CN116558548A - Stable amplitude control system of high-Q MEMS resonator - Google Patents

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

A Stable Amplitude Control System for High-Q MEMS Resonators

technical field

The invention belongs to the technical field of error signal processing, in particular to a stable amplitude control system of a high-Q value MEMS resonator.

Background technique

With the development of micromachining technology, MEMS silicon micromachined gyroscopes have been widely used in the fields of industrial automation, inertial navigation and automotive electronics. Compared with fiber optic gyroscopes and laser gyroscopes, MEMS silicon micromachined gyroscopes have the advantages of small size, high reliability, low cost, and mass production. However, due to processing errors and weak signals being easily disturbed, the accuracy of MEMS silicon micromachined gyroscopes is still at a relatively low level. Therefore, how to improve the accuracy of MEMS gyroscopes is the main direction of research. The MEMS gyroscope works on the basis of the Coriolis force principle. According to the Coriolis force formula, it is known that the driving vibration amplitude and frequency directly affect the scale factor and zero bias performance of the MEMS gyroscope. Maintaining the stability of the gyro drive mode is the key to achieving high-precision gyroscopes. key premise.

At present, the drive circuits of silicon micromachined gyroscopes all adopt closed-loop drive mode, among which AGC technology is used to realize driving stability, and PLL technology is used to realize frequency control. It greatly improves the Q value of the MEMS gyroscope and reduces the mechanical and thermal noise of the gyroscope. The high-Q value MEMS resonator with a quality factor between 10,000-1,000,000 has a high resonant peak and a narrow waveform bandwidth. , so a small frequency drift will lead to a large change in the output amplitude, which increases the difficulty of controlling the amplitude and frequency of the driving mode. Therefore, it is necessary to further improve the control accuracy of the system to meet the requirements of gyroscope driving modal stability. When the driving force of the gyroscope is increased enough, the driving capacitance of the MEMS gyroscope shows nonlinearity to the variation of the driving displacement, which will lead to mutual coupling between the phase angle condition and the gain condition of the AGC loop, making the control effect of the system worse , while the traditional PLL loop uses the CORDIC algorithm for frequency control. Since this algorithm is a numerical linear calculation approximation algorithm, its control accuracy is limited by the number of iterations, and the frequency resolution is not high. Disadvantages of poor phase noise for long hours. Therefore, it is necessary to provide a stable amplitude control method for a novel high-Q MEMS resonator.

Contents of the invention

The purpose of the present invention is to provide a stable amplitude control method of a high-Q MEMS resonator to solve the problem of insufficient control accuracy of the existing MEMS gyroscope closed-loop drive control loop for the high-Q MEMS resonator. On the basis of the existing MEMS gyroscope drive closed-loop system, the present invention obtains higher frequency resolution through DDS-PLL hybrid frequency synthesis technology, realizes high-precision control of the gyroscope drive mode, thereby improving the overall stability of the gyroscope and anti-interference ability.

The technical solution to realize the object of the present invention is: a stable amplitude control system of a high-Q MEMS resonator, said system comprising an AGC loop and a digital phase-locked loop;

The AGC loop is used to control the driving range;

The digital phase-locked loop is used to control the resonant frequency;

The AGC loop includes a sequentially connected first multiplication demodulation unit, a first low-pass filter unit and a first PI control unit; the digital signal corresponding to the MEMS resonator drive mode is subjected to amplitude resolution through the first multiplication demodulation unit The signal output by demodulation and demodulation obtains the amplitude information when the MEMS resonator is working through the first low-pass filter unit, which is compared with the reference value set by the system to obtain the amplitude deviation signal, and the first PI control unit according to the set An amplitude control amount output by the amplitude deviation signal is the amplitude gain of the system at this time, forming an AC driving force to feed back to the driving electrode, and realizing the closed-loop control of the amplitude;

The digital phase-locked loop includes a second multiplication demodulation unit, a second low-pass filter unit, a second PI control unit, a direct digital synthesis DDS algorithm frequency synthesis unit and a voltage-controlled oscillator DCO unit connected in sequence. The second multiplication demodulation unit and the second low-pass filter unit form a phase detector; the digital signal corresponding to the MEMS resonator drive mode passes through the second multiplication demodulation unit and the second low-pass filter unit to obtain a phase deviation signal, and then passes through The second PI control unit generates a frequency control signal Δω and outputs it to the direct digital synthesis DDS algorithm frequency synthesis unit; the frequency control signal Δω ₀ output by the direct digital synthesis DDS algorithm frequency synthesis unit is used as the input signal of the voltage-controlled oscillator DCO unit, so The DCO unit of the voltage-controlled oscillator generates a sine-cosine signal whose frequency is the resonant frequency, and then the phase error signal obtained by the DCO unit of the voltage-controlled oscillator Feedback to the output terminal of the phase detector to form a closed-loop control. The final output frequency signal and the amplitude control value of the AGC loop generate a driving feedback force to realize the driving stability of the MEMS gyroscope.

