A frequency modulated MEMS accelerometer based on a ring resonator

Abstract

The invention discloses a frequency modulation MEMS accelerometer based on a ring resonator, comprising two centrally symmetrical resonators I and II, wherein the resonators I and II are symmetrically connected to a mass block, and both the resonators I and II include a ring structure located in the middle, wherein the ring structure in the middle is connected to a central anchor point located in the middle of the ring structure through four groups of first decoupling beams, wherein the central anchor point is fixed on a substrate, wherein the left and right sides of the ring structure are respectively connected to a driving detection electrode, and the front and rear sides are respectively connected to an electrostatic tuning electrode, wherein the driving detection electrode and the electrostatic tuning electrode are both variable area comb teeth electrodes, and the left and right sides of each electrostatic tuning electrode are respectively connected to the front and rear ends of the displacement balance levers on the left and right sides, and the front and rear ends of each displacement balance lever are respectively connected to the L-shaped beams on the front and rear sides through second decoupling beams. The invention is conducive to the self-excited oscillation to accurately capture the natural frequency of the resonator and improve the control accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of accelerometers, and in particular relates to a frequency modulation MEMS accelerometer based on a ring resonator. Background Art

[0002] MEMS resonant accelerometer is a typical micro-mechanical electrical inertial device with the advantages of small size, light weight, high measurement accuracy, good stability, large dynamic range, and direct output of quasi-digital quantities. It is an important development direction of today's accelerometers. Its structure is generally composed of a mass block, a resonator, a lever amplification mechanism, and a support mechanism. The mass block is an inertial sensitive unit, the resonator is a force sensitive unit, the lever amplification mechanism amplifies the inertial force, and the support structure is the supporting link of the movable part of the structure. Under the action of external acceleration, the mass block generates an inertial force along the sensitive axis. The inertial force is amplified by the micro-lever amplification mechanism and transmitted to the resonator, causing the frequency of the resonant beam to change. The corresponding input acceleration value can be obtained by detecting the frequency change of a pair of differential resonators.

[0003] The most commonly used resonator today is a double-ended tuning fork structure (DETF), which consists of a resonant beam and comb capacitance (driving comb, detecting comb). The DC bias voltage acts on the resonant beam and the sensitive mass block to provide appropriate capacitive conduction gain. The driving voltage generates an electrostatic force through the driving comb, which acts on the comb connected to the resonant beam. The resonant beam vibrates at its natural frequency without acceleration input. The vibration displacement will cause the comb capacitance to change and generate a detection current. The detection current is then converted into a driving voltage through the peripheral circuit and applied to the driving comb, thus forming a closed-loop driving circuit. However, since the straight resonant beam in the tuning fork structure will inevitably produce mechanical nonlinearity when vibrating, the resonator will produce an amplitude-frequency coupling effect, resulting in nonlinearity in the accelerometer output, and severely limiting the high Q value of the accelerometer.

[0004] In recent years, resonant accelerometers with electrostatic tuning frequency detection as the core have become one of the key research objects. Resonant accelerometers with frequency detection have better stability and larger range. Patent CN113092817A proposes a high-precision, large-range acceleration sensor with switchable detection mode and its control method. The accelerometer working plane layer includes a sensitive mass block and three resonators, where the resonators on both sides include an inertial force amplification lever structure and a set of differential comb drive detection structures. The adjacent resonators are provided with electrostatic force by equidistant plate capacitors to form electrostatic coupling, realizing a high-precision accelerometer with a large range, high sensitivity and large dynamic measurement range. However, this electrostatic modulation accelerometer performs frequency tuning by changing the capacitor gap. If its output is to be linearly related to acceleration, it needs to be modulated by subsequent circuits, and the influence of the mechanical nonlinearity of the double-ended fixed tuning fork resonance beam on the performance of the accelerometer is not eliminated.

[0005] In summary, in view of the current performance requirements for MEMS microelectromechanical accelerometers, how to design a MEMS electrostatically tuned resonant accelerometer that can eliminate the mechanical nonlinearity of the existing double-ended fixed tuning fork beam and can output linearly has become an urgent problem to be solved by technical personnel in this field. Summary of the invention

[0006] The object of the present invention is to provide a frequency modulated MEMS accelerometer based on a ring resonator to solve the above problems.

