A high robustness singularity realization method in a single electronic resonator

Abstract

The application discloses a high-robustness singularity realization method in a single electronic resonator, and comprises the following steps: step one, time-reversal symmetry construction and mode synthesis, injecting a stable external signal into a single resonator, generating a synthetic mode by four-wave mixing, and forming time-reversal symmetry with an inherent mode; step two, establishing a system Hamiltonian, and fixing system eigenvalues at a stable injection frequency ω AWG Only ω1 is left as a sensing degree of freedom, step three, sensing measurement verification, an electronic resonator, an arbitrary signal generator and a coupling resistor R c An electronic circuit is composed, step four, a nonlinear bifurcation model, based on a nonlinear model P NL (t) analyzes bifurcation behavior; the application realizes high-robustness singularity in a single electronic resonator structure combined with a four-wave mixing mechanism without physical coupling, an artificial mode is synthesized by injecting an external stable signal, time-reversal symmetry is constructed, and system eigenvalues are anchored to an external frequency.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and more particularly to a method for realizing highly robust singularities in a single electronic resonator. Background Technology

[0002] Singularities, as topological singularities in non-Hermitian systems, have attracted much attention due to their high sensitivity in sensing. At a singularity, the system's eigenvalues ​​and eigenstates are simultaneously degenerate, making the frequency splitting caused by external perturbations proportional to the Nth root of the perturbation amplitude, thus significantly improving sensing performance. In recent years, electronic resonators have become an important platform for realizing singularity functionality due to their miniaturization, low cost, and efficient signal processing capabilities. However, traditional electronic resonators typically only support a single eigenmode, making it difficult to construct singularities using the multimode coupling strategies commonly used in optical systems. This results in the system being extremely sensitive to manufacturing errors and environmental fluctuations (such as temperature changes). For example, studies have shown that a change in ambient temperature of only 0.05°C can trigger phase transitions in multi-resonator systems, severely limiting the practical application of singularity sensing technology.

[0003] To address the vulnerability of singularities, researchers have proposed various solutions: for example, enhancing the signal-to-noise ratio through nonlinear effects, but this may introduce bistable or multi-valued output problems; or expanding the singularity parameter space using the concept of a "singularity plane" to improve robustness, but its implementation in electronic platforms faces challenges. Recent attempts have focused on constructing Jordan-type Hamiltonians using capacitively coupled dual resonators, but the lack of degenerate eigenmodes still makes it difficult to avoid the impact of environmental disturbances on the reference resonator frequency. These problems indicate that traditional solutions relying on physically coupled dual resonators have fundamental bottlenecks and urgently require new methods to overcome them. Therefore, this invention proposes a highly robust singularity implementation method in a single electronic resonator to address the problems existing in the prior art. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to propose a method for realizing highly robust singularities in a single electronic resonator. This method achieves significant performance breakthroughs by combining a single resonator architecture with a four-wave mixing mechanism. Compared to traditional multi-resonator schemes, it avoids physical mismatch problems by utilizing synthetic mode coupling, thereby improving detection sensitivity while maintaining system stability. Furthermore, it anchors system eigenvalues ​​through externally injected signals and enhances the signal-to-noise ratio of amplitude modulation by utilizing stochastic resonance effects.

[0005] To achieve the objectives of this invention, the invention is implemented through the following technical solution: a method for realizing highly robust singularities in a single electronic resonator, comprising the following steps:

[0006] Step 1: Parity-time antisymmetry construction. A stable external signal is injected into a single resonator, and a synthesized mode is generated using four-wave mixing to form parity-time antisymmetry with the intrinsic mode.

[0007] Step 2: Establish the system Hamiltonian and fix the system eigenvalues ​​at the stable injection frequency ω. AWG The above only leaves ω1 as the sensing degree of freedom, providing a highly robust architecture for the generation of singularities in electronic resonators;

[0008] Step 3: Sensor measurement verification, consisting of an electronic resonator, an arbitrary signal generator, and a coupling resistor R. c An electronic resonator is composed of a negative resistor -R, a capacitor C, and an inductor L, forming an electronic circuit.

[0009] Step 4: Nonlinear bifurcation model, based on nonlinear model P NL (t) Analyze bifurcation behavior;

[0010] Step 5: Noise and robustness assessment. Verify the system's noise characteristics and robustness through Allan bias analysis.

[0011] A further improvement is made in the following: the four-wave mixing generation formula in step one is:

[0012] ω2=2ω AWG -ω1.

[0013] A further improvement is made in that the system characteristic value measurement formula in step two is:

[0014]

[0015] After removing H0, it simplifies to:

[0016]

[0017] in,

[0018] A further improvement is that: in step three, any signal generator is connected to R... c Provide stable external injection, the measurement point P A and P B The voltage spectrum is used to verify the spectral response of the parity-time antisymmetry broken phase and the symmetric phase. The signal parameters of the arbitrary signal generator are amplitude 0.5V and frequency 8.6~9.9kHz.

