CN116558548A - Stable amplitude control system of high-Q MEMS resonator - Google Patents
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Abstract
The invention discloses a stable amplitude control system of a high-Q MEMS resonator, which is a digital closed-loop driving system taking a field programmable gate array as a control platform and adopting a DDS-PLL technology as a control scheme. The system realizes tracking of the vibration resonance frequency and the phase of the gyroscope by utilizing a digital phase-locked loop based on frequency synthesis of a DDS algorithm, the structure can provide a high-resolution frequency signal by utilizing the DDS algorithm to ensure small enough frequency stepping, and meanwhile, the bandpass characteristic of the PLL can well inhibit partial spurious in a DDS output frequency spectrum, so that the advantage complementation of the DDS and the PLL is realized, the dynamic performance of a high-Q MEMS resonator control system is improved, the stable precision of the amplitude and the frequency of the MEMS gyroscope is optimized, and the zero-bias output and the anti-interference capability of the MEMS gyroscope are further improved.
Description
Technical Field
The invention belongs to the technical field of error signal processing, and particularly relates to a stable amplitude control system of a high-Q MEMS resonator.
Background
With the development of micromachining technology, MEMS silicon micromachined gyroscopes have been widely used in the fields of industrial automation, inertial navigation, automotive electronics, and the like. Compared with fiber optic gyroscopes and laser gyroscopes, the MEMS silicon micromechanical gyroscope has the advantages of small volume, high reliability, low cost, mass production and the like. However, due to the processing errors and the susceptibility of weak signals to interference, the precision of the MEMS silicon micromechanical gyroscope is still at a low level at present, so how to improve the precision of the MEMS gyroscope is the main direction of research at present. The MEMS gyroscope works based on the Coriolis force principle, and the driving vibration amplitude and frequency are known according to the Coriolis force formula to directly influence the scale factor and zero bias performance of the MEMS gyroscope, so that the stability of the driving mode of the gyroscope is a key premise for realizing a high-precision gyroscope.
At present, a driving circuit of a silicon micromechanical gyroscope adopts a closed-loop driving mode, wherein driving amplitude stabilization is realized based on an AGC technology, and a scheme for realizing frequency control based on a PLL technology is mature, but because the existing MEMS gyroscope adopts a vacuum packaging technology, the Q value of the MEMS gyroscope is greatly improved, the mechanical thermal noise of the gyroscope is reduced, the resonance peak of a driving mode of the high Q value MEMS resonator with a quality factor between 10000 and 1000000 is very high, the bandwidth of a waveform is very narrow, therefore, small frequency drift can cause great change of the output amplitude, difficulty is increased for amplitude and frequency control of the driving mode, the original control scheme can not meet the requirement of control precision, the stability of a system on the driving mode control is reduced, and the requirement of the driving mode stability of the gyroscope can be met only by further improving the control precision of the system. When the gyro driving force is increased to be large enough, the driving capacitance of the MEMS gyroscope presents nonlinearity to the variation of the driving displacement, so that the phase angle condition and the gain condition of the AGC loop are mutually coupled, the control effect of the system is poor, the traditional PLL loop adopts the CORDIC algorithm to carry out frequency control, and the control precision is limited by iteration times, the frequency resolution is not high because the algorithm belongs to a numerical linear calculation approximation algorithm, and the PLL technology has the defects of long frequency conversion time and poor phase noise when the output step length is small. Therefore, it is necessary to provide a stable amplitude control method for a novel high Q MEMS resonator.
Disclosure of Invention
The invention aims to provide a stable amplitude control method of a high-Q MEMS resonator, which solves the problem that the control precision of the existing MEMS gyroscope closed-loop driving control circuit for the high-Q MEMS resonator is insufficient. On the basis of the existing MEMS gyroscope driving closed-loop system, the high frequency resolution is obtained through the DDS-PLL mixed frequency synthesis technology, and the high-precision control of the gyroscope driving mode is realized, so that the overall stability and the anti-interference capability of the gyroscope are improved.
