Method for measuring complex dielectric constant of irregular material based on resonant cavity

Abstract

The invention provides an irregular material complex dielectric constant measuring method based on a resonant cavity, and belongs to the technical field of microwave material electromagnetic parameter testing. The method comprises the following steps: firstly, analyzing a resonance mode of an air resonant cavity based on a characteristic mode, and determining an internal resonance mode by solving minimum internal resonance factors of different modes; calculating an electric field E and a magnetic field H of a resonance mode under different dielectric constants of the sample when the sample in the same shape is loaded, and further solving a corresponding minimum mode factor when the mode resonates so as to obtain a relative dielectric constant to be measured; and meanwhile, by utilizing the definition of a quality factor, substituting the relative dielectric constant, and finally solving to obtain the loss tangent of the sample. According to the method, the full-wave characteristic of the characteristic mode is utilized, the method is not limited by the size and shape of the material, the complex dielectric constant of the irregular material can be accurately tested based on the resonant cavity, the application range of the resonant cavity method is expanded, and the method has important engineering application significance.

Description

Technical Field

[0001] The invention belongs to the technical field of microwave material electromagnetic parameter testing, and in particular relates to a method for measuring the complex dielectric constant of irregular materials based on a resonant cavity. Background Art

[0002] The resonant cavity method offers high measurement sensitivity and accuracy and is widely used to measure the dielectric constant of low-loss materials. However, it places strict demands on the size and shape of the sample. For example, the coaxial cavity resonator method requires the sample to be a round rod of a specific size, while the high-Q cavity resonator method requires the sample to be a cylindrical sheet of a specific size. Before the material is formed, the sample can be precisely prepared according to the test requirements to measure the complex dielectric constant of the material. Even so, due to the limitations of the processing technology, the material may still have unpredictable defects such as non-uniformity after forming. Therefore, dielectric measurement of the formed sample is essential for material quality monitoring. Taking the quality monitoring of microwave traveling wave tube amplifiers as an example, accurately measuring the complex dielectric constant of dielectric clamping rods with various cross-sectional shapes (such as circular, rectangular, T-shaped, fan-shaped, trapezoidal, etc.) is of great significance for improving the process level of microwave traveling wave tubes.

[0003] The traditional resonant cavity method usually measures the complex dielectric constant of materials based on the perturbation method and mode matching method. The mode matching method decomposes the irregular material into multiple regular structure regions, places them in the center of the resonant cavity, and uses the matching mode function expansion to solve. However, the centering is only effective for longitudinally irregular materials and is not applicable to transversely irregular materials. The perturbation method is only applicable to the measurement of the complex dielectric constant of irregular materials with sufficiently small sizes, and requires calibration using standards of the same shape. The above methods are limited by mode function matching, sample size constraints, and standard sample preparation and calibration. There is uncertainty in the measurement of the complex dielectric constant of irregular materials, which makes it difficult to accurately measure the complex dielectric constant.

[0004] Therefore, how to design a resonant cavity method that is not constrained by material size and shape, so that the complex dielectric constant of irregular materials can be accurately measured in the resonant cavity, has become one of the current research focuses. Summary of the Invention

[0005] In view of the problem that the traditional resonant cavity method for measuring the complex dielectric constant is limited by the size and shape of the material, the purpose of the present invention is to provide a method for measuring the complex dielectric constant of irregular materials based on a resonant cavity. The method of the present invention is based on the characteristic that the resonant frequency and quality factor change differently due to the difference in the complex dielectric constant of the material to be measured. By measuring the resonant frequency and quality factor of the sample to be measured before and after being placed in the resonant cavity, and analyzing the resonant mode before and after the sample is loaded based on the characteristic mode, the resonant mode in the cavity is solved, and the change of the mode at the resonant frequency with the dielectric after the sample to be measured is analyzed. The minimum mode factor corresponding to the resonance of the mode is solved, and then the relative dielectric constant to be measured is determined; then the loss tangent to be measured is calculated based on the quality factor, resonant field and relative dielectric constant, so as to achieve accurate measurement of the complex dielectric constant of irregular materials.

