A device and method for broadband testing of the out-of-plane complex permittivity of a substrate

Abstract

The application aims to provide a device for testing the complex dielectric constant of a substrate in a wide frequency range, belonging to the technical field of microwave and millimeter wave material electromagnetic parameter testing. The device comprises a cylindrical resonant cavity shell, the bottom of which is provided with a plurality of slits penetrating the bottom wall, a sample is placed on the bottom of the cavity, the bottom outside the cavity is connected with a vacuum pumping device, so that the sample is completely attached to the bottom surface of the cylindrical resonant cavity, thereby improving the accuracy of the test results; meanwhile, a center feeding mode is adopted, one coaxial coupling hole is arranged on the top wall and the bottom wall of the cylindrical resonant cavity respectively, a metal probe is arranged in the coupling hole, and the metal probes do not extend into the cylindrical resonant cavity. Compared with the mode of inserting a magnetic excitation ring into both sides of the cavity, the feeding structure has more advantages, and can realize the ultra-wide frequency test of the substrate to be tested in the range of 1-60 GHz.

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 broadband testing device and method for complex permittivity outside the substrate surface. Background Technology

[0002] With the continuous development and technological innovation of the electronics industry, the importance of microwave dielectric substrate materials is becoming increasingly prominent. For example, in the design of radar antenna communication systems and microwave circuits, the dielectric constant of the microwave dielectric substrate has a significant impact on various performance indicators. Currently, most microwave dielectric substrates are composite materials, and therefore they usually exhibit anisotropy, meaning that the dielectric constants in the horizontal and normal directions of the substrate differ. When microwave dielectric substrates are used in the design of microwave circuits, the dielectric properties in the normal direction of the substrate will affect the characteristic impedance and electrical length of the circuit, thereby affecting the performance of the entire circuit system. Therefore, obtaining the out-of-plane complex dielectric constant of the microwave dielectric substrate has become one of the key issues.

[0003] Currently, common methods for obtaining the out-of-plane complex dielectric constant of dielectric substrates include the parallel-plate capacitor method and the stripline resonator method. The parallel-plate capacitor method involves clamping the sample material between two electrodes to form a capacitor, and then calculating the dielectric constant using the measured capacitance value. This method is simple to operate, but it is generally only applicable to low frequencies, ranging from 20Hz to 1GHz, and is easily affected by air gaps and electrode polarization effects, leading to significant errors. For example, in 2017, Yang Chenguang of Southeast University designed a novel parallel-plate capacitor test fixture, applicable to frequencies ranging from 10kHz to 100MHz, with test sample thicknesses from 0.1mm to 10mm, and testing medium-loss and high-loss samples. The stripline resonator method uses the sample under test as the dielectric material of the stripline. The complex permittivity of the dielectric material can be calculated by measuring the resonant frequency and quality factor. However, the losses of a stripline resonator include dielectric loss, conductor loss, and radiation loss. As the frequency increases, signal loss gradually increases due to issues such as surface roughness of the conductor band and overlap between higher-order resonant modes and the dominant mode, leading to a gradual increase in measurement error. This method is typically applicable to frequencies below 20 GHz. For example, in 2018, Zhang Yonghua et al. built a stripline resonator testing system to study high-frequency printed circuit board substrates. It could measure the complex permittivity of these substrates in the 7–14 GHz range, but the measurement results for the loss tangent at various frequencies showed significant errors. Both of these methods share similar characteristics: low accuracy and applicability to low to medium frequencies.

[0004] In the fields of 5G communication and millimeter-wave radar, it is necessary to investigate the operation of dielectric substrates at higher frequencies. Cylindrical resonant cavities, due to their simple structure, high quality factor, ease of field analysis, and high measurement accuracy, are commonly used for measuring the dielectric constant at high frequencies. Traditional cylindrical resonant cavity methods for complex dielectric constant measurement often employ a coupling method using magnetic excitation rings inserted on both sides of the cavity (Kaneko, Shogo, Hirokazu Kawabata, and Yoshio Kobayashi. "Improved perturbation method of complex permittivity using correction charts for TM010 and TM020 modes of a circular cylindrical cavity." 2010 Asia-Pacific Microwave Conference. IEEE, 2010.). This method limits the frequency range of the measured material's dielectric constant, and the measurement frequency cannot meet the requirements of ultra-high frequencies. Furthermore, to reduce polarization interference caused by sample placement, the sample under test is usually made into a rod shape, with a length greater than the cavity height. During testing, the electric field is parallel to the central axis of the rod-shaped sample, therefore, it is impossible to measure the out-of-plane complex dielectric constant of the substrate material. Summary of the Invention