The technical solution for realizing the purpose of the invention is as follows: a stable amplitude control system for a high Q MEMS resonator, the system comprising an AGC loop and a digital phase locked loop;
the AGC loop is used for controlling driving amplitude;
the digital phase-locked loop is used for controlling the resonant frequency;
the AGC loop comprises a first multiplication demodulation unit, a first low-pass filtering unit and a first PI control unit which are connected in sequence; the method comprises the steps that digital signals corresponding to a driving mode of the MEMS resonator are subjected to amplitude demodulation through a first multiplication demodulation unit, amplitude information of the MEMS resonator when the demodulated output signals work is obtained through a first low-pass filtering unit, the amplitude is compared with a reference value set by a system to obtain an amplitude deviation signal, a first PI control unit outputs an amplitude control quantity according to the amplitude deviation signal, namely, the amplitude gain of the system is achieved, an alternating current driving force is formed and fed back to a driving electrode, and amplitude closed-loop control is achieved;
the digital phase-locked loop comprises a second multiplication demodulation unit and a second low-pass filtering unit which are connected in sequenceThe direct digital synthesis DDS algorithm frequency synthesis unit and the voltage-controlled oscillator DCO unit form a phase discriminator; the digital signals corresponding to the MEMS resonator driving modes are subjected to phase deviation signals through a second multiplication demodulation unit and a second low-pass filtering unit, and then frequency control signals delta omega are generated through a second PI control unit and are output to a direct digital synthesis DDS algorithm frequency synthesis unit; the direct digital synthesis DDS algorithm frequency synthesis unit outputs a frequency control signal delta omega 0 As an input signal of a voltage-controlled oscillator (DCO) unit, the DCO unit generates sine and cosine signals with resonant frequency, and then the phase error signals obtained by the DCO unitAnd the feedback is fed back to the output end of the phase discriminator so as to form closed loop control, and finally, the output frequency signal and the amplitude control quantity of the AGC loop generate driving feedback force to realize the driving amplitude stabilization of the MEMS gyroscope.
Further, the direct digital synthesis DDS algorithm frequency synthesis unit comprises an FPGA frequency control word conversion unit, a phase accumulator, a waveform memory ROM, a digital low-pass filter and a system clock; the FPGA frequency control word conversion unit converts the frequency control signal delta omega output by the second PI control unit into a corresponding frequency control word M, wherein the conversion coefficient is K f The method comprises the steps of carrying out a first treatment on the surface of the Driven by the system clock, the phase accumulator linearly accumulates the frequency control word M while accumulating the frequency control word M for 2 N Taking the modulus operation, and taking the obtained sum as a phase value, wherein N is the word length of the phase accumulator; the binary phase addressing code output by the phase accumulator is sent to a waveform memory ROM for addressing, so that the binary phase addressing code outputs a corresponding discrete amplitude sequence, and then the discrete amplitude sequence waveform is smoothed by a digital low-pass filter to obtain a required frequency waveform.
Further, the frequency resolution of the output of the direct digital synthesis DDS algorithm frequency synthesis unit depends on the greater the number of bits N, N of the phase accumulator, the higher the frequency resolution.
Further, the minimum frequency resolution Δf output by the direct digital synthesis DDS algorithm frequency synthesis unit min The sum phase accumulator bit number N satisfies:
wherein f c Representing the system clock frequency, P representing the frequency division ratio of the phase locked loop, and R representing the reference frequency division ratio.
Further, the phase accumulator averages every 2 N The M clock cycles overflow once, and the frequency value delta f output by the direct digital synthesis DDS algorithm frequency synthesis unit can be obtained through the value of M in the system at the moment 0 The relationship between them satisfies:
further, the first low-pass filtering unit and the second low-pass filtering unit adopt FIR digital low-pass filters designed by a Kaiser window function design method.
Further, the parameters of the FIR digital low-pass filter include: the center frequency is set to be 500kHz, the passband frequency is set to be 500Hz, the stopband frequency is set to be 14kHz, the stopband attenuation is greater than 50dB, and the final order is 109; the total length D of the Kaiser window function satisfies:
wherein A is s Representing the stop band attenuation, Δf represents the normalized transition bandwidth.
Further, the digital phase-locked loop outputs phase noise L of the frequency signal o The following formula is satisfied:
L o ＝L DDS +20logP'
wherein L is DDS Frequency synthesis unit input representing direct digital synthesis DDS algorithmThe phase noise, P', is shown as the frequency multiplication times.
