехполюсника, входящего в состав первого 8 активного четырехполюсника; I2 - выходной ток третьего 32 генератора тока четырехполюсника, входящего в состав второго 9 активного четырехполюсника. Выходной ток I₃ первого 13 генератора тока равен I₃=I₁+I₄, где I₄ - выходной ток четвертого 33 генератора тока, входящего в состав второго 9 активного четырехполюсника. Выходной ток I₅ третьего 32 генератора тока четырехполюсника, входящего в состав первого 8 активного четырехполюсника, устанавливается много большим тока I₁ четвертого 33 генератора тока четырехполюсника, входящего в состав первого 8 активного четырехполюсника: I₅>>I₁. Выходной I₄ ток четвертого 33 генератора тока четырехполюсника, входящего в состав второго 9 активного четырехполюсника, устанавливается много большим тока I₂ третьего 32 генератора тока четырехполюсника, входящего в состав второго 9 активного четырехполюсника: I₄>>I₂.The non-linear impedance converter in the circuit of FIG. 3, FIG. 4 has a transfer characteristic given in the claims, the parameters of which are equal

where R1, R2 are the resistances of the first 10 and second 11 resistors, respectively; R3 and R4 are the resistances of the fifth 29 four-terminal resistors included in the first 8 and second 9 active four-terminal, respectively; I1 is the output current of the fourth 33 four-terminal current generator, which is part of the first 8 active four-terminal; I2 is the output current of the third 32 of the four-terminal current generator, which is part of the second 9 active four-terminal. The output current I _{3 of the} first 13 current generator is I ₃ = I ₁ + I ₄ , where I ₄ is the output current of the fourth 33 current generator, which is part of the second 9 active four-terminal network. The output current I _{5 of the} third 32 four-terminal current generator, which is part of the first 8 active four-terminal, is set much higher than the current I _{1 of the} fourth 33 four-terminal current generator, which is part of the first 8 active four-terminal: I ₅ >> I ₁ . The output I ₄ current of the fourth 33 four-terminal current generator, which is part of the second 9 active four-terminal, is set much higher than the current I _{2 of the} third 32 four-terminal current generator, which is part of the second 9 active four-terminal: I ₄ >> I ₂ .

The absolute value of R _{e the} equivalent negative resistance of the device with negative resistance is equal to the resistance of the fifth 29th resistor of the four-terminal network, which is part of the third 14 active four-terminal network. The output current of the second 15 current generator is equal to the output current of the fourth 33 of the four-terminal current generator, which is part of the third 14 active four-terminal. The output current of the third 16 current generator is equal to the output current of the third 32 four-terminal current generator, which is part of the third 14 active four-terminal. The output currents of the third and fourth current generators of the four-terminal network included in the third 14 active four-terminal network are selected by many large currents I ₁ and I ₂ .

The value of the resistances R5 of the resistors of the four-terminal 25, 26, 27, 28 and the values of the output currents I6 of the first 30 and second 31 current generators of the four-terminal are selected so that the potential difference between the emitter of the transistor 20 and the base of the transistor 22, and also between the emitter of the transistor 24 and the base of the transistor 19 in each active four-terminal network, it exceeded half the maximum voltage value between the first and second terminals of the active four-terminal network.

The current generators included in the circuit of FIG. 3, FIG. 4 are direct current sources.

In system (3), there are irregular self-oscillations characterized by positive values of the highest characteristic Lyapunov exponent. For example,

- at a = -5, b1 = b2 = 3, d1 = d2 = 1, A = 2.5, B = 7.7 ... 11.5, C = 3, this indicator is 0.4 ... 0.1, in particular, at B = 10 it is close to 0.28;

- at a = -5, b1 = -2, b2 = 6, d1 = 0.4, d2 = 1, A = 2, B = 7 ... 10, C = 3, this indicator is 0.38 ... 0.1, in particular, at = 10 it is close to 0.23;

- at a = -5, b1 = -2, b2 = 3, d1 = 0.07, d2 = 1, A = -5, B = 8.5 ... 10.5, C = 3, the senior characteristic Lyapunov exponent lies in the range from 0.27 to 0.1 in particular, at B = 10 it is close to 0.25.

Therefore, for given values of the coefficients a , b1, b1, d1, d2, A, B, C in the generator in FIG. 1 chaotic oscillations are observed.

Let R = 100 Ohm, R _E = 300 Ohm, R1 = 5760 Ohm, C1 = 40 nF, I ₀ = 100 μA. Then in the case a = -5, b1 = b2 = 3, d1 = d2 = 1, A = 2.5, B = 10, C = 3 chaotic oscillations in the circuit in FIG. 3 are observed at R2≈524 Ohm, R3 = R4≈720 Ohm, С2≈100 nF, L1≈900 μH, I ₁ = I ₂ ≈800 μA, I ₄ = I ₅ = 2 mA, I ₃ = 2.8 mA, R5 = 5 kΩ, I6 = 2 mA;

in the case a = -5, b1 = -2, b2 = 6, d1 = 0.4, d2 = 1, A = 2.5, B = 10, C = 3 - at R2≈640 Ohm, R3≈1920 Ohm, R4≈524 Ohm, C2≈100 nF, L1≈900 μH, I ₁ ≈120 μA, I ₂ ≈ 1.1 mA, I ₄ = 4 mA, I ₅ = 1 mA, I ₃ = 4.12 mA, R5 = 5 kOhm, I6 = 2 mA;

in the case a = -5, b1 = -2, b2 = 3, d1 = 0.07, d2 = 1, A = 2.5, B = 10, C = 3 - at R2≈960 Ohm, R3≈1920 Ohm, R4≈720 Ohm, C2≈100 nF, L1≈900 μH, I ₁ ≈20 μA, I ₂ ≈800 μA, I ₄ = 4 mA, I ₅ = 1 mA, I ₃ = 4.02 mA, R5 = 5 kOhm, I6 = 2 ma

