An acceleration sensor based on coupled beam 1:3 internal resonance phenomenon

By using the coupled beam-type 1 to 3 internal resonance phenomenon and electrostatic coupling technology in the MEMS acceleration sensor, the frequency response of the high-frequency tuning fork beam is detected, and the problems of energy loss and external environmental impact in the prior art are solved, thereby improving the sensitivity of the acceleration sensor and improving the system stability.

CN118584142BActive Publication Date: 2025-04-18INNER MONGOLIA UNIVERSITY
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Patent Information

Application Number
CN202410862317.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-06-28
Publication Date
2025-04-18
Estimated Expiration
2044-06-28

AI Technical Summary

Technical Problem

In long-term operation or high-frequency applications, existing MEMS resonant acceleration sensors may lead to reduced system performance and stability, and the oscillator is susceptible to external environment.

Method used

The acceleration sensor based on the phenomenon of 1 to 3 intra-resonance of coupled beams is adopted to improve the detection sensitivity by detecting the frequency response of the high-frequency tuning fork beams, and the coupling strength between the resonators is adjusted through electrostatic coupling to achieve the improvement of sensitivity.

Benefits of technology

The sensitivity of the acceleration sensor is improved by about 61%, and the sensitivity, detection range and resolution of the sensor can be adjusted online by adjusting the coupling voltage, improving the stability of the system.

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Abstract

The invention discloses an acceleration sensor based on a coupled beam type 1:3 internal resonance phenomenon, comprising: a mass block, a first micro-lever and a second micro-lever arranged on one side of the mass block in a horizontal direction and symmetrically arranged up and down, a first tuning fork beam and a second tuning fork beam arranged on one side of the mass block in a horizontal direction, two ends of the first tuning fork beam being fixed respectively by a first fixed end and a second fixed end; the first fixed end and the second fixed end being arranged on both sides of a detection electrode respectively; two ends of the second tuning fork beam being fixed respectively by a third fixed end, a first micro-lever and a second micro-lever; two ends of the second tuning fork beam being fixed respectively by the third fixed end, the first micro-lever and the second micro-lever; the first tuning fork beam and the second tuning fork beam being coupled by electrostatic coupling, a coupling power supply outputting a coupling voltage being loaded on the second fixed end connected to the first tuning fork beam, the first tuning fork beam detecting amplitude and frequency by a fixed detection electrode; the second tuning fork beam adjusting driving force by a fixed excitation electrode.
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Description

Technical Field

[0001] The present invention relates to the technical field of micro-electromechanical systems, and in particular to an acceleration sensor based on a coupled beam type 1:3 internal resonance phenomenon. Background Art

[0002] Early resonators were made of quartz crystals and ceramics. With the continuous improvement of performance requirements and the rapid development of micro-nano processing technology, MEMS resonators have gradually become a research hotspot due to their small size, high quality factor, and high sensitivity, and have broadened their applications in high-tech fields such as information, chemistry, biology, and medicine.

[0003] Among them, MEMS resonant accelerometers are based on the current situation at home and abroad. Most of their structures are mass block-lever-resonator modes. The sensitive mechanism of MEMS resonant accelerometers is based on the change of the axial force of the resonator caused by the inertial force of the mass block, and finally the magnitude and direction of acceleration are obtained.

[0004] In order to improve the performance of accelerometers, Xu Liu et al. proposed an enhancement method based on a synchronized oscillator in "Programmable synchronization enhanced MEMS resonant accelerometer [J]" (Microsystems and Nanoengineering, 2020, 6 (1): 654-663) to increase the resolution of microelectromechanical resonant accelerometers by five times, but the oscillator is easily affected by the external environment. Zhang Heming et al. combined weakly coupled resonators with mode localization in "a novel resonant accelerometer based on mode localization of weakly coupled resonatore" (International Conference on Solid-State Sensors, Actuators and Microsystems. 2015) and experimentally verified that the sensitivity of the resonator can be improved. However, the energy loss of weakly coupled resonators in long-term operation or high-frequency applications may lead to a decrease in system performance and stability. Summary of the invention

