Material electromagnetic parameter real-time measurement method and system based on frequency domain and time domain analysis

Abstract

The application discloses a material electromagnetic parameter real-time measurement method and system based on frequency domain and time domain analysis. The method can be applied to the case that the length of a tested sample is uncertain due to environmental or self characteristics, or the position of the tested sample in a clamp is unknown. Within the applicable conditions, the length of the tested sample and the position of the tested sample in the clamp do not need to be measured, and problems such as the length change of a high thermal expansion coefficient material after being loaded into the clamp, or the closed nature of the clamp leading to the difficulty in accurately measuring the length of the tested sample or the position of the tested sample can be avoided.

Description

Technical Field

[0001] This application relates to a real-time measurement method for electromagnetic parameters of materials based on frequency domain and time domain analysis, and belongs to the field of electromagnetic parameter measurement. Background Technology

[0002] Material electromagnetic parameters are characteristic parameters that describe the electromagnetic properties of materials and characterize the interaction between materials and electromagnetic fields. In broadband applications, they are often characterized using complex permittivity and complex permeability. Material electromagnetic parameters play an important guiding role in the design and selection of electromagnetic shielding and absorbing materials.

[0003] Based on the input parameters that need to be measured in each method, the main methods for measuring and calculating the electromagnetic parameters of materials using coaxial lines or rectangular waveguides are as follows: 1. Given the sample length, position, and sample cavity length. When using coaxial air wires, such as N-type coaxial wires or APC-7 type coaxial wires, the material under test is fabricated into a ring-shaped specimen. The coaxial core wire passes through the ring-shaped specimen and is then placed into the coaxial outer conductor cavity. When using a rectangular waveguide, the material under test is fabricated into a specimen with a rectangular cross-section and then placed into the rectangular waveguide cavity. A vector network analyzer is used, and the test end face is calibrated to both ends of the specimen cavity. The length of the specimen, the position of the specimen within the coaxial wire or rectangular waveguide, and the length of the specimen cavity are measured. The complex permittivity and complex permeability are then calculated using the traditional NRW algorithm. This method requires the measurement of many dimensional parameters, and measurement errors will directly affect the calculation results.

[0004] 2. The sample length is known, but the sample position and sample cavity length are unknown. The testing environment and samples used in this method are the same as in Method 1. The difference lies in that this method first connects one end of the coaxial or waveguide fixture to one test port of the vector network analyzer; then, using a full two-port calibration method, both test ports of the vector network analyzer are simultaneously calibrated to the other end of the coaxial or waveguide fixture; finally, the sample is placed in the fixture for testing. The calculation results of this method are independent of the sample's position in the fixture and the fixture's length. However, this method cannot avoid the influence of changes in the sample's length after it is placed in the fixture on the calculation results.

[0005] 3. Use a sample chamber or baffle to limit the length and position of the sample. This method uses a sample cavity or baffle to constrain the dimensions of the sample within the fixture, limiting the sample length and position, and eliminates the influence of the sample cavity or baffle through calibration compensation. However, this method suppresses the natural changes in material dimensions under different temperature conditions, especially for materials with high coefficients of thermal expansion, and the test results differ from the actual usage environment of the material.

[0006] 4. Multi-state method or multi-thickness method The multi-state method measures the complex reflection coefficient under short-circuit and open-circuit conditions at the sample termination within a coaxial or waveguide fixture. Its drawback is limitation in testing high-loss materials. This is because the amplitude and phase of the measured reflected signal change very little when the termination state is changed, reducing test accuracy.

[0007] The multi-thickness method measures the complex reflection coefficient of samples with different thicknesses within a coaxial or waveguide fixture, typically using a double-thickness method. This method requires both samples to be homogeneous. However, due to differences in the material properties of different samples and the variation in the accuracy of solving electromagnetic parameters with thickness, accurate results are difficult to obtain.