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

[0007] A method for measuring the complex dielectric constant of an irregular material based on a resonant cavity comprises the following steps:

[0008] Step 1: Measure the resonant frequency f0 and quality factor Q0 of the resonant cavity in the cavity state;

[0009] Step 2: Geometrically model the empty resonant cavity, establish the generalized eigenvalue equation of internal resonance, solve the internal resonance mode number r at frequency f0, and then solve the equivalent microwave surface resistance R of the metal cavity wall based on the quality factor Q0, the electric field E and magnetic field H under the internal resonance mode corresponding to the internal resonance mode number r. s ;

[0010] Step 3: Measure the resonant frequency f after the irregular material to be tested is placed in the resonant cavity d and quality factor Q d , geometric modeling of the material to be tested and the cavity is performed according to the placement of the irregular material to be tested; the modeled grid data is substituted into the generalized eigenvalue equation based on the volume integral equation, and the relative dielectric constant ε of the irregular material to be tested is set r 'Analysis range, within the analysis range with a certain step, calculate the resonance mode of the cavity at the frequency f d Different time r 'Corresponding mode factor γ, find the minimum mode factor γ min , the corresponding ε r ' is the relative dielectric constant of the irregular material;

[0011] Step 4: Substitute the ε obtained in step 3 r ' and R obtained in step 2 s Substitute Q d The calculation formula is used to invert the frequency f d The loss tangent tgδ to be measured.

[0012] Furthermore, the specific process of step 2 is:

[0013] The induced current f on the metal surface is represented by the RWG basis function defined on the triangular mesh. s , the generalized eigenvalue equation of the internal resonance of the cavity is established based on the electric field surface integral equation:

[0014] [Z Re (J s )][J s ]=α[Z Im (J s )][J s ] (1)

[0015]

[0016] Among them, J s (r') is the characteristic current at the source point r' on the inner surface S0 of the cavity, α is the characteristic value, Z Re and Z Im are the real and imaginary components of the impedance matrix operator Z, respectively, j is a complex unit, is the dyadic Green's function in free space, k0 and η0 are the wave number and wave impedance in free space, is the gradient operator about the source point r', is the gradient operator with respect to the field point r;

[0017] Solve the generalized eigenvalue equation of internal resonance, arrange the eigenvalues ​​from large to small, and calculate the internal resonance factor β of the first g modes at frequency f0 m ;

[0018]

[0019] E m =-Z(v m ·f s ) (4)

[0020]

[0021] Among them, R m is the equivalent microwave surface resistance of the metal cavity wall in the mth mode, the subscript m represents the mode number, M=max(R1,…R m ,…R g ), S r By moving S0 outward along the normal direction d0, v m is the eigenvector, k is the unit vector of the propagation direction of the electromagnetic wave;

[0022] Find the equation with the minimum β mThe mode number r is used to calculate the equivalent microwave surface resistance R of the metal cavity wall according to the electric field E, magnetic field H and Q0 under the internal resonance mode corresponding to the mode number r. s ;

[0023]

[0024] Where ε0 is the dielectric constant in free space, ω0 is the angular frequency, and H t is the tangential component of H, and V0 is the cavity area.

[0025] Furthermore, in step 2, the number of characteristic modes g is preferably 40.

[0026] Furthermore, in step 2, the distance d0 is preferably 0.05 free space wavelength.

[0027] Furthermore, in step 2, during the processing of the resonant cavity, due to the limitations of the processing technology, there is a certain deviation between the actual size of the resonant cavity and the preset size. Therefore, the size of the resonant cavity can be corrected before solving the internal resonance eigenvalue equation. The specific process is as follows:

[0028] Set the frequency range [f0-f1, f0+f1], solve equation (1), arrange the eigenmodes according to the absolute value of the eigenvalue from large to small, and find the internal resonant frequency f0' with at least two zero eigenvalues ​​from the first g modes.