[0005] In order to improve the sensitivity of the resonant acceleration sensor, the frequency detection signal of the low-frequency tuning fork beam is compared with the frequency signal of the high-frequency tuning fork beam. It is found that the frequency change sensitivity of the high-frequency tuning fork beam is higher than that of the low-frequency tuning fork beam. The present invention provides

[0006] An acceleration sensor based on coupled beam type 1:3 internal resonance phenomenon, comprising:

[0007] A mass, used to move laterally under the action of inertia;

[0008] A first micro-lever and a second micro-lever are arranged symmetrically in the horizontal direction of the mass block, and are used to amplify the force felt by the mass block;

[0009] The first micro-lever is arranged above the second micro-lever;

[0010] A first tuning fork beam and a second tuning fork beam disposed on one side of the mass block in the horizontal direction;

[0011] The second tuning fork beam is located at the lower side of the first tuning fork beam,

[0012] Two ends of the first tuning fork beam are fixed by a first fixed end and a second fixed end respectively;

[0013] The first fixed end and the second fixed end are respectively arranged on two sides of the detection electrode;

[0014] Two ends of the second tuning fork beam are respectively fixed by the third fixed end, the first micro-lever and the second micro-lever;

[0015] The first micro-lever, the second micro-lever, the first tuning fork beam and the second tuning fork beam are arranged on the same side of the mass block;

[0016] The second tuning fork beam is placed on the left side of the mass block;

[0017] The upper side and the lower side of the mass block are fixed to the first anchor point and the second anchor point respectively;

[0018] The upper side of the mass block is connected to the first anchor point through the first support beam,

[0019] The lower side of the mass block is connected to the second anchor point via the second support beam;

[0020] The mass block and the second tuning fork beam amplify the inertial force of the mass block and the force exerted on the second tuning fork beam through a lever structure;

[0021] Wherein, the first tuning fork beam and the second tuning fork beam are electrostatically coupled, and a coupling power supply outputs a coupling voltage which is loaded on a second fixed end connected to the first tuning fork beam, so as to adjust the electrostatic coupling strength between the first tuning fork beam and the second tuning fork beam;

[0022] The first tuning fork beam detects the amplitude and frequency through the detection electrode; the second tuning fork beam adjusts the driving force through the excitation electrode.

[0023] Furthermore, the first tuning fork beam and the second tuning fork beam have the same structure but different lengths, and the length of the second tuning fork beam is about 1.86 times the length of the first tuning fork beam;

[0024] Furthermore, the width of the second tuning fork beam is equal to the width of the first tuning fork beam; and the natural frequency of the first tuning fork beam is three times the natural frequency of the second tuning fork beam.

[0025] Furthermore, the length of the detection electrode is equal to the length of the fixed excitation electrode, and the width of the detection electrode is equal to the width of the fixed excitation electrode.

[0026] Furthermore, the length of the detection electrode is equal to the tuning fork length of the first tuning fork beam, and the width of the detection electrode is equal to the width of the first tuning fork beam; the length of the excitation electrode is equal to the tuning fork length of the second tuning fork beam, and the width of the excitation electrode is equal to the width of the second tuning fork beam.

[0027] Further, the gap between the detection electrode and the first tuning fork beam is equal to the gap between the excitation electrode and the second tuning fork beam, which is equal to the distance between the second tuning fork beam and the first tuning fork beam.

[0028] Furthermore, the excitation voltage of the excitation electrode is driven by a direct current voltage and an alternating current voltage.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] 1. The present invention has the characteristic of easy adjustment of coupling strength, and the coupling strength between the clamped beams can be changed only by voltage adjustment;

[0031] 2. The present invention improves the detection sensitivity by detecting the high-frequency tuning fork beam, and adopts a lever structure connected to the resonator to greatly amplify the inertial force of the mass block;

[0032] 3. The feasibility of the proposed structure is verified by an implementation example. The sensitivity is increased by 61% compared with the low-frequency tuning fork beam output with the high-frequency detection result ratio as the output sensitivity.