[0008] In summary, after the sample is loaded into a coaxial or waveguide fixture, the length and position of the sample are difficult to measure accurately due to the fixture's enclosed nature. For solid materials with low rigidity and easy deformation, such as thermally conductive and microwave-absorbing materials, deformation can easily occur due to compression and friction during material loading, affecting the material thickness and position. When measuring the electromagnetic parameters of materials over a wide temperature range, the sample length of materials with high thermal expansion coefficients changes significantly with temperature. Existing technical solutions cannot effectively address these issues. Summary of the Invention

[0009] According to one aspect of this application, a real-time measurement method for electromagnetic parameters of materials based on frequency domain and time domain analysis is provided. This method is applicable to situations where the length of the test sample changes with environmental or inherent characteristics and is unknown, or where the position of the test sample in the fixture is unknown. Within its applicable conditions, it is not necessary to measure the length of the test sample and its position in the fixture. This avoids problems such as the length of materials with low rigidity and high thermal expansion coefficient that change after being loaded into the fixture, or the difficulty in accurately measuring the length or position of the test sample due to the sealing of the fixture.

[0010] The method for measuring electromagnetic parameters includes the following steps: S1: Configure the vector network analyzer, where the lower frequency limit is denoted as... The upper limit of frequency is The number of sampling points is ; After the vector network analyzer has warmed up and stabilized, perform SOLT two-port calibration, that is, calibrate the first port and the second port to the corresponding two surfaces to be measured; S2: Use a vector network analyzer to measure the test fixture with the test sample to obtain the two-port scattering parameters of the test fixture. , , and ; S3: For frequency domain form and Perform a linear frequency modulated z-transform to obtain its corresponding time-domain form. and ; S4: Establish a time-domain reflectometry diagram; S5: Calculation and initial value and ; The length of the test sample : In the formula, The distance between the first port and the side of the test sample closer to the first port is denoted as . The distance between the second port and the test sample from the side closer to the second port. The length of the test sample. The length of the entire test fixture; S6: For isotropic test materials, their two-port scattering parameters are symmetrical, i.e. ; The sample position is adjusted based on the principle of minimizing the phase difference of the frequency domain reflection coefficients on both sides of the test sample, and a structure is constructed accordingly. and Objective function of the sum of absolute values ​​of phase differences : In the formula, and They are determined by the following formulas respectively: In the formula, For the frequency value of the corresponding sampling frequency point, the independent variable is... The distance between the first port to be adjusted and the side of the test sample closer to the first port is the distance between them. and They are respectively and The magnitude in exponential form, The imaginary unit, At the speed of light, The relative velocity transformation coefficient; S7: Use a genetic algorithm or least squares method to find the objective function. Minimum The value is denoted as The adjustment amount of the distance between the first port and the side of the test sample closer to the first port is: Based on this, the distance between the side of the test sample closer to the second port and the second port is... After making a translation adjustment, we get: In particular, the methods in steps S6 and S7 above are not only applicable to the fine-tuning of the position after estimating the length of a test sample of unknown length, but can also play a beneficial role in correcting deviations or changes in the position of a test sample of known length.

[0011] S8: Perform uncertainty analysis using the Monte Carlo method; Since the vector network analyzer has already been SOLT two-port calibrated in step S1, the delay and impedance deviation of the calibration components are no longer considered. In this case, the uncertainty of the above calculation method mainly comes from the phase uncertainty of the open-circuit calibration components and the short-circuit calibration components. For the first port and the second port, the two-port calibration model can be simplified to remove the two-port error term, and the single-port error correction can be performed using one response measurement and three error terms.

[0012] The port reflection parameter correction value is: In the formula, These are the measured values ​​of the reflection parameters. , , For the error term, specifically: In the formula, , and These are the measured reflection parameters under single-port loaded, short-circuited, and open-circuited conditions, respectively, after SOLT calibration: Based on the phase uncertainty of the open-circuit calibrator and the phase uncertainty of the short-circuit calibrator ; The normal distributions of the phase deviations of short-circuit and open-circuit components with specified mean and standard deviation are constructed as follows: And generate P groups of random numbers that follow this normal distribution; Therefore, the reflection coefficients of the standard short-circuit calibrator and the standard open-circuit calibrator are respectively: Therefore, the port reflection parameter correction value can be derived. And perform the linear frequency modulated z-transformation as in step S3, and calculate and ; Based on the Monte Carlo method, perform the above calculations P times repeatedly. and It also follows a normal distribution, from and The statistical standard deviation of the distribution of values, i.e., the uncertainty: In the formula, and Represent the i-th calculation, respectively. and The value; S9: Based on the above results , , And scattering parameters, the electromagnetic parameters of the material under test are solved using the Nicholson-Ross-Weir method to obtain , .