[0029] The equivalent size of the resonant cavity is modified so that f0'=f0. According to the adjusted size, the cavity geometry modeling is repeated, and then the internal resonance eigenvalue equation is solved.

[0030] Furthermore, f1 is preferably 200 MHz.

[0031] Furthermore, if the resonant cavity is a cylindrical cavity, the specific process of correcting the equivalent size of the resonant cavity is:

[0032] The radius is a, the height is l, and it works at TE 111 ,TM 010 The resonant frequencies of the mode cylindrical cavities are

[0033]

[0034] c is the speed of light in free space. According to the relationship between f0' and f0, adjust the corresponding resonant cavity structure parameters a and l to make f0'=f0;

[0035] If the resonant cavity is a rectangular cavity, the specific process of correcting the equivalent size of the resonant cavity is:

[0036] The size is a×b×l, and it works on TE 101 The resonant frequency of the mode rectangular cavity is

[0037]

[0038] According to the size relationship between f0' and f0, the corresponding resonant cavity structure parameters a and l are adjusted to set f0'=f0.

[0039] Furthermore, the specific process of step 3 is:

[0040] Step 3.1. Measure the resonant frequency f after the irregular material is placed in the resonant cavity d and quality factor Q d ;

[0041] Step 3.2. Use the RWG basis function f defined on the triangle mesh s represents the induced current J on the metal surface s , using the SWG basis function f defined on the tetrahedral mesh v Represents the induced current J of irregular materials v , establish the volume integral equation, as follows:

[0042]

[0043] Where μ0 is the magnetic permeability in free space, E inc is the external incident electric field, E total is the total electric field, V d is an irregular material body, and the subscript tan represents the tangential component;

[0044] Step 3.3. Substitute the impedance matrix [Z] of the volume integral equation into the generalized eigenvalue equation:

[0045] [Z Im ] sub J sn =α[Z Re ] sub J sn (9)

[0046] [Z] sub =[Z ss ]-[Z sv ][Z vv ] -1 [Z vs ] (10)

[0047] Among them, [Z ss ] and [Z vv ] are the self-impedance matrices of surface current and volume current, [Z sv ] and [Z vs ] is the mutual impedance matrix of surface current and volume current, J snis the surface characteristic current, α is the characteristic value, and the subscripts Im and Re represent the imaginary and real parts, respectively;

[0048] Step 3.4. Set the relative dielectric constant ε to be measured based on experience r 'Analysis range [ε r1 ',ε r2 '], with a certain step, in different ε r ', frequency f d Solve equation (9) to obtain the electric field E and magnetic field H, and then calculate the mode corresponding to the mode number r under different ε r 'The corresponding mode factor γ;

[0049]

[0050] E=-Z ss (v s ·f s )-Z vv (-[Z vv ] -1 [Z vs ]v s ·f v ) (12)

[0051]

[0052] Where N = max(T, ε r '∈[ε r1 ',ε r2 ']), S r The inner surface S0 of the cavity is moved outward along the normal direction by d0, v s is the eigenvector of pattern r;

[0053] Step 3.5. Find the minimum mode factor γ min , the corresponding ε r ' is the relative complex permittivity of the irregular material.

[0054] Furthermore, in step 3.4, the analysis range [ε r1 ',ε r2 '] is preferably [1, 30].

[0055] Furthermore, the specific calculation formula of step 4 is:

[0056]

[0057] Where E and H are the frequency f of mode r after loading the irregular material. d The electric and magnetic fields at H t is the tangential component of H, and V0 is the part of the cavity excluding the sample.

[0058] The mechanism of the present invention is as follows: the sample to be tested is placed in a resonant cavity. Due to the difference in electromagnetic parameters between the sample to be tested and the air medium in the cavity, the resonant frequency and electromagnetic field will change accordingly. The frequency and field changes caused by samples with different parameters are also different. Based on the uniquely determined resonant frequency and field, the complex dielectric constant of the sample to be tested can be solved.

