A method for predicting electromagnetic performance of a three-dimensional structural unit cell configuration and an impedance matching design method

Abstract

A method for predicting electromagnetic performance of a three-dimensional structure unit cell configuration and an impedance matching design method, the prediction method comprising: experimentally measuring the basic electromagnetic parameters of the lossy material used in the three-dimensional structure unit cell configuration, assuming that the lossy material is an isotropic medium, and calculating the equivalent electromagnetic parameters of each layer of the configuration according to the duty cycle; calculating the fractal dimension of the whole three-dimensional structure unit cell configuration and determining the duty cycle and thickness of each layer of the three-dimensional structure unit cell configuration; constructing a structure resonance effect factor by using the basic electromagnetic parameters of the lossy material, the fractal dimension and the duty cycle, and then correcting the impedance gradient correction coefficient; and establishing a model equation of the macroscopic equivalent physical characteristic parameters of the structure interface, and calculating the interface wave impedance and surface reflectivity of the three-dimensional structure unit cell configuration by using the model equation. The theoretical and simulation calculation absorption peak frequency points are basically consistent, the macroscopic equivalent calculation method can accurately predict the absorption peak frequency point position, and the effectiveness of the calculation method is illustrated.

Description

Technical Field

[0001] This invention relates to a method for predicting the electromagnetic properties of a three-dimensional structural unit cell configuration, used to solve the problem of predicting the electromagnetic properties of functional material structures. Background Technology

[0002] Lossy dielectric absorbing superstructures have become a research hotspot in recent years. Through rational multi-scale configuration design, they can achieve broadband microwave absorption, playing a crucial role in electromagnetic compatibility, electromagnetic radiation protection, and radar detection camouflage. The mechanism by which microwave absorbers interact with electromagnetic waves is understood to involve the interaction between the electromagnetic field and the molecular and electronic structures of the lossy dispersive medium, resulting in internal heating of the material. However, for absorbing materials with complex structural configurations, a reasonable theoretical method is lacking to calculate wave impedance and surface reflectivity, revealing their electromagnetic response characteristics and energy conversion laws under electromagnetic field influence. Summary of the Invention

[0003] The technical problem solved by this invention is to provide a method for predicting the electromagnetic performance of a three-dimensional structural unit cell configuration by constructing a physical model of a lossy dielectric absorbing superstructure.

[0004] The technical solution of this invention is: a method for predicting the electromagnetic properties of a three-dimensional structural unit cell configuration, wherein the three-dimensional structural unit cell configuration is a multilayer structure; comprising:

[0005] The experiment measured the basic electromagnetic parameters of the loss material used in the three-dimensional structural unit cell configuration. It was assumed that the loss material was an isotropic medium, and the equivalent electromagnetic parameters of each layer of the configuration were calculated according to the duty cycle. The basic electromagnetic parameters included negative permittivity and negative permeability.

[0006] The fractal dimension is calculated based on the overall three-dimensional structural unit cell configuration, and the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration are determined.

[0007] By using the basic electromagnetic parameters, fractal dimension, and duty cycle of the loss material, a structural resonance effect factor is constructed, and then the impedance gradient correction coefficient is corrected.

[0008] Based on the corrected impedance gradient correction coefficient, the thickness of each layer, and the equivalent electromagnetic parameters, a model equation for the macroscopic equivalent physical characteristic parameters of the structural interface is established. The model equation is used to calculate the interface wave impedance and surface reflectivity of the three-dimensional structural unit cell configuration, and the electromagnetic performance of the configuration is predicted based on the surface reflectivity.

[0009] Preferably, the formula for calculating the structural resonance effect factor is as follows:

[0010]

[0011] In the formula, Let k be the duty cycle of the k-th layer material. The fractal dimension of the structure. The dimension of the space occupied by the configuration is 3.

[0012] Preferably, the impedance gradient correction factor The calculation formula is as follows:

[0013] .

[0014] Preferably, the model equation is:

[0015]

[0016] In the formula, The input impedance of the k-th layer is... Let the thickness be the k-th layer. Let be the complex propagation constant of the k-th layer material. Let be the intrinsic impedance of the k-th layer material.

[0017] Preferably, for each frequency point across the entire radar detection band, the reflection coefficient is calculated to obtain the reflection coefficient variation curve of the current three-dimensional structural unit cell configuration with frequency.

