A method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials

Abstract

The present invention discloses a method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials, and the steps are: 1) establishing expressions of scattering parameters, relative dielectric constant and relative magnetic permeability of magnetic materials; 2) establishing a magnetic material simulation model according to the periodic structure Floquet theorem; 3) setting master-slave boundary conditions and Floquet ports of the magnetic material simulation model; 4) applying excitation to the magnetic material simulation model to obtain the electromagnetic parameters of the magnetic material. The present invention can extract the electromagnetic parameters of single-layer, multi-layer non-uniform and complex-structured magnetic materials in the low-frequency range, and make multi-layer non-uniform and complex-structured magnetic materials equivalent to single-layer uniform magnetic materials.

Description

Technical Field

[0001] The invention relates to the field of electromagnetic compatibility, and in particular to a method for extracting low-frequency equivalent electromagnetic parameters of complex multi-layer magnetic materials. Background Art

[0002] Electromagnetic parameters are important physical parameters of complex electromagnetic functional materials, which determine the application performance of electromagnetic functional materials in radar detection, electronic countermeasures, stealth materials, food processing, geological exploration, biomedicine and other fields. With the demand for high performance of strong electromagnetic equipment in various fields, low-frequency magnetic materials are gradually developing in the direction of composite and multi-layer. Accurately extracting the equivalent electromagnetic parameters of complex multi-layer magnetic materials has become the key and bottleneck in the design of magnetic performance of strong electromagnetic equipment.

[0003] At present, most methods use waveguide or reflection methods to extract electromagnetic parameters of materials, but ignore the particularity of extracting electromagnetic parameters of materials in the low-frequency range. In the field of ships, the strong electromagnetic equipment of various systems are mostly magnetic materials and are in a low-frequency electromagnetic environment. It is necessary to extract equivalent electromagnetic parameters for magnetic materials at low frequencies, and to make multi-layer non-uniform or complex-structured magnetic materials equivalent to single-layer uniform magnetic materials, and establish an equivalent electromagnetic parameter model, which lays the foundation for the low-frequency magnetic field distribution of strong electromagnetic equipment and the evaluation of the magnetic properties of strong electromagnetic equipment. Summary of the invention

[0004] The purpose of the present invention is to provide a method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials, comprising the following steps:

[0005] 1) Establish expressions for the scattering parameters, relative dielectric constant and relative magnetic permeability of magnetic materials.

[0006] The steps of establishing the expressions of scattering parameters of magnetic materials, relative dielectric constant and relative magnetic permeability of magnetic materials include:

[0007] 1.1) Let the electromagnetic wave pass through the magnetic material, and establish the relationship between the scattering parameters of the magnetic material based on the effect of the magnetic material on the vertically incident electromagnetic wave, that is:

[0008]

[0009]

[0010] In the formula, Γ represents the reflection coefficient of the plane wave propagating from the air to the boundary surface of the magnetic material, and T represents the transmission coefficient of the plane wave between the two surfaces of the magnetic material with a thickness of d. 11 is the reflection coefficient of the magnetic material. S 21 is the transmission coefficient of the magnetic material.

[0011] 1.2) Performing geometric series on formula (1) and formula (2), we get:

[0012]

[0013] 1.3) The reflection coefficient S of the magnetic material 11 and the transmission coefficient S of the magnetic material 21 Expressed in S parameters, we get:

[0014]

[0015] In the formula, K is an intermediate variable.

[0016] 1.4) Establish the relationship between the reflection coefficient Γ of the plane wave propagating from the air to the boundary surface of the dielectric plate, the transmission coefficient T of the plane wave between the two surfaces of the medium with a thickness of d, and the relative dielectric constant and relative magnetic permeability of the magnetic material, that is:

[0017]

[0018]

[0019] In the formula, ε r and μ r They represent the relative permittivity and relative permeability of the magnetic material respectively. k0 represents the wave number of the electromagnetic wave in free space. d represents the thickness of the magnetic material.

[0020] 1.5) Establish the relative dielectric constant ε r and relative magnetic permeability μ r The expression is:

[0021]

[0022] In the formula, the parameters

[0023] 2) Based on the periodic structure Floquet theorem, a magnetic material simulation model is established.

[0024] Tools for building simulation models of magnetic materials include the three-dimensional full-wave electromagnetic field simulation software HFSS.

[0025] The simulation model of the magnetic material includes a plurality of magnetic material simulation units, and the size of each unit is recorded as dx×dy.