[0013] Optionally, in step S1, the upper and lower limits of the frequency are selected according to the actual frequency working range of the fixture. Meanwhile, time-domain response resolution Smaller than the length of the test sample That is, it is necessary to be able to distinguish the response peaks at both ends of the test sample, i.e.: In the formula, At the speed of light, The excitation width conversion factor is related to the mode selected for time-domain transformation; The rise time is approximately half the width of the impact excitation or 10% to 90% of the rise time of the step excitation. The relative velocity transformation coefficient is: In the formula, Let be the relative permeability of the medium. The relative permittivity of the medium is given by the relative velocity change coefficient, such as approximately 0.66 for polyethylene, approximately 0.7 for polytetrafluoroethylene (PTFE), and approximately 1 for air lines.

[0014] Optionally, in step S1, simultaneously, the number of sampling points... The selection needs to make the range resolution To meet the requirements for distance accuracy measurement, including: In the formula, The lower bound of the time domain. The upper limit of the time domain, It is a measure of how accurately the peak of the response can be located in time or distance.

[0015] Optionally, in step S3, the frequency domain form and Perform a linear frequency modulated z-transform to obtain its corresponding time-domain form. and Specifically: in: For the Kaiser window function: In the formula, This represents the zeroth-order Bessel function of the first kind. It controls the roll-off amount of the window function.

[0016] Optionally, the establishment of the time-domain reflectometry diagram in step S4 specifically involves: In time to Do Divide into equal parts of the x-axis coordinates. and The moduli are the y-axis variables; Will and The x-axis coordinates corresponding to the maximum value of the modulus are denoted as follows: and .

[0017] Optionally, in step S5, the calculation and The specific formula is: , .

[0018] According to another aspect of this application, a real-time measurement system for electromagnetic parameters of materials based on frequency domain and time domain analysis is also provided, including a test fixture, a vector network analyzer, and a data processing module connected in sequence. The data processing module is used to perform the above calculations.

[0019] The beneficial effects that this application can produce include: 1) The measurement method provided in this application is applicable to situations where the length of the test sample is unknown due to environmental or self-characteristic factors, or the position of the test sample in the fixture is unknown. Within its applicable conditions, there is no need to measure the length of the test sample and its position in the fixture. This avoids problems such as the length of materials with low rigidity and easy deformation and high thermal expansion coefficient changing after being loaded into the fixture, or the difficulty in accurately measuring the length or position of the test sample due to the sealing of the fixture.

[0020] 2) The measurement method provided in this application adjusts the position of the test sample based on the principle that the phase difference of the frequency domain reflection coefficients on both sides of the test sample is the smallest. It is not only applicable to the fine-tuning of the position after estimating the length of the test sample of unknown length, but also can play a beneficial role in correcting the deviation or change in the position of the test sample of known length by direct measurement. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a test system according to one embodiment of this application; Figure 2 This is a schematic diagram illustrating the abstract principle of a test fixture in one embodiment of this application; Figure 3 This is a time-domain reflectometry diagram established in one embodiment of this application.

[0022] Explanation of reference numerals in the attached figures: D1: First port; D2: Second port; M1: Surface to be tested 1; M2: Surface to be tested, 2; M3: Surface to be tested, 3; M4: Surface to be tested, 4. Detailed Implementation

[0023] The present application is described in detail below with reference to the embodiments, but the present application is not limited to these embodiments.

[0024] According to one embodiment of this application, a coaxial transmission line testing device with a length of 80 mm is used to test the complex permittivity and complex permeability of a polytetrafluoroethylene sample with a length of approximately 49.5 mm in the following steps.

[0025] It should be noted that the method provided in this application does not require measuring the original length of the sample being tested. This is to avoid problems such as changes in length after materials with low rigidity and easy deformation are loaded into the fixture, or difficulty in accurately measuring the length of the sample being tested due to the sealing of the fixture.

