# Chaotic wave oscillator

FIELD: radio engineering; chaotic electromagnetic wave sources.

SUBSTANCE: proposed chaotic wave oscillator has negative-resistance nonlinear device, capacitor, two inductance components, and resistor; current-voltage characteristic of negative-resistance device is such that voltage across its terminals is unambiguous function of current flowing through this device.

EFFECT: minimized quantity of circuit components.

2 cl, 5 dwg

The alleged 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, VoI.E 70, No 8, P.744)containing the device with negative resistance, the first output of which is connected with the first findings of the first capacitor and a nonlinear resistor, the second terminal is connected with the second output of the first capacitor and the first findings of the second capacitor and the inductive element, the second, the conclusions of which is connected to the second output of the nonlinear resistor.

Also known generator of chaotic oscillations (Traumata. Chaos in electric circuits. TIER, 1987, CH, No. 8, P.67-68, figure 1 and figure 6), containing the device with negative resistance, in parallel with which is included a first capacitor, a first output which is connected to the first output resistor, the second terminal of which is connected to the first terminals of inductive element and the second capacitor, the second, the conclusions of which is connected to the second output of the first capacitor.

However, these generators in its original configuration, corresponding to the minimum number of circuit elements, contain the ideal resonant circuits without loss that involves changing their Messiah. elektricheskoi scheme for practical implementation.

The closest to the technical nature of the claimed device is a generator of chaotic oscillations (Prokopenko VG Generator of chaotic oscillations. Path of the Russian Federation. Publ. 27.09.2001. BIPM No. 27), containing the first inductive element, the first output of which is connected to the first output device with negative resistance, the second terminal of which is connected to the first resistor, the second terminal of which is connected to the first output of the second inductive element, the second terminal of which is connected to the first output capacitor.

The disadvantage of this generator of chaotic oscillations is that if the minimum number of circuit elements it contains the ideal resonant circuit, in which no elements, taking into account the energy dissipation, which involves the complication of its equivalent electrical scheme for practical implementation.

The aim of the invention is to develop a generator of chaotic oscillations, containing the minimum number of circuit elements of the equivalent electrical circuit which needs no complication if its practical implementation.

The purpose of the invention is achieved by the fact that the generator of chaotic oscillations, containing the first inductive element, the first output of which is connected to the first output device with negative resistance, the Torah, the output of which is connected to the first output resistor, the second output of which is connected to the first output of the second inductive element, the second terminal of which is connected to the first output capacitor, the first and second terminals of the capacitor according to your selection connected with the second output of the first inductive element and the first output resistor, and the current-voltage characteristic of the device with negative resistance such that the voltage on the findings of this device is a unique function of the flowing current through it.

With the aim of obtaining high temperature stability of the device with negative resistance contains the first transistor, the emitter of which, which is the first output device with negative resistance, is connected to the output of the first current generator, a collector connected to the emitter of the second transistor and the base of the third transistor, the collector of which is connected to the base of the first transistor and the emitter of the fourth transistor, the base and the collector of the second transistor is connected to the first output of the first resistor, the second terminal of which is connected to the common bus and the first output of the second resistor, the second terminal of which is connected to the base and collector of the fourth transistor, the emitter of the third transistor is connected to the output of the second current generator the first output of the third resistor and the emitter of the fifth transistor, the call is a torus which is connected to the emitter of the sixth transistor and the base of the seventh transistor, the collector of which is connected to the base of the fifth transistor and the emitter of the eighth transistor, the base and the collector of which is connected with the base and collector of the sixth transistor and the output of the third current generator, the emitter of the seventh transistor, the second output device with negative resistance, is connected to the output of the fourth current generator and the second output of the third resistor, the common bus of the third current generator connected to the first power bus, the common bus of the first, second 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 shows the electric diagram of the practical implementation of the generator of chaotic oscillations; figure 4, which shows an example of a projection dimensionless strange attractor on the plane (x,y); figure 5, which shows an example of dependence of the dimensionless variable x from time to time.

The generator of chaotic oscillations contains a device with negative resistance 1, condenser 2, the first 3 and second 4 inductive elements and the resistor 5, and the device with negative resistance contains the first 6, second 7, 8 third, everty 9, the fifth 10, 11 sixth, seventh 12 and 13 eighth transistors, the first 14 and second 15 and 16 third resistors, the first 17 and second 18, 19 third and fourth 20 generators.

