Automatic tuning and calibration method and system for crystal resonator

Abstract

The invention discloses an automatic tuning and calibration method and system for a crystal resonator, and relates to the technical field of automatic control. Comprising the following steps: S1, generating a multi-physics field coupling matrix: constructing three-dimensional space distribution of an electromagnetic-mechanical-thermal coupling field through a quantum dot sensor array, and generating the multi-physics field coupling matrix; s2, determining a compensation amount: determining time-varying characteristic parameters in the magnetic component, the mechanical component and the thermal component, constructing a nonlinear multi-body coupling state equation, and determining the corresponding compensation amount; and S3, multi-dimensional cooperative compensation: respectively carrying out mechanical compensation, capacitance compensation and light-operated tuning, and carrying out cooperative compensation through multiple actuators. According to the method, modeling is performed through high-precision three-dimensional space distribution of multiple physical fields, and the interaction of electromagnetic coupling, mechanical coupling and thermal coupling is quantified through the obtained total coupling strength among the resonators, so that the defect that the multi-body effect is ignored in a traditional method is overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic control, and particularly to a method and system for automatic tuning and calibration of crystal resonators. Background Art

[0002] A crystal resonator is a core component used to generate stable frequency signals in an electronic system, and is widely used in fields such as communication devices, clock circuits, sensors, Internet of Things (IoT) terminals, and aerospace. Its core function is to provide a high-precision frequency reference through the piezoelectric effect of a quartz crystal, ensuring the time synchronization, signal transmission, and data processing accuracy of electronic devices. However, with the development of electronic devices towards high frequency, high integration, and complexity, higher requirements are put forward for the frequency stability, temperature adaptability, and long-term reliability of crystal resonators.

[0003] The Chinese invention patent with the publication number CN119644862A discloses a method and device for tuning controller parameters in a servo system, and a computing device. The tuning method includes: sweeping the frequency characteristics of the controlled object in the servo system, and determining the open-loop transfer function for the controlled object according to the frequency characteristics; determining the full-frequency band constraint boundary for the servo system according to the user's constraints on the stability and disturbance rejection of the servo system; making the real and imaginary parts of the coordinates of the open-loop transfer function equal to the coordinates of the full-frequency band constraint boundary, and making the slopes of the open-loop transfer function and the full-frequency band constraint boundary equal at the intersection point, to determine a full-rank equation set; solving the full-rank equation set to obtain the target solution set of the controller parameters, and screening out the target controller parameters from the target solution set according to the maximum bandwidth criterion. This application can reduce the production costs of time and labor increased by redesigning the controller parameters when replacing the controlled object, and improve the production efficiency of industrial manufacturing.

[0004] However, in existing arrayed devices, due to the high-density integration among multiple crystal resonators, phenomena such as electromagnetic coupling (such as signal crosstalk caused by parasitic capacitance / inductance between adjacent electrodes) and mechanical coupling (such as resonance mode interference caused by substrate vibration transmission) will occur. Therefore, during the calibration process, the frequencies of each unit will interfere with each other, showing non-linear time-varying characteristics. And existing independent closed-loop control strategies (such as single-resonator PID regulation) often ignore the multi-body coupling effect during the tuning and calibration process, resulting in frequency competition instability and significant parameter isolation during the tuning and calibration process. At the same time, sensors and actuators will be repeatedly configured, causing resource waste. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and system for automatic tuning and calibration of crystal resonators, so as to solve the problems raised in the above background art.

[0006] To achieve the above object, the present invention provides the following technical solutions: An automatic tuning and calibration method for a crystal resonator, including:

[0007] S1: Generate a multi-physical field coupling matrix: Through a quantum dot sensor array, obtain the electromagnetic field intensity, mechanical vibration mode, and temperature gradient distribution, and construct a three-dimensional spatial distribution of the electromagnetic-mechanical-thermal coupling field to generate a multi-physical field coupling matrix;

[0008] S2: Determine the compensation amount: According to the multi-physical field coupling matrix, determine the time-varying characteristic parameters in the magnetic component, mechanical component, and thermal component, and construct a non-linear multi-body coupling state equation according to the time-varying characteristic parameters to determine the corresponding compensation amount;

[0009] S3: Multidimensional collaborative compensation: According to the compensation amount, perform mechanical compensation, capacitance compensation, and optical control tuning respectively, and perform collaborative compensation through multiple actuators, including:

[0010] S3.1: Mechanical compensation: According to the applied voltage in the MEMS actuator, the DAC module inputs a voltage with the same magnitude as the applied voltage to the MEMS actuator;

[0011] S3.2: Capacitance compensation: According to the threshold voltage to be adjusted, the DAC module inputs a voltage with the same magnitude as the threshold voltage to the ferroelectric domain wall memory, and converts the state of the ferroelectric domain wall memory into a domain wall state;

[0012] S3.3: Optical control tuning: According to the equivalent inductance change generated by the thermo-optic effect of the optical control micro-ring, obtain the phase change of the micro-ring resonator, and according to the phase change, apply a current through the micro-heater to change the refractive index of the liquid crystal molecules and adjust the resonant wavelength;

[0013] S3.4: Collaborative compensation: Integrate the mechanical compensation, capacitance compensation, and optical control tuning, and perform timing synchronization through FPGA control.

