Third-order circuit system based on sine nonlinear characteristics

Abstract

The invention belongs to the technical field of chaotic circuits, and discloses a sine nonlinear characteristic-based third-order circuit system, which comprises a sine nonlinear function circuit and a third-order linear differential equation circuit, the input end of the sine nonlinear function circuit is connected with the x output end of the third-order linear differential equation circuit, and the output end of the sine nonlinear function circuit is connected with the x output end of the third-order linear differential equation circuit. The output end is connected with one input end of the x integrator of the third-order linear differential equation circuit; the sine nonlinear function circuit is composed of a first operational amplifier A1, resistors R1 to R16 and diodes D1 to D6, and the output and the input of the sine nonlinear function circuit are in a sine nonlinear function relationship; the third-order linear differential equation circuit forms three anti-phase addition integrators by three anti-phase operational amplifiers, three capacitors and seven resistors, and the sine nonlinear function circuit provides nonlinear signals to generate three Chua's chaotic signal outputs of the sine nonlinear third-order Chua's circuit; according to the invention, various chaotic line systems and chaotic secret communication systems can be formed.

Description

Technical Field

[0001] This invention belongs to the field of chaotic circuit technology, and in particular relates to a third-order circuit system based on sinusoidal nonlinear characteristics. Background Technology

[0002] Nonlinear function circuits are a type of function circuit that can be applied to generate chaotic signals in chaotic circuits. While there are many nonlinear function circuits in chaotic circuits, their application to chaotic circuits is yet to be seen, which is a shortcoming of existing chaotic circuit technology. Summary of the Invention

[0003] The purpose of this invention is to provide a third-order circuit system based on sinusoidal nonlinear characteristics to solve the problems existing in the prior art.

[0004] To achieve the above objectives, this invention provides a third-order circuit system based on sinusoidal nonlinear characteristics, comprising a sinusoidal nonlinear function circuit and a third-order linear differential equation circuit. The third-order linear differential equation circuit includes a second operational amplifier A2, a third operational amplifier A3, a fourth operational amplifier A4, a fifth operational amplifier A5, several capacitors, and several resistors. The non-inverting input of the second operational amplifier A2 is grounded, and its inverting input is connected to the twentieth resistor R20, the first capacitor C1, and the output of the sinusoidal nonlinear function circuit. The output of the second operational amplifier A2 is connected to the first capacitor C1 and the input of the sinusoidal nonlinear function circuit. The second capacitor C2 and the nineteenth resistor R19 are connected in parallel between the inverting input and output of the third operational amplifier A3. The non-inverting input of the third operational amplifier A3 is grounded. The inverting input terminal of the third operational amplifier A3 is connected to the output terminal of the second operational amplifier A2 through the seventeenth resistor R17. The output terminal of the third operational amplifier A3 is connected to the inverting input terminal of the second operational amplifier A2 and the inverting input terminal of the fourth operational amplifier A4 through the twentieth resistor R20 and the twenty-first resistor R21, respectively. The non-inverting input terminal of the fourth operational amplifier A4 is grounded. A twenty-second resistor R22 is connected in parallel between the inverting input terminal and the output terminal of the fourth operational amplifier A4. The output terminal of the fourth operational amplifier A4 is connected to the inverting input terminal of the fifth operational amplifier A5 through the twenty-third resistor R23. The non-inverting input terminal of the fifth operational amplifier A5 is grounded. A third capacitor C3 is connected in parallel between the inverting input terminal and the output terminal of the fifth operational amplifier A5. The output terminal of the fifth operational amplifier A5 is connected to the inverting input terminal of the third operational amplifier A3 through the eighteenth resistor R18.

