A method and system for frequency stabilization of a MEMS resonator based on high-order nonlinearity

Abstract

A frequency stabilization method and system of a MEMS resonator based on high-order nonlinearity, according to a calibrated excitation intensity threshold, a stable oscillation of the MEMS resonator based on high-order nonlinearity is generated through a closed loop; a phase control signal is applied to the MEMS resonator based on high-order nonlinearity to regulate the working point of the MEMS resonator based on high-order nonlinearity, so that the working point is at a peak point; under the excitation intensity threshold, the skeleton line of the MEMS resonator based on high-order nonlinearity shows decoupling of frequency to amplitude, so that the amplitude-frequency conversion is inhibited, and the frequency stability of the MEMS resonator based on high-order nonlinearity is improved; the amplitude-frequency dependence of the resonator is regulated, the amplitude-frequency decoupling is realized, and the system phase noise is reduced; a small volume, low power consumption and high precision frequency reference can be provided in electronic devices such as communication, radar and inertial navigation, the performance of the system is greatly improved, the working error is reduced, and the stable output of the MEMS resonator frequency is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of micro-electro-mechanical system, and particularly relates to a MEMS resonator frequency stabilization method and system based on high-order nonlinearity. BACKGROUND

[0002] With the maturity of semiconductor processing technology, MEMS resonators gradually become a research hotspot. The size reduction of MEMS resonators brings advantages such as small power consumption, low cost and high integration, which makes MEMS resonators gradually replace traditional quartz crystal oscillators and be widely applied to various occasions requiring precise timing and high-precision sensing.

[0003] The stability of the resonator output frequency is a decisive factor for the performance of resonant sensors and timing devices. As the size of the resonator decreases, the scale effect makes the MEMS resonator more prone to nonlinear effects. In the nonlinear state, the frequency of the MEMS resonator exhibits a nonlinear dependence on the amplitude, and the amplitude noise is converted into frequency noise through this nonlinear dependence, thereby degrading the stability of the frequency. In order to provide a stable frequency reference source, the MEMS resonator is usually operated in the linear phase, and the improvement of short-term frequency stability is usually achieved through structural optimization design. According to the Robin frequency stability formula, increasing the quality factor of the MEMS resonator can significantly improve the output frequency stability of the MEMS resonator. Based on this, researchers usually increase the quality factor of the MEMS resonator through the design of phononic crystals to reduce the anchor loss ([1] Hsu F-C, Hsu J-C, Huang T-C, et al. Design of lossless anchors for microacoustic-wave resonators utilizing phononic crystal strips [J]. Applied Physics Letters, 2011, 98(14); [2] Ghadimi AH, Fedorov S A, Engelsen N J, et al. Elastic strain engineering for ultralow mechanical dissipation [J]. Science, 2018, 360(6390): 764-+), through hole digging to reduce the thermoelastic loss ([3] Zega V, Frangi A, Guercilena A, et al. Analysis of Frequency Stability and Thermoelastic Effects for Slotted Tuning Fork MEMS Resonators [J]. Sensors (Basel), 2018, 18(7).) and other means to improve the quality factor of the MEMS resonator, and then realize the short-term frequency stability of the MEMS resonator; but the means of structural design is complex to operate, and in the implementation, it needs to design a large area of auxiliary structure, and it cannot be compatible with all frequency band resonant devices, and the improvement effect is very limited. SUMMARY

[0004] In view of the defects in the prior art, the purpose of the present application is to provide a MEMS resonator frequency stabilization method and system based on high-order nonlinearity, which realizes amplitude-frequency decoupling, reduces system phase noise, and realizes stable output of the MEMS resonator frequency by regulating the amplitude-frequency dependence of the resonator, and can provide a small, low-power, high-precision frequency reference in electronic devices such as communication, radar, and inertial navigation, greatly improving the performance of the system and reducing the working error.

[0005] To achieve the above purpose, the present application adopts the following technical solutions:

[0006] A MEMS resonator frequency stabilization method based on high-order nonlinearity, comprising:

[0007] According to the calibrated excitation intensity threshold, the high-order nonlinear MEMS resonator generates self-excitation oscillation through a closed loop, thereby outputting a frequency reference signal; a phase control signal is applied to the high-order nonlinear MEMS resonator to regulate the operating point of the high-order nonlinear MEMS resonator, so that it operates at the peak point; under the excitation intensity threshold, the skeleton line of the high-order nonlinear MEMS resonator shows decoupling of frequency to amplitude, thereby realizing suppression of amplitude-frequency conversion and improving the frequency stability of the high-order nonlinear MEMS resonator.