[0026] When the electric field E inc When the magnetic material is incident from a direction perpendicular to the xoy plane, the corresponding position (x i +md x ,y i +nd y ,zi ) is shown below:

[0027]

[0028]

[0029] Where α0 and β0 represent the phase difference per unit length along the x-axis and y-axis, respectively. and Indicates any position (x i ,y i ,z i ) is the electric and magnetic fields at .

[0030] 3) Set the master-slave boundary conditions and Floquet ports of the magnetic material simulation model.

[0031] The master-slave boundary conditions include that the boundary surface, shape, size, and direction of the UV coordinate system of the master boundary and the slave boundary are consistent.

[0032] The Floquet ports are arranged on the Z axis of the coordinate system and are located on the upper surface and the lower surface of the magnetic material.

[0033] 4) Apply excitation to the magnetic material simulation model to obtain the electromagnetic parameters of the magnetic material.

[0034] It is worth noting that, according to the principle of free space method, the present invention establishes simulation unit models of air boxes and magnetic materials in HFSS, a three-dimensional full-wave electromagnetic field simulation software, and sets excitation and boundary conditions. Then, through the scattering parameters obtained by simulation, an algorithm program is written according to the free space method to extract the equivalent electromagnetic parameters of multi-layer non-uniform and complex structure magnetic materials, and then according to the algorithm, the multi-layer non-uniform and complex structure magnetic materials are equivalent to a single-layer uniform magnetic material, and the equivalent effect is verified by comparing the scattering parameters before and after the equivalent.

[0035] The technical effect of the present invention is unquestionable. The present invention can effectively extract the electromagnetic parameters of single-layer, multi-layer, and complex structure magnetic materials at low frequencies by establishing an air box and a magnetic material simulation unit, and can thereby convert multi-layer non-uniform or complex structure magnetic materials into equivalent single-layer uniform magnetic materials. It can provide accurate magnetic material parameters for basic research and engineering design personnel, and can thereby greatly simplify the radiation interference model of strong electromagnetic equipment when studying the radiation interference, thereby greatly reducing the computational complexity and computational resource requirements of low-frequency electromagnetic field simulation.

[0036] The present invention proposes a method for extracting low-frequency equivalent electromagnetic parameters of complex multi-layer magnetic materials. The method accurately obtains the scattering parameters between the two ends of the magnetic material based on the free space method, and then inverts the uniform equivalent electromagnetic parameters of the multi-layer and complex structure magnetic materials. Furthermore, the multi-layer non-uniform or complex structure magnetic materials can be equivalent to a single-layer uniform magnetic material, laying a foundation for further simulation analysis and design of strong electromagnetic equipment.

[0037] The present invention can extract electromagnetic parameters of single-layer, multi-layer non-uniform and complex-structured magnetic materials in a low-frequency range, and make multi-layer non-uniform and complex-structured magnetic materials equivalent to single-layer uniform magnetic materials.

[0038] Compared with the transmission / reflection method based on rectangular waveguide which is limited by the frequency of the rectangular waveguide itself, the present invention has a wide application frequency range and is not limited by frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the effect of magnetic materials on vertically incident plane waves;

[0040] Figure 2 It is a schematic diagram of an infinite periodic structure;

[0041] Figure 3 Schematic diagram for setting master-slave boundary conditions;

[0042] Figure 4 Set up a schematic for the Floquet port;

[0043] Figure 5 It is a three-layer magnetic structural material;

[0044] Figure 6 The inversion results of electromagnetic parameters of three-layer magnetic structure materials; Figure 6 (a) is the inversion result of equivalent dielectric constant; Figure 6 (b) is the equivalent permeability inversion result;

[0045] Figure 7 Comparison of S parameters before and after equivalent inversion of three-layer magnetic structure materials; Figure 7 (a) is the amplitude comparison result of S11; Figure 7 (b) is the phase contrast result of S11; Figure 7 (c) is the amplitude comparison result of S21; Figure 7 (d) is the phase contrast result of S21;

[0046] Figure 8 It is a simulation model of magnetic material with single-layer metal mesh structure;

[0047] Fig. 9 This is the electromagnetic parameter inversion result of the single-layer metal mesh structure magnetic material; Fig. 9 (a) is the inversion result of equivalent dielectric constant; Fig. 9 (b) is the equivalent permeability inversion result;

[0048] Fig.10 Comparison of S parameters before and after equivalent inversion of single-layer metal mesh structure magnetic material; Fig.10 (a) is the amplitude comparison result of S11; Fig.10 (b) is the phase contrast result of S11; Fig.10 (c) is the amplitude comparison result of S21; Fig.10 (d) is the phase contrast result of S21; DETAILED DESCRIPTION

[0049] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0050] Embodiment 1:

[0051] See also Figures 1 to 10 , a method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials, comprising the following steps:

[0052] 1) Establish expressions for the scattering parameters, relative dielectric constant and relative magnetic permeability of magnetic materials.