Further, the direct digital synthesis DDS algorithm frequency synthesis unit includes FPGA frequency control word conversion unit, phase accumulator, waveform memory ROM, digital low-pass filter and system clock; FPGA frequency control word conversion unit converts the second PI control unit The output frequency control signal Δω is converted into the corresponding frequency control word M, where the conversion coefficient is K _f ; driven by the system clock, the phase accumulator linearly accumulates the frequency control word M, and at the same time takes a modulo operation on 2 ^N to obtain and as the phase value, where N is the word length of the phase accumulator; the binary phase addressing code output by the phase accumulator is sent to the waveform memory ROM for addressing, so that it outputs the corresponding discrete amplitude sequence, and then through the digital The low-pass filter smoothes the discrete amplitude sequence waveform to obtain the desired frequency waveform.

Further, the frequency resolution output by the direct digital synthesis DDS algorithm frequency synthesis unit depends on the number of bits N of the phase accumulator, and the larger N is, the higher the frequency resolution is.

Further, the minimum frequency resolution Δf _min output by the direct digital synthesis DDS algorithm frequency synthesis unit and the number of bits N of the phase accumulator satisfy:

Among them, _fc represents the system clock frequency, P represents the frequency division ratio of the phase-locked loop, and R represents the reference frequency division ratio.

Further, the phase accumulator overflows once every 2 ^N /M clock cycles on average, and the frequency value Δf ₀ output by the direct digital synthesis DDS algorithm frequency synthesis unit can be obtained through the value of M in the system at this time, and the relationship between them satisfy:

Further, the first low-pass filtering unit and the second low-pass filtering unit adopt FIR digital low-pass filters designed by Kaiser window function design method.

Further, the parameters of the FIR digital low-pass filter include: the center frequency is set to 500kHz, the passband frequency is set to 500Hz, the stopband frequency is set to 14kHz, the stopband attenuation is greater than 50dB, and the final order is 109; Kaiser window The total length D of the function satisfies:

Among them, A _s represents the stopband attenuation, and Δf represents the normalized transition bandwidth.

Further, the phase noise _L of the digital phase-locked loop output frequency signal satisfies the following formula:

L _o ＝L _DDS +20logP'

In the formula, L _DDS represents the phase noise output by the frequency synthesis unit of the direct digital synthesis DDS algorithm, and P' represents the number of frequency multiplications.

Compared with the prior art, the present invention has the remarkable advantages of:

On the basis of the existing control method, on the one hand, the frequency control signal is generated by the DDS circuit to improve the voltage resolution of the original digital phase-locked loop frequency control signal, so that the amplitude and frequency of the gyro drive mode are higher Control accuracy, thereby improving the overall stability and anti-interference ability of the gyroscope. On the other hand, compared with the original PLL technology, the DDS-PLL hybrid technology combines the advantages of the two technologies. It has the characteristics of high precision, low phase noise, good suppression effect on spurious noise, good broadband and spectrum quality, and improves the Dynamic and steady-state characteristics of a high-Q MEMS resonator amplitude stabilization system. specifically:

(1) The digital phase-locked loop adopts the direct digital frequency synthesis technology DDS to generate the frequency control signal, and the DDS circuit provides a high-precision voltage signal input for the voltage-controlled oscillator of the phase-locked loop, and the DDS circuit has a small output step size and The advantage of lower phase noise, but more spurious noise, and PLL has a small output step size, the phase noise is poor, but the suppression effect on spurious noise is good, the solution of frequency synthesis using DDS and PLL hybrid technology combines the two The advantages of this technology enable the system design to meet the requirements of broadband and fast frequency conversion speed, and are suitable for the control of high-Q MEMS resonators to achieve better control effects.

(2) The frequency resolution output by the DDS algorithm frequency synthesis unit used in the present invention depends on the number of digits N of the phase accumulator. When N is large enough, the resolution accuracy that is difficult to achieve by traditional methods can be obtained, and the highest can reach the micro Hz level.

(3) The low-pass filtering unit has adopted the FIR digital low-pass filter of independent design, is easy to realize linear phase, is applicable to the signal that processing phase requirement is higher, what the present invention selects is the Kaiser window function design method, by parameter estimation and optimization The processing achieves good high-frequency suppression effect and does not attenuate low-frequency components, and has good filtering characteristics.

(4) In the feedback channel of the closed-loop control system, the frequency signal output by the DDS excitation PLL and the amplitude gain A _x formed by the AGC loop are used as the feedback AC drive signal, so that the gyroscope drive mode obtains a higher-precision resonant frequency signal, Furthermore, the amplitude stability and frequency stability of the driving mode of the high-Q MEMS resonator are improved.

