Method for starting silicon resonant accelerometer based on pseudo-random number principle
By simulating white noise excitation of the resonant beam using the pseudo-random number principle and a linear feedback displacement register, the problems of complex startup process and temperature sensitivity of silicon resonant accelerometers are solved, realizing an adaptive startup method that is suitable for engineering applications and other resonant sensors.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUNAN UNIV
- Filing Date
- 2025-07-08
- Publication Date
- 2026-07-10
AI Technical Summary
The startup process of traditional silicon resonant accelerometers is complex and temperature-sensitive, which limits their engineering applications and lacks a simple and adaptive startup method.
Based on the principle of pseudo-random numbers, the mechanical model of the resonant beam is analyzed and a pseudo-random number sequence is generated using a linear feedback displacement register to simulate white noise, thereby exciting the resonant beam to oscillate, and then switching to a phase-locked loop to maintain the oscillation.
It reduces the complexity of the startup process of the digital circuit of the silicon resonant accelerometer, improves the adaptive startup capability, and is suitable for engineering applications and other resonant sensor solutions.
Smart Images
Figure CN120908478B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of inertial navigation technology, and in particular to a method for activating a silicon resonant accelerometer based on the principle of pseudo-random numbers. Background Technology
[0002] The traditional startup process for digital circuits in silicon resonant accelerometers involves setting a frequency sweep range in the digital circuit, detecting whether the output amplitude of the resonant beam at different frequencies reaches a threshold to find the resonant frequency, and then maintaining the resonant frequency to sustain the resonant beam's oscillation. Since the resonant frequency of each manufactured silicon resonant accelerometer varies, a suitable resonant frequency range needs to be manually adjusted for each one, significantly increasing the complexity of the process and the time required for manual operation. Furthermore, because the resonant frequency of a silicon resonant accelerometer is temperature-sensitive, it varies with different temperatures. Therefore, if the resonant frequency changes with temperature and falls outside the set range, the silicon resonant accelerometer will fail to start normally. This severely limits the engineering application of digital circuits for silicon resonant accelerometers and hinders further performance improvements. Currently, there is still a lack of a simple and adaptive method for starting silicon resonant accelerometers in digital circuits. Summary of the Invention
[0003] Therefore, it is necessary to provide a method for starting a silicon resonant accelerometer based on the pseudo-random number principle, including:
[0004] S1: Based on the mechanical model of the resonant beam in the silicon resonant accelerometer, the vibration start-up condition of the resonant beam is analyzed. The vibration start-up condition is that the resonant beam starts to vibrate when the frequency of the input signal is near the resonant peak frequency of the resonant beam.
[0005] S2: A pseudo-random number sequence is generated in a digital circuit using a linear feedback shift register to simulate white noise, wherein the white noise includes the resonant peak frequency;
[0006] S3: Based on the pseudo-random number sequence to excite the resonant beam, when the amplitude of the silicon resonant accelerometer reaches the preset amplitude, it indicates that the resonant beam starts to oscillate. At this time, the sinusoidal signal of the phase-locked loop is switched to maintain the oscillation of the resonant beam, realizing the adaptive start of the silicon resonant accelerometer.
[0007] Preferably, S1 includes:
[0008] The resonant beam in the silicon resonant accelerometer is equivalent to a second-order spring-damped system. The kinematic equations of the second-order spring-damped system are then subjected to Laplace transform to obtain the transfer function. The modulus-amplitude frequency function of the transfer function is then calculated.
[0009] The amplitude-frequency function is differentiated and its derivative is set to 0. The resonant peak frequency is then determined. When the frequency of the input signal is near the resonant peak frequency of the resonant beam, the oscillation condition of the resonant beam is considered to be met, and the resonant beam begins to oscillate.
[0010] Preferably, the kinematic equations of the second-order spring-damped system are expressed as follows:
[0011] ;
[0012] in, This represents the equivalent mass of the resonant beam; This represents the acceleration of the resonant beam. This indicates the motion damping of the resonant beam; This indicates the velocity of the resonant beam. This represents the equivalent stiffness of the resonant beam. This represents the displacement of the resonant beam; This represents the input signal of the resonant beam.