[0053] The steps of establishing the expressions of scattering parameters of magnetic materials, relative dielectric constant and relative magnetic permeability of magnetic materials include:

[0054] 1.1) Let the electromagnetic wave pass through the magnetic material, and establish the relationship between the scattering parameters of the magnetic material based on the effect of the magnetic material on the vertically incident electromagnetic wave, that is:

[0055]

[0056]

[0057] In the formula, Γ represents the reflection coefficient of the plane wave propagating from the air to the boundary surface of the magnetic material, and T represents the transmission coefficient of the plane wave between the two surfaces of the magnetic material with a thickness of d. 11 is the reflection coefficient of the magnetic material. S 21 is the transmission coefficient of the magnetic material.

[0058] 1.2) Performing geometric series on formula (1) and formula (2), we get:

[0059]

[0060] 1.3) The reflection coefficient S of the magnetic material 11 and the transmission coefficient S of the magnetic material 21 Expressed in S parameters, we get:

[0061]

[0062] In the formula, K is an intermediate variable.

[0063] 1.4) Establish the relationship between the reflection coefficient Γ of the plane wave propagating from the air to the boundary surface of the dielectric plate, the transmission coefficient T of the plane wave between the two surfaces of the medium with a thickness of d, and the relative dielectric constant and relative magnetic permeability of the magnetic material, that is:

[0064]

[0065]

[0066] In the formula, ε r and μ r They represent the relative permittivity and relative permeability of the magnetic material respectively. k0 represents the wave number of the electromagnetic wave in free space. d represents the thickness of the magnetic material.

[0067] 1.5) Establish the relative dielectric constant ε r and relative magnetic permeability μ r The expression is:

[0068]

[0069] In the formula, the parameters

[0070] 2) Based on the periodic structure Floquet theorem, a magnetic material simulation model is established.

[0071] Tools for building simulation models of magnetic materials include the three-dimensional full-wave electromagnetic field simulation software HFSS.

[0072] The simulation model of the magnetic material includes a plurality of magnetic material simulation units, and the size of each unit is recorded as dx×dy.

[0073] When the electric field E inc When the magnetic material is incident from a direction perpendicular to the xoy plane, the corresponding position (x i +md x ,y i +nd y ,z i ) is shown below:

[0074]

[0075]

[0076] Where α0 and β0 represent the phase difference per unit length along the x-axis and y-axis, respectively. and Indicates any position (x i ,y i ,z i ) is the electric and magnetic fields at . m and n are the step sizes.

[0077] 3) Set the master-slave boundary conditions and Floquet ports of the magnetic material simulation model.

[0078] The master-slave boundary conditions include that the boundary surface, shape, size, and direction of the UV coordinate system of the master boundary and the slave boundary are consistent.

[0079] The Floquet ports are arranged on the Z axis of the coordinate system and are located on the upper surface and the lower surface of the magnetic material.

[0080] 4) Apply excitation to the magnetic material simulation model to obtain the electromagnetic parameters of the magnetic material.

[0081] Embodiment 2:

[0082] See also Figures 1 to 10 , a method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials, comprising the following steps:

[0083] (1) Based on the process of electromagnetic waves passing through magnetic materials, the relationship between the scattering parameters and the relative dielectric constant and relative magnetic permeability of the dielectric plate is derived.

