Millimeter wave dielectric testing system and method for low-loss material under low-frequency microwave electric field

Abstract

The application aims to provide a low-loss material millimeter wave dielectric test system and method under the action of low-frequency microwave electric field, and belongs to the technical field of microwave and millimeter wave dielectric material testing. The test system combines a quasi-optical cavity and a rectangular resonant cavity, controls the input excitation signal size through the rectangular resonant cavity to adjust the electric field intensity at the position of the low-loss material, so as to simulate the external environment; the millimeter wave band dielectric performance of the material to be tested is tested through the quasi-optical cavity method, the mode interference between the excitation signal and the test signal, the large frequency span in the vector network analyzer during testing and other problems are avoided, and the test accuracy is greatly improved; meanwhile, the dielectric test system designed by the application has the characteristics of high test precision, good test stability, low use and maintenance cost.

Description

Technical Field

[0001] This invention belongs to the field of microwave and millimeter-wave dielectric material testing technology, specifically relating to a millimeter-wave dielectric testing system and method for low-loss materials under the action of a low-frequency microwave electric field. Background Technology

[0002] Microwave electromagnetic materials are a crucial component of modern materials science, widely applied in fields such as millimeter-wave communication. Among these, low-loss electromagnetic materials, due to their broad application range—used in microwave devices such as dielectric waveguides, dielectric blocks in coaxial cables, circuit substrates, and radomes—are a significant branch of microwave electromagnetic materials. With technological advancements, the application of low-loss materials in millimeter-wave devices is increasing. Furthermore, the dielectric constant is one of the most fundamental parameters describing the characteristics of low-loss materials. If the dielectric properties of low-loss materials can be understood in advance and targeted design implemented, the performance of millimeter-wave devices can be effectively guaranteed.

[0003] With the rapid development of communication and IoT applications, various miniaturized, low-power base stations will be densely distributed in future wireless communication systems, and the electromagnetic energy of space electromagnetic radiation will increase year by year. However, millimeter-wave devices are easily affected by external electromagnetic interference, affecting the stability and safety of the devices. Therefore, it is particularly important to achieve dielectric testing of low-loss materials in the millimeter-wave band under a low-frequency microwave electric field environment equivalent to the external space.

[0004] Currently, the dielectric properties of low-loss materials are often tested using the resonant cavity method. However, research on testing the dielectric constant of low-loss materials in the millimeter-wave band under low-frequency microwave electric field conditions is scarce. The team led by Li En at the University of Electronic Science and Technology of China (Gao Yong. Research on Microwave Dielectric Properties of Typical Materials under High Power [D]. University of Electronic Science and Technology of China, 2019.) proposed using the multi-mode characteristics of resonant cavities to test the dielectric properties of materials under low-frequency microwave electric fields. However, their research focused on testing the dielectric constant of materials in the low-frequency microwave band under the influence of low-frequency microwave electric fields, meaning the generated microwave electric field environment and the microwave signal used to test the dielectric properties of the material are almost in the same or adjacent frequency bands. If the test frequency band is adjusted to the millimeter-wave band, the following problems arise: First, it is difficult for a single resonant cavity to simultaneously cover the low-frequency to millimeter-wave bands; second, even if a single resonant cavity can simultaneously cover the low-frequency to millimeter-wave bands through miscellaneous mode suppression technology, mode interference can easily occur between different modes, affecting the accuracy and precision of the test. Summary of the Invention

[0005] To address the problems existing in the background technology, the present invention aims to provide a millimeter-wave dielectric testing system and method for low-loss materials under the action of a low-frequency microwave electric field. This testing system combines a quasi-optical cavity and a rectangular resonant cavity. The rectangular resonant cavity controls the magnitude of the input excitation signal to adjust the electric field strength at the location of the low-loss material, thereby simulating the external environment. Furthermore, the quasi-optical cavity method avoids the problems of large frequency band spans and mode interference caused by excitation and testing within the rectangular resonant cavity, resulting in more accurate test results.

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

[0007] A millimeter-wave dielectric testing system for low-loss materials under low-frequency microwave electric field includes a first vector network analyzer 1, a second vector network analyzer 2, a first isolator 3, a power amplifier 4, a second isolator 5, a directional coupler 6, a matching load 11, a microwave electric probe 12, a rectangular resonant cavity 13, a quasi-optical cavity spherical mirror 14, a first quasi-optical cavity coaxial coupling ring 15, a second quasi-optical cavity coaxial coupling ring 16, and a quartz test tube 17.