[0026] Figure 2 In the test, there are media (such as air, polytetrafluoroethylene, etc.) between the four test surfaces: M1 and M2, and M3 and M4. Corresponding de-intercalation corrections are required for the media. at the same time, , , and These are the scattering parameters of the two end faces (M2 and M3) of the test sample, respectively.

[0027] S1: Configure the vector network analyzer, where the lower frequency limit is denoted as... The upper limit of frequency is The number of sampling points is ; In this embodiment, it is specifically set as follows: =300kHz, =9GHz, =8192; After the vector network analyzer has warmed up and stabilized, perform SOLT two-port calibration, i.e. calibrate the first port to the surface under test 1 and calibrate the second port to the surface under test 4. The upper and lower limits of the frequency are selected based on the actual operating frequency range of the fixture; Meanwhile, time-domain response resolution Smaller than the length of the test sample That is, it is necessary to be able to distinguish the response peaks at both ends of the test sample, i.e.: This is denoted as Equation (1); In the formula, At the speed of light, The excitation width conversion factor is related to the mode selected for time-domain transformation; The rise time is approximately half the width of the impact excitation or 10% to 90% of the rise time of the step excitation. The relative velocity transformation coefficient is: In the formula, Let be the relative permeability of the medium. The relative permittivity of the medium is given by the relative velocity change coefficient, such as approximately 0.66 for polyethylene, approximately 0.7 for polytetrafluoroethylene (PTFE), and approximately 1 for air lines. According to equation (1), in this embodiment, the setting of the upper and lower frequency limits affects the time-domain response resolution. =32mm, less than the length of the tested sample (49.5mm), where the air line Take 1, Take 1.95.

[0028] Meanwhile, the number of sampling points The selection needs to make the range resolution To meet the requirements for distance accuracy measurement, including: This is denoted as equation (2); In the formula, The lower bound of the time domain. The upper limit of the time domain, It is a measure of how accurately the peak of the response can be located in time or distance; In this embodiment, =-1ns, =1ns; Based on equation (2) range resolution =0.073mm, which meets the length accuracy measurement requirements.

[0029] S2: Use a vector network analyzer to measure the test fixture with the test sample to obtain the two-port scattering parameters of the test fixture. , , and .

[0030] Use the data processing module to perform the following data calculations: S3: For frequency domain form and Perform a linear frequency modulated z-transform to obtain its corresponding time-domain form. and Specifically: This is denoted as equation (3); This is denoted as equation (4); In equations (3) and (4): For the Kaiser window function: In the formula, This represents the zeroth-order Bessel function of the first kind. The imaginary unit, It controls the roll-off amount of the window function. In this embodiment... The value is 6.

[0031] S4: By time to Do Divide into equal parts of the x-axis coordinates. and The moduli are the y-axis variables; Will and The x-axis coordinates corresponding to the maximum value of the modulus are denoted as follows: and ; Establish a time-domain reflectometry diagram as follows Figure 3 As shown; In this embodiment =8.5460×10 -12 s, =1.9543×10 -10 s.

[0032] S5: Calculation and initial value and ; The specific formula is as follows: This is denoted as equation (5); It is denoted as equation (6). The length of the test sample : This is denoted as equation (7); In equation (7), The distance between the first port and the side of the test sample closer to the first port is denoted as . The distance between the second port and the test sample from the side closer to the second port. The length of the test sample. The length of the entire test fixture; In this embodiment, the calculation is obtained based on equations (5) and (6). and initial value =1.281mm, =29.280mm; Substituting into equation (7), the length of the measured sample is calculated. =49.439mm.