The present invention will be described in further detail below in conjunction with the accompanying drawings.

Description of drawings

FIG. 1 is a schematic diagram of a MEMS gyroscope closed-loop drive control in an embodiment.

Figure 2 is a schematic diagram of the DDS system used in one embodiment.

Fig. 3 is a simulation diagram of the DDS system adopted in one embodiment.

Fig. 4 is the DDS system emulation waveform chart that adopts in an embodiment, and wherein figure (a) is the waveform figure of DDS system synthesis required frequency, figure (b) is the power spectral density schematic diagram of synthesis waveform.

Fig. 5 is a simulation diagram of a digital phase-locked loop system in an embodiment.

Fig. 6 is a simulation diagram of signals before and after the FIR digital low-pass filter in one embodiment.

Fig. 7 is a schematic diagram of DDS-PLL technology in an embodiment.

FIG. 8 is a frequency characteristic diagram of the MEMS gyroscope closed-loop driving system in one embodiment.

FIG. 9 is a phase locus diagram of a MEMS gyroscope closed-loop drive system in one embodiment.

Detailed ways

In order to make the purpose, technical solution and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present application, and are not intended to limit the present application.

It should be noted that if there is a directional indication (such as up, down, left, right, front, back...) in the embodiment of the present invention, the directional indication is only used to explain the position in a certain posture (as shown in the accompanying drawing). If the specific posture changes, the directional indication will also change accordingly.

In addition, if there are descriptions involving "first", "second" and so on in the embodiments of the present invention, the descriptions of "first", "second" and so on are only for descriptive purposes, and should not be interpreted as indicating or implying Its relative importance or implicitly indicates the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include at least one of these features. In addition, the technical solutions of the various embodiments can be combined with each other, but it must be based on the realization of those skilled in the art. When the combination of technical solutions is contradictory or cannot be realized, it should be considered that the combination of technical solutions does not exist , nor within the scope of protection required by the present invention.

In one embodiment, referring to FIG. 1 , a stable amplitude control method of a high-Q MEMS resonator is provided, which is a digital double closed-loop drive control system based on AGC technology and DDS-PLL frequency synthesis technology. The driving mode of MEMS gyroscope becomes the voltage signal V reflecting the magnitude of the displacement x through the displacement voltage conversion circuit, and the analog signal is converted into a digital signal through ADC chip conversion, and then the sin(ωt) and cos(ωt) signals are respectively input and processed by the multiplier Amplitude demodulation and phase demodulation, after the demodulated output signal passes through the FIR digital low-pass filter, the amplitude information and phase difference information when the MEMS resonator is working are obtained. The vibration amplitude is compared with the reference value A set by the system to obtain a deviation signal, and the PI controller outputs an amplitude control value according to the deviation signal, which is the amplitude gain A _x of the system at this time, forming an AC driving force feedback to the drive electrode to realize amplitude closed-loop control. The phase deviation signal is obtained through demodulation and digital filtering, the frequency control signal Δω is generated through PI control, and the frequency control signal Δω ₀ with higher precision is output by FPGA control DDS algorithm as the input signal of the voltage controlled oscillator (DCO), and then passed The voltage-controlled oscillator (DCO) circuit generates a cosine signal cos(ω _d t) whose frequency is the resonant frequency, and the obtained phase error Feedback to the output terminal of the phase detector through P frequency division to form a closed-loop control loop. The final output frequency signal and the amplitude gain A _x formed by the AGC loop are used as the feedback AC drive signal, and the driving amplitude of the MEMS gyroscope is realized through the conversion of the DAC and the voltage-electrostatic force conversion coefficient K _vf .

Due to the miniaturization of the MEMS gyroscope, the output signal is very weak during operation, which is easily disturbed by parasitic effects and the coupling effect between the driving electrode and the sensitive electrode. 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 the DDS-PLL hybrid technology to improve the frequency resolution of the output signal. In addition to improving the control accuracy of the system, it also has fast frequency conversion speed, low phase noise and frequency drift, and the full digital structure is easy to integrate and expand functions. Broadband and Advantages of good spectral quality. The implementation principle of the DDS technology used is shown in Figure 2, including six parts: frequency control word conversion unit, frequency word register, phase accumulator, sine lookup table ROM, digital low-pass filter and system clock, where M is the frequency Control word, N is the word length of the phase accumulator, m is the number of ROM address lines. The frequency control signal Δω output by the PI controller is converted into a corresponding frequency control word M by the FPGA control unit, where the conversion coefficient is K _f . Driven by the 100MHz system clock f _c , the phase accumulator linearly accumulates the frequency control word M, and at the same time performs a modulo operation on 2 ^N , and the obtained sum is used as the phase value, and the sine function table ROM is queried in the form of binary code. Convert the phase information into the corresponding digital quantized sine amplitude value, and then use the digital low-pass filter to smooth the waveform to obtain the required frequency waveform, and finally use the frequency value processed by the DDS algorithm as the input control of the voltage-controlled oscillator Signal. Among them, the phase accumulator overflows every 2 ^N /M clock cycles on average, so the frequency control word M and the clock frequency f _c reflect the frequency value of the DDS output signal, and the output frequency can be obtained by reading the value of M in the system at this time value Δf ₀ , the relationship between them satisfies:

