RU2421877C1 - Chaotic vibration generator - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: chaotic vibration generator includes bipolar element with inductive reactance, the first and the second bipolar elements with capacitive resistance, resistor, the first non-linear impedance converter of the first type, the first bipolar element with capacitive resistance includes the first linear capacitance element and the first non-linear impedance converter of the second type, the second bipolar element with capacitive resistance includes the second linear capacitive element and the second non-linear impedance converter of the second type, bipolar element with inductive reactance includes linear inductive element and the second non-linear impedance converter of the first type.

EFFECT: enlarging control limits of parameters of generated chaotic signal.

24 dwg

Description

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

The well-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 a device with negative resistance, the first terminal of which is connected to the first terminals of the first capacitor and non-linear resistor, the second terminal is connected to the second terminal of the first capacitor and the first terminals of the second capacitor and inductive element, the second terminals of which are connected to the second terminal of the non-linear resistor.

A generator of chaotic oscillations is also known (T. Matsumoto. Chaos in electronic circuits. TIIER, 1987, v. 75, No. 8, p. 67-68, fig. 1 and fig. 6), containing a device with negative resistance, the first output of which connected to the first terminal of the first capacitor and the first terminal of the resistor, the second terminal of which is connected to the first terminal of the second capacitor and the first terminal of the inductor, the second terminal of which is connected to the second terminal of the second capacitor and the second terminal of the device with negative resistance.

The disadvantage of these generators is the limited ability to modify the chaotic attractor, which limits the possibility of tuning the parameters of the generated chaotic oscillations.

The closest in technical essence to the claimed device is a generator of chaotic oscillations (Prokopenko VG Generator of chaotic oscillations. Pat. 2273088. Publ. 2006, BIPM No. 9), containing a bipolar element with inductive resistance, the first output of which is connected to the first input output the first nonlinear impedance converter of the first type, the second input terminal of which is connected to the first terminal of the resistor, the second terminal of which is connected to the second terminal of the bipolar element with inductive resistance and th terminal of the first bipolar element with a capacitive impedance, a second terminal coupled to a first output terminal of the first nonlinear transformer of the impedance of the first type and the first terminal of the second bipolar element with a capacitive impedance, a second terminal connected to the second output terminal of the first nonlinear transformer of the first type of impedance.

The disadvantage of this generator of chaotic oscillations is that the properties of the chaotic attractor in it are determined by the characteristics of a single nonlinear element, which limits the possibility of tuning the parameters of the generated chaotic oscillations.

The aim of the invention is to expand the limits of regulation of the parameters of a chaotic signal by expanding the possibilities of modifying the configuration of the corresponding chaotic attractor.

The purpose of the invention is achieved in that in a chaotic oscillator containing a bipolar element with inductive resistance, the first output of which is connected to the first input terminal of the first nonlinear impedance converter of the first type, the second input terminal of which is connected to the first terminal of the resistor, the second terminal of which is connected to the second terminal a bipolar element with inductance and a first terminal of the first bipolar element with capacitive resistance, the second terminal of which is connected to the first yhodnym terminal of a first nonlinear transformer of the impedance of the first type and the first terminal of the second bipolar element with a capacitive impedance, a second terminal connected to the second output terminal of the first nonlinear transformer of the impedance of the first type, the transfer characteristic of the first nonlinear transformer of the first type of impedance is defined by the equation

,

, I₀ - граничный ток между средним, проходящим через начало координат, и боковыми участками передаточной характеристики, a и b - вещественные коэффициенты, имеющие противоположные знаки, M и N - целые неотрицательные числа, напряжение на первом входном выводе первого нелинейного преобразователя импеданса первого типа равно напряжению на первом выходном выводе первого нелинейного преобразователя импеданса первого типа, напряжение на втором входном выводе первого нелинейного преобразователя импеданса первого типа равно напряжению на втором выходном выводе первого нелинейного преобразователя импеданса первого типа, первый двухполюсный элемент с емкостным сопротивлением содержит первый линейный емкостный элемент, первый и второй выводы которого соединены соответственно с первым и вторым выводами первого нелинейного преобразователя импеданса второго типа, третий и четвертый выводы которого являются соответственно первым и вторым выводами первого двухполюсного элемента с емкостным сопротивлением, второй двухполюсный элемент с емкостным сопротивлением содержит второй линейный емкостный элемент, первый и второй выводы которого соединены соответственно с первым и вторым выводами второго нелинейного преобразователя импеданса второго типа, третий и четвертый выводы которого являются соответственно первым и вторым выводами второго двухполюсного элемента с емкостным сопротивлением, двухполюсный элемент с индуктивным сопротивлением содержит линейный индуктивный элемент, первый и второй выводы которого соединены соответственно с первым и вторым выводами второго нелинейного преобразователя импеданса первого типа, третий и четвертый выводы которого являются соответственно первым и вторым выводами двухполюсного элемента с индуктивным сопротивлением, переменный ток, протекающий в цепи первого двухполюсного элемента с емкостным сопротивлением, равен переменному току, протекающему в цепи первого линейного емкостного элемента, напряжение между выводами первого двухполюсного элемента с емкостным сопротивлением равно u₁(u_C1)=U₀H₁(x), где u_C1 - переменное напряжение на первом линейном емкостном элементе, U₀=I₀R, R - сопротивление резистора,

,where i ₂ (i ₁ ) is the current flowing through the output terminals of the first nonlinear impedance converter of the first type, i ₁ is the current flowing through the input terminals of the first nonlinear impedance converter of the first type,

,

, I ₀ is the boundary current between the average passing through the origin and the side sections of the transfer characteristic, a and b are real coefficients with opposite signs, M and N are non-negative integers, the voltage at the first input terminal of the first nonlinear impedance converter of the first type equal to the voltage at the first output terminal of the first nonlinear impedance converter of the first type, the voltage at the second input terminal of the first nonlinear impedance converter of the first type is equal to the voltage to the second the output terminal of the first non-linear impedance converter of the first type, the first bipolar element with capacitive resistance contains a first linear capacitive element, the first and second terminals of which are connected respectively to the first and second terminals of the first non-linear impedance converter of the second type, the third and fourth conclusions of which are respectively the first and second the findings of the first bipolar element with capacitive resistance, the second bipolar element with capacitive resistance contains a second a linear capacitive element, the first and second terminals of which are connected respectively to the first and second terminals of the second non-linear impedance converter of the second type, the third and fourth terminals of which are respectively the first and second terminals of the second bipolar element with capacitive resistance, the bipolar element with inductive resistance contains a linear inductive element , the first and second terminals of which are connected respectively to the first and second terminals of the second non-linear impedance converter and the first type, the third and fourth conclusions of which are respectively the first and second terminals of a bipolar element with inductive resistance, the alternating current flowing in the circuit of the first bipolar element with capacitive resistance is equal to the alternating current flowing in the circuit of the first linear capacitive element, the voltage between the terminals of the first bipolar element with capacitance is equal to u ₁ (u _C1 ) = U ₀ H ₁ (x), where u _C1 is the alternating voltage on the first linear capacitive element, U ₀ = I ₀ R, R is the resistance of the resistor,

