CN107070631B - Design method of multi-scroll chaotic attractor circuit - Google Patents

Abstract

The invention relates to the technical field of nonlinear dynamics, and provides a design method of a multi-scroll chaotic attractor circuit, which comprises the following steps: acquiring a reference state equation according to the state equation and the symbol function of the double-scroll Chua's circuit; generating a circuit state equation according to the multi-scroll Chua's circuit and the symbol function generating circuit; and acquiring device parameters in the multi-scroll Chua's circuit and the symbol function generating circuit according to the reference state equation and the circuit state equation. The invention constructs a new nonlinear generation chaotic multi-scroll attraction subsystem model by introducing a symbol function on the basis of the existing Chua's circuit, the system is stable and reliable and is easy to debug, 2n scrolls can be obtained by utilizing computer simulation, and a plurality of scrolls can be obtained in an actual hardware circuit.

Description

A design method for multi-scroll chaotic attractor circuit

Technical field

The invention relates to the technical field of nonlinear dynamics, and in particular to a design method of a multi-scroll chaotic attractor circuit.

Background technique

At present, in the hybrid field, methods have been proposed to use sine functions, triangular wave sequences, and time-delay functions to generate multiple scrolls. It is not surprising to use computers to simulate the chaotic attractor of more than 10 scrolls. However, it depends on the actual hardware. It is not easy to generate a chaotic attractor with more than 10 scrolls in a circuit. Judging from existing literature reports, the hardware experimental results of using a typical Chua circuit to obtain 11 scrolls in one direction are the latest research results. At the same time, research shows that encryption using low-dimensional simple chaotic systems can be deciphered, but high-dimensional multi-scrolls with complex behavior are still difficult to decipher. In summary, it is difficult to generate multi-vortices from hardware circuits in the existing technology. The problem of chaotic attractors of volumes.

Contents of the invention

The purpose of the present invention is to provide a design method for a multi-scroll chaotic attractor circuit, aiming to solve the problem in the prior art that it is difficult to generate a multi-scroll chaotic attractor from a hardware circuit.

The present invention is implemented as follows. The first aspect provides a design method for a multi-scroll chaotic attractor circuit, which is characterized in that the design method includes:

Obtain the baseline state equation based on the state equation and sign function of the double scroll Chua's circuit;

Generate circuit state equations based on multiscroll Chua's circuits and symbolic function generation circuits;

The device parameters in the multi-scroll Chua's circuit and the symbolic function generation circuit are obtained according to the reference state equation and the circuit state equation.

The present invention provides a design method for a multi-scroll chaotic attractor circuit. On the basis of the existing Chua's circuit, a symbolic function is introduced to construct a new nonlinear chaotic multi-scroll attractor system model. This system is stable, reliable, and easy to use. During debugging, computer simulation can be used to obtain 2n scrolls, and multiple scrolls can be obtained in actual hardware circuits.

Description of the drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings in the following description are only illustrative of the present invention. For some embodiments, for those of ordinary skill in the art, other drawings can be obtained based on these drawings without exerting creative efforts.

Figure 1 is a flow chart of a multi-scroll chaotic attractor design method provided by an embodiment of the present invention;

Figure 2 is a circuit diagram of a double scroll Chua's circuit provided by an embodiment of the present invention;

Figure 3 is a Chua diode volt-ampere characteristic curve diagram in a double-scroll Chua circuit provided by an embodiment of the present invention;

Figure 4 is a schematic diagram of the equilibrium point of the sign function of a multi-scroll chaotic attractor design method provided by an embodiment of the present invention;

Figure 5 is a schematic diagram of the Lyapunov spectrum in a multi-scroll chaotic attractor design method provided by an embodiment of the present invention;

Figure 6 is a MATLAB simulation result of an even number of scroll chaotic attractors from 2 to 4 of a multi-scroll chaotic attractor design method provided by an embodiment of the present invention;

Figure 7 is a circuit diagram of a basic Chua circuit in a multi-scroll chaotic attractor design method provided by an embodiment of the present invention;

Figure 8 is a circuit diagram of a multi-vortex Chua's circuit in a multi-vortex chaotic attractor design method provided by an embodiment of the present invention;

Figures 9(a) to 9(g) are diagrams of experimental results on a simulated oscilloscope of a multi-scroll chaotic attractor design method provided by an embodiment of the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention.

In order to illustrate the technical solution of the present invention, specific examples will be described below.

