Medium loading resonant cavity analysis method based on volume-surface integral equation

Abstract

The invention provides a medium loading resonant cavity analysis method based on a volume-surface integral equation, and belongs to the technical field of resonance characteristic numerical analysis. According to the method, an internal resonance generalized eigenvalue equation based on a body-surface integral equation and internal resonance factors representing internal resonance attributes of body and surface current characteristic modes are defined, so that accurate solution of a unique internal resonance mode is realized; the method avoids the problem that the traditional characteristic value method is difficult to directly solve the internal resonance mode and the mode field of the metal cavity with the aperture after the medium is loaded, is suitable for the loading medium and the metal cavity with any shape and placement relation, and achieves accurate modeling through the volume-surface mixed grid on the premise of guaranteeing the solving precision. Compared with a finite element method, the method has lower modeling complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical analysis of resonance characteristics, and in particular relates to a dielectric-loaded resonant cavity analysis method based on a volume integral equation. Background Art

[0002] In a microwave resonant cavity, loading media can be used to improve the quality factor of the resonant cavity or achieve multi-mode resonance. By introducing materials with specific electromagnetic properties into the resonant cavity, it can help to realize high-sensitivity filters or sensors. When the shape of the medium or cavity is irregular, the mode distribution in the cavity is complex and difficult to describe with analytical field solutions. In order to efficiently analyze the resonance problems of such complex structures, numerical methods are usually used for accurate solutions. It is worth noting that due to the presence of coupling and tuning holes on the cavity wall, and the size of the loading medium is generally much smaller than the cavity, these size differences lead to the generation of multi-scale geometric modeling problems. The finite element method is often used to analyze the resonant characteristics of a dielectric-loaded metal cavity of arbitrary shape, but due to the presence of holes, the number of unit cell grids increases sharply, making it even more difficult to avoid the generation of deformed grids.

[0003] The eigenmode theory based on the method of moments avoids these modeling shortcomings. It utilizes the high-precision, low-complexity geometric modeling of the method of moments to construct the eigenmode problem, accurately solving the resonant characteristics and mode fields of the external resonant modes. However, the resonant characteristics of dielectric-loaded cavities are internal resonance problems. Limited by the definition of infinite eigenvalues for internal resonant modes, methods that rely solely on finding the external resonant mode with a unique zero eigenvalue are no longer applicable in cavity analysis. This is particularly true in slotted cavities, where the absence of a unique internal resonant eigenvalue complicates analysis.

[0004] A SIE-based method for analyzing the resonant characteristics of open-hole metal cavities describes how to establish a generalized eigenvalue equation for the internal resonance of an open-hole metal cavity based on its characteristic modes and solve for the internal resonant mode fields. This method only analyzes metal cavities and is not applicable to dielectric-loaded metal cavities. Therefore, a method is needed that can better study the resonant characteristics of dielectric-loaded cavities of arbitrary shapes. Summary of the Invention

[0005] To address the challenges presented by the prior art, the present invention aims to provide a method for analyzing dielectric-loaded resonant cavities based on surface integral equations. This method, based on surface integral equations, solves the resonant characteristics and mode fields of resonant modes within a metal cavity loaded with dielectrics. While ensuring accurate solution accuracy, it achieves accurate modeling through a volume-surface hybrid mesh, resulting in a lower modeling complexity than the finite element method.

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

[0007] A dielectric-loaded resonant cavity analysis method based on a volume integral equation comprises the following steps:

[0008] Step 1: Use computer modeling software to model the dielectric-loaded resonant cavity: use triangular meshes to conformally mesh the inner surface of the metal cavity, use tetrahedral meshes to conformally mesh the dielectric body, and define the RWG basis function f on the triangular face element. s Indicates the surface current J s , define the SWG basis function f on the tetrahedral element v Represents the body current J v ;

[0009] Step 2: Set the surface current J s and body current J v Substitute into the volume integral equation and combine with the Galerkin method to obtain the moment method impedance matrix 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 bulk current;

[0010] Step 3: Construct the generalized eigenvalue equation of internal resonance: According to the condition that there is no external excitation source in the cavity, obtain [Z vs ]J s +[Z vv ]J v = 0, and substitute into the moment method impedance matrix [Z] to obtain the new equation [Z] sub J s =0, based on [Z] sub =[Z ss ]-[Z sv ][Z vv ] -1 [Z vs ]Construct the generalized eigenvalue equation of internal resonance[Z Re ] sub J sn =α[Z Im ] sub J sn ;