[0013] Preferably, the transfer function is expressed as:
[0014] , ;
[0015] in, The Laplace transform represents the output displacement of the resonant beam; The Laplace transform of the input signal to the resonant beam; This represents the equivalent mass of the resonant beam; This indicates the motion damping of the resonant beam; This represents the equivalent stiffness of the resonant beam. Represents a complex frequency variable; Indicates the imaginary part unit; This indicates the frequency of the input signal.
[0016] Preferably, the amplitude-frequency function is expressed as:
[0017] ;
[0018] in, Represents the amplitude-frequency function; Indicates the frequency of the input signal; This represents the equivalent mass of the resonant beam; This represents the equivalent stiffness of the resonant beam. This represents the motion damping of the resonant beam.
[0019] Preferably, the process of solving for the resonant peak frequency includes:
[0020] The amplitude-frequency function is rewritten as follows:
[0021] ; ; ;
[0022] ; ;
[0023] in, Represents the amplitude-frequency function; Indicates the frequency of the input signal; This represents the equivalent mass of the resonant beam; This represents the equivalent stiffness of the resonant beam. This indicates the motion damping of the resonant beam; This represents the natural frequency of the resonant beam; Indicates the damping ratio;
[0024] Differentiate the rewritten amplitude-frequency function and set its derivative to 0. Solve for the first relationship between the input signal frequency and the natural frequency of the resonant beam when the amplitude is at its maximum. The first relationship is expressed as:
[0025] ;
[0026] By performing a simple transformation on the first relation, we obtain the formula for calculating the resonant peak frequency, which is expressed as:
[0027] ;
[0028] in, This indicates the resonant peak frequency.
[0029] Preferably, S2 includes:
[0030] Step 1: Arrange the linear feedback shift register on the digital circuit, and set the number of bits and the primitive polynomial of the linear feedback shift register;
[0031] Step 2: Input the initial sequence into the linear feedback shift register, extract the state at the corresponding position in the initial sequence based on the taps set in the primitive polynomial, and perform an XOR operation on all extracted states to obtain the feedback bit;
[0032] The number of bits in the initial sequence corresponds to the number of bits in the linear feedback shift register, and each state in the initial sequence includes either 1 or 0; the leftmost bit of the initial sequence is the most significant bit, and the sequence decreases sequentially to the least significant bit.
[0033] Step 3: Shift each state in the initial sequence one bit to the right, remove the lowest bit of the initial sequence, and put the feedback bit into the highest bit to obtain the updated sequence; put the removed state into the pseudo-random number sequence;
[0034] Step 4: Replace the previous sequence with the updated sequence, and repeat steps 2-4 until the maximum cycle period is completed to obtain a pseudo-random number sequence. The states in the pseudo-random number sequence are arranged in the order they were put in.
[0035] When the number of bits is greater than or equal to 12, the power spectral density characteristics of the pseudo-random number sequence approach the power spectral density characteristics of white noise, thus realizing white noise simulation.
[0036] Preferably, the linear feedback shift register has 12 bits.
[0037] Preferably, the primitive polynomials include:
[0038] ;
[0039] in, The primitive polynomial representing a 12-bit linear feedback shift register; This indicates the highest bit of the tap in the 12-bit initial sequence; This indicates that the tap is the 6th tap from right to left in the 12-bit initial sequence; This indicates that the tap is the 4th tap from right to left in the 12-bit initial sequence; This indicates the least significant bit of the tap in the 12-bit initial sequence.
[0040] Preferably, when the number of bits is 12, the maximum cycle period of the linear feedback shift register is 4095 cycles.
[0041] Beneficial effects: This method is based on the mechanical model of the resonant beam in a silicon resonant accelerometer and analyzes the oscillation conditions of the resonant beam. Based on the principle of pseudo-random numbers, a pseudo-random number sequence is generated by a linear feedback displacement register to simulate white noise, which can excite the resonant beam with different resonant frequencies to start oscillation. This reduces the complexity of the startup process of the digital circuit of the silicon resonant accelerometer, improves the adaptive startup capability, and has strong engineering application value. Attached Figure Description
[0042] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0043] Figure 1 This is a flowchart of a method for starting a silicon resonant accelerometer based on the pseudo-random number principle in an embodiment of this application.