[0033] S6: In this embodiment, polytetrafluoroethylene is an isotropic material. For isotropic materials, their two-port scattering parameters are symmetrical, therefore... ; The sample position is adjusted based on the principle of minimizing the phase difference of the frequency domain reflection coefficients on both sides of the test sample, and a structure is constructed accordingly. and Objective function of the sum of absolute values ​​of phase differences : This is denoted as equation (8); In the formula, and They are determined by the following formulas respectively: This is denoted as equation (9); This is denoted as equation (10); In the formula, For the frequency value of the corresponding sampling frequency point, the independent variable is... The distance between the first port to be adjusted and the side of the test sample closer to the first port is the distance between them. and They are respectively and The magnitude in exponential form, At the speed of light, The relative velocity transformation coefficient; S7: Use a genetic algorithm or least squares method to find the objective function. Minimum The value is denoted as In this embodiment, =1.274mm; The adjustment amount of the distance between the first port and the side of the test sample closer to the first port is: This is denoted as equation (11); According to equation (11), in this embodiment, the adjustment amount is... =-0.007mm; Based on this, the distance between the side of the test sample closer to the second port and the second port is... After making a translation adjustment, we get: This is denoted as equation (12); According to equation (12), in this embodiment, =29.287mm; In particular, the methods in steps S6 and S7 above are not only applicable to the fine-tuning of the position after estimating the length of a test sample of unknown length, but can also play a beneficial role in correcting deviations or changes in the position of a test sample of known length.

[0034] S8: Perform uncertainty analysis using the Monte Carlo method; Since the vector network analyzer has already been SOLT two-port calibrated in step S1, the delay and impedance deviation of the calibration components are no longer considered. In this case, the uncertainty of the above calculation method mainly comes from the phase uncertainty of the open-circuit calibration components and the short-circuit calibration components. For the first port and the second port, the two-port calibration model can be simplified to remove the two-port error term, and the single-port error correction can be performed using one response measurement and three error terms.

[0035] The port reflection parameter correction value is: This is denoted as equation (13); In the formula, These are the measured values ​​of the reflection parameters. , , For the error term, specifically: This is denoted as equation (14); This is denoted as equation (15); This is denoted as equation (16); In the formula, , and These are the measured reflection parameters under single-port loaded, short-circuited, and open-circuited conditions, respectively, after SOLT calibration: This is denoted as equation (17); Based on the phase uncertainty of the open-circuit calibrator and the phase uncertainty of the short-circuit calibrator ; The normal distributions of the phase deviations of short-circuit and open-circuit components with specified mean and standard deviation are constructed as follows: This is denoted as equation (18); And generate P groups of random numbers that follow this normal distribution; Therefore, the reflection coefficients of the standard short-circuit calibrator and the standard open-circuit calibrator are respectively: This is denoted as equation (19); Substitute equations (17) and (19) into equations (14), (15), and (16), then into equation (13), and perform the same linear frequency modulation z-inverse transform as in equations (3) and (4) on equation (13). Then calculate according to steps S3-S7. and ; According to the Monte Carlo method, in this embodiment, Take 1°, Take 1° and repeat the above calculation for P=1000 sets. and It also follows a normal distribution, from and The statistical standard deviation of the distribution of values, i.e., the uncertainty: In the formula, and Represent the i-th calculation, respectively. and The value; The uncertainty in this embodiment is obtained. =0.067mm, =0.065mm.

[0036] S9: Based on the above results , , And scattering parameters, the electromagnetic parameters of the material under test are solved using the Nicholson-Ross-Weir method to obtain =2.1- 0.002 and =1- 0.

[0037] According to another aspect of this application, a real-time measurement system for electromagnetic parameters of materials based on frequency domain and time domain analysis is also provided, comprising a test fixture, a vector network analyzer, and a data processing module connected in sequence. The data processing module is used to perform the above calculations.

[0038] The above description is only a part of the embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and all fall within the scope of the technical solution.