[0018] An impedance matching design method for a three-dimensional structural unit cell configuration includes:

[0019] The electromagnetic performance prediction method is used to determine the input impedance of each layer of the three-dimensional structural unit cell configuration. It is then determined whether the input impedance of each layer of the three-dimensional structural unit cell configuration is arranged from large to small, starting from the surface layer. If so, the impedance matching design of the current three-dimensional structural unit cell configuration is completed. Otherwise, the duty cycle or thickness of each layer is adjusted until the input impedance of each layer is arranged from large to small, starting from the surface layer.

[0020] Preferably, the structure is adjusted according to the broadband electromagnetic loss law.

[0021] Preferably, when the three-dimensional structure unit cell configuration is a multi-layer honeycomb configuration, during the adjustment process, if the duty cycle of each layer remains unchanged, the thickness is adjusted according to the following rules:

[0022] When the total thickness of the structure changes, as the thickness of each individual layer increases, the frequency of the absorption peak shifts to a lower frequency band; the increase in the thickness of the outermost layer leads to a decrease in the corresponding reflection loss value and a narrowing of the frequency range of the peak point region; the increase in the thickness of the middle layer leads to a decrease in the corresponding reflection loss value and a widening of the frequency range of the peak point region.

[0023] Preferably, when the three-dimensional structure unit cell configuration is a multi-layer honeycomb configuration, if the total thickness of the configuration remains unchanged during the adjustment process, the adjustment is carried out according to the following rules:

[0024] By adjusting the thickness of the intermediate or surface layer, sacrificing some of the electromagnetic loss performance at the peak point (i.e., disregarding the positional change of the absorption peak frequency point), the frequency range of the region where the peak point is located is widened, thereby achieving the technical specifications of an effective absorption frequency band.

[0025] Preferably, when the three-dimensional structure unit cell configuration is a multi-layer honeycomb configuration, during the adjustment process, if the configuration thickness remains unchanged, the duty cycle is adjusted according to the following rules:

[0026] The duty cycle of each layer represents the wall thickness of the honeycomb structure. By increasing the wall thickness of the surface layer, the effective absorption bandwidth can be covered in the low-frequency band; by reducing the wall thickness of the middle layer, the electromagnetic loss performance at the peak point can be enhanced.

[0027] The beneficial effects of this invention compared to the prior art are as follows:

[0028] To construct a physical model of a lossy dielectric absorbing superstructure, this invention, based on equivalent dielectric theory and transmission line theory, analyzes the interaction between each dielectric interface and the electromagnetic field, introduces the equivalent electromagnetic parameters of each dielectric layer and the fractal dimension describing the geometric characteristics of the structure, and uses the impedance transfer method to calculate the input impedance of the surface layer, thereby obtaining the material's reflection coefficient. Furthermore, this invention can determine the reflection coefficient across the entire radar detection band for each frequency point, obtaining a curve showing the reflection coefficient's variation with frequency. This curve can then be used for practical engineering applications.

[0029] This invention constructs a resonance effect factor that conforms to the physical meaning of material-structure synergy, creates a macroscopic equivalent calculation method for the interface impedance of loss dielectric structures, and forms an impedance matching design and performance evaluation method for absorbing structures. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the honeycomb structure.

[0031] Figure 2 The theoretical and simulation calculations of the reflection loss frequency spectrum for cellular structures;

[0032] Figure 3 This represents the frequency spectrum of the impedance modes at the material interface of the honeycomb structure.

[0033] Figure 4 This is a schematic diagram of the stepped cone structure.

[0034] Figure 5 The theoretical and simulation calculations of the reflection loss frequency spectrum for the stepped cone structure;

[0035] Figure 6 The frequency spectrum of the material interface impedance mode of the stepped cone structure.

[0036] Figure 7 This is a schematic diagram of the configuration of a woodpile structure;

[0037] Figure 8 The theoretical and simulation calculations of the reflection loss frequency spectrum for the timber stack structure;

[0038] Figure 9 This represents the frequency spectrum of the material interface wave impedance mode of the wood pile structure.

[0039] Figure 10 This is a schematic diagram of the rectangular structure.

[0040] Figure 11 The theoretical and simulation calculations of the reflection loss frequency spectrum for the rectangular structure;

[0041] Figure 12 This represents the frequency spectrum of the material interface impedance modes of the rectangular structure.

[0042] Figure 13 This is a schematic diagram of the configuration of composite structure 1;

[0043] Figure 14 The theoretical and simulation calculations of the reflection loss frequency spectrum for combined structure 1 are performed.

[0044] Figure 15 The frequency spectrum of the material interface impedance mode of composite structure 1.

[0045] Figure 16 This is a schematic diagram of the configuration of combined structure 2;

[0046] Figure 17 The theoretical and simulation calculations of the reflection loss frequency spectrum for combined structure 2 are performed.

