A method for measuring the dielectric constant of an anisotropic material using an oblique incidence

Abstract

The present application relates to a kind of using the way of measuring anisotropic material dielectric constant with oblique incidence, comprising: measurement system, using measurement system to gather electromagnetic wave;The gathered electromagnetic wave is projected to the two sides of the two preset calibration pieces, and the measurement system is calibrated;According to the calibrated measurement system, the scattering matrix of the sample plate to be measured in different principal axis direction and the electric field direction parallel is respectively obtained, and the relative dielectric constant corresponding to each different principal axis direction of the sample plate to be measured is obtained according to the scattering matrix of the sample plate to be measured in different principal axis direction.The present application reduces the influence of the boundary of calibration piece on the measurement result of measurement system, guarantees the accuracy of the calibration of measurement system, and further improves the detection precision of dielectric constant.

Description

Technical Field

[0001] This invention relates to the field of microwave measurement technology, and more specifically to a method for measuring the dielectric constant of anisotropic materials using oblique incidence. Background Technology

[0002] Anisotropic materials are widely used in fields such as electromagnetic stealth and materials science. As electromagnetic materials, the relative permittivity of anisotropic materials is their most important electromagnetic parameter. Since the relative permittivity of anisotropic materials varies in different principal axis directions, measuring the permittivity of anisotropic materials is a challenge.

[0003] Traditional methods for measuring the dielectric constant of anisotropic materials include the resonant cavity method, microstrip line method, stripline method, and free space method. However, the resonant cavity method can only measure the dielectric constant at the resonant frequency. Traditional microstrip line methods for measuring anisotropic materials suffer from drawbacks. During measurement, the material under test is placed only below the conductor of the microstrip line, and due to the characteristics of the microstrip line itself, quasi-TEM modes are transmitted in the measured region, not TEM modes. This makes it impossible to ensure that the polarization direction of the electromagnetic field is consistent with the principal axis direction of the anisotropic material throughout the entire measurement band, thus hindering accurate measurement of anisotropic materials using microstrip lines. The stripline method requires four samples to measure the relative dielectric constant along the three principal axes of the anisotropic material, which undoubtedly increases measurement costs and inconvenience for samples that are difficult to manufacture.

[0004] Traditional free-space methods use time-domain gate technology and TRL calibration as calibration methods to calibrate the system. However, time-domain gate calibration has a large calibration error because time-domain gates cannot completely separate useful signals from interference signals. TRL calibration requires changing the distance between the receiving and transmitting antennas. At higher frequencies, the distance error caused by the movement will have a significant impact on the results. Therefore, all existing calibration techniques have errors, which greatly affect the accuracy of the final measured dielectric constant.

[0005] Therefore, there is a need to provide a method for measuring the dielectric constant of anisotropic materials using oblique incidence to solve the above problems. Summary of the Invention

[0006] This invention provides a method for measuring the dielectric constant of anisotropic materials using oblique incidence, thereby solving the problem that existing calibration techniques contain errors that greatly affect the accuracy of the final measured dielectric constant.

[0007] The present invention provides a method for measuring the dielectric constant of anisotropic materials using oblique incidence, which employs the following technical solution: including:

[0008] Electromagnetic waves are focused using a measurement system;

[0009] The focused electromagnetic waves are projected onto the two surfaces of two preset calibration components, and the measurement system is calibrated using T4R calibration technology.

[0010] Based on the calibrated measurement system, the scattering matrix of the sample plate under test is obtained when the principal axis direction is parallel to the electric field direction. Based on the scattering matrix of the sample plate under test when the principal axis direction is parallel to the electric field direction, the relative permittivity of the sample plate under test in each different principal axis direction is obtained.

[0011] The measurement system includes: a base;

[0012] The clamping assembly is rotatably mounted on the base around a horizontal axis and is used to clamp the sample plate to be tested in a vertical plane.

[0013] Two horn antennas are symmetrically arranged on the base about the clamping assembly;

[0014] The vector network analyzer has one port connected to one of the horn antennas and another port connected to another horn antenna.

[0015] And a convex lens antenna, one of which is provided between each horn antenna and the clamping assembly, and the two convex lens antennas are symmetrically arranged on the base about the clamping assembly.

[0016] Preferably, the horn openings of the two horn antennas correspond to each other, and the short side of the horn antenna is parallel to the horizontal plane.

[0017] Preferably, the clamping assembly includes a support plate, which is rotatably connected to the base via a support rod. A pressure plate is detachably connected to one side of the support plate. Both the pressure plate and the support plate have circular through holes to facilitate the passage of electromagnetic waves. The center of the circular through hole corresponds to the center of the two horn antennas and the convex lens antenna.

[0018] Preferably, the clamping assembly is located at the waist of the electromagnetic waves projected by the two convex lens antennas.

[0019] Preferably, the steps for calibrating the measurement system include:

[0020] Using a measurement system, the scattering matrix of the reflection standard corresponding to both sides of the calibration piece is measured, and used to obtain the scattering matrix of the through standard;

[0021] Obtain the length of the electromagnetic wave from the incident surface to the preset measurement reference surface under each reflection standard. Based on the scattering matrix and length corresponding to each reflection standard, obtain the propagation constant when each port of the vector network analyzer is used as the transmitting end of the electromagnetic wave.