[0033] In summary, in the process of resonator development, there are many ways to improve the performance of resonators. This article invents an acceleration sensor based on the coupled beam type 1 to 3 internal resonance phenomenon, which adopts the mechanism of detecting high-frequency tuning fork beams to improve the sensitivity of the resonator. Electrostatic coupling is adopted between the high-frequency tuning fork beam and the low-frequency tuning fork beam. By changing the coupling voltage, the coupling strength between the two tuning fork beams changes.

[0034] The present invention provides an acceleration sensor based on the coupled beam type 1 to 3 internal resonance phenomenon, and the high-frequency tuning fork beam has higher sensitivity. In the process of detecting acceleration, the electrostatic coupling strength between the resonators is changed by adjusting the coupling voltage. The left side of the mass block is connected to the resonator. Under the action of inertial force, when the mass block moves axially, the force amplified by the micro-lever structure acts on the resonator, causing the amplitude and frequency of the resonator to change. The acceleration magnitude is obtained by calculating the frequency change of the high-frequency tuning fork beam. The first tuning fork beam is detected by a fixed detection electrode, and the second tuning fork beam is driven by a fixed excitation electrode. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0036] Figure 1 Schematic diagram of the structure of a coupled resonant acceleration sensor according to an embodiment of the present invention;

[0037] Figure 2 is an amplitude-frequency characteristic diagram of the first tuning fork beam under acceleration disturbance from -1g to 0g in an embodiment of the present invention;

[0038] Figure 3 is an amplitude-frequency characteristic diagram of the second tuning fork beam under acceleration disturbance from -1g to 0g in an embodiment of the present invention;

[0039] Figure 4 It is a sensitivity comparison diagram of the relative frequency ratio change output mode when the coupling voltage is 10V in an embodiment of the present invention; a second tuning fork beam.

[0040] Figure numerals: 1-1, first micro-lever structure, 1-2, detection power supply, 1-3, excitation power supply, 1-4, second micro-lever; 2-1, first fixed end; 2-2 detection electrode; 2-3 second fixed end; 2-4, first tuning fork beam; 3-1, third fixed end; 3-2, excitation electrode, 3-3, second tuning fork beam; 4-1, first anchor point; 4-2, second anchor point, 4-3, mass block, 4-4, first support beam, 4-5, second support beam DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0042] The accelerometer with coupled beam type 1:3 internal resonance detects the external acceleration by detecting the frequency response of the high-frequency tuning fork beam. Compared with detecting the frequency of the low-frequency tuning fork beam, its sensitivity is increased by about 61%. Changes in the external environment will bring changes in the characteristic state and amplitude of the sensor, so it is necessary to improve the accelerometer.

[0043] Example 1: Figure 1 As shown, the present invention provides a structural schematic diagram of an acceleration sensor based on a coupled beam type 1:3 internal resonance phenomenon. The acceleration sensor comprises:

[0044] The mass block 4-3 is made of silicon material and is rectangular. Its function is: lateral movement. The mass block 4-3 will move laterally under the action of inertia. Due to the movement, the mass block will exert a strong effect on the tuning fork beam connected to the left side of the mass block through the micro-lever structure. At this time, the left tuning fork beam will be subjected to tension or pressure. Due to the different forces, the frequency of the tuning fork beam when it is deformed under the action of axial force is inconsistent, and the magnitude of acceleration is detected by the frequency change.

[0045] A first tuning fork beam 2-4 and a second tuning fork beam 3-3 are arranged on the left side of the mass block 4-3;

[0046] The first tuning fork beam is a high-frequency tuning fork beam, and the second tuning fork beam is a low-frequency tuning fork beam. The reason why the first tuning fork beam 2-4 is called a high-frequency tuning fork beam is that the natural frequency of the first tuning fork beam 2-4 is 569kHz, and the reason why the second tuning fork beam 3-3 is called a low-frequency tuning fork beam is that the natural frequency of the second tuning fork beam 3-3 is 188kHz. The natural frequency of the first tuning fork beam 2-4 is 3.17 times the natural frequency of the second tuning fork beam 3-3, which is about 3 times. Therefore, the first tuning fork beam 2-4 is called a high-frequency tuning fork beam, and the second tuning fork beam 3-3 is called a low-frequency tuning fork beam;