,

, d₁, h₁ и s₁ - вещественные коэффициенты, причем d₁>>1, M₁ и N₁ - целые неотрицательные числа, переменный ток, протекающий в цепи второго двухполюсного элемента с емкостным сопротивлением, равен переменному току, протекающему в цепи второго линейного емкостного элемента, напряжение между выводами второго двухполюсного элемента с емкостным сопротивлением равно u₂(u_C2)=U₀H₂(y), где u_C2 - переменное напряжение и на втором линейном емкостном элементе,

,

, d ₁ , h ₁ and s ₁ are real coefficients, and d ₁ >> 1, M ₁ and N ₁ are non-negative integers, the alternating current flowing in the circuit of the second bipolar element with capacitive resistance is equal to the alternating current flowing in the circuit the second linear capacitive element, the voltage between the terminals of the second bipolar element with capacitive resistance is equal to u ₂ (u _C2 ) = U ₀ H ₂ (y), where u _C2 is the alternating voltage on the second linear capacitive element,

,

d₂, h₂ и s₂ - вещественные коэффициенты, причем d₂>>1, M₂ и N₂ - целые неотрицательные числа, переменное напряжение между выводами двухполюсного элемента с индуктивным сопротивлением равно переменному напряжению на линейном индуктивном элементе, ток, протекающий в цепи двухполюсного элемента с индуктивным сопротивлением, равен i(i_L)=I₀H₃(z), где i_L - переменный ток, протекающий в цепи линейного индуктивного элемента,

,

d ₂ , h ₂ and s ₂ are real coefficients, and d ₂ >> 1, M ₂ and N ₂ are non-negative integers, the alternating voltage between the terminals of the bipolar element with inductive resistance is equal to the alternating voltage on the linear inductive element, the current flowing in the circuit of a bipolar element with inductive resistance is i (i _L ) = I ₀ H ₃ (z), where i _L is the alternating current flowing in the circuit of a linear inductive element,

,

d₃, h₃ и s₃ - вещественные коэффициенты, причем d₃>>1, M₃ и N₃ - целые неотрицательные числа.

d ₃ , h ₃ and s ₃ are real coefficients, and d ₃ >> 1, M ₃ and N ₃ are non-negative integers.

In order to obtain improved accuracy and temperature stability, the first non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the first input terminal of the first non-linear impedance converter of the first type and the first terminal of a nonlinear two-terminal device, the second terminal of which is connected to the first output of the voltage amplifier and the first terminal linear bipolar, the second output of which is connected to the first output terminal of the first nonlinear impedance converter and the first type and the non-inverting input of the voltage amplifier, the second output of which is connected to the second input and second output terminals of the first non-linear impedance converter of the first type and a common bus, the second non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the second input of the second non-linear converter the impedance of the first type and the first output of a nonlinear bipolar, the second output of which is connected to the first output of the voltage amplifier and the first a resistor water, the second output of which is connected to the second output of the second non-linear impedance converter of the first type and the non-inverting input of the voltage amplifier, the second output of which is connected to the first input and first output terminals of the second non-linear impedance converter of the first type, each non-linear impedance converter of the second type contains a voltage amplifier whose non-inverting input is connected to the first input and first output terminals of the non-linear impedance converter of the second IPA, the second input terminal of which is connected to the first output of the voltage amplifier and the first output of the resistor, the second terminal of which is connected to the inverting input of the voltage amplifier and the first output of a nonlinear bipolar, the second terminal of which is connected to the second output of the voltage amplifier and the second output of the nonlinear impedance converter of the second type , each nonlinear two-terminal network contains 1 + 2Max (Q, R) of series-connected active four-terminal networks, where Max (Q, R) is the larger of the numbers Q and R, which are equal to but the M and N in the nonlinear element that is part of the first nonlinear transformer of the first type, M ₁ impedance and the N ₁ in the nonlinear element that is part of the first nonlinear second type impedance converter, M ₂ and N ₂ in the nonlinear element that is part of the second a non-linear impedance converter of the second type, M ₃ and N ₃ in the non-linear two-terminal, which is part of the second non-linear impedance converter of the first type, the first and second terminals of the first active four-terminal are connected respectively to the first and second terminals of the nonlinear two-terminal network and the outputs of the corresponding first and second current generators of the nonlinear two-terminal network, the common buses of which are connected to the first power bus, the third and fourth terminals of each previous active four-terminal network are connected respectively to the first and second terminals of the subsequent active four-terminal network, the third and fourth conclusions of the last , 1 + 2Max (Q, R) -th, active four-terminal connected to the corresponding first and second terminals of the resistor, the linear two-terminal contains rubber a torus whose first and second terminals, which are the corresponding first and second terminals of the linear two-terminal network, are connected to the corresponding third and fourth terminals of the active four-terminal network, the first and second conclusions of which are connected to the outputs of the corresponding first and second current generators of the linear two-terminal network, whose common buses are connected to the first power bus, each active four-terminal network contains the first and second transistors, the emitters of which are the corresponding first and second conclusions of the active the four-terminal, connected to the corresponding first and second terminals of the first resistor, the collector of the first transistor is connected to the emitter of the third transistor and the base of the fourth transistor, the emitter of which is connected to the collector of the fifth transistor and the first terminal of the second resistor, the second terminal of which is connected to the base of the fifth transistor and the first terminal of the third a resistor, the second terminal of which is connected to the emitter of the fifth transistor, the base of the second transistor and the output of the first current generator, the common bus of which is connected and with the first power bus and the common bus of the second current generator, the output of which is connected to the base of the first transistor, the emitter of the sixth transistor and the first terminal of the fourth resistor, the second terminal of which is connected to the base of the sixth transistor and the first terminal of the fifth resistor, the second terminal of which is connected to the collector of the sixth the transistor and the emitter of the seventh transistor, the base of which is connected to the collector of the second transistor and the emitter of the eighth transistor, the base and collector of which are connected to the fourth terminal of the active a three-terminal network and the output of the third current generator, the common bus of which is connected to the collectors of the fourth and seventh transistors, the second power bus and the common bus of the fourth current generator, the output of which is connected to the base and collector of the third transistor and the third output of the active four-terminal, each voltage amplifier contains the first and second amplifier transistors, the bases of which are the corresponding non-inverting and inverting inputs of the voltage amplifier, the emitter of the first amplifier transistor is connected to the collector of the third amplifier transistor and the base of the fourth amplifier transistor, the emitter of which is connected to the output of the first amplifier current generator and the emitter of the third amplifier transistor, the base of which is connected to the collector of the fourth amplifier transistor and the emitter of the second amplifier transistor, the collector of which is connected to the base of the fifth amplifier transistor and the emitter of the sixth an amplifier transistor, the base and collector of which are connected to the output of the second amplifier current generator and the base of the seventh amplifier transistor the emitter of which is connected to the collector of the first amplifier transistor, the emitter of the fifth amplifier transistor is connected to the collector of the eighth amplifier transistor and the first output of the first amplifier resistor, the second output of which is connected to the base of the eighth amplifier transistor and the first output of the second amplifier resistor, the second output of which is connected to the emitter the eighth transistor of the amplifier, the output of the third amplifier current generator and the first output of the voltage amplifier, the collector of the fifth amplifier transistor is connected with the output of the fourth amplifier current generator and the emitter of the ninth amplifier transistor, the collector of which is connected to the output of the fifth amplifier current generator and the second voltage amplifier output, the base of the ninth amplifier transistor is connected to the third power bus, the common buses of the first, third, and fifth amplifier current generators are connected to the first power bus, common busbars of the second and fourth current generators of the amplifier are connected to the collector of the seventh transistor and to the second power 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 electrical circuit diagram of the first non-linear impedance converter of the first type, figure 4, which shows the electric circuit diagram of the second non-linear impedance converter of the first type, figure 5, which shows the electric circuit diagram of the first and second oh nonlinear impedance converters of the second type, Fig.6, which shows the circuit diagram of the electrical nonlinear bipolar circuit, Fig.7, which shows the circuit diagram of the active four-terminal active circuit, Fig.8, which shows the circuit diagram of the circuit voltage amplifier, Fig.9, which shows the dimensionless transfer characteristic of the first nonlinear impedance converter of the first type at M = 0, N = 1, Fig. 10, which shows the dimensionless transfer characteristic of the first and second nonlinear impedance converters of the second type and a second nonlinear transformer of the first type of impedance 11, which is an example of a strange attractor dimensionless projection onto the plane (x, y) when M ₁ = N ₁ = N ₂ = N ₂ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9, Fig. 12, illustrating the formation mechanism of the simplest composite multiattractor with N ₁ = 1, M ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9, Fig. 13, illustrating the formation mechanism of a composite multi-attractor at M ₁ = N ₁ = 2, M ₂ = N ₂ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9, Fig. 14, illustrating the mechanism the formation of a composite multiattractor with M ₂ = N ₂ = 2, M ₁ = N ₁ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9 15, illustrating the formation mechanism of a composite multi-attractor with M ₃ = N ₃ = 2, M ₁ = N ₁ = M ₂ = N ₂ = 0, M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9, Fig. 16, which shows a three-dimensional image of a dimensionless strange attractor at M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9, M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 1, d ₁ = d ₂ = d ₃ = 10, h ₁ ≈6.7, h ₂ ≈22.2, h ₃ ≈23.4, s ₁ = 0, s ₂ ≈ -7.5, s ₃ ≈-7.7, FIGS. 17, 18 and 19 which show examples of projection of this attractor on the (x, y), (x, z) and (y, z) planes, respectively, FIGS. 20, 21 and 22 which show the corresponding hao Fig. 16, examples of time dependences of dimensionless x, y, and z, Fig. 23, which shows the distribution of currents and voltages in the circuit of the first and second nonlinear impedance converters of the second type during their operation, Fig. 24, which shows the distribution of currents and voltages in the circuit of the second nonlinear impedance converter of the first type during its operation.

