MEMS resonator frequency stabilization method and system based on high-order nonlinearity

Abstract

The invention discloses a high-order nonlinear MEMS resonator frequency stabilization method and system, and the method comprises the steps: enabling a high-order nonlinear MEMS resonator to generate stable oscillation through a closed loop according to a calibrated excitation intensity threshold; applying a phase control signal to the high-order nonlinear MEMS resonator so as to regulate and control a working point of the high-order nonlinear MEMS resonator and enable the working point to work at a peak point; under the excitation intensity threshold value, a skeleton line of the high-order nonlinear MEMS resonator shows decoupling of frequency to amplitude, so that suppression of amplitude-frequency conversion is realized, and the frequency stability of the high-order nonlinear MEMS resonator is improved; decoupling of amplitude and frequency is realized by regulating and controlling the amplitude-frequency dependency relationship of the resonator, and the phase noise of the system is reduced; a frequency reference with small volume, low power consumption and high precision can be provided in electronic equipment for communication, radar, inertial navigation and the like, the performance of the system is greatly improved, the working error is reduced, and stable output of the frequency of the MEMS resonator is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-electromechanical systems, and in particular relates to a frequency stabilization method and system for a MEMS resonator based on high-order nonlinearity. Background Art

[0002] With the maturity of semiconductor processing technology, MEMS resonators have gradually become a research hotspot. The reduction in the size of MEMS resonators has brought advantages such as low power consumption, low cost, and high integration, which has enabled MEMS resonators to gradually replace traditional quartz crystal oscillators and be widely used in various occasions that require precise timing and high-precision sensing.

[0003] The stability of the resonator output frequency is a decisive factor in 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 shows a nonlinear dependence on the amplitude. The amplitude noise is converted into frequency noise through this nonlinear dependence, thereby degrading the frequency stability. In order to provide a stable frequency reference source, MEMS resonators usually work in the linear stage, 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 reduce anchor loss by designing phononic crystals ([1]Hsu FC, Hsu JC, Huang TC, 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 SA, Engelsen NJ, et al. Elastic strain engineering for ultralow mechanical dissipation[J]. Science, 2018, 360(6390):764-+) and reduce thermoelastic loss by digging holes ([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, thereby achieving the short-term frequency stability of the MEMS resonator; however, the structural design method is complicated to operate, and the implementation requires the design of a large-area auxiliary structure, and it is not compatible with resonant devices of all frequency bands, so the improvement effect is very limited. Summary of the invention

[0004] In view of the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method and system for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, which realizes the decoupling of amplitude and frequency by regulating the amplitude-frequency dependence of the resonator, reduces the phase noise of the system, and realizes the stable output of the MEMS resonator frequency; it can provide a small size, low power consumption, and high-precision frequency reference in electronic equipment such as communications, radars, and inertial navigation, greatly improves the performance of the system, and reduces working errors.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, comprising:

[0007] According to the calibrated excitation intensity threshold, the high-order nonlinear MEMS resonator is caused to generate self-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 adjust the working point of the high-order nonlinear MEMS resonator so that it works at a peak point; under the excitation intensity threshold, the skeleton line of the high-order nonlinear MEMS resonator shows frequency-to-amplitude decoupling, thereby achieving suppression of amplitude-frequency conversion and improving the frequency stability of the high-order nonlinear MEMS resonator.

[0008] A method for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity comprises the following steps:

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

[0010] Step 2, generating a corresponding harmonic driving signal according to the driving signal parameters of the working mode in step 1, applying the driving signal to the body of the high-order nonlinear MEMS resonator through the excitation electrode, and exciting the response of the high-order nonlinear MEMS resonator;

[0011] Step 3, collecting the response signal of step 2, demodulating the response phase, and calculating the difference between the phase setting value and the measured value;

[0012] Step 4: According to the phase difference in step 3, the frequency of the working mode excitation signal is adjusted to maintain the stable oscillation of the working mode;

[0013] Step 5, adjusting the phase setting value of the oscillation loop in step 3 until the oscillation amplitude of the working mode reaches the maximum, realizing amplitude-frequency decoupling, thereby improving the frequency stability of the high-order nonlinear MEMS resonator.