[0008] A MEMS resonator frequency stabilization method based on high-order nonlinearity, comprising the following steps:

[0009] Step 1: power on the high-order nonlinear MEMS resonator, initialize the drive signal parameters of the operating mode of the high-order nonlinear MEMS resonator, the drive signal parameters include but are not limited to the drive amplitude and drive frequency of the operating mode;

[0010] Step 2: according to the drive signal parameters of the operating mode in step 1, generate the corresponding harmonic drive signal, apply the drive signal to the body of the high-order nonlinear MEMS resonator through the excitation electrode, and excite the response of the high-order nonlinear MEMS resonator;

[0011] Step 3: collect the response signal of step 2, demodulate the response phase, and calculate the difference between the phase set value and the measured value;

[0012] Step 4: according to the phase difference value in step 3, adjust the frequency size of the operating mode excitation signal to maintain stable oscillation of the operating mode;

[0013] Step 5: regulate the phase set value of the oscillation loop in step 3 until the oscillation amplitude of the operating mode reaches the maximum, realize amplitude-frequency decoupling, and thereby improve the frequency stability of the high-order nonlinear MEMS resonator.

[0014] The parameter of the driving signal in step 1 is obtained through calibration, and the skeleton line of the MEMS resonator with high-order nonlinearity shows decoupling of frequency and amplitude under the parameter.

[0015] In step 3, the response signal of the MEMS resonator with high-order nonlinearity is input into the MEMS closed loop, the phase difference between the measured value and the set value is judged by the phase discriminator of the MEMS closed loop, the control algorithm stored in the internal oscillation system is maintained to adjust the excitation frequency in real time, so that the MEMS resonator with high-order nonlinearity realizes stable oscillation; the control algorithm is a PID algorithm, a predictive control algorithm, an adaptive control algorithm or a fuzzy control algorithm, and the control amount is calculated according to the phase difference; the excitation frequency adjustment is realized by a voltage controlled oscillator VCO or a digital controlled oscillator NCO, the voltage controlled oscillator VCO or the digital controlled oscillator NCO outputs the corresponding frequency according to the control amount calculated by the control algorithm, and maintains the corresponding output frequency value unchanged before the next control amount change; the frequency of the excitation signal is adjusted according to the output frequency and output to the excitation end of the MEMS resonator with high-order nonlinearity; the above regulation and control process is repeated until the phase difference is zero.

[0016] In step 5, the host computer system realizes the regulation and control of the phase set value of the MEMS closed loop, and makes the MEMS resonator with high-order nonlinearity work at the maximum amplitude by the control algorithm, realizes the decoupling of frequency and amplitude, and realizes the stable output of frequency by high-order nonlinearity; the control algorithm is a PID algorithm, and the PID algorithm calculates the phase regulation value required to compensate the amplitude difference according to the difference between the amplitude of the MEMS resonator with high-order nonlinearity demodulated and the maximum amplitude calibrated in advance, so as to change the phase set value in step 3, make the working phase point of the MEMS resonator move and finally move to the phase point corresponding to the maximum amplitude; at the maximum amplitude, the skeleton line of the MEMS resonator with high-order nonlinearity shows decoupling of frequency and amplitude, that is, the derivative of frequency to amplitude is zero, so as to suppress the conversion of amplitude noise to frequency fluctuation.

[0017] The stable system of the frequency stabilization method based on the MEMS resonator with high-order nonlinearity comprises:

[0018] The host computer system is used for initializing the working parameters of the MEMS resonator with high-order nonlinearity, and reading the amplitude and frequency of the MEMS resonator with high-order nonlinearity in real time, judging the working state of the resonator according to the oscillation amplitude, and outputting a phase control signal;

[0019] Oscillation maintaining system: connected with the host computer system, through the frequency control module, real-time demodulation of the oscillation phase value, according to the difference between the oscillation phase and the set phase, using the control algorithm to change the excitation frequency, realize the phase-locked stable closed loop oscillation, and connected with the host computer system, for executing the phase control signal output by the host computer system;

[0020] MEMS resonator system: connected with the host computer system and the oscillation maintaining system, for generating stable high-order oscillation, outputting frequency reference.