The chaotic oscillator contains the first 1 and second 2 bipolar elements with capacitive resistance, a bipolar element with inductive resistance 3, a resistor 4, a first nonlinear impedance converter of the first type 5, the first bipolar element with capacitive resistance contains a first linear capacitive element 6 and a first nonlinear impedance converter the second type 7, the second bipolar element with capacitive resistance contains a second linear capacitive element 8 and a second nonlinear impedance converter a second type 9, a two-pole element with an inductive resistance contains a linear inductive element 10 and a second non-linear impedance converter of the first type 11, the first non-linear impedance converter of the first type contains a voltage amplifier 12, a linear two-terminal 13 and a non-linear two-terminal 14, the second non-linear impedance converter of the first type contains a voltage amplifier 15, a resistor 16 and a non-linear two-terminal 17, each non-linear impedance converter of the second type contains a voltage amplifier 18, the resistor 19 and the non-linear two-terminal 20, the linear two-terminal contains a resistor 21, the active four-terminal 22, the first 23 and second 24 current generators of the linear two-terminal, the non-linear two-terminal contains a resistor 25, the active four-terminal 26, the first 27 and second 28 current generators of the non-linear two-terminal, each active four-terminal contains the first 29, second 30, third 31, fourth 32, fifth 33, sixth 34, seventh 35 and eighth 36 transistors, the first 37, second 38, third 39, fourth 40 and fifth 41 resistors, first 42, second 43, third 44 and fourth 4 5 current generators, each voltage amplifier contains the first 46, second 47, third 48, fourth 49, fifth 50, sixth 51, seventh 52, eighth 53 and ninth 54 amplifier transistors, first 55 and second 56 amplifier resistors, first 57, second 58 , third 59, fourth 60, and fifth 61 amplifier current generators.

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

where C1 and C2 are the capacities of the first 6 and second 8 linear capacitive elements; L is the inductance of the linear inductive element 10; R is the resistance of the resistor 4; u _C1 and u _C2 - alternating voltages on the first 6 and second 8 linear capacitive elements, respectively; i _C1 and i _C2 - alternating currents flowing in the circuits of the first 6 and second 8 linear capacitive elements, respectively; u _L and i _L are the alternating voltage at the linear inductive element 10 and the alternating current flowing through it, respectively.

,

,

, и разрешив уравнения (1) относительно производных

,

и

, получим следующую систему дифференциальных уравнений:Given that

,

,

, and solving equations (1) with respect to derivatives

,

and

, we obtain the following system of differential equations:

,

,

и безразмерное время

, представим полученные уравнения в безразмерном виде:Introducing dimensionless variables

,

,

and dimensionless time

, we present the obtained equations in a dimensionless form:

;

;Where

;

;

- dimensionless transfer characteristic of the first nonlinear impedance converter of the first type, w = H ₃ (z), H ₁ (x) - dimensionless transfer characteristic of the first nonlinear impedance converter of the first type, Н ₂ (y) - dimensionless transfer characteristic of the second nonlinear impedance converter of the second type , H ₃ (z) is the dimensionless transfer characteristic of the second nonlinear impedance converter of the first type.