[0014] The drive signal parameters in step 1 are obtained by calibration, and under these parameters, the skeleton line of the high-order nonlinear MEMS resonator shows decoupling of frequency from amplitude.

[0015] In the step 3, the response signal of the high-order nonlinear MEMS resonator is input into the MEMS closed-loop circuit, and the MEMS closed-loop phase detector determines the difference between the phase measurement value and the set value, and adjusts the excitation frequency in real time by maintaining the control algorithm stored in the internal storage of the oscillation system, so that the high-order nonlinear MEMS resonator can achieve 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 algorithm calculates the control amount according to the phase difference; the excitation frequency adjustment is implemented by a voltage-controlled oscillator VCO or a digitally controlled oscillator NCO, and the voltage-controlled oscillator VCO or the digitally 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 changes; 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-mentioned control process is repeated until the phase difference is zero.

[0016] In step 5, the host computer system implements the regulation of the MEMS closed-loop phase setting value, and through the control algorithm, the high-order nonlinear MEMS resonator operates at the maximum amplitude, realizes the decoupling of frequency and amplitude, and thus utilizes the high-order nonlinearity to achieve stable frequency output; the control algorithm is a PID algorithm, and the PID algorithm calculates the phase regulation value required to compensate for the amplitude difference based on the difference between the demodulated high-order nonlinear MEMS resonator amplitude and the pre-calibrated maximum amplitude, thereby changing 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 frequency and amplitude, that is, the derivative of frequency with respect to amplitude is zero, thereby suppressing the conversion of amplitude noise into frequency fluctuation.

[0017] A stabilization system for implementing the MEMS resonator frequency stabilization method based on high-order nonlinearity comprises:

[0018] Host computer system: used to initialize the working parameters of the high-order nonlinear MEMS resonator, and read the amplitude and frequency of the high-order nonlinear MEMS resonator in real time, judge the working state of the resonator according to the oscillation amplitude, and output the phase control signal;

[0019] Oscillation maintenance system: connected to the host computer system, demodulates the oscillation phase value in real time through the frequency control module, changes the excitation frequency according to the difference between the oscillation phase and the set phase using the control algorithm to achieve phase-locked, i.e., stable closed-loop oscillation, and is connected to the host computer system to execute the phase control signal output by the host computer system;

[0020] MEMS resonator system: connected to the host computer system and the oscillation maintenance system, used to generate stable high-order oscillations and output frequency reference.

[0021] The host computer system comprises:

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

[0023] Phase modulation module: receives the vibration amplitude signal collected by the oscillation reading module, is used to execute the phase modulation program, determines whether the oscillation amplitude reaches the maximum value, and generates a phase control signal;

[0024] Control output module: connected to the oscillation maintaining system, used to transmit the phase control signal generated by the phase modulation module to the oscillation maintaining system after digital / analog conversion.

[0025] The oscillation maintaining system comprises:

[0026] 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;

[0027] A frequency control module: connected to the driving 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 setting value, and apply the adjusted excitation signal to the excitation electrode of the MEMS resonator system, thereby achieving phase locking, i.e., stable oscillation;

[0028] Amplitude control module: connected to the host computer system and the MEMS resonator system, used to receive the initialization excitation parameters of the host computer system and adjust the amplitude of the excitation signal output by the oscillation maintenance system.

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

[0030] The MEMS resonator system includes: a body of the MEMS resonator supported by an anchor point, used to generate vibration under an excitation signal; an excitation electrode and a detection electrode, used to excite and detect the device; and an anchor point electrode, used to apply a DC bias to the body of the MEMS resonator.

[0031] The body of the MEMS resonator is an arched structure, and the inherent nonlinear stiffness of the MEMS resonator is adjusted through the arched structure, so that the MEMS resonator exhibits 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 present invention has the following beneficial effects:

[0034] In step 2 of the present invention, the MEMS resonator is driven by using a pre-calibrated threshold excitation intensity, which can make the MEMS resonator generate large-amplitude resonance and has the characteristic of improving the signal-to-noise ratio of the MEMS resonator.

[0035] The host computer system of the present invention adopts a control algorithm to maintain the working state of the MEMS resonator in a critical state of frequency and amplitude decoupling, and can suppress the conversion of amplitude noise into frequency fluctuation while increasing the signal-to-noise ratio of the MEMS resonator output signal. It has the characteristics of strong versatility and simple operation.