[0022] Based on the scattering matrix of the direct standard, each propagation constant, and the scattering matrix corresponding to each reflection standard, the error matrix of the measurement system between the transmitter and the preset measurement reference surface is obtained when the vector network analyzer is used as the transmitter of the electromagnetic wave.

[0023] Preferably, the steps for obtaining the scattering matrix of the sample plate under test when the principal axis directions are parallel to the electric field direction include:

[0024] The sample plate to be tested is clamped on the clamping assembly of the calibrated measurement system in different principal axis directions, and the transfer matrix corresponding to the sample plate to be tested when the principal axis direction is parallel to the electric field direction is obtained.

[0025] Based on the transmission matrix of the sample plate under test when it is parallel to the electric field direction in different principal axis directions, and the error matrix of the measurement system, the scattering matrix of the sample plate under test when it is parallel to the electric field direction in each different principal axis direction is obtained.

[0026] Preferably, obtaining the relative permittivity of the sample plate under test in each different principal axis direction includes:

[0027] The main axis direction includes the width, height, and thickness directions of the sample plate under test.

[0028] When the width direction of the sample plate under test is parallel to the electric field of the electromagnetic wave, the relative permittivity of the sample plate under test in the width direction is obtained.

[0029] When the height direction of the sample plate under test is parallel to the electric field of the electromagnetic wave, the relative permittivity of the sample plate under test in the height direction is obtained.

[0030] And when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute, the relative permittivity in the thickness direction of the sample plate is obtained.

[0031] Preferably, the step of obtaining the relative permittivity in the width direction of the sample plate to be tested includes:

[0032]

[0033]

[0034]

[0035] In the formula, ε rξ Represents the relative permittivity in the width direction of the sample plate under test;

[0036] S 21ξ This represents the parameter in the second row and first column of the scattering matrix when the sample plate under test is parallel to the electric field of the electromagnetic wave in the width direction;

[0037] ξ represents the width of the sample plate to be tested;

[0038] k0 represents the propagation constant in free space;

[0039] γ ξ This represents the propagation constant when the sample plate under test is parallel to the electric field of the electromagnetic wave in the width direction;

[0040] j represents a complex number;

[0041] d represents the thickness of the sample plate to be tested;

[0042] R ξ It represents the reflection coefficient of the sample plate under test when its width direction is parallel to the electric field of the electromagnetic wave.

[0043] Preferably, the steps for obtaining the dielectric constant of the height direction of the sample plate under test include:

[0044]

[0045]

[0046]

[0047] In the formula, ε rη The relative permittivity in the height direction of the sample plate under test;

[0048] S 21η This represents the parameter in the second row and first column of the scattering matrix when the sample plate under test is parallel to the electric field of the electromagnetic wave in the height direction;

[0049] η represents the height of the sample plate under test;

[0050] k0 represents the propagation constant in free space;

[0051] γ η This represents the propagation constant when the sample plate under test is parallel to the electric field of the electromagnetic wave in the height direction;

[0052] j represents a complex number;

[0053] d represents the thickness of the sample plate to be tested;

[0054] R η It represents the reflection coefficient of the sample plate under test when the height direction is parallel to the electric field of the electromagnetic wave.

[0055] Preferably, the step of obtaining the relative permittivity in the thickness direction of the sample plate to be tested includes:

[0056]

[0057]

[0058]

[0059] In the formula, ε rζ Represents the relative permittivity in the thickness direction of the sample plate under test;

[0060] S 21ζ This represents the parameter in the second row and first column of the scattering matrix when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute.

[0061] ζ represents the thickness direction of the sample plate to be tested;

[0062] k0 represents the propagation constant in free space;

[0063] γ ζ This represents the propagation constant when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute.

[0064] j represents a complex number;

[0065] d represents the thickness of the sample plate to be tested;

[0066] R ζ It represents the reflection coefficient of the sample plate under test when the angle between the normal direction and the incident direction of the electromagnetic wave is acute.

[0067] θ i This represents the angle between the direction of electromagnetic wave propagation and the normal direction of the sample plate under test.

[0068] θ t It represents the angle of refraction of the electromagnetic wave in the sample plate under test, indicating the direction of electromagnetic wave propagation.

[0069] The beneficial effects of this invention are:

[0070] 1. Two calibration pieces are used to calibrate the measurement system. During the calibration process, the electromagnetic waves are focused to ensure that the electromagnetic waves are projected in the middle of the calibration pieces, thereby reducing the influence of the boundary of the calibration pieces on the measurement results of the measurement system, thus ensuring the accuracy of the measurement system calibration, and thus ensuring the accuracy of the dielectric constant obtained subsequently.

[0071] 2. Because the traditional free-space method uses the parameter (S) in the first row and first column of the scattering matrix when solving for the dielectric constant. 11 When the sample undergoes slight rotation and translation, the effect on S... 11 It will have a significant impact because S 11 The path length depends on the sample's position relative to the reference plane; if the sample rotates slightly, the incident angle will be... At that time, the angle of the reflected signal is Therefore, the calculated dielectric constant will be inaccurate. However, in this invention, the parameter (S) in the second row and first column of the scattering matrix is ​​used. 21 To solve for the permittivity, because S 21 The path length depends only on the positions of the two ports of the vector network analyzer. Since the distance between the two ports of the measurement system of this invention is fixed, and the propagation directions of the incident signal before the sample plate and the transmitted signal after the electromagnetic wave passes through the sample plate are parallel, the slight rotation and translation of the sample plate will affect the path length of the sample. 21 The resulting error is negligible; therefore, the dielectric constant calculated using the parameters in the second row and first column of the scattering matrix is ​​more accurate.

