RLC chaotic circuit based on active inductor and resistor coupling

Abstract

The invention discloses an RLC chaotic circuit based on active inductor and resistor coupling, which is composed of three parts, an active inductor circuit I is composed of four resistors R1, R2, R3 and R4, a capacitor C1 and two operational amplifiers U1 and U2, a split-phase circuit II is composed of a resistor R5 and two capacitors C2 and C3, and a nonlinear negative resistance circuit III is composed of two operational amplifiers U3 and U4 and six resistors R6-R11. By changing the resistance values of R3 and R4 in the active inductor circuit I or the capacitance value of C1, the equivalent inductive reactance value L of the active inductor can be accurately changed. The active inductance circuit I and the split-phase circuit II can generate a self-oscillation dynamic process under a specific parameter condition, on the basis, a series of nonlinear phenomena such as bifurcation and chaos occur in an oscillation period through the nonlinear negative resistance circuit III, and the blank of realizing RLC chaotic circuit research based on active inductance and resistance coupling in the prior art is filled.

Description

Technical Field

[0001] The invention relates to an RLC chaotic circuit based on active inductance and resistance coupling, belonging to the technical field of chaotic electronics. Background Art

[0002] The classic Chua circuit occupies a very important position in the field of nonlinear dynamics due to its simple circuit structure. As scientific research goes deeper, scholars have found that by changing the topological structure or circuit element parameters of the Chua circuit, new chaotic phenomena can appear, which has very broad application prospects in signal detection, chaotic synchronization and secure communication.

[0003] Research has shown that the classic Chua's chaotic circuit is limited by passive inductance, which is not conducive to the generation of chaotic phenomena. Because the traditional passive inductor adjustment is extremely complicated, and the materials used to make passive inductors are different, even if the inductance is the same, there will be large errors, which is not conducive to the accuracy of the research.

[0004] In order to solve the above problems, the inventors built an active inductor circuit using an operational amplifier, a resistor and a capacitor. And by using the phase-splitting function of the phase-splitting circuit and the bifurcation function of the nonlinear negative resistance circuit, an RLC chaotic circuit based on active inductance and resistor coupling can be further designed. However, the prior art has not yet developed an RLC chaotic circuit based on active inductance and resistor coupling. Studies have shown that under specific parameter conditions, the RLC third-order autonomous dynamic circuit based on active inductance and resistor coupling can produce a self-excited oscillation process, showing a series of nonlinear behaviors such as chaos. Summary of the invention

[0005] In order to fill the gap in existing research, the present invention constructs an RLC chaotic circuit based on active inductance and resistance coupling.

[0006] An RLC chaotic circuit based on active inductance and resistance coupling consists of three parts. The active inductance circuit I consists of four resistors R1, R2, R3, R4, a capacitor C1 and two operational amplifiers U1 and U2, the phase splitting circuit II consists of a resistor R5 and two capacitors C2 and C3, and the nonlinear negative resistance circuit III consists of two operational amplifiers U3 and U4 and six resistors R6~R 11In the active inductor circuit I, the in-phase input terminals of the two operational amplifiers U1 and U2 are connected in parallel, and the output terminal of the operational amplifier U1 is divided into two branches, one of which is connected to the in-phase input terminal of U1 through a resistor R3, and the other branch is connected to the inverting input terminal of U1 through a capacitor C1. The output terminal of the operational amplifier U2 is connected to the inverting input terminal of U2 through a resistor R2, and the inverting input terminal is grounded through a resistor R1. The inverting input terminal of U1 and the output terminal of U2 are connected through a resistor R4. In the phase-splitting circuit II, the two capacitors C2 and C3 are connected in series with a resistor R5, wherein the resistor R5 plays a role in adjusting the phase difference between the capacitors C2 and C3. In the nonlinear negative resistance circuit III, the two operational amplifiers U3 and U4 have the same structure, and the in-phase input terminals of U3 and U4 are connected in parallel, wherein the two branches of the output terminal of the operational amplifier U3 are respectively connected to its in-phase input terminal and inverting input terminal through resistors R6 and R7, and in addition, the inverting input terminal of U3 is grounded through a resistor R8. The two branches at the output of operational amplifier U4 are connected through resistors R9 and R 10 are connected to its non-inverting input and inverting input respectively. In addition, the inverting input of U4 is connected to the inverting input of U4 through the resistor R 11 Ground.

