A modal localization electrometer based on self-adjustment of modal coupling frequency

Abstract

The application discloses a modal localization electrometer based on modal coupling frequency self-adjustment, and is characterized in that the application is based on a modal coupling mechanism, changes the vibration amplitude of a low-frequency resonant beam, dynamically controls the resonance frequency of a modal localization resonant beam, limits the amplitude ratio of a high-frequency resonant beam in a linear interval, solves the application problem of the nonlinearity of the sensitivity of the resonator, and realizes the coupling between the resonant beams by using electrostatic force, realizes flexible control of the coupling strength, and further realizes flexible expansion of the amplitude ratio linear working bandwidth; the application has the advantages of not introducing thermal noise, excellent real-time performance, high control precision and the like, and in combination with the greatly expanded linear working bandwidth, the measurement precision, the range and other indexes of the modal localization principle-based electrometer are significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of micromechanical systems and nonlinear dynamics, specifically relating to a modal localization electrometer based on modal coupling frequency self-adjustment. Background Technology

[0002] Micromechanical electrometers (MEMS) are widely used in nuclear industry, biological detection, and chemical analysis as measuring instruments capable of detecting extremely weak charges or potential differences. Micrometer-scale MEMS devices offer unparalleled economic and size advantages in improving the dynamic measurement range and accuracy of electrometers; however, improving their detection accuracy remains a significant challenge. High-sensitivity resonant sensors based on modal localization have attracted considerable attention. Compared to frequency variations, resonant sensors based on modal localization sense the measured object by varying amplitude, offering advantages such as high sensitivity, high resolution, and less susceptibility to environmental influences.

[0003] However, the current amplitude detection linear operating range of resonant sensors based on modal localization is generally small, and the sensitivity detection often exceeds the linear operating range. In addition, there are frequency matching problems caused by factors such as manufacturing errors. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a modal localization electrometer based on modal coupling frequency self-adjustment. This invention addresses the technical problems of frequency matching caused by factors such as the generally small linear working range of modal localization sensors, nonlinear sensitivity changes, and manufacturing errors. By adjusting the vibration amplitude of the nonlinear low-frequency resonant beam, the vibration frequency of the linear high-frequency resonant beam is changed, thereby affecting the modal localization amplitude ratio of the two high-frequency resonant beams, thus achieving the purpose of expanding the linear working bandwidth and ensuring sensitivity.

[0005] The present invention adopts the following technical solution:

[0006] A modal localization electrometer based on modal coupling frequency self-adjustment includes a modal frequency control module. A low-frequency resonant beam in the modal frequency control module and a first high-frequency resonant beam and a second high-frequency resonant beam in the modal localization sensing module are arranged side-by-side and electrostatically coupled through a first coupling plate, a second coupling plate, a third coupling plate, and a fourth coupling plate. The second high-frequency resonant beam is placed in a second oscillation circuit to generate self-excited oscillation, and the low-frequency resonant beam is placed in a first oscillation circuit to generate self-excited oscillation.

[0007] Based on the phase information of the second high-frequency resonant beam, a phase control signal is output to the first oscillation circuit. By changing the phase delay of the first oscillation circuit, the low-frequency resonant beam in the modal frequency control module can vibrate with different amplitudes. The equivalent stiffness and resonant frequency of the first high-frequency resonant beam in the modal localization module can be dynamically controlled. Through the modal coupling mechanism, the modal changes of the first and second high-frequency resonant beams are confined within the high-sensitivity region, thereby realizing the dynamic adjustment of the electrometer's sensitivity.

[0008] Specifically, a low-frequency resonant beam and its first excited electrode plate and first coupling electrode plate extending outward from the middle are suspended on a hollow substrate. The upper and lower ends of the low-frequency resonant beam are connected to a first anchor point and a second anchor point connected to the insulating layer of the substrate, respectively. A first excitation electrode plate is also suspended on the substrate. The first excitation electrode plate is connected to a seventh anchor point. The first excited electrode plate and the first excitation electrode plate form a capacitor electrode plate. A first metal electrode layer, a second metal electrode layer, and a seventh metal electrode layer are sputtered on the first anchor point, the second anchor point, and the seventh anchor point, respectively.

