CN112540234B - Dielectric constant measuring jig and measuring method based on parallel plate capacitance method - Google Patents
Dielectric constant measuring jig and measuring method based on parallel plate capacitance method Download PDFInfo
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- CN112540234B CN112540234B CN202011341277.2A CN202011341277A CN112540234B CN 112540234 B CN112540234 B CN 112540234B CN 202011341277 A CN202011341277 A CN 202011341277A CN 112540234 B CN112540234 B CN 112540234B
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- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
- G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
- G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
- G01R27/2617—Measuring dielectric properties, e.g. constants
- G01R27/2623—Measuring-systems or electronic circuits
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
- G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
- G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
- G01R27/2617—Measuring dielectric properties, e.g. constants
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Abstract
The invention discloses a dielectric constant measuring jig and a dielectric constant measuring method based on a parallel plate capacitance method, and belongs to the technical field of material measurement application. The measuring jig comprises an electrode system, a sliding frame system, a thickness measuring system and a bottom plate; the electrode system comprises an upper polar plate, a lower polar plate, a support column and a triangular support; the sliding frame system comprises a rotating hand wheel, a ball screw, a sliding rail and a sliding block, wherein the rotating hand wheel is connected with the ball screw, the sliding block moves on the sliding rail, an upper polar plate of the electrode system is fixed on the sliding block, and the sliding block is controlled to move and drive the upper polar plate to move by the rotating hand wheel; the thickness measuring system is used for measuring the relative displacement of the upper polar plate along with the movement of the slide block. The measured sample is placed between the upper polar plate and the lower polar plate, and the dielectric constant of the sample is calculated by utilizing the read capacitance value of the parallel plate capacitor, so that the edge effect is reduced, the precision of the measurement result is improved, and the requirements of test samples with different sizes are met.
Description
Technical Field
The invention belongs to the technical field of material measurement application, and particularly relates to a dielectric constant measuring jig and a measuring method based on a parallel plate capacitance method.
Background
The dielectric constant is a very important electromagnetic parameter that characterizes the ability of a material to hold induced polarization charges or polarization properties. Common measurement methods can be divided into, depending on the frequency range, material properties and size of the material: parallel plate capacitance, transmission line, coaxial probe, free space, and the like. Although the testing methods are various, each method has the restriction factors such as the applicable conditions and the purchase cost thereof.
The parallel plate capacitance method is the most classical and original measurement method, and is characterized in that a capacitor is formed by adding a measured sample between two electrodes, then the capacitance of the capacitor is measured, and the dielectric constant is calculated according to the measurement result. The method is simple to operate, but due to the influences of inductance, resistance, capacitor edge effect and the like of the lead, the measured capacitance has large errors, and the measured dielectric constant is not accurate enough. Factors affecting the measurement accuracy also include the positioning accuracy between the plates, such as parallelism and coaxiality, and especially when measuring very thin samples, small deviations in the plate spacing can cause large measurement errors. Some simple parallel plate capacitance measuring devices on the market cannot meet the requirements of measuring samples with various sizes because upper and lower electrode plates of the simple parallel plate capacitance measuring devices are fixed.
Therefore, it is necessary to design a high-precision dielectric constant measuring method and measuring jig which can reduce edge effect, improve measuring precision and be suitable for multi-size samples.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a dielectric constant measuring jig and a dielectric constant measuring method based on a parallel plate capacitance method, and aims to reduce the edge effect, improve the precision of the measuring result and meet the requirements of test samples with different sizes.
In order to achieve the above object, the present invention provides a dielectric constant measuring tool based on a parallel plate capacitance method, comprising: the electrode system, the carriage system, the thickness measurement system and the base plate are used to detect the capacitance of the sample in cooperation with an impedance analyzer, such as the IM3570 from the japanese laid-open company (HIOKI), to obtain the dielectric constant of the sample.
The electrode system is used for forming a parallel plate capacitor with a measured sample, so that the dielectric constant of the sample is calculated according to the measured capacitance value. The electrode system comprises an upper polar plate, a lower polar plate, a support column and a triangular support. The upper polar plate is connected with the supporting column and can move up and down through the fixed connection of the triangular support and the sliding frame system. The lower polar plate is fixed on the bottom plate through the support column.
Furthermore, the upper pole plate and the lower pole plate are both made of metal materials, and the radius of the upper pole plate and the radius of the lower pole plate are equal and are represented by R; the sample is required to be a disk-shaped solid material with radius r and thickness d, and two parallel surfaces. The thickness d of the sample is less than R; while the radius R is smaller than the plate radius R, so that a parallel electric field can be obtained in the sample.