[0059] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0060] The present invention introduces characteristic mode analysis into the dielectric constant measurement of materials using the resonant cavity method. Due to its full-wave characteristics, the influence of material size and shape on test modeling is avoided. Based on the uniqueness of the electromagnetic field disturbance in the cavity caused by loading materials with specific shapes and dielectric constants, the electromagnetic fields of the resonant modes before and after the irregular materials are placed in the resonant cavity are quantitatively analyzed, and the electromagnetic fields of the modes when the dielectric changes are compared to obtain the relative dielectric constant corresponding to the resonant state. Ultimately, the loss tangent can be solved, thereby achieving accurate measurement of irregular materials using the resonant cavity method. This method has important application value for dielectric measurement of molded materials in actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Diagram of the structure of a cylindrical sapphire rod inserted into a cylindrical metal cavity with a circular hole.

[0062] Figure 2 Schematic diagram of the process of measuring the complex dielectric constant of irregular materials based on resonant cavity.

[0063] Figure 3 These are the characteristic value curves of different modes in the cavity calculated by the method of the present invention.

[0064] Figure 4 The resonance factor curves of different modes in the cavity calculated by the method of the present invention.

[0065] Figure 5 The internal resonance mode 1 of the 1.60 mm sample after loading calculated by the method of the present invention is at the corresponding frequency f d Curve of mode factor changing with relative dielectric constant when .

[0066] Figure 6 The internal resonance mode 1 of the 0.97 mm sample after loading calculated by the method of the present invention is at the corresponding frequency f d Curve of mode factor changing with relative dielectric constant when . DETAILED DESCRIPTION

[0067] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the implementation methods and drawings.

[0068] Example 1

[0069] A resonant cavity-based method for measuring the complex dielectric constant of irregular materials uses a cylindrical resonant cavity to test cylindrical sapphire rods of different radii. A sample hole with a diameter of 1.64 mm is located in the center of the cylindrical resonant cavity. A sapphire rod with a diameter of 1.60 mm is placed in the center of the sample hole. A sapphire rod with a diameter of 0.977 mm is placed in the sample hole close to the side wall of the sample hole. The corresponding structure is as follows: Figure 1 shown.

[0070] The flow diagram of the measuring method of the present invention is as follows Figure 2 As shown, the following steps are included:

[0071] Step 1: Measure the resonant frequency f0 and quality factor Q0 of the resonant cavity in the cavity state;

[0072] Step 2: Design a cylindrical resonant cavity with a radius a and a height l of 10.7 mm, working in TM 010 The measured resonant frequency of the mode cylindrical cavity is 10.737 GHz.

[0073]

[0074] c is the speed of light in free space, and the equivalent radius a of the cylindrical resonant cavity is calculated to be 10.693 mm;

[0075] The induced current f on the metal surface is represented by the RWG basis function defined on the triangular mesh. s , the generalized eigenvalue equation of the internal resonance of the cavity is established based on the electric field surface integral equation:

[0076] [Z Re (J s )][J s ]=α[Z Im (J s )][J s ] (2)

[0077]

[0078] Among them, J s (r') is the characteristic current at the source point r' on the inner surface S0 of the cavity, α is the characteristic value, Z Re and Z Im are the real and imaginary components of the impedance matrix operator Z, respectively, j is a complex unit, is the dyadic Green's function in free space, k0 and η0 are the wave number and wave impedance in free space, is the gradient operator about the source point r', is the gradient operator with respect to the field point r;

[0079] Solve equation (2) and calculate the internal resonance factor β of the first 40 modes at frequency f0 m ;

[0080]

[0081] E m =-Z(v m ·f s ) (5)

[0082]