An embodiment of the present invention provides a multi-scroll chaotic attractor design method, as shown in Figure 1. The design method includes:

Step S101. Obtain the reference state equation according to the state equation and sign function of the double scroll Chua's circuit.

In the embodiment of the present invention, as shown in Figure 2, specifically, a double scroll Chua's circuit includes an inductor, a resistor, a first capacitor, a second capacitor and a diode. The first end of the inductor is connected to the first end of the resistor. terminal and the first terminal of the second capacitor, the second terminal of the resistor is connected to the first terminal of the first capacitor and the input terminal of the diode, and the second terminal of the inductor is connected to the third terminal of the second capacitor. two terminals, the second terminal of the first capacitor and the output terminal of the diode.

The state equation obtained from the double scroll Chua's circuit is:

Among them, the double scroll Chua's circuit includes an inductor L, a resistor R, a first capacitor C1 and a second capacitor C2. V1 is the voltage of the first capacitor, and V2 is the voltage of the second capacitor. As shown in Figure 3, g(Vc ₁ ) = G ₁ V ₁ +0.5(G ₀ -G ₁ )(|V ₁ +E|-|V ₁ -E|) is the Chua diode resistance characteristic curve, G1 and G0 are constant coefficients, and E is the turning point voltage;

Obtaining the baseline state equation based on the state equation and symbolic function is:

in, A＝10,B＝15,/>

The following is an example of generating 14 scroll chaotic attractors. At this time Solving the equilibrium point of the benchmark state equation means solving the zero point of the benchmark state equation, making the right side of the equation equal to zero, and simplifying it to:

The equilibrium point of the system is the zero point of h(x)=x-f(x). The zero point of h(x) is shown in Figure 4:

Obviously within the interval x∈(2i,2i+2), f(x) is continuous, and the equilibrium point of the system falls within the interval (2i,2i+2). It can be seen from Figure 3 that the stable equilibrium point is the intersection e _i =2i+1 of the ladder-shaped graph of the symbolic function and the straight line x=f(x), and there are 14 such stable equilibrium points. In addition, there are 13 jump points in Figure 4, which are the unstable equilibrium points of the system e _i = 2i. It can be seen from the figure that in the interval of Extreme point. According to the Fourier series convergence theorem, the Fourier series of h(x) converges, and when x is a continuous point of h(x), the series converges to h(x); when x is h(x) ), the series converges to Therefore, the system can produce chaotic vortices in each continuous interval, and the system has a homoclinic solution at each discontinuity point. The homoclinic orbit connects the vortices between regions, so that the system forms a 14-vortex attractor. That is, the stable equilibrium point corresponds to the scroll region, and the unstable equilibrium point corresponds to the key wave region. By analogy, when n takes a certain value, the system can produce 2n+2 vortex attractors.

The chaotic characteristics of the benchmark state equation were further analyzed, and the generation of 14 scrolls was taken as an example. MATLAB software was used to write the calculation program. The Lyapunov exponent spectrum obtained by simulation is shown in Figure 5. The Lyapunov exponents of the system are: LE1=0.209524, LE2=0.202634, LE3=-2.840734, and the Lyapunov dimension is: LD=2.1451. It can be seen from the basic state equation that the divergence of the system And LE1+LE2+LE3=-2.428571, therefore, the calculated Lyapunov index is reasonable. Secondly, this system produces a strange attractor with dimension LD = 2.1451, which is consistent with the geometric characteristics of chaotic attractors.

The Runge-Kutta method is used for integration of the base state equation system, the time length T = (0, 800), and the initial values {x, y, z} = {0.01, 0.02, 0.03}. The MATLAB simulation results are shown in Figure 6. In Figure 6, A, B, C, D, E, F, G and H are the X-Y direction phase diagrams of 2, 4, 6, 8, 10, 12 and 14 scrolls and the X-Z phase diagram of 14 scrolls respectively. Simulation results show that the system can generate multi-scroll chaotic attractors.

Step S102. Generate a circuit state equation based on the multi-scroll Chua's circuit and the sign function generation circuit.

