A capacitance resonance based pressure sensor and method

Through the pressure sensor structure based on capacitor resonance, electrode induction and resonant signal amplification are utilized to solve the problem of fixed sensitivity of traditional sensors, and achieve sensitivity improvement and enhanced adaptability without external excitation signals.

CN119469482BActive Publication Date: 2025-10-10ZHONGHANG ELECTRONIC MEASURING INSTR (XIAN) CO LTD
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Patent Information

Application Number
CN202411627558.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-11-14
Publication Date
2025-10-10
Estimated Expiration
2044-11-14

AI Technical Summary

Technical Problem

Traditional pressure sensors have fixed measurement range and sensitivity and cannot adapt to complex environments. Existing sensors that increase sensitivity through resonance require external signal input, which is relatively complicated.

Method used

A pressure sensor structure based on capacitive resonance is adopted, including a control substrate, a sensing substrate and a force-bearing substrate. By controlling the dot matrix and capacitive strain gauges on the substrate, electrode induction and resonant signal amplification are utilized to achieve improved sensitivity without external excitation signals.

Benefits of technology

The measurement sensitivity of the pressure sensor is improved, adapting to complex application scenarios without the need for external input excitation signals, thereby enhancing the adaptability and accuracy of the sensor.

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Abstract

The application discloses a kind of pressure sensor and method based on capacitance resonance, including control substrate and sensing substrate;Control substrate is located at the top of capacitive strain gauge, and sensing substrate bottom is provided with force receiving substrate, and the control substrate includes at least two points of dot matrix;The sensing substrate includes capacitive strain gauge;Controller is provided outside the control substrate, and the controller is connected with each point in dot matrix.No external input excitation signal is needed, which improves the sensitivity of pressure sensor measurement, and is further adapted to more complex application scenarios.
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Description

Technical Field

[0001] The present invention belongs to the field of pressure sensors and relates to a pressure sensor based on capacitor resonance and a method. Background Art

[0002] Most traditional pressure sensors convert physical quantities into analog quantities by changing the capacitance between strain gauges in response to an external force, thereby changing the output analog voltage or current. However, these sensors have a fixed measurement range and sensitivity, making them unsuitable for complex environments.

[0003] Most existing technologies for increasing the sensitivity of pressure sensors through resonance increase sensitivity by inputting an excitation signal to change the resonant frequency. However, such sensors require external signal input, which is relatively complex. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a pressure sensor and method based on capacitive resonance, which does not require an external input excitation signal, improves the sensitivity of the pressure sensor measurement, and is thus adapted to more complex application scenarios.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A pressure sensor based on capacitive resonance includes a control substrate and a sensing substrate;

[0007] The control substrate is located on top of the capacitive strain gauge, and a force-bearing substrate is provided at the bottom of the sensing substrate. The control substrate includes a dot matrix consisting of at least two points; the sensing substrate includes a capacitive strain gauge; a controller is provided outside the control substrate, and the controller is connected to each point in the dot matrix.

[0008] Preferably, the control substrate and the sensing substrate are encapsulated by epoxy resin adhesive.

[0009] Preferably, a groove is provided on the stress-bearing substrate, and the groove corresponds to the position of the capacitive strain gauge.

[0010] Furthermore, the size of the groove is larger than the size of the capacitive strain gauge, and the depth of the groove is larger than the maximum deformation of the capacitive strain gauge.

[0011] Furthermore, the sensing substrate and the stress-bearing substrate are encapsulated by epoxy resin adhesive.

[0012] Preferably, the dot matrix covers the corresponding area of ​​the capacitive strain gauge.

[0013] Preferably, the controller is provided with a plurality of buttons, the number of which is consistent with the number of dots in the dot matrix and which are connected in a one-to-one correspondence.

[0014] Preferably, the controller adopts MCU.

[0015] A capacitive resonance method of the pressure sensor comprises the following processes:

[0016] In the case that the pressure sensor is not working, the force-receiving substrate is cathode, the control substrate is cathode, and the controller converts the electrical property of part of points on the control substrate into anode, at this time, the control substrate and the force-receiving substrate are opposite in electrical property, electrode induction occurs, the capacitive strain gauge of the sensing substrate is subjected to a force, thereby the effective length of the capacitive strain gauge changes, the frequency of the pressure sensor also changes, the number of the electrical property conversion of the control points is adjusted to adjust the effective length of the capacitive strain gauge, and then the frequency of the pressure sensor gradually coincides with the characteristic frequency of the outside world until the pressure sensor and the outside world reach a resonance state.