[0009] Furthermore, the length of the low-frequency resonant beam is 400–600 μm; the lengths of the first excited electrode plate, the first excitation electrode plate, and the first coupling electrode plate are 150–300 μm; the first anchor point, the second anchor point, and the seventh anchor point are rectangular structures with side lengths of 150–300 μm, and the first metal electrode layer, the second metal electrode layer, and the seventh metal electrode layer are rectangular structures with side lengths of 100–250 μm.

[0010] Furthermore, the gap distance between the first excited electrode plate and the first excitation electrode plate is 2–6 μm.

[0011] Specifically, a first high-frequency resonant beam and its outwardly extending second and third coupling plates are suspended on a hollowed-out substrate. The upper and lower ends of the first high-frequency resonant beam are connected to the third and fourth anchor points, respectively, which are connected to the insulating layer of the substrate. A second high-frequency resonant beam and its outwardly extending fourth coupling plate and second excited plate are suspended on a hollowed-out substrate. The upper and lower ends of the second high-frequency resonant beam are connected to the fifth and sixth anchor points, respectively, which are connected to the insulating layer of the substrate. A second excitation plate is suspended on the substrate and connected to an eighth anchor point. A third metal electrode layer, a fourth metal electrode layer, a fifth metal electrode layer, a sixth metal electrode layer, and an eighth metal electrode layer are sputtered on the third, fourth, fifth, sixth, and eighth anchor points, respectively.

[0012] Furthermore, the first and second coupling plates form a capacitor plate, the third and fourth coupling plates form a capacitor plate, the second excited plate and the second excitation plate form a capacitor plate, and the gap between the second excited plate and the second excitation plate is 2 to 6 μm.

[0013] Furthermore, the lengths of the first and second high-frequency resonant beams are 200–400 μm; the lengths of the second, third, fourth, second excited, and second excitation plates are 150–300 μm; the third, fourth, fifth, sixth, and eighth anchor points are rectangular structures with side lengths of 150–300 μm; and the third, fourth, fifth, sixth, and eighth metal electrode layers are rectangular structures with side lengths of 100–250 μm.

[0014] Specifically, the gap distance between the first coupling plate, the second coupling plate, the third coupling plate, and the fourth coupling plate is 2 to 6 μm.

[0015] Specifically, the modal frequency control module also includes a first differential amplifier. The dynamic current flowing through the low-frequency resonant beam is converted into a voltage signal by the first differential amplifier. The voltage signal then passes through a filter, a phase shifter, and a comparator in sequence, in conjunction with a bias voltage V. dc1 It is fed back to the low-frequency resonant beam.

[0016] Furthermore, the modal localization sensing module includes a second differential amplifier. The dynamic current flowing through the second high-frequency resonant beam is converted into a voltage signal by the second differential amplifier, and then the phase change is output by the frequency control algorithm and fed back to the phase shifter.

[0017] Compared with the prior art, the present invention has at least the following beneficial effects:

[0018] A modal localization electrometer based on modal coupling frequency self-adjustment comprises a low-frequency resonant beam, a first high-frequency resonant beam, and a second high-frequency resonant beam arranged side-by-side. The resonant beams are coupled via electrostatic force generated by the potential difference between a first coupling plate, a second coupling plate, a third coupling plate, and a fourth coupling plate. The low-frequency resonant beam receives periodic excitation from a first excitation plate, changing its vibration frequency. The coupling force modulates the stiffness of the first high-frequency resonant beam, altering its resonant frequency. The second high-frequency resonant beam experiences axial stress from an axial voltage applied by a perturbation plate, changing its stiffness. Through the perturbation bias generated by the perturbation plate and the modulation effect of the low-frequency resonant beam, the amplitude ratio between the first and second high-frequency resonant beams can be altered. By modulating the equivalent stiffness of the first high-frequency resonant beam using low-frequency modes, the modal curve can be shifted. Modal coupling confines the operating mode to a high-sensitivity range while expanding the sensing range.

[0019] Furthermore, the bias voltage V d1 and V d2Acting on the first and second metal electrode layers respectively, a potential difference exists across the low-frequency resonant beam, generating a kinetic current due to the piezoresistive effect. This kinetic current signal passes through a first differential amplifier, a filter, a phase shifter, and a comparator to generate an AC voltage signal V. ac1 cos(ω1t), with bias voltage V dc1 Acting on the seventh metal electrode layer, it causes the low-frequency resonant beam to oscillate in a simple harmonic motion through the first excitation plate.