[0021] The host computer system comprises:

[0022] Oscillation reading module: connected with the oscillation maintaining system, for real-time reading of the oscillation amplitude, frequency and other signals of the high-order nonlinear MEMS resonator;

[0023] Phase modulation module: receiving the vibration amplitude signal collected by the oscillation reading module, for executing the phase modulation program, judging whether the oscillation amplitude reaches the maximum value, and generating the phase control signal;

[0024] Control output module: connected with the oscillation maintaining system, for transmitting the phase control signal generated by the phase modulation module to the oscillation maintaining system after digital-to-analog conversion.

[0025] The oscillation maintaining system comprises:

[0026] Phase control module: connected with the control output module of the host computer system, for executing the phase control signal of the host computer system, and real-time adjusting the set phase value;

[0027] Frequency control module: connected with the driving electrode of the MEMS resonator system, for real-time demodulation of the oscillation phase value, adjusting the excitation signal frequency according to the difference between the oscillation phase and the set phase value, and applying the adjusted excitation signal to the excitation electrode of the MEMS resonator system, so as to realize the phase-locked stable oscillation;

[0028] Amplitude control module: connected with the host computer system and the MEMS resonator system, for receiving the excitation parameter initialized by the host computer system, and adjusting the amplitude of the excitation signal output by the oscillation maintaining system.

[0029] The excitation signal form of the MEMS resonator is direct harmonic excitation signal, degenerate parameter excitation signal or non-degenerate parameter excitation signal.

[0030] The MEMS resonator system comprises: a body of the MEMS resonator supported by an anchor point, for generating vibration under the excitation signal; an excitation electrode and a detection electrode for exciting and detecting the device; an anchor point electrode for applying DC bias to the body of the MEMS resonator.

[0031] The body of the MEMS resonator is an arch structure, the inherent nonlinear stiffness of the MEMS resonator is adjusted through the arch structure, so that the MEMS resonator shows high-order nonlinearity.

[0032] The excitation detection form of the MEMS resonator is capacitive, piezoelectric, optical or electromagnetic.

[0033] Compared with the prior art, the application has the beneficial effects that:

[0034] The step 2 of the application drives the MEMS resonator by using the pre-calibrated threshold excitation strength, can make the MEMS resonator generate large amplitude resonance, and has the characteristics of improving the signal-to-noise ratio of the MEMS resonator.

[0035] The host computer system of the application uses a control algorithm to maintain the working state of the MEMS resonator in a critical state of frequency and amplitude decoupling, can increase the signal-to-noise ratio of the MEMS resonator output signal while suppressing the conversion of amplitude noise to frequency fluctuation, has the characteristics of strong universality and simple operation.

[0036] The oscillation maintenance system of the application uses a phase-locked scheme to realize closed-loop oscillation of the MEMS resonator, can make the MEMS resonator quickly start oscillation and can flexibly control the working state of the MEMS resonator by modifying the phase setting value, has the characteristics of rapid start and small circuit conduction noise.

[0037] The MEMS resonator system of the application uses an arch-shaped MEMS resonator body, can make the MEMS resonator show high-order nonlinear response without external electric heating, electrostatic nonlinear tuning means, has the characteristics of simple operation and strong robustness.

[0038] In summary, the application provides a MEMS resonator frequency stabilization method and system based on high-order nonlinearity, which utilizes high-order nonlinearity to realize the decoupling of the MEMS resonator output frequency from the amplitude, thereby realizing the suppression of amplitude-frequency conversion and improving the stability of the MEMS resonator output frequency. On the one hand, the MEMS resonator is operated at a threshold excitation strength generated by high-order nonlinear response, which suppresses the conversion of amplitude noise to frequency fluctuation while improving the signal-to-noise ratio of the MEMS resonator, significantly enhances the output frequency stability of the MEMS resonator, and avoids the device processing challenges of the complex structure design of the traditional frequency stability improvement scheme. On the other hand, the body of the MEMS resonator of the application adopts an arch structure, so that the MEMS resonator can exhibit high-order nonlinear response without the need for external nonlinear tuning, which simplifies the peripheral circuit and increases the robustness of the system. The application provides a new idea for the design of high-performance MEMS resonators, which can be easily integrated into various sensing and timing systems, and has very high theoretical and engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The application embodiment MEMS resonator system schematic diagram.