[0084] The effect of magnetic materials on vertically incident plane waves is as follows: Figure 1 As shown, the scattering parameter expression can be obtained as follows:

[0085]

[0086]

[0087] Where Γ represents the reflection coefficient of the plane wave propagating from the air to the boundary surface of the dielectric plate, and T represents the transmission coefficient of the plane wave between the two surfaces of the dielectric with a thickness of d. Assume that the relative dielectric constant and relative magnetic permeability of the dielectric material are ε r and μ r , k0 represents the wave number of electromagnetic waves in free space, then the expressions of reflection coefficient and transmission coefficient are:

[0088]

[0089]

[0090] From the sum of geometric series, we know that:

[0091]

[0092] Therefore, the expressions of the total reflection coefficient and transmission coefficient are:

[0093]

[0094]

[0095] The reflection coefficient and transmission coefficient are then expressed as S parameters:

[0096]

[0097] Therefore, the relative dielectric constant ε can be obtained from equations (3) and (4): r and relative magnetic permeability μ r The expression is:

[0098]

[0099] (2) According to the periodic structure Floquet theorem, a simulation unit for magnetic materials is established in the three-dimensional full-wave electromagnetic field simulation software HFSS.

[0100] like Figure 2 As shown in the figure, it shows an infinite periodic structure composite material with periodic extension in the x direction and y direction, whose periodic dimensions are dx and dy respectively, and it is assumed that the electric field E inc The incident light is perpendicular to the xoy plane.

[0101] The space in front is because the excitation is a plane wave and the material is a periodic extended structure, so

[0102] The relationship between the electromagnetic field quantities of the units also shows periodicity. and Representation unit Any position within (x i ,y i ,z i ) at the location. Then the corresponding position (x i +md x ,y i +nd y ,z i ) can be expressed as:

[0103]

[0104]

[0105] Among them, α0 and β0 represent the phase difference per unit length along the x-axis and y-axis respectively, and these two quantities are related to the incident direction and frequency of the incident electromagnetic wave.

[0106] Floquet's theorem shows the relationship between the electromagnetic fields of each unit in an infinite periodic structure. When the electromagnetic field of a unit in a periodic structure is known, the electromagnetic field value of any unit can be obtained through the field relationship in the above formula. Therefore, it is only necessary to analyze one unit in the infinite periodic structure to obtain the electromagnetic field distribution of the entire material. The introduction of Floquet's theorem solves the problem of high computing resource consumption when solving the electromagnetic field of an infinite periodic structure.

[0107] (3) According to the Floquet theorem, master-slave boundary conditions and Floquet ports are set in the three-dimensional full-wave simulation software HFSS.

[0108] The specific implementation steps are as follows: Figure 3 As shown, master-slave boundary conditions are set on two opposite surfaces of the air box to simulate the periodic expansion characteristics of the magnetic material. When setting the master-slave boundary conditions, special attention should be paid to the matching of the UV coordinate systems of the opposite surfaces. A pair of master-slave boundaries requires that the shape and size of the boundary surface and the direction of the UV coordinate system are completely consistent, otherwise errors will occur.

[0109] The next step is to set the ports in HFSS. There are special Floquet ports for excitation of infinite periodic structure plates, and they should be set on the upper and lower sides of the air box, such as Figure 4 As shown. According to the requirements of HFSS software, the Floquet port can only be set on the Z axis of the coordinate system, and the model should be adjusted according to the incident direction of the plane wave when modeling. When setting the Floquet port, you also need to pay attention to the problem of port inward movement. From the derived relationship between scattering parameters and electromagnetic parameters, it can be seen that the S parameters used in the calculation use the upper and lower surfaces of the magnetic material plate as reference ports, but when setting the port, it is placed on the upper and lower sides of the air box, which is a certain distance from the material surface. If the simulation is performed directly, the obtained S parameter phase does not meet the inversion requirements and errors will occur. Therefore, in order to ensure the accuracy of the phase, the Floquet port needs to be set so that it moves inward to the upper and lower surfaces of the material.

[0110] Embodiment 3:

[0111] See also Figures 1 to 10 , a simulation experiment of a method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials, including the following contents:

[0112] (1) Multilayer magnetic structural materials

[0113] There is a three-layer dielectric plate in the shape of a rectangular parallelepiped, such as Figure 5As shown, its side length is 10mm, the thickness of the upper layer of the dielectric plate is d1 = 0.5mm, and the relative dielectric constant is ε r1 =1, the relative magnetic permeability constant is μ r1 =100; the thickness of the middle layer of the dielectric plate is d2 = 1 mm, and the relative dielectric constant is ε r2 =1, the relative magnetic permeability constant is μ r2 =20; the thickness of the lower layer of the dielectric plate is d3 = 0.5 mm, and the relative dielectric constant is ε r3 =1, the relative magnetic permeability constant is μ r3 =200.