[0083] Among them, R m is the equivalent microwave surface resistance of the metal cavity wall in the mth mode, the subscript m represents the mode number, M=max(R1,…R m ,…R g ), S r By moving S0 outward along the normal direction d0, v m is the eigenvector, k is the unit vector of the propagation direction of the electromagnetic wave;

[0084] Find the equation with the minimum β m The mode number r is used to calculate the equivalent microwave surface resistance R of the metal cavity wall based on the electric field E, magnetic field H and Q0 of mode r. s ;

[0085]

[0086] The equivalent microwave surface resistance R of the metal cavity wall is calculated s 4.9372E7S / m;

[0087] Step 3: Measure the resonant frequency f after the irregular material is placed in the resonant cavity d and quality factor Q d ; Using the RWG basis function f defined on the triangular mesh s represents the induced current J on the metal surface s , using the SWG basis function f defined on the tetrahedral mesh v Represents the induced current J of irregular materials v ; Establish the volume integral equation as follows:

[0088]

[0089] Where μ0 is the magnetic permeability in free space, E inc is the external incident electric field (0 in the resonant cavity), E total is the total electric field, V d is an irregular material body, and the subscript tan represents the tangential component;

[0090] Substitute the impedance matrix [Z] of the volume integral equation into the generalized eigenvalue equation:

[0091] [Z Im ] sub J sn =α[Z Re ] sub J sn (10)

[0092] [Z] sub =[Z ss ]-[Z sv ][Z vv ] -1 [Z vs ] (11)

[0093] Among them, [Z ss ] and [Z vv ] are the self-impedance matrices of surface current and volume current, [Z sv ] and [Z vs ] is the mutual impedance matrix of surface current and volume current, J sn is the surface characteristic current, α is the characteristic value, and the subscripts Im and Re represent the imaginary and real parts, respectively;

[0094] Set the relative dielectric constant ε to be measured r 'Analysis range [ε r1 ',ε r2 '], at frequency f d Solve equation (10) at different ε r 'The corresponding mode factor γ;

[0095]

[0096] E=-Z ss (v s ·f s )-Z vv (-[Z vv ] -1 [Z vs ]v s ·f v ) (13)

[0097]

[0098] Where N = max(T, ε r '∈[ε r1 ',ε r2 ']), S r The inner surface S0 of the cavity is moved outward along the normal direction by d0, v s is the eigenvector of pattern r;

[0099] Find the minimum mode factor γ min , the corresponding ε r ' is the relative complex permittivity of the irregular material;

[0100] Step 4: Convert the obtained ε r ' and R s Substitute Q d The calculation formula is used to invert the frequency f d The loss tangent to be measured is tgδ;

[0101]

[0102] Where E and H are the frequency f of mode r after loading the irregular material. d The electric and magnetic fields at H t is the tangential component of H, and V0 is the part of the cavity excluding the sample.

[0103] Figure 3 The eigenvalue curves of different modes in the cavity calculated by the method of the present invention are given. Since we only focus on curves with eigenvalues ​​of 0, to avoid too many curves being confused, only the first four mode curves with eigenvalues ​​of 0 are given. From the figure, we can get the cavity f0.

[0104] Figure 4 The internal resonance factors of the first 40 modes at frequency f0 are given. It can be seen from the figure that mode 1 corresponding to the minimum internal resonance factor of 0.00111 is the internal resonance mode.

[0105] Figure 5 The corresponding frequency f of mode 1 after loading of a sample with a diameter of 1.60 mm is given. d The mode factor curve calculated when Figure 6 The corresponding frequency f of mode 1 after loading of a sample with a diameter of 0.97 mm is given. d The mode factor curve calculated when the relative dielectric constant ε r The analysis range is [1, 30]. As can be seen from the figure, the ε corresponding to the minimum mode factor is r ' is the value to be evaluated.