[0014] Furthermore, generating the multi-physical field coupling matrix includes:

[0015] S1.1: Sensor array deployment: According to the geometric structure of the crystal resonator array, set up a quantum dot sensor array to obtain the corresponding electromagnetic field intensity, mechanical vibration, and temperature gradient, specifically:

[0016]

[0017] Among them: is the energy level splitting value of the quantum dot, is the electric dipole moment, is the local electric field intensity, is the second-order polarizability, is the energy level shift of the quantum dot caused by strain, is the deformation potential constant, is the strain tensor, is the thermionic emission current, is the effective Richardson constant, is the absolute temperature, is the base of the natural logarithm, is the work function, is the Boltzmann constant;

[0018] S1.2: Set up the superconducting detector: Through the probe of the superconducting detector, obtain the integrated magnetic field in the superconducting loop, and determine the output voltage of the superconducting detector. Specifically:

[0019]

[0020] where: is the output voltage of the superconducting detector, is the change in magnetic flux, is the total magnetic flux in the superconducting loop;

[0021] S1.3: Perform three-dimensional field reconstruction: Integrate the electromagnetic field intensity, mechanical vibration, temperature gradient, and the output voltage of the superconducting detector to obtain a joint observation matrix and establish a coupling matrix.

[0022] Furthermore, establishing the coupling matrix includes:

[0023] S1.3.1: Construct the joint observation matrix: Through the electromagnetic field intensity, mechanical vibration, and temperature gradient, obtain the quantum dot sensor data. Through the output voltage of the superconducting detector, obtain the detector data. At the same time, based on the quantum dot sensor data and the detector data, obtain the joint observation matrix. Specifically:

[0024]

[0025] where: is the joint observation matrix, is the measurement matrix, is the three-dimensional field to be reconstructed, is the noise term;

[0026] S1.3.2: Determine the sparse coefficient vector: Through the constructed wavelet transform matrix and the joint observation matrix, construct an optimization problem. Specifically:

[0027]

[0028] where: is the joint observation matrix, is the measurement matrix, is the wavelet transform matrix, is the sparse coefficient vector, is the regularization parameter, is the square of the L2 norm, is the L1 norm;

[0029] S1.3.3: Establish the coupling matrix: Combine the sparse coefficient vector with the electromagnetic field strength, mechanical vibration, and temperature gradient to establish the coupling matrix, specifically:

[0030]

[0031] where: is the total coupling strength between the i-th resonator and the j-th resonator, is all regions in the crystal resonator array that have a significant impact on the coupling, is the electromagnetic coefficient, is the electric field strength of the i-th resonator, is the electric field strength of the j-th resonator, is the mechanical coefficient, is the mechanical strain field distribution of the i-th resonator, is the mechanical strain field distribution of the j-th resonator, is the thermal coupling coefficient, is the temperature gradient of the i-th resonator, is the temperature gradient of the j-th resonator, is the gap volume between the electrodes.

[0032] Furthermore, determine the corresponding compensation amount, including:

[0033] S2.1: Extract time-varying characteristic parameters: Through the coupling matrix, obtain the reconstructed electromagnetic field, mechanical strain field, and temperature field, and extract the time-varying characteristic parameters, specifically:

[0034]

[0035] where: is the time-varying parasitic capacitance, is the vacuum permittivity, is the relative permittivity, is the gap between the electrodes, is the time-varying value of the electrode spacing, is the electric field strength of the i-th resonator, is the electric field strength of the j-th resonator, is the gap volume between the electrodes, is the vibration transfer function, is the time-varying quality factor, is the excitation frequency, is the time-varying resonance frequency, is the temperature gradient of the resonator, is the small distance increment in the x direction in the temperature field, is the small distance increment in the y direction in the temperature field, is the small distance increment in the z direction in the temperature field, is the temperature at the spatial point (x, y, z) in the temperature field;

[0036] S2.2: Construct the non-linear multi-body coupling state equation: According to the time-varying characteristic parameters, construct the non-linear multi-body coupling state equation, specifically:

[0037]

[0038] Where: is the driving function of the charge change, is the time-varying coupling coefficient, is the electric charge quantity of the resonator, is the displacement generated during the mechanical vibration of the resonator, is the effective mass of the vibrating part of the resonator, is the vibration time of the resonator, is the damping coefficient, is the elastic coefficient, is the driving force function, is the density of the resonator material, is the specific heat capacity at constant pressure, is the local temperature of the material, is the heat conduction term, is the thermal conductivity, is the temperature gradient of the resonator, is the heat source term;

[0039] S2.3: Generate global optimization instructions: According to the non-linear multi-body coupling state equation, perform electromagnetic regulation, electrically controlled capacitance compensation, and mechanical stress compensation.

[0040] Furthermore, performing electromagnetic regulation, electrically controlled capacitance compensation, and mechanical stress compensation includes:

[0041] S2.3.1: Metasurface refractive index modulation: By dynamically modulating the refractive index of the metasurface, suppressing the electric field at the electrode edge, reducing the parasitic capacitance, and specifically, the parallel plate capacitance is inversely proportional to the distance, specifically:

[0042]

[0043] Where: is the time-varying parasitic capacitance, is the vacuum permittivity, is the relative permittivity, is the effective area of the electrode, is the equivalent electrode spacing after refractive index modulation;

[0044] S2.3.2: Electrically controlled capacitance compensation: By adjusting the ferroelectric domain wall switching threshold voltage and simultaneously adjusting the threshold voltage according to the capacitance deviation, specifically:

[0045]

[0046] where: is the threshold voltage, is the capacitance deviation;

[0047] S2.3.3: Mechanical stress compensation: By the displacement of the MEMS actuator, offset the frequency shift caused by mechanical strain, and at the same time the magnitude of the applied voltage in the MEMS actuator, specifically:

[0048]

[0049] where: is the applied voltage in the EMS actuator, is the piezoelectric driving coefficient, is the displacement offset.