[0007] The technical solution for achieving the purpose of the present invention is: a frequency modulated MEMS accelerometer based on a ring resonator, including two centrally symmetrical resonators I and resonator II, resonators I and resonator II are symmetrically connected to the mass block, resonators I and resonator II both include a ring structure located in the middle, the middle ring structure is connected to the central anchor point located in the middle of the ring structure through four groups of first decoupling beams, the central anchor point is fixed on the substrate, the left and right sides of the ring structure are respectively connected to a driving detection electrode, and the front and back sides are respectively connected to an electrostatic tuning electrode, the driving detection electrode and the electrostatic tuning electrode are both variable area comb teeth electrodes, the left and right sides of each electrostatic tuning electrode are respectively connected to the front and back ends of the displacement balance levers on the left and right sides, and the front and back ends of each displacement balance lever are respectively connected to the L-shaped beams on the front and back sides through the second decoupling beams.

[0008] Furthermore, the driving detection electrode is composed of a third movable comb-tooth electrode connected to the annular structure and a fixed comb-tooth electrode fixed on the substrate.

[0009] Furthermore, the electrostatic tuning electrode consists of a first movable comb-tooth electrode connected to the annular structure and a second movable comb-tooth electrode fixed to the substrate through four groups of folded beams and outer anchor points, and the comb-tooth openings of the electrostatic tuning electrodes on the front and rear sides of each resonator are set oppositely.

[0010] Furthermore, each group of first decoupling beams is at an angle of 45° to the left-right direction.

[0011] Furthermore, the vibration mode of the annular structure is a 2θ mode, the driving detection electrodes on the left and right sides of each resonator move in opposite directions, the electrostatic tuning electrodes on the front and back sides of each resonator move in opposite directions, and the movement direction is consistent with the antinode direction of the 2θ mode vibration mode of the annular structure.

[0012] Furthermore, the annular structure is composed of several layers of single-ring structures stacked radially and connected by spokes, or is a single-ring structure.

[0013] Furthermore, it also includes a support beam structure, which is used to support the mass block and enable it to work in the sensitive acceleration direction.

[0014] Furthermore, the resonant frequency ω of the accelerometer and its structural parameters satisfy:

[0015] .

[0016] where m1 and k1 represent the equivalent mass and equivalent stiffness of each ring resonator along the detection direction.

[0017] Furthermore, the distances from the front and rear groups of second decoupling beams to the midpoint of the displacement balancing lever are the same.

[0018] According to the acceleration measurement method of the frequency modulation MEMS accelerometer based on the ring resonator, when there is a sensitive direction acceleration input, the mass block of each resonator converts the acceleration into an inertial force, the L-shaped beam changes the direction of the inertial force by 90 degrees and transmits it to the displacement balance lever through the second decoupling beam, and the displacement balance lever transmits the inertial forces in opposite directions on the front and rear sides to the electrostatic tuning electrode, so that the displacement magnitudes of the second movable comb-tooth electrodes on the front and rear sides of the electrostatic tuning electrodes fixed on the substrate through the outer anchor points are consistent and opposite in direction. At this time, the two resonators are driven by the driving detection electrode and are in a 2θ mode. The input of acceleration causes the overlap area of ​​the capacitances of the electrostatic tuning electrodes on the front and rear sides to change in the same manner, the change in the magnitude of the electrostatic negative stiffness is consistent, the resonant frequency of the resonator changes, the detection current generated by the fixed comb-tooth electrode of the driving detection electrode changes, the change in the magnitude of the electrostatic negative stiffness of the two resonators is opposite, resulting in the opposite change in the resonant frequency of the two resonators, and the detection current output signals of the two resonators are subjected to differential processing and amplification to obtain the magnitude of the inertial space acceleration.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] The accelerometer of the present invention uses a ring resonant beam to replace the straight resonant beam in the traditional accelerometer, which greatly reduces the nonlinearity of the resonant beam during free vibration, can effectively increase the vibration amplitude and thus obtain a better signal-to-noise ratio, which is beneficial for the self-excited oscillation to accurately capture the natural frequency of the resonator and improve the control accuracy. At the same time, the design of the ring resonator can also effectively improve the scale factor of the accelerometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a front view schematic diagram of the MEMS accelerometer of the present invention.