[0072] 3. Based on the measurement system of the present invention, the width, height and thickness of the sample plate are adjusted in the measurement system. Then, the relative permittivity of the sample plate in the width and height directions can be measured by perpendicular incidence, and the relative permittivity of the sample plate in the thickness direction can be measured by oblique incidence, thereby realizing the measurement of the permittivity. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 This is a schematic diagram of the overall structure of an embodiment of a method for measuring the dielectric constant of anisotropic materials using oblique incidence according to the present invention;

[0075] Figure 2 This is a schematic diagram of the measurement system in an embodiment of a method for measuring the dielectric constant of anisotropic materials using oblique incidence according to the present invention;

[0076] Figure 3 This is a schematic diagram of the clamping component in the measurement system of the present invention;

[0077] Figure 4 This is a diagram showing the clamping state of the measurement system of the present invention when two standard parts are used as four reflection standards during the calibration process;

[0078] Figure 5 This is a state diagram of the electromagnetic wave of the measurement system of the present invention under oblique incidence.

[0079] In the figure: 1. Base; 2. Second horn antenna; 3. Convex lens antenna; 4. Clamping assembly; 5. Sample plate to be tested; 6. First horn antenna; 41. Support plate; 42. Pressure plate. Detailed Implementation

[0080] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] An embodiment of the present invention provides a method for measuring the dielectric constant of anisotropic materials using oblique incidence, such as... Figure 1 As shown, it includes:

[0082] S1. Focusing electromagnetic waves;

[0083] Specifically, a measurement system is used to focus electromagnetic waves.

[0084] In this embodiment, the measurement system, such as Figure 2 As shown, the specific components include: a base 1, a clamping assembly 4, a first horn antenna 6 and a second horn antenna 2 for electromagnetic waves, and a convex lens antenna 3. The clamping assembly 4 is rotatably mounted on the base 1 in the horizontal direction and is used to clamp the sample plate 5 to be tested in the vertical plane. The first horn antenna 6 and the second horn antenna 2 are symmetrically arranged on the base 1 about the clamping assembly 4, and both the first horn antenna 6 and the second horn antenna 2 for electromagnetic waves are connected to the ports of a vector network analyzer. One port of the vector network analyzer is connected to the first horn antenna 6 for electromagnetic waves, and the other port of the vector network analyzer is connected to the second horn antenna 2. A convex lens antenna 3 is provided between the first horn antenna 6 and the clamping assembly 4, and between the second horn antenna 2 and the clamping assembly 4. The two convex lens antennas 3 are symmetrically arranged on the base 1 about the clamping assembly 4. In this embodiment, the horn openings of the two horn antennas correspond, and the short side of the horn antenna is parallel to the horizontal plane (at this time, the electric field is in the horizontal direction). The convex lens antenna 3 realizes the focusing of electromagnetic waves.

[0085] Among them, such as Figure 3 As shown, the specific clamping component 4 includes a support plate 41, which is rotatably connected to the base 1 via a support rod. A pressure plate 42 is detachably connected to one side of the support plate 41. Both the pressure plate 42 and the support plate 41 have circular through holes to facilitate the passage of electromagnetic waves. In this embodiment, the diameter of the circular through hole is 20cm, and the center of the circular through hole corresponds to the center of the first horn antenna 6, the second horn antenna 2, and the convex lens antenna 3.

[0086] In order to ensure that the electromagnetic wave incident on the sample plate 5 is a plane wave, the clamping assembly in this embodiment is located at the waist position of the electromagnetic wave projected by the two convex lens antennas.

[0087] S2. Calibrate the measurement system;

[0088] Specifically, two preset calibration pieces are placed on the clamp assembly at the waist of the electromagnetic wave beam. The electromagnetic wave is then focused by a convex lens antenna and projected onto one side of the preset calibration piece. Rotating the support rod, i.e., rotating it 180 degrees, allows the standard piece to be rotated from one side to the other. Figure 4 The four reflection standards are shown in the schematic diagram. Figure 4 (d) is Figure 4 The calibration piece shown in (a) was obtained after rotating 180°, similarly. Figure 4 (c) is Figure 4 (b) shows the calibration piece after rotating 180°, and the measurement system is calibrated using T4R calibration technology. The specific calibration steps are as follows: using the measurement system, measure the scattering matrix of the reflection standard corresponding to the two sides of the calibration piece, and obtain the scattering matrix of the through standard; obtain the length of the electromagnetic wave from the incident surface to the preset measurement reference surface under each reflection standard; based on the scattering matrix and length corresponding to each reflection standard, obtain the propagation constant corresponding to each port of the vector network analyzer as the transmitting end of the electromagnetic wave; based on the scattering matrix of the through standard, each propagation constant, and the scattering matrix corresponding to each reflection standard, obtain the error matrix of the measurement system corresponding to the transmitting end of the vector network analyzer and the preset measurement reference surface when the transmitting end of the electromagnetic wave is used as the transmitting end. The structure of the standard piece is as follows: Figure 4 (a) and Figure 4 As shown in (b), one of them is a planar rectangular plate, and the other standard part is a circular plate that matches the circular through hole on the support plate 41. One side of the circular plate is provided with an annular clamping table, which is used to clamp the standard part between the pressure plate 42 and the support plate 41.