The image of the function H _j (w _j ), where j = 1, 2, 3, w ₁ = x, w ₂ = y, w ₃ = z, is shown in Fig. 10. It can be seen that it is a piecewise linear multi-segment function containing M _j + N _j + 1 segments with a unit slope and M _j + N _j segments with a slope -d _j . The length of the argument (x, y or z) of segments with a unit slope is 2h _j , the length of the argument of segments with a slope of -d _j is 2h _j / d _j . Coefficient s _j sets the value of the displacement of the function H _j (w _j ) relative to the coordinate origin along a segment with a unit slope passing through the coordinate origin.

This nonlinearity of the current – voltage characteristics of the reactive elements of the generator circuit is necessary in order to ensure the conditions for the formation of a composite multiattractor.

In the case of linear first 1 and second 2 capacitive and inductive 3 bipolar elements (with M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0, when H ₁ (x) = x, H ₂ (y) = y, H ₃ (z) = z) the claimed chaotic oscillation generator generates chaotic oscillations corresponding to the equations:

For example, with M = 0, N = 0, a = 20, b = -3, A = 0.5, B = 1.9, M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0, the oldest characteristic Lyapunov exponent is approximately equal to 0.15 (Fig. 11).

Now put M ₁ = 1, leaving N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0. In this case, the function H ₁ (x) will take the form shown in Fig. 12. In this case, the form of oscillations in the generator will depend on the values of the coefficients h ₁ and s ₁ that specify the position of the boundaries between the segments of the nonlinear function H ₁ (x).

As long as the boundaries do not intersect with the attractor, the oscillations in the generator do not differ from the case of the linear function H ₁ (x) = x, since the movement along the x coordinate occurs on the segment of the function H ₁ (x) with a unit slope passing through the origin. However, when h ₁ decreases to 6.7, when the maximum dimensions of the attractor along the x coordinate exceed the corresponding sizes of this segment, phase trajectories will sometimes intersect the boundary between the segments and go to the segment with the slope -d and then to the adjacent segment with a single slope.

When the operating point is found within the second linear segment with a single slope, the oscillations in the generator occur in accordance with the equations:

since the second linear segment with a unit slope is shifted relative to the first such segment along the x axis by the interval [2h ₁ -s ₁ ].

, получим систему уравненийIf we replace the variables x1 = x-2h ₁ + s ₁ and take into account that

we get the system of equations

which is no different from equations (1). Therefore, when moving on an adjacent (second) segment with a unit slope, the initial chaotic attractor is reproduced, shifted relative to the original attractor by the interval [2h ₁ -s ₁ ] along the x axis.

When the trajectory crosses the boundary between the segments again, the motion will return to the initial chaotic attractor, etc. As a result, a composite chaotic attractor is formed, combining two identical attractors (Fig. 12). Similarly, a composite multi-attractor is formed with a larger number of segments in the composition of the function H ₁ (x) (Fig. 13).

In the same way, the formation of composite multiattractors, consisting of copies of the original attractor arranged along the y and z axes, is achieved by the nonlinearities of the second nonlinear impedance converter of the second type and the second nonlinear impedance converter of the first type (Fig. 14 and Fig. 15, respectively).

If two functions H _j (w _j ) are simultaneously nonlinear, the “two-dimensional” composite multiattractors are implemented in the described manner (Figs. 17, 18 and 19).

And finally, when all three functions H _j (w _j ) contain several segments with a single slope, a “three-dimensional” composite multi-attractor is formed, an example of which is shown in FIG. 16 of the description of the invention.

The values of the senior characteristic Lyapunov exponent for various values of the coefficients of equations (3) corresponding to the situations considered above are equal to:

at M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9

- in the case of M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0 (FIG. 12), the senior characteristic Lyapunov exponent is approximately 0.15;

- in the case of M ₁ = N ₁ = 1, M ₂ = N ₂ = M ₃ = N ₃ = 0, d ₁ = 30, h ₁ ≈6.7, s ₁ = 0 (Fig. 13), the senior characteristic Lyapunov exponent is approximately equal 0.16;

- in the case of M ₂ = N ₂ = 1, M ₁ = N ₁ = M ₃ = N ₃ = 0, d ₂ = 30, h ₂ ≈ 22.2, s ₂ ≈-7.5 (Fig. 14), the senior characteristic Lyapunov exponent is approximately equal to 0.16;

- in the case of M ₃ = N ₃ = 1, M ₁ = N ₁ = M ₂ = N ₂ = 0, d ₃ = 30, h ₃ ≈23.4, s ₃ ≈-7.7, the senior characteristic Lyapunov exponent is approximately 0.16;

- in the case of M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 1, d ₁ = d ₂ = d ₃ = 30, h ₁ ≈6.7, h ₂ ≈22.2, h ₃ ≈23.4, s ₁ = 0, s ₂ ≈-7.5, s ₃ ≈-7.7, the senior characteristic Lyapunov exponent is close to 0.17.

For given values of the coefficients a , b, A, B, M, N, M _j , N _j , d _j , h _j , s _j , j = 1, 2, 3, random oscillations are observed in the inventive generator, characterized by the presence of a composite strange multi-attractor consisting of several copies of the chaotic attractor shown in Fig.11.

,

,

, где R3 - сопротивление резистора 21, входящего в состав линейного двухполюсника 13; R4 - сопротивление первого резистора 37, содержащегося в активном четырехполюснике 22, входящем в состав линейного двухполюсника 13; R5 - сопротивление первого резистора 37, содержащегося в первом активном четырехполюснике 26, входящем в состав нелинейного двухполюсника 14, содержащегося в первом нелинейном преобразователе импеданса первого типа; R6 - значение входящего в состав нелинейного двухполюсника 14 сопротивления резистора 25 и сопротивлений первых резисторов 37, содержащихся в остальных, со второго по 1+2Max(M,N)-й, активных четырехполюсниках 26, входящих в состав нелинейного двухполюсника 14, содержащегося в первом нелинейном преобразователе импеданса первого типа.The parameters of the transfer characteristic of the first nonlinear impedance converter of the first type are equal

,

,

where R3 is the resistance of the resistor 21, which is part of the linear two-terminal 13; R4 is the resistance of the first resistor 37 contained in the active four-terminal 22, which is part of the linear two-terminal 13; R5 is the resistance of the first resistor 37 contained in the first active four-terminal 26 included in the non-linear two-terminal 14 contained in the first non-linear impedance converter of the first type; R6 is the value of the resistance of the resistor 25 included in the non-linear two-terminal 14 and the resistances of the first resistors 37 contained in the second, 1 + 2Max (M, N) -th, active four-terminal 26 included in the non-linear two-terminal 14 contained in the first non-linear impedance converter of the first type.