[0008] The input end of the first isolator 3 and the coupling port 9 of the directional coupler are respectively connected to the two ports of the first vector network analyzer 1. The output end of the first isolator 3 is connected to the output ports 7 of the power amplifier 4, the second isolator 5 and the directional coupler 6 in sequence. The input end 8 of the directional coupler 6 is connected to the microwave probe 12. The isolation port 10 of the directional coupler is connected to the matching load 11. The microwave probe 12 is placed in the cavity at one end of the rectangular resonant cavity 13. A quartz test tube 17 with an open top is placed in the cavity at the other end of the rectangular resonant cavity 13. The height of the quartz test tube is the same as the height of the rectangular resonant cavity, and the quartz test tube 17 is placed at one-quarter of the cavity length of the rectangular resonant cavity 13 near the other end.

[0009] A quasi-optical cavity spherical mirror 14 is positioned directly above a quartz test tube 17, with the normal at the center of the quartz test tube passing through the center of the quasi-optical cavity spherical mirror. The material to be tested 18 is placed at the bottom center of the quartz test tube 17. A first quasi-optical cavity coaxial coupling ring 15 and a second quasi-optical cavity coaxial coupling ring 16 are symmetrically arranged on the quasi-optical cavity spherical mirror 14, and the first quasi-optical cavity coaxial coupling ring 15 and the second quasi-optical cavity coaxial coupling ring 16 are respectively connected to the second vector network analyzer 2.

[0010] Furthermore, the microwave probe 12 is connected to the input terminal 8 of the directional coupler to inject the excitation signal into the rectangular resonant cavity 13. The coupling terminal 9 of the directional coupler is connected to the first vector network analyzer 1 to couple and receive the signal reflected back from the excitation signal injected into the rectangular resonant cavity. The directional coupler 6 is used to accurately obtain the magnitude of the actual excitation signal power injected into the rectangular resonant cavity 13. The power amplifier 4 is used to amplify the excitation signal power. The first isolator 3 and the second isolator 5 are used to reduce the influence of the reflected signal on the first vector network analyzer 1 and the power amplifier 4.

[0011] Furthermore, the radius of the quartz test tube 17 should be greater than the waist radius of the Gaussian beam at the same height.

[0012] Furthermore, the surface of the quasi-optical cavity spherical mirror 14 is silver-plated.

[0013] Furthermore, the rectangular resonant cavity 13 is a standard rectangular resonant cavity, and the distance d2 between the center of the quasi-optical cavity spherical mirror 14 and the top of the quartz test tube 17 is equal to the difference between the length D of the quasi-optical cavity and the height d of the rectangular resonant cavity.

[0014] This invention also provides a method for dielectric testing of low-loss materials based on the above-described testing system, comprising the following steps:

[0015] Step 1. Adjust the distance d2 between the center of the collimated cavity spherical mirror 14 and the top of the quartz test tube 17 until a resonance peak appears in the second vector network analyzer 2;

[0016] Step 2. Fix the position of the quasi-cavity spherical mirror 14 in Step 1, and perform cavity testing without placing the test material 18. Use the second vector network analyzer 2 to record the cavity resonant frequency f0 at this time.

[0017] Step 3. Place the material to be tested 18 at the center of the bottom of the quartz test tube 17, and use the second vector network analyzer 2 to test the resonant frequency f of the material to be tested 18 under a specific microwave electric field intensity. L ;

[0018] Step 4. Based on the resonant frequency f when the material under test is loaded, as measured in Step 3. L Using the cavity resonant frequency f0 measured in step 2, the dielectric constant ε of the material under test is calculated. r The calculation process is as follows:

[0019]

[0020]

[0021]

[0022] ε r=n 2 (4)

[0023] Where R0 is the radius of curvature of the quasi-optical cavity, t is the thickness of the material to be tested, n is the refractive index of the sample to be tested, ω0 is the beam waist radius of the quasi-optical cavity, D is the cavity length of the quasi-optical cavity, c is the electromagnetic wave propagation speed, q is the longitudinal mode number of the resonant electromagnetic field in the quasi-optical cavity, k is the wave number when the sample to be tested is loaded into the quasi-optical cavity, and d1, d′ and s0 are all intermediate variables.