[0089] Step 21, measuring the scattering matrix of the two reflection standards corresponding to the two sides of the two calibration pieces, includes: sequentially installing the two calibration pieces between the pressure plate 42 and the support plate 41 of the measurement system to clamp the standard pieces; and using a vector network analyzer to measure the scattering matrix (i.e., S-parameters) of the four reflection standards, such as... Figure 4 (a) shows a calibration piece corresponding to a reflection standard, obtained by rotating the support plate 41 180° about the axis. Figure 4(d) Corresponding to another reflection standard, the two standard parts yield a total of four reflection standards. Then, the scattering matrix corresponding to each reflection standard is measured using a vector network analyzer. When no part is clamped between the pressure plate 42 and the support plate 41, the scattering coefficient of the through standard is measured by the vector network analyzer. The scattering matrix of the through standard is denoted as... It should be noted that in this embodiment, when measuring the scattering matrix using a vector network analyzer, the anisotropic material is placed at the waist of the beams of the two convex lens antennas. At this time, the electromagnetic waves incident on the anisotropic material region can be considered as plane waves.

[0090] Step 22 involves obtaining the propagation constants corresponding to each port of the vector network analyzer as the transmitting end of the electromagnetic wave.

[0091] Specifically, the length of the electromagnetic wave from the incident surface to the preset measurement reference surface is obtained under each reflection standard. Based on the scattering matrix and length corresponding to each reflection standard, the propagation constant corresponding to each port of the vector network analyzer as the transmitting end of the electromagnetic wave is obtained, that is, the propagation constants when port A and port B are respectively the transmitting ends are obtained.

[0092] Step 221, obtaining the length of the electromagnetic wave from the incident surface to the preset measurement reference surface under each reflection standard, includes: designating the ports of the vector network analyzer as port A and port B, and obtaining the length of the distance from the surface of the nearest standard component at ports A and B to the measurement reference surface (in this embodiment, the measurement reference surface is the position of the vertical center plane of the support plate 41) under each reflection standard. Figure 4 As shown, assuming the left side of the bracket is port A, and port A is the electromagnetic wave emission port, then for port A... Figure 4 The four reflection standards (a)-(d) shown have lengths of -10.33 mm, -5.22 mm, -0.11 mm, and 5 mm for the measurement reference surface, respectively. Assuming port B is the electromagnetic wave emission port, then for port B... Figure 4 The four reflection standards (a)-(d) shown have lengths of 5 mm, -0.11 mm, -5.22 mm, and -10.33 mm for the measurement reference surface, respectively. The distance between the positions of two adjacent reflection standards is 0.175λ, where λ is the wavelength corresponding to the center frequency, and the measurement frequency band is 8.5-12.4 GHz.

[0093] Specifically, in this embodiment, when port A is the electromagnetic wave emission port, the distance from the electromagnetic wave incident surface on the calibration piece (the incident surface is the surface of the calibration piece near port A) to the measurement reference surface of each reflection standard (the position of the vertical center plane of the support plate 41) is denoted as length l. AiWhen port B is the electromagnetic wave emission port, the distance from the electromagnetic wave incident surface on the calibration piece to the measurement reference surface of each reflection standard (the position of the vertical center plane of the support plate 41) is denoted as length l. Bi Let i = 0, 1, 2, 3 represent the i-th reflection standard, for example... Figure 4 (a) shows the first reflection standard with lengths l for ports A and B, respectively. A0 = -10.33mm, l B0 =5mm.

[0094] Step 222: Obtain the propagation constants corresponding to each port of the vector network analyzer as the electromagnetic wave transmitter, including:

[0095] For the four reflection standards, there exists an equation as follows (1):

[0096]

[0097] In the formula, P(γ) represents the coefficient matrix of equation (1). γ in this coefficient matrix is ​​taken as the parameter to be determined, hence it is denoted as P(γ).

[0098] x represents the column vector composed of the independent variables in equation (1);

[0099] E1′ A This represents the correction value of the first element in the error matrix when port A is used as the transmission port for electromagnetic waves.

[0100] E 2A This represents the value of the second element in the error matrix when port A is used as the transmission port for electromagnetic waves.

[0101] E3′ A This represents the correction value of the third element in the error matrix when port A is used as the transmission port for electromagnetic waves.

[0102] This represents the scattering parameter value (i.e., S) in the first row and first column of the scattering matrix measured using a vector network analyzer when measuring the i-th reflection standard. 11 ), where i takes the values ​​0, 1, 2, or 3, and E i ′ A =E iA Γ T ;Γ T E represents the reflection coefficient of the calibration piece. iA This represents the i-th element in the error matrix between port A and the measurement reference surface when port A is the emission port of the electromagnetic wave.

[0103] It should be noted that, ρ iγ represents the phase shift generated when the i-th reflected electromagnetic wave, under standard reflection, travels from the measurement reference plane to the electromagnetic wave incident surface of the calibrator (i.e., the surface of the calibrator closest to port A) and is reflected back to the measurement reference plane, with port A as the transmitting end. A It represents the propagation constant between the left surface position of the reflection standard when measuring the first reflection standard and the left surface position of the reflection standard when measuring the fourth reflection standard, as viewed from port A towards the area under test.