[0044] Figure 2 This is the Bode plot of the resonant beam in the embodiment of this application.
[0045] Figure 3 This is a schematic diagram of the structure of an n-bit linear feedback shift register in an embodiment of this application.
[0046] Figure 4 This is a waveform diagram of the pseudo-random number sequence in the embodiments of this application.
[0047] Figure 5 This is a power spectral density diagram of the pseudo-random number sequence in the embodiments of this application.
[0048] Figure 6 This is a diagram showing the simulation results of the entire process in the embodiments of this application.
[0049] Figure 7 The figure shows the simulation results of a white noise-excited resonant beam in the embodiments of this application.
[0050] Figure 8 This is a diagram illustrating the stabilization process of the phase-locked loop in an embodiment of this application. Detailed Implementation
[0051] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.
[0052] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0053] like Figure 1 As shown, this embodiment provides a method for starting a silicon resonant accelerometer based on the pseudo-random number principle, including:
[0054] S1: Based on the mechanical model of the resonant beam in the silicon resonant accelerometer, the vibration start-up condition of the resonant beam is analyzed. The vibration start-up condition is that the resonant beam starts to vibrate when the frequency of the input signal is near the resonant peak frequency of the resonant beam.
[0055] Specifically, the steps include:
[0056] The resonant beam in the silicon resonant accelerometer is equivalent to a second-order spring-damped system, and the kinematic equations of the second-order spring-damped system are subjected to Laplace transform to obtain the transfer function;
[0057] The kinematic equations of a second-order spring-damped system are expressed as follows:
[0058] ;
[0059] in, This represents the equivalent mass of the resonant beam; This represents the acceleration of the resonant beam. This indicates the motion damping of the resonant beam; This indicates the velocity of the resonant beam. This represents the equivalent stiffness of the resonant beam. This represents the displacement of the resonant beam; The input signal represents the electrostatic driving force applied to the resonant beam by the drive comb teeth.
[0060] The transfer function is expressed as:
[0061] , ;
[0062] in, The Laplace transform represents the output displacement of the resonant beam; The Laplace transform of the input signal to the resonant beam; This represents the equivalent mass of the resonant beam; This indicates the motion damping of the resonant beam; This represents the equivalent stiffness of the resonant beam. Represents a complex frequency variable; Indicates the imaginary part unit; This indicates the frequency of the input signal.
[0063] Due to the manufacturing process specifications of silicon resonant accelerometers, which involve vacuum packaging, the kinematic equations of the second-order spring-damped system are close to those of an undamped system. Therefore, the amplitude-frequency function is constructed by modulating the transfer function; the amplitude-frequency function is expressed as:
[0064] ;
[0065] in, Represents the amplitude-frequency function; Indicates the frequency of the input signal; This represents the equivalent mass of the resonant beam; This represents the equivalent stiffness of the resonant beam. This represents the motion damping of the resonant beam.
[0066] The amplitude-frequency function is differentiated and its derivative is set to 0. The resonant peak frequency is then determined. When the frequency of the input signal is near the resonant peak frequency of the resonant beam, the oscillation condition of the resonant beam is considered to be met, and the resonant beam begins to oscillate.
[0067] Specifically, the process of determining the resonant peak frequency includes:
[0068] The amplitude-frequency function is rewritten as follows:
[0069] ; ; ;
[0070] ; ;
[0071] in, Represents the amplitude-frequency function; Indicates the frequency of the input signal; This represents the equivalent mass of the resonant beam; This represents the equivalent stiffness of the resonant beam. This indicates the motion damping of the resonant beam; This represents the natural frequency of the resonant beam; This indicates the damping ratio.