[0020] Furthermore, the bias voltage V d5 and V d6 The potential difference between the two ends of the second high-frequency resonant beam acts on the fifth and sixth metal electrode layers respectively, generating a dynamic current due to the piezoresistive effect. The dynamic current signal passes through the second differential amplifier and is fed back to the phase shifter of the modal frequency control module through the frequency control algorithm. Then, it passes through the comparator in the modal frequency control module, affecting the AC voltage signal of the modal frequency control module and applying the AC voltage signal to the seventh metal electrode layer. When the stiffness of the second high-frequency resonant beam changes, the vibration amplitude of the low-frequency resonant beam will change accordingly.

[0021] In summary, this invention utilizes a modal localization mechanism to broaden the resonator's range. First, the stiffness control of the high-frequency resonant beam originates from the coupling electrostatic force, which is a natural byproduct of the parallel capacitor plates. This means that the modal coupling mechanism does not require meticulous structural design. Second, this adjustable resonator system can limit the amplitude ratio within the linear range and significantly improve the resonator's sensitivity, expanding its operating bandwidth. Finally, compared to the piezoresistive thermal method, the modal coupling mechanism offers faster response speed, better real-time performance, and does not introduce thermal noise, ensuring the frequency stability of the self-excited oscillation circuit.

[0022] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0023] Figure 1 This is a diagram of the MEMS resonant beam structure with modal localization mechanism of the present invention;

[0024] Figure 2 This is a schematic diagram illustrating the working principle of the modal localization mechanism of this invention.

[0025] Figure 3 To perform open-loop frequency sweep of the resonant beam of the modal localization sensing module, the amplitude-frequency response diagram of the high-frequency resonant beam is shown, where (a) is the first high-frequency resonant beam and (b) is the second high-frequency resonant beam.

[0026] Figure 4 This is a graph showing the relationship between the amplitude ratio and the disturbance stiffness of a high-frequency resonant beam.

[0027] Wherein: 1-1. First metal electrode layer; 1-2. First anchor point; 1-3. Low-frequency resonant beam; 1-4. First excited electrode plate; 1-5. Second metal electrode layer; 1-6. Second anchor point; 1-7. First coupling electrode plate; 2-1. Third metal electrode layer; 2-2. Third anchor point; 2-3. First high-frequency resonant beam; 2-4. Second coupling electrode plate; 2-5. Fourth metal electrode layer; 2-6. Fourth anchor point; 2-7. Third coupling electrode plate; 3-1. Fifth metal electrode layer; 3-2. Fifth anchor point; 3-3. Second high-frequency resonant beam. ; 3-4. Fourth coupling electrode; 3-5. Sixth metal electrode layer; 3-6. Sixth anchor point; 3-7. Second stimulated electrode; 4-1. Seventh metal electrode layer; 4-2. Seventh anchor point; 4-3. First excitation electrode; 5-1. Eighth metal electrode layer; 5-2. Eighth anchor point; 5-3. Second excitation electrode; 6-1. Perturbation electrode; 6-2. Ninth anchor point; 7-1. First differential amplifier; 7-2. Filter; 7-3. Phase shifter; 7-4. Comparator; 8-1. Second differential amplifier; 9-1. Frequency control algorithm unit. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "one side," "one end," and "one side," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. 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 indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0030] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0031] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0032] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0033] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0034] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0035] This invention provides a modal localization electrometer based on modal coupling frequency self-adjustment. By changing the disturbance bias, the stiffness of the second high-frequency resonant beam in the modal localization sensing module is altered. Through the modal coupling mechanism, the frequency of the low-frequency resonant beam in the modal frequency control module is dynamically adjusted, thereby changing the amplitude ratio of the first and second high-frequency resonant beams to achieve disturbance detection. The disturbance bias is output from the second differential amplifier, and a phase change is derived through a frequency control algorithm. The modal frequency control module is affected by this phase change, causing a change in the potential difference between the first excitation plate and the first stimulated plate. This allows adjustment of the coupling electrostatic force, increasing the control capability of the resonant beam frequency and amplitude in the modal localization sensing module, and modulating the resonator sensitivity within the linear range. This invention achieves flexible control of the resonant beam amplitude in the modal localization sensing module, significantly improving measurement sensitivity, expanding the operating bandwidth of the resonant sensor, and overcoming the problem of the resonant sensor's sensitivity being in the nonlinear operating range. Based on this, this invention can meet the application requirements of large-range measurements of resonant sensors and significantly improve the overall performance of resonant sensors.