[0007] The mathematical model of the active inductor circuit I is:

[0008]

[0009] Among them U o1 represents the output voltage of operational amplifier U2, U i It represents the input voltage of the same-direction input terminal of the operational amplifier U2. o represents the output voltage of the operational amplifier U1, j represents the imaginary unit, and w represents the frequency.

[0010] The mathematical model of the phase split circuit II is:

[0011]

[0012] Where u1 and u2 represent the voltages across capacitors C2 and C3 respectively, gu1 represents the equivalent impedance of the nonlinear negative resistance circuit III, and i L , L and r represent the current in the active inductor circuit I, the equivalent capacitive reactance and equivalent impedance of the active inductor respectively.

[0013] The mathematical model of the nonlinear negative resistance circuit III is:

[0014]

[0015] Where R eq Represents the equivalent impedance of the nonlinear negative resistance circuit, U iIt represents the input voltage of the same-direction input terminal of operational amplifiers U3 and U4, I i represents the current at the output of operational amplifier U3. g in the closed loop equation (2) represents the two R eq The result of parallel connection.

[0016] Equations (1), (2) and (3) together constitute the system equation of the chaotic circuit. After further arrangement, the system equation of the RLC chaotic circuit based on active inductance is obtained as follows:

[0017]

[0018] Where b, c and e are constants, x, y and z represent u1, u2 of the phase split circuit II and i of the active inductor circuit I respectively. L .

[0019] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0020] (1) The present invention proposes an RLC chaotic circuit based on active inductance and resistance coupling. Under appropriate circuit element parameter conditions, the chaotic signal obtained by the circuit is more stable and does not have to be limited by the problem that traditional passive inductance is difficult to adjust.

[0021] (2) By adjusting the value of the feedback resistor R5 in the phase split circuit II, three different chaotic models, single cycle, single vortex and double vortex, can be obtained. This active inductor has the advantages of simple and precise control of the inductance value, reducing the equivalent resistance loss caused by the traditional passive inductor, and solving the problem of the difficulty of adjusting the traditional passive inductor. At present, there is no application of RLC circuits based on active inductance and resistor coupling in chaotic circuits, which fills the research gap in the existing technology of realizing RLC chaotic circuits based on active inductance and resistor coupling. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings used in the description of some embodiments of the present invention or the prior art.

[0023] Attached Figure 1 A schematic diagram of an RLC chaotic circuit based on active inductance and resistance coupling designed in an embodiment of the present invention;

[0024] Attached Figure 2 It is a time domain waveform of state variables x and y related to capacitors C2 and C3 when the parameter of feedback resistor R5 is R5=1.6kΩ in an RLC chaotic circuit based on active inductance and resistor coupling;

[0025] Attached Figure 3It is a phase diagram of the state variables x and y related to C2 and C3 when the parameter of the feedback resistor R5 is R5=1.85kΩ in an RLC chaotic circuit based on active inductance and resistor coupling;

[0026] Attached Figure 4 The phase diagram of the state variables x and y related to C2 and C3 in an RLC chaotic circuit based on active inductance and resistance coupling when the feedback resistor R5 parameter R5 = 1.6kΩ. DETAILED DESCRIPTION

[0027] The technical solutions in some embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present invention.

[0028] This embodiment provides an RLC chaotic circuit based on active inductance and resistance coupling. Figure 1 As shown, an RLC chaotic circuit based on active inductance and resistance coupling consists of three parts. The active inductance circuit I consists of four resistors R1, R2, R3, R4, a capacitor C1 and two operational amplifiers U1 and U2, the phase splitting circuit II consists of a resistor R5 and two capacitors C2 and C3, and the nonlinear negative resistance circuit III consists of two operational amplifiers U3 and U4 and six resistors R6~R 11 In the active inductor circuit I, the in-phase input terminals of the two operational amplifiers U1 and U2 are connected in parallel, and the output terminal of the operational amplifier U1 is divided into two branches, one of which is connected to the in-phase input terminal of U1 through a resistor R3, and the other branch is connected to the inverting input terminal of U1 through a capacitor C1. The output terminal of the operational amplifier U2 is connected to the inverting input terminal of U2 through a resistor R2, and the inverting input terminal is grounded through a resistor R1. The inverting input terminal of U1 and the output terminal of U2 are connected through a resistor R4. In the phase-splitting circuit II, the two capacitors C2 and C3 are connected in series with a resistor R5, wherein the resistor R5 plays a role in adjusting the phase difference between the capacitors C2 and C3. In the nonlinear negative resistance circuit III, the two operational amplifiers U3 and U4 have the same structure, and the in-phase input terminals of U3 and U4 are connected in parallel, wherein the two branches of the output terminal of the operational amplifier U3 are respectively connected to its in-phase input terminal and inverting input terminal through resistors R6 and R7, and in addition, the inverting input terminal of U3 is grounded through a resistor R8. The two branches at the output of operational amplifier U4 are connected through resistors R9 and R 10 are connected to its non-inverting input and inverting input respectively. In addition, the inverting input of U4 is connected to the inverting input of U4 through the resistor R 11 Ground.

