A medium layer design method for enhancing performance of a phased array antenna

Abstract

The application belongs to the field of antenna design, and discloses a medium layer design method for enhancing the performance of a phased array antenna. The method mainly comprises two steps: step 1 is to establish an optimization model of the material properties of the medium layer and the size parameters of the metal layer suitable for the stacked antenna according to the wide-angle scanning characteristics of the phased array antenna; the optimal design parameters are obtained by solving the optimization model; step 2 is to design the unit cell or structure of the medium layer based on the scattering parameter inversion method according to the optimal parameter results of step 1, so as to design the medium layer with optimal dielectric characteristics, and then realize the expected wide-angle scanning characteristics. The wide-angle scanning characteristics of the phased array unit are realized by designing the medium layer unit, and the unit not only has good matching characteristics and polarization purity, but also realizes lightweight design.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of antenna design, and particularly relates to a medium layer design method for enhancing the performance of a phased array antenna. BACKGROUND

[0002] As a core component of modern communication and military radar systems, the fast transmission and beam pointing switching capability of the phased array antenna plays a crucial role in improving system performance, enhancing signal coverage, and improving target detection accuracy. However, with the continuous development of communication and radar technology, the performance requirements of phased array antennas are also increasing, especially the ability to achieve wide-angle scanning within a wide frequency band. Therefore, it is necessary to improve the impedance matching characteristics of the antenna to achieve wide-angle scanning within a wide frequency band.

[0003] Stacked medium layers are commonly used to achieve wide-angle scanning within a wide frequency band for phased array antennas. For example, CN118645801A proposes a four-layer substrate phased array antenna unit that operates at Ka band, uses L-type probe feeding, H-shaped slot coupling feeding, and multi-layer coupling feeding microstrip antenna broadband technology to achieve low-profile and broadband design of the antenna unit, with a relative bandwidth of 14.85% (26.18-30.34 GHz). The use of SIW resonant cavity structure, defect structure floor, and "L-shaped" parasitic patch structure on the decoupling surface reduces the mutual coupling between antenna elements, making the antenna have two-dimensional wide-angle scanning (> ± 47°), high isolation (> 19 dB), low profile (2.21 mm, about 0.2λ0), easy processing, etc. CN117977168A proposes a multi-layer phased array antenna design method that uses a metal grid as both a resonant cavity structure for antenna operation to achieve wide-angle scanning and provides a fixed screw mounting point. This design scheme realizes the collaborative design of antenna element radiation performance optimization and screw layout optimization without affecting the working characteristics of the antenna, solves the problem of multiple iterations and large calculation amount in the design of phased array antenna arrays based on existing design processes, and shortens the design cycle.

[0004] However, in the design of stacked antennas, the selection of medium layers is also crucial to improving the performance of the antenna. Currently, there are mismatches between the properties of traditional PCB materials (dielectric properties and thickness, etc.) and the properties of materials required to achieve antenna performance, which limits the space for improving the performance of the antenna and the flexibility of the design. In addition, 3D printing technology can achieve complex internal structures and material distribution design, which also provides unprecedented possibilities for designing medium layers with specific dielectric properties. Therefore, a medium layer design method that takes into account the feasibility of 3D printing technology and is suitable for improving the performance of phased array antennas is needed to provide technical support for improving the performance of the antenna. SUMMARY

[0005] The application provides a medium layer design method for enhancing the performance of a phased array antenna.

[0006] The application aims to achieve the following technical solutions:

[0007] The medium layer design method for enhancing the performance of a phased array antenna mainly includes two steps: step 1 is to establish an optimization model of the material properties of the medium layer and the size parameters of the metal layer suitable for the stacked antenna according to the wideband wide-angle scanning characteristics of the phased array antenna; the optimal design parameters are obtained by solving the optimization model; step 2 is to design the unit cell or structure of the medium layer based on the scattering parameter inversion method according to the optimal parameter results of step 1, so as to design the medium layer with optimal dielectric properties, and then realize the expected wideband wide-angle scanning characteristics.

[0008] In step 1, the optimization model takes the wideband wide-angle scanning characteristics of the stacked antenna as the design target, takes the dielectric properties and thickness of the medium layer and the size parameters of the radiation patch as the optimization variables, and solves the optimal result through an optimization algorithm, wherein the wideband wide-angle scanning characteristics take the standing wave ratio less than a specified value as the evaluation standard.

[0009] In step 2, the implementation of the method for designing the unit cell or structure of the medium layer based on the scattering parameter inversion method needs to first analyze the characteristics of the designed medium layer and the design factors to be considered, and then determine the design scheme of the material, and then determine the initial volume fraction of the medium layer required to have optimal material properties based on the empirical formula, and then determine the initial configuration of the unit cell and perform parameterized modeling, and then evaluate the dielectric constant of the medium layer based on the scattering parameter inversion method, and then obtain the optimal medium layer unit cell or configuration by establishing an optimization model, and finally obtain the medium layer microstructure with optimal dielectric properties by solving the intelligent optimization algorithm. In the process of designing the medium layer unit cell, the 3D printing precision and the implementability of the metal layer process are mainly considered to ensure the manufacturability of the designed medium layer.