In the embodiment of the present invention, as shown in Figure 7, specifically, the multi-scroll Chua's circuit includes resistor R01, resistor R02, resistor R03, resistor R04, resistor R05, resistor R06, resistor R07, resistor R08, resistor R09, resistor R11, resistor R12, resistor R13, resistor R21, resistor R22, resistor R23, resistor R31, resistor Rf1, resistor Rf2, resistor Rf3, capacitor C01, capacitor C02, capacitor C03, comparator U1, comparator U2, comparator U3, Comparator U4, comparator U5, comparator U6, comparator U7, comparator U8 and comparator U9;

The first end of the resistor R13 is the first input end of the multi-scroll Chua's circuit, and the second end of the resistor R13 is connected to the inverting input end of the comparator U1, the first end of the resistor R11, and the inverting input end of the resistor R12. The first terminal and the first terminal of the resistor Rf1, the second terminal of the resistor R11 are connected to the output terminal of the comparator U7, the second terminal of the resistor R12 is connected to the output terminal of the comparator U5, the first terminal of the capacitor C02 and the third terminal of the resistor R05. One end, the second end of the resistor Rf1 is connected to the output end of the comparator U1 and the first end of the resistor R01, the second end of the resistor R01 is connected to the inverting input end of the comparator U4 and the first end of the capacitor C01, the capacitor C01 The second terminal, the output terminal of the comparator U4, the first terminal of the resistor R04 and the first terminal of the resistor R21 are connected together and form the second input terminal of the multi-scroll Chua's circuit. The second terminal of the resistor R04 is connected to the third terminal of the resistor R07. One end is connected to the inverting input end of comparator U7, the second end of resistor R07 is connected to the output end of comparator U7, and the second end of resistor R21 is connected to the first end of resistor R22, the first end of resistor R23, and the first end of resistor Rf2. The first terminal and the inverting input terminal of the comparator U2, the second terminal of the resistor R22 is connected to the output terminal of the comparator U8, the first terminal of the resistor R31 and the first terminal of the resistor R08, and the second terminal of the resistor R23 is connected to the capacitor C03 The first end of the comparator U6 and the first end of the resistor R06. The second end of the resistor Rf2 is connected to the output end of the comparator U2 and the first end of the resistor R02. The second end of the resistor R02 is connected to the capacitor C02. The second terminal of the resistor R05 is connected to the inverting input terminal of the comparator U5. The second terminal of the resistor R05 is connected to the second terminal of the resistor R08 and the inverting input terminal of the comparator U8. The second terminal of the resistor R31 is connected to the inverting input terminal of the comparator U3. terminal and the first terminal of resistor Rf3, the second terminal of resistor Rf3 is connected to the output terminal of comparator U3 and the first terminal of resistor R03, the second terminal of resistor R03 is connected to the inverting input terminal of comparator U6 and the third terminal of capacitor C03. Two ends, the second end of the resistor R06 is connected to the inverting input end of the comparator U9 and the first end of the resistor R09. The second end of the resistor R09 is commonly connected to the output end of the comparator U9 and forms the output of the multi-scroll Chua circuit. terminal, the non-inverting input terminal of comparator U1, the non-inverting input terminal of comparator U2, the non-inverting input terminal of comparator U3, the non-inverting input terminal of comparator U4, the non-inverting input terminal of comparator U5, the non-inverting input terminal of comparator U6, The non-inverting input terminal of comparator U7, the non-inverting input terminal of comparator U8 and the non-inverting input terminal of comparator U9 are grounded.

In the embodiment of the present invention, as shown in Figure 8, specifically, the symbolic function generation circuit includes battery E1, battery E2, resistor R41, resistor R42, resistor R43, resistor R44, resistor R45, resistor R46, resistor R47, resistor R48 , Resistor R49, Resistor R50, Resistor R51, Resistor R52, Resistor R53, Resistor R54, Resistor R55, Resistor R56, Resistor R57, Resistor R58, Resistor R59, Resistor R60, Resistor R61, Resistor R62, Resistor R63, Resistor R64, Resistor R65, resistor R66, resistor R67, resistor R68, comparator U11, comparator U12, comparator U13, comparator U14, comparator U15, comparator U16, comparator U17, comparator U18, comparator U19, comparator U20 , comparator U21, comparator U22, comparator U23, comparator U24, comparator U25, switch S1, switch S2, switch S3, switch S4, switch S5 and switch S6;