[0005] Optionally, the sinusoidal nonlinear function circuit includes a first resistor R1. One end of the first resistor R1 is connected to the output terminal of the second operational amplifier A2, and the other end is connected to the inverting input terminal of the first operational amplifier A1, one end of the second resistor R2, the anode of the first diode D1, the anode of the second diode D2, the anode of the third diode D3, the cathode of the fourth diode D4, the cathode of the fifth diode D5, and the cathode of the sixth diode D6. The non-inverting input terminal of the first operational amplifier A1 is grounded. The cathodes of the first diode D1 are connected to the third resistor R3 and the ninth resistor R9, the cathodes of the second diode D2 are connected to the fourth resistor R4 and the tenth resistor R10, the cathodes of the third diode D3 are connected to the fifth resistor R5 and the eleventh resistor R11, and the anodes of the fourth diode D4 are connected to the sixth resistor R6. Resistor R6 and twelfth resistor R12 are connected. The anode of the fifth diode D5 is connected to the seventh resistor R7 and the thirteenth resistor R13. The anode of the sixth diode D6 is connected to the eighth resistor R8 and the fourteenth resistor R14. The second resistor R2, the third resistor R3, the fourth resistor R4, the fifth resistor R5, the sixth resistor, the seventh resistor, and the eighth resistor are connected in parallel and all connected to the output terminal of the first operational amplifier A1. The output terminal of the first operational amplifier A1 is connected to the inverting input terminal of the second operational amplifier A2. The ninth resistor R9, the tenth resistor R10, and the eleventh resistor R11 are all connected to the positive terminal of power supply EC1. The twelfth resistor R12, the thirteenth resistor R13, and the fourteenth resistor R14 are all connected to the negative terminal of power supply EC2. Power supply EC1 and power supply EC2 are connected in series.

[0006] The technical effects of this invention are as follows:

[0007] Compared with existing technologies, the circuit provided by this invention can observe the nonlinear curve of a sinusoidal function, and can output three voltage waveform signals and three voltage phase diagram signals of a sinusoidal nonlinear Chua's circuit. It can be applied to chaotic circuit design and can be used to perform various other experiments with a sinusoidal nonlinear third-order Chua's circuit on an oscilloscope. This invention is suitable for analog electronics science education, experimental teaching and demonstration, and popular science experimental demonstrations. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0010] Figure 1 This is a schematic diagram of a sinusoidal nonlinear third-order Chua's circuit in an embodiment of the present invention;

[0011] Figure 2 This is the output waveform diagram of the sinusoidal nonlinear third-order Chua's circuit X in an embodiment of the present invention;

[0012] Figure 3 This is a waveform diagram of the Y-output of the sinusoidal nonlinear third-order Chua's circuit in an embodiment of the present invention.

[0013] Figure 4 This is a diagram showing the Z-output waveform of the sinusoidal nonlinear third-order Chua's circuit in an embodiment of the present invention.

[0014] Figure 5 The XY output phase diagram of the sinusoidal nonlinear third-order Chua's circuit in this embodiment of the invention;

[0015] Figure 6 The XZ output phase diagram of the sinusoidal nonlinear third-order Chua's circuit in this embodiment of the invention;

[0016] Figure 7 This is the YZ output phase diagram of the sinusoidal nonlinear third-order Chua's circuit in this embodiment of the invention;

[0017] Figure 8 The above are the EWB simulation results of the sinusoidal nonlinear third-order Chua's circuit in the embodiments of the present invention. Detailed Implementation

[0018] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0019] It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the invention. Furthermore, with respect to numerical ranges in this invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Every smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included in this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0020] Various modifications and variations can be made to the specific embodiments described in this specification without departing from the scope or spirit of the invention, as will be apparent to those skilled in the art. Other embodiments derived from this specification will also be obvious to those skilled in the art. This application specification and embodiments are merely exemplary.

[0021] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] like Figure 1 - Figure 8 As shown, this embodiment provides a sinusoidal nonlinear third-order Chua's circuit composed of a sinusoidal nonlinear function circuit and a third-order linear differential equation circuit, which can output three chaotic voltage signals of the sinusoidal nonlinear Chua's chaotic circuit.

[0024] This embodiment consists of a sinusoidal nonlinear function circuit and a third-order linear differential equation circuit. The input terminal of the sinusoidal nonlinear function circuit is connected to the x-output terminal of the third-order linear differential equation circuit, and the output terminal is connected to one input terminal of the x-integrator of the third-order linear differential equation circuit. The sinusoidal nonlinear function circuit consists of a first operational amplifier A1, resistors R1 to R16, and diodes D1 to D6, and its output has a sinusoidal nonlinear function relationship with the input. The third-order linear differential equation circuit consists of three inverting operational amplifiers, three capacitors, and seven resistors forming three inverting adder integrators. The nonlinear signal provided by the sinusoidal nonlinear function circuit generates three Chua's chaotic signal outputs of the sinusoidal nonlinear third-order Chua's circuit. This circuit can be used to construct various chaotic circuit systems and chaotic secure communication systems.