With M = N, the current I ₁ is equal to the value of the output currents of the third 44 and fourth 45 current generators, which are part of the active four-terminal 26 contained in the nonlinear two-terminal 14, which is part of the first nonlinear impedance converter of the first type. In this case, the value of the output currents I _{2 of} the current generators 27 and 28 contained in the non-linear two-terminal 14, which is part of the first non-linear impedance converter of the first type, is determined by the expression I ₂ = KI ₁ , where K = 1 + 2Max (M, N) is the number active four-terminal 26 as part of a non-linear two-terminal 14, which is part of the first non-linear impedance converter of the first type. The value of the output currents I _{3 of the} third 44 and the fourth 45 current generators included in the active four-terminal 22 contained in the linear two-terminal 13 is equal to the value of the output currents I _{4 of the} current generators 23 and 24 contained therein, I ₃ = I ₄ . Moreover, the values of currents I ₃ and I _{4 are} determined by the expression I ₃ = I ₄ ≥2I ₂ .

The case M> N differs from the case M = N in that the output currents of the third current generators 44, which are part of the 2nd (MN) 1st and 2nd (MN) -1st active four-terminal 26, contained in the nonlinear two-terminal 14 included in the composition of the first nonlinear impedance converter of the first type, respectively, increase and decrease by the same amount ΔI = (0.7 ... 0.9) I ₁ .

The case N> M differs from the case M = N in that the output currents of the fourth current generators 45 included in the 2 (NM) and 2 (NM) of the 1st active four-terminal 26 contained in the nonlinear two-terminal 14 included in the composition of the first nonlinear impedance converter of the first type, respectively, increase and decrease by the same amount ΔI = (0.7 ... 0.9) I ₁ .

,

,

,

,

, при условии, что

, где R7_j - сопротивление резистора 19, входящего в состав j-го нелинейного преобразователя импеданса второго типа; R8_j - сопротивление первого резистора 37, содержащегося в первом активном четырехполюснике 26, входящем в состав нелинейного двухполюсника 20, содержащегося в j-м нелинейном преобразователе импеданса второго типа; R9_j - значение сопротивления входящего в состав нелинейного двухполюсника 20 резистора 25 и сопротивлений первых резисторов 37, содержащихся в остальных, со второго по 1+2Max(M_j,N_j)-й, активных четырехполюсниках 26, входящих в состав нелинейного двухполюсника 20, содержащегося в j-м нелинейном преобразователе импеданса второго типа.The parameters of the transfer characteristic of the j-th nonlinear impedance converter of the second type are equal

,

,

,

,

, provided that

where R7 _j is the resistance of the resistor 19, which is part of the j-th non-linear impedance converter of the second type; R8 _j is the resistance of the first resistor 37 contained in the first active four-terminal 26, which is part of the nonlinear two-terminal 20, contained in the j-th non-linear impedance converter of the second type; R9 _j is the resistance value of the resistor 25 included in the nonlinear bipolar 20 and the resistances of the first resistors 37 contained in the second, 1 + 2Max (M _j , N _j ) -th, active four-terminal 26, included in the nonlinear bipolar 20, contained in the j-th nonlinear impedance converter of the second type.

With M _j = N _{j, the} currents I _1j and J _1j are equal to the values of the output currents of the third 44 and fourth 45 current generators, which are part of the odd, with the exception of the first, active four-terminal 26, and the values of the output currents of the fourth 45 and third 44 current generators included in the composition of even active four-terminal 26 contained in the nonlinear two-terminal 20, which is part of the j-th non-linear impedance converter of the second type. The value of the output currents I _{2j of} the current generators 27 and 28 contained in the nonlinear two-terminal network 20, which is part of the j-th nonlinear impedance converter of the second type, is determined by the expression I _2j = K _j (I _1j + J _1j ) + I _3j , where K _j = Max (M _j , N _j ), I _3j is the value of the output currents of the third 44 and fourth 45 current generators, which are part of the first active four-terminal 26, contained in the nonlinear two-terminal 20, which is part of the j-th non-linear impedance converter of the second type, and the current I _3j is several times greater than the current Max (I _1j , J _1j ), where Max (I _1j , J _1j ) is the largest of the currents I _1j and J _1j , that is, I _3j = (2 ... 5) Max (I _1j , J _1j ).

The case M _j <N _j differs from the case M _j = N _j in that the output current of the third 44 current generator included in the 1 + 2 (N _j -M _j ) active four-terminal 26 contained in the nonlinear two-terminal 20 included the j-th non-linear impedance converter of the second type is set equal to the current I _3j , and the output current of the third 44 current generator, which is part of the first active four-terminal 26 contained in the non-linear two-terminal 20, which is part of the j-th non-linear impedance converter of the second type is set equal oku I _1j.

The case N _j <M _j differs from the case M _j = N _j in that the output current of the fourth 45 current generator, which is part of the 1 + 2 (M _j -N _j ) active four-terminal 26, contained in the nonlinear two-terminal 20, included the j-th non-linear impedance converter of the second type is equal to the current I _3j , and the output current of the fourth 45 current generator, which is part of the first active four-terminal 26, contained in the non-linear two-terminal 20, which is part of the j-th non-linear impedance converter of the second type, is set equal to the current J _1j .

,

,

,

,

, притом что

, где R10 - сопротивление резистора 16, входящего в состав нелинейного преобразователя тока; R11 - сопротивление первого резистора 37, содержащегося в первом активном четырехполюснике 26, входящем в состав нелинейного двухполюсника 17, содержащегося во втором нелинейном преобразователе импеданса первого типа; R12 - значение входящего в состав нелинейного двухполюсника 17 сопротивления резистора 25 и сопротивлений первых резисторов 37, содержащихся в остальных, со второго по 1+2Max(M₃,N₃)-й, активных четырехполюсниках, входящих в состав нелинейного двухполюсника 17, содержащегося во втором нелинейном преобразователе импеданса первого типа.The parameters of the transfer characteristic of the second nonlinear impedance converter of the first type are equal

,

,

,

,

, despite the fact that

where R10 is the resistance of the resistor 16, which is part of the nonlinear current transducer; R11 is the resistance of the first resistor 37 contained in the first active four-terminal 26, which is part of the nonlinear two-terminal 17, contained in the second nonlinear impedance converter of the first type; R12 is the value of the resistance of the resistor 25 included in the non-linear two-terminal 17 and the resistances of the first resistors 37 contained in the second, 1 + 2Max (M ₃ , N ₃ ) -th, active four-terminal, included in the non-linear two-terminal 17 contained in a second non-linear impedance converter of the first type.