[0017] Preferably, the frequency of the pressure sensor is , wherein T is tension, is linear density, and L is the length of the capacitive strain gauge.

[0018] Compared with the prior art, the present application has the following beneficial effects:

[0019] The present application sets the control substrate, the sensing substrate and the force-receiving substrate, sets the dot matrix on the control substrate, sets the capacitive strain gauge on the sensing substrate, constitutes the pressure sensor, sets the controller outside the pressure sensor, the controller can control the electrode change of the dot matrix, thereby the electrode induction of the control substrate and the force-receiving substrate makes the sensing substrate be subjected to force, the effective length of the capacitive strain gauge is controlled according to the change of the dot matrix, the frequency of the pressure sensor is changed according to the effective length, in addition, the above-mentioned method can change the upper limit of the capacitance of the capacitive strain gauge, the upper limit of the output signal is increased, the upper limit of the pressure detection is increased. At the same time, when the frequency of the outside world is close to the frequency of the pressure sensor, the two send resonance, the signal generated after the resonance is amplified, thereby the sensitivity of the pressure sensor measurement is improved, and then the more complex application scenarios are adapted. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a structure schematic diagram of a pressure sensor based on capacitive resonance proposed by the embodiment of the present application;

[0021] Figure 2 is a structure schematic diagram of a strain gauge controlled by a pressure sensor according to the embodiment of the present application.

[0022] Among them, the above drawings include the following reference signs:

[0023] 1-control substrate, 2-sensing substrate, 3-force-receiving substrate, 4-dot matrix, 5-capacitive strain gauge, 6-groove, 7-controller. DETAILED DESCRIPTION

[0024] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limiting the present invention.

[0025] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like, indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the said features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0026] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention pertains. The terms "installed", "connected", and "connected" should be understood in a broad sense, for example, they can be fixedly connected, detachably connected, or integrally connected; they can be mechanically connected, electrically connected, or able to communicate with each other; they can be directly connected, or indirectly connected through an intermediate medium, or they can be internally connected between two elements or an interactive relationship between two elements. The term "and / or" used herein includes any and all combinations of one or more related listed items. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0027] The disclosure below provides many different embodiments or examples for realizing different structures of the present invention. In order to simplify the disclosure of the present invention, the components and settings of specific examples are described below. Of course, they are merely examples and are not intended to limit the present invention. In addition, the present invention may repeat reference numbers and / or reference letters in different examples. Such repetition is for the purpose of simplicity and clarity and does not in itself indicate the relationship between the various embodiments and / or settings discussed. In addition, the present invention provides examples of various specific processes and materials, but those skilled in the art will recognize the application of other processes and / or the use of other materials.

[0028] like Figure 1 As shown, the embodiment of the present application proposes a pressure sensor based on capacitive resonance, which mainly includes a control substrate 1, a sensing substrate 2 and a force-bearing substrate 3.

[0029] The control substrate 1 and the sensing substrate 2 , as well as the sensing substrate 2 and the force-bearing substrate 3 are encapsulated by epoxy resin adhesive.

[0030] The control substrate 1 includes a dot matrix 4 consisting of n points, and two capacitive strain gauges 5 are attached to the sensing substrate 2. The number is not specifically limited in this application, and the dot matrix 4 fully covers the corresponding area of ​​the capacitive strain gauge 5.

[0031] The stressed substrate 3 is provided with a groove 6 to accommodate strain gauges of varying sizes. The groove 6 is larger than the capacitive strain gauge 5 and its depth is greater than the maximum deformation of the capacitive strain gauge 5. When the strain gauge is subjected to force, the groove 6 mates with the capacitive strain gauge 5, allowing the stressed portion to fully deform. This prevents sensor output errors caused by incomplete or uneven deformation, thereby ensuring the sensor's accuracy and stability.

[0032] A controller 7 is mounted on the outside of the control substrate 1. Specifically, an MCU (microcontroller unit) is used here. The MCU adjusts the electrical properties of the dot matrix 4 via multiple buttons. The number of buttons on the controller 7 matches the number of dots in the dot matrix 4. Each button controls the electrical state of a corresponding dot in the dot matrix 4. By pressing different buttons on the controller 7, the electrical properties of different dots in the dot matrix 4 can be adjusted, thereby controlling the sensitivity and detection range of the pressure sensor.