[0011] Among them, J sn is the surface characteristic current, α is the characteristic value, and the subscripts Re and Im represent the real and imaginary parts, respectively;

[0012] Step 4: Solve the generalized eigenvalue equation of the internal resonance in the frequency range of interest to obtain the eigenvalue:

[0013] Arrange the modes from large to small according to the absolute value of the eigenvalue. In the frequency range of interest, the frequency and the eigenvalue correspond one to one to form an eigenvalue curve. Analyze the slope of each point on the eigenvalue curve of the first g modes, filter out the slope discontinuity point and set the eigenvalue of the point to 0, and find the internal resonant frequency f with t zero eigenvalues at the same time. r ;

[0014] Step 5: Solve for the frequency f r The generalized eigenvalue equation of intra-time resonance is used to obtain the first g modes related to J sn The associated eigenvector v s , calculated with the body characteristic current J vn The associated eigenvector v v , v v =-[Z vv ] -1 [Z vs ]v s ;

[0015] Step 6: Based on the feature vector v obtained in step 5 s and the eigenvector v v Calculate the internal resonance factor β of the first g modes m :

[0016]

[0017] Wherein, the subscript m represents the mth mode, M=max(R1,…,R m ,…,R g ), point r is the surface S r Point on S r The electric field E is obtained by moving the inner surface S0 of the cavity outward along the normal direction by a distance d. m =-Z ss (v sm ·f s )-Z vv (v vm ·f v ),magnetic field η0 is the wave impedance in free space, k is the unit vector of the electromagnetic wave propagation direction;

[0018] Step 7: Find the minimum β m , the mode numbered m corresponds to the internal resonance mode, based on the J sn and J vn The jointly generated electric field E and magnetic field H are used to calculate the loaded quality factor Q.

[0019] Furthermore, in step 4, the frequency range of interest is any continuous frequency interval within the microwave frequency band, and the frequency interval is ≤10 MHz.

[0020] Furthermore, in step 4, the calculated frequency interval is adjusted according to the frequency accuracy requirement of the frequency of interest, and then step 4 is repeated until the required accuracy of f is obtained. r .

[0021] Furthermore, in step 4, the number g of characteristic patterns is preferably 40.

[0022] Furthermore, in step 4, t≥2.

[0023] Furthermore, in step 6, the outward shift distance d is preferably 0.05λ, where λ is the free space wavelength.

[0024] Furthermore, in step 7, the specific calculation process of the loaded quality factor Q is:

[0025]

[0026] Where ε0 is the dielectric constant of free space, ε r Is the dielectric V d The relative dielectric constant, V0, is the dielectric constant of the cavity without V d For the rest of the part, tgδ is the loss tangent of the dielectric body, ω0 is the angular frequency, and R s is the microwave surface resistance of the metal cavity wall, H t is the tangential component of H.

[0027] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0028] (1) The dielectric-loaded resonant cavity analysis method proposed in the present invention, by defining the generalized eigenvalue equation of internal resonance based on the volume integral equation and the internal resonance factor that characterizes the internal resonance properties of the volume and surface current characteristic modes, achieves the accurate solution of the unique internal resonant mode, avoiding the problem that the traditional eigenvalue method is difficult to directly solve the internal resonant mode and mode field of the metal cavity with a hole after the dielectric is loaded.

[0029] (2) The dielectric-loaded resonant cavity analysis method based on the volume integral equation proposed in the present invention is a full-wave numerical method, and is therefore applicable to loaded media and metal cavities of arbitrary shapes and placement relationships. At the same time, triangular and tetrahedral meshes are used to segment and model dielectric-loaded cavities of arbitrary shapes and multi-scales, integrating the low-complexity geometric modeling advantages of the volume integral equation method, and having the characteristics of easy modeling and accurate solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a structural diagram of a local field compression metal cavity with a circular dielectric rod inserted into a circular hole in Example 1 of the present invention.

[0031] Figure 2Schematic diagram of the flow of the dielectric-loaded resonant cavity analysis method based on the volume integral equation in Example 1 of the present invention.

[0032] Figure 3 These are characteristic value curves of different modes calculated in Example 1 of the present invention.

