# Random-vibrations generator

**FIELD: radio engineering.**

**SUBSTANCE: proposed generator of integrated design that can be used as source of random electromagnetic waves has two resistors, two capacitors, negative-conductivity device, and negative-conductivity parallel RC circuit.**

**EFFECT: simplified design, enlarged operating frequency range.**

**2 cl, 6 dwg**

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

Known generator of chaotic oscillations (N.Inaba, T.Saito and S.Mori. Chaotic phenomena in a circuit with negative resistance and ideal swith of diodes //The transactions of IEICE, 1987, Vol.E 70, No 8, P.744)containing the device with negative resistance, the first output of which is connected to the first conclusions of the first capacitance and nonlinear resistor, the second terminal is connected with the second output of the first capacitance and the first conclusions of the second capacitor and inductor, the second, the conclusions of which is connected to the second output of the nonlinear resistor.

Also known generator of chaotic oscillations (Aromasi. Chaotic relaxation oscillator. Izvestiya vuzov “Applied nonlinear dynamics”,1994, Vol.2, No. 2, P.50), which is a blocking oscillator, in the collector circuit of the transistor which includes an additional capacitor.

However, the oscillatory system of these generators contains inductance, which limits the possibility of their implementation in integrated circuits.

The closest to the technical nature of the claimed device is a generator of chaotic oscillations (A.Namajunas, A.Tamasevicius. Modified Wien-bridge oscillator for chaos //Electronics Letters, 1995, Vol.31, No. 5, S-336), containing the first resistor, the first and second findings of which are connected with the first findings from therefore, its first and second capacitors, the second terminal of the first capacitor is connected to the first output of the second resistor.

The disadvantage of this generator of chaotic oscillations is that its construction is based on the use of the operational amplifier voltage, which significantly complicates its implementation in the integrated design, and significantly reduces the upper limit of the range of operating frequencies.

The aim of the invention is to simplify the implementation of the generator of chaotic oscillations in the integrated design and expansion of the range of operating frequencies.

The purpose of the invention is achieved by the fact that the generator of chaotic oscillations, containing the first resistor, the first and second findings of which are connected with the first pins respectively of the first and second capacitors, the second terminal of the first capacitor is connected to the first output of the second resistor, the adjustment device with negative conductivity and a parallel RC-circuit with negative impedance, the first and second conclusions which are connected respectively with the first output of the second resistor and the second output of the first resistor, a first output which is connected to the first output device with negative conductivity, the second terminal of which is connected with the second pins of the second resistor and the second capacitor, and a work plot the current-voltage characteristics of the device is tion with negative conductivity is defined by the equation
where i is the current flowing between the terminals on the unit with negative conductivity under the action of applied thereto the voltage u, R1 is the resistance of the first resistor, U_{0}- boundary voltage between the medium passing through the origin, and the side sections of the volt-ampere characteristic, a and b are constants, satisfying the relations a<0, b>.

To improve thermal stability of a parallel RC-circuit with negative impedance contains the first impedance Converter, the first and second input conclusions which are respectively the first and second pins of the parallel RC-circuit with negative impedance, connected to the outputs of the respective first and second current generators, a common bus which is connected to the first power bus, the first load output of the first impedance Converter connected with the first conclusions of the third resistor and the third capacitor, the second, the conclusions of which is connected to the second load output of the first impedance Converter, a device with negative conductivity contains the second impedance Converter, the first and second load conclusions which which are respectively the first and second outputs of a device with negative conductivity, connected respectively with the first and second findings of the fourth resistor, the first and second input in the water of the second impedance Converter connected with the first conclusions of the respective fifth and sixth resistors, the latter findings are connected to a common bus, each of the impedance Converter includes first and second transistors, the emitters of which are respectively the first and second input terminals of the Converter impedance, the base of which is connected to the respective emitters of the third and fourth transistors and the outputs of the respective first and second current generators of the impedance Converter, a common bus which is connected to the first power bus, the collector of the first transistor is connected to the base of the fourth transistor and the emitter of the fifth transistor, the base of which is connected to the collector of the third transistor and the emitter of the sixth transistor, the base and the collector of which is connected to the output of the third current generator Converter impedance and the collector of the fifth transistor that is the first load output of the impedance Converter, the collector of the second transistor is connected to the base of the third transistor and the emitter of the seventh transistor, the base of which is connected to the collector of the fourth transistor and the emitter of the eighth transistor, the base and the collector of which is connected to the output of the fourth current generator Converter impedance and the collector of the seventh transistor, the second load output of the impedance Converter, the common bus of the third and fourth current generators are connected with the second power bus.