Compared with the prior art, the invention has the remarkable advantages that:
on the basis of the existing control method, on one hand, the voltage resolution of the frequency control signal of the original digital phase-locked loop is improved by generating the frequency control signal through the DDS circuit, so that the amplitude and the frequency of the driving mode of the gyroscope are controlled with higher precision, and the overall stability and the anti-interference capability of the gyroscope are improved. On the other hand, compared with the original PLL technology, the DDS-PLL hybrid technology integrates the respective advantages of the two technologies, has the characteristics of high precision, low phase noise, good spurious noise suppression effect and good broadband and spectrum quality, and improves the dynamic and steady state characteristics of the high-Q MEMS resonator amplitude stabilization system. Specifically:
(1) The digital phase-locked loop adopts a direct digital frequency synthesis technology DDS to generate a frequency control signal, the DDS circuit provides a high-precision voltage signal input for a voltage-controlled oscillator of the phase-locked loop, the DDS circuit has the advantages of small output step length and lower phase noise, but more spurious noise, and the PLL has poor phase noise when the output step length is small, but good suppression effect on spurious noise, and the scheme of realizing frequency synthesis by adopting the DDS and PLL mixed technology integrates the advantages of the two technologies, so that the system design meets the requirements of broadband and fast frequency conversion speed, is suitable for controlling a high-Q MEMS resonator, and realizes better control effect.
(2) The frequency resolution of the output of the DDS algorithm frequency synthesis unit adopted by the invention depends on the bit number N of the phase accumulator, and when N is large enough, the resolution accuracy which is difficult to realize by the traditional method can be obtained, and the highest resolution can reach a micro Hz level.
(3) The low-pass filter unit adopts an FIR digital low-pass filter which is designed independently, is easy to realize linear phase, is suitable for processing signals with higher phase requirements, and is selected by a Kaiser window function design method, and the method achieves good high-frequency inhibition effect through parameter estimation and optimization processing, does not attenuate low-frequency components and has good filter characteristics.
(4) The DDS is excited in the feedback channel of the closed-loop control systemAmplitude gain A formed by frequency signal output by PLL and AGC loop x As a feedback alternating current driving signal, the gyroscope driving mode obtains a resonance frequency signal with higher precision, and further the amplitude stability and the frequency stability of the high-Q MEMS resonator driving mode are improved.
The invention is described in further detail below with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of a MEMS gyroscope closed loop drive control in one embodiment.
Fig. 2 is a schematic diagram of a DDS system employed in one embodiment.
Fig. 3 is a simulation diagram of a DDS system employed in one embodiment.
Fig. 4 is a schematic waveform diagram of a DDS system according to an embodiment, where fig. (a) is a waveform diagram of a frequency required for DDS system synthesis, and fig. (b) is a power spectrum density diagram of a synthesized waveform.
Fig. 5 is a simulation diagram of a digital phase locked loop system in one embodiment.
Fig. 6 is a diagram of signal simulations before and after a FIR digital low-pass filter in one embodiment.
Fig. 7 is a schematic diagram of DDS-PLL technology in one embodiment.
FIG. 8 is a graph of the frequency characteristics of a closed loop drive system for a MEMS gyroscope in one embodiment.
FIG. 9 is a phase diagram of a MEMS gyroscope closed loop drive system in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
It should be noted that, if directional indications (such as up, down, left, right, front, and rear … …) are included in the embodiments of the present invention, the directional indications are merely used to explain the relative positional relationship, movement conditions, etc. between the components in a specific posture (as shown in the drawings), and if the specific posture is changed, the directional indications are correspondingly changed.
In addition, if there is a description of "first", "second", etc. in the embodiments of the present invention, the description of "first", "second", etc. is for descriptive purposes only and is not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In addition, the technical solutions of the embodiments may be combined with each other, but it is necessary to base that the technical solutions can be realized by those skilled in the art, and when the technical solutions are contradictory or cannot be realized, the combination of the technical solutions should be considered to be absent and not within the scope of protection claimed in the present invention.
