Weak signal detection circuit based on third-order memristor

Abstract

The application discloses a weak signal detection circuit based on a third-order memristor, which comprises a third-order memristor M, a capacitor C1, a capacitor C2 and a resistor R, wherein the third-order memristor M, the capacitor C1 and the capacitor C2 are sequentially connected with a power supply AC to form a closed loop, and the resistor R is connected in parallel with the capacitor C2; the third-order memristor M changes the resistance value by adjusting the amplitude or frequency of an applied excitation signal or by modifying the internal element parameters of the memristor; the specific values of the capacitor C1, the capacitor C2 and the resistor R are obtained according to the resistance value of the third-order memristor used and the specific parameters of a chaotic oscillator defined by the user. The weak signal detection circuit of the application does not rely on complex electronic elements, electronic controllers and programming chips, but only uses simple basic circuit elements to build, has strong sensitivity to weak signals, has certain immunity to noise, and therefore has sensitivity and anti-noise performance at the same time, and has the characteristics of simple structure, economy and applicability.

Description

Technical Field

[0001] This invention belongs to the field of chaotic system signal generator technology, and relates to a weak signal detection circuit based on a third-order memristor. Background Technology

[0002] Chaotic systems, characterized by highly complex and nonlinear dynamics, have attracted widespread research interest in recent years across various fields, including communications, biomedicine, and environmental science, offering new perspectives for understanding and exploring the complexity of nature. In exploring the practical applications of chaotic systems, detecting weak signals is a particularly important research area, as it directly relates to understanding system behavior and the feasibility of signal transmission and control. Traditional detection methods are largely limited by their linear system basis, often suffering from drawbacks such as simultaneous amplification of signal and noise, and excessive signal loss after filtering. In contrast, chaotic systems are characterized by high sensitivity and complexity, capable of generating strong responses even under weak external disturbances. Therefore, chaotic systems possess significant advantages in weak signal detection.

[0003] In recent years, memristors, as a novel nonlinear element, have gradually attracted attention for their application in chaotic systems. This device is an electronic device with a memory effect; its resistance changes depending on the historical state of current and voltage, hence the name memristor. Due to its nonlinear characteristics and memory properties, memristors can generate complex voltage waveforms that match the behavior of chaotic systems, providing an opportunity to construct weak signal detection circuits based on memristors. Summary of the Invention

[0004] The purpose of this invention is to provide a weak signal detection circuit based on a third-order memristor, which solves the problem of existing technologies based on linear systems, where signals and noise are amplified simultaneously, and the signal is lost too much after filtering.

[0005] The technical solution adopted in this invention is a weak signal detection circuit based on a third-order memristor, including a third-order memristor M, capacitor C1, capacitor C2, and resistor R. The third-order memristor M, capacitor C1, and capacitor C2 are connected to the power supply AC in sequence to form a closed loop, while the resistor R is connected in parallel with the capacitor C2.

[0006] The weak signal detection circuit based on a third-order memristor of the present invention is further characterized in that:

[0007] The third-order memristor M can change its resistance by adjusting the amplitude or frequency of the external excitation signal, or by modifying the internal component parameters of the memristor.

[0008] The specific value of capacitor C1 is determined based on the resistance value of the third-order memristor used and the specific parameters of the custom chaotic oscillator.

[0009] The specific value of capacitor C2 is determined based on the resistance value of the third-order memristor used and the specific parameters of the custom chaotic oscillator.

[0010] The specific value of the resistor R is determined based on the resistance value of the third-order memristor used and the specific parameters of the custom chaotic oscillator.

[0011] The specific parameters of the chaotic oscillator can be selected according to the user's needs, such as damping ratio coefficient, nonlinear restoring force coefficient, or periodic driving force coefficient; when the circuit of this invention is used for weak signal detection, the critical state periodic driving force amplitude is γ = 8.475.

[0012] The beneficial effects of this invention are that the weak signal detection circuit based on a third-order memristor (hereinafter referred to as the circuit of this invention) has strong sensitivity to weak signals and a certain degree of immunity to noise. Therefore, the weak signal detection system built on the basis of the circuit of this invention has both sensitivity and noise resistance. The circuit of this invention does not rely on complex electronic components, electronic controllers and programming chips. It can build a real circuit using only simple basic circuit components. Therefore, it is easy to build and has the advantages of convenience and economy in practical applications. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the circuit connection of the present invention;

[0014] Figure 2 This is a bifurcation diagram of the chaotic system in the circuit of this invention;

[0015] Figure 3 The Lyapunov exponent diagram of the chaotic system in the circuit of this invention;

[0016] Figure 4a The system phase trajectory is shown when γ = 1.24. Figure 4b The time-domain waveform is shown when γ = 1.24.