[0005] To address the problems existing in the background technology, the present invention aims to provide a broadband testing device and method for the complex permittivity outside the substrate surface. The device includes a cylindrical resonant cavity housing with several slits penetrating the bottom wall. The sample is placed inside the bottom of the cavity, and the bottom of the cavity is connected to a vacuum pump, ensuring complete contact between the sample and the bottom surface of the cylindrical resonant cavity, thereby improving the accuracy of the test results. Simultaneously, a coupling hole is designed to be coaxial with the cylindrical resonant cavity. This invention not only enables high-frequency testing but also broadens the frequency testing range.

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

[0007] A broadband testing device for complex permittivity outside the substrate surface includes a cylindrical resonant cavity 1 and a vacuum loading unit;

[0008] The cylindrical resonant cavity 1 has a first coupling hole 3 at the center of the top wall 7 and a second coupling hole at the center of the bottom wall. The two coupling holes are coaxial with the cylindrical resonant cavity. The first coupling hole is used to place a metal probe to generate resonance, and the second coupling hole is used to place a metal probe to receive the excitation signal. The metal probe does not extend into the cylindrical resonant cavity. The bottom wall of the cylindrical resonant cavity is uniformly provided with m identical radial slits 4 that penetrate the bottom. The substrate 2 to be tested is placed at the bottom of the cylindrical resonant cavity, and the side of the substrate to be tested is in close contact with the surrounding cavity wall.

[0009] The vacuum loading unit is used to evacuate the bottom wall of the cylindrical resonant cavity, thereby reducing the air gap between the substrate under test and the bottom wall of the cylindrical resonant cavity.

[0010] Furthermore, the vacuum loading unit includes a cylindrical gas chamber 5, a gas pipe 6, and a vacuum pump 12; the top wall of the cylindrical gas chamber is the bottom wall of the cylindrical resonant cavity, and the second coupling hole penetrates through the center of the bottom wall of the gas chamber and extends into the cylindrical resonant cavity; the gas pipe is disposed on the side wall of the cylindrical gas chamber and is connected to the vacuum pump 12.

[0011] Furthermore, the broadband testing device for complex permittivity also includes a pressure loading unit; the pressure loading unit includes a pressure sensor 8, a support block 9, a lifting platform 10, and a bracket 11; the bracket consists of a horizontal arm, a vertical arm, and a fixed arm, with the lifting platform placed on the horizontal wall, one end of the horizontal wall connected to one end of the vertical arm, the other end of the vertical arm connected to one end of the fixed arm, and the other end of the fixed arm disposed on the top wall surface of the cylindrical resonant cavity 1; the air chamber 5, the support block 9, the pressure sensor 8, and the lifting platform 10 are arranged sequentially from top to bottom; by adjusting the lifting platform and cooperating with the fixed arm, the cylindrical resonant cavity and the cylindrical air chamber are brought into close contact.

[0012] Furthermore, the number of gaps m is a positive integer, preferably 6.

[0013] Furthermore, if the gap is rectangular, its dimensions are preferably 20mm in length and 0.3mm in width.

[0014] Furthermore, the top wall of the cylindrical resonant cavity can be separated from the main body of the cylindrical resonant cavity for placing and taking the substrate under test.

[0015] Furthermore, the inner wall of the cylindrical cavity shell is polished and silver-plated to improve the quality factor of the resonant cavity.

[0016] Furthermore, the dimensions of the substrate to be tested should be adapted to the inner diameter of the cylindrical resonant cavity to reduce the air gap between it and the sidewall. The thickness of the substrate to be tested should be uniform to reduce the dielectric constant error caused by uneven thickness and improve the measurement accuracy.