The non-inverting input terminal of the comparator U24 is the first output terminal of the sign function generating circuit, and the inverting input terminal of the comparator U24 is connected to the output terminal of the comparator U24, the inverting input terminal of the comparator U11, and the inverting input terminal of the comparator U12. terminal, the inverting input terminal of comparator U13, the inverting input terminal of comparator U14, the inverting input terminal of comparator U15, the inverting input terminal of comparator U16, the inverting input terminal of comparator U17, the inverting input terminal of comparator U18 The inverting input terminal of comparator U19, the inverting input terminal of comparator U20, the inverting input terminal of comparator U21, the inverting input terminal of comparator U22 and the inverting input terminal of comparator U23 , the non-inverting input end of comparator U11 is connected to the second end of resistor R41 and the first end of resistor R42, the non-inverting input end of comparator U12 is connected to the second end of resistor R42 and the first end of resistor R43, the non-inverting end of comparator U13 The input terminal is connected to the second terminal of the resistor R43 and the first terminal of the resistor R44, the non-inverting input terminal of the comparator U14 is connected to the second terminal of the resistor R44 and the first terminal of the resistor R45, and the non-inverting input terminal of the comparator U15 is connected to the resistor R45. The second terminal and the first terminal of the resistor R46, the non-inverting input terminal of the comparator U16 are connected to the second terminal of the resistor R46 and the first terminal of the resistor R47, the non-inverting input terminal of the comparator U16, the second terminal of the resistor R47 and the resistor R67 The second end of the comparator U18 is connected to the ground. The non-inverting input end of the comparator U18 is connected to the second end of the resistor R61 and the first end of the resistor R62. The non-inverting input end of the comparator U19 is connected to the second end of the resistor R62 and the first end of the resistor R63. On one end, the non-inverting input end of the comparator U20 is connected to the second end of the resistor R63 and the first end of the resistor R64. The non-inverting input end of the comparator U21 is connected to the second end of the resistor R64 and the first end of the resistor R65. The comparator U22 The non-inverting input end of the comparator U23 is connected to the second end of the resistor R65 and the first end of the resistor R66. The non-inverting input end of the comparator U23 is connected to the second end of the resistor R66 and the first end of the resistor 67. The first end of the resistor R41 is connected to the battery E1. The positive electrode of battery E1 and the positive electrode of battery E2 are connected to the ground. The negative electrode of battery E2 is connected to the first end of resistor R61. The output end of comparator U11 is connected to the first end of resistor R48. The second end of resistor R48 is connected to the ground. The first terminal of switch S1 and the first terminal of resistor R55, the second terminal of resistor R55 is connected to the output terminal of comparator U18, the output terminal of comparator U12 is connected to the first terminal of resistor R49, and the second terminal of resistor R49 is connected to the switch. The second terminal of S1, the first terminal of switch S2 and the first terminal of resistor R56. The second terminal of resistor R56 is connected to the output terminal of comparator U19. The output terminal of comparator U13 is connected to the first terminal of resistor R50. Resistor R50 The second end of the switch S2 is connected to the second end of the switch S3 and the first end of the resistor R57. The second end of the resistor R57 is connected to the output end of the comparator U20. The output end of the comparator U14 is connected to the resistor R51. The first terminal and the second terminal of the resistor R51 are connected to the second terminal of the switch S3, the first terminal of the switch S4 and the first terminal of the resistor R58. The second terminal of the resistor R58 is connected to the output terminal of the comparator U21 and the comparator U15. The output terminal is connected to the first terminal of the resistor R52, the second terminal of the resistor R52 is connected to the second terminal of the switch S4, the first terminal of the switch S5 and the first terminal of the resistor R59, and the second terminal of the resistor R59 is connected to the output of the comparator U22. terminal, the output terminal of comparator U15 is connected to the first terminal of resistor R52, the second terminal of resistor R52 is connected to the second terminal of switch S4, the first terminal of switch S5 and the first terminal of resistor R59, the second terminal of resistor R59 The output terminal of comparator U22 is connected, the output terminal of comparator U16 is connected to the first terminal of resistor R53, the second terminal of resistor R53 is connected to the second terminal of switch S5, the first terminal of switch S6, the resistor R54 and the third terminal of resistor R68. On one end, the second end of the resistor R60 is connected to the output end of the comparator U23, the output end of the comparator U17 is connected to the first end of the resistor R54, and the second end of the resistor R54 is connected to the second end of the switch S6 and the first end of the resistor R68. terminal, the second terminal of resistor R68 is connected to the inverting input terminal of comparator U25, the non-inverting input terminal of comparator U25 is connected to ground, and the output terminal of comparator U25 is the second output terminal of the sign function generating circuit.