[0047] The first micro-lever 1-1, the second micro-lever 1-3, the first tuning fork beam 2-4 and the second tuning fork beam 3-3 are arranged on the left side of the mass block 4-3;

[0048] The first tuning fork beam and the second tuning fork beam have the same structure but different lengths, and the length of the second tuning fork beam is about 1.86 times the length of the first tuning fork beam;

[0049] The first tuning fork beam 2-4 is placed on the left side of the mass block 4-3.

[0050] The first tuning fork beam 2-4 has its two ends fixed by a first fixed end 2-1 and a second fixed end 2-3 respectively, and the first fixed end 2-1 and the second fixed end 2-3 also function as coupling electrodes;

[0051] The two ends of the second tuning fork beam 3-3 are respectively fixed by the third fixed end 3-1, the first micro-lever 1-1 and the second micro-lever 1-3; the tuning fork beam connected to the micro-lever, under the dual action of the lever force and the coupling force, the frequency of its deformation will change according to the different acceleration sizes when the mass block 4-3 moves. By detecting the frequency change of the first tuning fork beam 2-4 and the frequency change of the second tuning fork beam 3-3 and comparing them, the former has a high sensitivity to frequency change.

[0052] The upper side of the mass block 4-3 is fixed by a first anchor point 4-1;

[0053] The lower side of the mass block 4-3 is fixed by a second anchor point 4-2;

[0054] The function of the first anchor point 4-1 and the second anchor point 4-2 is to connect with the mass block through the support beam 4-4 and the support beam 4-5, and fix the mass block in the vertical direction.

[0055] The upper side of the mass block 4-3 is connected to the first anchor point 4-1 through the first support beam 4-4.

[0056] The lower side of the mass block 4-3 is connected to the second anchor point 4-2 via the second support beam 4-5;

[0057] The mass block 4-3 and the second tuning fork beam 3-3 amplify the inertial force of the mass block 4-3 and the force exerted on the second tuning fork beam 3-3 through a lever structure;

[0058] Among them, the first tuning fork beam 2-4 and the second tuning fork beam 3-3 are electrostatically coupled, and the coupling power supply outputs a coupling voltage which is loaded on the second fixed end 2-3 connected to the first tuning fork beam 3-1, so as to adjust the electrostatic coupling strength between the first tuning fork beam 2-4 and the second tuning fork beam 3-3;

[0059] The first tuning fork beam 2-4 detects the amplitude and frequency through the detection electrode 2-2;

[0060] The second tuning fork beam 3-3 adjusts the driving force by fixing the excitation electrode 3-2;

[0061] The length of the detection electrode 2-2 is equal to the length of the driving electrode 3-2, and the width of the detection electrode 2-2 is equal to the width of the fixed electrode 3-2;

[0062] The length of the second tuning fork beam 3 - 3 is not equal to the length of the first tuning fork beam 2 - 4 .

[0063] The length of the second tuning fork beam 3-3 is about 1.86 times the length of the first tuning fork beam 2-4.

[0064] right

[0065] The width of the second tuning fork beam 3 - 3 is equal to the width of the first tuning fork beam 2 - 4 .

[0066] The natural frequency of the second tuning fork beam 3 - 3 is 1 / 3 of the natural frequency of the first tuning fork beam 3 - 1 ;

[0067] The length of the detection electrode 2 - 2 is equal to the length of the tuning fork of the first tuning fork beam 2 - 4 , and the width of the detection electrode 2 - 2 is equal to the width of the first tuning fork beam 2 - 4 .

[0068] The length of the excitation electrode 3 - 2 is equal to the length of the tuning fork of the second tuning fork beam 3 - 3 , and the width of the excitation electrode 3 - 2 is equal to the width of the second tuning fork beam 3 - 3 .