The minimum frequency resolution of the DDS is related to the word length of the phase accumulator. By selecting an appropriate word length N, a very high frequency resolution can be achieved, up to micro Hz level. Through the simulation analysis of the DDS system model, as shown in Figure 3, it can be seen that the spectral quality of the output signal is very high, and the spurious components are very small.

The module realizing the frequency control function of the system of the present invention is a digital phase-locked loop link, controls the frequency of the output signal by detecting the phase difference of the signal, and keeps the input signal and the output signal having the same frequency and phase information. The main module of the digital PLL consists of three parts: a phase detector, a PI controller and a voltage-controlled oscillator (DCO). The phase detector is composed of a multiplier and a FIR digital low-pass filter. The specific simulation model is shown in Figure 4 Show.

Among them, the low-pass filter module adopts the self-designed FIR digital low-pass filter, which is easy to realize the linear phase and is suitable for processing signals with high phase requirements. The Kaiser window function design method is selected in this scheme, and the parameters are estimated and optimized. A good high-frequency suppression effect is achieved without attenuating low-frequency components. From Figure 5, it can be seen that the waveform amplitude after low-pass filtering and the waveform amplitude before filtering satisfy the double relationship and the output curve is smooth, so the filter has good filtering characteristic.

The DDS-PLL hybrid technology adopted in 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 has a good control effect, and the amplitude and frequency stability of the driving detection output signal are improved. Figure 6 is a schematic diagram of high-precision frequency control based on DDS-PLL hybrid technology, and the driving mode displacement signal is where A _x (t) is the vibration amplitude, ω ₀ is the initial frequency of the DCO, Δω is the frequency modulation output of the PI controller, /> is the phase shift of the driving mode. The phase difference signal obtained by multiplying the driving displacement signal with the cos(ω ₀ +Δω)t signal for phase demodulation and digital low-pass filtering/> for /> Adjust the size of Δω by setting the reference value of the PI controller to 0, and then use the FPGA to control the DDS algorithm to synthesize a higher-precision frequency control signal Δω ₀ , which is used as the input signal of the DCO circuit, and the phase error signal obtained by the voltage-controlled oscillator / > Feedback to the output terminal of the phase detector, if the phase or frequency of the input signal changes, through the feedback control of the voltage-controlled oscillator module, the output signal of the loop, that is, the frequency and phase of the voltage-controlled oscillator, will track the change of the input signal . Where the VCO output phase /> and the input control voltage v _c (t) satisfy:

Among them, D ₀ represents the voltage control sensitivity of the voltage controlled oscillator.

In order to further illustrate that the amplitude control system of the present invention has good dynamic and steady-state characteristics, frequency characteristic analysis and phase locus diagram analysis of the drive closed-loop system are performed, as shown in Fig. 7 and Fig. 8 . It can be seen from the Bode diagram that the frequency point with an amplitude-frequency response of -3dB is 145Hz, so the bandwidth of the closed-loop system is 145Hz, which meets the bandwidth requirements of high-Q MEMS resonators and makes the system more robust. It can be seen from Figure 8 that the root locus curves of the system are all located on the left half of the imaginary axis, two point to infinity from the pole, and one point to zero from the pole. Changing the loop gain will not destroy the stability of the system. When the loop gain is small, the influence of poles away from the imaginary axis on the system can be ignored, 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 imaginary axis will produce zero-pole cancellation with the zero point, and the system characteristics are determined by the conjugate pole far away from the imaginary axis. Obviously, when the loop gain is larger, the loop is more stable.

The system proposed by the present invention utilizes a digital phase-locked loop for frequency synthesis based on the DDS algorithm to track the resonant frequency and phase of the gyro vibration. This structure can utilize the DDS algorithm to provide a high-resolution frequency signal to ensure a sufficiently small frequency step, and at the same time The band-pass characteristic of PLL can also suppress some spurs in the DDS output spectrum very well, realize the complementary advantages of DDS and PLL, improve the dynamic performance of the high-Q MEMS resonator control system, and optimize the amplitude of the MEMS gyroscope And the stable accuracy of the frequency, thereby improving the zero bias output and anti-interference ability of the MEMS gyroscope.

The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments. The above-mentioned embodiments and descriptions only illustrate the principles of the present invention. Within the spirit and principles, any modifications, equivalent replacements, improvements, etc., shall be included in the protection scope of the present 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.