According to the above circuit, the obtained circuit state equation is:

Perform time scale transformation on the circuit state equation, and let τ=t/RC, where R=R ₀₁ , C=C ₀₁ , R ₀₁ =R ₀₂ =R ₀₃ , C ₀₁ =C ₀₂ =C ₀₃ , to obtain The following circuit state equation:

Step S103. Obtain the device parameters in the multi-scroll Chua's circuit and the sign function generation circuit according to the reference state equation and the circuit state equation.

Perform differential-integral conversion on the base state equation to obtain the following base state equation:

Compare the circuit state equation with the reference state equation to obtain device parameters;

in, Take/> A=10, B=15, let R _f =10k.

Performing hardware experiments on the circuits shown in Figures 7 and 8 can obtain the experimental results shown in Figure 9(a) to Figure 9(g). The experimental results were obtained from an analog oscilloscope using a digital camera. By controlling the on and off of the switch, the number of scrolls is controlled. When S ₁ , S ₂ , S ₃ , S ₄ , S ₅ , and S ₆ are all disconnected, the circuit generates a double scroll chaotic attractor; when S ₁ , S ₂ , S 3 , S ₄ , _{S 5 ,} S ₆ When both are closed, the circuit produces 14 scrolls. Whenever an additional switch is closed, the system adds two scrolls to the original basis.

Among them, 1/RC is the time scale change factor. By changing the values of R and C, the spectrum range of the chaotic signal can be changed. Here, R=5kΩ and C=33nF.

The present invention provides a design method for a multi-scroll chaotic attractor circuit. On the basis of the existing Chua's circuit, a symbolic function is introduced to construct a new nonlinear chaotic multi-scroll attractor system model. This system is stable, reliable, and easy to use. During debugging, computer simulation can be used to obtain 2n scrolls, and multiple scrolls can be obtained in actual hardware circuits.

The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be concluded that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, any equivalent substitutions or obvious modifications made without departing from the spirit of the present invention, and with the same performance or use, shall be deemed to belong to the present invention according to the submitted claims. The scope of patent protection determined by the book.

Claims (4)