[0069] The gap between the detection electrode 2-2 and the first tuning fork beam 2-4 is equal to the gap between the excitation electrode 3-2 and the second tuning fork beam 3-3, and equal to the distance between the second tuning fork beam 3-3 and the first tuning fork beam 2-4.

[0070] The excitation electrode 3 - 2 and the fixed detection electrode 2 - 2 are completely fixed to the chip.

[0071] The voltage source of the detection electrode 2-2 is driven by direct current.

[0072] The voltage source of the excitation electrode 3 - 2 is driven by both alternating current and direct current.

[0073] Embodiment 2:

[0074] The present invention provides a schematic structural diagram of an acceleration sensor based on a coupled beam type 1:3 internal resonance phenomenon. The acceleration sensor comprises:

[0075] The mass block 4-3 is made of silicon material and is rectangular.

[0076] A first micro-lever and a second micro-lever are symmetrically arranged up and down on the right side of the mass block 4-3;

[0077] The first micro-lever 1-1 is arranged above the second micro-lever 1-3;

[0078] A first tuning fork beam 2-4 and a second tuning fork beam 3-3 arranged on the left side of the mass block 4-3 in the horizontal direction;

[0079] The connection methods and requirements of other components are the same as those of Example 1.

[0080] The present invention provides an acceleration sensor based on the coupled beam type 1:3 internal resonance phenomenon, which realizes online adjustment of sensor sensitivity, detection range and resolution by adjusting the coupling voltage to change the electrostatic coupling strength. The second tuning fork beam is driven by a fixed excitation electrode. When the mass block moves under the action of external acceleration, the axial force of the second tuning fork beam changes through a lever, thereby changing the frequency. The magnitude of the acceleration can be obtained by detecting the frequency changes of the first tuning fork beam and the second tuning fork beam. The first tuning fork beam is a high-frequency tuning fork beam, and the second tuning fork beam is a low-frequency tuning fork beam. The detection sensitivity of the first tuning fork beam is higher than that of the second tuning fork beam.

[0081] The following is a specific example to illustrate an acceleration sensor based on the coupled beam type 1:3 internal resonance phenomenon provided by the present invention.

[0082] like Figure 1 The structure schematic diagram of an acceleration sensor based on the coupled beam type 1:3 internal resonance phenomenon in an embodiment of the present invention is shown, in which a mass block is connected to an anchor point through support beams on the upper and lower sides, and is connected to a tuning fork beam on the left side. Under the action of external acceleration, the mass block will undergo axial movement, thereby changing the axial stress of the resonator and breaking the tuning fork beam in a balanced state, changing the frequency of the tuning fork beam, and calculating the magnitude of the external acceleration by detecting the frequency change of the output resonator.

[0083] Compared with the traditional mechanical coupling structure, the electrostatic coupling adopted in the present invention can adjust the coupling strength in real time and easily achieve low coupling stiffness. Figure 2 FIG. 1 is an amplitude-frequency characteristic diagram of the first tuning fork beam of the acceleration sensor of the present invention when the first tuning fork beam is in a state of -1g to 0g according to the dimensions in Table 1 of the structural parameters of the present invention in an embodiment of the present invention, wherein the abscissa is the frequency (Hz) and the ordinate is the amplitude (μm). Figure 3 It shows the amplitude-frequency characteristic diagram of the second tuning fork beam of the accelerometer sensor of the present invention when it is in the state of -1g to 0g according to the dimensions in the structural parameter table 1 of the present invention in an embodiment of the present invention, wherein the abscissa is the frequency (Hz) and the ordinate is the amplitude (μm).

