A method for testing metal surface resistivity based on quasi-optical resonant cavity

Abstract

The purpose of this invention is to provide a method for testing the surface resistivity of metals based on a quasi-optical resonant cavity, belonging to the field of electromagnetic parameter testing technology for microwave and millimeter-wave materials. This method measures the cavity quality factor of the dual-spherical cavity, the quality factor of the plano-concave cavity formed by the sample surface and the left quasi-optical cavity spherical surface, and the quality factor of the plano-concave cavity formed by the sample surface and the right quasi-optical cavity spherical surface. Based on the measurement results of these three quality factors, the mirror loss of the two spherical surfaces of the dual-spherical cavity is deducted. Using this testing method, high-precision testing of metal surface resistivity can be achieved, with improved accuracy at high frequencies. Tests were conducted on two typical metals, copper and stainless steel, at 360 GHz and 460 GHz respectively, and the measurement results show that the overall measurement error is less than 15%.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic parameter testing technology for microwave and millimeter-wave materials, specifically relating to a method for testing the resistivity of metal surfaces based on a quasi-optical resonant cavity. Background Technology

[0002] The resistivity of metallic materials is one of the important indicators for measuring electromagnetic loss, and it is of great significance for the preparation, production, and practical application of metallic materials. In the microwave frequency band, electromagnetic waves in conductors exhibit the skin effect; therefore, the microwave surface resistance of a conductor, i.e., the resistance per square meter of a conductor with a thickness equal to the skin depth, is used to measure the conductor's conductivity. The main methods for measuring microwave surface resistance include the parallel plate resonator method, the microstrip line resonator method, the high-Q cavity method, the dielectric resonator method, and the quasi-optical resonator method. Among these, the quasi-optical resonator method, due to its semi-open structure, avoids metal loss in the cavity walls, has a higher cavity quality factor, and can achieve higher testing accuracy.

[0003] In 2000, scholars such as Cui Furong and Luo Zhengxiang developed a quasi-optical cavity high-temperature superconducting surface resistance testing system operating at 94 GHz; in the same year, scholars such as Guo Gaofeng developed a quasi-optical cavity surface resistance testing system operating at 95.5 GHz. Both systems first test the quality factor Q0 of the double-spherical cavity, then load the sample to be tested to the center of the double-spherical cavity, so that the surface to be tested and one of the spherical mirrors form a plano-concave cavity, and measure its quality factor Q. L The surface resistivity of a sample is measured by measuring the change in the Q-value of the cavity after it is emptied and a metal sample is loaded. This testing method treats the two half-cavities as identical; however, due to differences in the mirror processing precision of the quasi-optical cavity, the surface roughness of the mirrors in the two half-cavities will not be exactly the same, thus affecting the accuracy of the test results. Furthermore, the cavity is affected by external factors such as oxidation and wear over time and due to environmental influences, further amplifying the error caused by the different ohmic losses of the two half-cavities. Existing technologies do not consider these systematic errors during testing, resulting in a significant impact on the final measurement results.

[0004] Based on the above analysis, how to test the microwave surface resistivity of metallic materials using a quasi-optical resonant cavity testing system, and how to ensure that the test results can overcome system measurement errors and improve measurement accuracy, has become an urgent problem to be solved. Summary of the Invention

[0005] To address the problems existing in the background technology, the purpose of this invention is to provide a method for testing the surface resistivity of metals based on a quasi-optical resonant cavity. This method measures the cavity quality factor of the dual-spherical cavity, the quality factor of the plano-concave cavity formed by the sample surface and the left quasi-optical cavity spherical surface, and the quality factor of the plano-concave cavity formed by the sample surface and the right quasi-optical cavity spherical surface. Based on the measurement results of these three quality factors, the mirror loss of the two spherical surfaces of the dual-spherical cavity is deducted, thus achieving accurate measurement of surface resistance.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A method for measuring the resistivity of a metal surface based on a quasi-optical resonant cavity includes the following steps:

[0008] Step 1. Debug the quasi-optical resonator test system, and set the frequency range and number of scan points of the vector network analyzer according to the test frequency and the test time required;

[0009] Step 2. Without placing the metal to be tested, measure the resonant frequency f0 and quality factor Q0 of the quasi-optical resonant cavity test system in the cavity state;

[0010] Step 3. Place the metal to be tested at the center of the left and right quasi-optical cavity spherical surfaces, and make the test surface of the metal to be tested face the reflecting surface of the left quasi-optical cavity spherical surface to form a plano-concave cavity. The Gaussian beam is focused at the center of the metal to be tested. Then remove the right quasi-optical cavity spherical surface and its corresponding coupling device in the quasi-optical resonator test system.