[0050] Furthermore, the change in the refractive index of the metasurface satisfies the following formula, specifically:

[0051]

[0052] where: is the change in refractive index, is the refractive index of extraordinary light, is the refractive index of ordinary light, is the applied driving voltage, is the threshold voltage.

[0053] Furthermore, the mechanical compensation, capacitance compensation, and optical control tuning are triggered for compensation in sequence and synchronized through a PLL phase-locked loop.

[0054] A crystal resonator automatic tuning and calibration system uses the crystal resonator automatic tuning and calibration method described in any one of the above.

[0055] Compared with the prior art, the beneficial effects of the present invention are:

[0056] First: By deploying quantum dot sensors, the present invention can obtain the electromagnetic field intensity, mechanical strain, and temperature gradient in real time. At the same time, superconducting detectors are combined to capture transient magnetic field fluctuations, thereby realizing the high-precision three-dimensional spatial distribution modeling of multiple physical fields. By obtaining the total coupling strength between resonators, the interaction of electromagnetic, mechanical, and thermal coupling is quantified, thus avoiding the defect of ignoring many-body effects in traditional methods.

[0057] Second: The present invention extracts the parasitic capacitance nonlinear coefficient, time-varying quality factor, and temperature gradient from the coupling matrix, and dynamically characterizes the system state. At the same time, a differential equation of charge-displacement-temperature coupling is constructed, and a time-varying coupling coefficient and heat source term are introduced, making the dynamic interaction of multiple physical fields more accurate.

[0058] Third: The present invention cancels the displacement offset caused by thermal expansion through the reverse displacement of the MEMS actuator, dynamically adjusts the threshold voltage of the ferroelectric domain wall, corrects the parasitic capacitance deviation, uses the change in the refractive index of liquid crystal to adjust the micro-ring phase, indirectly corrects the equivalent inductance, triggers compensation in stages, and uses a PLL phase-locked loop for synchronization, thus avoiding conflicts between multiple actuators. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a schematic flow chart of the automatic tuning and calibration method of the crystal resonator of the present invention;

[0060] Figure 2 is an analysis diagram of the mechanical compensation effect of the present invention;

[0061] Figure 3 is an analysis diagram of the collaborative compensation effect of capacitance and optical control of the present invention;

[0062] Figure 4 is an analysis diagram of the coordination effect of multiple actuators of the present invention;

[0063] Figure 5 is a verification curve graph of the temperature and frequency drift of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0064] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0065] In existing array devices, high-density integration is carried out among multiple crystal resonators. Therefore, phenomena such as electromagnetic coupling (e.g., signal crosstalk caused by parasitic capacitance / inductance between adjacent electrodes) and mechanical coupling (e.g., resonance mode interference caused by substrate vibration transmission) will occur. Thus, during the calibration process, the frequencies of each unit will interfere with each other, showing non-linear time-varying characteristics. In the existing independent closed-loop control strategies (such as single-resonator PID regulation), the multi-body coupling effect is often ignored during the tuning and calibration process, resulting in frequency competition instability and significant parameter isolation during the tuning and calibration process. At the same time, sensors and actuators will be repeatedly configured, causing waste of resources. The technical solution of this application uses a quantum dot sensor array to obtain the electromagnetic field intensity, mechanical vibration mode, and temperature gradient distribution, establish a multi-physical field coupling matrix, and determine the time-varying characteristic parameters from the magnetic component, mechanical component, and thermal component, namely the parasitic capacitance non-linear coefficient, vibration transfer function, and thermal conductivity gradient. At the same time, a non-linear multi-body coupling state equation is constructed to determine the corresponding compensation amount, and mechanical compensation, capacitance compensation, and optical control tuning are coordinated according to the compensation amount to reduce frequency offset.

[0066] Embodiment 1

[0067] Reference Figures 1-4 , this embodiment provides a method for automatic tuning and calibration of crystal resonators. The method for automatic tuning and calibration of crystal resonators includes the following steps:

[0068] Step S1: Generate a multi-physical field coupling matrix. That is, through the constructed quantum dot sensor array, obtain the electromagnetic field intensity, mechanical vibration mode, and temperature gradient distribution, obtain the coupled field fluctuation signal through a superconducting detector, and at the same time, according to the obtained electromagnetic field intensity, mechanical vibration mode, temperature gradient distribution, and coupled field fluctuation signal, construct the three-dimensional spatial distribution of the electromagnetic-mechanical-thermal coupled field to generate a multi-physical field coupling matrix. Specifically as follows:

[0069] Step S1.1: Deployment of the sensor array. That is, deploy quantum dot sensors at the geometric key points (such as electrode edges, vibration nodes, heat conduction paths) of the crystal resonator array to form a spatial sampling grid. Specifically, 6 quantum dot sensors are deployed around each resonator, with 2 quantum dot sensors arranged on each side of the electrode and 1 quantum dot sensor arranged on each of the upper and lower surfaces. It should be noted that the distance between adjacent two sensors is set to the sub-micron level, such as 200 nm, so as to cover the electromagnetic field gradient and mechanical vibration mode.