[0084] Table 1

[0085]

[0086] Figure 4 : This is the sensitivity situation when the relative frequency ratio is used as the sensitivity output in the embodiment of this article, where (a) is the sensitivity of the first tuning fork beam, and (b) is the sensitivity of the second tuning fork beam. It is obtained by simulation in the range of -1g to 0g. The sensitivity output when the relative frequency ratio of the first tuning fork beam is used as the sensitivity output is 61% higher than that when the relative frequency ratio of the second tuning fork beam is used as the sensitivity output.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An acceleration sensor based on coupled beam type 1:3 internal resonance phenomenon, characterized in that: include: A mass block (4-3) for lateral movement under the action of inertia; A first micro-lever (1-1) and a second micro-lever (1-3) are arranged on one side of the mass block (4-3) in the horizontal direction and are symmetrically arranged up and down, and are used to amplify the force felt by the mass block (4-3); The first micro-lever (1-1) is arranged above the second micro-lever (1-3); A first tuning fork beam (2-4) and a second tuning fork beam (3-3) arranged on one side of the mass block (4-3) in the horizontal direction; The second tuning fork beam (3-3) is located at the lower side of the first tuning fork beam (2-4), The first tuning fork beam (2-4) has two ends fixed respectively by a first fixed end (2-1) and a second fixed end (2-3); The first fixed end (2-1) and the second fixed end (2-3) are respectively arranged on both sides of the detection electrode (2-2); Two ends of the second tuning fork beam (3-3) are respectively fixed by a third fixed end (3-1), the first micro-lever (1-1) and the second micro-lever (1-3); The first micro-lever (1-1), the second micro-lever (1-3), the first tuning fork beam (2-4) and the second tuning fork beam (3-3) are arranged on the same side of the mass block; The upper side and the lower side of the mass block (4-3) are respectively fixed to the first anchor point (4-1) and the second anchor point (4-2); The upper side of the mass block (4-3) is connected to the first anchor point (4-1) via a first support beam (4-4). The lower side of the mass block (4-3) is connected to the second anchor point (4-2) via a second support beam (4-5); The mass block (4-3) and the second tuning fork beam (3-3) amplify the inertial force of the mass block (4-3) and the force exerted on the second tuning fork beam (3-3) through a lever structure; The first tuning fork beam (2-4) and the second tuning fork beam (3-3) are coupled via electrostatic coupling, and a coupling power supply outputs a coupling voltage which is loaded on a second fixed end (2-3) connected to the first tuning fork beam (2-4), so as to adjust the electrostatic coupling strength between the first tuning fork beam (2-4) and the second tuning fork beam (3-3); The first tuning fork beam (2-4) detects the amplitude and frequency through the detection electrode (2-2); the second tuning fork beam (3-3) adjusts the driving force through the excitation electrode (3-2); The width of the second tuning fork beam (3-3) is equal to the width of the first tuning fork beam (2-4); the natural frequency of the first tuning fork beam (2-4) is three times the natural frequency of the second tuning fork beam (3-3); The excitation voltage of the excitation electrode (3-2) is driven by a direct current voltage and an alternating current voltage.

2. The acceleration sensor based on coupled beam type 1:3 internal resonance phenomenon according to claim 1, characterized in that: The first tuning fork beam and the second tuning fork beam have the same structure but different lengths. The length of the second tuning fork beam is about 1.86 times the length of the first tuning fork beam.

3. The acceleration sensor based on coupled beam type 1:3 internal resonance phenomenon according to claim 1, characterized in that: The length of the detection electrode (2-2) is equal to the length of the fixed excitation electrode (3-2), and the width of the detection electrode (2-2) is equal to the width of the fixed excitation electrode (3-2).

4. The acceleration sensor based on coupled beam type 1:3 internal resonance phenomenon according to claim 1, characterized in that: The length of the detection electrode (2-2) is equal to the tuning fork length of the first tuning fork beam (2-4), and the width of the detection electrode (2-2) is equal to the width of the first tuning fork beam (2-4); the length of the excitation electrode (3-2) is equal to the tuning fork length of the second tuning fork beam (3-3), and the width of the excitation electrode (3-2) is equal to the width of the second tuning fork beam (3-3).

5. The acceleration sensor based on coupled beam type 1:3 internal resonance phenomenon according to claim 1, characterized in that: The gap between the detection electrode (2-2) and the first tuning fork beam (2-4) is equal to the gap between the excitation electrode (3-2) and the second tuning fork beam (3-3), and equal to the distance between the second tuning fork beam (3-3) and the first tuning fork beam (2-4).

Citation Information

Patent Citations

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