[0040] Figure 2 The application embodiment MEMS resonator frequency stabilization method based on high-order nonlinearity flow chart.

[0041] Figure 3 The application embodiment MEMS resonator frequency stabilization system based on high-order nonlinearity schematic diagram.

[0042] Figure 4 The application embodiment test result diagram; wherein (a) is a high-order nonlinear response diagram and a non-monotonic skeleton line in a high-order nonlinear state; (b) is a phase noise compression schematic diagram of degenerate parameter resonance; (c) is an Allan variance after amplitude-frequency decoupling.

[0043] In the figure: 1-1. Double-end fixed support tuning fork arch-shaped MEMS resonator; 1-2. Resonator first excited electrode; 1-3. Resonator first detected electrode; 2-1. First fixed support anchor point; 2-2. First metal electrode layer; 2-3. Second fixed support anchor point; 2-4. Second metal electrode layer; 3-1. Resonator first excitation electrode plate; 3-2. Third metal electrode layer; 3-3. Resonator first detection electrode plate; 3-4. Fourth metal electrode layer. DETAILED DESCRIPTION

[0044] The application provides a MEMS resonator frequency stabilization method and system based on high-order nonlinearity, which comprises a MEMS resonator system, an oscillation maintenance system and an upper computer system; amplitude-frequency decoupling under large amplitude is realized through high-order nonlinearity, and the frequency stability of the MEMS resonator is comprehensively improved in combination with the improvement of the signal-to-noise ratio under the nonlinear state. The technical scheme of the application is specifically described below by taking a double-end fixed support tuning fork arched MEMS resonator as an example.

[0045] Referring to Figure 1 The MEMS resonator system in the embodiment comprises a double-end fixed support tuning fork arched MEMS resonator 1-1, the left and right ends of the double-end fixed support tuning fork arched MEMS resonator 1-1 are connected with a first fixed support anchor point 2-1 and a second fixed support anchor point 2-3, the double-end fixed support tuning fork arched MEMS resonator 1-1 is supported by the first fixed support anchor point 2-1 and the second fixed support anchor point 2-3 and is used for generating vibration under a driving signal; a first metal electrode layer 2-2 is sputtered on the first fixed support anchor point 2-1, and a second metal electrode layer 2-4 is sputtered on the second fixed support anchor point 2-3, which are used for grounding the MEMS resonator; the upper and lower sides of the double-end fixed support tuning fork arched MEMS resonator 1-1 are connected with a resonator first excited electrode 1-2 and a resonator first detected electrode 1-3; the resonator first excited electrode 1-2 is adjacent to a resonator first excitation electrode plate 3-1, a third metal electrode layer 3-2 is sputtered on the resonator first excitation electrode plate 3-1, and the resonator first excitation electrode plate 3-1 and the third metal electrode layer 3-2 provide excitation force for the resonator first excited electrode 1-2; the resonator first detected electrode 1-3 is adjacent to a resonator first detection electrode plate 3-3, a fourth metal electrode layer 3-4 is sputtered on the resonator first detection electrode plate 3-3, and the resonator first detection electrode 3-3 and the fourth metal electrode layer 3-4 constitute a detection capacitor with the resonator first detected electrode 1-3, which is used for detecting the movement of the double-end fixed support tuning fork arched MEMS resonator 1-1.

[0046] The arched MEMS resonator has inherent mechanical high-order nonlinearity through structural design, and the arched structure is excited by electrostatic force. The expression modes of other types of high-order nonlinearity, resonator structures and excitation modes are slightly different, but the internal mechanism is consistent.