In one embodiment, in conjunction with fig. 1, a method for controlling the stable amplitude of a high Q MEMS resonator is provided, which is a digital dual closed loop drive control system based on AGC technology and DDS-PLL frequency synthesis technology. The MEMS gyroscope driving mode is changed into a voltage signal V reflecting the displacement x through a displacement voltage conversion circuit, an analog signal is converted into a digital signal through ADC chip conversion, sin (ωt) and cos (ωt) signals are input into the analog signal through a multiplier respectively for amplitude demodulation and phase demodulation, and amplitude information and phase difference information of the MEMS resonator during working are obtained after the demodulated output signals pass through an FIR digital low-pass filter. The vibration amplitude is compared with a reference value A set by the system to obtain a deviation signal, and the PI controller outputs an amplitude control quantity according to the deviation signal, namely the amplitude gain A of the system x And an alternating current driving force is formed and fed back to the driving electrode, so that amplitude closed-loop control is realized. The phase deviation signal is obtained through demodulation and digital filtering, the frequency control signal delta omega is generated through PI control, and the frequency control signal delta omega with higher precision is output by adopting an FPGA control DDS algorithm 0 As the input signal of the voltage-controlled oscillator (DCO), the cosine signal cos (omega) with the resonance frequency is generated by the voltage-controlled oscillator (DCO) circuit d t), the phase error obtainedAnd feeding back to the output end of the phase discriminator through P frequency division to form a closed-loop control loop. Amplitude gain A formed by final output frequency signal and AGC loop x As a feedback AC drive signal, through DAC and voltage-electrostatic force conversion coefficient K vf The conversion of the MEMS gyroscope realizes the driving stable amplitude of the MEMS gyroscope.
Because the MEMS gyroscope has the characteristic of microminiaturization, the signal output during operation is very weak and is easy to be interfered by parasitic effect and the coupling effect of the driving electrode and the sensitive electrode, and in addition, the resonator with high Q value has the characteristics of high sensitivity and small mechanical bandwidth. Therefore, the control system needs to meet the characteristics of high control precision and good dynamic characteristics. The invention adopts DDS-PLL hybrid technology to improve the frequency resolution of the output signal, and has the advantages of rapid frequency conversion speed, low phase noise and frequency drift, easy integration and function expansion of the full-digital structure, and good broadband and spectrum quality besides improving the control precision of the system. The implementation principle of the DDS technology adopted is shown in fig. 2, and the DDS technology comprises a frequency control word conversion unit, a frequency word register, a phase accumulator, a sine lookup table ROM, a digital low-pass filter and a system clock, wherein M is a frequency control word, N is the word length of the phase accumulator, and M is the number of bits of ROM address lines. The frequency control signal delta omega output by the PI controller is converted into a corresponding frequency control word M through an FPGA control unit, wherein the conversion coefficient is K f . System clock f at 100MHz c Driven by (2), the phase accumulator linearly accumulates the frequency control word M, while for 2 N And taking the sum obtained by the modulo operation as a phase value, inquiring a sine function table ROM in a binary code form, converting phase information into a corresponding digital quantized sine amplitude value, smoothing the waveform by using a digital low-pass filter to obtain a required frequency waveform, and finally taking the frequency value processed by the DDS algorithm as an input control signal of the voltage-controlled oscillator. Wherein the phase accumulator averages every 2 N Overflow once per M clock cycles, thus frequency control word M and clock frequency f c The frequency value of the DDS output signal is reflected, and the output frequency value can be obtained by reading the value of M in the system at the momentΔf 0 The relationship between them satisfies:
the minimum frequency resolution of the DDS is related to the word length of the phase accumulator, and by selecting a proper word length N, the extremely high frequency resolution can be realized, and the maximum frequency resolution can reach a micro Hz level. By performing simulation analysis on the DDS system model, as shown in FIG. 3, it can be seen that the spectrum quality of the output signal is high and the spurious component is small.
The module for realizing the frequency control function of the system is a digital phase-locked loop link, and the frequency of the output signal is controlled by detecting the phase difference of the signals, so that the input signal and the output signal have the same frequency and phase information. The main module of the digital PLL comprises three parts, namely a phase detector, a PI controller and a voltage controlled oscillator (DCO), wherein the phase detector consists of a multiplier and an FIR digital low-pass filter, and a specific simulation model is shown in fig. 4.
The low-pass filter module adopts an autonomous FIR digital low-pass filter, so that the linear phase is easy to realize, the method is suitable for processing signals with higher phase requirements, the scheme selects a Kaiser window function design method, a good high-frequency inhibition effect is achieved through parameter estimation and optimization processing, low-frequency components are not attenuated, and the waveform amplitude after low-pass filtering and the waveform amplitude before filtering satisfy a double relation and an output curve is smooth, so that the filter has good filtering characteristics.