[0104] The process of obtaining the propagation constant when each port of the vector network analyzer is used as the emitting end of the electromagnetic wave includes: taking the values ​​of the first row and first column of the scattering matrix measured by the four reflection standards as the scattering parameter values. And the length of the electromagnetic wave incident surface from the measurement reference surface when port A is the emitting end of the electromagnetic wave under each reflection standard, substituted into (1), and the equation detP(γ) is solved using the Newton iteration method. A ) = 0, thus obtaining the propagation constant γ A Similarly, the values ​​in the second row and second column of the scattering matrix measured by the four reflection standards (S) 22 ) as the scattering parameter value And when port B is the emitting end of the electromagnetic wave under each reflection standard, the length of the electromagnetic wave incident surface from the measurement reference surface is substituted into equation (1), and the equation detP(γ) is solved using the Newton-Raphson iteration method. B ) = 0, thus obtaining the propagation constant γ B .

[0105] Step 23: Obtain the error matrix of the measurement system between the transmitting end and the preset measurement reference surface when each port of the vector network analyzer is used as the transmitting port of the electromagnetic wave;

[0106] Specifically, the propagation constant γ A And the scattering matrix of the reflection standard, substituting it into the following equation (2) to solve for E′ 1A E 2A and E′ 3A :

[0107]

[0108] In the formula, E′ 1A This represents the correction value of the first element in the error matrix when port A is used as the transmission port for electromagnetic waves.

[0109] E 2A This represents the value of the second element in the error matrix when port A is used as the transmission port for electromagnetic waves.

[0110] E′ 3A This represents the correction value of the third element in the error matrix when port A is used as the transmission port for electromagnetic waves.

[0111] Let E′ represent the scattering parameter values ​​in the first row and first column of the scattering matrix obtained when measuring the i-th reflection standard using a vector network analyzer, where i takes values ​​of 0, 1, 2, and 3, and E′ represents the scattering parameter values. iA =E ia Γ T ;Γ T E represents the reflection coefficient of the calibration piece. iA This represents the i-th element in the error matrix between port A and the measurement reference surface when port A is the emission port of the electromagnetic wave.

[0112] ρ i γ represents the phase shift generated when the i-th reflected electromagnetic wave, under standard reflection, travels from the measurement reference plane to the electromagnetic wave incident surface of the calibrator (i.e., the surface of the calibrator closest to port A) and is reflected back to the measurement reference plane, with port A as the transmitting end. A This represents the propagation constant between the left surface position of the reflection standard when measuring the first reflection standard and the left surface position of the reflection standard when measuring the fourth reflection standard, as viewed from port A towards the area under test; Ai When port A is the emission port of electromagnetic waves, the distance between the electromagnetic wave incident surface (the incident surface is the surface of the calibrator near port A) and the measurement reference surface of the i-th reflection standard (the position of the vertical center plane of the support plate 41) is indicated.

[0113] Similarly, using equation (1) in step S2 and equation (2) in step S3, we can find E′. 1B E 2B and E′ 3B , where, at this time This represents the value (S) in the second row and second column of the scattering matrix measured using a vector network analyzer when measuring the i-th reflection standard. 22 ), E′ 1B This represents the correction value of the first element in the error matrix between port B and the measurement reference surface when port B is the emission port of the electromagnetic wave; E 2B E′ represents the value of the second element in the error matrix between port B and the measurement reference surface when port B is the emission port of the electromagnetic wave. 3B This represents the correction value of the third element in the error matrix between port B and the measurement reference surface when port B is the emission port of the electromagnetic wave.

[0114] The formula for calculating the reflection coefficient of the calibration piece is Equation (3):

[0115]

[0116] In the formula, Γ TThe reflection coefficient of the calibrated component is represented by Γ for the four reflection standards. T The same, because the four reflection standards are made of the same material, generally the obtained Γ T It is a complex number, i.e., Γ T = in the form of a + jb, where a represents Γ T The real part, b, represents Γ. T The imaginary part of Γ, the criterion for choosing the sign of equation (3) is to make Γ T The real part 'a' is negative.

[0117] E′ 1A This represents the correction value of the first element in the error matrix between port A and the measurement reference surface when port A is used as the transmission port of the electromagnetic wave.

[0118] E 2A This represents the value of the second element in the error matrix between port A and the measurement reference surface when port A is the emission port of the electromagnetic wave.

[0119] E′ 3A This represents the correction value of the third element in the error matrix between port A and the measurement reference surface when port A is the emission port of the electromagnetic wave.

[0120] E′ 1B This represents the correction value of the first element in the error matrix between port B and the measurement reference surface when port B is the emission port of the electromagnetic wave.

[0121] E 2B This represents the value of the second element in the error matrix between port B and the measurement reference surface when port B is the emission port of the electromagnetic wave.

[0122] E′ 3B This represents the correction value of the third element in the error matrix between port B and the measurement reference surface when port B is the emission port of the electromagnetic wave.

[0123] This represents the scattering matrix of the through-standard.

[0124] Specifically, based on the scattering matrix of the direct standard, each propagation constant, and the scattering matrix corresponding to each reflection standard, the error matrix of the measurement system corresponding to each port of the vector network analyzer as the electromagnetic wave transmission port is obtained, that is, combined with E′ i =E i Γ T E′ 1A E 2A and E′ 3A and E′ 1B E 2B and E′ 3B You can then obtain:

[0125] When port A is used as the electromagnetic wave emission port, the error matrix E between port A and the measurement reference surface is... A for:

[0126]

[0127] When port B is used as the electromagnetic wave emission port, the error matrix E between port B and the measurement reference plane is... B for:

[0128]

[0129] In the formula, E A The error matrix represents the measurement error between the electromagnetic wave transmission port and the measurement reference surface when port A is the transmission port of the electromagnetic wave. This error matrix represents the effect of the horn antenna, convex lens antenna and free space in the region on the propagation of electromagnetic waves in the region from port A of the vector network analyzer to the measurement reference surface.

