Method and apparatus for characterizing resonator capacitance dielectric charge accumulation effects

Abstract

The application provides a resonator capacitance medium charge accumulation effect characterization method and device, comprising obtaining a regular, stable frequency signal and angle signal output in a stable angular velocity self-precession state of a resonator mode shape; Fourier fitting is performed on the frequency signal and the change of the angle signal every fixed time to obtain a fitting waveform corresponding to the fixed time period; the highest frequency point and the lowest frequency point in the fitting waveform of each fixed time period are obtained to determine the frequency difference between the highest frequency point and the lowest frequency point in each fixed time period; the characterization of the stiffness change in the resonator is completed based on the change relationship between the frequency difference and the applied stiffness in the resonator dynamics model; and the relationship between the equivalent bias voltage generated by the charge accumulation and the equivalent electrostatic negative stiffness generated by the charge accumulation is obtained according to the negative stiffness effect. The method can accurately characterize the change characteristics of the charge accumulation in the charging and discharging process of the capacitance medium.

Description

Technical Field

[0001] This invention relates to the field of resonator technology, and in particular to a method and apparatus for characterizing the dielectric charge accumulation effect of resonator capacitors. Background Technology

[0002] As a core component of many high-performance sensors, resonators are widely used in fields such as inertial guidance of ammunition, attitude measurement of mechanical and electronic products, and acceleration sensing. Most resonators rely on capacitive structures to achieve electrostatic actuation and detection. Under a strong electric field, the dielectric layer near the electrodes traps charge, causing charge accumulation within the dielectric. This accumulated charge alters the internal electric field distribution of the device, causing output drift and significantly reducing the long-term stability of high-precision devices. With increasingly stringent performance requirements for resonators, the charge accumulation effect has gradually become a crucial factor affecting resonator performance improvement and long-term stability.

[0003] Currently, some studies have been conducted on charge accumulation in relatively simple capacitor devices. Furthermore, a characterization method based on resonators has been proposed, involving applying an external voltage and measuring the equivalent bias voltage generated by charge accumulation. However, this approach requires periodic measurements and calculations, resulting in disadvantages such as long operation time and cumbersome procedures. Summary of the Invention

[0004] To address the technical problems existing in the prior art, this invention proposes a method and apparatus for characterizing the dielectric charge accumulation effect of resonator capacitors.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] On one hand, the present invention provides a method for characterizing the charge accumulation effect of a resonator capacitor dielectric, comprising:

[0007] Obtain the regularity, stability, frequency signal, and angle signal output by the resonator mode under the state of stable angular velocity precession;

[0008] The frequency signal obtained is subjected to Fourier fitting at fixed time intervals to observe the change of the angle signal, and the fitted waveform for the corresponding fixed time interval is obtained.

[0009] Obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point.

[0010] The stiffness variation in the resonator is characterized based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model.

[0011] Based on the negative stiffness effect, the relationship between the equivalent bias voltage generated by charge accumulation and the generated equivalent electrostatic negative stiffness is obtained, thus completing the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

[0012] On the other hand, the present invention provides a device for characterizing the dielectric charge accumulation effect of a resonator capacitor, comprising:

[0013] The first module is used to obtain the regularity, stable frequency signal and angle signal output by the resonator mode under the state of self-precession at a stable angular velocity;

[0014] The second module is used to perform Fourier fitting on the changes of the frequency signal with the angle signal at fixed intervals to obtain the fitted waveform for the corresponding fixed time period.

[0015] The third module is used to obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point.

[0016] The fourth module is used to characterize the stiffness variation in the resonator based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model.

[0017] The fifth module is used to obtain the relationship between the equivalent bias voltage generated by charge accumulation and the equivalent electrostatic negative stiffness generated based on the negative stiffness effect. This completes the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

[0018] On the other hand, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0019] Obtain the regularity, stability, frequency signal, and angle signal output by the resonator mode under the state of stable angular velocity precession;

[0020] The frequency signal obtained is subjected to Fourier fitting at fixed time intervals to observe the change of the angle signal, and the fitted waveform for the corresponding fixed time interval is obtained.

[0021] Obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point.

[0022] The stiffness variation in the resonator is characterized based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model.