1. A design method for a multi-scroll chaotic attractor circuit, characterized in that the design method includes: Obtain the baseline state equation based on the state equation and sign function of the double scroll Chua's circuit; Generate circuit state equations based on multiscroll Chua's circuits and symbolic function generation circuits; Obtain device parameters in the multi-scroll Chua's circuit and symbolic function generation circuit according to the reference state equation and circuit state equation; The acquisition of the reference state equation based on the state equation and sign function of the double scroll Chua's circuit includes: The state equation obtained from the double scroll Chua's circuit is: Wherein, the double scroll Chua's circuit includes an inductor L, a resistor R, a first capacitor C1 and a second capacitor C2, V1 is the first capacitor voltage, V2 is the second capacitor voltage, g(Vc ₁ )=G ₁ V ₁ +0.5(G ₀ -G ₁ )(|V ₁ +E|-|V ₁ -E|) is the Chua diode resistance characteristic curve, G1 and G0 are constant coefficients, and E is the turning point voltage; Obtaining the baseline state equation based on the state equation and symbolic function is: in, The circuit state equation generated based on the multi-scroll Chua's circuit and the sign function generation circuit includes: The obtained circuit state equation is: Perform time scale transformation on the circuit state equation, and let τ=t/RC, where R=R ₀₁ , C=C ₀₁ , R ₀₁ =R ₀₂ =R ₀₃ , C ₀₁ =C ₀₂ =C ₀₃ , Obtain the following circuit state equation: The method of obtaining the device parameters in the multi-scroll Chua's circuit and the symbolic function generation circuit based on the reference state equation and the circuit state equation includes: Perform differential-integral conversion on the base state equation to obtain the following base state equation: Compare the circuit state equation with the reference state equation to obtain device parameters; in, R _f =10k. 2. The design method according to claim 1, wherein the double scroll Chua's circuit includes an inductor, a resistor, a first capacitor, a second capacitor and a diode, and the first end of the inductor is connected to the resistor. The first terminal is connected to the first terminal of the second capacitor, the second terminal of the resistor is connected to the first terminal of the first capacitor and the input terminal of the diode, and the second terminal of the inductor is connected to the second capacitor. the second terminal of the first capacitor and the output terminal of the diode. 3. The design method according to claim 1, wherein the multi-scroll Chua's circuit includes resistors R01, R02, R03, R04, R05, R06, R07, R08, R09, R11, resistor R12, resistor R13, resistor R21, resistor R22, resistor R23, resistor R31, resistor Rf1, resistor Rf2, resistor Rf3, capacitor C01, capacitor C02, capacitor C03, comparator U1, comparator U2, comparator U3, Comparator U4, comparator U5, comparator U6, comparator U7, comparator U8 and comparator U9; The first end of the resistor R13 is the first input end of the multi-scroll Chua circuit, and the second end of the resistor R13 is connected to the inverting input end of the comparator U1 and the first end of the resistor R11 , the first end of the resistor R12 and the first end of the resistor Rf1, the second end of the resistor R11 is connected to the output end of the comparator U7, and the second end of the resistor R12 is connected to the comparator The output end of U5, the first end of the capacitor C02 and the first end of the resistor R05, the second end of the resistor Rf1 is connected to the output end of the comparator U1 and the first end of the resistor R01, The second end of the resistor R01 is connected to the inverting input end of the comparator U4 and the first end of the capacitor C01. The second end of the capacitor C01, the output end of the comparator U4, and the resistor The first end of R04 and the first end of the resistor R21 are connected together and constitute the second input end of the multi-scroll Chua's circuit. The second end of the resistor R04 is connected to the first end of the resistor R07 and the first end of the resistor R07. The inverting input terminal of the comparator U7, the second terminal of the resistor R07 is connected to the output terminal of the comparator U7, the second terminal of the resistor R21 is connected to the first terminal of the resistor R22 and the resistor R23 The first end of the resistor Rf2 and the inverting input end of the comparator U2. The second end of the resistor R22 is connected to the output end of the comparator U8 and the first end of the resistor R31. terminal and the first terminal of the resistor R08, the second terminal of the resistor R23 is connected to the first terminal of the capacitor C03, the output terminal of the comparator U6 and the first terminal of the resistor R06, the resistor The second end of Rf2 is connected to the output end of the comparator U2 and the first end of the resistor R02. The second end of the resistor R02 is connected to the second end of the capacitor C02 and the inverse phase of the comparator U5. Input terminal, the second terminal of the resistor R05 is connected to the second terminal of the resistor R08 and the inverting input terminal of the comparator U8, and the second terminal of the resistor R31 is connected to the inverting input of the comparator U3. terminal and the first terminal of the resistor Rf3, the second terminal of the resistor Rf3 is connected to the output terminal of the comparator U3 and the first terminal of the resistor R03, the second terminal of the resistor R03 is connected to the comparison The inverting input end of the comparator U6 and the second end of the capacitor C03, the second end of the resistor R06 is connected to the inverting input end of the comparator U9 and the first end of the resistor R09, the resistor R09 The second terminal is connected in common with the output terminal of the comparator U9 and constitutes the output terminal of the multi-scroll Chua's circuit. The non-inverting input terminal of the comparator U1, the non-inverting input terminal of the comparator U2, the The non-inverting input terminal of the comparator U3, the non-inverting input terminal of the comparator U4, the non-inverting input terminal of the comparator U5, the non-inverting input terminal of the comparator U6, the non-inverting input terminal of the comparator U7, the The non-inverting input terminal of the comparator U8 and the non-inverting input terminal of the comparator U9 are grounded. 