[0022] Figure 2 FIG. 4 is a schematic diagram of a resonator of a MEMS accelerometer of the present invention.

[0023] Figure 3 It is a schematic diagram of a single-ring structure resonator of the MEMS accelerometer of the present invention.

[0024] Figure 4 The 2θ vibration mode diagram of the ring structure differential of the MEMS accelerometer of the present invention; wherein A is the main direction and B is the oblique 45° direction.

[0025] Figure 5 Schematic diagram of the driving mode of the MEMS accelerometer of the present invention.

[0026] Figure 6 It is a schematic diagram of the 2θ detection mode of the MEMS accelerometer of the present invention.

[0027] Figure 7 This is a simplified dynamic model of the MEMS accelerometer of the present invention.

[0028] Description of reference numerals:

[0029] 1-resonator I, 2-resonator II, 3-ring structure, 301-single ring structure, 302-spoke, 4-driving detection electrode, 401-third movable comb tooth electrode, 402-fixed comb tooth electrode, 5-central anchor point, 6-first decoupling beam, 7-electrostatic tuning electrode, 701-first movable comb tooth electrode, 702-second movable comb tooth electrode, 8-folding beam, 9-displacement balance lever, 10-L-beam, 11-mass block, 12-support beam structure, 13-outer anchor point, 14-second decoupling beam, 100-accelerometer. DETAILED DESCRIPTION

[0030] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0031] like Figure 1As shown, an embodiment of the present invention discloses a frequency modulation MEMS accelerometer 100 based on a ring resonator, comprising two centrosymmetrical resonators Ⅰ1 and resonator Ⅱ2, a ring structure 3 in the middle of the resonator, four groups of first decoupling beams 6 placed inside the ring structure 3, the middle ring structure 3 is connected to the central anchor point 5 through the four groups of first decoupling beams 6, the central anchor point 5 is fixed on the substrate, a driving detection electrode 4 for driving the MEMS accelerometer resonator structure to vibrate along a first direction and a second direction perpendicular to each other in a generalized space and detecting the vibration frequency of the MEMS accelerometer resonator, a variable area electrostatic tuning electrode 7 for changing the vibration frequency of the MEMS accelerometer resonator, a displacement balancing lever 9 for maintaining the same displacement of movable comb teeth of the front and rear electrostatic tuning electrodes 7 of the MEMS accelerometer resonator, an L-shaped beam 10 for transmitting and changing the direction of inertial force, a mass block 11 for converting the acceleration in the sensitive direction into inertial force, and a supporting beam structure 12 for supporting the mass block 11 and making it work in the sensitive acceleration direction.

[0032] like Figure 2 As shown, when resonator Ⅰ1 and resonator Ⅱ2 work in the 2θ mode, the ring structure 3 is composed of a plurality of layers of single ring structures 301 superimposed and connected by spokes 302. Figure 3 The ring resonator composed of a single-ring structure is shown. The mechanical property that the ring will not produce stretching when it vibrates freely is used to eliminate the mechanical nonlinearity of the ring resonator when it is working. There are two drive detection electrodes 4 and two electrostatic tuning electrodes 7 on the outside of each ring structure 3, and all four electrodes are variable-area comb-tooth electrodes. The drive detection electrodes 4 on the left and right sides are composed of a third movable comb-tooth electrode 401 located on the ring structure 3 and a fixed comb-tooth electrode 402 fixed on the substrate. The electrostatic tuning electrodes 7 on the front and back sides are composed of a first movable comb-tooth electrode 701 located on the ring structure 3 and a second movable comb-tooth electrode 702 fixed on the substrate through four groups of folded beams 8 and outer anchor points 13. The comb openings of the electrostatic tuning electrodes 7 on the front and back sides are set oppositely. The electrostatic tuning detection method can isolate the resonator from external stress and reduce the interference of external stress on the working mode of the resonator. The drive detection electrode 4 uses a variable area capacitor to make the capacitance change linearly related to the comb tooth displacement, and the mechanical gain can be freely changed by adjusting the number and distribution of comb teeth; the electrostatic tuning electrode 7 uses a variable area capacitor to effectively reduce the electrode electrostatic nonlinearity and capacitance nonlinearity, so that the square of the accelerometer output frequency is linearly related to the acceleration. The differential output of the detection current is achieved by setting two resonators, suppressing nonlinearity and common mode errors, and further improving the stability and vibration resistance of the MEMS accelerometer.