[0011] Adjust the distance between the metal surface to be tested and the spherical surface of the left collimated cavity so that the resonant frequency f0 of the plano-concave cavity is the same as the resonant frequency during the dual-spherical cavity test in step 2, and then measure the quality factor Q1 at this time.

[0012] Step 4. Restore the right quasi-optical cavity spherical surface and its corresponding coupling device in the quasi-optical resonator test system, remove the left quasi-optical cavity spherical surface and its corresponding coupling device, flip the metal under test so that the test surface of the metal under test tested in Step 3 is aligned with the reflecting surface of the right quasi-optical cavity spherical surface, adjust the distance between the center of the metal under test and the right quasi-optical cavity spherical surface so that the resonant frequency of the quasi-optical resonator test system is still f0, and measure the quality factor at this time as Q2.

[0013] Step 5. Based on the quality factors Q0, Q1, and Q2 obtained from the three measurements, calculate the microwave surface resistance of the metal material to be tested. The specific calculation method is as follows:

[0014]

[0015] Among them, Q ohm_met Q is the ohmic loss of the metal under test;ohm_0 Q ohm_1 Q ohm_2 These are the mirror losses of the dual-cavity system, the mirror loss of the left spherical surface, and the mirror loss of the right spherical surface, respectively. These three values ​​satisfy the following relationship:

[0016]

[0017] Surface resistance R s The calculation formula is:

[0018]

[0019] In the formula, f0 is the resonant frequency, μ0 is the free permeability, and H is the magnetic field vector inside the plano-concave cavity. t It is the tangential magnetic field vector on the surface of the metal to be measured, V is the volume of the plano-concave cavity containing the electromagnetic field, and S is the volume of the cavity containing the electromagnetic field. met The surface area of ​​the metal to be measured is denoted as .

[0020] Further, in step 1, the quasi-optical resonator testing system includes a left quasi-optical cavity spherical surface, a right quasi-optical cavity spherical surface, a coupling device, and a vector network analyzer. The left and right quasi-optical cavity spherical surfaces are respectively connected to the calibrated vector network analyzer through the coupling device. The left and right quasi-optical cavity spherical surfaces are adjusted so that the two reflecting surfaces of the two quasi-optical cavity spherical surfaces are horizontally aligned.

[0021] Furthermore, Q ohm_met The ohmic loss of the metal under test is calculated from the quality factor obtained by three measurements, ignoring diffraction loss and coupling loss introduced by weak coupling in the cavity.

[0022] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0023] 1. This invention utilizes the Q value obtained from three measurements to eliminate the influence of mirror loss of the quasi-optical cavity on the calculation, and avoids the influence of mirror oxidation, wear and other conditions on the test results, effectively improving the accuracy and repeatability of the surface resistance test process.

[0024] 2. The testing method of this invention enables high-precision testing of the surface resistance of metals, with improved accuracy at high frequencies. Tests were conducted on two typical metals, copper and stainless steel, at 360 GHz and 460 GHz respectively, and the results showed that the overall measurement error was less than 15%. In contrast, existing technologies exhibited errors exceeding 15% at a testing frequency of only 95.5 GHz, with the error increasing further with increasing testing frequency. Therefore, the testing method of this invention significantly improves the accuracy of test results, especially at high frequencies. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the quasi-optical resonant cavity testing system used in the metal surface resistivity testing method of the present invention.

[0026] Figure 2 This is a schematic diagram of the system after the metal to be tested and the spherical surface of the optical cavity on the left side form a plano-concave cavity according to the present invention.

[0027] Figure 3 This is a schematic diagram of the system after the metal to be tested and the spherical surface of the optical cavity on the right side form a plano-concave cavity according to the present invention.