The DDS-PLL mixing technology adopted by the invention improves the frequency resolution of the control system and improves the dynamic and steady-state characteristics of the system. The vibration amplitude of the high-Q MEMS resonator is well controlled, and the amplitude and frequency stability of the driving detection output signal are improved. FIG. 6 is a schematic diagram of a DDS-PLL hybrid technique for high accuracy frequency control, driving modal displacement signals asWherein A is x (t) is vibrationAmplitude, omega of motion 0 Is the initial frequency of DCO, Δω is the frequency modulation amount output by PI controller, ++>Is the phase shift of the drive mode. Driving displacement signal and cos (omega) 0 Phase difference signal ++Deltaomega) t signal obtained by multiplying and phase demodulating and digital low-pass filtering>Is->The reference value of the PI controller is set to be 0 to adjust the delta omega, and then the FPGA is used for controlling the DDS algorithm to synthesize a higher-precision frequency control signal delta omega 0 As an input signal of the DCO circuit, a phase error signal obtained via a voltage controlled oscillator +.>And if the phase or frequency of the input signal changes, the output signal of the loop, namely the frequency and the phase of the voltage-controlled oscillator, is tracked by the feedback control of the voltage-controlled oscillator module. Wherein the voltage controlled oscillator outputs a phase +>And input control voltage v c (t) satisfies:
wherein D is 0 Indicating the voltage-controlled sensitivity of the voltage-controlled oscillator.
To further illustrate that the amplitude control system of the present invention has good dynamic and steady state characteristics, frequency characteristic analysis and phase trajectory diagram analysis were performed on the driven closed loop system, as shown in fig. 7 and 8. The frequency point with the amplitude-frequency response of-3 dB is 145Hz from the Bode diagram, so that the bandwidth of the closed-loop system is 145Hz, the bandwidth requirement of the high-Q MEMS resonator is met, and the system has higher robustness. From fig. 8, it can be known that the root track curves of the system are all located at the left half part of the virtual axis, two points from the pole to infinity, and one points from the pole to the zero, so that the stability of the system is not damaged by changing the loop gain. At low loop gains, the effect of poles away from the imaginary axis on the system is negligible, and the system characteristics are determined by the conjugate poles near the imaginary axis. When the loop gain is large, the pole close to the virtual axis will be cancelled by the zero to generate zero pole, and the system characteristic is determined by the conjugate pole far from the virtual axis. Obviously, the loop is more stable as the loop gain is greater.
The system provided by the invention realizes tracking of the vibration resonance frequency and the phase of the gyroscope by utilizing the digital phase-locked loop based on the frequency synthesis of the DDS algorithm, the structure can provide a high-resolution frequency signal by utilizing the DDS algorithm to ensure small enough frequency stepping, and meanwhile, the bandpass characteristic of the PLL can well inhibit partial spurious in the DDS output frequency spectrum, so that the advantage complementation of the DDS and the PLL is realized, the dynamic performance of a high-Q MEMS resonator control system is improved, the stable precision of the amplitude and the frequency of the MEMS gyroscope is optimized, and the zero-bias output and the anti-interference capability of the MEMS gyroscope are further improved.
The foregoing has outlined and described the basic principles, features, and advantages of the present invention. It will be understood by those skilled in the art that the foregoing embodiments are not intended to limit the invention, and the above embodiments and descriptions are meant to be illustrative only of the principles of the invention, and that various modifications, equivalent substitutions, improvements, etc. may be made within the spirit and scope of the invention without departing from the spirit and scope of the invention.
