Chaotic oscillation generator

FIELD: electricity.

SUBSTANCE: chaotic oscillation generator contains two inductive elements, two capacitors, two resistors, a semiconductor voltage converter by means of which the characteristics of generated oscillations are regulated, and a load.

EFFECT: providing of signal modelling described by piecewise and linear differential equations characterizing the occurring periodic, quasi-periodic and chaotic oscillations.

2 cl, 5 dwg

 

The invention relates to electrical engineering, in particular to radio engineering and can be used as a source of harmonic, quasi-periodic and chaotic oscillations in the simulation and development of switching power supplies, relay modeling of automatic control systems and information transmission systems, the study of noise immunity of different systems, etc.

Known generator of chaotic oscillations, performed at a tunnel diode included in one of the branches of the LC-oscillating circuit (see Smirnov V. V. Generators on tunnel diodes. Meters, Energy, 1971, p. 11, Fig.5).

The disadvantage of the object is not sufficiently high stability of the average value of the amplitude of the output random signals.

Also known generator of chaotic oscillations (A. S. Pikovsky, M. I. Rabinovich. A simple oscillator with stochastic behavior. Reports of the USSR Academy of Sciences, 1978, vol. 239, No. 2, p. 302), comprising a tunnel diode, the anode of which is connected to the first output resistor, the second terminal of which is connected with the first output inductor, the second terminal of which is connected to the first output device with negative resistance, the second terminal of which is connected to the cathode of tunnel diode and in parallel with the tunnel diode and the device with negative resistance under�mediately respectively the first and second capacitors.

Its disadvantage is that the elements required for the operation of the generator nonlinearity must also have certain physical values, which imposes restrictions on the possibility of independent change of parameters of nonlinearity.

The closest adopted for the prototype, is the generator of chaotic oscillations (patent for invention of the Russian Federation No. 2305891, CL. NV 29/00, 2007), containing common features with the proposed invention: inductive element, a capacitor, a resistor, a second resistor (a device with negative resistance) and non-linear capacitive element.

Known object cannot be used to study the dynamics and modeling of a wide class of systems described by piecewise linear differential equations (relay automatic control systems, switching power supplies), as it has an excellent type of the equations of motion derived from the use of the device with negative impedance.

The technical result is to increase the capabilities of the invention by providing the ability to simulate systems described by piecewise linear differential equations in which there are harmonic, quasi-periodic and chaotic oscillations, and explore the dynamic properties of this class of systems./p>

The technical result is achieved in that the generator of chaotic oscillations comprises a first inductive element, a first capacitor, first resistor, second resistor and second capacitor. It introduced a semiconductor voltage Converter and the second inductive element, coupled with its first output to the second terminal of the second resistor, the first output of which is connected with the third output of the voltage Converter and the second output is connected with the first conclusions of parallel connected second capacitor and the load resistance connected your second outputs from the fourth and fifth findings of a semiconductor voltage Converter, and my initial findings with his sixth output, wherein the second semiconductor Converter output voltage is connected with the second output of the first capacitor and the negative potential of the power source, the positive potential which is connected through series-connected first resistor and the first inductive element to the first semiconductor Converter output voltage and the first output of the first capacitor.

To improve the stability and control characteristics of the generated oscillation semiconductor voltage Converter includes a direct circuit and a feedback circuit, connected via a shared bus � his second, the fourth and sixth pins, and first and second Comparators, wherein the first output is connected to the R input and a second output to the S input of an RS flip flop, the output of which through the fourth resistor is connected with the base of n-p-n transistor connected by its emitter to the common bus and its collector gate field-effect transistor and a third resistor, the other terminal of which is simultaneously connected with the first output (input) semiconductor voltage Converter and the source of the field-effect transistor, the drain of which is connected directly with the third and output through the diode, connected cathode to the drain of the fourth semiconductor Converter output voltage, in addition, the first input of the first comparator is connected with the collector of the variable resistor, which is connected by its output via a seventh resistor to the negative potential of the driving power source and the common bus, and the second output through the fifth resistor, with its positive potential and directly to a first input of the second comparator, a second input connected to the second input of the first comparator and the mid-point of the voltage divider on the eighth and ninth resistors connected his findings with the fifth and sixth conclusions semiconductor voltage Converter.

To illustrate the proposed invention in Fig. 1 shows �electric schematic diagram of the generator of chaotic oscillations and shows the currents and voltages in the circuit when it is functioning, Fig. 2 is an electrical schematic diagram of a physical implementation of the generator of Fig. 3 - phase portrait of U2(U1) harmonic oscillations of the generator of Fig. 4 - the phase portrait of U2(U1) quasi-periodic oscillations of the generator of Fig. 5 - the phase portrait of U2(U1) chaotic oscillations of the generator.