[0017] The present invention also provides a method for testing the complex permittivity based on the above-mentioned testing device, comprising the following steps:

[0018] Step 1: Test the cavity resonant frequency f0 and quality factor Q0 of the cylindrical resonant cavity when no substrate is placed;

[0019] Step 2: Place the substrate under test inside the cylindrical resonant cavity. Evacuate the space between the substrate under test and the bottom wall of the cylindrical resonant cavity to ensure complete contact between them. Measure the resonant frequency f of the cylindrical resonant cavity at this point. s and quality factor Q s ;

[0020] Step 3: Calculate the geometric factor G based on the field distribution inside the cylindrical resonant cavity. ε And the equivalent surface resistance R of the cavity wall is estimated using the geometric factor and the cavity quality factor Q0. S Corrections were made, and the Q-factor Q related to the cavity wall conductor loss was derived. c and the Q factor Q which is only related to the dielectric loss of the sample d The specific calculation formula is as follows:

[0021]

[0022]

[0023]

[0024] Among them, G 0n0 The geometric factor of the cavity without the substrate under test is ω, where ω is the angular frequency, μ0 is the free permeability, and H is the total magnetic field inside the cavity. t A magnetic field tangent to the cavity wall. Let L be the cavity resonant angular frequency, L be the cavity length of the cylindrical resonant cavity, and D be the diameter. V is the resonant angular frequency after the substrate under test is placed inside, V is the cavity volume, S is the cavity inner surface area, * indicates conjugate, (·) -1 This indicates finding the inverse;

[0025] Step 4: Based on the known in-plane complex permittivity ε || Using transcendental differential equations, the out-of-plane complex permittivity ε of the substrate under test is calculated. ⊥ The calculation formula is as follows:

[0026]

[0027] k z tan(k z h)+ε || k z0 tan[k z0 [(Lh)]=0

[0028]

[0029]

[0030] Where, k z and k z0 p is a constant parameter 0n ω is the nth root of the first kind of Bessel function, c is the speed of light in vacuum, h is the thickness of the substrate to be measured, j is the imaginary number, f is the resonant frequency of the resonant cavity, ω' is the real part of the angular frequency ω, and ω” is the imaginary part of the angular frequency ω.

[0031] Furthermore, in steps 1 and 2, the pressure regulator is adjusted to ensure that the pressure sensor readings remain consistent before and after placing the substrate under test.

[0032] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0033] 1. This invention employs a center-fed method, with a coupling hole coaxial with the resonant cavity at the center of both the top and bottom walls. Metal probes are placed within these coupling holes, but neither probe extends into the cylindrical resonant cavity. This feeding structure is superior to inserting magnetic excitation rings on both sides of the cavity because the inserted metal probes disturb the cavity field and cannot be eliminated in the algorithm. This invention enables ultra-wideband testing of the substrate under test in the range of 1–60 GHz.

[0034] 2. This invention features several slits connected to an air chamber on the bottom wall of a cylindrical resonant cavity. An air pipe is located on the side wall of the air chamber and connected to a vacuum pump. The vacuum pump extracts air from between the sample and the bottom surface of the resonant cavity, ensuring complete contact between the sample and the bottom surface. Since the air gap between the sample and the bottom wall of the resonant cavity is randomly generated in terms of volume, position, and shape when the sample is placed at the bottom, existing theoretical algorithms do not consider the existence of this air gap, leading to errors in the test results. This invention utilizes a vacuum device to significantly reduce the air gap and ensure a flat, edge-free sample, thereby improving the accuracy of the out-of-plane complex permittivity test of the cylindrical resonant cavity substrate material.

[0035] 3. The cylindrical resonant cavity housing of the present invention has a polished silver-plated inner wall. At the same time, by applying pressure, good contact is made between the top cover and the side wall of the resonant cavity. Applying the same pressure before and after placing the sample can ensure that the cavity length L remains unchanged during cavity calibration, which is the same as after placing the sample. This effectively improves the quality factor of the resonant cavity and achieves higher accuracy and ultra-wide frequency testing. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the complex permittivity broadband testing device according to Embodiment 1 of the present invention.

[0037] Figure 2 This is a cross-sectional view and an overall structural diagram of the cylindrical resonant cavity and gas chamber in the broadband test device for complex permittivity of Embodiment 1 of the present invention.

[0038] Figure 3 This is a top view of the bottom wall of the cylindrical resonant cavity in the broadband test device for complex permittivity of Embodiment 1 of the present invention.

[0039] Figure 4 This is a cross-sectional view of the cylindrical resonant cavity in Comparative Example 1.

[0040] Figure 5The image shows the S21 test curve obtained based on the wideband complex permittivity test device of Embodiment 1 of the present invention.