[0033] The working principle of the pressure sensor based on the capacitance resonance provided in the scheme mainly comprises: the controller 7 can control the change of the electric property of each point in the dot matrix 4 by controlling the button, in the case that the pressure sensor does not work, the stress substrate 3 is cathode, and the control substrate 1 is cathode, when the button of the controller 7 is pressed, the electric property of the corresponding dot matrix 4 on the control substrate 1 is changed to anode, at this time, the electric property of the control substrate 1 and the stress substrate 3 is opposite, electrode induction occurs, and the capacitance strain gauge 5 of the induction substrate 2 will be affected by a force, so that the effective length of the strain gauge will change.

[0034] In an embodiment, in the above-mentioned pressure sensor, the effective length of the strain gauge changes, when the pressure sensor is affected by external force, the deformation amount of the strain gauge will change, and the upper limit of the capacitance value will increase. When the controller 7 controls different dot matrix 4, the area of the strain gauge increases, so that more electric charges can be stored, the upper limit of the capacitance value also increases, so that the upper limit of the output signal of the pressure sensor increases, and the upper limit of the pressure detection increases.

[0035] In another embodiment, in the above-mentioned pressure sensor, the effective length of the strain gauge changes, and the frequency of the pressure sensor also changes, at the same time, when the frequency of the pressure sensor is close to or the same as the frequency of the external environment, the two will resonate, at this time, the output signal of the pressure sensor will be enhanced, so that the sensitivity of the pressure sensor to the frequency of the external environment increases. By controlling the electric property of the point in the different dot matrix 4 by the controller 7, the sensitivity of the pressure sensor to different frequency signals of the external environment can be modulated.

[0036] Through this structure, the sensitivity of the pressure sensor at a specific frequency and the range of the output signal can be adjusted according to the external environment, for example, when the frequency of the external environment is f0, the electrode of the corresponding dot matrix 4 can be changed by controlling the control button, so that the effective length of the strain gauge on the induction plate is changed, and the characteristic frequency of the pressure sensor is changed to f0, at this time, the pressure sensor and the external environment resonate, that is, the sensitivity is improved. At the same time, the change of the effective length of the strain gauge will cause the change of the deformation amount, so that the upper limit of the capacitance value increases, and the upper limit of the output signal increases, so that the upper limit of the pressure detection increases.

[0037] As shown in Figure 2 , the specific principle of the resonance process is that the controller 7 controls the button X1, the electric property of the P1 point of the dot matrix 4 changes, at this time, the effective length is L1, when the control button X2 is controlled, the electric property of the P2 point of the dot matrix 4 changes, at this time, the effective length of the strain gauge is L2, according to the different buttons, L1 ​is the line density, L is the length of the capacitive strain gauge 5, it can be obtained that the frequency f1 at L1 at this time is greater than f2, and the characteristic frequency of the outside world is f2 at this time, that is, it is necessary to control the X2 button, so the current pressure sensor resonates with the outside world. When the resonance state is reached, the signal quality transmitted after the pressure sensor collects data is improved, thereby improving the sensitivity.

[0038] The specific principle of changing the output upper limit is: when the control button X1, the electrical properties of point P1 of the dot matrix 4 undergo electrode changes, and the effective length at this time is L1. When the control button X2, the electrical properties of point P2 of the dot matrix 4 undergo electrode changes, and the effective length of the strain gauge is L2. The change in the effective length of the strain gauge increases the area of ​​the strain gauge, so that it can store more charge, and the upper limit of the capacitance will also increase, thereby increasing the upper limit of the capacitance of the pressure sensor, which will cause the upper limit of the output signal to increase, and increase the upper limit of pressure detection.

[0039] In this capacitive resonance-based pressure sensor, the dot matrix 4 and the controller 7 are key components. They work together to achieve flexible control of the pressure sensor's sensitivity, frequency response, and detection range. The dot matrix 4 and the controller 7 in this embodiment are respectively introduced in detail below.

[0040] The dot matrix 4 is an electrical control network composed of multiple independent points arranged on the control substrate 1. Each point in the dot matrix 4 can independently control its electrical state, thereby selectively activating different areas. The following are the main features and functions of the dot matrix 4:

[0041] 1. Dot Matrix 4 Composition: Dot Matrix 4 consists of multiple evenly distributed points (P1, P2, P3, etc.). The number and arrangement of these points can be flexibly designed based on application requirements. In actual operation, each point can be independently controlled by controller 7, resulting in different sensitivity of the pressure sensor to changes in external force in different areas, thereby achieving precise response to external pressure.

[0042] 2. Electrical Property Change Control: Each point can switch its electrical state (for example, from cathode to anode), thereby changing the electrical distribution between the control substrate 1 and the stress-bearing substrate 3. This electrical property change causes the electric field between the control substrate 1 and the stress-bearing substrate 3 to change, causing varying degrees of stress and strain on the capacitive strain gauge 5 on the sensing substrate 2. This adjustable electrical state allows the pressure sensor to more flexibly respond to varying external pressure and frequency signals in its applications.