The inventive generator of chaotic oscillations is illustrated by figure 1, which shows its schematic electrical diagram, figure 2, which shows the distribution of currents and voltages in the circuit of the generator during its operation, figure 3, which is given to the electric circuit of the practical implementation of the generator of chaotic oscillations, figure 4, which shows the electric circuit of the impedance converters that are included with the generator of chaotic oscillations, figure 5, which shows an example of a projection dimensionless strange attractor on the plane (y, z), and 6, which shows an example of dependence of the dimensionless variable y from time to time.

The generator of chaotic oscillations contains a parallel RC-circuit with negative impedance 1, the device with negative conductivity 2, the first 3 and second 4 resistors, the first 5 and second 6 capacitors, parallel RC-circuit with negative impedance contains the first impedance Converter 7, the first 8 and second 9 current generators, the third resistor 10 and the third capacitor 11, the device with negative conductivity contains the second impedance Converter 12, 13 fourth, fifth, 14 and 15 sixth resistors, each impedance Converter includes first 16 and second 17, the third 18, 19 fourth, fifth 20 sixth 21, 22 seventh and eighth transistors 23, the first 24 and second 25, the third 26 and fourth 27 generators envelope the RA of the impedance.

We write the equations describing the dynamics of the generator (see figure 2):

where R1, R2, R3 is the resistance of the first 3, the second 4 and the third 10 resistors, respectively; C1, C2, C3 is the capacitance of the first 5 second 6 and third 11 capacitors; u_{C1}u_{C2}and u_{C3}variable voltage on the first, second and third capacitors, respectively; i(u) - dynamic volt-ampere characteristic of the device with negative conductivity.

Solving the equation (1) with respect toandwe get the following system of differential equations:

Introducing the normalized variables(where U_{0}- the value of the boundary voltage between the middle and side sections of the current-voltage characteristics of the device with negative conductivity) and the dimensionless time
here equation (2) to the dimensionless form:

where- dimensionless dynamic volt-ampere characteristic of the device with negative conductivity;

In system (3) there are irregular self-oscillations, characterized by positive values of the senior characteristic Lyapunov exponent. For example, when a=-0.5, b=1, A=7...7.3, B=7, C=0.2, D=1, this index is equal to 0.3...0.5, in particular when a=-0.5, b=1, A=7, B=7, C=0.2, D=1, it is close to 0.5; a=-0.5, b=-0.2, A=8, B=8.1...9, p=0.3, D=1 senior characteristic Lyapunov exponent is in the range from 0.16 to 0.27; when a=-2, b=2, A=6.9...7, B=7, C=0.1, D=1 it is approximately equal to 0.35...0.7. Therefore, when these values of the coefficients a, b, a, b, C, D in the proposed generator are observed chaotic oscillations.

In the diagram in figure 3 and 4 the device with negative conductivity is given in the claims the volt-ampere characteristic, ifandwhere R4 is the resistance value of the fourth resistor 13, R5 - value of the fifth resistance 14 and 15 sixth resistors. The boundary voltage between the middle and side sections of the volt-ampere characteristics as the specific well
where I_{K1}- the value of the output currents of the first 24 and second 25 of the current generators of the second impedance Converter, I_{K2}- the value of the output currents of the third 26 and fourth 27 current generators of the second impedance Converter. The values of the output currents of the current generators of the first impedance Converter must satisfy the relation I_{K2}=I_{K1}+I_{0}where I_{0}- the value of the output currents of the first 8 and second 9 current generator. Output currents of the third and fourth current generators of the first impedance Converter should be a lot more output currents of the third and fourth current generators of the second impedance Converter.