[0024] Furthermore, in step 3, the microwave electric field strength can be changed by adjusting the input power of the first vector network analyzer 1. The specific relationship between the microwave electric field strength and the input power is as follows:

[0025] Adjust the excitation signal frequency so that the rectangular resonant cavity operates at TE. 102 Mode, for rectangular resonator TE 102 The electromagnetic field distribution within the cavity is as follows:

[0026]

[0027] Where E0 is the amplitude of the low-frequency microwave electric field intensity, Z TE Let η be the wave impedance of the TE mode, η be the free space wave impedance, a be the length of the rectangular resonant cavity, and d be the height of the rectangular resonant cavity.

[0028] If the rectangular resonant cavity only experiences conductivity loss due to the cavity wall, then the cavity loss P c for:

[0029]

[0030] Among them, H t Let R be the tangential magnetic field component of the cavity wall surface, b be the width of the rectangular resonant cavity, and R be the tangential magnetic field component of the cavity wall surface. s η is the surface resistance of the rectangular resonant cavity, λ is the operating wavelength of the electromagnetic wave at resonance, and η is the wave impedance.

[0031] The quality factor Q of a rectangular resonant cavity under no-load conditions c for:

[0032]

[0033] Where k1 is the wavenumber of the rectangular resonant cavity at resonance, and ω0 is the resonant angular frequency;

[0034] When the rectangular resonant cavity is in a resonant state, its electric field stores energy W. e Equal to magnetic field energy storage W m ,

[0035]

[0036] Where ε is the dielectric constant within the rectangular resonant cavity. For E y The conjugate of , where V is the volume inside the rectangular resonant cavity;

[0037] Assume the microwave input power P of the excitation resonant cavity TE102 All of the material is injected into the resonant cavity, considering only the cavity wall metal loss P. c By definition of the quality factor:

[0038]

[0039] Combining equations (5), (6), (7), (8), and (9), the maximum electric field strength inside the rectangular resonant cavity and at the material under test is obtained as follows:

[0040]

[0041] The mechanism of this invention is as follows: By using two vector network analyzers, the test signal and the electric field excitation signal are separated. One vector network analyzer excites a high-frequency test signal in a quasi-optical cavity, while the other vector network analyzer excites a low-frequency microwave electric field in a rectangular resonant cavity. Utilizing these two independent and compatible microwave devices—the rectangular resonant cavity and the quasi-optical cavity—the millimeter-wave dielectric properties of low-loss materials under the influence of a low-frequency microwave electric field are measured. The millimeter-wave test signal from the quasi-optical cavity and the low-frequency electric field from the rectangular resonant cavity do not interfere with each other, thus avoiding the problems of large frequency band spans and mode interference caused by simultaneously exciting a low-frequency electric field and performing millimeter-wave measurements in a single resonant cavity.

[0042] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0043] This invention innovatively combines a rectangular resonant cavity and a quasi-optical cavity. The rectangular resonant cavity is used to control the electric field intensity at the material under test, while the quasi-optical cavity is used to test the millimeter-wave dielectric properties of the material under test. This avoids problems such as mode interference between the excitation signal and the test signal, and the large frequency band span of the vector network analyzer during testing, thus greatly improving the accuracy of the test. At the same time, the dielectric testing system designed in this invention has the characteristics of high testing accuracy, good testing stability, and low use and maintenance costs. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the millimeter-wave dielectric testing system for low-loss materials under the action of a low-frequency microwave electric field, as described in this invention.

[0045] Figure 2 This is a schematic diagram of the rectangular resonant cavity in the dielectric testing system of the present invention.

[0046] Wherein, 1 is the first vector network analyzer, 2 is the second vector network analyzer, 3 is the first isolator, 4 is the power amplifier, 5 is the second isolator, 6 is the directional coupler, 7 is the output port of the directional coupler, 8 is the input port of the directional coupler, 9 is the coupling port of the directional coupler, 10 is the isolation port of the directional coupler, 11 is the matched load, 12 is the microwave probe, 13 is the rectangular resonant cavity, 14 is the quasi-optical cavity spherical mirror, 15 is the first quasi-optical cavity coaxial coupling ring, 16 is the second quasi-optical cavity coaxial coupling ring, 17 is the quartz test tube, and 18 is the material to be tested. Detailed Implementation

[0047] 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.