[0029] The system equation of the active inductor circuit I is:

[0030]

[0031] Among them, i L represents the current flowing through the active inductor circuit, U i It represents the input voltage of the same-direction input terminal of the operational amplifier U2. o Represents the output voltage of operational amplifier U1.

[0032] Specifically, the system equation establishment process of the active inductor circuit I is as follows:

[0033] According to Kirchhoff's voltage law and Ohm's law, combined with the "virtual short" and "virtual open" characteristics of the operational amplifier, where R1 = R2, the equation in the active inductor circuit I is described as:

[0034]

[0035] Among them U o1 represents the output voltage of operational amplifier U2, U i It represents the input voltage of the same-direction input terminal of the operational amplifier U2. o represents the output voltage of the operational amplifier U1, j represents the imaginary unit, and w represents the frequency.

[0036] After simplification, we get:

[0037] L=C1R3R4(7)

[0038] Wherein, L represents the equivalent inductance value of the active inductor circuit. It can be seen from formula (7) that by changing the resistance value of R3 and R4 or the capacitance value of C1 in the active inductor circuit I, the equivalent inductive reactance value L of the active inductor can be accurately changed.

[0039] The mathematical model of the phase split circuit II is:

[0040]

[0041] Where u1 and u2 represent the voltages across capacitors C2 and C3 respectively, gu1 represents the equivalent impedance of the nonlinear negative resistance circuit III, and i L , L and r represent the current flowing through the active inductor circuit I, the equivalent capacitive reactance and the equivalent impedance of the active inductor respectively.

[0042] The system equation of the nonlinear negative resistance circuit III is:

[0043]

[0044] Where R eq Represents the equivalent impedance of the nonlinear negative resistance circuit, U i It represents the input voltage of the same-direction input terminal of operational amplifiers U3 and U4, Ii represents the current at the output of operational amplifier U3.

[0045] Equations (6), (8), and (9) together constitute a system equation of an RLC chaotic circuit based on active inductance and resistance coupling:

[0046]

[0047] After simplification, we get:

[0048]

[0049] Where b, c and e are constants, x, y and z represent u1, u2 of the phase split circuit II and i of the active inductor circuit I respectively. L .

[0050] In this embodiment, R1=R2=10kΩ, R3=2kΩ, R4=5kΩ, C1=1800pF, C2=100nF, C3=10nF, R6=R7=220Ω, R8=2.2kΩ, R9=R 10 =22kΩ, R 11 =3.3kΩ, the system equations were numerically simulated using the Muitisim simulation platform, and the following Figure 2 , Attachment Figure 3 and attached Figure 4 The chaotic waveform shown. Figure 2 The time domain waveforms of the state variables x and y of the capacitors C2 and C3 in an RLC chaotic circuit based on active inductance and resistance coupling are shown in FIG. Figure 3 This is a phase diagram of the state variables x and y of C2 and C3 in an RLC chaotic circuit based on active inductance and resistance coupling when the feedback resistor R5 parameter R5 = 1.85kΩ; Figure 4 This is a phase diagram of the state variables x and y of C2 and C3 in an RLC chaotic circuit based on active inductance and resistance coupling when the feedback resistor R5 parameter R5=1.6kΩ. The results show that: under the appropriate parameter setting, the circuit can show rich chaotic dynamics behavior.

[0051] The above describes in detail some embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, any equivalent structural modification or replacement made using the embodiments of the present invention, or directly or indirectly applying the present invention in related technical fields, falls within the scope of patent protection of the present invention.