[0025] The circuit provided in this embodiment specifically includes:

[0026] like Figure 1 As shown, the x-output terminal of the third-order linear differential equation circuit is connected to the input terminal of the sinusoidal nonlinear function circuit, and the output terminal of the sinusoidal nonlinear function circuit is connected to one input terminal of the third-order linear differential equation circuit.

[0027] The sinusoidal nonlinear function circuit includes an operational amplifier, six diodes, fourteen resistors, and two power supplies. The input terminal V... 输入The first resistor R1 is connected to the first resistor R1 and the sixteenth resistor R16; the other end of the first resistor R1 is connected to the second resistor R2, the anode of the first diode D1, the anode of the second diode D2, the anode of the third diode D3, the cathode of the fourth diode D4, the cathode of the fifth diode D5, the cathode of the sixth diode D6, and the inverting input terminal of the first operational amplifier A1; the non-inverting input terminal of the first operational amplifier A1 is grounded, and its output terminal is connected to the second resistor R2, the third resistor R3, the fourth resistor R4, the fifth resistor R5, the sixth resistor R6, the seventh resistor R7, the eighth resistor R8, and the fifteenth resistor R15; the cathode of the first diode D1 is connected to the third resistor R3 and the ninth resistor R9; the cathode of the second diode D2 is connected to the fourth resistor R4. The tenth resistor R10 is connected; the cathode of the third diode D3 is connected to the fifth resistor R5 and the eleventh resistor R11; the anode of the fourth diode D4 is connected to the sixth resistor R6 and the twelfth resistor R12; the anode of the fifth diode D5 is connected to the seventh resistor R7 and the thirteenth resistor R13; the anode of the sixth diode D6 is connected to the eighth resistor R8 and the fourteenth resistor R14; the ninth resistor R9, the tenth resistor R10, and the eleventh resistor R11 are connected to the positive terminal of the first power supply EC1; the twelfth resistor R12, the thirteenth resistor R13, and the fourteenth resistor R14 are connected to the negative terminal of the second power supply EC2; the other end of the fifteenth resistor R15 and the other end of the sixteenth resistor R16 are connected to the output terminal of the sinusoidal nonlinear function circuit.

[0028] The third-order linear differential equation circuit includes three inverting operational amplifiers, three capacitors, and seven resistors forming three inverting adder-integrators. The input terminal of the third-order linear differential equation circuit is connected to the twentieth resistor R20, the first capacitor C1, and the inverting input terminal of the second operational amplifier A2. The output terminal of the third-order linear differential equation circuit is connected to the seventeenth resistor R17, the first capacitor C1, and the output terminal of the second operational amplifier A2. The non-inverting input terminal of the third operational amplifier A3 is grounded, and its inverting input terminal is connected to the seventeenth resistor R17, the eighteenth resistor R18, the nineteenth resistor R19, and the second capacitor C2. Its output terminal is connected to the nineteenth resistor R19, the twentieth resistor R20, the twenty-first resistor R21, and the second capacitor C2. The second operational amplifier A2 has its non-inverting input grounded, its inverting input connected to the twentieth resistor R20, the first capacitor C1, and the input of the third-order linear differential equation circuit, and its output connected to the first capacitor C1 and the output of the third-order linear differential equation circuit. This output is output terminal X. The fourth operational amplifier A4 has its non-inverting input grounded, its inverting input connected to the twenty-first resistor R21 and the twenty-second resistor R22, and its output connected to the twenty-second resistor R22 and the twenty-third resistor R23. This output is output terminal Y. The fifth operational amplifier A5 has its non-inverting input grounded, its inverting input connected to the third capacitor C2 and the twenty-third resistor R23, and its output connected to the eighteenth resistor R18. This output is output terminal Z.

[0029] The component parameters for this embodiment are as follows:

[0030] A1 is model TL082 or TL084, and the diode model is 2CK11;

[0031] R1=R2=5.1KΩ, R3=R6=18KΩ, R4=R7=6.8KΩ, R5=R8=1.3KΩ;

[0032] R9=R12=129KΩ, R10=R13=28.5KΩ, R11=R14=4.56KΩ, R15=69KΩ;

[0033] R16=6.5KΩ, R17=1.7KΩ, R18=1KΩ, R19=R22=10KΩ, R20=3.9KΩ;

[0034] R21=560KΩ, R23=5.6KΩ.