The sliding frame system is connected with an upper polar plate in the electrode system and used for precisely controlling the upper polar plate to slide up and down, and comprises a rotating hand wheel, a ball screw, a sliding rail and a sliding block.
The rotary hand wheel is connected with the ball screw, an upper polar plate in the electrode system is fixed on the sliding block, and the sliding block is accurately controlled to move up and down through rotating the hand wheel. The slide rail limits the moving range of the slide block, so that the slide block vertically moves up and down.
Further, the distance L between the sliding frame system serving as the central support of the measuring clamp and the two-pole plate is far larger than the measuring distance of the two-pole plate, and the influence of the device part on the measuring result is reduced.
Further, the coaxiality of the slide rail support opening and the slide block opening is tightly matched, and the moving verticality of the slide block is guaranteed.
The thickness measuring system is composed of a grating ruler, is fixed on the sliding frame system and is used for accurately measuring the vertical movement displacement of the upper polar plate.
The invention also provides a dielectric constant measuring method based on the parallel plate capacitance method, which comprises the following steps:
(1) the measured sample is placed on the lower polar plate (the more uniform the magnetic field of the parallel plate capacitor is close to the middle part, the radius of the selected sample is smaller than that of the polar plate), and the sample is just clamped between the upper polar plate and the lower polar plate by rotating the hand wheel. Clamping the four-terminal probe of the impedance analyzer on the upper polar plate and the lower polar plate respectively to enable the measuring jig and the impedance analyzer to form a complete dielectric constant measuring system;
(2) reading the capacitance value C of a parallel plate capacitorp. Because the radius of the sample is smaller than that of the polar plate, the measured capacitance value is actually the parallel mixed capacitance of the sample and air. Considering the influence of the fringe capacitance of the dual-electrode system, the fringe capacitance needs to be corrected, and the empirical formula of the corrected capacitance value is as follows:
obtaining a dielectric constant calculation formula;
where d is the distance between the two plates, R is the radius of the plates, R is the radius of the sample, ε0Is a vacuum dielectric constant of 8.854X 10-12F/m。
The formula (2) considers the correction of the edge effect, so that the given dielectric constant has higher precision.
(3) In order to further improve the measurement precision of the dielectric constant, the invention provides a dielectric constant high-precision measurement method combined with finite element analysis, which specifically comprises the following steps:
(3.1) according to the capacitor structure parameters, using the sample dielectric constant obtained in the formula (2) as an initial value, building a plate capacitor simulation model in finite element software, and carrying out finite element calculation to obtain a capacitance value CFEM。
(3.2) calculating the error delta C of the finite element result and the measurement result as CFEM-CpUsing Δ C to correct the dielectric constant, the correction formula is
And (3.3) substituting the corrected dielectric constant into a finite element model for checking calculation, and if the capacitance value obtained by calculation and the measured value have errors, repeating the process until the errors meet the requirements.
Through the technical scheme, compared with the prior art, the invention has the following beneficial effects:
(1) the invention provides a measuring method and a measuring jig for measuring the dielectric constant of a sample based on a parallel plate capacitance method, the principle of the measuring method and the experimental operation are simple, and the cost is low.
(2) The upper polar plate and the lower polar plate of the measuring clamp are respectively connected with the sliding frame system and the bottom plate through the cylindrical support columns, the upper polar plate and the lower polar plate are fixed more stably and cannot shake, and the parallelism and the coaxiality of the upper polar plate and the lower polar plate can be better guaranteed when the upper polar plate moves up and down.
(3) The radius R of the upper and lower polar plates of the electrode system and the thickness d of the sample meet R & gt d, and the influence of the edge effect on measurement is reduced. The distance L between the carriage system part and the bipolar plate, which is used as the central support of the measuring clamp, is far larger than the thickness d of the sample, so that the influence of the device part on the measuring result is reduced.
(4) The sliding frame system of the measuring clamp utilizes the rotating hand wheel with larger radius, so that the adjustment is more convenient, and the distance adjustment of the polar plate is more accurate.
(5) The thickness measuring system of the measuring clamp is fixed with the sliding frame system, and the distance between the upper polar plate and the lower polar plate is measured by using the grating ruler, so that the positioning precision of less than 1 mu m can be obtained, and the measuring clamp is very important for accurately measuring very thin samples.