[0070] Furthermore, through the set quantum dot sensor array, obtain the corresponding electromagnetic field intensity, mechanical vibration, and temperature gradient, specifically:

[0071]

[0072] wherein: is the energy level splitting value of the quantum dot, is the electric dipole moment, is the local electric field strength, is the second-order polarizability, is the quantum dot energy level shift caused by strain, is the deformation potential constant, is the strain tensor, is the thermionic emission current, is the effective Richardson constant, is the absolute temperature, is the base of the natural logarithm, is the work function, is the Boltzmann constant.

[0073] In the process of specific implementation, the Stark effect of the quantum dot is utilized to measure the electric field strength through the photoluminescence frequency shift. The electric field strength in the electrode gap is 1.2×10 6 V / m ± 0.3%. Further, based on the energy band offset caused by lattice deformation, the strain is measured through Raman spectroscopy. The strain at the root of the cantilever is 0.05% ± 0.005%. Further, the temperature is measured through the thermionic emission current, sampled at a sampling interval of 1 ms with a gradient resolution of 0.1 K / μm. The temperature gradient near the heat source is 50 K / mm ± 0.5 K / mm.

[0074] Step S1.2: Set the superconducting detector. That is, the probe of the superconducting detector is placed close to the surface of the resonator to detect the alternating magnetic field caused by electromagnetic coupling. At the same time, the distance between the probe and the surface of the resonator is not greater than 10 μm, and the sampling frequency is set to 10 times the operating frequency of the resonator to capture transient fluctuations.

[0075] In this embodiment, the integral quantity of the magnetic field in the superconducting loop is obtained through the magnetic field strength in the superconducting loop of the superconducting detector, so as to obtain the voltage response caused by the change in magnetic flux and obtain the output voltage of the superconducting detector. Specifically:

[0076]

[0077] wherein: is the output voltage of the superconducting detector, is the change in magnetic flux, is the total magnetic flux in the superconducting loop.

[0078] Further, the formula for obtaining the total magnetic flux in the superconducting loop is specifically:

[0079]

[0080] Wherein: is the total magnetic flux in the superconducting ring, is the magnetic flux quantum number, is the magnetic flux quantum in the superconducting ring.

[0081] In the process of specific implementation, during the signal capture of the superconducting detector, it is synchronized with the clock of the quantum dot sensor to capture the magnetic field fluctuations in the electrode gap, specifically 5*10 -15 T, and the corresponding electric field fluctuation is 1.5 V / m.

[0082] Step S1.3: Perform three-dimensional field reconstruction. That is, according to the electromagnetic field intensity, mechanical vibration, and temperature gradient obtained in step S1.1, and the output voltage obtained in step S1.2, fuse them to obtain a joint observation matrix. At the same time, according to the joint observation matrix, construct an optimization problem and establish a coupling matrix. Specifically as follows:

[0083] Step S1.3.1: Construct a joint observation matrix. That is, through N quantum dot sensors set, three types of physical quantities are obtained, namely electromagnetic field intensity, mechanical vibration, and temperature gradient. That is to say, according to the quantum dot sensor array in step S1.1, the corresponding electromagnetic field intensity, mechanical vibration, and temperature gradient are obtained, that is, the corresponding quantum dot sensor data is .

[0084] Furthermore, through M probes of the superconducting detector, detector data is obtained within T time points, that is, the output voltage of the superconducting detector. That is to say, according to the superconducting detector in step S1.2, the corresponding output voltage of the superconducting detector is obtained, that is, the corresponding detector data is .

[0085] Furthermore, fuse the quantum dot sensor data and the detector data to obtain a joint observation matrix, that is .

[0086] Specifically, fuse the quantum dot sensor data and the detector data through the three-dimensional field to be reconstructed to obtain the final measurement matrix, that is . That is to say, the acquisition formula of the joint observation matrix is specifically:

[0087]

[0088] Wherein: is the joint observation matrix, is the measurement matrix, is the three-dimensional field to be reconstructed, is the noise term.

[0089] In the process of specific implementation, 100 quantum dot sensors are set, and each quantum dot sensor collects 3 types of data. Therefore, the quantum dot sensor data is . At the same time, the superconducting detector is provided with 10 probes, and 1000 time points are set within 1ms. Therefore, the detector data is .

[0090] Step S1.3.2: Determine the sparse coefficient vector. That is, through the constructed wavelet transform matrix , and at the same time, according to the joint observation matrix obtained in step S1.3.1, an optimization problem is constructed, specifically:

[0091]

[0092] Where: is the joint observation matrix, is the measurement matrix, is the wavelet transform matrix, is the sparse coefficient vector, is the regularization parameter, is the square of the L2 norm, is the L1 norm.

[0093] Step S1.3.3: Establish the coupling matrix. That is, according to the sparse coefficient vector determined in step S1.3.2, and at the same time, combine it with the obtained electromagnetic field intensity, mechanical vibration and temperature gradient to establish the coupling matrix and obtain the total coupling strength between different resonators.