[0033] Figure 4 These are the resonance factor curves of different modes calculated in Example 1 of the present invention.

[0034] Figure 5 1 is a comparison of the normalized distribution diagrams of the internal resonant electric field calculated by the HFSS software and the method of the present invention at the y=38.75 mm section in Example 1 of the present invention.

[0035] Figure 6 This is a structural diagram of a cylindrical metal cavity with a circular hole in which a rectangular dielectric rod is partially inserted according to Example 2 of the present invention.

[0036] Figure 7 These are characteristic value curves of different modes calculated in Example 2 of the present invention.

[0037] Figure 8 These are the resonance factor curves of different modes calculated in Example 2 of the present invention.

[0038] Figure 9 3. Comparison of the normalized distribution diagrams of the internal resonant electric field on the xoz plane calculated by the HFSS software and the method of the present invention in Example 2 of the present invention. DETAILED DESCRIPTION

[0039] 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.

[0040] Example 1

[0041] A dielectric-loaded resonant cavity analysis method based on the volume integral equation is proposed. The resonant cavity is a dielectric-loaded metal cavity. The metal cavity is a local field compression cavity. There is a 5mm radius circular hole at the field compression position on the upper surface. A cylindrical dielectric rod with a radius of 4mm is inserted in the center of the circular hole. The relative dielectric constant ε of the medium is r is 6, the loss tangent tgδ is 0.0023, and the microwave surface resistance Rs of the metal cavity wall is 5.8×10 7 S / m, the structure of the dielectric and metal cavity Figure 1 As shown;

[0042] The schematic flow diagram of the analytical method of the present invention is as follows Figure 2 As shown, the following steps are included:

[0043] Step 1: Use computer modeling software to model the dielectric-loaded resonant cavity. Use triangular meshes to conformally mesh the inner surface of the metal cavity and tetrahedral meshes to conformally mesh the dielectric body. Define the RWG basis function f on the triangular face element. s Indicates the surface current J s , define the SWG basis function f on the tetrahedral element v Represents the body current J v ;

[0044] Step 2: Substitute into the volume integral equation as follows:

[0045]

[0046] in,

[0047]

[0048] Where j is a complex unit, is the scattered electric field of the cavity inner surface S0, Is the dielectric V d The scattered electric field, E inc (r) is the external incident electric field (E inc (r)=0), E(r) is the total electric field, ω0 is the angular frequency, μ0 is the magnetic permeability in free space, r is the position vector of the field point, r' is the position vector of the source point, is the dyadic Green's function in free space;

[0049] Combined with the Galerkin method to obtain the moment method impedance matrix 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 bulk current;

[0050] Step 3: Construct the generalized eigenvalue equation of internal resonance: According to the condition that there is no external excitation source in the cavity, obtain [Z vs ]J s +[Z vv ]J v = 0, and substitute into the moment method impedance matrix [Z] to obtain the new equation [Z] sub J s =0, and then based on [Z] sub =[Z ss ]-[Z sv ][Z vv ] -1 [Z vs ]Construct the generalized eigenvalue equation of internal resonance[Z Re ]sub J sn =α[Z Im ] sub J sn ;

[0051] Among them, J sn is the surface characteristic current, α is the characteristic value, and the subscripts Re and Im represent the real and imaginary parts, respectively;

[0052] Step 4: Solve the generalized eigenvalue equation of the internal resonance in the frequency range of 2 GHz to 3 GHz with a frequency interval of 10 MHz to obtain the eigenvalue; arrange the modes from large to small according to the absolute value of the eigenvalue, analyze the slope of each point on the eigenvalue curve of the first 40 modes, filter out the slope discontinuity points and set their eigenvalues to 0, and find the internal resonance frequency f with multiple zero eigenvalues at the same time. r ;

[0053] Furthermore, according to the frequency accuracy requirements, the calculation frequency interval can be reduced and step 4 can be repeated until the required accuracy of f is obtained. r ;

[0054] In the frequency range of interest, frequencies and eigenvalues correspond one to one to form a curve. Figure 3 The eigenvalue curves of different modes 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 shown in the figure. The calculation frequency interval is 10MHz, and the resonant frequency is found to be around 2.44GHz. The calculation frequency interval is set to 1MHz, and the final result is 2.435GHz.