[0047] Figure 18 The frequency spectrum of the material interface impedance mode of composite structure 2.

[0048] Figure 19 This is a schematic diagram of the configuration of composite structure 3;

[0049] Figure 20 The theoretical and simulation calculations of the reflection loss frequency spectrum for combined structure 3 are performed.

[0050] Figure 21 The frequency spectrum of the impedance mode of the material interface of composite structure 3. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings. The present invention relates to a class of microwave absorbing functional materials with multi-scale fractal structure and a method for calculating their electromagnetic parameters, the steps of which are as follows:

[0052] (1) The basic electromagnetic parameters of the loss material used in the three-dimensional structural unit cell configuration were experimentally measured using the rectangular waveguide method. It was assumed that the loss material was an isotropic medium, and the equivalent electromagnetic parameters of each layer of the configuration were calculated according to the duty cycle. The basic electromagnetic parameters included negative permittivity and negative permeability.

[0053] The formulas for calculating the equivalent permittivity and equivalent permeability are as follows:

[0054]

[0055]

[0056] Let k be the duty cycle of the k-th layer material. Let be the equivalent complex permittivity of the k-th layer material. Let be the complex permittivity of the k-th layer material. Let be the complex permittivity of air, with a value of 1. Let be the equivalent permeability of the k-th layer material. Let be the complex permeability of the k-th layer material. Let be the complex permeability of air, with a value of 1.

[0057] (2) Calculate the fractal dimension based on the overall three-dimensional structure unit cell configuration, and determine the duty cycle and thickness of each layer of the three-dimensional structure unit cell configuration;

[0058] The fractal dimension of the structural configuration is calculated using the box-counting dimension method from fractal geometry. The fractal dimension is calculated as follows:

[0059] Construct a geometric model of a three-dimensional structural unit cell configuration, and use cubic meshes of different scales to contain the three-dimensional space occupied by the geometric model;

[0060] Calculate the number of cubic meshes containing objects, Nr;

[0061] right and In least squares regression analysis, the slope of the fitted line is the fractal dimension.

[0062] Where r is the side length of the cubic grid, and r decreases by a factor of 10 to cover at least 3 orders of magnitude.

[0063] (3) By constructing the structural resonance effect factor through the basic electromagnetic parameters, fractal dimension, and duty cycle of the loss material, the impedance gradient correction coefficient is then corrected.

[0064] The formula for calculating the structural resonance effect factor is as follows:

[0065]

[0066] In the formula, The fractal dimension of the structure. The dimension of the space occupied by the configuration is 3.

[0067] Impedance gradient correction factor The calculation formula is as follows:

[0068]

[0069] (4) Based on the corrected impedance gradient correction coefficient, the thickness of each layer, and the equivalent electromagnetic parameters, establish a model equation for the macroscopic equivalent physical characteristic parameters of the structural interface with adaptability and compatibility, calculate the interface wave impedance and surface reflectivity of the loss dielectric structure, and predict the electromagnetic performance of the configuration based on the surface reflectivity.

[0070] The aforementioned model equation, i.e., the input impedance of the k-th layer of the three-dimensional structural unit cell configuration, is:

[0071] ;

[0072] If there is a reflective liner The value is 0; if there is no reflective liner, The value is 1.

[0073] In the formula, Let be the thickness of the k-th layer.

[0074] The intrinsic impedance of the k-th layer material. The calculation formula is as follows:

[0075]

[0076] In the formula, It is the equivalent dielectric constant. It is the equivalent permeability.

[0077] Complex propagation constant of the k-th layer material The calculation formula is as follows:

[0078]

[0079] In the formula, It is the equivalent dielectric constant. ρ is the equivalent permeability, c is the speed of light, and f is the frequency.

[0080] The formula for calculating the reflection coefficient of the aforementioned structural surface is as follows:

[0081]

[0082] In the formula, The input impedance is the surface impedance of the structure.

[0083] This invention also provides an impedance matching design method for a three-dimensional structural unit cell configuration, comprising:

[0084] The electromagnetic performance prediction method is used to determine the input impedance of each layer of the three-dimensional structural unit cell configuration. It is then determined whether the input impedance of each layer of the three-dimensional structural unit cell configuration is arranged from large to small, starting from the surface layer. If so, the impedance matching design of the current three-dimensional structural unit cell configuration is completed. Otherwise, the duty cycle or thickness of each layer is adjusted until the input impedance of each layer is arranged from large to small, starting from the surface layer.