Claims

1. A method for real-time measurement of material electromagnetic parameters based on frequency domain and time domain analysis, characterized in that, Includes the following steps: S1: Configure the vector network analyzer, and denote its lower frequency limit as... The upper limit of frequency is The number of sampling points is ; After the vector network analyzer has warmed up and stabilized, perform SOLT two-port calibration. S2: Use a vector network analyzer to measure the test fixture with the test sample to obtain the two-port scattering parameters of the test fixture. , , and ; S3: For frequency domain form and Perform a linear frequency modulated z-transform to obtain its corresponding time-domain form. and ; S4: Establish a time-domain reflectometry diagram; The step S4 of establishing the time-domain reflectometry map specifically involves: In time to Do Divide into equal parts of the x-axis coordinates. and The moduli are the y-axis variables; Will and The x-axis coordinates corresponding to the maximum value of the modulus are denoted as follows: and ; S5: Calculation and initial value and ; The calculation in step S5 and The specific formula is: ， ； In the formula, At the speed of light, The relative velocity transformation coefficient; The length of the test sample : In the formula, The distance between the first port and the side of the test sample closer to the first port is denoted as . The distance between the second port and the test sample from the side closer to the second port. The length of the test sample. The length of the entire test fixture; S6: For isotropic test materials, their two-port scattering parameters are symmetrical, i.e. ; The sample position is adjusted based on the principle of minimizing the phase difference of the frequency domain reflection coefficients on both sides of the test sample, and a structure is constructed accordingly. and Objective function of the sum of absolute values ​​of phase differences : In the formula, and They are determined by the following formulas respectively: In the formula, For the frequency value of the corresponding sampling frequency point, the independent variable is... The distance between the first port to be adjusted and the side of the test sample closer to the first port is the distance between them. and They are respectively and The magnitude in exponential form, The imaginary unit, At the speed of light, The relative velocity transformation coefficient; S7: Use a genetic algorithm or least squares method to find the objective function. Minimum The value is denoted as The adjustment amount of the distance between the first port and the side of the test sample closer to the first port is: Based on this, the distance between the side of the test sample closer to the second port and the second port is... After making a translation adjustment, we get: ； S8: Uncertainty analysis was performed using the Monte Carlo method, and the correction value for the port reflection parameter was: In the formula, These are the measured values ​​of the reflection parameters. , , For the error term, specifically: In the formula, , and These are the measured reflection parameters when the calibration device is loaded on a single port, short-circuited, and open-circuited. After SOLT calibration: Based on the phase uncertainty of the open-circuit calibrator and the phase uncertainty of the short-circuit calibrator ; The normal distributions of the phase deviations of short-circuit and open-circuit components with specified mean and standard deviation are constructed as follows: And generate P groups of random numbers that follow this normal distribution; Therefore, the reflection coefficients of the standard short-circuit calibrator and the standard open-circuit calibrator are respectively: Therefore, the port reflection parameter correction value can be derived. And perform the linear frequency modulated z-transformation as in step S3, and calculate and ; Based on the Monte Carlo method, perform the above calculations P times repeatedly. and It also follows a normal distribution, from and The statistical standard deviation of the distribution of values, i.e., the uncertainty: In the formula, and Representing the i-th calculation and The value; S9: Based on the above results , , And scattering parameters, the electromagnetic parameters of the material under test are solved using the Nicholson-Ross-Weir method to obtain , .

2. The real-time measurement method for material electromagnetic parameters based on frequency domain and time domain analysis according to claim 1, characterized in that, In step S1, the upper and lower limits of the frequency are selected according to the actual frequency working range of the fixture. Meanwhile, time-domain response resolution Smaller than the length of the test sample ,Right now: In the formula, At the speed of light, To calculate the conversion factor for the excitation width, The relative velocity transformation coefficient is: In the formula, The relative permeability of the medium. is the relative permittivity of the medium.

3. The real-time measurement method for material electromagnetic parameters based on frequency domain and time domain analysis according to claim 2, characterized in that, In step S1, the number of sampling points The selection needs to make the range resolution To meet the requirements for distance accuracy measurement, including: In the formula, The lower bound of the time domain. This represents the upper limit of the time domain.

4. The real-time measurement method for material electromagnetic parameters based on frequency domain and time domain analysis according to claim 3, characterized in that, In step S3, a linear frequency modulation inverse z-transform is performed, that is, the frequency domain form is transformed. and Perform a linear frequency modulated z-transform to obtain its corresponding time-domain form. and Specifically: in: For the Kaiser window function: In the formula, This represents the zeroth-order Bessel function of the first kind. It controls the roll-off amount of the window function.

5. A real-time measurement system for material electromagnetic parameters based on frequency domain and time domain analysis, characterized in that, It includes a test fixture, a vector network analyzer, and a data processing module connected in sequence; The data processing module is used to execute the measurement method according to any one of claims 1 to 4.

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