[0094] In this embodiment, the acquisition formula of the coupling matrix is specifically:

[0095]

[0096] Where: is the total coupling strength between the i-th resonator and the j-th resonator, is all regions in the crystal resonator array that have a significant impact on coupling, is the electromagnetic coefficient, is the electric field strength of the i-th resonator, is the electric field strength of the j-th resonator, is the mechanical coefficient, is the mechanical strain field distribution of the i-th resonator, is the mechanical strain field distribution of the j-th resonator, is the thermal coupling coefficient, is the temperature gradient of the i-th resonator, is the temperature gradient of the j-th resonator, is the gap volume between the electrodes.

[0097] In the process of specific implementation, the electromagnetic coefficient is set to 8.85*10 -12 F / m, the mechanical coefficient is set to 5 eV, and the thermal coupling coefficient is set to 0.01 W / (m·K). Therefore, the coupling strength between the first resonator and the second resonator is 2.1 fF ± 0.05 fF.

[0098] Step S2: Determine the compensation amount. That is, according to the coupling matrix constructed in step S1.3.2, obtain the time-varying characteristic parameters in the magnetic component, mechanical component, and thermal component, and construct a nonlinear multi-body coupling state equation based on the time-varying characteristic parameters, so as to determine the corresponding compensation amount. Specifically as follows:

[0099] Step S2.1: Extract the time-varying characteristic parameters. That is, according to the coupling matrix established in step S1.3.3, obtain the reconstructed electromagnetic field, mechanical strain field, and temperature field, and separate the reconstructed electromagnetic field, mechanical strain field, and temperature field into magnetic components, mechanical components, and thermal components through wavelet transform.

[0100] Furthermore, from the separated magnetic component, mechanical component, and thermal component, extract the corresponding time-varying characteristic parameters, that is, obtain the parasitic capacitance nonlinear coefficient, vibration transfer function, and thermal conductivity gradient. Specifically:

[0101]

[0102] Among them: is the time-varying parasitic capacitance, is the vacuum permittivity, is the relative permittivity, is the gap between the electrodes, is the time-varying value of the electrode spacing, is the electric field strength of the i-th resonator, is the electric field strength of the j-th resonator, is the gap volume between the electrodes, is the vibration transfer function, is the time-varying quality factor, is the excitation frequency, is the time-varying resonance frequency, is the temperature gradient of the resonator, is the small distance increment in the x direction in the temperature field, is the small distance increment in the y direction in the temperature field, is the small distance increment in the z direction in the temperature field, is the temperature at the spatial point (x, y, z) in the temperature field.

[0103] During the specific implementation process, the parasitic capacitance between the electrodes will be dynamically adjusted according to the temperature gradient and the electric field distribution. In this embodiment, the initial distance between the electrodes is 200 nm. When the temperature rises to 10 K, the time-varying value of the electrode distance is 200.0052 nm. Further, the gap between the electrodes is set to 1 μm. 3 , the vacuum permittivity is set to 8085×10 -12 F / m, the relative permittivity is set to 3.9. At the same time, the initial time-varying parasitic capacitance is 2.1 fF. When the temperature rises to 10 K, the time-varying parasitic capacitance is 2.5 fF. Further, the initial time-varying quality factor is set to 1000. Since the increase in temperature will lead to an increase in damping, the time-varying quality factor is set to 800, and the time-varying resonance frequency is 4.98 MHz. Further, the temperature gradient value of the initial gradient at the heat source center is the largest, which is 0.8 K / μm. Then, after 1 ms, it diffuses to 0.3 K / μm.

[0104] Step S2.2: Construct a non-linear multi-body coupling state equation. That is, through the parasitic capacitance non-linear coefficient, vibration transfer function, and thermal conductivity gradient obtained in step S2.1, construct a non-linear multi-body coupling state equation, specifically:

[0105]

[0106] Where: is the driving function of the charge change, is the time-varying coupling coefficient, is the charge quantity of the resonator, is the displacement generated during the mechanical vibration of the resonator, is the effective mass of the vibrating part of the resonator, is the vibration time of the resonator, is the damping coefficient, is the elastic coefficient, is the driving force function, is the density of the resonator material, is the specific heat capacity at constant pressure, is the local temperature of the material, is the heat conduction term, is the thermal conductivity, is the temperature gradient of the resonator, is the heat source term.

[0107] Step S2.3: Generate global optimization instructions. That is, through the non-linear multi-body coupling state equation constructed in step S2.2, perform electromagnetic regulation, electronic control capacitance compensation, and mechanical stress compensation. Specifically as follows:

[0108] Step S2.3.1: Refractive index modulation of the metasurface. That is, by dynamically modulating the refractive index of the metasurface, the electric field at the electrode edge is suppressed, the parasitic capacitance is reduced, and the electromagnetic coupling interference is decreased. Specifically, a quartz substrate material is covered on the surface of the liquid crystal layer, and the electrode structure is set as an interdigital electrode with a spacing of 200 mm. At the same time, the liquid crystal cell size is set to 10*10 μm 2 , and they are arranged in an array to cover the electrode edge. Further, the metasurface structure is composed of liquid crystal cells, and the arrangement direction of molecules in each cell can be controlled by voltage to change the equivalent refractive index.

[0109] In this embodiment, the refractive index change of the liquid crystal molecules satisfies the following formula, specifically:

[0110]

[0111] Where: is the refractive index change amount, is the extraordinary light refractive index, is the ordinary light refractive index, is the applied driving voltage, is the threshold voltage.