[0043] 3. Impact on the Strain Gauge: Controlling the electrical properties of dot matrix 4 indirectly affects the effective length of the strain gauge. By activating different points in dot matrix 4, the effective length of the capacitive strain gauge 5 on the sensing substrate 2 can be changed, thereby adjusting the operating frequency or output limit of the pressure sensor. For example, activating point P1 changes the effective length of the strain gauge to L1; activating point P2 changes the length to L2. Controlling dot matrix 4 not only adjusts the physical parameters of the strain gauge but also alters the operating frequency and upper capacitance limit of the pressure sensor.

[0044] In this embodiment, the dot matrix 4 actually refers to an array of multiple independent electrodes arranged on the control substrate 1. Each "dot" in the dot matrix 4 is a small electrode, whose electrical state can be individually adjusted (e.g., switched from cathode to anode) by the control circuit. In actual use, these dots are typically made of conductive materials (such as copper, aluminum, or gold), forming a regularly arranged network of tiny electrodes, similar to the pads or contact points on an electronic circuit board.

[0045] The dot matrix 4 uses multiple electrode contacts, depositing multiple small metal electrodes on the control substrate 1 to form an array. These electrodes are connected to the controller 7 (MCU) via wires, and the electrical state of each electrode can be independently changed under the control of the controller 7.

[0046] Each point is connected to the MCU through a separate control line. The MCU controls the electrical changes of different electrode contacts to form the desired electric field distribution and control the sensitivity and frequency response of the pressure sensor.

[0047] In summary, the dot matrix 4 is a network of multiple independently controllable tiny electrode points (contacts). Their electrical properties are individually adjusted by the controller 7, enabling the pressure sensor to flexibly respond to external pressure and frequency changes.

[0048] The MCU, as the core controller of the pressure sensor system, is responsible for regulating the electrical state of the dot matrix. The following are the main functions of the MCU:

[0049] 1. Multi-button control: The MCU uses multiple buttons to correspond one-to-one with each dot in the dot matrix 4. Each button controls the electrical state of a single dot, and pressing different buttons allows precise control of the electrical state of each dot. The number of buttons on the controller 7 matches the number of dots in the dot matrix 4, allowing each button to directly control the electrical state transition of the corresponding dot.

[0050] Since the external environment frequency at a fixed location remains unchanged, the pressure sensor frequency will not be too frequent. In this embodiment, the MCU can be manually controlled by an external host computer to gradually increase the number of button triggers and gradually adjust the pressure sensor frequency until the pressure sensor frequency is the same or nearly the same as the external frequency. The control is stopped and the state of the dot matrix 4 remains unchanged at this time.

[0051] The MCU can also process it adaptively. When the external environment changes, the external environment frequency value is written to the MCU in advance. The MCU gradually increases or presses the button trigger number, and gradually adjusts the pressure sensor frequency. The MCU judges the difference between the pressure sensor frequency and the external frequency in real time until the pressure sensor frequency is the same or close to the external frequency. The button trigger is stopped and the state of dot matrix 4 remains unchanged at this time.

[0052] 2. Electrical Reversal: When the pressure sensor is at rest, both the stress-bearing substrate 3 and the control substrate 1 are cathodes. Pressing a control button causes the corresponding dot matrix point 4 to switch from cathode to anode, creating an electrical reversal effect. This electrical reversal induces a change in the electric field between the control substrate 1 and the stress-bearing substrate 3, affecting and deforming the capacitive strain gauge 5 on the sensing substrate 2. This operation enables the MCU to achieve sensitive response to external pressure changes through a simple electrical switching.

[0053] 3. Frequency and Sensitivity Adjustment: By controlling different buttons, you can adjust the characteristic frequency of the pressure sensor. For example, when button X1 activates point P1, the corresponding frequency is f1; when button X2 activates point P2, the corresponding frequency is f2. If the external frequency is close to or identical to the pressure sensor frequency, the two will resonate, amplifying the pressure sensor's output signal and thus increasing sensitivity. By controlling different button combinations, the MCU can adjust the pressure sensor to achieve maximum sensitivity at specific frequencies, enabling it to respond sensitively to signals at specific frequencies.

[0054] 4. Adjusting the upper capacitance limit: Pressing different buttons to activate different points on the dot matrix 4 controls the electrical reversal locations on substrate 1, changing the effective length of the strain gauge. This increases the gauge's surface area and, consequently, its charge storage capacity. This directly increases the upper capacitance limit of the pressure sensor, allowing it to operate within a wider pressure range and raising its detection limit.

