CN115307788A - Method for determining capacitance of non-contact type round conductive film variable capacitor - Google Patents

Method for determining capacitance of non-contact type round conductive film variable capacitor Download PDF

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CN115307788A
CN115307788A CN202210797640.4A CN202210797640A CN115307788A CN 115307788 A CN115307788 A CN 115307788A CN 202210797640 A CN202210797640 A CN 202210797640A CN 115307788 A CN115307788 A CN 115307788A
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conductive film
circular conductive
variable capacitor
electrode plate
pressure
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孙俊贻
颜志强
何晓婷
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Chongqing University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L1/00—Measuring force or stress, in general
    • G01L1/14—Measuring force or stress, in general by measuring variations in capacitance or inductance of electrical elements, e.g. by measuring variations of frequency of electrical oscillators
    • G01L1/142—Measuring force or stress, in general by measuring variations in capacitance or inductance of electrical elements, e.g. by measuring variations of frequency of electrical oscillators using capacitors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L25/00—Testing or calibrating of apparatus for measuring force, torque, work, mechanical power, or mechanical efficiency
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L27/00—Testing or calibrating of apparatus for measuring fluid pressure
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L9/00—Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means
    • G01L9/12—Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means by making use of variations in capacitance, i.e. electric circuits therefor

Abstract

The invention discloses a method for determining the capacitance of a non-contact circular conductive film variable capacitor, which comprises the following steps: a circular conductive film which is initially flat and is fixedly clamped at the periphery with the radius a, the thickness h, the Young modulus E and the Poisson ratio v is used as a movable electrode plate of the variable capacitor, a fixed electrode plate of the variable capacitor is parallel to the circular conductive film which is initially flat, an insulating layer with the thickness t is coated on the fixed electrode plate, a medium between the insulating layer and the circular conductive film which is initially flat is air, the distance is g, pressure q is applied to the circular conductive film, and the circular conductive film generates axisymmetric flexural deformation to one side of the fixed electrode plate but does not contact the insulating layer, so that the variable capacitor is changed from the initial parallel plate capacitor to a non-parallel plate capacitor after the pressure q is applied, and the capacitance C of the variable capacitor can be determined by using the measured value of the pressure q based on the static balance analysis of the axisymmetric flexural deformation.