[0036] Please see Figure 1 This invention discloses a modal localization electrometer based on modal coupling frequency self-adjustment, comprising a modal frequency control module and a modal localization sensing module. The low-frequency resonant beam 1-3 in the modal frequency control module and the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 in the modal localization sensing module are arranged side-by-side and electrostatically coupled through a first coupling plate 1-7, a second coupling plate 2-4, a third coupling plate 2-7, and a fourth coupling plate 3-4. The amplitude-frequency response of the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 is obtained by an open-loop measurement circuit. The second high-frequency resonant beam 3-3 is placed in a second oscillation circuit to generate self-excited oscillation. The low-frequency resonant beam 1-3... The low-frequency resonant beam 1-3 is placed in the first oscillation circuit to generate self-excited oscillation. The frequency change of the low-frequency resonant beam 1-3 is obtained by the closed-loop circuit. According to the phase information of the second high-frequency resonant beam 3-3, the phase control signal is output to the first oscillation circuit. By changing the phase delay of the first oscillation circuit, the low-frequency resonant beam 1-3 in the modal frequency control module can vibrate with different amplitudes. This dynamically controls the equivalent stiffness and resonant frequency of the first high-frequency resonant beam 2-3 in the modal localization module. Through the modal coupling mechanism, the modal changes of the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 are limited to the high sensitivity region, and the linear working range of the sensitivity is increased. At the same time, the sensitivity of the electrometer can be dynamically adjusted.

[0037] Please refer to Figure 2The modal frequency control module includes a first metal electrode layer 1-1, a first anchor point 1-2, a low-frequency resonant beam 1-3, a first excited electrode plate 1-4, a second metal electrode layer 1-5, a second anchor point 1-6, a first coupling electrode plate 1-7, a seventh metal electrode layer 4-1, a seventh anchor point 4-2, a first excitation electrode plate 4-3, a first differential amplifier 7-1, a filter 7-2, a phase shifter 7-3, and a comparator 7-4.

[0038] A low-frequency resonant beam 1-3 is suspended on a hollowed-out substrate. The upper and lower ends of the low-frequency resonant beam 1-3 are connected to the first anchor point 1-2 and the second anchor point 1-6, which are fixed to the insulating layer of the substrate, respectively. The first excited electrode plate 1-4 extending outward from the middle of the low-frequency resonant beam 1-3 is suspended on the hollowed-out substrate. The first coupling electrode plate 1-7 extending outward from the middle of the low-frequency resonant beam 1-3 is suspended on the hollowed-out substrate. The first excitation electrode plate 4-3 extending outward from the seventh anchor point 4-2 is suspended on the hollowed-out substrate. The first excited electrode plate 1-4 and the first excitation electrode plate 4-3 form a capacitor electrode plate, which provides electrostatic excitation force for the low-frequency resonant beam 1-3. The first anchor point 1-2, the second anchor point 1-6, and the seventh anchor point 4-2 are respectively sputtered with a first metal electrode layer 1-1, a second metal electrode layer 1-5, and a seventh metal electrode layer 4-1 for the transmission of electrical signals.

[0039] The modal frequency control module adopts a closed-loop measurement circuit with a bias voltage V. d1 and V d2 The interaction creates a potential difference across the low-frequency resonant beam 1-3. When the low-frequency resonant beam 1-3 vibrates, its resistance changes due to the piezoresistive effect, generating a kinetic current flowing through it. The first differential amplifier 7-1, with its built-in transimpedance amplifier, converts the kinetic current signal into a voltage signal and improves its signal-to-noise ratio. The voltage signal, after passing through the first differential amplifier 7-1, is input to the filter 7-2 to filter out higher harmonics. The phase shifter 7-3 controls the phase difference between the plate oscillation signal and the feedback signal. The comparator 7-4 outputs phase information. and Simultaneously provides AC voltage signal With bias voltage V dc1 The combined forces act on the low-frequency resonant beams 1-3, producing simple harmonic oscillations.