[0055] Step 5: Solve for the frequency f r The generalized eigenvalue equation of intra-time resonance is used to obtain the J sn The associated eigenvector v s , calculate the body characteristic current J vn The eigenvector v v =-[Z vv ] -1 [Z vs ]v s ;

[0056] Calculate the internal resonance factors of the first g modes Wherein, the subscript m represents the mode number, M=max(R1,LR m L,R g ), point r is the surface S r Point on S r The electric field E is obtained by moving the inner surface S0 of the cavity outward by 0.05 free space wavelength along the normal direction. m =-Zss (v sm ·f s )-Z vv (v vm ·f v ),magnetic field η0 is the wave impedance in free space, k is the unit vector of the electromagnetic wave propagation direction;

[0057] Step 6: Find the minimum β m , get the internal resonance mode number, based on the J sn and J vn The jointly generated electric field E and magnetic field H are used to calculate the loaded quality factor Q;

[0058] The calculation of Q is as follows:

[0059]

[0060] Where ε0 is the dielectric constant of free space, ε r Is the dielectric V d The relative dielectric constant, V0, is the dielectric constant of the cavity without V d For the rest of the part, tgδ is the loss tangent of the dielectric body, ω0 is the angular frequency, and R s is the microwave surface resistance of the metal cavity wall, H t is the tangential component of H.

[0061] Figure 4 The internal resonance factors of the first 40 modes at 2.435 GHz are given. It can be seen from the figure that mode 17 with the smallest internal resonance factor of 0.0048 is the internal resonance mode.

[0062] Figure 5 The normalized distribution of the internal resonant electric field calculated by HFSS software and the method of the present invention on the y=38.75mm section is given. The consistency of the results of the present method and HFSS can be seen from the comparison of the results of the two methods. Table 1 shows the calculation results of the resonance parameters using the method of the present invention and HFSS software respectively, and compares the meshing conditions, resonant frequency and quality factor calculation values of the different methods. The consistency of the results of the present method and HFSS software method can be seen from the calculation results. It illustrates the accuracy of the method of the present invention in analyzing the resonance characteristics of a dielectric-loaded metal cavity, and at the same time, it can significantly reduce the complexity of geometric modeling compared with the finite element method used by HFSS software.

[0063] Table 1 Comparison of solution results between the method of the present invention and the HFSS method

[0064] Mesh division Resonant frequency (GHz) Quality factor Method of the present invention 1206 (triangle) 444 (tetrahedron) 2.435 8641.96 HFSS simulation 289467 (tetrahedron) 2.435 8628.61

[0065] Example 2

[0066] This example calculates the resonance characteristics of a dielectric-loaded metal cavity at frequencies of 5 GHz to 6 GHz, with a frequency interval of 5 MHz. The metal cavity is a cylindrical cavity with a small circular hole in the center. A rectangular dielectric rod is placed adjacent to the hole, and the dielectric rod is partially inserted into the cylindrical cavity. The relative dielectric constant ε of the medium is r is 9.5, the loss tangent tgδ is 0.00002, and the microwave surface resistance Rs of the metal cavity wall is 5.8×10 7 S / m, the structure of the dielectric and metal cavity Figure 6 shown.

[0067] Figure 7 The eigenvalue curves of the characteristic modes calculated by the method of the present invention are shown. Since we are only interested in curves with eigenvalues of 0, to avoid curve confusion, only the curves of the first six modes with eigenvalues of 0 are shown. The calculation frequency interval is 5 MHz, and the resonant frequency is found to be around 5.695 GHz. The calculation frequency interval is set to 1 MHz and the final result is obtained.

[0068] Figure 8 The internal resonance factors of the first 40 characteristic modes at 5.696 GHz are given. It can be seen from the figure that mode 1 is the internal resonance mode.

[0069] Figure 9 The normalized distribution of the internal resonant electric field on the xoz surface calculated by HFSS software and the method of the present invention is given. The consistency of the results of the present method and HFSS can be seen from the comparison of the results of the two methods.

[0070] Table 2 shows the calculation results using the method of the present invention and HFSS software, respectively, indicating that the method of the present invention can significantly reduce the complexity of geometric modeling while accurately obtaining the calculation results when analyzing the resonance characteristics of the dielectric-loaded metal cavity.