[0085] The three-dimensional structural unit cell configurations of this invention include honeycomb configuration, stepped cone configuration, woodpile configuration, square frame configuration, and combined configuration; the honeycomb configuration is a multi-layered honeycomb gradient arrangement, stacked from largest to smallest; the stepped cone configuration is a multi-layered cubic gradient arrangement, stacked from largest to smallest; the woodpile configuration is a multi-layered staggered arrangement of cuboids; the square frame configuration is a multi-layered cubic gradient arrangement, stacked from largest to smallest; and the combined configuration is a multi-layered arrangement of cuboids and square frames.

[0086] This invention reveals the broadband electromagnetic loss characteristics of absorbing materials with topological structures through extensive research. Taking a multilayer honeycomb configuration as an example, through extensive research and experiments, the location of absorption peak frequencies and related influencing factors are analyzed. The influence of thickness and duty cycle on the location of absorption peak frequencies is determined. Based on the obtained characteristics, the configuration can be quickly adjusted.

[0087] (1) In the analysis of the factors affecting the location of the absorption peak frequency, the 01 honeycomb structure is taken as the research object. When the total thickness of the structure changes, the frequency of the absorption peak shifts to the lower frequency band as the thickness of each individual layer increases. The variation law of the reflection loss value of the peak point is different. The increase of the thickness of the surface layer (4th layer) will lead to a corresponding decrease in the reflection loss value and a narrowing of the frequency range of the peak point region. The variation law caused by the increase of the thickness of the middle layer (2nd and 3rd layers) is the opposite. Therefore, in the structural design, if effective absorption covering the low frequency range is considered, the total thickness should be increased while balancing the thickness matching of the surface layer and the middle layer to achieve a minimum reduction in reflection loss and a widening of the frequency range of the peak point region.

[0088] (2) When the total thickness of the structure remains constant, by adjusting the thickness of two of the layers, it is shown that as the thickness of the intermediate layer increases, the position of the absorption peak frequency point remains basically unchanged, the corresponding reflection loss value increases, and the frequency range of the peak point region widens. Therefore, in structural design, when the total thickness of the structure is constrained, the thickness of the intermediate layer or the surface layer can be adjusted to sacrifice part of the electromagnetic loss performance at the peak point, thereby widening the frequency range of the peak point region and achieving the technical indicators of the effective absorption frequency band.

[0089] (3) When the thickness remains constant and the duty cycle changes, the changes in the absorption peak frequency position caused by the change in the duty cycle of each layer are different. For the middle layer, as the duty cycle of the second layer decreases, the absorption peak frequency position moves towards higher frequencies, the corresponding reflection loss value decreases, and the frequency range of the peak point region narrows. As the duty cycle of the third layer decreases, the absorption peak frequency position remains basically unchanged, the reflection loss value corresponding to the first absorption peak decreases, the frequency range of the peak point region narrows, the reflection loss value corresponding to the second absorption peak increases, and the frequency range of the peak point region widens. For the surface layer, as the duty cycle of the fourth layer decreases, the absorption peak frequency position moves towards higher frequencies, the corresponding reflection loss value shows a decreasing trend, and the frequency range of the peak point region narrows. Therefore, in the structural design, the duty cycle of each layer represents the wall thickness of the honeycomb configuration. By increasing the wall thickness of the surface layer, the effective absorption bandwidth can be covered in the low-frequency band; by reducing the wall thickness of the middle layer, the electromagnetic loss performance at the peak point can be enhanced.

[0090] Example 1

[0091] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the 01 honeycomb structure were calculated according to the method described in this invention:

[0092] Comparison of surface reflectivity theory and simulation calculation of honeycomb structure with configuration 01 Figure 2 As shown, macroscopic equivalent calculations reveal three absorption peaks within the 2-18 GHz frequency band, located at 2.4 GHz, 7.4 GHz, and 13.3 GHz, with corresponding reflection losses of -11.7 dB, -21.8 dB, and -24.1 dB. The effective absorption bandwidths less than -10 dB are 2.4-2.7 GHz and 5.4-18 GHz, while the absorption bandwidths less than -8 dB are 2.4-3.2 GHz and 4.6-18 GHz. Simulation calculations show three absorption peaks within the 2-18 GHz frequency band, located at 2.8 GHz, 7.7 GHz, and 15.5 GHz, with corresponding reflection losses of -26.5 dB, -26.6 dB, and -31.7 dB, and an effective absorption bandwidth less than -10 dB of 2.2-18 GHz. Through comparative analysis, the absorption peak frequency locations calculated by theory and simulation are basically consistent. The macroscopic equivalent calculation method can accurately predict the absorption peak frequency location. Within the frequency range, the absorption peak frequency location appears in the S-band, C-band and Ku-band.