[0114] According to the simulation model constructed in the HFSS software as mentioned above, the working frequency of the plane wave ranges from 1kHz to 10kHz, and the frequency step is 0.09kHz. According to the proposed method of extracting equivalent electromagnetic parameters of magnetic materials based on the free space method in the low-frequency range, the electromagnetic parameters of the equivalent single-layer uniform magnetic material are obtained as follows: Figure 6 As shown in Figure 2, the comparison of scattering parameters before and after equivalent inversion is as follows: Figure 7 shown.

[0115] (2) Single-layer metal mesh structure material

[0116] There is a single-layer metal mesh structure with a side length of 10 mm, a thickness of d = 1 mm, and a relative dielectric constant of ε r =1, the relative magnetic permeability constant is μ r =4000. Its simulation model is as follows Figure 8 shown.

[0117] According to the simulation model constructed in the HFSS software as mentioned above, the working frequency of the plane wave ranges from 1kHz to 10kHz, and the frequency step is 0.09kHz. According to the proposed method of extracting equivalent electromagnetic parameters of magnetic materials based on the free space method in the low-frequency range, the electromagnetic parameters of the equivalent single-layer uniform magnetic material are obtained as follows: Fig. 9 As shown in Figure 2, the comparison of scattering parameters before and after equivalent inversion is as follows: Fig.10 shown.

Claims

1. A method for extracting low-frequency equivalent electromagnetic parameters of complex multi-layer magnetic materials, characterized in that: The following steps are involved: 1) Establish expressions for scattering parameters, relative dielectric constant and relative magnetic permeability of magnetic materials; 2) Establish a magnetic material simulation model based on the periodic structure Floquet theorem; 3) Set the master-slave boundary conditions and Floquet ports of the magnetic material simulation model; 4) Applying excitation to the magnetic material simulation model to obtain the electromagnetic parameters of the magnetic material; The steps to establish the scattering parameter expression of magnetic materials include: A1) Let the electromagnetic wave pass through the magnetic material, and establish the relationship between the scattering parameters of the magnetic material based on the effect of the magnetic material on the vertically incident electromagnetic wave, that is: Where Γ represents the reflection coefficient of the plane wave propagating from the air to the boundary surface of the magnetic material, T represents the transmission coefficient of the plane wave between the two surfaces of the magnetic material with a thickness of d; S 11 is the reflection coefficient of the magnetic material; S 21 is the transmission coefficient of the magnetic material; A2) Performing geometric series on formula (1) and formula (2), we get: A3) The reflection coefficient S of the magnetic material 11 and the transmission coefficient S of the magnetic material 21 Expressed in S parameters, we get: In the formula, K is the intermediate variable; The steps to establish the expressions for the relative permittivity and relative permeability of magnetic materials include: B1) Establish the relationship between the reflection coefficient Γ of the plane wave propagating from the air to the boundary surface of the dielectric plate, the transmission coefficient T of the plane wave between the two surfaces of the medium with a thickness of d, and the relative dielectric constant and relative magnetic permeability of the magnetic material, that is: In the formula, ε r and μ r They represent the relative dielectric constant and relative magnetic permeability of the magnetic material respectively; k0 represents the wave number of the electromagnetic wave in free space; d represents the thickness of the magnetic material; B2) Establish the relative dielectric constant ε r and relative magnetic permeability μ r The expression is: In the formula, the parameters 2. The method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials according to claim 1, characterized in that: Tools for building simulation models of magnetic materials include the three-dimensional full-wave electromagnetic field simulation software HFSS.

3. The method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials according to claim 2 is characterized in that: The simulation model of magnetic materials includes a plurality of simulation units of magnetic materials, and the size of each simulation unit is recorded as dx×dy; When the electric field E inc When the magnetic material is incident from a direction perpendicular to the xoy plane, the corresponding position (x i +md x ,y i +nd y ,z i ) is shown below: Where α0 and β0 represent the phase difference per unit length along the x-axis and y-axis respectively; and Indicates any position (x i ,y i ,z i ) at a point in time; m and n are the step sizes.

4. The method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials according to claim 1, characterized in that: The master-slave boundary conditions include that the boundary surface, shape, size, and direction of the UV coordinate system of the master boundary and the slave boundary are consistent.

5. The method for extracting low-frequency equivalent electromagnetic parameters of complex multilayer magnetic materials according to claim 1, characterized in that: The Floquet ports are arranged on the Z axis of the coordinate system and are located on the upper surface and the lower surface of the magnetic material.

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