[0040] The first coupling plate 1-7 and the second coupling plate 2-4 form capacitor plates, and the third coupling plate 2-7 and the fourth coupling plate 3-4 form capacitor plates, generating electrostatic coupling force. The magnitude of the electrostatic coupling force depends on the potential difference between the coupling plates.

[0041] The potential difference between the first coupling plate 1-7 and the second coupling plate 2-4 is ΔV1, and the potential difference between the third coupling plate 2-7 and the fourth coupling plate 3-4 is ΔV2.

[0042] ΔV1 depends on the bias voltage V d1 V d2 V d3 and V d4 The size is calculated using the following formula:

[0043] ΔV1=|V d1 +V d2 -V d3 -V d4 | / 2

[0044] ΔV2 depends on V d3 V d4 V d5 and V d6 The size is calculated using the following formula:

[0045] ΔV2=|V d3 +V d4 -V d5 -V d6 | / 2

[0046] By adjusting the bias voltage V d1 V d2 V d3 V d4 V d5 and V d6 The size of the electrostatic coupling force can be flexibly adjusted according to the present invention.

[0047] The low-frequency resonant beam 1-3 achieves equivalent stiffness control of the first high-frequency resonant beam 2-3 through electrostatic coupling force, and the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 achieve modal coupling through electrostatic coupling force.

[0048] Please see Figure 2 The modal localization sensing module includes a third anchor point 2-2, a third metal electrode layer 2-1, a fourth anchor point 2-6, a fourth metal electrode layer 2-5, a fifth anchor point 3-2, a fifth metal electrode layer 3-1, a sixth anchor point 3-6, a sixth metal electrode layer 3-5, an eighth anchor point 5-2, an eighth metal electrode layer 5-1, a ninth anchor point 6-2, a first high-frequency resonant beam 2-3, a second high-frequency resonant beam 3-3, a second coupling electrode plate 2-4, a third coupling electrode plate 2-7, a fourth coupling electrode plate 3-4, a second stimulated electrode plate 3-7, a second excitation electrode plate 5-3, a perturbation electrode plate 6-1, a second differential amplifier 8-1, and a frequency control algorithm unit 9-1.

[0049] The first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 are suspended on a hollowed-out substrate. The upper and lower ends of the first high-frequency resonant beam 2-3 are connected to the third anchor point 2-2 and the fourth anchor point 2-6, which are fixed to the insulating layer of the substrate, respectively. The third coupling plate 2-7, which extends outward from the middle of the first high-frequency resonant beam 2-3, is suspended on the hollowed-out substrate. The upper and lower ends of the second high-frequency resonant beam 3-3 are connected to the fifth anchor point 3-2 and the sixth anchor point 3-6, which are fixed to the insulating layer of the substrate, respectively. The fourth coupling plate 3-4, which extends outward from the middle of the second high-frequency resonant beam 3-3, is suspended on the hollowed-out substrate. The third coupling plate 2-7 and the fourth coupling plate 3-4... -4 form capacitor plates; the second excitation plate 5-3 extending outward from the eighth anchor point 5-2 is suspended on the hollow substrate, and the second excited plate 3-7 and the second excitation plate 5-3 form capacitor plates to provide electrostatic excitation force for the second high-frequency resonant beam 3-3; the third anchor point 2-2, the fourth anchor point 2-6, the fifth anchor point 3-2, the sixth anchor point 3-6, the eighth anchor point 5-2 and the ninth anchor point 6-2 are respectively sputtered with the third metal electrode layer 2-1, the fourth metal electrode layer 2-5, the fifth metal electrode layer 3-1, the sixth metal electrode layer 3-5, the eighth metal electrode layer 5-1 and the perturbation plate 6-1 for the transmission of electrical signals.

[0050] The modal localization sensing module uses an open-loop measurement circuit, with an AC voltage signal V. ac3 cos(ω3t), with bias voltage V dc3 The electrostatic excitation force generated causes the second high-frequency resonant beam 3-3 to undergo self-excited vibration. The intensity f of the electrostatic excitation force is... d3 Proportional to V ac3 ·V dc3 Bias voltage V d5 and V d6 The two ends of the second high-frequency resonant beam 3-3 are connected to generate a potential difference. When the second high-frequency resonant beam 3-3 undergoes self-excited vibration, the resistance of the second high-frequency resonant beam 3-3 changes due to the piezoresistive effect, thereby generating a dynamic current flowing through the second high-frequency resonant beam 3-3. The second differential amplifier 8-1 has a built-in transimpedance amplifier that converts the dynamic current signal into a voltage signal and improves the signal-to-noise ratio of the voltage signal. After passing through the frequency control algorithm, the feedback signal is sent to the phase shifter 7-3 of the low-frequency module.