[0036] The oscillation maintaining system of the present invention adopts a phase-locked scheme to realize closed-loop oscillation of the MEMS resonator, which can enable the MEMS resonator to start oscillation quickly and can flexibly regulate the working state of the MEMS resonator by modifying the phase setting value, and has the characteristics of rapid oscillation start-up and low circuit conduction noise.

[0037] The MEMS resonator system of the present invention adopts a MEMS resonator body with an arched structure, which can make the MEMS resonator exhibit high-order nonlinear response without external electrothermal and electrostatic nonlinear tuning means, and has the characteristics of simple operation and strong robustness.

[0038] In summary, the present invention provides a method and system for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, which utilizes high-order nonlinearity to achieve decoupling of the output frequency of the MEMS resonator from the amplitude, thereby suppressing the amplitude-frequency conversion and improving the stability of the output frequency of the MEMS resonator. On the one hand, the present invention operates the MEMS resonator at the threshold excitation intensity generated by the high-order nonlinear response, while improving the signal-to-noise ratio of the MEMS resonator, suppressing the conversion of amplitude noise to frequency fluctuations, significantly enhancing the output frequency stability of the MEMS resonator, and avoiding the challenges of the device processing technology posed by the complex structural design of the traditional frequency stability improvement solution; on the other hand, the body of the MEMS resonator of the present invention adopts an arched structure, so that the MEMS resonator can exhibit a high-order nonlinear response without the need for external nonlinear tuning, simplifying the peripheral circuit and increasing the robustness of the system. The present invention 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 extremely high theoretical and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of a MEMS resonator system according to an embodiment of the present invention.

[0040] Figure 2 The figure is a flow chart of a method for frequency stabilization of a MEMS resonator based on high-order nonlinearity according to an embodiment of the present invention.

[0041] Figure 3 Schematic diagram of a MEMS resonator frequency stabilization system based on high-order nonlinearity according to an embodiment of the present invention.

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

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

[0044] The present invention provides a method and system for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, including a MEMS resonator system, an oscillation maintenance system, and a host computer system; the high-order nonlinearity realizes amplitude-frequency decoupling under large amplitudes, and combined with the improvement of the signal-to-noise ratio under the nonlinear state, the frequency stability of the MEMS resonator is comprehensively improved. The following takes a double-end fixed-end tuning fork arch MEMS resonator as an example to specifically describe the technical solution of the present invention.

[0045] Reference Figure 1 The MEMS resonator system of this embodiment includes a double-ended fixed tuning fork arch MEMS resonator 1-1, the left and right ends of the double-ended fixed tuning fork arch MEMS resonator 1-1 are connected to a first fixed anchor point 2-1 and a second fixed anchor point 2-3, and the double-ended fixed tuning fork arch MEMS resonator 1-1 is supported by the first fixed anchor point 2-1 and the second fixed anchor point 2-3, and is used to generate vibration under a driving signal; a first metal electrode layer 2-2 is sputtered on the first fixed anchor point 2-1, and a second metal electrode layer 2-4 is sputtered on the second fixed anchor point 2-3, which is used to ground the MEMS resonator; the upper and lower sides of the double-ended fixed tuning fork arch MEMS resonator 1-1 are connected to the first excited electrode 1-2 and the resonator The first detected electrode 1-3 of the resonator; the first excited electrode 1-2 of the resonator is adjacent to the first excitation electrode plate 3-1 of the resonator, and the third metal electrode layer 3-2 is sputtered on the first excitation electrode plate 3-1 of the resonator. The first excitation electrode plate 3-1 of the resonator and the third metal electrode layer 3-2 provide excitation force for the first excited electrode 1-2 of the resonator; the first detected electrode 1-3 of the resonator is adjacent to the first detection electrode plate 3-3 of the resonator, and the fourth metal electrode layer 3-4 is sputtered on the first detection electrode plate 3-3 of the resonator. The first detection electrode 3-3 of the resonator and the fourth metal electrode layer 3-4 form a detection capacitor with the first detected electrode 1-3 of the resonator, which is used to detect the movement of the double-ended fixed tuning fork arch 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. Other types of high-order nonlinearity, resonator structure and excitation methods have slightly different expressions, but the internal mechanism is the same.