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

where L_{1}and L_{2}- inductance of the inductive elements 3 and 4; C is the capacitance of the capacitor 2; i_{L1}and i_{L2}variables currents flowing respectively in inductive elements 3 and 4; u_{c}- AC voltage on the capacitor; u(i_{L1}dynamic volt-ampere characteristic of the device with negative resistance.

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

Introducing dimensionless variablesand the dimensionless time, will present the equations in dimensionless form:

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

.

The device with negative resistance in the circuit in figure 3 has a volt-ampere characteristic;

where u is the voltage, in necause between pins of the device with negative resistance under the action of the flowing current i_{
L1}, R is the resistance of the resistor, I_{0}- boundary current between the medium passing through the origin, and the side sections of the volt-ampere characteristic, a=-2R1/R and b=(R2-2R1)/R.

Thus the output current I_{1}, I_{2}, I_{3}, I_{4}accordingly, the first, second, third and fourth current generators have the following meanings I_{3}=2I_{0}, I_{4}=I_{0}, I_{2}=I_{0}+I_{1}, I_{1}>>I_{0}.

The corresponding dimensionless volt-ampere characteristic in equations (3) has the form:

When a<-1, b<0 in the system (3), (5) there are irregular self-oscillations, characterized by positive values of the senior characteristic Lyapunov exponent. For example, if a=-1.3, b=-0.7, A=1,≈ 0.6... 0.7 index is equal to 0.01 0.08..., in particular when a=-1.3, b=-0.7, A=1, B=0.63 he is close to 0.08; when a=-1.1, b=-0.9, A=1, B=0.6 0.69... senior characteristic Lyapunov exponent is in the range from 0.06 to 0.01.

Therefore, when these values of the coefficients a, b, And, in the generator of figure 1 are observed chaotic oscillations.

Let R=200 Ω, C=nF. Then if A=1, B=0.63, a=-1.3, b=-0.7 chaotic oscillations in the scheme of figure 3 are observed at R1≈ 130 Ω, R_{2}≈_{}120 Ohm, L1=L2≈ 126 mH. Putting the I_{0}=200ua, I_{1}=2mA, get that output currents of the second, third and fourth artego current generators respectively I_{
2}=MA, I_{3}=M, 14=mA.

Corresponding to these values of the parameters of the generator examples dimensionless strange attractor and the dependence of the dimensionless variable x with time is shown in figure 4 and 5.

Equivalent electrical circuit of the generator of chaotic oscillations do not need to be adjusted in the practical implementation, because the loss in the first inductive element is easily accounted for by changing the corresponding parameters of the volt-ampere characteristic is connected in series with them devices with negative resistance and losses in the second inductive element and the capacitor is a corresponding change in the resistance of the resistor.

High temperature stability of the device with negative resistance due to the fact that its volt-ampere characteristic is almost independent of the parameters of the transistors due to the mutual compensation of the emitter resistances of the transistors 6 and 7, 8 and 9, 10 and 11, 12 and 13.

1. The generator of chaotic oscillations, containing the first inductive element, the first output of which is connected to the first output device with negative resistance, the second terminal of which is connected to the first resistor, the second terminal of which is connected to the first output of the second inductive element, the second terminal of which is connected to the first vivado the capacitor, characterized in that the first and second terminals of the capacitor are connected respectively with the second output of the first inductive element and the first output resistor, and the current-voltage characteristic of the device with negative resistance such that the voltage on the findings of this device is a unique function of the flowing current through it.

2. The generator of chaotic oscillations according to claim 1, characterized in that the device with negative resistance contains the first transistor, the emitter of which, which is the first output device with negative resistance, is connected to the output of the first current generator, a collector connected to the emitter of the second transistor and the base of the third transistor, the collector of which is connected to the base of the first transistor and the emitter of the fourth transistor, the base and the collector of the second transistor is connected to the first output of the first resistor, the second terminal of which is connected to the common bus and the first output of the second resistor, the second terminal of which is connected to the base and collector of the fourth transistor, the emitter of the third transistor is connected to the output of the second current generator, the first output of the third resistor and the emitter of the fifth transistor, the collector of which is connected to the emitter of the sixth transistor and the base of the seventh transistor, the collector of which is connected to the base of the fifth transistor and the emitter of the eighth transistor, the base and collector of which is connected with the base and collector of the sixth transistor and the output of the third current generator, the emitter of the seventh transistor, the second output device with negative resistance, is connected to the output of the fourth current generator and the second output of the third resistor, the common bus of the third current generator connected to the first power bus, the common bus of the first, second and fourth current generators are connected with the second power bus.

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