[0023] Based on the negative stiffness effect, the relationship between the equivalent bias voltage generated by charge accumulation and the generated equivalent electrostatic negative stiffness is obtained, thus completing the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

[0024] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the following steps:

[0025] Obtain the regularity, stability, frequency signal, and angle signal output by the resonator mode under the state of stable angular velocity precession;

[0026] The frequency signal obtained is subjected to Fourier fitting at fixed time intervals to observe the change of the angle signal, and the fitted waveform for the corresponding fixed time interval is obtained.

[0027] Obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point.

[0028] The stiffness variation in the resonator is characterized based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model.

[0029] Based on the negative stiffness effect, the relationship between the equivalent bias voltage generated by charge accumulation and the generated equivalent electrostatic negative stiffness is obtained, thus completing the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

[0030] Compared with the prior art, the technical effects of the present invention are as follows:

[0031] This invention utilizes the relationship between resonator frequency difference, high-frequency axis angle, and charge accumulation in capacitor dielectric to characterize the charge accumulation process through a self-precession test method. This method simplifies the testing process, allows for real-time data measurement, and, based on the frequency difference change detected by fitting, can more accurately characterize the changes in charge accumulation during the charging and discharging of capacitor dielectric. It overcomes the problems of traditional voltage testing methods, such as cumbersome testing, long testing time, and measurement data error interference caused by the need to introduce external bias voltage.

[0032] This invention innovatively utilizes mode precession to accurately identify subtle perturbations in the electrostatic field of a resonator. By exploiting the micro-perturbations caused by charge accumulation in the electrostatic field, it achieves high-precision characterization of charge accumulation in the resonator, thus solving the problem of difficulty in characterizing and measuring the charge accumulation effect in resonators. This is of great significance for further improving resonator performance. Compared with traditional methods for characterizing charge accumulation in resonant devices, this method has a simpler testing procedure; moreover, because it can measure and characterize subtle perturbations in the electrostatic field in real time, the testing efficiency is higher; and the frequency difference is calculated through function fitting, resulting in more accurate test values. Theoretically, it is applicable to various capacitor-driven resonant devices, possessing the advantage of wide adaptability. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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 the structures shown in these drawings without creative effort.

[0034] Figure 1 This is a flowchart of an embodiment;

[0035] Figure 2 This is a schematic diagram of the resonator capacitor structure and charge accumulation location in one embodiment;

[0036] Figure 3 This is a schematic diagram of the high-frequency mode shape and high-frequency axis of the resonator in one embodiment;

[0037] Figure 4 This is a fitting result diagram of the mode shape self-precession in one embodiment, where (a) is the frequency-angle fitting result diagram of short-time sampling when the mode shape of the resonator is in normal self-precession, and (b) is the frequency-angle fitting result diagram of short-time sampling when the resonator is experiencing charge accumulation.

[0038] Figure 5 This is a fitting result diagram of the resonator frequency difference changing with time during the charge accumulation process in one embodiment. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0040] In one embodiment of the present invention, a method for characterizing the charge accumulation effect of a resonator capacitor dielectric is provided, comprising:

[0041] Obtain the regularity, stability, frequency signal, and angle signal output by the resonator mode under the state of stable angular velocity precession;

[0042] The frequency signal obtained is subjected to Fourier fitting at fixed time intervals to observe the change of the angle signal, and the fitted waveform for the corresponding fixed time interval is obtained.

[0043] Obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point.

[0044] The stiffness variation in the resonator is characterized based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model.

[0045] Based on the negative stiffness effect, the relationship between the equivalent bias voltage generated by charge accumulation and the generated equivalent electrostatic negative stiffness is obtained, thus completing the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

[0046] The obtained frequency signal is subjected to Fourier fitting as it changes with the angle signal, and the fitting equation is as follows:

[0047] f(ω)=a0+a1cos(cx)+b1sin(cx)+a2cos(2cx)+b2sin(2cx)

[0048] Let the measured angle signal be the dependent variable x, ω be the frequency signal, and a0, a1, a2, b1, b2, and c be the set fitting parameters.

