RU2548064C1 - Method to measure dielectric permeability of materials and device for its realisation - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: method is based on measurement of complex ratio of reflection of electromagnetic waves from a section of a transmission line, at the end of which they install calibration measures, and a tested material sample, with subsequent processing of materials. At the section of the transmission line with wave resistance Zw in parallel to it they connect a resistive element with resistance R=(0.1-0.2)Zw, using results of calibration measurements they determine parameters of scattering of a circuit that connects plane of measurement of reflection ratio with plane of connection of the tested section of the line with the tested sample. By processing of data array they find dielectric permeability and tangent of angle of losses of the tested material. The device is proposed for method realisation.

EFFECT: increased accuracy of determination of dielectric permeability in wide range of frequencies.

5 cl, 5 dwg, 1 tbl

Description

The invention relates to the field of measuring the characteristics of materials and can be used to determine the dielectric constant and the tangent of the dielectric loss angle of insulating, composite and other materials.

A known method for determining the dielectric constant and the tangent of the dielectric loss angle of materials based on measuring the modules and phases of the reflection and transmission coefficients of electromagnetic waves reflected and transmitted through a sample placed in a waveguide or coaxial line. The phases of the coefficients contain information on the dielectric constant, and the modules on the tangent of the dielectric loss angle [see Brant A.A. The study of dielectrics at microwave frequencies. - M .: Fizmatgiz, 1963. - Page 189].

The disadvantage of this method is the low accuracy of determining the dielectric constant and the dielectric loss tangent due to the relatively low phase sensitivity of the reflection and transmission coefficients to the dielectric constant, and their modules to the loss tangent.

A known method of determining the dielectric constant and the tangent of the dielectric loss angle of materials based on measuring the resonant frequency and quality factor of the resonator with a sample of material of a given shape placed in it. Information on the dielectric constant is contained in the resonant frequency, and on the dielectric loss tangent is in the Q factor of the resonator [see Brant A.A. The study of dielectrics at microwave frequencies. - M .: Fizmatgiz, 1963. - Page 120].

The method has high accuracy in measuring the dielectric constant and the dielectric loss tangent, however, it allows to obtain information only at one frequency within the sub-ranges: 4-7 ... 15-20, determined by the geometry and dielectric constant of the samples. It is not possible to carry out measurements in the low-frequency part of the microwave range because of the limited size of standard samples of plates of insulating materials, which are widely used in integrated circuits and in the production of electronic components.

As a prototype, a method for measuring the dielectric constant and tangent of the loss angle of materials and a device for its implementation, which is essentially close to the proposed one (see the publication "Fundamentals of measuring the dielectric properties of materials. Application notes" by Agilent Technologies, pp. 20-22 ) The method consists in performing the calibration procedure of a vector network analyzer by connecting calibration measures and in measuring the complex reflection coefficient and transmission of electromagnetic waves of a segment of a transmission line of a given length into which a test sample of a certain length is installed, with subsequent processing of the results. A device for implementing the method comprises a transmission line segment with the possibility of installing a test sample in it, a measuring device and calibration measures. The method and device provide operation with a waveguide section 140 mm long in the frequency range from 8.2 to 12.4 GHz with Plexiglass samples (as an example) 25 and 31 mm long, measurement error ± 0.1 or (3-5%) .

However, the accuracy of measurements and the frequency range can be even higher, and the equipment used is significantly cheaper when improving the method and device for its implementation.

The present invention solves the problem of expanding the technological capabilities of the method and device for its implementation.

The technical result of the claimed invention is improving the accuracy of determining the dielectric constant and the loss tangent of the tested materials in a wide frequency range while reducing the cost of the equipment used.

This technical result is achieved by the fact that in the method of measuring the dielectric constant of materials, which consists in measuring the complex reflection coefficient of electromagnetic waves from a section of a transmission line, at the end of which calibration measures and a section of a line with a test sample are established, with subsequent processing of the results, at the input of a section of a transmission line with wave impedance Zв parallel to it, connect a resistive element with resistance R = (0.1-0.2) Zв, according to the results of calibration measurements, determine the new scattering parameters of the circuit connecting the plane of measurement of the complex reflection coefficient with the plane of connection of the line section with the test sample, while the dielectric constant and the loss tangent of the test material are determined by processing the data array for the reflection coefficient module having the form of a comb function of the frequency of electromagnetic waves and its analytical expressions through the wave parameters of scattering and the complex reflection coefficient from the portion of the line with the test sample, m length of the transmission line segment is selected more than half of the wavelength at the lower frequency range in which measurement is performed;