Description

Method for determining capacitance of non-contact type round conductive film variable capacitor
Technical Field
The invention relates to a method for determining the capacitance of a non-contact variable capacitor by using a circular conductive film as a movable electrode plate.
Background
Films are widely used in many engineering fields. Many membranes have good elastic deformability and can exhibit large elastic deflections under transverse loading, which provides possibilities for designing and developing devices based on elastic deflection of the membrane. The circular non-contact type capacitance pressure sensor is a pressure sensor based on elastic deflection of a conductive film, and the key component of the pressure sensor is a variable capacitor which adopts the circular conductive film as a movable electrode plate. The moving electrode plate of the variable capacitor is an initially flat and circumferentially fixedly clamped circular conductive film. The fixed electrode plates of the variable capacitor are parallel to the initially flat circular conductive film, thereby making the variable capacitor initially a parallel plate capacitor. The fixed electrode plate is coated with an insulating layer, the insulating layer and the initially flat circular conductive film are spaced from each other by a certain distance, and the medium between the insulating layer and the initially flat circular conductive film is air. Under pressure, the circular conductive film, which serves as the moving electrode plate of the variable capacitor, is subjected to axisymmetric flexural deformation toward the fixed electrode plate side, so that the variable capacitor is changed from a parallel plate capacitor before pressure is applied to a non-parallel plate capacitor after pressure is applied. By controlling the amount of pressure applied (i.e., by controlling the pressure applied to the pressure sensor), the circular conductive film can be made to have a maximum elastic deflection less than the separation between the insulating layer and the initially flat circular conductive film, thereby forming a non-contact variable capacitance non-parallel plate capacitor. Thus, the change in pressure causes a change in elastic deflection of the circular conductive film, which in turn causes a change in capacitance of the variable capacitor. Therefore, the pressure, the elastic deflection and the capacitance are in one-to-one corresponding analytical relationship. Therefore, as long as the analytical relationship exists, the pressure can be determined by measuring the capacitance, which is the basic principle of the circular non-contact capacitive pressure sensor.
However, since the problem of large deflection of the thin film is strongly nonlinear, it is almost impossible to obtain an accurate analytical relationship among the pressure, elastic deflection and capacitance of the noncontact capacitive pressure sensor. The invention is dedicated to the research of a circular non-contact capacitance pressure sensor, and obtains more accurate analytic relations between pressure and elastic deflection as well as between pressure and capacitance. The research result of the invention is not seen from the new research result of the prior literature.
Disclosure of Invention
The invention aims at the research of a circular non-contact type capacitance pressure sensor, obtains an analytic solution about axisymmetrical flexural deformation of a circular conductive film in a non-contact type variable capacitor, and provides a method for determining the capacitance of the non-contact type circular conductive film variable capacitor on the basis of the analytic solution.
A method for determining the capacitance of a non-contact circular conductive film variable capacitor comprises the following steps: a circular conductive film which is initially flat and is fixedly clamped at the periphery with the radius of a, the thickness of h, the Young modulus of elasticity of E and the Poisson ratio of v is used as a movable electrode plate of the variable capacitor, a fixed electrode plate of the variable capacitor is parallel to the circular conductive film which is initially flat, an insulating layer with the thickness of t is coated on the fixed electrode plate, a medium between the insulating layer and the circular conductive film which is initially flat is air, the distance between the insulating layer and the circular conductive film which is initially flat is g, applying a pressure q to the circular conductive film to cause axisymmetrical flexural deformation to the fixed electrode plate side without contacting the insulating layer on the fixed electrode plate, thereby changing the variable capacitor from a parallel plate capacitor before applying the pressure q to a non-parallel plate capacitor after applying the pressure q
Figure BDA0003736322120000021
Wherein r is the distance from one point on the circular conductive film to the symmetry axis of the circular conductive film, epsilon 0 Is a vacuum dielectric constant of ∈ 1 To fix the relative dielectric constant, epsilon, of the insulating layer on the electrode plate 2 Is the relative dielectric constant of air, pi is the circumferential ratio, and
Figure BDA0003736322120000022
Figure BDA0003736322120000023
Figure BDA0003736322120000024
Figure BDA0003736322120000025
Figure BDA0003736322120000031
Figure BDA0003736322120000032