[0130] E B The error matrix represents the measurement error between the electromagnetic wave transmission port and the measurement reference surface when port B is the transmission port of the electromagnetic wave. This error matrix represents the effect of the horn antenna, lens antenna and free space in the region on the propagation of electromagnetic waves in the region from port B of the vector network analyzer to the measurement reference surface.

[0131]

[0132] E t Indicates E A and E B The normalized matrix of the two error matrices, i.e., for E A and E B The parameters in the second row and second column of the two error matrices are normalized;

[0133] This represents the parameter in the first row and second column of the scattering matrix corresponding to the through standard;

[0134] This represents the parameter in the second row and first column of the scattering matrix corresponding to the direct standard.

[0135] det calculates the determinant of a matrix;

[0136] It should be noted that E here t The method for selecting the sign is to set E to the left or right sign. A and E B and Et substitution Two transmission matrices Tt are obtained, and the two Tt are respectively compared with the measured values ​​of the transmission matrix of the pass-through standard. After subtraction, the second norm of the matrix obtained by subtraction is calculated. The sign of the result with the smaller second norm is determined as the final sign in equation (6). Furthermore, equations (1) to (6) in this embodiment are all formulas in T4R technology, i.e., existing technical formulas, and will not be elaborated further in this embodiment.

[0137] At this point, the calibration of the measurement system is complete (i.e., the error matrices between the two ports and the measurement reference surface are calculated, and the scattering matrix of the sample area can be calculated from the scattering matrix measured at the two ports of the vector network analyzer when measuring the sample in subsequent steps).

[0138] S3. Obtain the relative permittivity of the sample plate under test in each principal axis direction;

[0139] Specifically, based on the calibrated measurement system, the scattering matrix of the sample plate under test is obtained when two of the three principal axis directions are parallel to the electric field direction, and the scattering matrix of the remaining principal axis direction is at an angle to the electric field direction. Based on the scattering matrix of the sample plate under test in different placement directions, the relative permittivity of the sample plate under test in each different principal axis direction is obtained.

[0140] Assume the width, height, and thickness of the sample plate to be tested correspond to the three principal axes ξ, η, and ζ, respectively, and their dielectric constants correspond to ε. rξ ,ε rη and ε rζ The thickness of the sample plate under test is d. When measuring the sample plate, the sample plate is first placed with the ξ and η directions parallel to the short side of the horn antenna (parallel to the short side, i.e., parallel to the electric field direction) using a perpendicular incidence method. The scattering matrix of the sample plate in the ξ and η directions is then measured. That is, the sample plate is clamped on the clamping assembly of the calibrated measurement system with different principal axis directions, and the transmission matrix corresponding to the sample plate when the principal axis direction is parallel to the electric field direction is obtained. Based on the transmission matrix corresponding to the sample plate when the principal axis direction is parallel to the electric field direction, and the error matrix of the measurement system, the scattering matrix of the sample area corresponding to the sample plate when the principal axis direction is parallel to the electric field direction is obtained.

[0141] That is, according to equation (7), the measured value of the transmission matrix between the two ports of the vector network analyzer when the sample plate to be tested is placed is obtained.

[0142]

[0143] In the formula, S 21This represents the parameter in the second row and first column of the scattering matrix between the two ports when the sample plate is placed, as measured by a vector network analyzer.

[0144] S 11 This represents the parameter in the first row and first column of the scattering matrix between the two ports when the sample plate is placed, as measured by a vector network analyzer.

[0145] S 22 This represents the parameter in the second row and second column of the scattering matrix between the two ports when the sample plate is placed, as measured by a vector network analyzer.

[0146] detS represents the determinant of the scattering matrix of the sample plate between the two ports when the sample plate is placed, as measured by a vector network analyzer.

[0147] The transfer matrix T between the two surfaces of the sample under test is obtained according to equation (8):

[0148]

[0149] In the formula, E A The error matrix represents the measurement error between the electromagnetic wave transmission port and the measurement reference surface when port A is the transmission port of the electromagnetic wave. This error matrix represents the effect of the horn antenna, convex lens antenna and free space in the region on the propagation of electromagnetic waves in the region from port A of the vector network analyzer to the measurement reference surface.

[0150] E B The error matrix represents the measurement error between the electromagnetic wave transmission port and the measurement reference surface when port B is the transmission port of the electromagnetic wave. This error matrix represents the effect of the horn antenna, lens antenna and free space in the region on the propagation of electromagnetic waves in the region from port B of the vector network analyzer to the measurement reference surface.