in a device for measuring the dielectric constant of materials containing a segment of a transmission line with the possibility of installing at its end a portion of a line with a test sample and calibration measures, a resistive element is connected at the input of a segment of a transmission line to which a measuring device is connected through a junction or connector;

when performing a segment of the transmission line in the form of a waveguide, a resistive film or a capacitive diaphragm with a resistor installed between the flanges of the coaxial waveguide transition and the waveguide is used as a resistive element;

when performing a segment of a transmission line in the form of a coaxial or strip line, a resistor is used as a resistive element, installed between the center or strip conductor and the screen, connected through a connector or a coaxial-strip transition to the measuring device;

A vector reflectometer was used as a measuring device.

Connecting a resistive element to a segment of a transmission line with a length of more than half the wavelength at the lower frequency of the range allows a method for measuring the permittivity ε, combining high accuracy with a wide frequency range. Like the resonance method, high accuracy in determining ε is ensured by accurately measuring the frequencies corresponding to the vertices of the “teeth” of the comb function. The sharpness of the “teeth” and their number in a selected wide frequency range are determined by the length of the line segment and the line section with the test sample, as well as the ratio of the wave impedance Z to the resistance R of the resistor included in the transmission line.

The scattering wave parameters of the circuit connecting the measurement plane of the complex reflection coefficient with the plane of connection of the line section with the test sample are determined to obtain an analytical expression for the reflection coefficient module having the form of a comb function.

The length of the length of the transmission line is chosen to be more than half the wavelength at the lower frequency of the range in which measurements are performed, because otherwise, the reflection coefficient module will contain a small number of “teeth” of the comb function and the error in determining the dielectric constant will increase.

The method is implemented using the device, the block diagram of which is shown in figure 1, figure 2 shows a graph of the complex reflection coefficient module, figure 3 - 3D model of the device used in the example implementation of the method, figure 4 - installation of the chip a resistor in a coaxial line in an example implementation of the method, FIG. 5 is a graphical illustration of the determination of dielectric constant and loss tangent at a frequency of 9.9959 GHz in an example implementation of the method.

A device for measuring the dielectric constant and the tangent of the loss of material contains a segment 1 of the transmission line with the possibility of installing at its end a section of the line with the test sample 2 and calibration measures 3, a measuring device 4. At the other end of the segment 1 of the transmission line, a resistive element 5 is connected in parallel with it to which a measuring device 4 is connected through a junction or connector 6.

When performing section 1 of the transmission line in the form of a waveguide, a resistive film or a capacitive diaphragm with a resistor mounted between the flanges of the coaxial waveguide transition 6 and the waveguide can be used as the resistive element 5.

When performing section 1 of the transmission line in the form of a coaxial or strip line, a resistor with a resistance R = (0.1-0.2) Zv, where Zv is the wave resistance of the transmission line installed between the center or strip conductor and the screen, is used as a resistive element 5 connected via a connector or coaxial-stripe transition to the measuring device.

As a measuring device 4, it is advisable to use a CABAN R54 or CABAN R140 vector reflectometer, which are significantly cheaper than the commonly used vector network analyzer.

The method is implemented as follows. To the segment 1 of the transmission line with the resistive element 5 through the transition 6 connect the measuring device 4 (vector reflectometer). At the other end of the segment 1 of the transmission line, calibration measures 3 are also installed, and then a section of the line with the test sample 2.

The essence of the proposed method for measuring the dielectric constant and the tangent of the angle of loss of materials on the microwave is to measure in a standard 50 Ohm coaxial channel in a wide frequency range of the complex reflection coefficient of electromagnetic waves from the parallel connection of the resistive element R with a segment of the transmission line, at the end of which three or more calibration measures 3 with known reflection coefficients, and then a portion of the line with the test sample. From the results of calibration measurements of the scattering wave parameters (S-parameters) of the circuit connecting the reflection coefficient measurement plane with the plane connecting the line section with the test sample, the dielectric constant ε and the loss tangent tgδ of the test material are found at individual points in the frequency range using scattering wave parameters (S-parameters) and special processing of the data array for the reflection coefficient module having the form of a comb frequency function, with the length L For transmission line 1, choose more than half the wavelength at the lower frequency of the range, and the resistance of the resistor of R = (0.1-0.2) ZB (ZB is the wave resistance of segment 1 of the transmission line), a standard set of calibration gauges is connected to segment 1 of the transmission line measures 3: coaxial (short circuit, idle, matched load or four short-circuited lines of different lengths), waveguide (short circuit, quarter-wave length, matched load or four short-circuited waveguide sections of different lengths), and in the case of a strip new line - three or more samples with specified geometric dimensions, dielectric constant and loss tangent. Using the vector reflectometer, the complex reflection coefficients Г _i in the measurement plane are used to determine the scattering wave parameters (S-parameters) of the circuit connecting the standard 50-ohm channel with the line section with the test sample 2 from the system of equations at all frequencies f _k range:

, $$i=\overline{\mathrm{1,}I}$$

, $$k=\overline{\mathrm{1,}K}$$

$$G_i\left(f_k\right)=S_{\mathrm{eleven}}\left(f_k\right)+\frac{S_{12}{S}_{21}\left(f_k\right)G_i\left(f_k\right)}{\mathrm{one}-S_{22}\left(f_k\right)G_i\left(f_k\right)}$$

, $$i=\overline{\mathrm{one,}I}$$

, $$k=\overline{\mathrm{one,}K}$$

here S ₁₂ S ₂₁ (f _k ) is the product of the direct and inverse transmission coefficients, and S ₁₁ (f _k ) and S ₂₂ (f _k ) are the input and output reflection coefficients of the circuit, G _i (f _k ) are complex reflection coefficients from calibration measures 3. Then connect a portion of the line with the test sample 2 of material with known geometric dimensions and measure the reflectance of the complex reflection coefficient G.

The dielectric constant and the loss tangent of the test material is determined using special processing of the data array for the reflection coefficient module G, having the form of a comb frequency function (Fig. 2) and its analytical representation, expressed through S-parameters and the complex reflection coefficient G (f _k ) from the line section with the sample:

$$\left|G\left(f_k,\epsilon ,tg\delta \right)\right|=\left|S_{\mathrm{eleven}}\left(f_k\right)+\frac{S_{12}{S}_{21}\left(f_k\right)\left|G\right|\left(f_k,tg\delta \right)\exp \left[\arg G\left(f_k,\epsilon \right)\right]}{\mathrm{one}-S_{22}\left(f_k\right)\left|G\right|\left(f_k,tg\delta \right)\exp \left[\arg G\left(f_k,\epsilon \right)\right]}\right|\text{(one)}$$

The base of the "comb" is determined by the reflection coefficient module S ₁₁ (f _k ) of the circuit connecting the vector reflectometer with a section of the line and a sample (smooth line in figure 2). The position of the “teeth” of the “comb” is determined by the electric length of the length of the transmission line and the portion of the line with the test sample, therefore, the dielectric constant and geometrical dimensions of the sample, and the sharpness of the “teeth” - both the length and the wave resistance of the transmission line. The height of the teeth is determined by the modulus of the reflection coefficient from the portion of the transmission line, which, in turn, is determined by the loss tangent of the sample of the test material.

It is essential that the values of the dielectric constant ε _k and the tangent of the loss angle tanδ _{k of the} material in a wide frequency range are determined by the coordinates [f _k , G _k ] of the vertices of the comb function of the reflection coefficient modulus.

The following is an example implementation of the method. Figure 3 shows a 3D model of the device. As calibration measures, a moving short circuit is used. During calibration, the movement of the short circuit is carried out using a micrometer screw. When measuring samples (insulating plates of aluminum oxide - polycor 60 × 48 × 1 mm in size), the short circuit is in the extreme position. An example of installing a chip resistor in a coaxial transmission line is shown in FIG. 4. A section of the line with the test sample is inserted into the gap between the device cover and the base close to the short circuit.

To assess the measurement error by the proposed method, a device model based on a 23 × 10 mm rectangular waveguide was used, as in the prototype, a coaxial waveguide transition, a capacitive diaphragm with a resistor and a 200 mm length of the waveguide. Half the wavelength at the lower frequency (8 GHz) of the range was 112 mm. The capacitive diaphragm was modeled with a capacitance of 0.16 pF, and the resistor resistance was R = 58.4 Ohms, the ratio R / Zв = 0.13 was in the range 0.1-0.2. As a section of the line with the test sample 31 mm long (as in the prototype), a 100 mm long waveguide model with an air dielectric and a 31 mm long model with a dielectric with a sample were used.

The device was calibrated using models of four short-circuited waveguide sections 30, 18.5, 11.43 and 7.05 mm long.