[0019] A further improvement lies in the following: the formula for analyzing bifurcation behavior in step four is:

[0020]

[0021] Where v(t) is the linear solution of the Hamiltonian, χ (k) For the equivalent nonlinear coefficient, k∈Z is the nonlinear order caused by four-wave mixing.

[0022] A further improvement is made in the following: the formula for sensitivity S in step four is:

[0023]

[0024] Where δ represents frequency splitting, ε represents the frequency splitting from ω. AMG The perturbation, bifurcation of singularities and ε 1 / 2 Proportional.

[0025] The further improvement lies in the fact that the noise characteristics in step five are mainly white noise on a short time scale, and approach quantized noise on a long time scale.

[0026] The beneficial effects of this invention are as follows: This invention achieves a significant performance breakthrough by combining a single resonator architecture with a four-wave mixing mechanism. Compared with the traditional multi-resonator scheme, it avoids the physical mismatch problem by using synthetic mode coupling, improves detection sensitivity while maintaining system stability, anchors system eigenvalues ​​by injecting external signals, and improves the signal-to-noise ratio of amplitude modulation by using random resonance effect. Attached Figure Description

[0027] Figure 1 This is a flowchart of the steps of the present invention;

[0028] Figure 2 This is a schematic diagram of the experimental verification system of the present invention;

[0029] Figure 3 The diagram shows the experimental phenomena of this invention.

[0030] Figure 4 This is a diagram showing the stable effect of the present invention. Detailed Implementation

[0031] To enhance understanding of the present invention, the present invention will be further described in detail below with reference to embodiments. These embodiments are only used to explain the present invention and do not constitute a limitation on the scope of protection of the present invention.

[0032] An electronic resonator is a frequency-selective device based on the principle of circuit oscillation. Its core function is to generate a significant signal response near a specific frequency. Commonly used resonators are quartz crystal resonators and ceramic resonators. They generate frequency, are stable, and have good anti-interference performance, making them widely used in various electronic products. Quartz crystal resonators have higher frequency accuracy than ceramic resonators, but they are also more expensive. Resonators primarily function for frequency control; all electronic products involving frequency transmission and reception require resonators. Resonators can be categorized by their external form factor into through-hole and surface-mount types.

[0033] Based on this, according to Figure 1 , Figure 2 , Figure 3 , Figure 4 As shown, this embodiment provides a method for achieving highly robust singularities in a single electronic resonator, including the following steps:

[0034] Step 1: Parity-time antisymmetry construction. A stable external signal is injected into a single resonator, and a synthesized mode is generated using four-wave mixing to form parity-time antisymmetry with the intrinsic mode.

[0035] The formula for generating four-wave mixing is:

[0036] ω2=2ω AWG -ω1;

[0037] By replacing physical multiresonator coupling with synthetic artificial modes, the mismatch problem of traditional architecture is avoided, laying the foundation for robust generation of singularities. At the same time, frequency locking improves the system's anti-interference capability.

[0038] Step 2: Establish the system Hamiltonian and fix the system eigenvalues ​​at the stable injection frequency ω. AWG By leaving only ω1 as the sensing degree of freedom, a robust architecture is provided for the generation of singularities in the electronic resonator. A non-Hermitian Hamiltonian model containing modes ω1 and ω2 is established, and the system eigenvalues ​​are anchored to ω. AWG Only ω1 is retained as the sensing degree of freedom, eliminating the influence of environmental disturbances on the reference frequency in the multi-resonator, and providing a theoretical framework for the stable existence of singularities.

[0039] The formula for measuring system eigenvalues ​​is:

[0040]

[0041] After removing P0, it simplifies to:

[0042]

[0043] in,

[0044] Step 3: Sensor measurement verification, consisting of an electronic resonator, an arbitrary signal generator, and a coupling resistor R. c An electronic resonator is composed of a negative resistor -R, a capacitor C, and an inductor L, forming an electronic circuit.

[0045] Arbitrary signal generator via R c Provides stable external injection, measuring probe P A and P B The voltage spectrum was used to verify the spectral response of the parity-time antisymmetry broken phase and the symmetric phase. The arbitrary signal generator had signal parameters of amplitude 0.5V and frequency 9.2kHz. More than 40 singular bifurcations were observed in the experiment, verifying the spectral response of the parity-time antisymmetry broken phase and the symmetric phase. The chiral spectral characteristics near the singular points were captured for the first time, providing experimental evidence for nonlinear dynamics.