[0151] E t Indicates E A and E B The normalized matrix of the two error matrices;

[0152] Equation (9) is derived from the relationship between the scattering matrix and the transmission matrix. Based on Equation (9), the scattering matrix between the two surfaces of the sample plate under test (i.e., the sample region) measured by the vector network analyzer is obtained:

[0153]

[0154] In the formula, T 11 This represents the parameter value in the first row and first column of the transmission matrix T;

[0155] T 12 This represents the parameter value in the first row and second column of the transmission matrix T;

[0156] T 21 This represents the parameter value in the second row and first column of the transmission matrix T;

[0157] T 22 This represents the parameter value in the second row and second column of the transmission matrix T;

[0158] This completes the measurement of the scattering matrix when the sample plate is placed parallel to the short side of the horn antenna along the ξ and η directions. The next step is as follows: Figure 5 As shown, the sample plate to be tested is placed with an acute angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave. The sample plate is clamped and then the scattering matrix of the sample plate to be tested is obtained according to equations (7) to (9) when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute.

[0159] The dielectric constant tensor of the sample plate under test is expressed as:

[0160]

[0161] In the formula, The dielectric constant tensor of the sample plate under test;

[0162] ε0 represents the dielectric constant of free space;

[0163] ε rξ This represents the relative permittivity of the sample plate under test in the width direction;

[0164] ε rη This represents the relative permittivity of the sample plate under test in the height direction;

[0165] ε rζ This represents the relative permittivity of the sample plate under test in the thickness direction;

[0166] That is, during measurement, the relative permittivity in three directions can be solved using only a square sample plate.

[0167] Specifically, the relative permittivity of the sample under test in the width direction is determined by measuring the scattering matrix of the sample under test when it is parallel to the electric field of the electromagnetic wave in the width direction. The specific steps for determining the relative permittivity of the sample under test in the width direction include:

[0168]

[0169]

[0170]

[0171] By combining the three equations, we can find the answer to the given S. 21ξ Solve for ε given k0 and d. rξ ;

[0172] In the formula, ε rξ This represents the relative permittivity of the sample plate under test in the width direction;

[0173] S 21ξ This represents the second row of the scattering matrix when the sample plate under test is parallel to the electric field of the electromagnetic wave in the width direction.

[0174] A column of parameters;

[0175] ξ represents the width of the sample plate to be tested;

[0176] k0 represents the propagation constant in free space;

[0177] γ ξ This represents the propagation constant when the sample plate under test is parallel to the electric field of the electromagnetic wave in the width direction;

[0178] j represents a complex number;

[0179] d represents the thickness of the sample plate to be tested;

[0180] R ξ It represents the reflection coefficient of the sample plate under test when its width direction is parallel to the electric field of the electromagnetic wave.

[0181] Specifically, the relative permittivity of the sample under test in the height direction is determined by measuring the scattering matrix of the sample under test when it is parallel to the electric field of the electromagnetic wave in the height direction. The specific steps for determining the relative permittivity of the sample under test in the height direction include:

[0182]

[0183]

[0184]

[0185] By combining the three equations, we can find the answer to the given S. 21η Solve for ε given k0 and d. rη ;

[0186] In the formula, ε rη This represents the relative permittivity of the sample plate under test in the height direction;

[0187] S 21η This represents the second row of the scattering matrix when the sample plate under test is parallel to the electric field of the electromagnetic wave in the height direction.

[0188] A column of parameters;

[0189] η represents the height of the sample plate under test;

[0190] k0 represents the propagation constant in free space;

[0191] γ η This represents the propagation constant when the sample plate under test is parallel to the electric field of the electromagnetic wave in the height direction;

[0192] j represents a complex number;

[0193] d represents the thickness of the sample plate to be tested;

[0194] R η It represents the reflection coefficient of the sample plate under test when the height direction is parallel to the electric field of the electromagnetic wave.

[0195] Specifically, the relative permittivity in the thickness direction of the sample is calculated by measuring the sample under test when the angle between the normal direction and the incident direction of the electromagnetic wave is acute, and when the width direction of the sample is parallel to the long side of the horn antenna. The specific steps for solving the relative permittivity in the thickness direction of the sample include:

[0196]

[0197]

[0198]

[0199] By combining the three equations, we can find the answer to the given S. 21ζ 、k0、θ i Solve for ε in the case of d rζ ;

[0200] In the formula, ε rζ This represents the relative permittivity of the sample plate under test in the thickness direction;

[0201] S 21ζ This represents the parameter in the second row and first column of the scattering matrix when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute.

[0202] ζ represents the thickness direction of the sample plate to be tested;

[0203] k0 represents the propagation constant in free space;

[0204] γ ζ This represents the propagation constant when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute.

[0205] j represents a complex number;

[0206] d represents the thickness of the sample plate to be tested;

[0207] R ζ It represents the reflection coefficient of the sample plate under test when the angle between the normal direction and the incident direction of the electromagnetic wave is acute.

[0208] θ i θ represents the angle between the direction of electromagnetic wave propagation and the normal direction of the sample plate under test; t It represents the angle of refraction of the electromagnetic wave in the sample plate under test, indicating the direction of electromagnetic wave propagation.

[0209] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the dielectric constant of anisotropic materials using oblique incidence, characterized in that, include: Electromagnetic waves are focused using a measurement system; The focused electromagnetic waves are projected onto the two surfaces of two preset calibration components, and the measurement system is calibrated using T4R calibration technology. Based on the calibrated measurement system, the scattering matrix of the sample plate under test is obtained when the principal axis direction is parallel to the electric field direction. Based on the scattering matrix of the sample plate under test when the principal axis direction is parallel to the electric field direction, the relative permittivity of the sample plate under test in each different principal axis direction is obtained. The measurement system includes: a base; The clamping assembly is rotatably mounted on the base around a horizontal axis and is used to clamp the sample plate to be tested in a vertical plane. Two horn antennas are symmetrically arranged on the base about the clamping assembly; The vector network analyzer has one port connected to one of the horn antennas and another port connected to another horn antenna. And a convex lens antenna, one of which is provided between each horn antenna and the clamping assembly, and the two convex lens antennas are symmetrically arranged on the base about the clamping assembly.