[0047] When the MEMS resonator system of this embodiment is excited by parameters, its dynamic equation can be expressed as:

[0048]

[0049] in

[0050]

[0051] Where τ is the dimensionless time, Q is the quality factor, λ is the dimensionless parameter pump, ω is the dimensionless driving frequency, u is the dimensionless lateral 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 mode vibration shape, d0 is the distance between the plates, The arch height of the arched beam is 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; through the multi-scale method, the dependence of the resonator peak frequency on the amplitude (skeleton line) is:

[0052]

[0053] in, is an effective cubic nonlinearity, is the effective quintic nonlinearity, and a is the dimensionless amplitude; it can be seen from formulas (2)-(6) that 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 value of the secondary and quartic nonlinearities can be actively regulated by increasing the arch height of the arch structure to achieve the regulation of the amplitude-frequency dependence curve (skeleton line), so that the MEMS resonator shows a non-monotonic skeleton line. Among them, at small amplitudes, the secondary nonlinearity dominates the response, and the MEMS resonator shows a spring softening characteristic; at large amplitudes, 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 is decoupled from the frequency. Based on this feature, this embodiment discloses a frequency stabilization method and system for a MEMS resonator based on high-order nonlinearity. When the MEMS resonator works at the extreme point of the calibrated skeleton line, the frequency fluctuation is suppressed by the amplitude-frequency decoupling characteristics at the extreme point, combined with the high signal-to-noise ratio of the nonlinear state, wherein the signal-to-noise ratio is the ratio of the response amplitude to the total system noise, and the noise value is a fixed value independent of the working state.

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

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

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

[0057] Step 2, the oscillation maintaining 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 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 setting value and the measured value;

[0059] The response signal of the high-order nonlinear MEMS resonator is input into the MEMS closed-loop circuit, and the built-in phase detector of the frequency control module of the MEMS closed-loop circuit determines the difference between the phase measurement value and the set value, and adjusts the excitation frequency in real time through the built-in control algorithm of the frequency control module, so as to achieve 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 achieved by a voltage-controlled oscillator VCO or a digitally controlled oscillator NCO, and the VCO or 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 changes; 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-mentioned control process is repeated until the phase difference is zero;

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

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

[0062] The host computer system realizes the modulation of the closed-loop phase setting value. The phase modulation module has a built-in phase modulation program. When the processor executes the modulation program, it determines whether the oscillation amplitude reaches the maximum value, and outputs a phase control signal by controlling the output module, so that the high-order nonlinear MEMS resonator works at the maximum amplitude, realizes the decoupling of frequency and amplitude, and thus utilizes the high-order nonlinearity to realize the stable output of frequency; the control algorithm is a PID algorithm, and the PID algorithm calculates the phase control value required to compensate for the amplitude difference according to the difference between the amplitude of the high-order nonlinear MEMS resonator obtained by demodulation and the pre-calibrated maximum amplitude, thereby changing 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 the decoupling of amplitude and frequency, that is, the derivative of frequency with respect to amplitude is zero, thereby suppressing the conversion of amplitude noise into frequency fluctuation.

[0063] Reference Figure 3 , a stabilization system for realizing the frequency stabilization method of MEMS resonator based on high-order nonlinearity, including a host computer system, an oscillation maintenance system and a MEMS resonator system; wherein the host computer system is used to initialize the working parameters of the MEMS resonator, and read the amplitude and frequency of the MEMS resonator in real time through an oscillation reading module, judge the working state of the MEMS resonator according to the oscillation amplitude, and output a phase control signal to the oscillation maintenance system; the oscillation maintenance system is connected to the host computer system, and demodulates the oscillation phase value in real time through a phase control module, and changes the excitation frequency according to the difference between the oscillation phase and the set phase by using a control algorithm to realize phase-locked, i.e., stable closed-loop oscillation, and receives a phase control signal from the host computer, executes a phase setting value change instruction, and adjusts the phase working point of the resonator; the MEMS resonator system is connected to the above-mentioned host computer system and the oscillation maintenance system, and is used to generate stable high-order oscillations and output a frequency reference.