[0093] Frequency spectrum of interface wave impedance modes in a cellular structure as follows Figure 3As shown, the values ​​of the interface wave impedance modes vary significantly in the 2-2.4 GHz frequency range, causing impedance mismatch. In the 2.4-18 GHz frequency range, the values ​​of the four interface wave impedance modes vary between 0.3 and 1.2. The impedance gradient changes well in the 6.1-18 GHz range, resulting in reflection losses of less than -10 dB in this frequency band. The wave impedance modes at the three absorption peak frequencies are (0.67, 0.49, 0.30, 0.12), (0.85, 0.66, 0.34, 0.60), and (0.88, 0.48, 0.62, 0.26). The wave impedance matching at the absorption peak frequencies is good, and the surface wave impedance is close to the free-space impedance, which enhances electromagnetic loss performance in the absorption peak frequency region.

[0094] Example 2

[0095] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the stepped cone structure with configuration 02 were calculated according to the method described in this invention:

[0096] Comparison of surface reflectivity theory and simulation calculations for configuration 02 stepped cone structure, for example Figure 5 As shown, macroscopic equivalent calculations reveal three absorption peaks within the 2–18 GHz frequency band, located at 2.4 GHz, 6.5 GHz, and 13.2 GHz, with corresponding reflection losses of -6.8 dB, -10.0 dB, and -9.2 dB, respectively. The absorption frequency band with losses less than -8 dB is 4.8–18 GHz. Simulation calculations show two absorption peaks within the 2–18 GHz frequency band, located at 2.2 GHz and 13.8 GHz, with corresponding reflection losses of -25.4 dB and -32.9 dB, respectively. The effective absorption frequency band is 2–18 GHz. Comparative analysis shows that the predicted frequencies of the first and third absorption peaks using the macroscopic equivalent calculation method are largely consistent with the simulation results. The simulation results show that the reflection loss curve changes smoothly in the 4-8 GHz frequency band, and all reach less than -10 dB. The second peak point of the macroscopic equivalent calculation appears in this frequency band, which can reveal that the absorption peak captured in this frequency band effectively expands the absorption bandwidth.

[0097] The frequency spectrum of the interface wave impedance mode of the stepped cone structure with configuration 02 is as follows: Figure 6As shown, the impedance modes of the interface waves vary significantly in the 2–2.4 GHz frequency range, causing impedance mismatch. In the 2.4–18 GHz frequency range, the values ​​of the four interface wave impedance modes vary from 0.24 to 1.15. The impedance gradient changes well in the 9.1–18 GHz range, resulting in reflection losses of less than -10 dB in this frequency band. The impedance modes at the three absorption peak frequencies are (0.55, 0.40, 0.25, 0.12), (0.51, 0.40, 0.31, 0.69), and (0.48, 0.37, 0.40, 0.26). The impedance matching at the first and third absorption peak frequencies is good, showing a clear minimum reflection loss peak. The impedance matching at the second absorption peak frequency is poor, and no clear peak was captured in the simulation calculation.

[0098] Example 3

[0099] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the woodpile structure with configuration 03 were calculated according to the method described in this invention:

[0100] Comparison of surface reflectivity theory and simulation calculation of configuration 03 woodpile structure, for example Figure 8 As shown, macroscopic equivalent calculations reveal three absorption peaks within the 2–18 GHz frequency band, located at 6.1 GHz, 11.3 GHz, and 16.3 GHz, with corresponding reflection losses of -18.7 dB, -15.6 dB, and -10.1 dB, respectively. The effective absorption frequency band is 4.5–18 GHz, and the absorption frequency band with losses less than -8 dB is 3.9–18 GHz. Simulation calculations show three absorption peaks within the 2–18 GHz frequency band, located at 2.3 GHz, 7.1 GHz, and 13.0 GHz, with corresponding reflection losses of -18.3 dB, -19.8 dB, and -13.0 dB, respectively. The effective absorption frequency bands are 2–3.2 GHz and 5.2–15.2 GHz. Through comparative analysis, the trends of reflection loss with frequency in theoretical and simulation calculations are basically consistent. The positions of the two absorption peak frequencies predicted by the macroscopic equivalent calculation method are close to the simulation results, appearing in the C-band and Ku-band.