[0048] This invention provides a millimeter-wave dielectric testing system for low-loss materials under a low-frequency microwave electric field. A schematic diagram of the overall structure of the system is shown below. Figure 1 As shown, it includes a first vector network analyzer 1, a second vector network analyzer 2, a first isolator 3, a power amplifier 4, a second isolator 5, a directional coupler 6, a matching load 11, a microwave electrical probe 12, a rectangular resonant cavity 13, a quasi-optical cavity spherical mirror 14, a first quasi-optical cavity coaxial coupling ring 15, a second quasi-optical cavity coaxial coupling ring 16, and a quartz test tube 17.

[0049] The input terminal of the first isolator 3 and the coupling port 9 of the directional coupler are connected to the first vector network analyzer 1, respectively. The output terminal of the first isolator 3 is connected in sequence to the output ports 7 of the power amplifier 4, the second isolator 5, and the directional coupler 6. The input terminal 8 of the directional coupler 6 is connected to the microwave probe 12, and the isolation port 10 of the directional coupler is connected to the matching load 11. The microwave probe 12 is placed in the cavity at one end of the rectangular resonant cavity 13. A quartz test tube 17 with an open top is placed in the cavity at the other end of the rectangular resonant cavity 13. The height of the quartz test tube is the same as the height of the rectangular resonant cavity, and the quartz test tube 17 is located at one-quarter of the cavity length of the rectangular resonant cavity 13, near the other end. The structural schematic diagram of the rectangular resonant cavity is shown below. Figure 2 As shown;

[0050] The input terminal 8 of the directional coupler is connected to the microwave probe 12 and is used to inject the excitation signal into the rectangular resonant cavity 13. The coupling terminal 9 of the directional coupler is connected to the first vector network analyzer 1 and is used to couple and receive the signal reflected back from the excitation signal injected into the rectangular resonant cavity. The directional coupler 6 is used to accurately obtain the magnitude of the actual excitation signal power injected into the rectangular resonant cavity 13. The power amplifier 4 is used to amplify the excitation signal power. The first isolator 3 and the second isolator 5 are used to reduce the influence of the reflected signal on the first vector network analyzer 1 and the power amplifier 4.

[0051] A quasi-optical cavity spherical mirror 14 is positioned directly above a quartz test tube 17, with the normal at the center of the quartz test tube passing through the center of the quasi-optical cavity spherical mirror. The material to be tested 18 is placed at the bottom center of the quartz test tube 17. A first quasi-optical cavity coaxial coupling ring 15 and a second quasi-optical cavity coaxial coupling ring 16 are symmetrically arranged on the quasi-optical cavity spherical mirror 14, and the first quasi-optical cavity coaxial coupling ring 15 and the second quasi-optical cavity coaxial coupling ring 16 are respectively connected to the second vector network analyzer 2.

[0052] Example 1

[0053] A method for dielectric testing of low-loss materials based on a millimeter-wave dielectric testing system for low-loss materials includes the following steps:

[0054] Step 1. Adjust the distance d2 between the center of the collimated cavity spherical mirror 14 and the top of the quartz test tube 17 until a resonance peak appears or the resonance peak is obvious in the second vector network analyzer 2;

[0055] Step 2. Fix the position of the quasi-cavity spherical mirror 14 in Step 1, and perform cavity testing without placing the test material 18. Use the second vector network analyzer 2 to record the cavity resonant frequency f0 at this time.

[0056] Step 3. Place the material to be tested 18 at the center of the bottom of the quartz test tube 17, and use the second vector network analyzer 2 to test the resonant frequency f of the material to be tested 18 under a specific microwave electric field intensity. L ;

[0057] The microwave electric field strength can be changed by adjusting the input power of the first vector network analyzer 1. The microwave electric field strength E y0max and input power P TE102 The specific relationship between them is as follows:

[0058] Adjust the excitation signal frequency so that the rectangular resonant cavity operates at TE. 102 Mode, for rectangular resonator TE 102 The electromagnetic field distribution within the cavity is as follows:

[0059]

[0060] Where E0 is the amplitude of the low-frequency microwave electric field intensity, Z TE Let η be the wave impedance of the TE mode, η be the free space wave impedance, a be the length of the rectangular resonant cavity, and d be the height of the rectangular resonant cavity.

[0061] If the rectangular resonant cavity only experiences conductivity loss due to the cavity wall, then the cavity loss P c for:

[0062]

[0063] Among them, Ht Let R be the tangential magnetic field component of the cavity wall surface, b be the width of the rectangular resonant cavity, and R be the tangential magnetic field component of the cavity wall surface. s η is the surface resistance of the rectangular resonant cavity, λ is the operating wavelength of the electromagnetic wave at resonance, and η is the wave impedance.