[0028] Figure reference numerals: 1 is the vector network analyzer, 2a is the coupling device connected to the left optical cavity spherical surface, 2b is the coupling device connected to the right optical cavity spherical surface, 3 is the left optical cavity spherical surface, 4 is the right optical cavity spherical surface, 5 is the metal to be tested, and 6 is the host computer. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0030] A method for measuring the resistivity of a metal surface based on a quasi-optical resonant cavity includes the following steps:

[0031] Step 1. Debugging the quasi-optical resonator test system: The structural schematic diagram of the quasi-optical resonator test system is shown below. Figure 1 As shown, the system includes a left quasi-optical cavity spherical surface 3, a right quasi-optical cavity spherical surface 4, a coupling device, and a vector network analyzer 1. The left quasi-optical cavity spherical surface 3 and the right quasi-optical cavity spherical surface 4 are adjusted so that the two reflecting surfaces of the two quasi-optical cavity spherical surfaces are horizontally aligned. The left quasi-optical cavity spherical surface 3 is connected to the first port of the vector network analyzer 1 through the coupling device 2a, and the right quasi-optical cavity spherical surface 4 is connected to the second port of the vector network analyzer 1 through the coupling device 2b. The host computer 6 is connected to the vector network analyzer and is used to control the vector network analyzer to perform tests.

[0032] Calibrate the vector network analyzer by setting its frequency range and number of frequency points according to actual testing requirements.

[0033] Step 2. Without placing the metal to be tested, measure the resonant frequency f0 and quality factor Q0 of the quasi-optical resonant cavity test system in the cavity state;

[0034] Step 3. Place the metal to be tested at the center of the left and right quasi-optical cavity spherical surfaces, ensuring the test surface of the metal is directly opposite the reflecting surface of the left quasi-optical cavity spherical surface, and the center of the metal to be tested is at the same position as the converging center of the left quasi-optical cavity spherical surface. Then, remove the right quasi-optical cavity spherical surface and its corresponding coupling device from the quasi-optical resonator test system. The resulting structural schematic diagram is shown below. Figure 2As shown;

[0035] Then adjust the distance between the center of the metal under test and the spherical surface of the left quasi-optical cavity so that the resonant frequency of the quasi-optical resonant cavity test system is still f0, and measure the quality factor Q1 at this time.

[0036] Step 4. Restore the right quasi-optical cavity spherical surface and its corresponding coupling device in the quasi-optical resonator testing system, remove the left quasi-optical cavity spherical surface and its corresponding coupling device, and rotate the metal under test so that the test surface of the metal under test is directly aligned with the reflecting surface of the right quasi-optical cavity spherical surface. The resulting structural schematic diagram is shown below. Figure 3 As shown;

[0037] Then adjust the distance between the center of the metal under test and the spherical surface of the right quasi-optical cavity so that the resonant frequency of the quasi-optical resonant cavity test system is still f0, and measure the quality factor Q2 at this time.

[0038] Step 5. Ignoring coupling loss and diffraction loss, calculate the microwave surface resistance of the concave metal material based on the quality factors Q0, Q1, and Q2 obtained from the three measurements. The specific calculation method is as follows:

[0039]

[0040] Among them, Q ohm_0 Q ohm_1 Q ohm_2 These are the mirror losses of the dual-cavity system, the mirror loss of the left spherical surface, and the mirror loss of the right spherical surface, respectively. Q ohm_met It is the ohmic loss of the metal under test;

[0041] Surface resistance R s The calculation formula is as follows:

[0042]

[0043] In the formula, f0 is the resonant frequency, μ0 is the free permeability, and H is the magnetic field vector inside the plano-concave cavity. t It is the tangential magnetic field vector on the surface of the metal to be measured. The volume integral region V is the cavity space volume containing the electromagnetic field in the plano-concave cavity, and the surface integral region S is... met The surface area of ​​the metal to be measured is denoted as .

[0044] Example 1

[0045] The test method of this invention was used to test a uniform copper surface with a surface finish of Ra = 0.2 μm at 460 GHz, and the surface resistance of the copper was measured to be 344 mΩ.

[0046] The theoretical value was calculated using a roughness gradient model at the same frequency, and the theoretical calculation result was 367mΩ.

[0047] In this embodiment, the error between the tested value and the theoretical value is 6.3%.

[0048] Example 2

[0049] The test method of this invention was used to test a uniform stainless steel surface with a surface finish Ra = 0.2 μm at 360 GHz, and the surface resistance of the copper was measured to be 1281 mΩ.

[0050] The theoretical value was calculated using the roughness gradient model at the same frequency, and the theoretical calculation result was 1116 mΩ.

[0051] In this embodiment, the error between the tested value and the theoretical value is 14.7%.

[0052] Comparative Example 1

[0053] The tests were conducted using an existing quasi-optical resonant cavity test system with dual spherical cavities. Three typical metallic materials, namely hard aluminum, brass, and iron, were measured at 10 GHz. At the same time, theoretical values ​​were calculated at the same frequency using a roughness gradient model.