[0101] The frequency spectrum of the interface wave impedance mode of the wood pile structure with configuration 03 is as follows: Figure 9As shown, the interface wave impedance modes vary significantly in the 2–3.7 GHz frequency range, causing impedance mismatch. In the 3.7–18 GHz frequency range, the values ​​of the four interface wave impedance modes vary between 0.16 and 1.16. The impedance gradient is relatively good in the 7.6–18 GHz range, resulting in reflection losses of less than -10 dB in this frequency band. The surface wave impedance is greater than the free-space wave impedance in the low-frequency band, leading to ineffective wave absorption in the low-frequency range. Furthermore, the wave impedance modes near the bottom interface are larger in the mid-to-high frequency band, causing an increasing trend in reflection loss, but without significant impact. Therefore, the surface wave impedance affects electromagnetic wave incidence, while the intermediate layer affects electromagnetic wave dissipation. The structural design of the timber stack requires further adjustment of its geometric dimensions, focusing on the combination of parameters related to the number of layers and duty cycle.

[0102] Example 4

[0103] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the configuration 04 combined structure were calculated according to the method described in this invention:

[0104] Comparison of surface reflectivity theory and simulation calculations for configuration 04 combined structure Figure 11 As shown, macroscopic equivalent calculations reveal three absorption peaks within the 2–18 GHz frequency band, located at 2.4 GHz, 7.8 GHz, and 15.0 GHz, with corresponding reflection losses of -13.1 dB, -10.9 dB, and -14.0 dB, respectively. The effective absorption frequency bands are 2.3–2.7 GHz and 6.6–18 GHz, while the absorption frequency bands with losses less than -8 dB are 2.3–3.0 GHz and 5.8–18 GHz. Simulation calculations show one absorption peak within the 2–18 GHz frequency band, located at 2.3 GHz, with a corresponding reflection loss of -29.2 dB. The effective absorption frequency bands are 2.0–3.1 GHz and 6.5–18 GHz. Comparative analysis shows that the theoretical and simulation calculations show a consistent trend in reflection loss with frequency. The frequency location of one absorption peak predicted by the macroscopic equivalent calculation method is consistent with the simulation results, appearing in the S-band. After the S-band, the simulated reflection loss curve changes smoothly. The second and third peak points of the macroscopic equivalent calculation appear in the C-band and Ku-band, revealing the expansion of the effective absorption bandwidth in the mid-to-high frequency range.

[0105] The frequency spectrum of the interface wave impedance mode of the configuration 04 combined structure is as follows Figure 12As shown, the values ​​of the interface wave impedance modes vary significantly in the 2–2.4 GHz frequency range, causing impedance mismatch. In the 2.4–18 GHz frequency range, the values ​​of the four interface wave impedance modes vary from 0.19 to 0.90. The impedance gradient is relatively good in the 6.8–18 GHz range, resulting in reflection losses of less than -10 dB in this frequency band. The impedance modes at the three absorption peak frequencies are (0.40, 0.30, 0.19, 0.09), (0.57, 0.45, 0.29, 0.43), and (0.88, 0.48, 0.62, 0.26). This indicates that the surface wave impedance is highest at the absorption peak frequencies and is close to the free-space impedance, meaning that electromagnetic waves are effectively dissipated when they enter the structure.

[0106] Example 5

[0107] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the configuration 05 combined structure were calculated according to the method described in this invention:

[0108] Comparison of surface reflectivity theory and simulation calculations for configuration 05 combined structure Figure 14 As shown, macroscopic equivalent calculations reveal two absorption peaks within the 2–18 GHz frequency band, located at 2.1 GHz and 5.3 GHz, with corresponding reflection losses of -11.3 dB and -8.6 dB, respectively. The effective absorption frequency bands (less than -8 dB) are 2.0–2.4 GHz and 4.5–18 GHz. Simulation calculations show two absorption peaks within the 2–18 GHz frequency band, located at 2.4 GHz and 7.3 GHz, with corresponding reflection losses of -30.1 dB and -18.4 dB, respectively. The effective absorption frequency band is 2–18 GHz. Comparative analysis shows that the trends of the reflection loss curves and the absorption peak frequencies are largely consistent. The macroscopic equivalent calculation method can accurately predict the absorption peak frequencies. Within this frequency range, the absorption peak frequencies appear in the S-band and C-band.

[0109] The frequency spectrum of the interface wave impedance mode of the configuration 05 combined structure is as follows: Figure 15As shown, the impedance modes at the two absorption peak frequencies are (1.67, 0.36, 0.17) and (0.46, 0.37, 0.79), respectively, while the values ​​of the three interface impedance modes vary within the range of 0.17 to 1.67. Although the impedance values ​​vary significantly at low frequencies, the surface impedance value varies around 1.0, which is close to the impedance in free space. Furthermore, the interface impedance gradient changes, leading to the first peak in electromagnetic wave loss. In the mid-to-high frequency range, due to the relatively small surface impedance, the interface impedance does not form a good transition, causing the reflection loss curve to gradually shift upwards.