Claims (8)
1. A stable amplitude control system of a high Q MEMS resonator, the system comprising an AGC loop and a digital phase locked loop;
the AGC loop is used for controlling driving amplitude;
the digital phase-locked loop is used for controlling the resonant frequency;
the AGC loop comprises a first multiplication demodulation unit, a first low-pass filtering unit and a first PI control unit which are connected in sequence; the method comprises the steps that digital signals corresponding to a driving mode of the MEMS resonator are subjected to amplitude demodulation through a first multiplication demodulation unit, amplitude information of the MEMS resonator when the demodulated output signals work is obtained through a first low-pass filtering unit, the amplitude is compared with a reference value set by a system to obtain an amplitude deviation signal, a first PI control unit outputs an amplitude control quantity according to the amplitude deviation signal, namely, the amplitude gain of the system is achieved, an alternating current driving force is formed and fed back to a driving electrode, and amplitude closed-loop control is achieved;
the digital phase-locked loop comprises a second multiplication demodulation unit, a second low-pass filtering unit, a second PI control unit, a direct digital synthesis DDS algorithm frequency synthesis unit and a voltage-controlled oscillator DCO unit which are connected in sequence, wherein the second multiplication demodulation unit and the second low-pass filtering unit form a phase discriminator; the digital signals corresponding to the MEMS resonator driving modes are subjected to phase deviation signals through a second multiplication demodulation unit and a second low-pass filtering unit, and then frequency control signals delta omega are generated through a second PI control unit and are output to a direct digital synthesis DDS algorithm frequency synthesis unit; the direct digital synthesis DDS algorithm frequency synthesis unit outputs a frequency control signal delta omega 0 As an input signal of a voltage-controlled oscillator (DCO) unit, the DCO unit generates sine and cosine signals with resonant frequency, and then the phase error signals obtained by the DCO unitAnd the feedback is fed back to the output end of the phase discriminator so as to form closed loop control, and finally, the output frequency signal and the amplitude control quantity of the AGC loop generate driving feedback force to realize the driving amplitude stabilization of the MEMS gyroscope.
2. The stable amplitude control system of high Q MEMS resonator according to claim 1, wherein the direct digital synthesis DDS algorithm frequency synthesis unit comprises an FPGA frequency control word conversion unit, a phase accumulatorA waveform memory ROM, a digital low pass filter and a system clock; the FPGA frequency control word conversion unit converts the frequency control signal delta omega output by the second PI control unit into a corresponding frequency control word M, wherein the conversion coefficient is K f The method comprises the steps of carrying out a first treatment on the surface of the Driven by the system clock, the phase accumulator linearly accumulates the frequency control word M while accumulating the frequency control word M for 2 N Taking the modulus operation, and taking the obtained sum as a phase value, wherein N is the word length of the phase accumulator; the binary phase addressing code output by the phase accumulator is sent to a waveform memory ROM for addressing, so that the binary phase addressing code outputs a corresponding discrete amplitude sequence, and then the discrete amplitude sequence waveform is smoothed by a digital low-pass filter to obtain a required frequency waveform.
3. The stable amplitude control system of a high Q MEMS resonator according to claim 2, wherein the frequency resolution of the direct digital synthesis DDS algorithm frequency synthesis unit output depends on the number of bits N, N of the phase accumulator, the greater the frequency resolution.
4. A stable amplitude control system for high Q MEMS resonator according to claim 3, wherein the direct digital synthesis DDS algorithm frequency synthesis unit outputs a minimum frequency resolution Δf min The sum phase accumulator bit number N satisfies:
wherein f c Representing the system clock frequency, P representing the frequency division ratio of the phase locked loop, and R representing the reference frequency division ratio.
5. The stable amplitude control system of high Q MEMS resonator of claim 2, wherein the phase accumulator averages every 2 N The M clock cycles overflow once, and the frequency value delta f output by the direct digital synthesis DDS algorithm frequency synthesis unit can be obtained through the value of M in the system at the moment 0 The relationship between them is fullFoot:
6. the stable amplitude control system of a high Q MEMS resonator according to claim 1, wherein the first low pass filter unit and the second low pass filter unit employ FIR digital low pass filters designed by a Kaiser window function design method.
7. The stable amplitude control system of a high Q MEMS resonator of claim 6, wherein the parameters of the FIR digital low pass filter comprise: the center frequency is set to be 500kHz, the passband frequency is set to be 500Hz, the stopband frequency is set to be 14kHz, the stopband attenuation is greater than 50dB, and the final order is 109; the total length D of the Kaiser window function satisfies:
wherein A is s Representing the stop band attenuation, Δf represents the normalized transition bandwidth.
8. The stable amplitude control system of a high Q MEMS resonator of claim 1, wherein the digital phase locked loop outputs phase noise L of a frequency signal o The following formula is satisfied:
L o ＝L DDS +20logP'
wherein L is DDS The phase noise output by the direct digital synthesis DDS algorithm frequency synthesis unit is represented, and P' represents the frequency multiplication times.
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