[0051] Specifically, the low-frequency resonant beam 1-3 has a length of 400–600 μm, a width of 5–20 μm, and a thickness of 15–30 μm; the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 have a length of 200–400 μm, a width of 5–20 μm, and a thickness of 15–30 μm; the first excited electrode 1-4, the second excited electrode 3-7, the first excitation electrode 4-3, the second excitation electrode 5-3, the first coupling electrode 1-7, the second coupling electrode 2-4, the third coupling electrode 2-7, and the fourth coupling electrode 3-4 have a length of 150–300 μm, a width of 5–10 μm, and a thickness of 15–30 μm; the first anchor point 1-2, the second anchor point 1-6, the third anchor point 2-2, the fourth anchor point 2-6, the fifth anchor point 3-2, the sixth anchor point 3-6, the seventh anchor point 4-2, and the eighth anchor point 5- 2 is a rectangular structure with a side length of 150–300 μm; the ninth anchor point 6-2 is a rectangular structure with a side length of 250–600 μm; the first metal electrode layer 1-1, the second metal electrode layer 1-5, the third metal electrode layer 2-1, the fourth metal electrode layer 2-5, the fifth metal electrode layer 3-1, the sixth metal electrode layer 3-5, the seventh metal electrode layer 4-1, and the eighth metal electrode layer 5-1 are rectangular structures with a side length of 100–250 μm; the perturbation electrode plate 6-1 is a rectangular structure with a side length of 150–600 μm; the gap distance between the first excited electrode plate 1-4 and the first excitation electrode plate 4-3, the second excited electrode plate 3-7 and the second excitation electrode plate 5-3, the first coupling electrode plate 1-7 and the second coupling electrode plate 2-4, the third coupling electrode plate 2-7 and the fourth coupling electrode plate 3-4 is 2–6 μm.

[0052] Open-loop characterization experiments were conducted on the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 with the above-mentioned structural dimensions. Under weak coupling conditions, the nonlinear characteristics of the low-frequency resonant beam 1-3 were utilized to enable large-range amplitude control of the low-frequency resonant beam.

[0053] Specifically, after adding the modal frequency modulation module, the dynamic models of the low-frequency resonant beam 1-3, the first high-frequency resonant beam 2-3, and the second high-frequency resonant beam 3-3 are as follows:

[0054]

[0055]

[0056]

[0057] Where x, y, and z are the equivalent displacements of the low-frequency resonant beam 1-3, the first high-frequency resonant beam 2-3, and the second high-frequency resonant beam 3-3, respectively; m1, m2, and m3 are the equivalent masses of the low-frequency resonant beam 1-3, the first high-frequency resonant beam 2-3, and the second high-frequency resonant beam 3-3, respectively; c1, c2, and c3 are the equivalent dampings of the low-frequency resonant beam 1-3, the first high-frequency resonant beam 2-3, and the second high-frequency resonant beam 3-3, respectively; k1, k2, and k3 are the equivalent stiffnesses of the low-frequency resonant beam 1-3, the first high-frequency resonant beam 2-3, and the second high-frequency resonant beam 3-3, respectively; k c k represents the coupling stiffness. e α1 is the disturbance stiffness applied to the second high-frequency resonant beam; α1 is the tuning coefficient of the first high-frequency resonant beam 2-3; γ1 is the nonlinear stiffness of the low-frequency resonant beam 1-3; f d1 The external excitation intensity of low-frequency resonant beams 1-3; and f represents the instantaneous phase and phase delay of the oscillation; d3 ω3 represents the external excitation intensity of the second high-frequency resonant beam 3-3; ω3 represents the external excitation frequency of the second high-frequency resonant beam 3-3.

[0058] Charge quantity and disturbance stiffness k e The relationship is as follows:

[0059]

[0060] in, Let q be the electrostatic force caused by the charge, l be the input charge, A be the length of the second high-frequency resonant beam, ε0 be the overlapping area of ​​the driving capacitors, and ε0 be the dielectric constant in vacuum.