[0064] The quality factor Q of a rectangular resonant cavity under no-load conditions c for:

[0065]

[0066] Where k1 is the wavenumber of the rectangular resonant cavity at resonance, and ω0 is the resonant angular frequency;

[0067] When the rectangular resonant cavity is in a resonant state, its electric field stores energy W. e Equal to magnetic field energy storage W m ,

[0068]

[0069] Where ε is the dielectric constant within the rectangular resonant cavity. For E y The conjugate of , where V is the volume inside the rectangular resonant cavity;

[0070] Assume the microwave input power P of the excitation resonant cavity TE102 All of the material is injected into the resonant cavity, considering only the cavity wall metal loss P. c By definition of the quality factor:

[0071]

[0072] Combining equations (11), (12), (13), (14), and (15), the maximum electric field intensity inside the rectangular resonant cavity and at the material under test is obtained as follows:

[0073]

[0074] Step 4. Based on the resonant frequency f when the material under test is loaded, as measured in Step 3. L Using the cavity resonant frequency f0 measured in step 2, the dielectric constant ε of the material under test is calculated. r The calculation process is as follows:

[0075]

[0076]

[0077]

[0078] ε r =n 2 (20)

[0079] Where R0 is the radius of curvature of the quasi-optical cavity, t is the thickness of the material to be tested, n is the refractive index of the sample to be tested, ω0 is the beam waist radius of the quasi-optical cavity, D is the cavity length of the quasi-optical cavity, c is the electromagnetic wave propagation speed, q is the longitudinal mode number of the resonant electromagnetic field in the quasi-optical cavity, k is the wave number when the sample to be tested is loaded into the quasi-optical cavity, and d1, d′ and s0 are all intermediate variables.

[0080] Step 5. Change the power of the excitation signal to obtain different microwave electric field intensities in the region of the material under test. Repeat steps 3 and 4 to obtain the millimeter-wave dielectric properties of the absorbing material under different low-frequency microwave electric fields.

[0081] 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 millimeter-wave dielectric testing system for low-loss materials under low-frequency microwave electric field, characterized in that, It includes a first vector network analyzer (1), a second vector network analyzer (2), a first isolator (3), a power amplifier (4), a second isolator (5), a directional coupler (6), a matching load (11), a microwave probe (12), a rectangular resonant cavity (13), a quasi-optical cavity spherical mirror (14), a first quasi-optical cavity coaxial coupling ring (15), a second quasi-optical cavity coaxial coupling ring (16), and a quartz test tube (17); The input end of the first isolator (3) and the coupling end (9) of the directional coupler are respectively connected to the two ports of the first vector network analyzer (1). The output end of the first isolator (3) is connected to the output end (7) of the power amplifier (4), the second isolator (5) and the directional coupler (6) in sequence. The input end (8) of the directional coupler (6) is connected to the microwave probe (12). The isolation end (10) of the directional coupler is connected to the matching load (11). The microwave probe (12) is placed in the cavity at one end of the rectangular resonant cavity (13). A quartz test tube (17) with a top opening is placed in the cavity at the other end of the rectangular resonant cavity (13). The height of the quartz test tube is the same as the height of the rectangular resonant cavity. The quartz test tube (17) is placed at one-quarter of the cavity length of the rectangular resonant cavity (13) near the other end. A quasi-optical cavity spherical mirror (14) is positioned directly above a quartz test tube (17), with the normal at the center of the quartz test tube passing through the center of the quasi-optical cavity spherical mirror. The material to be tested (18) is placed at the bottom center of the quartz test tube (17). A first quasi-optical cavity coaxial coupling ring (15) and a second quasi-optical cavity coaxial coupling ring (16) are symmetrically positioned on the quasi-optical cavity spherical mirror (14), and the first quasi-optical cavity coaxial coupling ring (15) and the second quasi-optical cavity coaxial coupling ring (16) are respectively connected to the two ends of the second vector network analyzer (2).

2. The millimeter-wave dielectric testing system for low-loss materials under low-frequency microwave electric field as described in claim 1, characterized in that, The microwave probe (12) is used to inject the excitation signal into the rectangular resonant cavity (13); the directional coupler (6) is used to accurately obtain the magnitude of the excitation signal power actually injected into the rectangular resonant cavity (13); the power amplifier (4) is used to amplify the excitation signal power; the first isolator (3) and the second isolator (5) are used to reduce the influence of the reflected signal on the first vector network analyzer (1) and the power amplifier (4).