[0033] When the MEMS accelerometer 100 is in use, the two resonators are driven by a fixed comb electrode 402 fixed on the substrate. Under the action of the first decoupling beam 6, the resonator vibrates along the first direction X (radial) and the second direction Y (radial) perpendicular to each other, forming a differential 2θ vibration mode in the driving direction. Through the coupling effect of the intermediate ring structure 3, the radial movement of the first movable comb electrode 701 located on the ring structure 3 is driven. The ring structure 3 is connected to the central anchor point 5 in the center through four groups of first decoupling beams 6 to eliminate the vibration mode of the differential 2θ vibration mode of the resonator in the oblique 45° direction, ensuring that the driving mode of the resonator is the main direction. Figure 4 A and B show the vibration modes of the resonator in the main direction and the 45° direction respectively. Figure 5 As shown, when there is acceleration in the inertial space, the second movable comb-tooth electrodes 702 of the two resonators fixed on the substrate by four groups of folded beams 8 produce displacement changes due to the inertial force, and the electrostatic negative stiffness of the electrostatic tuning electrode 7 changes, resulting in changes in the resonant frequency and vibration displacement of the 2θ vibration mode of the resonator, and changes in the detection current generated by the fixed comb-tooth electrode 402 fixed on the substrate. Finally, the magnitude of the acceleration in the inertial space is obtained through the differential output of the detection currents of the two resonators.

[0034] Working mode of the accelerometer: In the driving working mode, an AC driving voltage signal is applied through the fixed comb-tooth electrode 402 of the driving detection electrode 4 located outside the ring structure 3, generating a driving force to drive the electrostatic tuning electrodes 7 on the front and rear sides of the resonator to perform reciprocating resonant motion in the radial direction. A DC voltage is applied to the electrostatic tuning electrode 7 to generate electrostatic negative stiffness. The first movable comb-tooth electrode 701 of the electrostatic tuning electrode is fixed to the outer anchor point 13 on the substrate through four groups of Y-direction folded beams 8. The Y-direction stiffness is very large and it remains stationary under the action of the electrostatic force. The stable control of the driving displacement amplitude and frequency is achieved through the automatic gain control (AGC) and phase-locked loop (PLL) closed-loop circuit.

[0035] In the sensitive detection working mode, when there is an acceleration input in the Y direction in the inertial space, for each resonator, the mass block 11 converts the acceleration into an inertial force in the Y direction, the L-shaped beam 10 converts the inertial force in the Y direction into an inertial force in the X direction and transmits it to the displacement balance lever 9 through the second decoupling beam 14 in the Y direction. The distances from the midpoints of the front and rear groups of second decoupling beams 14 to the displacement balance lever 9 are the same. The displacement balance lever 9 transmits the inertial forces in opposite directions on the front and rear sides to the electrostatic tuning electrode 7, so that the displacements of the second movable comb-tooth electrodes 702 fixed on the substrate by the outer anchor points 13 on the front and rear sides of the electrostatic tuning electrodes 7 are consistent in magnitude and opposite in direction. At this time, the two resonators are driven by the driving detection electrode 4 and are in the 2θ mode. The input of acceleration causes the overlapping area of ​​the capacitances of the front and rear electrostatic tuning electrodes 7 to change in the same manner, and the change in the magnitude of the electrostatic negative stiffness is consistent. The resonant frequency of the resonator changes, and the detection current generated by the fixed comb-tooth electrode 402 of the driving detection electrode 4 changes. Since the two resonators are centrally symmetrically arranged, the changes in the overlapping area of ​​the capacitances of the two electrostatic tuning electrodes 7 and the magnitude of the electrostatic negative stiffness are opposite. Finally, the detection current output signals of the two resonators are differentially processed and amplified to obtain the magnitude of the inertial space acceleration.