[0071] Table 2 Comparison of the solution results of the method of the present invention and the HFSS method

[0072] Mesh division Resonant frequency (GHz) Quality factor Method of the present invention 499 (triangle) 518 (tetrahedron) 5.696 7655.42 HFSS simulation 58153 (tetrahedron) 5.696 7651.91

[0073] 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 dielectric-loaded resonant cavity analysis method based on volume integral equation, characterized in that: The following steps are involved: Step 1: Use computer modeling software to model the dielectric-loaded resonant cavity: use triangular meshes to conformally mesh the inner surface of the metal cavity, use tetrahedral meshes to conformally mesh the dielectric body, and define the RWG basis function f on the triangular face element. s Indicates the surface current J s , define the SWG basis function f on the tetrahedral element v Represents the body current J v ; Step 2: Set the surface current J s and body current J v Substitute into the volume integral equation and combine with the Galerkin method to obtain the moment method impedance matrix 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 bulk current; Step 3: Construct the generalized eigenvalue equation of internal resonance: According to the condition that there is no external excitation source in the cavity, obtain [Z vs ]J s +[Z vv ]J v = 0, and substitute into the moment method impedance matrix [Z] to obtain the new equation [Z] sub J s =0, based on [Z] sub =[Z ss ]-[Z sv ][Z vv ] -1 [Z vs ]Construct the generalized eigenvalue equation of internal resonance[Z Re ] sub J sn =α[Z Im ] sub J sn ; Among them, J sn is the surface characteristic current, α is the characteristic value, and the subscripts Re and Im represent the real and imaginary parts, respectively; Step 4: Solve the generalized eigenvalue equation of the internal resonance in the frequency range of interest to obtain the eigenvalue: Arrange the modes from large to small according to the absolute value of the eigenvalue. In the frequency range of interest, the frequency and the eigenvalue correspond one to one to form an eigenvalue curve. Analyze the slope of each point on the eigenvalue curve of the first g modes, filter out the slope discontinuity point and set the eigenvalue of the point to 0, and find the internal resonant frequency f with t zero eigenvalues at the same time. r ; Step 5: Solve for the frequency f r The generalized eigenvalue equation of intra-time resonance is used to obtain the first g modes related to J sn The associated eigenvector v s , calculated with the body characteristic current J vn The associated eigenvector v v , v v =-[Z vv ] -1 [Z vs ]v s ; Step 6: Based on the feature vector v obtained in step 5 s and the eigenvector v v Calculate the internal resonance factor β of the first g modes m : Wherein, the subscript m represents the mth mode, M=max(R1,…,R m ,…,R g ), point r is the surface S r Point on S r The electric field E is obtained by moving the inner surface S0 of the cavity outward along the normal direction by a distance d. m =-Z ss (v sm ·f s )-Z vv (v vm ·f v ),magnetic field η0 is the wave impedance in free space, k is the unit vector of the electromagnetic wave propagation direction; Step 7: Find the minimum β m , the mode numbered m corresponds to the internal resonance mode, based on the J sn and J vn The jointly generated electric field E and magnetic field H are used to calculate the loaded quality factor Q.

2. The dielectric-loaded resonant cavity analysis method according to claim 1, wherein: In step 4, the frequency range of interest is any continuous frequency interval within the microwave frequency band, and the frequency interval is ≤10 MHz.

3. The dielectric-loaded resonant cavity analysis method according to claim 1, wherein: In step 4, adjust the frequency interval according to the frequency accuracy requirement of the frequency of interest, and then repeat step 4 until the required accuracy of f is obtained. r .

4. The dielectric-loaded resonant cavity analysis method according to claim 1, wherein: In step 4, the number of characteristic patterns g is 40.

5. The dielectric-loaded resonant cavity analysis method according to claim 1, wherein: In step 4, t≥2.

6. The dielectric-loaded resonant cavity analysis method according to claim 1, wherein: In step 6, the outward shift distance d is 0.05λ, where λ is the free space wavelength.

7. The dielectric-loaded resonant cavity analysis method according to claim 1, wherein: In step 7, the specific calculation process of the loaded quality factor Q is: Where ε0 is the dielectric constant of free space, ε r Is the dielectric V d The relative dielectric constant, V0, is the dielectric constant of the cavity without V d For the rest of the part, tgδ is the loss tangent of the dielectric body, ω0 is the angular frequency, and R s is the microwave surface resistance of the metal cavity wall, H t is the tangential component of H.

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