[0017] Figure 5a The system phase trajectory diagram is shown when γ = 2.53. Figure 5b The time-domain waveform is shown when γ = 2.53;

[0018] Figure 6a The system phase trajectory is shown when γ = 3.89. Figure 6b The time-domain waveform is shown when γ = 3.89;

[0019] Figure 7a The system phase trajectory diagram is shown when γ = 4.22. Figure 7bThe time-domain waveform is shown when γ = 4.22.

[0020] Figure 8a The system phase trajectory is shown when γ = 6.34. Figure 8b The time-domain waveform is shown when γ = 6.34.

[0021] Figure 9a The system phase trajectory is shown when γ = 7.92. Figure 9b The time-domain waveform is shown when γ = 7.92.

[0022] Figure 10a The system phase trajectory is shown when γ = 8.57. Figure 10b The time-domain waveform is shown when γ = 8.57.

[0023] Figure 11a This is a phase diagram under critical conditions without the application of a weak signal. Figure 11b A weak signal phase diagram is added to the critical state;

[0024] Figure 12 The time series diagram is for Gaussian white noise;

[0025] Figure 13a This is a phase diagram without weak signals under noise interference. Figure 13b A phase diagram with a weak signal is added under noise interference. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0027] Reference Figure 1 The circuit structure of the present invention includes a third-order memristor M, capacitor C1, capacitor C2, and resistor R. The third-order memristor M, capacitor C1, and capacitor C2 are connected to the power supply AC in sequence to form a closed loop, and the resistor R is connected in parallel with the capacitor C2.

[0028] The third-order memristor M changes its resistance by adjusting the amplitude or frequency of the external excitation signal, or by modifying the internal component parameters of the memristor.

[0029] The specific values ​​of capacitors C1 and C2 and resistor R are determined based on the resistance value of the third-order memristor used and the specific parameters of the custom chaotic oscillator. The specific parameters of the chaotic oscillator are selected according to the custom requirements, such as damping ratio coefficient, nonlinear restoring force coefficient, and periodic driving force coefficient.

[0030] The circuit of this invention is built using simple, basic circuit components and is highly sensitive to minute changes in excitation voltage and frequency, exhibiting rich dynamic behaviors under different conditions; it also possesses a certain degree of immunity to noise interference. Based on these characteristics, the dynamic behavior features of the circuit of this invention are analyzed below, and the circuit is used to perform weak signal detection, while also verifying the anti-interference performance of the circuit of this invention.

[0031] (i) The working principle of the circuit of this invention.

[0032] Assume the magnetic flux through the third-order memristor M The relationship between the charge q and the charge q is as follows α and b are both nonlinear restoring force parameters, α < 0, b > 0; excitation source e(t) = U m cosωt,U m ω is the excitation voltage extreme value, ω is the input excitation frequency, and t is the input excitation time. Figure 1 The circuit in the diagram has the following expression:

[0033]

[0034] Where C1 and C2 are the capacitances of capacitors C1 and C2 respectively, and R is the resistance of resistor R; U c1 It is the voltage across capacitor C1, U c2 It is the voltage across capacitor C2.

[0035] After rearranging equation (1), we get the following expression:

[0036]

[0037] Since the charge flowing through capacitor C1 is the same as the charge flowing through third-order memristor M, the following expression applies to charge q:

[0038]

[0039] Differentiating both sides of equation (3) with respect to time t, we obtain the following expression:

[0040]

[0041] Combining equations (2), (3), and (4), we obtain the following expression:

[0042]

[0043] make y = U c2 Then we have the following expression:

[0044]

[0045] The expression derived from equation (6) is as follows:

[0046]

[0047] The resulting expression is as follows:

[0048]

[0049] Then transform equation (8) into the following form:

[0050]

[0051] In equation (9), ε is a small parameter located in (0,1], ω0 is the natural frequency of the system; εβ(1-μx 2 ) is the system damping ratio term, and β and μ are both damping ratio coefficients; It is a nonlinear restoring force term. α and γ are both nonlinear restoring force parameters; γ and γ0 are both periodic driving force amplitudes, and the relevant parameters are defined as follows:

[0052]

[0053] For ease of analysis, equation (9) is rewritten, and ε is set to 1. When α = 1, β = 0.1, ω = 1, μ = 1, γ = γ0, the expression transforms into:

[0054]

[0055] To analyze the dynamic behavior of the circuit of this invention, numerical simulation was performed using MATLAB software, and the mathematical model is given by equation (2). The bifurcation diagram of the oscillation system of the circuit of this invention is shown below. Figure 2 As shown, the Lyapunov exponent diagram of the circuit of this invention is as follows: Figure 3 As shown in the diagram, the bifurcation diagram and Lyapunov exponent diagram reveal that the circuit of this invention is highly sensitive to the value of the periodic driving force amplitude γ. By changing the periodic driving force amplitude γ, the circuit of this invention exhibits a wide range of dynamic behaviors.

[0056] Based on equation (2), the system phase trajectory diagram and time domain waveform diagram are plotted. The corresponding parameters are as described above. By changing the γ term, the following embodiments are illustrated.