[0041] Reference numerals: 1. Cylindrical resonant cavity; 2. Substrate sample; 3. Coupling hole; 4. Bottom wall gap of cylindrical resonant cavity; 5. Gas chamber; 6. Gas tube; 7. Top wall of cylindrical resonant cavity; 8. Pressure sensor; 9. Support block; 10. Z-axis lifting stage; 11. Bracket; 12. Vacuum pump; 13. Pressure value display; 14. Cylindrical resonant cavity with side wall opening; 15. Side wall coupling hole; 16. Rod-shaped sample filled in the cylindrical resonant cavity with side wall opening. Detailed Implementation

[0042] 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.

[0043] Example 1

[0044] A broadband testing device for complex permittivity outside the substrate surface, the overall structure of which is shown in the schematic diagram below. Figure 1 As shown, it includes a cylindrical resonant cavity 1, a vacuum loading unit, and a pressure loading unit;

[0045] A first coupling hole 3 is provided at the center of the top wall 7 of the cylindrical resonant cavity 1, and a second coupling hole is provided at the center of the bottom wall. Both coupling holes are coaxial with the cylindrical resonant cavity. The first coupling hole is used to place a metal probe to generate resonance, and the second coupling hole is used to place a metal probe to receive the excitation signal, without the metal probe extending into the cylindrical resonant cavity. A top view of the bottom wall of the cylindrical resonant cavity is shown below. Figure 3 As shown (viewed from the top wall to the bottom wall of the cylindrical cavity), six identical radial rectangular slits 4 are evenly arranged on it, running through the bottom. The rectangular slits are 20mm long and 0.3mm wide, with semi-circular ends, which are only for actual processing. The substrate 2 to be tested is placed at the bottom of the cylindrical resonant cavity, and the side of the substrate to be tested is in close contact with the surrounding cavity walls. The top wall of the cylindrical resonant cavity can be separated from the cavity body for opening and removing the substrate to be tested.

[0046] The vacuum loading unit is used to evacuate the bottom wall of the cylindrical resonant cavity, reducing the air gap between the substrate under test and the bottom wall of the cylindrical resonant cavity; the vacuum loading unit includes a cylindrical air chamber 5, an air pipe 6, and a vacuum pump 12; the cross-sectional view of the cylindrical resonant cavity and the air chamber is shown below. Figure 2 As shown in the diagram, the overall structure is as follows: Figure 2 As shown, the top wall of the cylindrical gas chamber is the bottom wall of the cylindrical resonant cavity. The second coupling hole passes through the center of the bottom wall of the gas chamber and extends into the cylindrical resonant cavity. The gas pipe is set on the side wall of the cylindrical gas chamber and connected to the vacuum pump 12.

[0047] The pressure loading unit includes a pressure sensor 8, a support block 9, a lifting platform 10, and a bracket 11. The bracket consists of a horizontal arm, a vertical arm, and a fixed arm. A vertically movable lifting platform is placed on the horizontal wall. One end of the horizontal wall is connected to one end of the vertical arm, and the other end of the vertical arm is connected to one end of the fixed arm. The other end of the fixed arm is fixedly connected to the top wall surface of the cylindrical resonant cavity 1. The air chamber 5, the support block 9, the pressure sensor 8, and the lifting platform 10 are arranged sequentially from top to bottom. The pressure sensor 8 is connected to the pressure display 13. By adjusting the lifting platform and cooperating with the fixed arm, the cylindrical resonant cavity and the cylindrical air chamber are brought into close contact.

[0048] During use, the presence of the air chamber and vacuum pump causes the air between the substrate under test and the cylindrical resonant cavity to be evacuated, reducing the dielectric constant error caused by the air gap. At the same time, the same pressure is applied before and after placing the sample under test through the pressure loading unit, which can ensure that the cavity length L remains unchanged during cavity calibration, the same as after placing the sample. In addition, the pressurization can press the top cover tightly against the top of the resonant cavity sidewall, reducing the gap and improving the quality factor, thereby improving the accuracy of the out-of-plane complex dielectric constant of the cylindrical resonant cavity test substrate material and the test frequency.

[0049] The complex permittivity test is performed using the aforementioned out-of-plane complex permittivity test apparatus. The specific process includes the following steps:

[0050] Step 1: Test the cavity resonant frequency f0 and quality factor Q0 of the cylindrical resonator without placing the substrate under test. During the test, the lifting platform needs to be adjusted to make good contact between the top cover and the side wall of the cylindrical resonator using pressure. Record the pressure sensor reading at this time.