Figure BDA0003736322120000033
Figure BDA0003736322120000034
Figure BDA0003736322120000035
Figure BDA0003736322120000041
Figure BDA0003736322120000042
Figure BDA0003736322120000043
Figure BDA0003736322120000051
Figure BDA0003736322120000061
Figure BDA0003736322120000062
and b 0 Is given by the equation
Figure BDA0003736322120000063
Figure BDA0003736322120000064
Figure BDA0003736322120000065
Figure BDA0003736322120000066
Figure BDA0003736322120000071
Figure BDA0003736322120000081
Figure BDA0003736322120000091
Figure BDA0003736322120000101
Figure BDA0003736322120000102
Figure BDA0003736322120000103
Figure BDA0003736322120000104
Figure BDA0003736322120000111
Figure BDA0003736322120000112
Figure BDA0003736322120000113
Figure BDA0003736322120000114
Figure BDA0003736322120000115
And (4) determining.
Thus, as long as the value of the pressure q is measured, the equation can be derived
Figure BDA0003736322120000121
Determining the capacitance C of the non-contact circular conductive film variable capacitor when the circular conductive film is subjected to pressure q, wherein the unit of C is picofarad (pF), epsilon 0 The units of (A) are picofarads per millimeter (pF/mm), the units of a, h, t, g, and r are all millimeters (mm), and the units of E, q are all newtons per square millimeter (N/mm) 2 ) V, b 0 、b 2 、b 4 、b 6 、b 8 、b 10 、b 12 、b 14 、c 0 、c 2 、c 4 、c 6 、c 8 、c 10 、c 12 、c 14 、Q、ε 1 、ε 2 And pi are dimensionless quantities.
Drawings
Fig. 1 is a schematic diagram of an axisymmetric deflection of a noncontact circular conductive film variable capacitor when the circular conductive film is subjected to a pressure q, where 1 is the circular conductive film after the axisymmetric deflection, 2 is a fixed electrode plate of the variable capacitor, 3 is an insulating layer on the fixed electrode plate, 4 is a vent hole through which air passes, 5 is an outer edge fixing and clamping device of an initially flat circular conductive film, 6 is a support of the variable capacitor, 7 is a plane in which a geometric middle plane of the initially flat circular conductive film is located, a is an outer radius of the initially flat circular conductive film and an inner radius of the outer edge fixing and clamping device thereof, t is a thickness of the insulating layer on the fixed electrode plate, g is a distance between the insulating layer and the initially flat circular conductive film, o is a coordinate origin (centroid located in the geometric middle plane of the initially flat circular conductive film), r is a radial coordinate (used to indicate a distance from a point on the circular conductive film before or after the deformation to a symmetric axis of the circular conductive film before or after the deformation), w is a lateral coordinate (used to indicate a circular deflection of the axisymmetric deformation), and q indicates a circular conductive film applied pressure q on the circular conductive film.
Detailed Description
The technical scheme of the invention is further explained by combining the specific cases as follows:
as shown in FIG. 1, use is made ofInitial flat radius of mass a =100mm, thickness h =1mm, young's modulus of elasticity E =7.84N/mm 2 A circular conductive film with a Poisson ratio v =0.47 and fixed and clamped periphery is used as a movable electrode plate of a variable capacitor, a fixed electrode plate of the variable capacitor is parallel to an initially flat circular conductive film, an insulating layer with the thickness t =0.1mm is coated on the fixed electrode plate, the medium between the insulating layer and the initially flat circular conductive film is air, the distance g =41mm, pressure q is applied to the circular conductive film, the circular conductive film generates axisymmetric flexural deformation to one side of the fixed electrode plate and does not contact the insulating layer on the fixed electrode plate, so that the variable capacitor is changed from a parallel plate capacitor before the application of the pressure q to a non-parallel plate capacitor after the application of the pressure q, and the pressure q =0.021225MPa is measured
Figure BDA0003736322120000131
Figure BDA0003736322120000132
Figure BDA0003736322120000133
Figure BDA0003736322120000134
Figure BDA0003736322120000135
Figure BDA0003736322120000141
Figure BDA0003736322120000151
Figure BDA0003736322120000161
Figure BDA0003736322120000162
Figure BDA0003736322120000163
Figure BDA0003736322120000164
Figure BDA0003736322120000171
Figure BDA0003736322120000172
Figure BDA0003736322120000173
Figure BDA0003736322120000174
Figure BDA0003736322120000175
To obtain b 0 =0.214308 and c 2 ＝-0.315815、c 4 ＝-0.047998、c 6 ＝-1.650838×10 -2 、c 8 ＝-7.352749×10 -3 、c 10 ＝-3.731051×10 -3 、c 12 ＝-2.050382×10 -3 、c 14 ＝-1.189700×10 -3 Then by the equation
Figure BDA0003736322120000181
To obtain c 0 =0.396696, final equation
Figure BDA0003736322120000182
Obtaining the capacitance C =26.59pF of the non-contact circular conductive film variable capacitor when the circular conductive film is subjected to the pressure of q =0.021225MPa, wherein r is the distance from one point on the circular conductive film to the symmetry axis of the circular conductive film, pi is the circumference ratio, and the vacuum dielectric constant epsilon 0 ＝8.854×10 -3 pF/mm, relative dielectric constant ε of insulating layer on fixed electrode plate 1 =2.5, relative dielectric constant ε of air 2 ＝1.00053。