[0035] Will Figure 1 Connecting the three output terminals Vx, Vy, and Vz to the signal terminals of an oscilloscope or a relevant computer interface allows the display of chaotic waveform signals at these three output terminals. Using the oscilloscope's phase diagram mode, chaotic phase diagrams for xy, xz, and yz can be displayed. The three chaotic waveforms at the Vx, Vy, and Vz output terminals are shown below. Figure 2 , Figure 3 , Figure 4 As shown, the chaotic phase diagrams of xy, xz, and yz are as follows: Figure 5 , Figure 6 , Figure 7 As shown. Measurements were performed using EWB circuit simulation software, and the results are as follows. Figure 8 As shown. By Figures 2 to 8 This proves the effectiveness of this embodiment.

[0036] Compared with existing technologies, this embodiment can observe the nonlinear curve of a sinusoidal function and output three voltage waveform signals and three voltage phase diagram signals of a sinusoidal nonlinear Chua's circuit. It can be applied to chaotic circuit design and various other experiments on sinusoidal nonlinear third-order Chua's circuit can be performed on an oscilloscope. This embodiment is suitable for analog electronics science education, experimental teaching and demonstration, and popular science experimental demonstrations.

[0037] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A third-order circuit system based on sinusoidal nonlinear characteristics, characterized in that, The circuit includes a sinusoidal nonlinear function circuit and a third-order linear differential equation circuit. The third-order linear differential equation circuit includes a second operational amplifier A2, a third operational amplifier A3, a fourth operational amplifier A4, a fifth operational amplifier A5, several capacitors, and several resistors. The non-inverting input of the second operational amplifier A2 is grounded, and its inverting input is connected to the twentieth resistor R20, the first capacitor C1, and the output of the sinusoidal nonlinear function circuit. The output of the second operational amplifier A2 is connected to the first capacitor C1 and the input of the sinusoidal nonlinear function circuit. The second capacitor C2 and the nineteenth resistor R19 are connected in parallel between the inverting input and output of the third operational amplifier A3. The non-inverting input of the third operational amplifier A3 is grounded, and its inverting input is connected to the seventeenth resistor R17. The output of the second operational amplifier A2 is connected to the output of the third operational amplifier A3. The output of the third operational amplifier A3 is connected to the inverting input of the second operational amplifier A2 and the inverting input of the fourth operational amplifier A4 through the twentieth resistor R20 and the twenty-first resistor R21, respectively. The non-inverting input of the fourth operational amplifier A4 is grounded. A twenty-second resistor R22 is connected in parallel between the inverting input and the output of the fourth operational amplifier A4. The output of the fourth operational amplifier A4 is connected to the inverting input of the fifth operational amplifier A5 through the twenty-third resistor R23. The non-inverting input of the fifth operational amplifier A5 is grounded. A third capacitor C3 is connected in parallel between the inverting input and the output of the fifth operational amplifier A5. The output of the fifth operational amplifier A5 is connected to the inverting input of the third operational amplifier A3 through the eighteenth resistor R18.

2. The system according to claim 1, characterized in that, The sinusoidal nonlinear function circuit includes a first resistor R1. One end of the first resistor R1 is connected to the output terminal of the second operational amplifier A2, and the other end is connected to the inverting input terminal of the first operational amplifier A1, one end of the second resistor R2, the anode of the first diode D1, the anode of the second diode D2, the anode of the third diode D3, the cathode of the fourth diode D4, the cathode of the fifth diode D5, and the cathode of the sixth diode D6. The non-inverting input terminal of the first operational amplifier A1 is grounded. The cathodes of the first diode D1 are connected to the third resistor R3 and the ninth resistor R9, the cathodes of the second diode D2 are connected to the fourth resistor R4 and the tenth resistor R10, the cathodes of the third diode D3 are connected to the fifth resistor R5 and the eleventh resistor R11, and the anodes of the fourth diode D4 are connected to the sixth resistor R10. Resistor 6 is connected to resistor R12. The anode of the fifth diode D5 is connected to resistors R7 and R13. The anode of the sixth diode D6 is connected to resistors R8 and R14. Resistors R2, R3, R4, R5, R6, R7, and R8 are connected in parallel and all connected to the output of the first operational amplifier A1. The output of the first operational amplifier A1 is connected to the inverting input of the second operational amplifier A2. Resistors R9, R10, and R11 are all connected to the positive terminal of power supply EC1. Resistors R12, R13, and R14 are all connected to the negative terminal of power supply EC2. Power supplies EC1 and EC2 are connected in series.

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