[0036] The simplified model of the accelerometer 100 disclosed in the embodiment of the present invention can be used Figure 7 The multi-degree-of-freedom dynamic model representation is shown. Figure 7 The figure A shows the dynamic model of the sensitive structure of the 1 / 4 accelerometer, where a is the acceleration in the X direction of the inertial space, M / 4 represents 1 / 4 of the total mass of the accelerometer mass block, represents the equivalent stiffness of the folded beam of the supporting structure, represents the equivalent stiffness of the L-beam, represents the equivalent stiffness of the force balancing lever and the decoupling beam connected to it, represents the equivalent stiffness of each set of decoupling beams of the movable comb electrode, is the X-direction displacement of the movable comb electrode fixed on the substrate by four sets of decoupling beams. The dynamic formula of the simplified model is:

[0037]

[0038]

[0039]

[0040] in is the total displacement of the entire 1 / 4 sensitive structure, is the total equivalent stiffness of 1 / 4 sensitive structure, 1 is the displacement of 1 / 4 of the total mass of the mass block.

[0041] Figure 7Figure B shows the dynamic model of the accelerometer resonator. , and denote the equivalent mass, equivalent stiffness and equivalent damping of the resonator respectively, represents the electrostatic negative stiffness of the electrostatic tuning electrode. The working principle of this simplified model is: through the driving force force When vibrating in the driving direction (X direction), Figure 6 When there is an acceleration in the X direction in the inertial space in Figure A, the mass block 11 converts the acceleration into the displacement of the movable comb electrode in the X direction through the sensitive structure. , Figure 6 The electrostatic negative stiffness of the resonator in Figure B The dynamics formula of the simplified model is:

[0042]

[0043]

[0044]

[0045] Where x represents the overlap length of the electrostatic tuning electrode capacitance comb teeth, b represents the thickness of the electrostatic tuning electrode capacitance comb teeth, V represents the electrostatic tuning electrode capacitance potential difference, d represents the electrostatic tuning electrode capacitance gap, represents the dielectric constant of air. From the expression of the resonant frequency ω, it can be obtained by adjusting the equivalent mass , equivalent stiffness and electrostatic negative stiffness , that is, the equivalent mass of the ring structure, the radius and width of a single ring, the overlapping length of the electrostatic tuning electrode capacitance comb teeth, the thickness, the potential difference and the gap to adjust the frequency difference between the working mode and other interference modes.

[0046] The driving electrode of the accelerometer of the present invention excites the annular resonator at its natural frequency, and the external acceleration changes the overlapping area of ​​the parallel capacitor plates of the tuning electrode, thereby generating electrostatic negative stiffness, changing the vibration frequency of the annular resonator, and finally converting the mechanical vibration of the annular resonator into a current signal by the detection electrode, and reflecting the acceleration change by detecting the frequency change of the output current. The present invention innovatively uses an annular structure to replace the straight resonant beam in the classical frequency modulation accelerometer, which can theoretically eliminate the nonlinearity of the straight resonant beam during free vibration, increase the resonator signal-to-noise ratio, and improve the scale factor of the accelerometer. The present invention innovatively proposes an annular structure to replace the straight resonant beam in the classical frequency modulation accelerometer, which can theoretically eliminate the nonlinearity of the straight resonant beam during free vibration, increase the resonator signal-to-noise ratio, and improve the scale factor of the accelerometer. The frequency tuning of the resonator is performed using electrostatic negative stiffness, and the resonator is separated from the sensitive structure of the accelerometer, thereby improving the dynamic stability and vibration resistance of the MEMS device.