With M ₃ = N _{3, the} currents I ₁₃ and J ₁₃ are equal to the values of the output currents of the fourth 45 and third 44 current generators, which are part of the odd, with the exception of the first, active four-terminal 26, and the values of the output currents of the third 44 and fourth 45 current generators, respectively included in the composition of even active four-terminal 26 contained in the nonlinear two-terminal 17, which is part of the second nonlinear impedance converter of the first type. The value of the output currents I _{23 of} the current generators 27 and 28 contained in the nonlinear two-terminal network 17, which is part of the second nonlinear impedance converter of the first type, is determined by the expression I ₂₃ = K ₃ (I ₁₃ + J ₁₃ ) + I ₃₃ , where K ₃ = Max (M ₃ , N ₃ ), I ₃₃ is the value of the output currents of the third 44 and fourth 45 current generators, which are part of the first active four-terminal 26, contained in the nonlinear two-terminal 17, which is part of the second nonlinear impedance converter of the first type, and the current I ₃₃ is several times more current Max (I _13, J _13), g e Max (I _13, J _13), - the highest of the currents I ₁₃ and J _13, i.e. I ₃₃ = (2 ... 5) Max (I _13, J _13).

The case of M ₃ <N ₃ differs from the case of M ₃ = N ₃ in that the output current of the third 44 current generator included in the 1 + 2 (N ₃ -M ₃ ) active four-terminal 26 contained in the nonlinear two-terminal 17 included the composition of the second non-linear impedance converter of the first type is set equal to the current I ₃₃ , and the output current of the third 44 current generator included in the first active four-terminal 26 contained in the non-linear two-terminal 17 included in the second non-linear impedance converter of the first type is set I equal current J ₁₃ .

The case of N ₃ <M ₃ differs from the case of M ₃ = N ₃ in that the output current of the fourth 45 current generator, which is part of the 1 + 2 (M ₃ -N ₃ ) active four-terminal 26, contained in the nonlinear two-terminal 17, included the second non-linear impedance converter of the first type is equal to the current I ₃₃ , and the output current of the fourth 45 current generator, which is part of the first active four-terminal 26, contained in the non-linear two-terminal 17, which is part of the second non-linear impedance converter of the first type, is set to current I ₁₃ .

The resistances of the second 38, third 39, fourth 40 and fifth 41 resistors and the output currents of the first 42 and second 43 current generators contained in each active four-terminal network are connected by the following relations I ₅ R14 = (1.2 ... 2) U _be , R13 = (1 ... 10) R14, where R13 is the resistance value of the second 38 and fifth 41 resistors, R14 is the resistance value of the third 39 and fourth 40 resistors, I ₅ is the value of the output currents of the first 42 and second 43 current generators, U _be is the value of the fifth emitter 33 and sixth 34 transistors that are part of the active four lusnika.

The output currents of the current generators contained in the voltage amplifier must satisfy the following relations: I _yl = 2I _y2 , I _y3 + I _y5 = I _y4 , where I _y1 is the output current of the first 57 current generator of the amplifier, I _y2 is the output current of the second 58 generator amplifier current, I _y3 is the output current of the third 59 amplifier current generator, I _y4 is the output current of the fourth 60 amplifier current generator, I _y5 is the output current of the fifth 61 amplifier current generator. Moreover, the values of the currents I _y3 and I _y5 should be several times higher than the values of the output currents of the first 27 and second 28 current generators contained in the nonlinear two-terminal network, which is part of the nonlinear impedance converter together with this voltage amplifier.

The resistances of the first 55 and second 56 amplifier resistors and the output current of the third 59 current generator contained in the voltage amplifier are related by the following relationships: I _y3 R15 = (1.2 ... 2) U _be , R15 = (1 ... 15) R16, where R15 and R16 - the values of the resistances of the first 55 and second 56 resistors of the amplifier, U _be - the value of the base-emitter voltage of the eighth 53 transistor of the amplifier.

The first and second non-linear impedance converters of the second type (Fig.23) are impedance converters that change the impedance by converting voltage (U-PI). They work as follows. Each of them contains a differential voltage amplifier with a high gain having an additional current output. The amplifier has high input impedances at both inputs and a low output impedance at the first output. An additional (second) output is the output of a current repeater, with a high output resistance. Its purpose is to generate a current equal to the current flowing through the first low-resistance amplifier output, so that the alternating current flowing into the first amplifier output is equal to the alternating current flowing from the second amplifier output (Fig. 23).

Given that the potential difference between the inputs of the voltage amplifier and its input currents is negligible, the voltage drop across the resistor R1 is equal to the voltage drop across the linear capacitive element (capacitor), therefore, the current i ₁ flowing in this resistor is u _C / R1 ; the same current flows in the circuit of the nonlinear resistor R _NL , the voltage on which depends on the value of the current i ₁ flowing through it, and therefore on the voltage across the capacitor u _NL (i ₁ ) = u _NL (u _C / R1).

Due to the negligible potential difference between the amplifier inputs, the voltage between the first and second outputs of the second type non-linear impedance converter is equal to the voltage drop across the non-linear resistor u _NL (u _C / R1). In this case, the current flowing through the capacitor is equal to the sum of the current i ₁ flowing in the circuit of the resistors R1 and R _NL , and the current i _C -i ₁ flowing in the circuit of the first and second outputs of the amplifier. Therefore, a current equal to the current flowing through the linear capacitive element flows through the output of the non-linear impedance converter of the second type (Fig. 23).

Thus, when a linear capacitive element is connected to an external circuit through a non-linear impedance converter of the second type, a current equal to the current flowing in the linear capacitive element flows through the outputs of the converter, and the voltage drop between the outputs of the converter is equal to u _NL (u _C / R1). In the case of the first nonlinear impedance converter of the second type, u ₁ (u _C1 ) = u _НЛ (u _C1 / R1), in the case of the second nonlinear impedance converter of the second type, u ₂ (u _C2 ) = u _НЛ (u _C2 / R1). That is, the combination of a capacitor and a non-linear impedance converter of the second type forms an equivalent non-linear capacitive element with a given current-voltage characteristic.