4. The design method according to claim 1, wherein the symbolic function generating circuit includes a battery E1, a battery E2, a resistor R41, a resistor R42, a resistor R43, a resistor R44, a resistor R45, a resistor R46, a resistor R47, Resistor R48, Resistor R49, Resistor R50, Resistor R51, Resistor R52, Resistor R53, Resistor R54, Resistor R55, Resistor R56, Resistor R57, Resistor R58, Resistor R59, Resistor R60, Resistor R61, Resistor R62, Resistor R63, Resistor R64 , resistor R65, resistor R66, resistor R67, resistor R68, comparator U11, comparator U12, comparator U13, comparator U14, comparator U15, comparator U16, comparator U17, comparator U18, comparator U19, comparison Comparator U20, comparator U21, comparator U22, comparator U23, comparator U24, comparator U25, switch S1, switch S2, switch S3, switch S4, switch S5 and switch S6; The non-inverting input terminal of the comparator U24 is the first output terminal of the sign function generating circuit, and the inverting input terminal of the comparator U24 is connected to the output terminal of the comparator U24 and the inverting terminal of the comparator U11. input terminal, the inverting input terminal of the comparator U12, the inverting input terminal of the comparator U13, the inverting input terminal of the comparator U14, the inverting input terminal of the comparator U15, the comparison The inverting input terminal of the comparator U16, the inverting input terminal of the comparator U17, the inverting input terminal of the comparator U18, the inverting input terminal of the comparator U19, the inverting input terminal of the comparator U20 terminal, the inverting input terminal of the comparator U21, the inverting input terminal of the comparator U22 and the inverting input terminal of the comparator U23, the non-inverting input terminal of the comparator U11 is connected to the resistor R41 The second terminal and the first terminal of the resistor R42, the non-inverting input terminal of the comparator U12 are connected to the second terminal of the resistor R42 and the first terminal of the resistor R43, and the non-inverting input terminal of the comparator U13 The second end of the resistor R43 is connected to the first end of the resistor R44. The non-inverting input end of the comparator U14 is connected to the second end of the resistor R44 and the first end of the resistor R45. The comparison The non-inverting input end of the comparator U15 is connected to the second end of the resistor R45 and the first end of the resistor R46, and the non-inverting input end of the comparator U16 is connected to the second end of the resistor R46 and the first end of the resistor R47. One end, the non-inverting input end of the comparator U16, the second end of the resistor R47 and the second end of the resistor R67 are commonly connected to the ground, and the non-inverting input end of the comparator U18 is connected to the second end of the resistor R61. The second terminal and the first terminal of the resistor R62, the non-inverting input terminal of the comparator U19 are connected to the second terminal of the resistor R62 and the first terminal of the resistor R63, and the non-inverting input terminal of the comparator U20 The second end of the resistor R63 is connected to the first end of the resistor R64. The non-inverting input end of the comparator U21 is connected to the second end of the resistor R64 and the first end of the resistor R65. The comparison The non-inverting input terminal of the comparator U22 is connected to the second terminal of the resistor R65 and the first terminal of the resistor R66, and the non-inverting input terminal of the comparator U23 is connected to the second terminal of the resistor R66 and the first terminal of the resistor R67. One end, the first end of the resistor R41 is connected to the positive electrode of the battery E1, the negative electrode of the battery E1 and the positive electrode of the battery E2 are connected to the ground, and the negative electrode of the battery E2 is connected to the third terminal of the resistor R61. On one end, the output end of the comparator U11 is connected to the first end of the resistor R48, and the second end of the resistor R48 is connected to the first end of the switch S1 and the first end of the resistor R55. The second end of the resistor R55 is connected to the output end of the comparator U18, the output end of the comparator U12 is connected to the first end of the resistor R49, and the second end of the resistor R49 is connected to the second end of the switch S1. terminal, the first terminal of the switch S2 and the first terminal of the resistor R56, the second terminal of the resistor R56 is connected to the output terminal of the comparator U19, the output terminal of the comparator U13 is connected to the resistor The first end of R50 and the second end of the resistor R50 are connected to the second end of the switch S2, the first end of the switch S3 and the first end of the resistor R57. The second end of the resistor R57 The output terminal of the comparator U20 is connected, the output terminal of the comparator U14 is connected to the first terminal of the resistor R51, and the second terminal of the resistor R51 is connected to the second terminal of the switch S3 and the switch S4. and the first end of the resistor R58, the second end of the resistor R58 is connected to the output end of the comparator U21, the output end of the comparator U15 is connected to the first end of the resistor R52, The second end of the resistor R52 is connected to the second end of the switch S4, the first end of the switch S5 and the first end of the resistor R59. The second end of the resistor R59 is connected to the comparator U22. The output end of the comparator U15 is connected to the first end of the resistor R52, and the second end of the resistor R52 is connected to the second end of the switch S4, the first end of the switch S5 and the The first end of the resistor R59, the second end of the resistor R59 is connected to the output end of the comparator U22, the output end of the comparator U16 is connected to the first end of the resistor R53, the third end of the resistor R53 The two terminals are connected to the second terminal of the switch S5, the first terminal of the switch S6, the resistor R54 and the first terminal of the resistor R68. The second terminal of the resistor R60 is connected to the comparator U23. The output end of the comparator U17 is connected to the first end of the resistor R54, and the second end of the resistor R54 is connected to the second end of the switch S6 and the first end of the resistor R68. The second end of the resistor R68 is connected to the inverting input end of the comparator U25, the non-inverting input end of the comparator U25 is connected to ground, and the output end of the comparator U25 is the second output end of the sign function generating circuit.