[0049] The highest and lowest frequency points within a fixed time period are denoted as ω. max ω min The frequency difference Δ between the highest and lowest frequency points within a fixed time period is expressed as:

[0050] Δ=ω max -ω min

[0051] The relationship between the frequency difference Δ, the high-frequency axis angle, and the applied stiffness in the resonator frequency splitting model is expressed as follows:

[0052]

[0053] Where Δ0 is the initial frequency difference of the resonator, ψ0 is the initial high-frequency angle of the resonator, and λ... k k is a coefficient related to the structure of the harmonic oscillator. jand θ j These represent the stiffness change and angle at the location where charge accumulation occurs, respectively; Δ is the final frequency difference of the resonator; and ψ1 is the final high-frequency axis angle of the resonator.

[0054] like Figure 1 The diagram shows the specific structure of the resonator capacitor section in one embodiment. When a bias voltage is applied to the resonator, the dielectric exposed between the electrodes will be under a strong electric field, and the charge will be captured and accumulated on the surface of the dielectric.

[0055] Charge accumulation can be characterized by the resulting electrostatic negative stiffness. For example, Figure 1 For the capacitor structure shown, let S be the area of ​​the charge accumulation part of the dielectric, d be the gap between the electrode and the resonant structure, Δd be the vibration displacement of the overlapping part of the resonator and the electrode unit, and ε be the vacuum permittivity.

[0056] When a charge accumulates on one of the electrodes in the resonator due to charging, the accumulated charge can be considered to generate an equivalent bias voltage V. i Equivalent bias voltage V i This results in a change in electrostatic stiffness. The equivalent bias voltage V generated at this time is due to charge accumulation. i The relationship between the generated equivalent electrostatic negative stiffness Δk and the static negative stiffness is expressed as:

[0057]

[0058] A resonator with stiffness error can be equivalently represented as an ideal ring resonator model with a spring structure, such as the capacitor structure of the resonator. Figure 2 As shown, this includes the upper plate 1 of the resonator capacitor structure, the lower plate 3 of the resonator capacitor structure, and the dielectric 2 present near the resonator capacitor structure. The azimuth angle of the equivalent electrostatic negative stiffness Δk is θ. A schematic diagram of the frequency splitting model is shown below. Figure 3 Let the maximum frequency of the ideal circular harmonic oscillator be ω. max Its operating reference frame is derived from the detection axis. An orthogonal coordinate system xoy is established with the sensing electrode of the detection axis as a reference and is defined as the ideal working axis. Here, the y-axis is the direction where the sensing electrode of the detection axis is located, and the x-axis is the ideal driving axis orthogonal to the y-axis.

[0059] Let the stiffness of the spring in which the stiffness is non-uniform be equivalent to k. j There are N items, and their positions are θ. j Non-uniform stiffness distribution will produce two vibration modes with different frequencies. The relationship between the azimuth angle ψ of the higher-frequency vibration mode and the following is:

[0060]

[0061] The two mode frequencies are ω1 and ω2, which are the maximum and minimum frequencies of the resonator. These two frequencies can be expressed as:

[0062]

[0063]

[0064] Where α is the ratio of radial amplitude to tangential amplitude, and S0 is the elastic potential energy of the resonator in the n=2 mode. For a resonator vibrating at high frequencies, the stiffness error is very small, and the resonant frequency after frequency fragmentation is not significantly different from the resonant frequency ω0 of the original ideal resonator. Therefore, it can be considered that:

[0065] ω1+ω2≈2ω0 (5 Simplify formulas (3)(4)(5) to obtain the difference between the frequency maxima and minima:

[0066]

[0067] Considering the actual initial frequency difference Δ0 and initial high-frequency axis angle ψ0 of the resonator, the relationship between the frequency difference Δ, the high-frequency axis angle, and the stiffness can be expressed as a vector relationship:

[0068]

[0069] This yields the stiffness change k. j At time, the relationship between frequency difference Δ and high-frequency axis angle ψ1 and stiffness is given, where Δ0 is the initial frequency difference of the resonator, ψ0 is the initial high-frequency angle of the resonator, and λ is the initial high-frequency angle of the resonator. k k is a coefficient related to the structure of the harmonic oscillator. j and θ j These represent the stiffness change and angle at the location where charge accumulation occurs, respectively; Δ is the final frequency difference of the resonator; and ψ1 is the final high-frequency axis angle of the resonator.