[0112] During the specific implementation process, the extraordinary light refractive index is set to 1.7, the ordinary light refractive index is set to 1.5. Then, when the applied driving voltage is 2 times the threshold voltage, the refractive index change amount is 0.1.

[0113] Further, since the electric field strength at the electrode edge is inversely proportional to the refractive index, that is, when the electric field strength at the electrode edge drops by 5%, the refractive index will rise by 5%. At the same time, the parallel plate capacitance is inversely proportional to the spacing, specifically:

[0114]

[0115] Where: is the time-varying parasitic capacitance, is the vacuum permittivity, is the relative permittivity, is the effective area of the electrode, is the equivalent electrode spacing after refractive index modulation.

[0116] During the specific implementation process, the initial time-varying parasitic capacitance is 2.5 fF, and at the same time, the initial equivalent electrode spacing is 200 nm, and the effective area of the electrode is 10*10 μm 2 , then the equivalent electrode spacing after refractive index modulation is 310 nm, and the time-varying parasitic capacitance is 1.75 fF, that is, it has decreased by 30%.

[0117] Step S2.3.2: Electrically controlled capacitor compensation. That is, by adjusting the ferroelectric domain wall switching threshold voltage, the parasitic capacitance deviation is compensated to stabilize the resonance frequency. Specifically, according to the actually obtained time-varying parasitic capacitance, the capacitance deviation is obtained, and based on the obtained capacitance deviation, the threshold voltage is adjusted. Specifically:

[0118]

[0119] Where: is the threshold voltage, is the capacitance deviation.

[0120] During the specific implementation process, the capacitance deviation is set to 0.3 fF, and the threshold voltage is 0.53 V. That is, the threshold voltage is output to the ferroelectric domain wall memory through a digital-to-analog converter, and the domain wall state is switched to adjust the equivalent capacitance.

[0121] Step S2.3.3: Mechanical stress compensation. That is, the frequency shift caused by mechanical strain is offset by the displacement of the MEMS actuator. Specifically, the local strain is measured by a quantum dot sensor, and based on the local strain, the displacement offset is determined. At the same time, based on the displacement offset, the magnitude of the applied voltage in the MEMS actuator is determined. Specifically:

[0122]

[0123] Where: is the applied voltage in the EMS actuator, is the piezoelectric drive coefficient, is the displacement offset.

[0124] During the specific implementation process, the displacement offset is set to 10 nm, the piezoelectric drive coefficient is set to 50 V / μm, and the applied voltage in the EMS actuator is 0.5 V.

[0125] Step S3: Multidimensional collaborative compensation. That is, through metasurface refractive index modulation, electrically controlled capacitor compensation, and mechanical stress compensation, mechanical compensation, capacitor compensation, and optical control tuning are carried out in sequence. Through the collaborative compensation between multiple actuators, the frequency deviation is reduced. Specifically as follows:

[0126] Step S3.1: Mechanical compensation. That is, according to the magnitude of the applied voltage determined in the MEMS actuator, the DAC module inputs a voltage with the same magnitude as the applied voltage to the MEMS actuator and makes it generate a reverse displacement.

[0127] Reference Figure 2 , Figure 2 is the mechanical compensation effect analysis diagram, from Figure 2It can be seen that the compensation starts at the 3rd minute, that is, the system responds quickly after detecting the deviation. Further, the MEMS actuator performs a reverse displacement of -2.6 nm to completely offset the frequency deviation caused by thermal expansion.

[0128] Step S3.2: Capacitance compensation. That is, the capacitance deviation is obtained through the quantum dot sensor array, and the threshold voltage to be adjusted is determined according to the adjustment formula of the threshold voltage. Further, according to the threshold voltage to be adjusted, a voltage of the same magnitude as the threshold voltage is input to the ferroelectric domain wall memory through the DAC module and it is switched to the domain wall state.

[0129] Step S3.3: Optical control tuning. That is, the phase change of the microring resonator is obtained according to the equivalent inductance change generated by the thermo-optic effect of the optical control microring. Further, a current is applied through the microheater to change the refractive index of the liquid crystal molecules and adjust the resonant wavelength.

[0130] Reference Figure 3 , Figure 3 is the analysis diagram of the collaborative compensation effect of capacitance and optical control. It can be seen from Figure 3 that the capacitance compensation starts at the 6th minute, continuously providing a correction amount of +13 ppm. At the same time, the optical control compensation starts at the 8th minute, superimposing a correction amount of +13 ppm. Specifically, the capacitance compensation offsets the parasitic capacitance deviation by adjusting the ferroelectric domain wall threshold voltage. The optical control compensation indirectly corrects the frequency by changing the equivalent inductance through the microring phase adjustment.

[0131] Step S3.4: Collaborative compensation. That is, according to the mechanical compensation in step S3.1, the capacitance compensation in step S3.2, and the optical control tuning in step S3.3, the timing synchronization is controlled by the FPGA to trigger the corresponding mechanical compensation, capacitance compensation, and optical control tuning in a time-sharing manner. It should be noted that the mechanical compensation, capacitance compensation, and optical control tuning are triggered for compensation in sequence, and are synchronized through the PLL phase-locked loop.