Generator of chaotic oscillations, contains the first resistor 1, the first inductive element 2, a first capacitor 3, a semiconductor voltage Converter 4, a second resistor 5, the second inductive element 6, the second capacitor 7, the load resistance 8, a semiconductor voltage Converter are the third resistor 9, the field effect transistor 10, diode 11, a fifth resistor 12, a sixth resistor 13, a seventh resistor 14, the first comparator 15, the second comparator 16, an RS-flip-flop 17, the fourth resistor 18, the n-p-n transistor 19, the eighth resistor 20, the ninth resistor 21.

The proposed invention operates as follows: when the supply voltage to the input of the generator (the first terminal of the first resistor 1 and the second terminal of the first capacitor 3) voltage at load resistance 8 is compared in amplitude Comparators 15 and 16 with the predetermined voltage is supplied to the divider of the resistors 12, 13 and 14), further, if the voltage at load resistance 8 is less than the specified,the output RS flip-flop 17 is set to a logical one, which is fed through a resistor 18 to the base of n-p-n transistor 19 and opens it, thereby opening the field effect transistor 10, through which in turn starts the chain of current to flow from the power source to the load resistance 8, when the voltage at load resistance 8 is compared with a preset or exceeds, the output of the RS flip-flop 17 is set to logical zero, which is supplied via a resistor 18 to the base of n-p-n transistor 19 and closes it thereby closing the field-effect transistor 10 and preventing the flow of current from the power source to the load resistance 8, etc. by Changing the supply voltage generator, the dead zone, which is determined by the Comparators 15 (lower bound) and 16 (upper bound), the load resistance 8, can be obtained at the output of the generator of periodic, quasiperiodic and chaotic oscillations.

The technical result of the invention (see Fig. 2) based on the following system of piecewise-linear differential equations that describe the dynamics of the generator of chaotic oscillations:

where

or

In the system of equations: C1and C2- capacity of the first 3 and 7 second capacitors, respectively; L1and L2- inductance of the first 2 and second in�aktivnih elements, respectively; R1, R2, Rn- resistance of the first 1, second 5 resistor and the load resistance 8, respectively; i1and i2the currents flowing in the first resistor 1, the first inductive element 2 and the second resistor 5, the second inductive element 6, respectively; i is the current flowing at the input of the semiconductor Converter 4; UnU1U2U - supply voltage generator, the voltage on the first capacitor 2 and the second capacitor 7, the voltage output from the semiconductor voltage Converter, respectively, ε=UWsignal applied to the input of the Comparators 15 and 16, KFsignal at the output of the RS flip-flop 17.

After transformation of a system of differential equations(1), (2), (3) will look as follows:

We introduce the notation:

Then the system of differential equations can be represented in the form:

where

g1=η(-x1-x2+Ω);

ε(X)=UW-KOSx4;

In matrix form the system of differential equations will look as follows:

Examples of phase portraits based U 2(U1) illustrating the operation of the generator shown in Fig. 3 for harmonic oscillations, Fig. 4 for quasiperiodic oscillations, Fig. 5. for chaotic oscillations.

Thus, using the invention it is possible to investigate the dynamics and simulate systems described by piecewise linear differential equations (6).

1. Generator of chaotic oscillations, containing the first inductive element, a first capacitor, first resistor, second resistor and second capacitor, characterized in that it introduced a semiconductor voltage Converter and the second inductive element, coupled with its first output to the second terminal of the second resistor, the first output of which is connected with the third output of the voltage Converter and the second output is connected with the first conclusions of parallel connected second capacitor and the load resistance connected your second outputs from the fourth and fifth findings of a semiconductor voltage Converter, and my initial findings with his sixth output wherein the second semiconductor Converter output voltage is connected with the second output of the first capacitor and the negative potential of the power source, the positive potential which is connected through series-connected first resistor and first� inductive element to the first semiconductor Converter output voltage and the first output of the first capacitor.

2. Generator of chaotic oscillations according to claim 1, characterized in that a semiconductor voltage Converter includes a direct circuit and a feedback circuit, connected via a shared bus with his second, fourth and sixth pins, and first and second Comparators, wherein the first output is connected to the R input and a second output to the S input of an RS flip flop, the output of which through the fourth resistor is connected with the base of n-p-n transistor connected by its emitter to the common bus and its collector gate field-effect transistor and a third resistor, the other terminal of which is simultaneously connected with the first output (input) semiconductor voltage Converter and the source of the field-effect transistor, the drain of which is connected directly with the third output through the diode cathode connected to the drain of the fourth semiconductor Converter output voltage, in addition, the first input of the first comparator is connected with the collector of the variable resistor, which is connected by its output via a seventh resistor to the negative potential of the driving power source and the common bus, and the second output through the fifth resistor, with its positive potential and directly to a first input of the second comparator, a second input connected to the second input of the first comparator and the mid-point of the voltage divider eighth�ohms and ninth resistors, United their findings with the fifth and sixth conclusions semiconductor voltage Converter.



 

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