2. The method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 1, characterized in that, The two horn antennas have corresponding horn openings, and the short side of the horn antenna is parallel to the horizontal plane.

3. The method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 1, characterized in that, The clamping assembly includes a support plate, which is rotatably connected to the base via a support rod. A pressure plate is detachably connected to one side of the support plate. Both the pressure plate and the support plate have circular through holes to facilitate the passage of electromagnetic waves. The center of the circular through hole corresponds to the center of the two horn antennas and the convex lens antenna.

4. The method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 1, characterized in that, The clamping assembly is located at the waist of the electromagnetic waves projected by the two convex lens antennas.

5. The method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 1, characterized in that, The steps for calibrating a measurement system include: Using a measurement system, the scattering matrix of the reflection standard corresponding to both sides of the calibration piece is measured, and used to obtain the scattering matrix of the through standard; Obtain the length of the electromagnetic wave from the incident surface to the preset measurement reference surface under each reflection standard. Based on the scattering matrix and length corresponding to each reflection standard, obtain the propagation constant when each port of the vector network analyzer is used as the transmitting end of the electromagnetic wave. Based on the scattering matrix of the direct standard, each propagation constant, and the scattering matrix corresponding to each reflection standard, the error matrix of the measurement system between the transmitter and the preset measurement reference surface is obtained when the vector network analyzer is used as the transmitter of the electromagnetic wave.

6. The method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 1, characterized in that, The steps for obtaining the scattering matrix of the sample plate under test when the principal axes are parallel to the electric field direction include: The sample plate to be tested is clamped on the clamping assembly of the calibrated measurement system in different principal axis directions, and the transfer matrix corresponding to the sample plate to be tested when the principal axis direction is parallel to the electric field direction is obtained. Based on the transmission matrix of the sample plate under test when it is parallel to the electric field direction in different principal axis directions, and the error matrix of the measurement system, the scattering matrix of the sample plate under test when it is parallel to the electric field direction in each different principal axis direction is obtained.

7. The method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 1. Its features are, Obtain the relative permittivity of the sample plate under test in each different principal axis direction. include: The main axis direction includes the width, height, and thickness directions of the sample plate under test. When the width direction of the sample plate under test is parallel to the electric field of the electromagnetic wave, the relative permittivity of the sample plate under test in the width direction is obtained. When the height direction of the sample plate under test is parallel to the electric field of the electromagnetic wave, the relative permittivity of the sample plate under test in the height direction is obtained. And when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute, the relative permittivity in the thickness direction of the sample plate is obtained.

8. A method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 7, characterized in that, The steps for obtaining the relative permittivity in the width direction of the sample plate to be tested include: In the formula, ε rξ This represents the relative permittivity in the width direction of the sample plate under test. S 21ξ This represents the parameter in the second row and first column of the scattering matrix when the sample plate under test is parallel to the electric field of the electromagnetic wave in the width direction; ξ represents the width direction of the sample plate to be tested; k0 represents the propagation constant in free space; γ ξ This represents the propagation constant when the sample plate under test is parallel to the electric field of the electromagnetic wave in the width direction; j represents a complex number; d represents the thickness of the sample plate to be tested; R ξ It represents the reflection coefficient of the sample plate under test when its width direction is parallel to the electric field of the electromagnetic wave.

9. A method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 7, characterized in that, The steps for obtaining the relative permittivity of the sample plate under test in the height direction include: In the formula, This represents the relative permittivity along the height direction of the sample plate under test. This represents the parameter in the second row and first column of the scattering matrix when the sample plate under test is parallel to the electric field of the electromagnetic wave in the height direction; η represents the height direction of the sample plate to be tested; k0 represents the propagation constant in free space; γ η This represents the propagation constant when the sample plate under test is parallel to the electric field of the electromagnetic wave in the height direction; j represents a complex number; d represents the thickness of the sample plate to be tested; R η It represents the reflection coefficient of the sample plate under test when the height direction is parallel to the electric field of the electromagnetic wave.

10. A method for measuring the dielectric constant of anisotropic materials using oblique incidence as described in claim 7, characterized in that, The steps for obtaining the relative permittivity in the thickness direction of the sample plate to be tested include: In the formula, ε rζ This represents the relative permittivity of the sample plate under test in the thickness direction; S 21ζ This represents the parameter in the second row and first column of the scattering matrix when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute. ζ represents the thickness direction of the sample plate to be tested; k0 represents the propagation constant in free space; γ ζ This represents the propagation constant when the angle between the normal direction of the sample plate and the incident direction of the electromagnetic wave is acute. j represents a complex number; d represents the thickness of the sample plate to be tested; R ζ It represents the reflection coefficient of the sample plate under test when the angle between the normal direction and the incident direction of the electromagnetic wave is acute. θ i This represents the angle between the direction of electromagnetic wave propagation and the normal direction of the sample plate under test. θ t It represents the angle of refraction of the electromagnetic wave in the sample plate under test, indicating the direction of electromagnetic wave propagation.

Images