[0132] Reference Figure 4 , Figure 4 is the analysis diagram of the coordination effect of multiple actuators. It can be seen from Figure 4 that when the temperature rises to 10 K, it causes the frequency to continuously shift by -26 ppm. At the same time, starting from the 3rd minute, the MEMS actuator completely offsets the thermal expansion deviation through reverse displacement, and the frequency returns to 0 ppm. Starting from the 6th minute, the capacitance compensation is carried out to correct +13 ppm to solve the residual deviation or new disturbance. Starting from the 8th minute, the optical control compensation is carried out to further correct +13 ppm to ensure the frequency stability. And after all the compensations are superimposed, the total frequency deviation is zero. That is to say, the multi-actuator phased collaboration can gradually correct the complex environmental interference (thermal, electrical, and optical coupling) and finally achieve zero deviation.

[0133] This embodiment also provides a crystal resonator automatic tuning and calibration system, which uses the above-mentioned crystal resonator automatic tuning and calibration method.

[0134] Embodiment 2

[0135] This embodiment provides a crystal resonator automatic tuning and calibration method. The specific implementation method is the same as that of Embodiment 1. The difference is that the constructed non-linear multi-body coupling state equation is verified to ensure the accuracy of the non-linear multi-body coupling state equation. The present invention will be illustrated below in conjunction with the specific implementation manners of this embodiment.

[0136] In this embodiment, the verification of the non-linear multi-body coupling state equation is as follows:

[0137] The resonator is placed in a temperature control chamber and heated to 10K at a rate of 1K / min and kept stable. Further, frequency sampling is performed through a high-precision frequency counter, such as a frequency counter of model Keysight 53230A with a resolution of 0.001ppm. At the same time, the resonance frequency is recorded every 10 seconds for 10 minutes. At the same time, through the established non-linear multi-body coupling state equation, the temperature gradient is set to 10K to calculate the corresponding frequency drift.

[0138] Further, referring to Figure 5 , Figure 5 is the verification curve graph of temperature and frequency drift. The solid curve is the measured temperature change, the dashed curve is the frequency drift predicted by the non-linear multi-body coupling state equation, and the scatter curve is the data points of the measured frequency drift. It can be seen from Figure 5 that:

[0139] The solid curve gradually heats up from the initial temperature of 293K to 303K and remains stable at 303K, that is, the actual temperature control system has a gradual heating characteristic and is not an instantaneous mutation. The frequency drift predicted by the non-linear multi-body coupling state equation is stable at -100ppm, while the measured frequency drift is stable at -98ppm, and the error between it and the frequency drift predicted by the non-linear multi-body coupling state equation is 2%.

[0140] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended embodiments and their equivalents.

Claims

1. An automatic tuning and calibration method for a crystal resonator, characterized in that, It includes: S1: Generate a multi-physical-field coupling matrix: Through a quantum dot sensor array, obtain the electromagnetic field intensity, mechanical vibration mode, and temperature gradient distribution, construct the three-dimensional spatial distribution of the electromagnetic-mechanical-thermal coupling field, and generate a multi-physical-field coupling matrix; S2: Determine the compensation amount: According to the multi-physical-field coupling matrix, determine the time-varying characteristic parameters in the magnetic component, mechanical component, and thermal component, and construct a non-linear multi-body coupling state equation according to the time-varying characteristic parameters to determine the corresponding compensation amount; S3: Multi-dimensional collaborative compensation: According to the compensation amount, perform mechanical compensation, capacitive compensation, and optical control tuning respectively, and perform collaborative compensation through multiple actuators, including: S3.1: Mechanical compensation: According to the applied voltage in the MEMS actuator, the DAC module inputs a voltage with the same magnitude as the applied voltage to the MEMS actuator; S3.2: Capacitive compensation: According to the threshold voltage to be adjusted, the DAC module inputs a voltage with the same magnitude as the threshold voltage to the ferroelectric domain wall memory and converts the state of the ferroelectric domain wall memory into a domain wall state; S3.3: Optical control tuning: According to the equivalent inductance change generated by the thermo-optic effect of the optical control micro-ring, obtain the phase change of the micro-ring resonator, and according to the phase change, apply a current through the micro-heater to change the refractive index of the liquid crystal molecules and adjust the resonance wavelength; S3.4: Collaborative compensation: Integrate the mechanical compensation, capacitive compensation, and optical control tuning, and perform timing synchronization through FPGA control.

2. The automatic tuning and calibration method of a crystal resonator according to claim 1, characterized in that, Generating a multi-physical-field coupling matrix includes: S1.1: Sensor array deployment: According to the geometric structure of the crystal resonator array, set the quantum dot sensor array to obtain the corresponding electromagnetic field intensity, mechanical vibration, and temperature gradient. Specifically: Wherein: is the energy level splitting value of the quantum dot, is the electric dipole moment, is the local electric field strength, is the second-order polarizability, is the quantum dot energy level shift caused by strain, is the deformation potential constant, is the strain tensor, is the thermionic emission current, is the effective Richardson constant, is the absolute temperature, is the base of the natural logarithm, is the work function, is the Boltzmann constant; S1.2: Set the superconducting detector: Through the probe of the superconducting detector, obtain the integral of the magnetic field in the superconducting ring and determine the output voltage of the superconducting detector. Specifically: Wherein: is the output voltage of the superconducting detector, is the change in magnetic flux, is the total magnetic flux in the superconducting loop; S1.3: Perform three-dimensional field reconstruction: Integrate the electromagnetic field intensity, mechanical vibration, temperature gradient, and the output voltage of the superconducting detector to obtain a joint observation matrix and establish a coupling matrix.