(6) In the measuring method, the error influence of the edge effect is evaluated and corrected by using an empirical formula, so that higher measuring precision can be obtained.
(7) The invention provides a method for processing and optimizing data by using a finite element technology, which can completely eliminate the influence of edge effect theoretically and obtain the accurate value of the dielectric constant of the sample. And comparing the result of the finite element simulation with the result obtained by the correction formula, and verifying the effectiveness of the measuring method.
Drawings
FIG. 1 is a schematic structural diagram of a dielectric constant measuring tool based on a parallel plate capacitance method according to the present invention;
FIG. 2 is a schematic structural diagram of an electrode system of a measuring jig;
FIG. 3 is a schematic structural diagram of a measuring tool carriage system;
FIG. 4 is a simulation of a parallel plate capacitor in the Ansys finite element software;
wherein, 1 is an electrode system, 2 is a sliding frame system, 3 is a thickness measuring system, 4 is an upper polar plate, 5 is a lower polar plate, 6 is a supporting column, 7 is a triangular support, 8 is a bottom plate, 9 is a sliding rail, 10 is a rotating hand wheel, 11 is a sliding block, 12 is a ball screw, 13 is an air domain, 14 is an upper and a lower polar plates, and 15 is a measuring sample.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a dielectric constant measuring jig based on a parallel plate capacitance method, which comprises the following steps: the electrode system, the carriage system, the thickness measurement system and the base plate are used to detect the capacitance of the sample in cooperation with an impedance analyzer, such as the IM3570 from the japanese laid-open company (HIOKI), to obtain the dielectric constant of the sample.
The electrode system is used for forming a parallel plate capacitor with a measured sample, so that the dielectric constant of the sample is calculated according to the measured capacitance value. The electrode system comprises an upper polar plate, a lower polar plate, a support column and a triangular support. The upper polar plate is connected with the supporting column and can move up and down through the fixed connection of the triangular support and the sliding frame system. The lower polar plate is fixed on the bottom plate through the support column.
Specifically, the upper pole plate and the lower pole plate are both made of metal materials, and the radius of the upper pole plate and the radius of the lower pole plate are equal and are represented by R; the sample is required to be a disk-shaped solid material with radius r and thickness d, and two parallel surfaces. The thickness d of the sample is less than R; while the radius R is smaller than the plate radius R, so that a parallel electric field can be obtained in the sample.
The sliding frame system is connected with an upper polar plate in the electrode system and used for precisely controlling the upper polar plate to slide up and down, and comprises a rotating hand wheel, a ball screw, a sliding rail and a sliding block.
The rotary hand wheel is connected with the ball screw, an upper polar plate in the electrode system is fixed on the sliding block, and the sliding block is accurately controlled to move up and down through rotating the hand wheel. The slide rail limits the moving range of the slide block, so that the slide block vertically moves up and down.
In particular, the distance L between the carriage system as the central pillar of the measuring clamp and the bipolar plate is far larger than the measuring distance of the bipolar plate, so that the influence of the device part on the measuring result is reduced.
Specifically, the coaxiality of the slide rail support opening and the slide block opening is tightly matched, and the verticality of the slide block moving is guaranteed.
The thickness measuring system is composed of a grating ruler, is fixed on the sliding frame system and is used for accurately measuring the vertical movement displacement of the upper polar plate.
Referring to fig. 1, an embodiment of the present invention provides a measurement fixture for measuring a dielectric constant of a sample based on a parallel plate capacitance method, including: an electrode system, a carriage system and a thickness measurement system;
as shown in fig. 2, the upper electrode plate 4 of the electrode system is connected with a support column 6 and fixed on the sliding frame system through a triangular bracket 7; the lower polar plate 5 is fixed on the bottom plate 8 through a support column.
As shown in fig. 3, in the carriage system, a rotating hand wheel 10 is connected to the top end of a ball screw 12, a slide block 11 is fixed on the screw 12, and the roller motion range of the slide block 11 is fixed in the slide rail 9. The rotating hand wheel 10 is rotated to move the slide block 11 up and down, so that the upper electrode plate 4 of the electrode system fixed on the slide block 11 can vertically move up and down.
In the thickness measuring system, a reading head of a grating ruler is installed and fixed on the side edge of a sliding frame system, a main ruler is installed on a sliding block 11 and moves along with the up-down movement of the sliding block, and the relative displacement of the sliding block can be read from the reading head.