[0047] When the MEMS resonator system in the embodiment is excited by parameters, the kinetic equation thereof can be expressed as:

[0048]

[0049] wherein

[0050]

[0051] where τ is dimensionless time, Q is the quality factor, λ is dimensionless parameter pump, ω is dimensionless driving frequency, u is dimensionless transverse displacement, κ i (i = 2, 3, 4, 5) is the i-th order structural nonlinear stiffness, η i (i = 2, 3, 4, 5) is the i-th order nonlinear damping, x is the coordinate position along the beam length, φ1(x) is the characteristic function of the first order modal shape, d0 is the inter-plate spacing, is the arch height of the arch beam, represents the mass of the MEMS resonator, ω1 is the resonant angular frequency of the MEMS resonator, is the length of the MEMS resonator, is the aspect ratio parameter of the MEMS resonator; by the multi-scale method, the dependence of the resonator peak frequency on the amplitude (skeleton line) is:

[0052]

[0053] wherein, is the effective cubic nonlinearity, is the effective quintic nonlinearity, a is the dimensionless amplitude; as can be seen from formulas (2)-(6), the frequency of the MEMS resonator working at the peak point of the amplitude-frequency response shows a nonlinear dependence on the oscillation amplitude, the values of the quadratic and quartic nonlinearities can be actively controlled by increasing the arch height of the arch structure, so as to realize the control of the amplitude-frequency dependence curve (skeleton line), so that the MEMS resonator shows a non-monotonic skeleton line. Among them, at a small amplitude, the quadratic nonlinearity dominates the response, and the MEMS resonator shows a spring softening characteristic; at a large amplitude, the quartic nonlinearity dominates the response, and the MEMS resonator shows a spring hardening characteristic. At the extreme point of the skeleton line, the amplitude and frequency are decoupled. Based on this feature, the embodiment discloses a MEMS resonator frequency stabilization method and system based on high-order nonlinearity. When the MEMS resonator works at the extreme point of the calibrated skeleton line, the amplitude-frequency decoupling characteristic at the extreme point is combined with the high signal-to-noise ratio of the nonlinear state to realize the suppression of frequency fluctuation, wherein the signal-to-noise ratio is the ratio of the response amplitude to the total noise of the system, and the noise value is a fixed value independent of the working state.

[0054] Referring to Figure 2 , a MEMS resonator frequency stabilization method based on high-order nonlinearity, comprising the following steps:

[0055] Step 1, the high-order nonlinear MEMS resonator is powered on and works, and the drive signal parameters of the working mode of the high-order nonlinear MEMS resonator are initialized by the control output module of the upper computer system, including the drive amplitude and the drive frequency of the working mode;

[0056] The driving signal parameters are obtained through calibration, and the skeleton line of the MEMS resonator shows frequency-amplitude decoupling under the parameters;

[0057] Step 2, the oscillation maintenance system generates a corresponding driving signal according to the driving parameters of the working mode in step 1, and applies the driving signal to the body of the high-order nonlinear MEMS resonator through the excitation electrode plate to excite the response of the high-order nonlinear MEMS resonator;

[0058] Step 3, the oscillation maintenance system collects the response signal of step 2, demodulates the response phase, and calculates the difference between the phase set value and the measured value;

[0059] The response signal of the high-order nonlinear MEMS resonator is input into the MEMS closed loop, and the phase difference between the measured value and the set value is judged by the phase detector built in the frequency control module of the MEMS closed loop. Through the control algorithm built in the frequency control module, the excitation frequency is adjusted in real time, so as to realize the stable oscillation of the high-order nonlinear MEMS resonator; the control algorithm is a PID algorithm, a predictive control algorithm, an adaptive control algorithm or a fuzzy control algorithm, and the control algorithm calculates the control amount according to the phase difference; the excitation frequency adjustment is realized through a voltage controlled oscillator VCO or a digital controlled oscillator NCO, the VCO or the NCO outputs the corresponding frequency according to the control amount calculated by the control algorithm, and maintains the corresponding output frequency value unchanged before the next control amount change; the frequency of the excitation signal is adjusted according to the output frequency and output to the excitation end of the high-order nonlinear MEMS resonator; the above regulation and control process is repeated until the phase difference is zero;

[0060] Step 4, the oscillation maintenance system adjusts the frequency of the working mode excitation signal according to the phase difference in step 3 to maintain the stable oscillation of the working mode;

[0061] Step 5, the host computer system adjusts the phase set value of the oscillation loop in step 3 until the oscillation amplitude of the working mode reaches the maximum, realizes amplitude-frequency decoupling, and improves the frequency stability of the high-order nonlinear MEMS resonator;