Claims

1. An RLC chaotic circuit based on active inductance and resistance coupling, characterized in that: The RLC chaotic circuit consists of three parts: active inductance circuit I, phase splitting circuit II, and nonlinear negative resistance circuit III; The active inductor circuit I is composed of four resistors R1, R2, R3, R4, a capacitor C1 and two operational amplifiers U1, U2; Phase split circuit II consists of a resistor R5 and two capacitors C2 and C3; The nonlinear negative resistance circuit III consists of two operational amplifiers U3 and U4 and six resistors R6 to R 11 composition; In the active inductor circuit I, the in-phase input terminals of the two operational amplifiers U1 and U2 are connected in parallel, and the output terminal of the operational amplifier U1 is divided into two branches, one of which is connected to the in-phase input terminal of U1 through a resistor R3, and the other branch is connected to the inverting input terminal of U1 through a capacitor C1. The output terminal of the operational amplifier U2 is connected to the inverting input terminal of U2 through a resistor R2, and the inverting input terminal is grounded through a resistor R1. The inverting input terminal of U1 and the output terminal of U2 are connected through a resistor R4. In the phase-splitting circuit II, two capacitors C2 and C3 are connected in series with a resistor R5, wherein the resistor R5 plays a role in adjusting the phase difference between capacitors C2 and C3. In the nonlinear negative resistance circuit III, the two operational amplifiers U3 and U4 have the same structure, and the in-phase input terminals of U3 and U4 are connected in parallel, wherein the two branches of the output terminal of the operational amplifier U3 are respectively connected to its in-phase input terminal and inverting input terminal through resistors R6 and R7, and in addition, the inverting input terminal of U3 is grounded through a resistor R8. The two branches at the output of operational amplifier U4 are connected through resistors R9 and R 10 are connected to its non-inverting input and inverting input respectively. In addition, the inverting input of U4 is connected to the inverting input of U4 through the resistor R 11 Ground.

2. The RLC chaotic circuit based on active inductance and resistance coupling according to claim 1, characterized in that: The equation in the active inductor circuit I is: Among them U o1 represents the output voltage of operational amplifier U2, U i It represents the input voltage of the same-direction input terminal of the operational amplifier U2. o represents the output voltage of the operational amplifier U1, j represents the imaginary unit, and w represents the frequency.

3. The RLC chaotic circuit based on active inductance and resistance coupling according to claim 2, characterized in that: The equation in the phase split circuit II is: Where u1 and u2 represent the voltages across capacitors C2 and C3 respectively, gu1 represents the equivalent impedance of the nonlinear negative resistance circuit III, and i L , L and r represent the current in the active inductor circuit I, the equivalent capacitive reactance and equivalent impedance of the active inductor respectively.

4. The RLC chaotic circuit based on active inductance and resistance coupling according to claim 3, characterized in that: The equation in the nonlinear negative resistance circuit III is: Where R eq Represents the equivalent impedance of the nonlinear negative resistance circuit, U i It represents the input voltage of the same-direction input terminal of operational amplifiers U3 and U4, I i represents the current at the output of operational amplifier U3. g in the closed loop equation (2) represents the two R eq The result of parallel connection.

5. The RLC chaotic circuit based on active inductance and resistance coupling according to claim 4, characterized in that: The mathematical model of the RLC chaotic circuit is established by the following steps: Step 1: Select appropriate resistance parameters R3, R4, capacitance parameters C1 and operational amplifiers U1, U2 to form an active inductor circuit I. According to Kirchhoff's voltage law and the "virtual short" and "virtual open" characteristics of the operational amplifier, R1 = R2. After transformation, we get formula (4): Step 2: According to the state-dependent Kirchhoff's current law, the mathematical models of the equivalent inductance L in the active inductor circuit I and the capacitors C2, C3, and the resistor R5 in the phase-splitting circuit II are obtained as follows: Step 3: According to Ohm's law, the equivalent resistance in the nonlinear negative resistance circuit III is obtained as formula (6): Combining equations (4), (5) and (6), we can obtain the system equation of the RLC chaotic circuit based on active inductance and resistance coupling: After simplification, we get: Where b, c and e are constants, x, y and z represent u1, u2 of the phase split circuit II and i of the active inductor circuit I respectively. L .

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