3. The millimeter-wave dielectric testing system for low-loss materials under low-frequency microwave electric field as described in claim 1, characterized in that, The radius of the quartz test tube (17) should be greater than the waist radius of the Gaussian beam at the same height.

4. The millimeter-wave dielectric testing system for low-loss materials under low-frequency microwave electric field as described in claim 1, characterized in that, The surface of the quasi-optical cavity spherical mirror (14) is silver-plated.

5. The millimeter-wave dielectric testing system for low-loss materials under low-frequency microwave electric field as described in claim 1, characterized in that, The rectangular resonant cavity (13) is a standard rectangular resonant cavity. The distance d2 between the center of the quasi-optical cavity spherical mirror (14) and the top of the quartz test tube (17) is equal to the difference between the length D of the quasi-optical cavity and the height d of the rectangular resonant cavity.

6. A method for dielectric testing of low-loss materials based on the millimeter-wave dielectric testing system for low-loss materials under the action of a low-frequency microwave electric field as described in any one of claims 1-5, characterized in that, Includes the following steps: Step 1. Adjust the distance d2 between the center of the collimated cavity spherical mirror and the top of the quartz test tube until a resonance peak appears on the second vector network analyzer; Step 2. Fix the position of the quasi-cavity spherical mirror in Step 1, and perform cavity testing without placing the material to be tested. Use the second vector network analyzer to record the cavity resonant frequency f0 at this time. Step 3. Place the material to be tested at the center of the bottom of the quartz test tube, and use a second vector network analyzer to test the resonant frequency f of the material under the required microwave electric field strength. L ; Step 4. Based on the resonant frequency f when the material under test is loaded, as measured in Step 3. L Using the cavity resonant frequency f0 measured in step 2, the dielectric constant ε of the material under test is calculated. r The specific calculation process is as follows: e r =n 2 (4) Where R0 is the radius of curvature of the quasi-optical cavity, t is the thickness of the material to be tested, n is the refractive index of the sample to be tested, ω0 is the beam waist radius of the quasi-optical cavity, D is the cavity length of the quasi-optical cavity, c is the electromagnetic wave propagation speed, q is the longitudinal mode number of the resonant electromagnetic field in the quasi-optical cavity, k is the wave number when the sample to be tested is loaded into the quasi-optical cavity, and d1, d′ and s0 are all intermediate variables.

7. The method for dielectric testing of low-loss materials as described in claim 6, characterized in that, In step 3, the microwave electric field strength is changed by adjusting the input power of the first vector network analyzer. The specific relationship between the microwave electric field strength and the input power is as follows: Adjust the excitation signal frequency so that the rectangular resonant cavity operates at TE. 102 Mode, for rectangular resonator TE 102 The electromagnetic field distribution within the cavity is as follows: Where E0 is the amplitude of the low-frequency microwave electric field intensity, Z TE Let η be the wave impedance of the TE mode, η be the free space wave impedance, a be the length of the rectangular resonant cavity, and d be the height of the rectangular resonant cavity. If the rectangular resonant cavity only experiences conductivity loss due to the cavity wall, then the cavity loss P c for: Among them, H t Let R be the tangential magnetic field component of the cavity wall surface, b be the width of the rectangular resonant cavity, and R be the tangential magnetic field component of the cavity wall surface. s η is the surface resistance of the rectangular resonant cavity, λ is the operating wavelength of the electromagnetic wave at resonance, and η is the wave impedance. The quality factor Q of a rectangular resonant cavity under no-load conditions c for: Where k1 is the wavenumber of the rectangular resonant cavity at resonance, and ω0 is the resonant angular frequency; When the rectangular resonant cavity is in a resonant state, its electric field stores energy W. e Equal to magnetic field energy storage W m , Where ε is the dielectric constant within the rectangular resonant cavity. For E y The conjugate of , where V is the volume inside the rectangular resonant cavity; Assume the microwave input power P of the excitation resonant cavity TE102 All of the material is injected into the resonant cavity, considering only the cavity wall metal loss P. c By definition of the quality factor: Combining equations (5), (6), (7), (8), and (9), the maximum electric field strength inside the rectangular resonant cavity and at the material under test is obtained as follows:

Images