[0055] In general, a capacitive resonance-based pressure sensor can flexibly adjust its operating frequency, sensitivity, and output signal limit by controlling the electrical properties of the dot matrix 4 on substrate 1, thereby accurately detecting and adjusting to varying external pressures and frequencies. This technology not only improves the adaptability of the pressure sensor but also makes it more accurate and reliable in practical applications.

[0056] The serial numbers of the above embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0057] In the above embodiments of the present application, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, please refer to the relevant description of other embodiments.

[0058] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only exemplary. For example, the division of the units can be a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0059] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0060] The above is only a preferred embodiment of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

[0061] It should be understood that the above description is for illustration and not for limitation. Many embodiments and many applications beyond the examples provided will be apparent to those skilled in the art upon reading the above description. Therefore, the scope of this patent should not be determined with reference to the above description, but rather with reference to the preceding claims and the full scope of equivalents to which such claims are entitled. For the purpose of completeness, all articles and references, including disclosures of patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein from the preceding claims is not a disclaimer of such subject matter, nor should it be considered that the applicants did not consider such subject matter to be part of the disclosed inventive subject matter.

Claims

1. A pressure sensor based on capacitive resonance, characterized in that: It comprises a control substrate (1) and a sensing substrate (2); The control substrate (1) is located on top of the capacitive strain gauge (5), and a force-bearing substrate (3) is provided at the bottom of the sensing substrate (2). The control substrate (1) includes a dot matrix (4) consisting of at least two points; the sensing substrate (2) includes a capacitive strain gauge (5); a controller (7) is provided outside the control substrate (1), and the controller (7) is connected to each point in the dot matrix (4); When the pressure sensor is not working, the stressed substrate (3) is the cathode and the control substrate (1) is the cathode. When the button of the controller (7) is pressed, the corresponding dot matrix (4) on the control substrate (1) is electrically converted to the anode. At this time, the electrical properties of the control substrate (1) and the stressed substrate (3) are opposite, and electrode induction occurs. The dot matrix (4) fully covers the corresponding area of ​​the capacitive strain gauge (5).

2. The pressure sensor based on capacitive resonance according to claim 1, characterized in that: The control substrate (1) and the sensing substrate (2) are packaged by epoxy resin adhesive.

3. The pressure sensor based on capacitive resonance according to claim 1, characterized in that: A groove (6) is provided on the stress-bearing substrate (3), and the position of the groove (6) corresponds to that of the capacitive strain gauge (5).

4. The capacitive resonance-based pressure sensor according to claim 3, characterized in that: The size of the groove (6) is larger than the size of the capacitive strain gauge (5), and the depth of the groove (6) is larger than the maximum deformation of the capacitive strain gauge (5).

5. The pressure sensor based on capacitive resonance according to claim 3, characterized in that: The sensing substrate (2) and the force-bearing substrate (3) are encapsulated by epoxy resin adhesive.

6. The capacitive resonance-based pressure sensor according to claim 1, characterized in that: The dot matrix (4) covers the corresponding area of ​​the capacitive strain gauge (5).

7. The pressure sensor based on capacitive resonance according to claim 1, characterized in that: The controller (7) is provided with a plurality of buttons, the number of which is consistent with the number of points in the dot matrix (4) and is connected in a one-to-one correspondence.

8. The pressure sensor based on capacitive resonance according to claim 1, characterized in that: The controller (7) adopts MCU.

9. A method for operating a pressure sensor based on capacitive resonance according to any one of claims 1 to 8, characterized in that: The following processes are included: When the pressure sensor is not working, the stressed substrate (3) is the cathode and the control substrate (1) is the cathode. The controller (7) converts the electrical properties of some points on the control substrate (1) into anodes. At this time, the electrical properties of the control substrate (1) and the stressed substrate (3) are opposite, and electrode induction occurs. The capacitive strain gauge (5) of the induction substrate (2) is subjected to a force, so that the effective length of the capacitive strain gauge (5) changes, and the frequency of the pressure sensor also changes. By controlling the number of electrical conversions at the control points, the effective length of the capacitive strain gauge (5) is adjusted, and the frequency of the pressure sensor is gradually made consistent with the characteristic frequency of the outside world until the pressure sensor reaches a resonant state with the outside world.

10. The working method according to claim 9, characterized in that: The frequency of the pressure sensor is , where T is the tension, is the linear density, and L is the length of the capacitive strain gauge (5).

Citation Information

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