[0057] Example 1

[0058] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the amplitude of the periodic driving force is γ = 1.24, the following is obtained: Figure 4a System phase trajectory diagram and Figure 4b The time-domain waveform diagram.

[0059] Example 2

[0060] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the amplitude of the periodic driving force is γ = 2.53, the following is obtained: Figure 5a System phase trajectory diagram and Figure 5b The time-domain waveform diagram.

[0061] Example 3

[0062] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the periodic driving force amplitude is γ = 3.89, the following is obtained: Figure 6a System phase trajectory diagram and Figure 6b The time-domain waveform diagram.

[0063] Example 4

[0064] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the amplitude of the periodic driving force is γ = 4.22, the following is obtained: Figure 7a System phase trajectory diagram and Figure 7b The time-domain waveform diagram.

[0065] Example 5

[0066] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the amplitude of the periodic driving force is γ = 6.34, the following is obtained: Figure 8a System phase trajectory diagram and Figure 8b The time-domain waveform diagram.

[0067] Example 6

[0068] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the amplitude of the periodic driving force is γ = 7.92, the following is obtained: Figure 9a System phase trajectory diagram and Figure 9b The time-domain waveform diagram.

[0069] Example 7

[0070] use Figure 1 The circuit structure shown is used for the dynamic behavior characteristic analysis of the circuit of this invention. When the periodic driving force amplitude is γ = 8.57, the following is obtained: Figure 10a System phase trajectory diagram and Figure 10b The time-domain waveform diagram.

[0071] It is evident that the system phase diagram exhibits different dynamic states when γ takes different values.

[0072] (ii) Analysis used for weak signal detection.

[0073] Because the circuit of this invention is highly sensitive to the periodic driving force amplitude γ, when the critical value at which the circuit changes from a chaotic state to a periodic state is used as the initial value of the periodic driving force amplitude γ, any slight disturbance to the periodic driving force amplitude γ may change the dynamic state of the entire circuit system. Based on this principle, the circuit of this invention can be used for weak signal detection.

[0074] Through the bifurcation diagram ( Figure 2 ) and Lyapunov index plot ( Figure 3 It can be seen that the critical value of the driving force amplitude for the circuit of the present invention to transition from the chaotic state to the periodic state is approximately γ = 8.45. Through further precise calculation of the phase diagram trajectory, the critical state periodic driving force amplitude of the circuit of the present invention is finally determined to be γ = 8.475.

[0075] Weak signal detection simulation was performed using MATLAB software. The periodic driving force amplitude γ was set as the critical value. Based on equation (10), a weak signal term acost was added, where a is the amplitude of the weak signal. The mathematical model is then shown in equation (11):

[0076]

[0077] When the input excitation signal does not contain weak signals, the circuit of this invention is in a chaotic state, such as... Figure 11a As shown. When a weak input signal a = 0.001, the system is in a periodic state, as... Figure 11b As shown in the figure. Simulation results demonstrate that the circuit of this invention is highly sensitive to the periodic driving amplitude γ of the input signal and can successfully detect whether the input signal contains weak signals.

[0078] (iii) Testing and analysis of the noise immunity capability of the circuit of the present invention.

[0079] Gaussian white noise n(t) is added to equation (11), and the timing diagram of the input Gaussian white noise is referenced. Figure 12 As shown, the mathematical model at this time is as shown in equation (12):

[0080]

[0081] Figure 13a This is a phase diagram without weak signals under noise interference. Figure 13b A phase diagram with a weak signal added under noise interference. Figure 13a , Figure 13bAs can be seen, when the system is under noise interference, the phase diagram of the circuit of the present invention still transforms from a chaotic state to a periodic state when a weak signal is added. This result shows that the circuit of the present invention is not only highly sensitive to weak signals, but also immune to noise interference.

[0082] In summary, under simulation conditions, the circuit of this invention successfully completed the weak signal detection task, proving that the circuit of this invention has practical working capability, practical application value, and great potential for further development and in-depth research in related fields.

Claims

1. A weak signal detection circuit based on a third-order memristor, characterized in that: Including third-order memristors ,capacitance ,capacitance ,resistance Among them, the third-order memristor ,capacitance ,capacitance With power supply AC Connect them sequentially to form a closed loop, and the resistance... With capacitor in parallel; Third-order memristor The resistance of a memristor is changed by modifying the parameters of its internal components; capacitors ,capacitance ,resistance The specific value is determined based on the resistance value of the third-order memristor used and the specific parameters of the custom chaotic oscillator. The specific parameters of the chaotic oscillator can be selected according to the user's needs, such as the damping ratio coefficient, nonlinear restoring force coefficient, or periodic driving force coefficient. When this circuit is used for weak signal detection, the critical state periodic driving amplitude is [value missing]. = 8.

475.

2. The weak signal detection circuit based on a third-order memristor according to claim 1, characterized in that: Third-order memristor The resistance value can be changed by adjusting the amplitude or frequency of the external excitation signal.

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