[0051] Step 2: Adjust the lifting platform to open the top wall of the cylindrical resonant cavity. Place the substrate to be tested at the bottom of the resonant cavity. Turn on the vacuum pump to remove the air between the substrate to be tested and the bottom surface of the cylindrical resonant cavity, so that the substrate to be tested is completely attached to the bottom surface. Then put the top wall of the cylindrical resonant cavity back to form the complete cavity. Then adjust the pressure device to make the pressure sensor reading consistent with that in Step 1. Test the resonant frequency f of the cylindrical resonant cavity after the substrate to be tested is placed in it. s and quality factor Q s ;

[0052] Step 3: Calculate the geometric factor G based on the field distribution inside the resonant cavity. ε And the equivalent surface resistance R of the cavity wall is estimated using the geometric factor and the cavity quality factor Q0. S Corrections were made, and the Q-factor Q related to the cavity wall conductor loss was derived. c Q, which is only related to the dielectric loss of the sample d The new angular frequency ω when the sample is loaded is calculated. The specific calculation process is as follows:

[0053]

[0054]

[0055]

[0056] Among them, G 0n0 The geometric factor of the cavity without the substrate under test is ω, where ω is the angular frequency, μ0 is the free permeability, and H is the total magnetic field inside the cavity. t A magnetic field tangent to the cavity wall. Let L be the cavity resonant angular frequency, L be the cavity length of the cylindrical resonant cavity, and D be the diameter. V is the resonant angular frequency after the substrate under test is placed inside, V is the cavity volume, S is the cavity inner surface area, * indicates conjugate, (·) -1 This indicates finding the inverse;

[0057] Step 4: Based on the known in-plane complex permittivity ε || The out-of-plane complex permittivity ε of the substrate under test was calculated using transcendental differential equations. ⊥ The calculation process is as follows:

[0058]

[0059] k z tan(k z h)+ε || k z0 tan[k z0 [(Lh)]=0

[0060]

[0061]

[0062] Where, k z and k z0 p is a constant parameter 0n ω is the nth root of the first kind of Bessel function, c is the speed of light in vacuum, h is the thickness of the substrate to be measured, j is the imaginary number, f is the resonant frequency of the resonant cavity, ω' is the real part of the angular frequency ω, and ω” is the imaginary part of the angular frequency ω.

[0063] Comparative Example 1

[0064] The cross-sectional view of the cylindrical resonant cavity used in this comparative example is shown below. Figure 4 As shown, the cylindrical resonant cavity has two coupling holes on its sidewall. One coupling hole is used to place the coupling ring to generate resonance, and the other coupling hole is used to place the coupling ring receiving device. The sample under test is placed at the center of the resonant cavity and is coaxial with the resonant cavity.

[0065] The magnetic excitation method of the sidewall opening limits the frequency range of the dielectric constant of the test material, allowing measurements only to be performed in TM010 and TM020 modes, operating at 2.3 octaves, which makes the measurement frequency unsuitable for ultra-high frequencies. Furthermore, the sample is placed at the center of the resonant cavity and coaxial with it; here, the electric field direction is parallel to the central axis of the rod-shaped sample, which cannot meet the requirements for measuring the out-of-plane complex dielectric constant of the substrate material.

[0066] Figure 5 The figure shows the S21 test curve obtained based on the wideband complex permittivity testing device of Embodiment 1 of the present invention. As can be seen from the figure, there are 10 resonance peaks in the ultra-wideband range of 1-60 GHz, and the specific resonance frequency values ​​are shown in Table 1.

[0067] Table 1

[0068]

[0069]

[0070] from Figure 5 As can be seen from Table 1, the wideband complex permittivity testing device of the present invention can perform measurements in 10 modes and can operate at 14.25 octaves, meaning that the measurement frequency of the device of the present invention can meet the requirements of ultra-high frequency.

[0071] 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 broadband testing device for the complex permittivity of a substrate outside its surface, characterized in that, Includes a cylindrical resonant cavity and a vacuum-loaded unit; A first coupling hole is provided at the center of the top wall of the cylindrical resonant cavity, and a second coupling hole is provided at the center of the bottom wall. The two coupling holes are coaxial with the cylindrical resonant cavity. The first coupling hole is used to place a metal probe to excite and generate resonance, and the second coupling hole is used to place a metal probe to receive the excitation signal. The metal probe does not extend into the cylindrical resonant cavity. The bottom wall of the cylindrical resonant cavity is uniformly provided with m identical radial slits that penetrate the bottom wall. The substrate to be tested is placed at the bottom of the cylindrical resonant cavity, and the side of the substrate to be tested is in close contact with the surrounding cavity wall. The vacuum loading unit is used to evacuate the bottom wall of the cylindrical resonant cavity, thereby reducing the air gap between the substrate under test and the bottom wall of the cylindrical resonant cavity.