[0061] The modal expressions for the first high-frequency resonant beam 2-3 and the second high-frequency resonant beam 3-3 are as follows:

[0062]

[0063] Where i = 1, 2.

[0064] Please see Figure 3 Figure 1 shows the amplitude-frequency response of the first high-frequency resonant beam 2-3 and the amplitude-frequency response of the second high-frequency resonant beam 3-3. The peak displacement of the resonant beam in the figure varies with k. e It changes and shifts, resulting in modal localization.

[0065] Please see Figure 4 Modal AR i With stiffness disturbance k eThe relationship between the two modes is such that when the two modes approach each other, the trajectories of the two modes of the coupled system suddenly turn with high local curvature near the zero point, and exhibit nonlinear changes near the turning point. The range marked by the dashed box is the linear range of the first mode, which has high sensitivity.

[0066] This invention utilizes the low-frequency resonant beam in the modal frequency control module to dynamically adjust the equivalent stiffness of the first high-frequency resonant beam, thereby achieving the translation of the modal curve and limiting the working range of the first mode to the high-sensitivity region.

[0067] Specifically, before modulation, the linear operating range of the first mode is... Figure 4 The solid line within the dashed box; by adjusting the equivalent stiffness of the first high-frequency resonant beam by the coefficient α1, the original turning point shifts to the left, the nonlinearity of the mode near the zero point is weakened, and the linear range of the first mode is expanded compared to before the adjustment, i.e. Figure 4 The dashed lines within the dashed box indicate the range within which the electrometer exhibits high sensitivity, easily identifies interference, and thus expands the detection range.

[0068] In summary, this invention provides a modal localization electrometer based on modal coupling frequency self-adjustment. Based on the modal coupling mechanism, it modulates the vibration amplitude of the low-frequency resonant beam, dynamically controlling the resonant frequency of the modally localized resonant beam, and confining the amplitude ratio of the high-frequency resonant beam within the linear range, thus solving the application problem of nonlinear resonator sensitivity. Furthermore, this invention utilizes electrostatic force to achieve coupling between the resonant beams, enabling flexible control of the coupling strength and thus flexibly expanding the linear operating bandwidth of the amplitude ratio. The method provided by this invention has advantages such as no thermal noise introduction, excellent real-time performance, and high control accuracy. Combined with a significantly expanded linear operating bandwidth, the measurement accuracy and range of the electrometer based on the modal localization principle are significantly improved.

[0069] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A modal localization electrometer based on modal coupling frequency self-adjustment, characterized in that, The system includes a modal frequency control module. The low-frequency resonant beam (1-3) in the modal frequency control module and the first high-frequency resonant beam (2-3) and the second high-frequency resonant beam (3-3) in the modal localization sensing module are arranged side by side and electrostatically coupled through the first coupling plate (1-7), the second coupling plate (2-4), the third coupling plate (2-7), and the fourth coupling plate (3-4). The second high-frequency resonant beam (3-3) is placed in the second oscillation circuit to generate self-excited oscillation, and the low-frequency resonant beam (1-3) is placed in the first oscillation circuit to generate self-excited oscillation. Based on the phase information of the second high-frequency resonant beam (3-3), a phase control signal is output to the first oscillation circuit. By changing the phase delay of the first oscillation circuit, the low-frequency resonant beam (1-3) in the modal frequency control module can vibrate with different amplitudes. The equivalent stiffness and resonant frequency of the first high-frequency resonant beam (2-3) in the modal localization module can be dynamically controlled. Through the modal coupling mechanism, the modal changes of the first high-frequency resonant beam (2-3) and the second high-frequency resonant beam (3-3) are limited to the high sensitivity region, thereby realizing the dynamic adjustment of the sensitivity of the electrometer. The modal frequency control module also includes a first differential amplifier (7-1). The dynamic current flowing through the low-frequency resonant beam (1-3) is converted into a voltage signal by the first differential amplifier (7-1). The voltage signal is then passed through a filter (7-2), a phase shifter (7-3), and a comparator (7-4) in sequence, in conjunction with a bias voltage. The feedback is fed to the low-frequency resonant beam (1-3). The modal localization sensing module includes a second differential amplifier (8-1). The dynamic current flowing through the second high-frequency resonant beam (3-3) is converted into a voltage signal by the second differential amplifier (8-1), and then the phase change is output by the frequency control algorithm (9-1) and fed back to the phase shifter (7-3).

2. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 1, characterized in that, A low-frequency resonant beam (1-3) and its first excited electrode plate (1-4) and first coupling electrode plate (1-7) extending outward from the middle are suspended on a hollow substrate. The upper and lower ends of the low-frequency resonant beam (1-3) are connected to the first anchor point (1-2) and the second anchor point (1-6) connected to the substrate insulating layer, respectively. A first excitation electrode plate (4-3) is also suspended on the substrate. The first excitation electrode plate (4-3) is connected to the seventh anchor point (4-2). The first excited electrode plate (1-4) and the first excitation electrode plate (4-3) form a capacitor electrode plate. A first metal electrode layer (1-1), a second metal electrode layer (1-5), and a seventh metal electrode layer (4-1) are sputtered on the first anchor point (1-2), the second anchor point (1-6), and the seventh anchor point (4-2), respectively.

3. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 2, characterized in that, The length of the low-frequency resonant beam (1-3) is 400~600μm; the lengths of the first excited electrode plate (1-4), the first excitation electrode plate (4-3) and the first coupling electrode plate (1-7) are 150~300μm; the first anchor point (1-2), the second anchor point (1-6) and the seventh anchor point (4-2) are rectangular structures with a side length of 150~300μm, and the first metal electrode layer (1-1), the second metal electrode layer (1-5) and the seventh metal electrode layer (4-1) are rectangular structures with a side length of 100~250μm.

4. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 2, characterized in that, The gap between the first excited electrode (1-4) and the first excitation electrode (4-3) is 2~6μm.

5. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 1, characterized in that, The first high-frequency resonant beam (2-3) and its outwardly extending second coupling plate (2-4) and third coupling plate (2-7) are suspended on the hollow substrate. The upper and lower ends of the first high-frequency resonant beam (2-3) are connected to the third anchor point (2-2) and the fourth anchor point (2-6) connected to the substrate insulating layer, respectively. The second high-frequency resonant beam (3-3) and its outwardly extending fourth coupling plate (3-4) and second excited plate (3-7) are suspended on the hollow substrate. The upper and lower ends of the second high-frequency resonant beam (3-3) are connected to the substrate insulating layer, respectively. The fifth anchor point (3-2) and the sixth anchor point (3-6) are connected; a second excitation electrode (5-3) is suspended on the substrate, and the second excitation electrode (5-3) is connected to the eighth anchor point (5-2); a third metal electrode layer (2-1), a fourth metal electrode layer (2-5), a fifth metal electrode layer (3-1), a sixth metal electrode layer (3-5), and an eighth metal electrode layer (5-1) are sputtered on the third anchor point (2-2), the fourth anchor point (2-6), the fifth anchor point (3-2), the sixth anchor point (3-6), and the eighth anchor point (5-2), respectively.

6. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 5, characterized in that, The first coupling plate (1-7) and the second coupling plate (2-4) form a capacitor plate, the third coupling plate (2-7) and the fourth coupling plate (3-4) form a capacitor plate, the second excited plate (3-7) and the second excitation plate (5-3) form a capacitor plate, and the gap distance between the second excited plate (3-7) and the second excitation plate (5-3) is 2~6μm.

7. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 5, characterized in that, The lengths of the first high-frequency resonant beam (2-3) and the second high-frequency resonant beam (3-3) are 200~400μm; the lengths of the second coupling plate (2-4), the third coupling plate (2-7), the fourth coupling plate (3-4), the second excited plate (3-7), and the second excitation plate (5-3) are 150~300μm; the lengths of the third anchor point (2-2), the fourth anchor point (2-6), the fifth anchor point (3-2), the sixth anchor point (3-6), and the eighth anchor point (5-2) are rectangular structures with a side length of 150~300μm; the lengths of the third metal electrode layer (2-1), the fourth metal electrode layer (2-5), the fifth metal electrode layer (3-1), the sixth metal electrode layer (3-5), and the eighth metal electrode layer (5-1) are rectangular structures with a side length of 100~250μm.

8. The modal localization electrometer based on modal coupling frequency self-adjustment according to claim 1, characterized in that, The gap between the first coupling plate (1-7), the second coupling plate (2-4), the third coupling plate (2-7), and the fourth coupling plate (3-4) is 2~6μm.

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