[0046] Step 4: Nonlinear bifurcation model, based on nonlinear model P NL (t) Analysis of bifurcation behavior, combined with stochastic resonance effect, improves the signal-to-noise ratio of 0.2% amplitude modulation by 6dB, breaking through the linear sensitivity limit of traditional sensors;

[0047] The formula for analyzing bifurcation behavior is:

[0048]

[0049] Where v(t) is the linear solution of the Hamiltonian, χ (k) For the equivalent nonlinear coefficient, k∈Z is the nonlinear order caused by the four-wave mixing effect.

[0050] The sensitivity formula is:

[0051]

[0052] Where δ represents frequency splitting, ε represents the frequency splitting from ω. AMG The perturbation, bifurcation of singularities and ε 1 / 2 Proportional.

[0053] Step 5: Noise and Robustness Assessment. The noise characteristics and robustness of the system are verified through Allan bias analysis. The noise characteristics are mainly white noise on a short time scale, while on a long time scale, the noise approaches quantized noise. The single resonator transforms thermal disturbances into deterministic chaotic dynamics and constrains noise diffusion through nonlinear phase space trajectory. Compared with multi-resonator systems, this reduces environmental sensitivity, improves Allan variance stability, and meets the industrial-grade requirements of high-precision micro-nano sensing.

[0054] This method for achieving highly robust singularities in a single electronic resonator involves injecting a stable frequency signal into the resonator, generating a synthesized mode using a four-wave mixing effect, and constructing parity-time antisymmetry with the intrinsic mode ω1. A non-Hermi Hamiltonian model is then established to anchor the system's eigenvalues ​​to ω. AMG This makes ω1 an independent degree of freedom for sensing; experimentally, using a negative resistance-LC resonant circuit and a signal generator with an amplitude of 0.5V and a frequency of 8.6–9.9kHz, more than 40 EP bifurcations and chiral spectral characteristics were verified; based on a nonlinear model, the sensitivity S∝ε was achieved. 1 / 2 The bifurcation response, combined with stochastic resonance, improves the signal-to-noise ratio of 0.2% amplitude modulation by 6 dB. Allan bias analysis shows that the system transforms thermal disturbances into deterministic chaos, exhibiting white noise and quantization noise characteristics in the short and long time paths, respectively, significantly improving environmental robustness and overcoming the mismatch bottleneck of traditional multi-resonator EP.

[0055] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for achieving highly robust singularities in a single electronic resonator, comprising the following steps: Step 1: Parity-time antisymmetry construction. A stable external signal is injected into a single resonator, and a synthesized mode is generated using four-wave mixing to form parity-time antisymmetry with the intrinsic mode. Step 2: Establish the system Hamiltonian and fix the system eigenvalues ​​at a stable injection frequency. Above, only the inherent frequency remains. As a sensing degree of freedom, it provides a highly robust architecture for the generation of singularities in electronic resonators; The formula for generating four-wave mixing is: ; in, For the synthesis frequency, For injection frequency, It is the natural frequency; Step 3: Sensing measurement verification. An electronic circuit consisting of an electronic resonator, an arbitrary signal generator, and a coupling resistor Rc is used. The electronic resonator comprises a negative resistor -R, a capacitor C, and an inductor L; the arbitrary signal generator is connected via... R c Provides stable external injection, measurement probe P A and P B The voltage spectrum was used to verify the spectral response of the parity-time antisymmetry broken phase and the symmetric phase. The signal parameters of the arbitrary signal generator were amplitude 0.5V and frequency 8.6~9.9 kHz. Step 4: Nonlinear bifurcation model, based on the nonlinear model Analyze bifurcation behavior; Step 5: Noise and robustness assessment. Verify the system's noise characteristics and robustness through Allan bias analysis.

2. The method for realizing a highly robust singularity in a single electronic resonator according to claim 1, characterized in that: The system characteristic value measurement formula in step two is: Remove Later simplified to: in, .

3. The method for realizing a highly robust singularity in a single electronic resonator according to claim 1, characterized in that: The formula for analyzing bifurcation behavior in step four is as follows: in, It is a linear solution of the Hamiltonian. The equivalent nonlinear coefficients are t, representing the current time, and τ, representing the integration variable, representing the past time. Z represents the nonlinear order caused by four-wave mixing, and Z is an integer.

4. The method for realizing a highly robust singularity in a single electronic resonator according to claim 1, characterized in that: Sensitivity in step four S The formula is: ,in The perturbation, bifurcation of singularities and Proportional.

5. The method for realizing highly robust singularities in a single electronic resonator according to claim 1, characterized in that: The noise characteristics in step five are predominantly white noise on short time scales, and approach quantized noise on long time scales.

6. The method for realizing a highly robust singularity in a single electronic resonator according to claim 1, characterized in that: In step five, the single resonator transforms the thermal disturbance into deterministic chaotic dynamics.

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