2. The broadband testing device for complex permittivity as described in claim 1, characterized in that, The vacuum loading unit includes a cylindrical air chamber, an air pipe, and a vacuum pump; the top wall of the cylindrical air chamber is the bottom wall of the cylindrical resonant cavity, and the second coupling hole passes through the center of the bottom wall of the air chamber and extends into the cylindrical resonant cavity; the air pipe is disposed on the side wall of the cylindrical air chamber and is connected to the vacuum pump.

3. The broadband testing device for complex permittivity as described in claim 1, characterized in that, The broadband testing device for complex permittivity also includes a pressure loading unit; the pressure loading unit includes a pressure sensor, a support block, a lifting platform, and a bracket; the bracket consists of a horizontal arm, a vertical arm, and a fixed arm, with the lifting platform placed on the horizontal arm, one end of the horizontal arm connected to one end of the vertical arm, the other end of the vertical arm connected to one end of the fixed arm, and the other end of the fixed arm disposed on the top wall surface of the cylindrical resonant cavity; the gas chamber, support block, pressure sensor, and lifting platform are arranged sequentially from top to bottom; by adjusting the lifting platform and cooperating with the fixed arm, the cylindrical resonant cavity and the cylindrical gas chamber are made into close contact.

4. The broadband testing device for complex permittivity as described in claim 1, characterized in that, The number of radial slits, m, is 6.

5. The broadband testing device for complex permittivity as described in claim 4, characterized in that, If the radial gap is rectangular, its length is 20mm and its width is 0.3mm.

6. The broadband testing device for complex permittivity as described in claim 1, characterized in that, The top wall of the cylindrical resonant cavity can be separated from the main body of the cylindrical resonant cavity for placing and taking the substrate under test.

7. The broadband testing device for complex permittivity as described in claim 1, characterized in that, The inner wall of the cylindrical resonant cavity shell is polished and silver-plated.

8. The broadband testing device for complex permittivity as described in claim 1, characterized in that, The dimensions of the substrate to be tested should be adapted to the inner diameter of the cylindrical resonant cavity to reduce the air gap between it and the sidewall. The thickness of the substrate to be tested should be uniform to reduce the dielectric constant error caused by uneven thickness and improve the measurement accuracy.

9. A test method based on the broadband test apparatus for complex permittivity as described in any one of claims 1-8, characterized in that, Includes the following steps: Step 1: Test the cavity resonant frequency of the cylindrical resonant cavity when no substrate is placed. and quality factor ; Step 2: Place the substrate under test inside the cylindrical resonant cavity. Evacuate the space between the substrate under test and the bottom wall of the cylindrical resonant cavity to ensure complete contact between them. Measure the cavity resonant frequency of the cylindrical resonant cavity at this point. and quality factor ; Step 3: Calculate the geometric factor based on the field distribution inside the cylindrical resonant cavity. And utilize geometric factors and cavity quality factors Equivalent surface resistance of cavity wall Corrections were made, and the Q-factor related to the cavity wall conductor loss was derived. and the Q factor that is only related to the dielectric loss of the sample The specific calculation formula is as follows: ， ， ， ， ， in, The geometric factor of the cavity when the substrate under test is not placed. Angular frequency, Where is the free permeability, and H is the total magnetic field inside the cavity. A magnetic field tangent to the cavity wall. Let L be the cavity resonant angular frequency, L be the cavity length of the cylindrical resonant cavity, and D be the diameter. V is the resonant angular frequency after the substrate under test is placed inside, V is the cavity volume, S is the cavity inner surface area, * indicates conjugate, (·) -1 This indicates finding the inverse; Step 4: Based on the known in-plane complex permittivity Using transcendental differential equations, the out-of-plane complex permittivity of the substrate under test is calculated. The calculation formula is as follows: ， ， ， ， in, and For constant parameters, is the nth root of the first kind of Bessel function, c is the speed of light in vacuum, h is the thickness of the substrate to be measured, j is an imaginary number, and f is the resonant frequency of the resonant cavity. Angular frequency The real part, Angular frequency The imaginary part.

10. The test method as described in claim 9, characterized in that, In steps 1 and 2, the pressure regulator is adjusted to ensure that the pressure sensor readings remain consistent before and after placing the substrate under test.

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