[0106] Table 1 shows the complex dielectric constant results calculated by the embodiments of the present invention. Due to the large sample size, the perturbation method is not applicable. In addition, since the 0.97 mm diameter sample was not placed in the center, only the 1.60 mm diameter sample was calculated using the pattern matching method for comparison. As can be seen from Table 1, the relative dielectric constant and loss tangent obtained by the method of the present invention have a very small test error compared with the results obtained by the pattern matching method, indicating that the method of the present invention can accurately measure the complex dielectric constant of irregular materials.

[0107] Table 1 Resonant frequency, quality factor and complex dielectric constant test values ​​of the sample before and after loading

[0108]

[0109] The above description is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equivalent or alternative features with similar purposes; all disclosed features, or all steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for measuring the complex dielectric constant of irregular materials based on a resonant cavity, characterized in that: The following steps are involved: Step 1: Measure the resonant frequency f0 and quality factor Q0 of the resonant cavity in the cavity state; Step 2: Geometrically model the empty resonant cavity, establish the generalized eigenvalue equation of internal resonance, solve the internal resonance mode number r at frequency f0, and then solve the equivalent microwave surface resistance R of the metal cavity wall based on the quality factor Q0, the electric field E and magnetic field H under the internal resonance mode corresponding to the internal resonance mode number r. s ; Step 3: Measure the resonant frequency f after the irregular material to be tested is placed in the resonant cavity d and quality factor Q d , geometric modeling of the material to be tested and the cavity is performed according to the placement of the irregular material to be tested; the modeled grid data is substituted into the generalized eigenvalue equation based on the volume integral equation, and the relative dielectric constant ε of the irregular material to be tested is set r 'Analysis range, within the analysis range with a certain step, calculate the resonance mode of the cavity at the frequency f d Different time r 'Corresponding mode factor γ, find the minimum mode factor γ min , the corresponding ε r ' is the relative dielectric constant of the irregular material; Step 4: Substitute the ε obtained in step 3 r ' and R obtained in step 2 s Substitute Q d The calculation formula is used to invert the frequency f d The loss tangent tgδ to be measured.

2. The method for measuring the complex dielectric constant of irregular materials according to claim 1, wherein: The specific process of step 2 is: The induced current f on the metal surface is represented by the RWG basis function defined on the triangular mesh. s , the generalized eigenvalue equation of the internal resonance of the cavity is established based on the electric field surface integral equation: [FROM Re (J s )][J s ]=α[Z Im (J s )][J s ] (1) Among them, J s (r') is the characteristic current at the source point r' on the inner surface S0 of the cavity, α is the characteristic value, Z Re and Z Im are the real and imaginary components of the impedance matrix operator Z, respectively, j is a complex unit, is the dyadic Green's function in free space, k0 and η0 are the wave number and wave impedance in free space, is the gradient operator about the source point r', is the gradient operator with respect to the field point r; Solve the generalized eigenvalue equation of internal resonance, arrange the eigenvalues ​​from large to small, and calculate the internal resonance factor β of the first g modes at frequency f0 m ; E m =-Z(in m ·f s ) (4) Among them, R m is the equivalent microwave surface resistance of the metal cavity wall in the mth mode, the subscript m represents the mode number, M=max(R1,…R m ,…R g ), S r By moving S0 outward along the normal direction d0, v m is the eigenvector, k is the unit vector of the propagation direction of the electromagnetic wave; Find the equation with the minimum β m The mode number r is used to calculate the equivalent microwave surface resistance R of the metal cavity wall according to the electric field E, magnetic field H and Q0 under the internal resonance mode corresponding to the mode number r. s ; Where ε0 is the dielectric constant in free space, ω0 is the angular frequency, and H t is the tangential component of H, and V0 is the cavity area.

3. The method for measuring the complex dielectric constant of irregular materials according to claim 2, wherein: The number of characteristic modes g is 40.

4. The method for measuring the complex dielectric constant of irregular materials according to claim 2, wherein: In step 2, the distance d0 is 0.05 free-space wavelengths.