[0062] The host computer system realizes modulation of the phase setting value of the closed loop, a phase modulation module is built-in with a phase modulation program, and the processor judges whether the oscillation amplitude reaches the maximum value when executing the modulation program, and outputs a phase control signal through a control output module, so that the high-order nonlinear MEMS resonator works at the maximum amplitude, realizes decoupling of the frequency and the amplitude, and thus realizes stable output of the frequency by using the high-order nonlinearity; the control algorithm is a PID algorithm, the PID algorithm calculates the phase control value required for compensating the amplitude difference according to the difference between the amplitude of the high-order nonlinear MEMS resonator obtained by demodulation and the maximum amplitude calibrated in advance, so as to change the phase setting value in step 3, so that the working phase point of the MEMS resonator moves and finally moves to the phase point corresponding to the maximum amplitude; at the maximum amplitude, the skeleton line of the high-order nonlinear MEMS resonator shows decoupling of the amplitude and the frequency, that is, the derivative of the frequency with respect to the amplitude is zero, so as to suppress the conversion of the amplitude noise to the frequency fluctuation.

[0063] Referring to Figure 3 The stable system of the high-order nonlinear MEMS resonator frequency stabilization method comprises a host computer system, an oscillation maintaining system and a MEMS resonator system; the host computer system is used for initializing the working parameters of the MEMS resonator, reading the amplitude and the frequency of the MEMS resonator in real time through an oscillation reading module, judging the working state of the MEMS resonator according to the oscillation amplitude, and outputting a phase control signal to the oscillation maintaining system; the oscillation maintaining system is connected with the host computer system, demodulates the oscillation phase value in real time through a phase control module, changes the excitation frequency by using a control algorithm according to the difference between the oscillation phase and the set phase, realizes phase-locked closed loop oscillation, accepts the phase control signal from the host computer, executes the phase setting value change instruction, and adjusts the phase working point of the resonator; the MEMS resonator system is connected with the host computer system and the oscillation maintaining system, and is used for generating stable high-order oscillation and outputting a frequency reference.

[0064] The host computer system in the embodiment comprises:

[0065] The oscillation reading module is connected with the oscillation maintaining system, and is used for reading the oscillation amplitude, the frequency and other signals of the high-order resonator in real time;

[0066] The phase modulation module receives the vibration amplitude signal collected by the oscillation reading module, executes a phase modulation program, judges whether the oscillation amplitude reaches the maximum value, and generates a phase control signal;

[0067] The control output module is connected with the oscillation maintaining system, and is used for transmitting the phase control signal generated by the phase modulation module to the oscillation maintaining system after digital-to-analog conversion.

[0068] The oscillation maintaining system in the embodiment comprises:

[0069] Phase control module: connected with the control output module of the host computer system, for executing the host computer system phase control signal, real-time adjustment of the set phase value;

[0070] Frequency control module: connected with the detection electrode of the MEMS resonator system, the built-in phase detector is used for real-time demodulation of the oscillation phase value, according to the difference between the oscillation phase and the phase set value, the frequency of the excitation signal output by the oscillation maintenance system is adjusted, so as to realize the phase-locked and stable oscillation;

[0071] Amplitude control module: connected with the host computer system and the MEMS resonator system, for receiving the host computer system initialization excitation parameters, and adjusting the amplitude of the excitation signal output by the oscillation maintenance system.

[0072] The excitation signal form of the MEMS resonator is direct harmonic excitation signal, degenerate parameter excitation signal or non-degenerate parameter excitation signal; the excitation detection form is capacitive, piezoelectric, optical or electromagnetic.

[0073] Figure 4 In the figure, (a) is the amplitude-frequency response graph of the MEMS resonator under the degenerate parameter excitation of the embodiment at different excitation intensities and its skeleton line, from the figure, it can be seen that the MEMS resonator shows mixed dynamic behavior under the interaction of high-order nonlinearity, the skeleton line shows non-monotonic characteristics, by using this characteristic, the MEMS resonator can be operated at the extreme point of the skeleton line, the amplitude-frequency decoupling can be carried out, the frequency fluctuation can be reduced, and the frequency stability can be improved.