[0064] In this embodiment, the host computer system includes:

[0065] An oscillation reading module, connected to the oscillation maintaining system, for reading the oscillation amplitude, 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, is used to execute the phase modulation program, determine whether the oscillation amplitude reaches the maximum value, and generate a phase control signal;

[0067] The control output module is connected to the oscillation maintaining system and is used to transmit the phase control signal generated by the phase modulation module to the oscillation maintaining system after digital / analog conversion.

[0068] In this embodiment, the oscillation maintenance system includes:

[0069] 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;

[0070] Frequency control module: connected to the detection electrode of the MEMS resonator system, the built-in phase detector is used to demodulate the oscillation phase value in real time, and adjust the excitation signal frequency output by the oscillation maintenance system according to the difference between the oscillation phase and the phase setting value, so as to achieve phase locking, that is, stable oscillation;

[0071] Amplitude control module: connected to the host computer system and the MEMS resonator system, used to receive the initialization excitation parameters of the host computer system and adjust the amplitude of the excitation signal output by the oscillation maintenance system.

[0072] The excitation signal form of the MEMS resonator is a direct harmonic excitation signal, a degenerate parameter excitation signal or a 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 diagram and skeleton line of the MEMS resonator under degenerate parameter excitation at different excitation intensities in the embodiment. It can be seen from the figure that the MEMS resonator exhibits mixed dynamic behavior under the interaction of high-order nonlinearities, and the skeleton line presents a non-monotonic characteristic. By utilizing this characteristic, the MEMS resonator is operated at the extreme point of the skeleton line to perform amplitude-frequency decoupling, reduce frequency fluctuations, and achieve improved frequency stability.

[0074] Figure 4 In the figure, (b) is a comparison of the phase noise of the degenerate parameter-excited MEMS resonator and the directly-excited MEMS resonator under the same amplitude (oscillation energy) of the embodiment, where the solid line is the phase noise of the directly-excited MEMS resonator, and the dotted line is the phase noise of the degenerate parameter-excited MEMS resonator. It can be seen from the figure that the phase noise of the parameter-excited MEMS resonator is smaller, which is manifested as phase noise compression.

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

[0076] In summary, the present invention provides a method and system for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, which utilizes the non-monotonic skeleton line generated by the interaction of the high-order nonlinear stiffness of the MEMS resonator to decouple the amplitude noise from the frequency noise, thereby improving the frequency stability of the MEMS resonator. At the same time, combined with the high signal-to-noise ratio in the nonlinear state, the output stability of the MEMS resonator is further improved. Thus, the frequency-stable output of the MEMS resonator is achieved.

[0077] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, characterized in that: include: According to the calibrated excitation intensity threshold, the high-order nonlinear MEMS resonator is made to generate self-oscillation through a closed loop, thereby outputting a frequency reference signal; Applying a phase control signal to the high-order nonlinear MEMS resonator to adjust the operating point of the high-order nonlinear MEMS resonator so that it operates at a peak point; Under the excitation intensity threshold, the skeleton line of the high-order nonlinear MEMS resonator shows decoupling of amplitude and frequency, thereby suppressing the amplitude-frequency conversion and improving the frequency stability of the high-order nonlinear MEMS resonator.

2. A method for stabilizing the frequency of a MEMS resonator based on high-order nonlinearity, characterized in that: The following steps are involved: Step 1, the high-order nonlinear MEMS resonator is powered on to initialize the drive signal parameters of the working mode of the high-order nonlinear MEMS resonator, where the drive signal parameters include but are not limited to the drive amplitude and drive frequency of the working mode; Step 2, generating a corresponding driving signal according to the driving signal parameters of the working mode in step 1, applying the driving signal to the body of the high-order nonlinear MEMS resonator through the excitation electrode, and exciting the response of the high-order nonlinear MEMS resonator; Step 3, collecting the response signal of step 2, demodulating the response phase, and calculating the difference between the phase setting value and the measured value; Step 4: According to the phase difference in step 3, the frequency of the working mode excitation signal is adjusted to maintain the stable oscillation of the working mode; Step 5, adjusting the phase setting value of the oscillation loop in step 3 until the oscillation amplitude of the working mode reaches the maximum, realizing amplitude-frequency decoupling, thereby improving the frequency stability of the high-order nonlinear MEMS resonator.