5. The method for measuring the complex dielectric constant of irregular materials according to claim 1, wherein: In step 2, before solving the internal resonance eigenvalue equation, the size of the resonant cavity is corrected. The specific process is as follows: Set the frequency range [f0-f1, f0+f1], solve equation (1), arrange the eigenmodes according to the absolute value of the eigenvalue from large to small, and find the internal resonant frequency f0' with at least two zero eigenvalues ​​from the first g modes. The equivalent size of the resonant cavity is modified so that f0'=f0. According to the adjusted size, the cavity geometry modeling is repeated, and then the internal resonance eigenvalue equation is solved.

6. The method for measuring the complex dielectric constant of irregular materials according to claim 5, wherein: f1 is 200MHz.

7. The method for measuring the complex dielectric constant of irregular materials according to claim 5, wherein: If the resonant cavity is a cylindrical cavity, the specific process of correcting the equivalent size of the resonant cavity is: The radius is a, the height is l, and it works at TE 111 ,TM 010 The resonant frequencies of the mode cylindrical cavities are c is the speed of light in free space. According to the relationship between f0' and f0, adjust the corresponding resonant cavity structure parameters a and l to make f0'=f0; If the resonant cavity is a rectangular cavity, the specific process of correcting the equivalent size of the resonant cavity is: The size is a×b×l, and it works on TE 101 The resonant frequency of the mode rectangular cavity is According to the size relationship between f0' and f0, the corresponding resonant cavity structure parameters a and l are adjusted to set f0'=f0.

8. The method for measuring the complex dielectric constant of irregular materials according to claim 1, wherein: The specific process of step 3 is: Step 3.

1. Measure the resonant frequency f after the irregular material is placed in the resonant cavity d and quality factor Q d ; Step 3.

2. Use the RWG basis function f defined on the triangle mesh s represents the induced current J on the metal surface s , using the SWG basis function f defined on the tetrahedral mesh v Represents the induced current J of irregular materials v , establish the volume integral equation, as follows: Where μ0 is the magnetic permeability in free space, E inc is the external incident electric field, E total is the total electric field, V d is an irregular material body, and the subscript tan represents the tangential component; Step 3.

3. Substitute the impedance matrix [Z] of the volume integral equation into the generalized eigenvalue equation: [WITH Im ] sub J sn =α[Z Re ] sub J sn (9) [WITH] sub =[Z ss ]-[WITH sv ][WITH vv ] 1 [WITH vs ] (10) Among them, [Z ss ] and [Z vv ] are the self-impedance matrices of surface current and volume current, [Z sv ] and [Z vs ] is the mutual impedance matrix of surface current and volume current, J sn is the surface characteristic current, α is the characteristic value, and the subscripts Im and Re represent the imaginary and real parts, respectively; Step 3.

4. Set the relative dielectric constant ε to be measured based on experience r 'Analysis range [ε r1 ',ε r2 '], with a certain step, in different ε r ', frequency f d Solve equation (9) to obtain the electric field E and magnetic field H, and then calculate the mode corresponding to the mode number r under different ε r 'The corresponding mode factor γ; E=-Z ss (in s ·f s )-Z vv (-[Z vv ] -1 [With vs ]v s ·f v ) (12) Where N = max(T, ε r '∈[ε r1 ',ε r2 ']), S r The inner surface S0 of the cavity is moved outward along the normal direction by d0, v s is the eigenvector of pattern r; Step 3.

5. Find the minimum mode factor γ min , the corresponding ε r ' is the relative complex permittivity of the irregular material.

9. The method for measuring the complex dielectric constant of irregular materials according to claim 8, wherein: The analysis range in step 3.4 [ε r1 ',ε r2 '] is [1, 30].

10. The method for measuring the complex dielectric constant of irregular materials according to claim 2, wherein: The specific calculation formula for step 4 is: Where E and H are the frequency f of mode r after loading the irregular material. d The electric and magnetic fields at H t is the tangential component of H, and V0 is the part of the cavity excluding the sample.

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