[0072] Differentiate the rewritten amplitude-frequency function and set its derivative to 0. Solve for the first relationship between the input signal frequency and the natural frequency of the resonant beam when the amplitude is at its maximum. The first relationship is expressed as:
[0073] ;
[0074] By performing a simple transformation on the first relation, we obtain the formula for calculating the resonant peak frequency, which is expressed as:
[0075] ;
[0076] in, This indicates the resonant peak frequency. Because silicon resonant accelerometers have a very good quality factor (typically in the tens of thousands), the resonant beam has excellent frequency selectivity. The resonant beam only has a large amplitude response near the resonant peak frequency. Therefore, when the input signal frequency is near the resonant peak frequency of the resonant beam, the resonant beam will oscillate.
[0077] In this embodiment, the specific parameter values of the resonant beam of the silicon resonant accelerometer are shown in Table 1.
[0078] Table 1 Summary of specific parameters of the resonant beam
[0079]
[0080] From the above parameters, we can obtain Figure 2 The Bode plot of the resonant beam shown in the figure shows that the resonant beam has a large amplification gain only near the resonant peak frequency. Therefore, the frequency of the electrostatic driving force applied to the resonant beam by the driving comb must be near the resonant peak frequency in order to satisfy the oscillation condition of the resonant beam.
[0081] S2: In digital circuits, a pseudo-random number sequence is generated using a linear feedback shift register to simulate white noise. Since the power spectral density of white noise is constant at all frequencies, the resonant peak frequency is also necessarily contained in the white noise. Therefore, a resonant beam can be started by simulating white noise.
[0082] Specifically, the steps include:
[0083] Step 1: Arrange the linear feedback shift register on the digital circuit, and set the number of bits and the primitive polynomial of the linear feedback shift register;
[0084] Step 2: Input the initial sequence into the linear feedback shift register, extract the state at the corresponding position in the initial sequence based on the taps set in the primitive polynomial, and perform an XOR operation on all extracted states to obtain the feedback bit;
[0085] The number of bits in the initial sequence corresponds to the number of bits in the linear feedback shift register, and each state in the initial sequence includes either 1 or 0; the leftmost bit of the initial sequence is the most significant bit, and the sequence decreases sequentially to the least significant bit.
[0086] Step 3: Shift each state in the initial sequence one bit to the right, remove the lowest bit of the initial sequence, and put the feedback bit into the highest bit to obtain the updated sequence; put the removed state into the pseudo-random number sequence;
[0087] Step 4: Replace the previous sequence with the updated sequence, and repeat steps 2-4 until the maximum cycle period is completed to obtain a pseudo-random number sequence. The states in the pseudo-random number sequence are arranged in the order they were put in.
[0088] When the number of bits is greater than or equal to 12, the power spectral density characteristics of the pseudo-random number sequence approach those of white noise, thus realizing white noise simulation.
[0089] In this embodiment, the structure of the linear feedback shift register is as follows: Figure 3 As shown, the input of its highest-level register The relationship between its state and the state of subsequent registers can be expressed as:
[0090] ;
[0091] in, , , These represent the coefficients preceding each register level; This represents the XOR operation; , , These represent the inputs to the lowest-level register, the second-lowest-level register, and the second-highest-level register, respectively.
[0092] Based on the above state relationship, the linear feedback shift register can be represented as a polynomial, as follows:
[0093] ;
[0094] in, Represents a polynomial; This indicates the highest bit of the tap in the initial sequence; This indicates that the tap is the second highest bit in the initial sequence; This indicates the second lowest bit of the tap in the initial sequence; This indicates the least significant bit of the tap in the initial sequence;
[0095] As shown in the above formula, after setting the initial sequence, the linear feedback shift register will cycle through one period. An n-bit linear feedback shift register can only iterate through a maximum of 2^n cycles. n -1 state, to ensure the maximum cycle period (cycle 2) n (-1 degree), setting the polynomial to a primitive polynomial, the resulting sequence is a pseudo-random number sequence.
[0096] In this embodiment, the linear feedback shift register has 12 bits. When the number of bits is 12, the maximum cycle time of the linear feedback shift register is 4095 cycles.