The second non-linear impedance converter of the first type is an impedance converter that changes the impedance by converting current (I-PI), which operates as follows (Fig.24). It contains the same amplifier as the first and second non-linear impedance converters of the second type. Since the potential difference between the inputs of the amplifier is negligible, the voltage between the outputs of the second nonlinear impedance converter of the first type is equal to the voltage on the linear inductive element (for example, the inductor), in addition, the voltages on the linear and nonlinear resistors are equal. A current equal to the current in the circuit of the linear inductive element flows through the non-linear resistor. As a result, a voltage drop u _НЛ (i _L ) depending on the current in the linear inductive element arises, under the action of which a current i (i _L ) = u _НЛ (i _L ) / R1 flows in the circuit of the linear resistor. At the same time, the current i _L -i (i _L ) enters the first, low-impedance output of the amplifier, the same current flows from the second output of the amplifier and, together with the current i _L, enters the external circuit. That is, the current flowing in the circuit of the linear resistor i (i _L ) enters the external circuit.

Thus, when a linear inductive element is connected to an external circuit through a second non-linear impedance converter of the first type, a current i (i _L ) flows through the outputs of the converter, and a voltage u _L drops between them. That is, the combination of the linear inductance and the second nonlinear impedance converter of the first type forms an equivalent nonlinear inductive element with the required current-voltage characteristic.

An example of a practical implementation of the claimed generator of chaotic oscillations is a circuit having the following parameters.

Let R = 1000 Ohm, C1 = 0.02 μF, R3 = 1500 Ohm, R5 = 500 Ohm, R7 ₁ = R7 ₂ = R10 = 1033 Ohm, I ₀ = 120 μA. Then, in the case M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 1, d ₁ = d ₂ = d ₃ = 30, h ₁ ≈6.7, h ₂ ≈22.2, h ₃ ≈23.7, s ₁ = 0, s ₂ ≈-7.5, s ₃ ≈-7.7, for M = 0, N = 1, a = 20, b = -3, A = 0.5, B = 1.9, chaotic oscillations corresponding to these parameters of the equations ( 3), are observed at the following values of the oscillatory system of the generator: C2≈0.01 μF, L1≈52.6 mH, of the first nonlinear impedance converter of the first type: R4≈150 Ohm, R6≈440 Ohm, I ₁ ≈0.9 mA, I ₂ ≈2.7 mA, I ₃ = I ₄ ≈6 mA, the first non-linear impedance converter of the second type: R8 ₁ ≈31 kOhm, R9 ₁ ≈1 kOhm, I ₁₁ ≈0.8 mA, I ₂₁ ≈5.6 mA, I ₃₁ ≈4 mA, the second non-linear impedance converter second type : R8 ≈31 ₂ kilohms, R9 ≈1 ₂ kohm, I ≈1.8 ₁₂ mA, J ≈3.7 ₁₂ mA, I ≈25.5 ₂₂ mA, I ₃₂ ≈20 mA second nonlinear transformer of the impedance of the first type: R11≈31 ohms, R12 ≈1 kOhm, I ₁₃ ≈1.8 mA, J ₁₃ ≈4.8 mA, I ₂₃ ≈36.6 mA, I ₃₃ ≈30 mA, voltage amplifier: R15≈15 kOhm, R16≈1 kOhm, I _y1 ≈400 μA, I _y2 ≈ 200 μA, I _y3 = I _y5 ≈15 mA, I _y4 ≈30 mA, elements of DC bias circuits in non-linear impedance converters: R13≈5 kOhm, R14≈1 kOhm, I ₅ ≈2 mA.

The examples of the dimensionless strange attractor corresponding to these values of the parameters of the generator, its projections on the (x, y), (x, z) and (y, z) planes, as well as examples of the dependence of the dimensionless variables x, y and z on time, are shown in Fig. 16 -22.

The increased accuracy and temperature stability of non-linear impedance converters is due to the fact that their transfer characteristics are practically independent of the parameters of the transistors, due to the mutual compensation of the emitter resistances of the transistors 29 and 31, as well as 30 and 36 as part of active four-terminal devices, as well as due to an increase in the gain and minimization DC voltage differences on the inverting and non-inverting inputs of the voltage amplifier due to the introduction of transistors 46, 47 and 50, 51.

Thus, the claimed chaotic oscillation generator compares favorably with the prototype and analogues, in which the chaotic signal can be tuned only by changing the parameters of the initial chaotic attractor, in that it allows you to implement a composite chaotic multiattractor obtained by combining the original chaotic attractor with one or more copies of it as a result of which its restructuring can be additionally carried out by changing the number and relative position of its constituent components, Thanks to what stated generator has a much greater capacity adjustment parameters of the generated chaotic signal.

Claims (1)

A chaotic oscillation generator containing a bipolar element with inductive resistance, the first output of which is connected to the first input terminal of the first nonlinear impedance converter of the first type, the second input terminal of which is connected to the first output of the resistor, the second output of which is connected to the second terminal of the bipolar element with inductive resistance the output of the first bipolar element with capacitance, the second output of which is connected to the first output terminal of the first non-linear pre the first type of impedance generator and the first output of the second bipolar element with capacitance, the second output of which is connected to the second output terminal of the first non-linear impedance converter of the first type, characterized in that the transfer characteristic of the first non-linear impedance converter of the first type is determined by the equation

where i ₂ (i ₁ ) is the current flowing through the output terminals of the first nonlinear impedance converter of the first type;
i ₁ is the current flowing through the input terminals of the first nonlinear impedance converter of the first type,

,

,
I ₀ is the boundary current between the average passing through the origin and the side sections of the transfer characteristic; a and b are real coefficients having opposite signs; M and N are non-negative integers,
the voltage at the first input terminal of the first nonlinear impedance converter of the first type is equal to the voltage at the first output terminal of the first nonlinear impedance converter of the first type, the voltage at the second input terminal of the first nonlinear impedance converter of the first type is equal to the voltage at the second output terminal of the first nonlinear impedance converter of the first type, the first bipolar the capacitance element contains a first linear capacitive element, the first and second conclusions of which are connected respectively, with the first and second terminals of the first non-linear impedance converter of the second type, the third and fourth terminals of which are respectively the first and second terminals of the first bipolar element with capacitance, the second bipolar element with capacitance contains a second linear capacitive element, the first and second terminals of which are connected respectively, with the first and second terminals of the second non-linear impedance converter of the second type, the third and fourth conclusions of which are I, respectively, the first and second terminals of the second bipolar element with capacitive resistance, the bipolar element with inductive resistance contains a linear inductive element, the first and second terminals of which are connected respectively to the first and second terminals of the second nonlinear impedance converter of the first type, the third and fourth conclusions of which are respectively the first and the second terminals of the bipolar element with inductive resistance, alternating current flowing in the circuit of the first bipolar element nta with capacitance is equal to the alternating current flowing in the circuit of the first linear capacitive element, the voltage between the terminals of the first bipolar element with capacitance is u ₁ (u _C1 ) = U ₀ H ₁ (x),
where u _C1 is the alternating voltage at the first linear capacitive element; U ₀ = I ₀ R, R is the resistance of the resistor,