[0074] Figure 4 In the figure, (b) is the phase noise comparison of the degenerate parameter excitation MEMS resonator and the direct excitation MEMS resonator under the same amplitude (oscillation energy), wherein the solid line is the phase noise of the direct excitation MEMS resonator, and the dotted line is the phase noise of the degenerate parameter excitation MEMS resonator, from the figure, it can be seen that the phase noise of the parameter excitation MEMS resonator is smaller, which shows phase noise compression.

[0075] Figure 4 In the figure, (c) is the frequency stability of the MEMS resonator when working at the peak point under different parameter excitation intensities, wherein the frequency stability is defined by Allan variance, the integral time of the corresponding Allan variance of the left figure is 1.0s, and the integral time of the corresponding Allan variance of the right figure from top to bottom is 0.1, 0.2, 0.5 and 1.0s, from Figure 4 From (a) and (c) in the figure, it can be seen that when the MEMS resonator works at the extreme point of the high-order nonlinear skeleton line, the frequency stability can be significantly improved.

[0076] In summary, the frequency stability method and system of the MEMS resonator based on high-order nonlinearity, utilize the non-monotonic skeleton line generated by the high-order nonlinear stiffness interaction of the MEMS resonator, decouple the amplitude noise and the frequency noise, thereby improving the frequency stability of the MEMS resonator. At the same time, combined with the high signal-to-noise ratio under the nonlinear state, further improve the output stability of the MEMS resonator. Thus, the frequency stable output of the MEMS resonator is realized.

[0077] The above is only to illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the claims of the present application.

Claims

1. A frequency stabilization method for MEMS resonators based on high-order nonlinearity, characterized in that, include: Based on the calibrated excitation intensity threshold, a high-order nonlinear MEMS resonator is made to generate self-excited oscillation through a closed loop, thereby outputting a frequency reference signal. A phase control signal is applied to a high-order nonlinear MEMS resonator to adjust its operating point so that it operates at the peak point. Under the specified excitation intensity threshold, the skeleton lines of the high-order nonlinear MEMS resonator exhibit decoupling of amplitude and frequency, thereby suppressing amplitude-frequency conversion and improving the frequency stability of the high-order nonlinear MEMS resonator. The frequency stabilization method for MEMS resonators based on high-order nonlinearity includes the following steps: Step 1: Power on the high-order nonlinear MEMS resonator and initialize the driving signal parameters of the high-order nonlinear MEMS resonator operating mode. The driving signal parameters include, but are not limited to, the driving amplitude and driving frequency of the operating mode. Step 2: Based on the driving signal parameters of the working mode in Step 1, generate the corresponding driving signal, and apply the driving signal to the body of the high-order nonlinear MEMS resonator through the excitation electrode to excite the response of the high-order nonlinear MEMS resonator. Step 3: Acquire the response signal from Step 2, demodulate the response phase, and calculate the difference between the phase setpoint and the measured value; Step 4: Based on the phase difference value in Step 3, adjust the frequency of the working mode excitation signal to maintain stable oscillation of the working mode; Step 5: Adjust the phase setting value of the oscillation circuit in step 3 until the oscillation amplitude of the working mode reaches the maximum, thereby achieving amplitude-frequency decoupling and improving the frequency stability of the high-order nonlinear MEMS resonator. In step 1, the driving signal parameters are obtained through calibration. Under these parameters, the skeleton line of the high-order nonlinear MEMS resonator exhibits frequency decoupling from amplitude. In step 3, the response signal of the high-order nonlinear MEMS resonator is input into the MEMS closed-loop circuit. The phase detector in the MEMS closed-loop circuit determines the difference between the measured phase value and the set value. By maintaining the control algorithm stored internally in the oscillation system, the excitation frequency is adjusted in real time, thereby enabling the high-order nonlinear MEMS resonator to achieve stable oscillation. The control algorithm is a PID algorithm, predictive control algorithm, adaptive control algorithm, or fuzzy control algorithm. The control algorithm calculates the control quantity based on the phase difference. The excitation frequency adjustment is achieved through a voltage-controlled oscillator (VCO) or a digitally controlled oscillator (NCO). The VCO or NCO outputs the corresponding frequency based on the control quantity calculated by the control algorithm and maintains the corresponding output frequency value unchanged until the next change in the control quantity. The frequency of the excitation signal is adjusted according to the output frequency and output to the excitation terminal of the high-order nonlinear MEMS resonator. The above adjustment process is repeated until the phase difference is zero. In step 5, the host computer system controls the phase setting value of the MEMS closed-loop circuit. Through the control algorithm, the high-order nonlinear MEMS resonator operates at its maximum amplitude, achieving decoupling between frequency and amplitude, thereby utilizing the high-order nonlinearity to achieve stable frequency output. The control algorithm is a PID algorithm. The PID algorithm calculates the phase adjustment value required to compensate for the amplitude difference based on the difference between the demodulated amplitude of the high-order nonlinear MEMS resonator and the pre-calibrated maximum amplitude, thereby changing the phase setting value in step 3, causing the operating phase point of the MEMS resonator to shift and eventually move to the phase point corresponding to the maximum amplitude. At the maximum amplitude, the skeleton line of the high-order nonlinear MEMS resonator exhibits decoupling between amplitude and frequency, that is, the derivative of frequency with respect to amplitude is zero, thereby suppressing the conversion of amplitude noise into frequency fluctuations.