[0097] In this embodiment, the primitive polynomial is:
[0098] ;
[0099] in, The primitive polynomial representing a 12-bit linear feedback shift register; This indicates the highest bit of the tap in the 12-bit initial sequence; This indicates that the tap is the 6th tap from right to left in the 12-bit initial sequence; This indicates that the tap is the 4th tap from right to left in the 12-bit initial sequence; This represents the least significant bit of the tap in the 12-bit initial sequence. Other forms of primitive polynomials can be chosen depending on the specific application.
[0100] In this embodiment, when the initial sequence is 010100011010, the waveform of the generated pseudo-random number sequence is as follows: Figure 4As shown, the power spectral density obtained from this pseudo-random number sequence is as follows: Figure 5 As shown, from Figure 5 It can be seen that the pseudo-random number sequence has energy that is basically uniformly distributed in different frequency bands, and its power spectral density characteristics are similar to those of white noise. Therefore, digital circuits can generate pseudo-random number sequences through linear feedback shift registers to simulate white noise excitation of resonant beams.
[0101] S3: Based on the pseudo-random number sequence to excite the resonant beam, when the amplitude of the silicon resonant accelerometer reaches the preset amplitude, it indicates that the resonant beam starts to oscillate. At this time, the sinusoidal signal of the phase-locked loop is switched to maintain the oscillation of the resonant beam, realizing the adaptive start of the silicon resonant accelerometer.
[0102] In this embodiment, a pseudo-random number sequence generated by a 12-bit linear feedback shift register is used for resonance simulation, and the simulation results for the entire process are as follows: Figure 6 The simulation results of the white noise-excited resonant beam are shown below. Figure 7 As shown, the stabilization process of the phase-locked loop is as follows: Figure 8 As shown in the simulation results, after inputting a pseudo-random number sequence into the resonant beam at the initial moment, due to the frequency selection characteristics of the resonant beam, it only outputs signals within the resonant peak frequency range. As energy accumulates, it eventually reaches the preset amplitude, switching to a phase-locked loop to maintain the oscillation of the resonant beam, thus completing the startup of the silicon resonant accelerometer. The simulation results demonstrate that the pseudo-random number sequence can achieve the startup of the resonant beam, proving the feasibility and correctness of the startup method provided in this implementation.
[0103] The method for starting a silicon resonant accelerometer based on the pseudo-random number principle provided in this embodiment has the following beneficial effects:
[0104] This method is based on the mechanical model of the resonant beam in a silicon resonant accelerometer, and analyzes the oscillation conditions of the resonant beam. Based on the principle of pseudo-random numbers, a pseudo-random number sequence is generated by a linear feedback displacement register to simulate white noise, which can excite the resonant beam with different resonant frequencies to start oscillation. It has good applicability to adaptively start silicon resonant accelerometers based on digital circuits. At the same time, it can be extended to other resonant sensor schemes, and has universality and versatility.