[0054] The measured values ​​for duralumin and theoretical values ​​were 43.23 mΩ and 33.4 mΩ, respectively, with an error of 29.45%; for brass, the measured values ​​were 63.43 mΩ and 52 mΩ, respectively, with an error of 21.98%; and for iron, the measured values ​​were 72.81 mΩ and 62.83 mΩ, respectively, with an error of 15.88%.

[0055] Comparative Example 1

[0056] The tests were conducted using an existing quasi-optical resonant cavity test system with dual spherical cavities. Three typical metallic materials, namely hard aluminum, brass, and iron, were measured at 95.5 GHz. At the same time, theoretical values ​​were calculated at the same frequency using a roughness gradient model.

[0057] The measured values ​​for duralumin and theoretical values ​​were 133.61 mΩ and 100 mΩ, respectively, with an error of 33.61%; for brass, the measured values ​​were 196.01 mΩ and 160.7 mΩ, respectively, with an error of 21.97%; and for iron, the measured values ​​were 224.99 mΩ and 191.3 mΩ, respectively, with an error of 17.61%.

[0058] The results of Examples 1, 1, and 2 show that, even at frequencies below 100 GHz, the measured surface resistance of existing methods deviates from the theoretically calculated value by more than 15%, and the measurement error increases significantly with increasing test frequency. Therefore, the test method of this invention can achieve high-precision testing of metal surface resistance, especially at high frequencies, where the effect is even more significant.

[0059] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A method for measuring the resistivity of a metal surface based on a quasi-optical resonant cavity, characterized in that, Includes the following steps: Step 1. Debug the quasi-optical resonator test system, and set the frequency range and number of scan points of the vector network analyzer according to the test frequency and the test time required; Step 2. Without placing the metal to be tested, measure the resonant frequency of the quasi-optical resonant cavity test system in the cavity state. and quality factor ; Step 3. Place the metal to be tested at the center of the left and right quasi-optical cavity spherical surfaces, and make the test surface of the metal to be tested face the reflecting surface of the left quasi-optical cavity spherical surface to form a plano-concave cavity. The Gaussian beam is focused at the center of the metal to be tested. Then remove the right quasi-optical cavity spherical surface and its corresponding coupling device in the quasi-optical resonator test system. Adjust the distance between the metal surface to be tested and the spherical surface of the left quasi-optical cavity to achieve the resonant frequency of the plano-concave cavity. The resonant frequency is the same as that used in the dual-cavity test in step 2, and then the quality factor is measured at this time. ; Step 4. Restore the right quasi-optical cavity spherical surface and its corresponding coupling device in the quasi-optical resonator testing system. Remove the left quasi-optical cavity spherical surface and its corresponding coupling device. Flip the metal under test so that the test surface of the metal under test tested in Step 3 is aligned with the reflecting surface of the right quasi-optical cavity spherical surface. Adjust the distance between the center of the metal under test and the right quasi-optical cavity spherical surface so that the resonant frequency of the quasi-optical resonator testing system remains unchanged. The quality factor at this time is measured to be ; Step 5. Based on the quality factor obtained from the three measurements , , The microwave surface resistivity of the metal material under test is calculated using the following method: ， in, It is the ohmic loss of the metal under test, which is calculated from the quality factor obtained by three measurements, ignoring diffraction loss and coupling loss introduced by weak coupling in the cavity. , , These are the mirror losses of the dual-cavity system, the mirror loss of the left spherical surface, and the mirror loss of the right spherical surface, respectively. These three values ​​satisfy the following relationship: ， Surface resistivity It is calculated using the following formula: ， In the formula, It is the resonant frequency. The permeability of free space, It is the magnetic field vector inside the plano-concave cavity. It is the tangential magnetic field vector on the surface of the metal to be tested, and V is the volume of the plano-concave cavity containing the electromagnetic field. The surface area of ​​the metal to be measured is denoted as .

2. The method for testing the resistivity of a metal surface as described in claim 1, characterized in that, In step 1, the quasi-optical resonator testing system includes a left quasi-optical cavity spherical surface, a right quasi-optical cavity spherical surface, a coupling device, and a vector network analyzer. The left and right quasi-optical cavity spherical surfaces are connected to the calibrated vector network analyzer through the coupling device. The left and right quasi-optical cavity spherical surfaces are adjusted so that the two reflecting surfaces of the two quasi-optical cavity spherical surfaces are horizontally aligned.

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