[0070] The equivalent bias voltage generated by charge accumulation (or dissipation) is generally considered to change exponentially with time. For example, when charge accumulates on n electrodes in a resonator, the equivalent bias voltage V generated by the charge accumulation... i The exponential model over time is expressed as:

[0071]

[0072] Where the equivalent bias voltage V i It is decomposed into n exponentially regular charge accumulation processes, and the maximum value A in each independent charge accumulation process is... n The time constant is τ n The elapsed time is t n .

[0073] From the relationship between frequency difference, high-frequency axis, electrostatic negative stiffness, and equivalent bias voltage, it can be concluded that the bias voltage will generate a corresponding electrostatic negative stiffness. At the same time, the change of electrostatic negative stiffness can be characterized by the change of frequency difference and high-frequency axis, so that the change trend of frequency difference and high-frequency axis with respect to the generated equivalent bias voltage can be obtained.

[0074] The method of this invention is used to characterize resonators that experience charge accumulation after charging. The mode shape precession is achieved by applying external conditions to cause the resonator mode shape to precess at a stable angular velocity, resulting in the output of regular and stable frequency and angle signals. The output signals are collected over a period of time, and the relationship between the resonator frequency and angle is obtained using Fourier transform. The difference between the highest and lowest values ​​of the fitted curve is used to calculate the resonator frequency difference over a short period and the high-frequency axis angle corresponding to the highest value. However, when charge accumulation occurs, the accumulated charge disturbs the electrostatic field in the original resonator, affecting the acquired and fitted resonance characteristics. Figure 4 As shown, Figure 4 Figures (a) and (b) show the frequency-angle fitting results of short-time sampling when the resonator mode is in normal self-precession and when charge accumulation occurs, respectively. It can be seen that the electrostatic field disturbance caused by charge accumulation will significantly affect the resonant characteristics of the device.

[0075] Based on equations (1), (7), and (8), a relationship model between the resonant characteristics, stiffness, and equivalent bias voltage of charge accumulation can be obtained. In this model, the magnitude of the equivalent bias voltage generated by charge accumulation at the electrodes of the resonator under specific frequency differences and high-frequency axis angles can be calculated, thus completing the description of the charge accumulation process occurring in the resonator. Using this model, a function fit is performed on the data points obtained after testing, and the goodness of fit R between the data and the obtained model is calculated. 2 A value greater than 0.96 indicates that the obtained frequency difference data can be well fitted by the frequency difference-voltage model, and the variation law of the frequency difference can characterize charge accumulation. For example... Figure 5 The figure shown is a fitting result of the resonator frequency difference changing with time during the dissipation of accumulated charge in one embodiment.

[0076] The above embodiments cleverly utilize the relationship between the resonator charge accumulation and the electrostatic field disturbance and the resonator resonance characteristics, and characterize the resonator charge accumulation by identifying the resonator resonance characteristics through mode precession.

[0077] In another embodiment, a device for characterizing the dielectric charge accumulation effect of a resonator capacitor is provided, comprising:

[0078] The first module is used to obtain the regularity, stable frequency signal and angle signal output by the resonator mode under the state of self-precession at a stable angular velocity;

[0079] The second module is used to perform Fourier fitting on the changes of the frequency signal with the angle signal at fixed intervals to obtain the fitted waveform for the corresponding fixed time period.

[0080] The third module is used to obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point.

[0081] The fourth module is used to characterize the stiffness variation in the resonator based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model.

[0082] The fifth module is used to obtain the relationship between the equivalent bias voltage generated by charge accumulation and the equivalent electrostatic negative stiffness generated based on the negative stiffness effect. This completes the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

[0083] The implementation methods of the above modules and the construction of the model can all adopt the methods described in any of the foregoing embodiments, and will not be repeated here.

[0084] On the other hand, the present invention provides a computer device including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the resonator capacitor dielectric charge accumulation effect characterization method provided in any of the above embodiments. The computer device may be a server. The computer device includes a processor, a memory, a network interface, and a database connected via a system bus. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores sample data. The network interface of the computer device is used for communication with external terminals via a network connection.

[0085] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the resonator capacitor dielectric charge accumulation effect characterization method provided in any of the above embodiments.

[0086] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0087] Matters not covered in this invention are common knowledge.