Let R1=500 Ω, C1=5 nF. Then when A=7, B=7, C=0.2, D=1, a=-0.5, b=1 chaotic oscillations in the scheme of figure 3 are observed when R2≈2500 Ohms, R3≈500 Ohms, C2≈0.7 nF, C3≈0.7 nF, R4≈500 Ohm, R5≈167 Ohms. Putting U_{0}=333 mV and setting in both impedance converters I_{K1}=0.4 mA, get that output currents of the third and fourth current generators of the second impedance Converter is equal to I_{K2}=1.4 mA. Thus the output currents of the third and fourth current generators of the first impedance Converter can be equal, for example, I_{K2}=5.4 mA and the output currents of the first and second generator current I_{0}=I_{K2}-I_{K1}=5 mA.

Corresponding to these values of the parameters of the generator examples dimensionless strange attra the Torah and according to the dimensionless variable at a time is shown in figure 5 and 6.

Thus, the proposed generator of chaotic oscillations differs from prototype and analogs, because it does not contain elements that hinder its implementation in the integrated design and significantly limiting the range of operating frequencies. High temperature stability of the parallel RC-circuit with negative impedance device with negative conductivity is due to the fact that the equivalent impedance of these devices is practically not depend on the parameters of the transistors forming part of the impedance converters, due to the mutual compensation of the emitter resistances of transistors 16 and 20, 17 and 22, 18 and 21, 19 and 23.

1. The generator of chaotic oscillations, containing the first resistor, the first and second findings of which are connected with the first pins respectively of the first and second capacitors, the second terminal of the first capacitor is connected to the first output of the second resistor, characterized in that it introduced the device with negative conductivity and a parallel RC-circuit with negative impedance, the first and second conclusions which are connected respectively with the first output of the second resistor and the second output of the first resistor, a first output which is connected to the first output device with negative conductivity, the second terminal of which is connected with the second pins of the second through the Stora and the second capacitor, with a working area of the current-voltage characteristics of the device with negative conductivity is defined by the equation

where i is the current flowing between the terminals on the unit with negative conductivity under the action of applied thereto the voltage u,

R1 is the resistance of the first resistor

U_{0}- boundary voltage between the medium passing through the origin, and the side sections of the volt-ampere characteristic,

a and b are constants, satisfying the relations a<0, b>.

2. The generator of chaotic oscillations according to claim 1, characterized in that the parallel RC-circuit with negative impedance contains the first impedance Converter, the first and second input conclusions which are respectively the first and second pins of the parallel RC-circuit with negative impedance, connected to the outputs of the respective first and second current generators, a common bus which is connected to the first power bus, the first load output of the first impedance Converter connected with the first conclusions of the third resistor and the third capacitor, the second, the conclusions of which is connected to the second load output of the first impedance Converter, a device with negative conductivity contains the second impedance Converter, the first and second load pickup is s which, which are respectively the first and second outputs of a device with negative conductivity, connected respectively with the first and second findings of the fourth resistor, the first and second input findings of the second impedance Converter connected with the first conclusions of the respective fifth and sixth resistors, the latter findings are connected to a common bus, each of the impedance Converter includes first and second transistors, the emitters of which are respectively the first and second input terminals of the Converter impedance, the base of which is connected to the respective emitters of the third and fourth transistors and the outputs of the respective first and second current generators of the impedance Converter, a common bus which is connected to the first power bus, the collector of the first transistor is connected to the base of the fourth transistor and the emitter of the fifth transistor, the base of which is connected to the collector of the third transistor and the emitter of the sixth transistor, the base and the collector of which is connected to the output of the third current generator Converter impedance and the collector of the fifth transistor, the first load output of the impedance Converter, the collector of the second transistor is connected to the base of the third transistor and the emitter of the seventh transistor, the base of which is connected to the collector of the fourth transistor and emit the rum of the eighth transistor, the base and collector of which is connected to the output of the fourth current generator Converter impedance and the collector of the seventh transistor, the second load output of the impedance Converter, the common bus of the third and fourth current generators of the impedance Converter is connected with the second power bus.

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