2. A stable system implementing the frequency stabilization method for MEMS resonators based on high-order nonlinearity as described in claim 1, characterized in that, include: The host computer system is used to initialize the operating parameters of the MEMS resonator, read the amplitude and frequency of the MEMS resonator in real time, determine the operating state of the resonator based on the oscillation amplitude, and output the phase control signal. Oscillation Maintenance System: Connected to the host computer system, it demodulates the oscillation phase value in real time through the frequency control module. Based on the difference between the oscillation phase and the set phase, it changes the excitation frequency using a control algorithm to achieve phase-locked, i.e., stable closed-loop oscillation. It is also connected to the host computer system to execute the phase control signal output by the host computer system. MEMS resonator system: connected to the host computer system and oscillation maintenance system, used to generate stable high-order oscillations and output frequency reference.

3. The stable system according to claim 2, characterized in that, The host computer system includes: Oscillation reading module: connected to the oscillation maintenance system, used to read the oscillation amplitude and frequency signal of the MEMS resonator in real time; Phase modulation module: Receives the vibration amplitude signal acquired by the oscillation reading module, executes the phase modulation program, determines whether the oscillation amplitude has reached its maximum value, and generates a phase adjustment signal; Control output module: connected to the oscillation maintenance system, used to transmit the phase control signal generated by the phase modulation module to the oscillation maintenance system after digital-to-analog conversion.

4. The stable system according to claim 2, characterized in that, The oscillation sustaining system includes: Phase control module: connected to the control output module of the host computer system, used to execute the phase control signal of the host computer system and adjust the set phase value in real time; Frequency control module: connected to the drive electrode of the MEMS resonator system, used to demodulate the oscillation phase value in real time, adjust the excitation signal frequency according to the difference between the oscillation phase and the phase set value, and apply the adjusted excitation signal to the excitation electrode of the MEMS resonator system to achieve phase lock, i.e., stable oscillation; Amplitude control module: connected to the host computer system and MEMS resonator system, used to receive the initial excitation parameters of the host computer system and adjust the amplitude of the output excitation signal of the oscillation maintenance system.

5. The stable system according to claim 2, characterized in that, The excitation signal of the MEMS resonator can be a direct harmonic excitation signal, a degenerate parameter excitation signal, or a non-degenerate parameter excitation signal.

6. The stable system according to claim 2, characterized in that, The MEMS resonator system includes: a body of the MEMS resonator supported by an anchor point for generating vibration under an excitation signal; excitation electrodes and detection electrodes for exciting and detecting the device; and anchor point electrodes for applying a DC bias to the body of the MEMS resonator.

7. The stable system according to claim 2, characterized in that, The MEMS resonator is designed with an arched structure. The inherent nonlinear stiffness of the MEMS resonator is adjusted by the arched structure, thereby enabling the MEMS resonator to exhibit higher-order nonlinearity.

8. The stable system according to claim 2, characterized in that, The excitation and detection methods of the MEMS resonator can be capacitive, piezoelectric, optical, or electromagnetic.

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