[0088] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0089] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0090] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for characterizing the charge accumulation effect in the dielectric of a resonator capacitor, characterized in that, include: Obtain the regularity, stability, frequency signal, and angle signal output by the resonator mode under the state of stable angular velocity precession; The frequency signal obtained is subjected to Fourier fitting at fixed time intervals to change with the angle signal, and the fitted waveform for the corresponding fixed time interval is obtained. Obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point. The stiffness variation in the resonator is characterized based on the relationship between the frequency difference, high-frequency axis angle, and applied stiffness in the resonator frequency splitting model. The relationship between the frequency difference, high-frequency axis angle, and applied stiffness in the resonator frequency splitting model is expressed as follows: Where Δ0 is the initial frequency difference of the resonator, ψ0 is the initial high-frequency axis angle of the resonator, and λ k k is a coefficient related to the structure of the harmonic oscillator. j and θ j These represent the change in stiffness and angle at the location where charge accumulation occurs, respectively. ψ1 is the final frequency difference of the resonator, and ψ2 is the final high-frequency axis angle of the resonator. Based on the negative stiffness effect, the relationship between the equivalent bias voltage generated by charge accumulation and the generated equivalent electrostatic negative stiffness is obtained. This completes the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle, and the equivalent bias voltage generated by charge accumulation. V i With the generated equivalent electrostatic negative stiffness The relationship between them is represented as: in S It is the area of ​​the charge accumulation region of the dielectric. d It is the gap between the electrode and the resonant structure. The vibration displacement of the overlapping portion of the harmonic oscillator and the electrode unit. ε It is the vacuum permittivity.

2. The method for characterizing the charge accumulation effect of the resonator capacitor dielectric according to claim 1, characterized in that, The obtained frequency signal is subjected to Fourier fitting as it changes with the angle signal, and the fitting equation is: Let the measured angle signal be the dependent variable. x , ω It is a frequency signal. a 0、 a 1. a 2. b 1. b 2. c These are all the fitted parameters that were set.

3. The method for characterizing the dielectric charge accumulation effect of a resonator capacitor according to claim 1 or 2, characterized in that, The highest and lowest frequency points within a fixed time period are denoted as: ω max , ω min The frequency difference between the highest and lowest frequency points within a fixed time period Represented as: 。 4. The method for characterizing the dielectric charge accumulation effect of a resonator capacitor according to claim 3, characterized in that, When the resonator n After charge accumulation occurs near each electrode, the equivalent bias voltage generated by the charge accumulation V i The exponential model over time is expressed as: The maximum value in each individual charge accumulation process A n The time constant is τ n After a period of time t n .

5. A device for characterizing the dielectric charge accumulation effect of a resonator capacitor, used to implement the method for characterizing the dielectric charge accumulation effect of a resonator capacitor as described in claim 1, characterized in that, include: The first module is used to obtain the regularity, stable frequency signal and angle signal output by the resonator mode under the state of self-precession of stable angular velocity; The second module is used to perform Fourier fitting on the changes of the frequency signal with the angle signal at fixed intervals to obtain the fitted waveform for the corresponding fixed time period. The third module is used to obtain the highest and lowest frequency points in the fitted waveforms for each fixed time period, determine the frequency difference between the highest and lowest frequency points within each fixed time period, and the high-frequency axis angle corresponding to the highest frequency point. The fourth module is used to characterize the stiffness variation in the resonator based on the relationship between the frequency difference, high-frequency axis angle and applied stiffness in the resonator frequency splitting model. The fifth module is used to obtain the relationship between the equivalent bias voltage generated by charge accumulation and the equivalent electrostatic negative stiffness generated based on the negative stiffness effect. This completes the characterization of capacitor charge accumulation based on resonator frequency difference and high-frequency axis angle.

6. The resonator capacitor dielectric charge accumulation effect characterization device according to claim 5, characterized in that, In the second module, Fourier fitting is performed on the obtained frequency signal as a function of the angle signal, and the fitting equation is: Let the measured angle signal be the dependent variable. x , ω It is a frequency signal. a 0、 a 1. a 2. b 1. b 2. c These are all the fitted parameters that were set.

7. The resonator capacitor dielectric charge accumulation effect characterization device according to claim 5, characterized in that, The third module records the highest and lowest frequency points within a fixed time period as follows: ω max , ω min , the highest point ω max The corresponding angle is represented by the high-frequency axis angle ψ, which is the frequency difference between the highest and lowest frequency points within a fixed time period. Represented as: 。

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