[0105] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0106] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A method for starting a silicon resonant accelerometer based on the principle of pseudo-random numbers, characterized in that, include: S1: Based on the mechanical model of the resonant beam in the silicon resonant accelerometer, the vibration initiation condition of the resonant beam is analyzed. The vibration initiation condition is that the resonant beam starts to vibrate when the input signal frequency is near the resonant peak frequency of the resonant beam, including: The resonant beam in the silicon resonant accelerometer is equivalent to a second-order spring-damped system. The kinematic equations of this system are then subjected to a Laplace transform to obtain the transfer function. The magnitude of the transfer function is calculated to construct the amplitude-frequency function, which is expressed as: ； in, Represents the amplitude-frequency function; Indicates the frequency of the input signal; This represents the equivalent mass of the resonant beam; This represents the equivalent stiffness of the resonant beam. This indicates the motion damping of the resonant beam; The amplitude-frequency function is differentiated and its derivative is set to 0. The resonant peak frequency is then determined. When the frequency of the input signal is near the resonant peak frequency of the resonant beam, the oscillation condition of the resonant beam is considered to be met, and the resonant beam begins to oscillate. The process of determining the resonant peak frequency includes: The amplitude-frequency function is rewritten as follows: ； ； ； ； ； in, This represents the natural frequency of the resonant beam; Indicates the damping ratio; Differentiate the rewritten amplitude-frequency function and set its derivative to 0. Solve for the first relationship between the input signal frequency and the natural frequency of the resonant beam when the amplitude is at its maximum. The first relationship is expressed as: ； By performing a simple transformation on the first relation, we obtain the formula for calculating the resonant peak frequency, which is expressed as: ； in, Indicates the resonant peak frequency; S2: In digital circuits, a linear feedback shift register is used to generate a pseudo-random number sequence to simulate white noise. The white noise includes a resonant peak frequency, comprising: Step 1: Arrange the linear feedback shift register on the digital circuit, and set the number of bits and the primitive polynomial of the linear feedback shift register; Step 2: Input the initial sequence into the linear feedback shift register, extract the state at the corresponding position in the initial sequence based on the taps set in the primitive polynomial, and perform an XOR operation on all extracted states to obtain the feedback bit; The number of bits in the initial sequence corresponds to the number of bits in the linear feedback shift register, and each state in the initial sequence includes either 1 or 0; the leftmost bit of the initial sequence is the most significant bit, and the sequence decreases sequentially to the least significant bit. Step 3: Shift each state in the initial sequence one bit to the right, remove the lowest bit of the initial sequence, and put the feedback bit into the highest bit to obtain the updated sequence; put the removed state into the pseudo-random number sequence; Step 4: Replace the previous sequence with the updated sequence, and repeat steps 2-4 until the maximum cycle period is completed to obtain a pseudo-random number sequence. The states in the pseudo-random number sequence are arranged in the order they were put in. When the number of bits is greater than or equal to 12, the power spectral density characteristics of the pseudo-random number sequence approach the power spectral density characteristics of white noise, thus realizing white noise simulation; S3: Based on the pseudo-random number sequence to excite the resonant beam, when the amplitude of the silicon resonant accelerometer reaches the preset amplitude, it indicates that the resonant beam starts to oscillate. At this time, the sinusoidal signal of the phase-locked loop is switched to maintain the oscillation of the resonant beam, realizing the adaptive start of the silicon resonant accelerometer.
2. The method for starting a silicon resonant accelerometer based on the pseudo-random number principle according to claim 1, characterized in that, The kinematic equations of a second-order spring-damped system are expressed as follows: ； in, This represents the equivalent mass of the resonant beam; This represents the acceleration of the resonant beam. This indicates the motion damping of the resonant beam; This indicates the velocity of the resonant beam. This represents the equivalent stiffness of the resonant beam. This represents the displacement of the resonant beam; This represents the input signal of the resonant beam.
3. The method for starting a silicon resonant accelerometer based on the pseudo-random number principle according to claim 1, characterized in that, The transfer function is expressed as: ， ； in, The Laplace transform represents the output displacement of the resonant beam; The Laplace transform of the input signal to the resonant beam; This represents the equivalent mass of the resonant beam; This indicates the motion damping of the resonant beam; This represents the equivalent stiffness of the resonant beam. Represents a complex frequency variable; Indicates the imaginary part unit; This indicates the frequency of the input signal.
4. The method for starting a silicon resonant accelerometer based on the pseudo-random number principle according to claim 1, characterized in that, The linear feedback shift register has 12 bits.
5. The method for starting a silicon resonant accelerometer based on the pseudo-random number principle according to claim 4, characterized in that, Primitive polynomials include: ； in, The primitive polynomial representing a 12-bit linear feedback shift register; This indicates the highest bit of the tap in the 12-bit initial sequence; This indicates that the tap is the 6th tap from right to left in the 12-bit initial sequence; This indicates that the tap is the 4th tap from right to left in the 12-bit initial sequence; This indicates the least significant bit of the tap in the 12-bit initial sequence.
6. The method for starting a silicon resonant accelerometer based on the pseudo-random number principle according to claim 1, characterized in that, When the bit length is 12, the maximum cycle time of the linear feedback shift register is 4095 cycles.