[0110] Example 6

[0111] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the configuration 06 combined structure were calculated according to the method described in this invention:

[0112] Comparison of surface reflectivity theory and simulation calculations for configuration 06 combined structure Figure 17 As shown, macroscopic equivalent calculations reveal three absorption peaks within the 2–18 GHz frequency band, located at 2.5 GHz, 7.9 GHz, and 15.1 GHz, with corresponding reflection losses of -7.2 dB, -8.9 dB, and -9.8 dB. The absorption bands with losses less than -8 dB are 6.8–9.6 GHz and 13.3–17.0 GHz. Simulation calculations show two absorption peaks within the 2–18 GHz frequency band, located at 2.5 GHz and 7.3 GHz, with corresponding reflection losses of -23.5 dB and -7.8 dB, and an effective absorption band of 2.0–3.5 GHz. Comparative analysis shows that the trends of the reflection loss curves from theoretical and simulation calculations are basically consistent. The predicted frequencies of the first and second absorption peaks from the macroscopic equivalent calculation method are largely consistent with the simulation results. Within this frequency range, the absorption peak frequencies appear in the S-band and C-band.

[0113] The frequency spectrum of the interface wave impedance mode of the 06 combined structure is as follows: Figure 18 As shown, the impedance modes of the four interfaces vary within the range of 0.1 to 1.5. The impedance gradient changes well within the 2.0 to 2.5 GHz range, resulting in low reflection loss in this frequency band, indicating good electromagnetic loss performance in the low-frequency range. In the wider frequency range, due to the significant difference between the surface impedance and free-space impedance, and the lack of a gradient change in impedance at the four interfaces, electromagnetic waves are less likely to penetrate the structure, resulting in a narrow effective absorption bandwidth of less than -10 dB. The results of macroscopic equivalent calculations and simulations are consistent.

[0114] Example 7

[0115] To further illustrate the advantages of this scheme, the interface wave impedance and surface reflectivity of the configuration 07 combined structure were calculated according to the method described in this invention:

[0116] Comparison of surface reflectivity theory and simulation calculations for configuration 07 combined structure Figure 20 As shown, macroscopic equivalent calculations reveal two absorption peaks within the 2–18 GHz frequency band, located at 2.5 GHz and 11.5 GHz, with corresponding reflection losses of -15.8 dB and -9.2 dB, respectively. The effective absorption frequency bands are 2.4–2.7 GHz and 5.4–18 GHz, with an absorption frequency band less than -8 dB between 2.3 and 3.2 GHz. Simulation calculations show one absorption peak within the 2–18 GHz frequency band, located at 2.9 GHz, with a corresponding reflection loss of -22.0 dB. The effective absorption frequency band within this range is 2.4–3.8 GHz. Comparative analysis shows that the trends of the reflection loss curves from theoretical and simulation calculations are basically consistent. The frequency position of the first absorption peak predicted by the macroscopic equivalent calculation method is basically consistent with the simulation results. The macroscopic equivalent calculation method can accurately predict the frequency position of the absorption peak. Within the frequency range, the absorption peak frequency position appears in the S-band and X-band.

[0117] The frequency spectrum of the interface wave impedance mode of the 07 combined structure is as follows: Figure 21 As shown, the impedance modes at the absorption peak frequency are (1.4, 0.76, 0.23, 0.11). The values ​​of the impedance modes at the four interfaces vary within the range of 0.1 to 1.5. The impedance gradient changes well within the range of 2.0 to 3.1 GHz, and the surface impedance mode is close to the free-space impedance, resulting in low reflection loss in this frequency range, indicating good electromagnetic loss performance in the low-frequency band. In a wider frequency range, due to the significant difference between the surface impedance and the free-space impedance, and the lack of a gradient change in impedance at the four interfaces, electromagnetic waves are less likely to penetrate the structure, resulting in a narrow effective absorption bandwidth of less than -10 dB. The results of macroscopic equivalent calculations and simulation calculations are consistent.

[0118] The undisclosed technologies in this invention are common knowledge to those skilled in the art.