When connecting the model of each short-circuited waveguide section to the transition model with a waveguide segment and a resistor, the value of the complex reflection coefficient Гi in the measurement plane was determined.

The S-parameters of the circuit connecting the plane of measurement of the reflection coefficient in a standard 50-ohm coaxial path to the plane of connection of the line section (waveguide section) with the test sample were determined from the system of equations (1). To evaluate the error of the proposed method, the short circuit lengths in the S-parameter determination program were set with an error of 0.1 mm.

The dielectric constant and the loss tangent were determined by processing the data array for the reflection coefficient module from the device model, which has the form of a comb function of the frequency of electromagnetic waves and analytical expression through the scattering wave parameters and the complex reflection coefficient from the portion of the line with the test sample.

An illustration of the determination of dielectric constant and loss tangent at a frequency of 9.9959 GHz is shown in the graph of FIG. 5 and in the table. The second and fourth columns of the table correspond to the true values, the third and fifth - to the measurement results. In the example, the proposed method is simulated. The dielectric constant of a sample is a linear function of frequency. Therefore, the second column is a model of the true value of the dielectric constant at frequencies corresponding to the teeth of the comb function. For simplicity, the loss tangent over the entire frequency range was assumed to be a constant value of 0.005 — the fourth column. Columns 3 and 5 are the result of processing, which consists in determining the dielectric constant and the loss tangent at the top of the teeth using the analytical expression of the comb function.

As follows from the table, the maximum error in determining the dielectric constant was ± 0.011, and the standard error was σ = 0.0074 (0.32%).

The resulting error estimate fits into the standards in accordance with GOST P 8.623-2006. Relative permittivity and dielectric loss tangent of solid dielectrics. Measurement procedures in the microwave range.

Analysis of analogues shows that the proposed solution meets the criterion of "novelty", the set of essential features that provide a positive result, indicates compliance with the criterion of "inventive step", and laboratory tests confirm industrial applicability.

Table Frequency, GHz ε arr ε meas tgδ arr tgδ meas 8.203 2.389 2.394 0.005 0.0053 8.482 2.374 2.372 0.005 0.0049 8.76 2.36 2.362 0.005 0.0049 9.037 2.345 2.342 0.005 0.0048 9.333 2.329 2.327 0.005 0.0052 9.654 2.312 2.32 0.005 0.005 9.996 2.294 2.285 0.005 0.0048 10.353 2.275 2.28 0.005 0.0052 10.718 2.256 2.27 0.005 0.0048 11.091 2.236 2.225 0.005 0.005 11.462 2.217 2.225 0.005 0.0052 11.826 2.197 2.205 0.005 0.0046

Claims (5)

1. The method of measuring the dielectric constant of materials, which consists in measuring the complex reflection coefficient of electromagnetic waves from a section of a transmission line, at the end of which set calibration measures and a section of a line with a test sample, followed by processing the results, characterized in that at the input of a section of a transmission line with a wave impedance Z is connected _in parallel to the resistive element with resistance R = (0,1-0,2) Z _a, the results of calibration measurements determine the scattered wave parameters I chain connecting the plane of measurement of the complex reflection coefficient with the plane of connection of the line section with the test sample, while the dielectric constant and the loss tangent of the test material are determined by processing the data array for the reflection coefficient module, having the form of a comb function of the frequency of electromagnetic waves and its analytical expression through wave scattering parameters and the complex reflection coefficient from the line section with the test sample, and the length of the line cottages selected more than half of the wavelength at the lower frequency range in which measurement is performed. 2. A device for measuring the dielectric constant of materials, containing a segment of a transmission line with the possibility of installing at its end a section of a line with a test sample and calibration measures, a measuring device, characterized in that a resistive element is connected at the input of a segment of a transmission line to it, through which connected measuring device. 3. The device according to claim 2, characterized in that when performing a segment of the transmission line in the form of a waveguide, a resistive film or a capacitive diaphragm with a resistor installed between the flanges of the coaxial waveguide transition and the waveguide is used as a resistive element. 4. The device according to claim 2, characterized in that when performing a segment of the transmission line in the form of a coaxial or strip line, a resistor is used as a resistive element, installed between the center or strip conductor and the screen, connected through a coaxial connector in the case of a coaxial line or coaxial strip transition in the case of a strip line to the measuring device. 5. The device according to claim 2, characterized in that a vector reflectometer is used as a measuring device.

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