[0010] The application utilizes the medium layer design method for enhancing the performance of a phased array antenna to realize the wideband wide-angle scanning characteristics of the phased array unit through the design of the medium layer unit, and the unit not only has good matching characteristics and polarization purity, but also realizes lightweight design. BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 The design flowchart of the application is shown in the following figure:

[0012] Figure 2 The double Floquet port network schematic diagram of the application is shown in the following figure: (a) is an exploded view, and (b) is a whole view.

[0013] Figure 3 Typical structure diagram of the phased array antenna with matching layer of the present application: (a) unit cell structure; (b) dielectric properties;

[0014] Figure 4 Unit cell configuration and dielectric properties of the matching layer of the present application: (a) unit cell structure; (b) dielectric properties;

[0015] Figure 5 Unit cell configuration and dielectric properties of the medium layer 1 of the present application;

[0016] Figure 6 Design configuration of the medium layer 2 of the present application;

[0017] Figure 7 Overall scheme of the designed antenna after optimization of the present application;

[0018] Figure 8 Overall scheme of the designed antenna after optimization of the present application and the scan standing wave ratio of the reference antenna: (a) normal standing wave ratio, (b) E-plane scan standing wave ratio, (c) H-plane scan standing wave ratio;

[0019] Figure 9 Pattern of the designed antenna of the present application: (a) E-plane pattern, (b) H-plane pattern; DETAILED DESCRIPTION

[0020] The technical solutions of the present application will be further described below in combination with the drawings.

[0021] Example 1: Medium layer design method based on enhanced phased array antenna performance

[0022] The design process of the design method is shown in Figure 1 The implementation steps can be summarized as a two-step method: Step 1 is the optimization design of the medium layer material properties and the metal layer parameters; Step 2 is the design of the medium layer unit cell / structure based on the scattering parameter inversion method.

[0023] Step 1: For the wide-angle scanning characteristics requirement of the phased array antenna, an optimization model of the medium layer material properties and the metal layer size parameters is established, and the optimal dielectric constant and metal layer size parameters are obtained by solving the optimization model.

[0024] Step 2: According to the optimal result in Step 1, the unit cell or structure of the medium layer is designed based on the scattering parameter inversion method, which needs to consider the 3D printing accuracy and the implementability of the metal layer process. Specifically, first, the design scheme of each medium layer is determined by analyzing the hierarchical relationship and design points of each medium layer, and then the initial volume fraction of the material is determined according to the optimal dielectric constant according to the empirical formula (1): wherein, εreff εopt i εi i Vi 11 is the volume of the ith material; the initial size parameters of the designed dielectric layer microstructure are determined according to the above volume ratio; then, the medium properties of the designed dielectric layer material are evaluated based on the scattering parameter inversion method; the scattering parameter inversion method is based on the equivalent medium theory, which equivalently regards the actual artificial medium as a uniform medium, and determines the key parameters such as equivalent relative dielectric constant, equivalent relative magnetic permeability, refractive index and wave impedance by analyzing scattering parameters (S 21 ). The advantage of this method is that it can accurately evaluate the dielectric properties of artificial medium materials, and provide a reliable theoretical basis for designing dielectric layer cells or structures with specific dielectric properties; when designing the microstructure, the initial cell configuration of the design is modeled by parameters and array design is performed to ensure that the dielectric layer has stable dielectric properties and structural strength.

[0025] Figure 2 is a schematic diagram of a two-port network of the scattering parameter inversion method, mainly involving four parameters: equivalent relative dielectric constant (ε eff ), equivalent relative magnetic permeability (μ eff ), refractive index (n) and wave impedance (z). The above four parameters can be calculated by scattering parameters (S 11 and S 21 ) based on formula (2) :

[0026]

[0027] Finally, taking the optimal dielectric constant value as the optimization objective, taking the microstructure size as the design variable, and taking the 3D printing precision as the constraint condition, an optimal dielectric layer microstructure optimization model is established, and the intelligent optimization algorithm is used to solve the microstructure of the dielectric layer material with specific dielectric constant.