Claims

1. A method for predicting the electromagnetic properties of a three-dimensional structural unit cell configuration, wherein the three-dimensional structural unit cell configuration is a multilayer structure; characterized in that... :include The experiment measured the basic electromagnetic parameters of the loss material used in the three-dimensional structural unit cell configuration. It was assumed that the loss material was an isotropic medium, and the equivalent electromagnetic parameters of each layer of the configuration were calculated according to the duty cycle. The basic electromagnetic parameters included negative permittivity and negative permeability. Based on the three-dimensional structural unit cell configuration, the fractal dimension of the entire configuration is calculated using the box-counting dimension calculation method in fractal geometry, and the duty cycle and thickness of each layer of the three-dimensional structural unit cell configuration are determined. By using the basic electromagnetic parameters, fractal dimension, and duty cycle of the loss material, a structural resonance effect factor is constructed, and then the impedance gradient correction coefficient is corrected. Based on the corrected impedance gradient correction coefficient, the thickness of each layer, and the equivalent electromagnetic parameters, a model equation for the macroscopic equivalent physical characteristic parameters of the structural interface is established. The model equation is used to calculate the interface wave impedance and surface reflectivity of the three-dimensional structural unit cell configuration, and the electromagnetic performance of the configuration is predicted based on the surface reflectivity. The formula for calculating the structural resonance effect factor is as follows: In the formula, Let k be the duty cycle of the k-th layer material. The fractal dimension of the structure. The dimension of the space occupied by the configuration, with a value of 3; The model equations are as follows: In the formula, The input impedance of the k-th layer is the interface wave impedance. Let the thickness be the k-th layer. Let be the complex propagation constant of the k-th layer material. Let be the intrinsic impedance of the k-th layer material.

2. The method for predicting the electromagnetic properties of a three-dimensional structural unit cell configuration according to claim 1, characterized in that: Impedance gradient correction factor The calculation formula is as follows: 。 3. The method for predicting the electromagnetic properties of a three-dimensional structural unit cell configuration according to claim 1, characterized in that: For each frequency point across the entire radar detection band, the reflection coefficient is calculated to obtain the curve of the reflection coefficient of the current three-dimensional structural unit cell configuration as a function of frequency.

4. An impedance matching design method for a three-dimensional structural unit cell configuration, characterized in that... include: The input impedance of each layer of the three-dimensional structural unit cell configuration is determined using the electromagnetic performance prediction method described in claim 1. Determine whether the input impedance of each layer in the three-dimensional structural unit cell configuration, starting from the surface and working inwards, is arranged in descending order. If so, the impedance matching design of the current three-dimensional structural unit cell configuration is complete; otherwise, adjust the duty cycle or thickness of each layer until the input impedance of each layer, starting from the surface and working inwards, is arranged in descending order.

5. The impedance matching design method for a three-dimensional structural unit cell configuration according to claim 4, characterized in that: Structural adjustments were made based on the broadband electromagnetic loss characteristics.

6. The impedance matching design method for a three-dimensional structural unit cell configuration according to claim 5, characterized in that: When the three-dimensional structure's unit cell configuration is a multi-layer honeycomb configuration, during the adjustment process, if the duty cycle of each layer remains unchanged, the thickness adjustment is carried out according to the following rules: When the total thickness of the structure changes, as the thickness of each individual layer increases, the frequency of the absorption peak shifts to a lower frequency band; the increase in the thickness of the outermost layer leads to a decrease in the corresponding reflection loss value and a narrowing of the frequency range of the peak point region; the increase in the thickness of the middle layer leads to a decrease in the corresponding reflection loss value and a widening of the frequency range of the peak point region.

7. The impedance matching design method for a three-dimensional structural unit cell configuration according to claim 5, characterized in that: When the three-dimensional structure unit cell configuration is a multi-layer honeycomb configuration, during the adjustment process, if the total thickness of the configuration remains unchanged, the adjustment shall be carried out according to the following rules: By adjusting the thickness of the intermediate or surface layer, sacrificing some of the electromagnetic loss performance at the peak point (i.e., disregarding the positional change of the absorption peak frequency point), the frequency range of the region where the peak point is located is widened, thereby achieving the technical specifications of an effective absorption frequency band.

8. The impedance matching design method for a three-dimensional structural unit cell configuration according to claim 5, characterized in that: When the three-dimensional structure's unit cell configuration is a multi-layer honeycomb configuration, during the adjustment process, if the configuration thickness remains unchanged, the duty cycle is adjusted according to the following rules: The duty cycle of each layer represents the wall thickness of the honeycomb structure. By increasing the wall thickness of the surface layer, the effective absorption bandwidth can be covered in the low-frequency band; by reducing the wall thickness of the middle layer, the electromagnetic loss performance at the peak point can be enhanced.

Images