3. A method for automatically tuning and calibrating a crystal resonator according to claim 2, characterized in that Establishing a coupling matrix includes: S1.3.1: Construct a joint observation matrix: Through the electromagnetic field intensity, mechanical vibration, and temperature gradient, obtain the quantum dot sensor data, and through the output voltage of the superconducting detector, obtain the detector data. At the same time, according to the quantum dot sensor data and the detector data, obtain the joint observation matrix. Specifically: Wherein: is the joint observation matrix, is the measurement matrix, is the three-dimensional field to be reconstructed, is the noise term; S1.3.2: Determine the sparse coefficient vector: Construct an optimization problem through the constructed wavelet transform matrix and the joint observation matrix. Specifically: Wherein: is the joint observation matrix, is the measurement matrix, is the wavelet transform matrix, is the sparse coefficient vector, is the regularization parameter, is the square of the L2 norm, is the L1 norm; S1.3.3: Establish a coupling matrix: Combine the sparse coefficient vector with the electromagnetic field intensity, mechanical vibration, and temperature gradient to establish a coupling matrix. Specifically: Wherein: is the total coupling strength between the i-th resonator and the j-th resonator, is all regions in the crystal resonator array that have a significant impact on coupling, is the electromagnetic coefficient, is the electric field strength of the i-th resonator, is the electric field strength of the j-th resonator, is the mechanical coefficient, is the mechanical strain field distribution of the i-th resonator, is the mechanical strain field distribution of the j-th resonator, is the thermal coupling coefficient, is the temperature gradient of the i-th resonator, is the temperature gradient of the j-th resonator, is the gap volume between the electrodes.

4. A method for automatically tuning and calibrating a crystal resonator according to claim 1, characterized in that, Determining the corresponding compensation amount includes: S2.1: Extract time-varying characteristic parameters: Through the coupling matrix, obtain the reconstructed electromagnetic field, mechanical strain field, and temperature field, and extract time-varying characteristic parameters. Specifically: Wherein: is the time-varying parasitic capacitance, is the vacuum permittivity, is the relative permittivity, is the gap between the electrodes, is the time-varying value of the electrode spacing, is the electric field strength of the i-th resonator, is the electric field strength of the j-th resonator, is the volume of the gap between the electrodes, is the vibration transfer function, is the time-varying quality factor, is the excitation frequency, is the time-varying resonance frequency, is the temperature gradient of the resonator, is the small distance increment in the x direction in the temperature field, is the small distance increment in the y direction in the temperature field, is the small distance increment in the z direction in the temperature field, is the temperature at the spatial point (x, y, z) in the temperature field; S2.2: Construct a non - linear multi - body coupling state equation: According to the time - varying characteristic parameters, construct a non - linear multi - body coupling state equation, specifically: Wherein: is the driving function of the charge change, is the time-varying coupling coefficient, is the electric charge quantity of the resonator, is the displacement generated during the mechanical vibration of the resonator, is the effective mass of the vibrating part of the resonator, is the vibration time of the resonator, is the damping coefficient, is the elastic coefficient, is the driving force function, is the density of the resonator material, is the specific heat capacity at constant pressure, is the local temperature of the material, is the heat conduction term, is the thermal conductivity, is the temperature gradient of the resonator, is the heat source term; S2.3: Generate a global optimization instruction: According to the non - linear multi - body coupling state equation, perform electromagnetic regulation, electrically controlled capacitor compensation, and mechanical stress compensation.

5. A method for automatic tuning and calibration of a crystal resonator according to claim 4, characterized in that, Performing electromagnetic regulation, electrically controlled capacitor compensation, and mechanical stress compensation includes: S2.3.1: Metasurface refractive index modulation: By dynamically modulating the refractive index of the metasurface, suppress the electric field at the electrode edge, reduce the parasitic capacitance. At the same time, the parallel - plate capacitance is inversely proportional to the spacing, specifically: Wherein: is a time-varying parasitic capacitance, is the vacuum permittivity, is the relative permittivity, is the effective area of the electrode, is the equivalent electrode spacing after refractive index modulation; S2.3.2: Electrically controlled capacitor compensation: By adjusting the ferroelectric domain wall switching threshold voltage, and at the same time, according to the capacitance deviation, adjust the threshold voltage, specifically: Wherein: is the threshold voltage, is the capacitance deviation; S2.3.3: Mechanical stress compensation: By the displacement of the MEMS actuator, offset the frequency shift caused by mechanical strain. At the same time, the magnitude of the applied voltage in the MEMS actuator, specifically: Wherein: is the applied voltage in the EMS actuator, is the piezoelectric drive coefficient, is the displacement offset.

6. The automatic tuning and calibration method of a crystal resonator according to claim 5, wherein The change in the refractive index of the metasurface satisfies the following formula, specifically: Wherein: is the refractive index change amount, is the extraordinary light refractive index, is the ordinary light refractive index, is the applied driving voltage, is the threshold voltage.

7. A method for automatic tuning and calibration of a crystal resonator according to claim 1, characterized in that The mechanical compensation, capacitor compensation, and optical control tuning are triggered for compensation in sequence and synchronized through a PLL phase - locked loop.

8. An automatic tuning and calibration system for a crystal resonator, characterized in that, An automatic tuning and calibration method for a crystal resonator as claimed in any one of claims 1 - 7 is used.

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