The embodiment of the invention provides a high-precision measurement method for measuring the dielectric constant of a sample based on a parallel plate capacitance method, which comprises the following steps:
(1) three disk-shaped polytetrafluoroethylene samples with different sizes are selected as samples to be detected, the radiuses of the samples are all 50mm, and the thicknesses of the samples are respectively 10mm, 20mm and 50 mm. The dielectric constant of the polytetrafluoroethylene is known, and meanwhile, the material has stable performance and is slightly influenced by the environment such as frequency, temperature and the like, so that the polytetrafluoroethylene is used for testing the effectiveness of the measuring method. The sample to be measured is placed on the lower polar plate 5, and the upper polar plate 4 and the lower polar plate 5 just clamp the sample by rotating the hand wheel 10. The four-terminal probe of the impedance analyzer is respectively clamped on the upper polar plate 4 and the lower polar plate 5, so that the measuring clamp and the impedance analyzer form a complete dielectric constant measuring system;
(2) reading the capacitance value C of a parallel plate capacitorp. Because the radius of the sample is smaller than that of the polar plate, the measured capacitance value is actually the parallel mixed capacitance of the sample and air. Considering the influence of the fringe capacitance of the dual-electrode system, the fringe capacitance needs to be corrected, and the empirical formula of the corrected capacitance value is as follows:
obtaining a dielectric constant calculation formula;
where d is the distance between the two plates, R is the radius of the plates, R is the radius of the sample, ε0Is a vacuum dielectric constant of 8.854X 10-12F/m。
The formula (2) considers the correction of the edge effect, so that the given dielectric constant has higher precision.
(3) In order to further improve the measurement precision of the dielectric constant, the invention provides a dielectric constant high-precision measurement method combined with finite element analysis, which specifically comprises the following steps:
(3.1)according to the measured and known parameters of capacitor construction, taking a sample of polytetrafluoroethylene with a thickness of 50mm as an example: the radius of the two electrode plates is 80mm, the radius of the sample is 50mm, the distance between the two electrode plates is set to be 50mm, and a plate capacitor simulation model is built in finite element software, as shown in figure 4. Performing finite element calculation to obtain a capacitance value CFEM。
(3.2) calculating the error delta C of the finite element result and the measurement result as CFEM-CpUsing Δ C to correct the dielectric constant, the correction formula is
(3.3) the obtained
And substituting the capacitance value obtained by calculation into a finite element model for checking calculation, and if the capacitance value and the measured value still have errors, repeating the process until the errors meet the requirements.
The dielectric constant of the ptfe sample calculated by the modified equation and finite element simulation was compared to the known dielectric constant, and the results are shown in table 1:
TABLE 1
The results show that the relative error of the relative dielectric constant of the polytetrafluoroethylene obtained by the empirical formula is less than 5%, and the relative error obtained by finite element optimization is less than 2.5%, which indicates the effectiveness of the two measurement methods.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (3)
1. A dielectric constant measuring method based on a parallel plate capacitance method is characterized by comprising the following steps:
(1) placing a sample to be measured on a lower polar plate, and driving an upper polar plate to vertically move up and down by rotating a hand wheel so that the upper polar plate and the lower polar plate just clamp the sample to be measured;
(2) capacitance value C of parallel plate capacitor read by impedance analyzer on upper and lower platespCalculating the dielectric constant of the measured sample:
wherein, CpIs the capacitance of the parallel plate capacitor, d is the distance between the two plates, the radius of the upper plate and the lower plate is the same, R is the radius of the plate, R is the radius of the measured sample, epsilon0Is the dielectric constant in vacuum.
2. The measurement method of claim 1, wherein the radius of the measured sample is less than the plate radius and the thickness of the measured sample is substantially less than the plate radius.
3. The measurement method of claim 1, further comprising the steps of:
(3.1) according to the structural parameters of the parallel plate capacitor, using the dielectric constant of the measured sample obtained in the step (2) as an initial value, building a simulation model of the parallel plate capacitor in finite element software, and carrying out finite element calculation to obtain a capacitance value CFEM；
(3.2) calculating the error Δ C ═ C between the finite element results and the capacitance of the parallel plate capacitorFEM-CpAnd correcting the dielectric constant by using the delta C, wherein the correction formula is as follows:
and (3.3) substituting the corrected dielectric constant into a finite element model for checking calculation, and repeating the steps (3.1) - (3.2) if the calculated capacitance value still has an error with the capacitance value of the parallel plate capacitor until the error meets the requirement.
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