Claims (1)

1. A method for determining capacitance of a non-contact circular conductive film variable capacitor is characterized in that: the method comprises the steps of adopting a circular conductive film which is initially flat and is fixedly clamped at the periphery with the radius a, the thickness h, the Young modulus E and the Poisson ratio v as a movable electrode plate of the variable capacitor, enabling a fixed electrode plate of the variable capacitor to be parallel to the initially flat circular conductive film, coating an insulating layer with the thickness t on the fixed electrode plate, enabling a medium between the insulating layer and the initially flat circular conductive film to be air and enabling the space to be g, applying pressure q to the circular conductive film to enable the circular conductive film to generate axisymmetric flexural deformation to one side of the fixed electrode plate without contacting the insulating layer on the fixed electrode plate, and changing the variable capacitor from a parallel plate capacitor before applying the pressure q to a non-parallel plate capacitor after applying the pressure q
Figure FDA0003736322110000011
Figure FDA0003736322110000012
Figure FDA0003736322110000013
Figure FDA0003736322110000014
Figure FDA0003736322110000021
Figure FDA0003736322110000031
Figure FDA0003736322110000041
Figure FDA0003736322110000051
Figure FDA0003736322110000052
Figure FDA0003736322110000053
Figure FDA0003736322110000054
Figure FDA0003736322110000061
Figure FDA0003736322110000062
Figure FDA0003736322110000063
Figure FDA0003736322110000064
Figure FDA0003736322110000065
Determination of b 0 And b 2 、b 4 、b 6 、b 8 、b 10 、b 12 、b 14 、c 2 、c 4 、c 6 、c 8 、c 10 、c 12 、c 14 Then by the equation
Figure FDA0003736322110000066
Determination of c 0 Is finally given by the equation
Figure FDA0003736322110000071
Determining the capacitance C of the non-contact circular conductive film variable capacitor when the circular conductive film is subjected to pressure q, wherein r is the distance from one point on the circular conductive film to the symmetry axis of the circular conductive film, epsilon 0 Is a vacuum dielectric constant of ∈ 1 To fix the relative dielectric constant, epsilon, of the insulating layer on the electrode plate 2 Is the relative dielectric constant of air, pi is the circumference ratio, and the unit of C is picofarad (pF), epsilon 0 The units of (a) are picofarads per millimeter (pF/mm), the units of a, h, t, g, r are all millimeters (mm), and the units of E, q are all newtons per square millimeter (N/mm) 2 ) V, b 0 、b 2 、b 4 、b 6 、b 8 、b 10 、b 12 、b 14 、c 0 、c 2 、c 4 、c 6 、c 8 、c 10 、c 12 、c 14 、Q、ε 1 、ε 2 And pi are dimensionless quantities.
CN202210797640.4A 2022-07-08 2022-07-08 Method for determining capacitance of non-contact type round conductive film variable capacitor Pending CN115307788A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116625326A (en) * 2023-07-20 2023-08-22 湖南大学 High-linearity depth gauge for deep sea measurement

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6532834B1 (en) * 1999-08-06 2003-03-18 Setra Systems, Inc. Capacitive pressure sensor having encapsulated resonating components
WO2015051729A1 (en) * 2013-10-08 2015-04-16 无锡华润上华半导体有限公司 Capacitive type mems pressure sensor
CN112730071A (en) * 2020-12-09 2021-04-30 重庆大学 Method for determining elastic energy of circular prestressed film under gas pressure
CN112880950A (en) * 2021-01-18 2021-06-01 重庆大学 Method for determining deflection of circular prestressed film with limited maximum deflection under air pressure

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6532834B1 (en) * 1999-08-06 2003-03-18 Setra Systems, Inc. Capacitive pressure sensor having encapsulated resonating components
WO2015051729A1 (en) * 2013-10-08 2015-04-16 无锡华润上华半导体有限公司 Capacitive type mems pressure sensor
CN112730071A (en) * 2020-12-09 2021-04-30 重庆大学 Method for determining elastic energy of circular prestressed film under gas pressure
CN112880950A (en) * 2021-01-18 2021-06-01 重庆大学 Method for determining deflection of circular prestressed film with limited maximum deflection under air pressure

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ZHENG, ZL, ET AL.: "Nonlinear Free Vibration Analysis of Axisymmetric Polar Orthotropic Circular Membranes under the Fixed Boundary Condition", 《MATHEMATICAL PROBLEMS IN ENGINEERING》, 30 April 2014 (2014-04-30) *
何晓婷;吴建梁;郑周练;陈山林;: "均布荷载下受有预加张力圆薄膜的轴对称变形", 重庆大学学报, no. 01, 15 January 2010 (2010-01-15) *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116625326A (en) * 2023-07-20 2023-08-22 湖南大学 High-linearity depth gauge for deep sea measurement
CN116625326B (en) * 2023-07-20 2023-10-24 湖南大学 High-linearity depth gauge for deep sea measurement

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