,

, d ₁ , h ₁ and s ₁ are real coefficients, and d ₁ >> l, M ₁ and N ₁ are non-negative integers, the alternating current flowing in the circuit of the second bipolar element with capacitive resistance is equal to the alternating current flowing in the circuit the second linear capacitive element, the voltage between the terminals of the second bipolar element with capacitance is equal to u ₂ (u _C2 ) = U ₀ H ₂ (y),
where u _C2 is the alternating voltage at the second linear capacitive element,

,

, d ₂ , h ₂ and s ₂ are real coefficients, and d ₂ >> l, M ₂ and N ₂ are non-negative integers, the alternating voltage between the terminals of the bipolar element with inductive resistance is equal to the alternating voltage on the linear inductive element, the current flowing in the circuit of a bipolar element with inductive resistance, is equal to i (i _L ) = I ₀ H ₃ (z),
where i _L is the alternating current flowing in the circuit of a linear inductive element;

,

, d ₃ , h ₃ and s ₃ are real coefficients, and d ₃ >> l, M ₃ and N ₃ are non-negative integers, and the first non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the first input terminal of the first a non-linear impedance converter of the first type and the first output of a non-linear two-terminal, the second output of which is connected to the first output of the voltage amplifier and the first output of a linear two-terminal, the second output of which is connected to the first output of the first non-linear the first type of impedance converter and a non-inverting input of the voltage amplifier, the second output of which is connected to the second input and second output terminals of the first non-linear impedance converter of the first type and a common bus, the second non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the second input of the second non-linear an impedance converter of the first type and the first output of a nonlinear bipolar, the second output of which is connected to the first output of the force dividing voltage and the first output of the resistor, the second output of which is connected to the second output of the second non-linear impedance converter of the first type and the non-inverting input of the voltage amplifier, the second output of which is connected to the first input and first output terminals of the second non-linear impedance converter of the first type, each non-linear impedance converter of the second type contains a voltage amplifier, the non-inverting input of which is connected to the first input and first output terminals of the nonlinear an impedance generator of the second type, the second input terminal of which is connected to the first output of the voltage amplifier and the first output of the resistor, the second terminal of which is connected to the inverting input of the voltage amplifier and the first output of a nonlinear two-terminal device, the second output of which is connected to the second output of the voltage amplifier and the second output terminal of the nonlinear converter of the impedance of the second type, each nonlinear two-terminal network contains 1 + 2Max (Q, R) series-connected active four-terminal networks, where Max (Q, R) is the larger of the numbers Q and R which are respectively M and N in the nonlinear two-terminal, which is part of the first nonlinear impedance converter of the first type, M ₁ and N ₁ in the non-linear two-terminal, which is part of the first nonlinear impedance converter of the second type, M ₂ and N ₂ in the nonlinear two-terminal, included the second nonlinear impedance converter of the second type, M ₃ and N ₃ in the nonlinear bipolar, which is part of the second nonlinear impedance converter of the first type, the first and second terminals of the first active four-terminal connected respectively to the first and second terminals of the nonlinear bipolar and the outputs of the corresponding first and second current generators of the nonlinear bipolar, the common buses of which are connected to the first power bus, the third and fourth terminals of each previous active four-terminal are connected respectively to the first and second terminals of the subsequent active four-terminal, the third and the fourth conclusions of the last, 1 + 2Max (Q, R) -th, active four-terminal are connected to the corresponding first and second conclusions of the resistor, are linear the two-terminal network contains a resistor, the first and second terminals of which are the corresponding first and second terminals of the linear two-terminal network, connected to the corresponding third and fourth terminals of the active four-terminal network, the first and second conclusions of which are connected to the outputs of the corresponding first and second current generators of the linear two-terminal network, whose common buses are connected with the first power bus, each active four-terminal network contains the first and second transistors, the emitters of which are corresponding to the first and the second terminals of the active four-terminal, connected to the corresponding first and second terminals of the first resistor, the collector of the first transistor is connected to the emitter of the third transistor and the base of the fourth transistor, the emitter of which is connected to the collector of the fifth transistor and the first terminal of the second resistor, the second terminal of which is connected to the base of the fifth transistor and the first terminal of the third resistor, the second terminal of which is connected to the emitter of the fifth transistor, the base of the second transistor and the output of the first current generator, whose common bus is connected to the first power bus and the common bus of the second current generator, the output of which is connected to the base of the first transistor, the emitter of the sixth transistor and the first terminal of the fourth resistor, the second terminal of which is connected to the base of the sixth transistor and the first terminal of the fifth resistor, the second terminal of which is connected with the collector of the sixth transistor and the emitter of the seventh transistor, the base of which is connected to the collector of the second transistor and the emitter of the eighth transistor, the base and collector of which are connected to each output of the active four-port and the output of the third current generator, the common bus of which is connected to the collectors of the fourth and seventh transistors, the second power bus and the common bus of the fourth current generator, the output of which is connected to the base and collector of the third transistor and the third output of the active four-port, each voltage amplifier contains the first and second transistors of the amplifier, the bases of which are the corresponding non-inverting and inverting inputs of the voltage amplifier, the emitter of the first trans the amplifier source is connected to the collector of the third amplifier transistor and the base of the fourth amplifier transistor, the emitter of which is connected to the output of the first amplifier current generator and the emitter of the third amplifier transistor, the base of which is connected to the collector of the fourth amplifier transistor and the emitter of the second amplifier transistor, the collector of which is connected to the base of the fifth transistor the amplifier and emitter of the sixth transistor of the amplifier, the base and collector of which are connected to the output of the second current generator of the amplifier and bases the seventh amplifier transistor, the emitter of which is connected to the collector of the first amplifier transistor, the emitter of the fifth amplifier transistor is connected to the collector of the eighth amplifier transistor and the first output of the first amplifier resistor, the second output of which is connected to the base of the eighth amplifier transistor and the first output of the second amplifier resistor, the second output of which connected to the emitter of the eighth transistor of the amplifier, the output of the third current generator of the amplifier and the first output of the voltage amplifier, the collector of the fifth The amplifier nsistor is connected to the output of the fourth amplifier current generator and the emitter of the ninth amplifier transistor, the collector of which is connected to the output of the fifth amplifier current generator and the second voltage amplifier output, the base of the ninth amplifier transistor is connected to the third power bus, common buses of the first, third, and fifth amplifier current generators connected to the first power bus, common buses of the second and fourth current generators of the amplifier are connected to the collector of the seventh transistor and to the second power bus.

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