3. The method for stabilizing the frequency of a MEMS resonator according to claim 2, characterized in that: The driving signal parameters in step 1 are obtained by calibration, under which the skeleton line of the high-order nonlinear MEMS resonator shows decoupling of frequency from amplitude; In the step 3, the response signal of the high-order nonlinear MEMS resonator is input into the MEMS closed loop, and the MEMS closed loop phase detector determines the difference between the phase measurement value and the set value, and adjusts the excitation frequency in real time by maintaining the control algorithm stored in the internal storage of the oscillation system, so that the high-order nonlinear MEMS resonator can achieve 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 algorithm calculates the control amount according to the phase difference; the excitation frequency adjustment is achieved by a voltage-controlled oscillator VCO or a digitally controlled oscillator NCO, and the VCO or 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 changes; 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-mentioned control process is repeated until the phase difference is zero; In step 5, the host computer system implements the regulation of the MEMS closed-loop phase setting value, and through the control algorithm, the high-order nonlinear MEMS resonator works at the maximum amplitude, realizes the decoupling of frequency and amplitude, and thus utilizes the high-order nonlinearity to achieve stable frequency output; the control algorithm is a PID algorithm, and the PID algorithm calculates the phase control value required to compensate for the amplitude difference based on the difference between the demodulated high-order nonlinear MEMS resonator amplitude and the pre-calibrated maximum amplitude, thereby changing 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 amplitude and frequency, that is, the derivative of frequency with respect to amplitude is zero, thereby suppressing the conversion of amplitude noise into frequency fluctuation.

4. A stabilization system for implementing the MEMS resonator frequency stabilization method based on high-order nonlinearity as described in claims 1-3, characterized in that: include: Host computer system: used to initialize the working parameters of the MEMS resonator, and read the amplitude and frequency of the MEMS resonator in real time. According to the oscillation amplitude, it determines the working state of the resonator and outputs the phase control signal. Oscillation maintenance system: connected to the host computer system, demodulates the oscillation phase value in real time through the frequency control module, changes the excitation frequency according to the difference between the oscillation phase and the set phase using the control algorithm to achieve phase-locked, i.e., stable closed-loop oscillation, and is 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 the oscillation maintenance system, used to generate stable high-order oscillations and output frequency reference.

5. The stabilization system according to claim 4, characterized in that: The host computer system comprises: Oscillation reading module: connected to the oscillation maintaining 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 collected by the oscillation reading module, is used to execute the phase modulation program, determines whether the oscillation amplitude reaches the maximum value, and generates a phase control signal; Control output module: connected to the oscillation maintaining system, used to transmit the phase control signal generated by the phase modulation module to the oscillation maintaining system after digital / analog conversion.

6. The stabilization system according to claim 4, characterized in that: The oscillation maintaining system comprises: 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; A frequency control module: connected to the driving 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 setting value, and apply the adjusted excitation signal to the excitation electrode of the MEMS resonator system, thereby achieving phase locking, i.e., stable oscillation; Amplitude control module: connected to the host computer system and the MEMS resonator system, used to receive the initialization excitation parameters of the host computer system and adjust the amplitude of the excitation signal output by the oscillation maintenance system.

7. The stabilization system according to claim 4, characterized in that: The excitation signal of the MEMS resonator is in the form of a direct harmonic excitation signal, a degenerate parameter excitation signal or a non-degenerate parameter excitation signal.

8. The stabilization system according to claim 4, characterized in that: The MEMS resonator system includes: a body of the MEMS resonator supported by an anchor point, used to generate vibration under an excitation signal; an excitation electrode and a detection electrode, used to excite and detect the device; and an anchor point electrode, used to apply a DC bias to the body of the MEMS resonator.

9. The stabilization system according to claim 4, characterized in that: The body of the MEMS resonator is designed as an arch structure, and the inherent nonlinear stiffness of the MEMS resonator is adjusted through the arch structure, so that the MEMS resonator exhibits high-order nonlinearity.

10. The stabilization system according to claim 4, characterized in that: The excitation detection form of the MEMS resonator is capacitive, piezoelectric, optical or electromagnetic.

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