[0047] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A frequency modulated MEMS accelerometer based on a ring resonator, characterized in that: The invention comprises two centrally symmetrical resonators I (1) and II (2), wherein the resonators I (1) and II (2) are symmetrically connected to a mass block (11). Resonator I (1) and resonator II (2) both include a ring structure (3) located in the middle, the ring structure (3) in the middle is connected to a central anchor point (5) located in the middle of the ring structure (3) through four groups of first decoupling beams (6), the central anchor point (5) is fixed on a substrate, the left and right sides of the ring structure (3) are respectively connected to a driving detection electrode (4), and the front and rear sides are respectively connected to an electrostatic tuning electrode (7), the driving detection electrode (4) and the electrostatic tuning electrode (7) are both variable area comb teeth electrodes, the left and right sides of each electrostatic tuning electrode (7) are respectively connected to the front and rear ends of the displacement balance levers (9) on the left and right sides, and the front and rear ends of each displacement balance lever (9) are respectively connected to the L-shaped beams (10) on the front and rear sides through second decoupling beams (14).

2. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 1, characterized in that: The driving detection electrode (4) is composed of a third movable comb-tooth electrode (401) connected to the annular structure (3) and a fixed comb-tooth electrode (402) fixed on the substrate.

3. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 2, characterized in that: The electrostatic tuning electrode (7) is composed of a first movable comb-tooth electrode (701) connected to the annular structure (3) and a second movable comb-tooth electrode (702) fixed on the substrate via four groups of folded beams (8) and outer anchor points (13), and the comb-tooth openings of the electrostatic tuning electrodes (7) on the front and rear sides of each resonator are arranged in opposite directions.

4. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 3, characterized in that: Each group of first decoupling beams (6) is angled at 45 degrees to the left and right directions.

5. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 4, characterized in that: The vibration mode of the ring structure (3) is a 2θ mode, the driving detection electrodes (4) on the left and right sides of each resonator move in opposite directions, and the electrostatic tuning electrodes (7) on the front and rear sides of each resonator move in opposite directions, and the movement direction is consistent with the antinode direction of the 2θ mode vibration mode of the ring structure (3).

6. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 5, characterized in that: The annular structure (3) is composed of a plurality of layers of single-ring structures stacked radially and connected by spokes (302), or is a single-ring structure.

7. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 5, characterized in that: It also comprises a supporting beam structure (12), wherein the supporting beam structure (12) is used to support the mass block (11) and enable it to work in a sensitive acceleration direction.

8. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 5, characterized in that: The resonant frequency ω of the accelerometer and its structural parameters satisfy: ， where m1 and k1 represent the equivalent mass and equivalent stiffness of each ring resonator along the detection direction.

9. The frequency modulated MEMS accelerometer based on a ring resonator according to claim 5, characterized in that: The distances from the midpoints of the front and rear groups of second decoupling beams (14) to the displacement balancing lever (9) are the same.

10. The acceleration measurement method of the frequency modulated MEMS accelerometer based on the ring resonator according to any one of claims 5 to 9, characterized in that: When there is an acceleration input in a sensitive direction, the mass block (11) of each resonator converts the acceleration into an inertial force, the L-shaped beam (10) changes the direction of the inertial force by 90 degrees and transmits it to the displacement balance lever (9) through the second decoupling beam (14), and the displacement balance lever (9) transmits the inertial forces in opposite directions on the front and rear sides to the electrostatic tuning electrode (7), so that the displacement magnitudes of the second movable comb-tooth electrodes (702) fixed on the substrate through the outer anchor points (13) on the front and rear sides of the electrostatic tuning electrodes (7) are consistent and opposite in direction. At this time, the two resonators are driven by the driving detection electrode (4) and are in a 2θ mode. The input of acceleration causes the overlap area of ​​the capacitances of the electrostatic tuning electrodes (7) on the front and rear sides to change in the same manner, and the magnitude of the change in the magnitude of the electrostatic negative stiffness is consistent, the resonant frequency of the resonator changes, the detection current generated by the fixed comb-tooth electrode (402) of the driving detection electrode (4) changes, and the magnitude of the change in the magnitude of the electrostatic negative stiffness of the two resonators is opposite, resulting in the magnitude of the change in the resonant frequency of the two resonators being opposite. The detection current output signals of the two resonators are subjected to differential processing and amplification to obtain the magnitude of the inertial space acceleration.

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