The claimed generator of chaotic oscillations compares favorably with analogues and prototype in that it provides an additional, in comparison with them, ability to control the parameters of the generated chaotic signal by restructuring the geometry of the strange attractor when changing the slope of the segments of the transfer characteristic of the nonlinear impedance transducer and the position of the boundaries between them.

The increased accuracy and temperature stability of the transfer characteristic of the nonlinear impedance converter and the equivalent negative resistance of a device with negative resistance is due to the fact that the parameters of the active four-terminal devices are practically independent of the parameters of the transistors, due to the mutual compensation of the emitter resistances of the transistors 17 and 19, 18 and 22, and negligible on its parameters emitter resistances of transistors 21 and 23.

Claims (5)

1. A chaotic oscillation generator containing a resistor, the first 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 device with negative resistance, the first terminal of the bipolar element with inductive resistance and the first terminal of the second bipolar element with capacitive resistance, the second terminal of which is connected to the second terminal of the bipolar element with inductive resistance, characterized in that a linear impedance converter, the first and second input terminals of which are connected respectively to the second terminal of the device with negative resistance and the second terminal of the bipolar element with inductive resistance, the first terminal of the resistor is connected to the first output terminal of the nonlinear impedance converter, the second output terminal of which is connected to the second terminal of the resistor, the transfer characteristic of the nonlinear impedance converter is such that the current flowing through the output terminals of the nonlinear transform impedance generator is an unambiguous function of the current flowing through the input terminals of the nonlinear impedance converter, the voltage at the first input terminal of the nonlinear impedance converter is equal to the voltage at the first output terminal of the nonlinear impedance converter, the voltage at the second input terminal of the nonlinear impedance converter is equal to the voltage at the second output terminal of the nonlinear converter impedance. 2. The generator of chaotic oscillations according to claim 1, characterized in that the transfer characteristic of the nonlinear impedance converter is determined by the equation

where i _out (i _in ) is the current flowing through the output terminals of the nonlinear impedance converter under the action of the current i _in flowing through the input terminals of the nonlinear impedance converter, I ₀₁ and I ₀₂ are the absolute values of the boundary currents between the average passing through the origin, and the lateral sections of the transfer characteristic, and a, b1 and b2 are the material coefficients that determine the slope of the middle, first and second side segments of the transfer characteristic, respectively. 3. The chaotic oscillation generator according to claim 2, characterized in that the non-linear impedance converter comprises a voltage amplifier, the non-inverting input of which is connected to the first input terminal of the non-linear impedance converter, the first terminal of the first resistor and the first terminals of the first and second active four-terminal devices, the second terminals of which are connected with the second terminal of the first resistor, the first terminal of the second resistor and the output of the voltage amplifier, the inverting input of which is connected to the first output terminal of nonline of the second impedance converter, the second output of the second resistor, the output of the first current generator and the output of the current mirror, the input of which is connected to the third terminals of the first and second active four-terminal, the fourth conclusions of which are connected to the first power bus and the common bus of the current mirror, the common bus of the first current generator is connected with a second power bus, a second input and second output terminals of a nonlinear impedance converter are connected to a common bus, a device with a negative resistance contains a third a active four-terminal, the first and third conclusions of which are connected to the first output of the device with negative resistance and the output of the second current generator, the common bus of which is connected to the first power bus and the common bus of the third current generator, the output of which is connected to the second and fourth terminals of the third active four-terminal and second the output of a device with negative resistance, each active four-terminal network contains a first transistor, the base and collector of which are the first and third outputs dams of the active four-terminal, the second transistor, the base and collector of which are the corresponding second and fourth terminals of the active four-terminal, the emitter of the first transistor is connected to the collector of the third transistor and the base of the fourth transistor, the emitter of which is connected to the first terminal of the first resistor of the four-terminal and the collector of the fifth transistor, the base of which is connected with the second terminal of the first four-terminal resistor and the first terminal of the second four-terminal resistor, the second terminal of which is connected is connected with the emitter of the fifth transistor, the base of the sixth transistor and the output of the first four-terminal current generator, the common bus of which is connected to the second power bus and the common bus of the second four-terminal current generator, the output of which is connected to the base of the third transistor, the emitter of the seventh transistor and the first output of the third four-terminal resistor, the second terminal of which is connected to the base of the seventh transistor and the first terminal of the fourth resistor of the four-terminal, the second terminal of which is connected to the collector of the seventh trans the source and the emitter of the eighth transistor, the base of which is connected to the emitter of the second transistor and the collector of the sixth transistor, the emitter of which is connected to the output of the third four-terminal current generator and the first terminal of the fifth four-terminal resistor, the second terminal of which is connected to the output of the fourth four-terminal current generator and the emitter of the third transistor, collectors the fourth and eighth transistors are connected to the first power bus, common buses of the third and fourth current generators enes with the second power supply bus.

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