[0028] Embodiment 2: The typical structure of the X-band stacked phased array antenna is taken as the design object to realize the optimization of its scanning characteristics

[0029] Figure 3 is the typical structure of the X-band stacked phased array antenna, and the overall size of the unit is 12mm x 12mm, which is composed of a feeding area, a radiation area and a matching area;

[0030] The feeding area consists of a 50Ω coaxial cable, a signal hole, a lower metal ground, a two-way stripline, an upper metal ground with an I-shaped gap, two layers of Rogers RT / duroid 6002 dielectric plates, and an intermediate bonding sheet. The 50Ω coaxial cable serves as a signal input channel, the signal hole transmits current to the stripline, and the stripline achieves impedance conversion (from 50Ω to 100Ω) by splitting the cable into two. The lower metal ground and metal shielding tape provide shielding and grounding, and the upper metal ground with an I-shaped gap couples the signal upward to the radiation area.

[0031] The radiation zone is composed of a lower metal radiation layer 1 with a cut corner, an upper metal radiation layer 2 with a cut corner, a dielectric layer 2 between the metal radiation layers 1 and 2, and a dielectric layer 1 between the upper metal ground and the lower metal radiation layer 1. The metal radiation layer 1 and the metal radiation layer 2 interact with each other through the dielectric layer in between to generate a dual-frequency resonance mode to achieve signal radiation.

[0032] The matching area is composed of a matching dielectric layer and a foam layer, wherein the matching dielectric layer is used to adjust the matching characteristics of the antenna, and the foam layer is used to adjust the distance between the matching layer and the metal radiation layer.

[0033] The X-band stacked phased array antenna is designed for wide bandwidth and angle scanning to achieve impedance matching performance of the phased array antenna at different scanning angles, with the difference between the normal standing wave ratio and the target value 2 (f FX =VSWR-2), the difference between the E-surface scanning to 60° and the target value of 2.5 (f E =VSWR-2.5), the difference between the H-surface scanning to 60° VSWR and the target value (2.5) (f H =VSWR-2.5) is minimized as the objective function. At the same time, parameters that have a significant impact on the radiation mechanism and impedance matching characteristics of the antenna are selected, including the dielectric constant (ε r1 ) and thickness (h1), foam layer thickness (h foam ), the dielectric constant of the dielectric layer 1 in the radiation zone (ε r2 ) and thickness (h2), dielectric constant of dielectric layer 2 (ε r3 ) and thickness (h3), the size of metal radiation layer 1 (x1, y1), the size of metal radiation layer 2 (x2, y2) as design variables, and the cross-section height H (<10mm) as a constraint, the following optimization model is established:

[0034]

[0035] The antenna is processed by powder 3D printing technology, and the material is nylon PA12. The waveguide method is used to test the solid sample to obtain the specific values ​​of dielectric constant 2.45 and dielectric loss 0.017. Considering that the minimum size that can be achieved by 3D printing is 0.5mm, the lower bound lb of the above optimization model can be determined as [1,1,1,1,1,1,1,7,8,4,7], and the upper bound ub =[2.45,3,3,2.45,3,2.45,3,9,10,6,9], and take its initial value as X initial =[2.45,2,2,2.45,2,2.45,2,8,5,8], performance simulation was carried out using high-frequency simulation software HFSS, and the optimization model was solved using Matlab-HFSS-API combined with genetic algorithm. The optimal solution is X=[1.9,1.77,2.21,1.49,2.53,1.57,2.20,7.85,9.23,4.71,7.90]. At this time, the normal VSWR is less than 2, the E-plane scan to 60° VSWR is less than 2.5, and the H-plane scan to 60° VSWR is less than 2.5.

[0036] The dielectric layer design is based on the optimal solution of the above optimization. The following optimization model is established to design a dielectric layer with specific dielectric properties:

[0037]

[0038] Among them, χ is the optimization variable, lb is its lower bound, and ub is its upper bound; f εr is the equivalent dielectric constant of the dielectric layer composed of a unit cell, f goal is the optimal value of the dielectric layer parameters.

[0039] Figure 4 The unit cell configuration and dielectric properties of the antenna matching layer in this embodiment are as follows. Taking nylon PA12 powder for 3D printing as an example, to achieve the design requirement of a dielectric constant of 1.9, Figure 4 The "cross" shaped unit cell in (a) is parametrically modeled, and then a 4×4 unit cell arrangement is used to form a complete dielectric layer to ensure that the dielectric layer has stable dielectric properties and structural strength. The final dielectric layer is composed of nylon and air (dielectric constant 1). The initial volume ratio V can be obtained from formula (4). Nylon :V air =0.62:0.38, the initial value of dimension a is 1.15mm, and the value range is [0.5,2]. This value range can ensure that the designed dielectric layer can be realized by 3D printing technology. By solving the optimization model (4), it can be obtained that when the key parameter a = 1.3, the dielectric constant is 1.9 and the loss tangent is 0.02, as shown in Figure 4 (b) shown.

[0040] Figure 5 The cell configuration and dielectric properties of the antenna dielectric layer 1 in the embodiment; similarly, the dielectric layer 1 adopts the "cross" cell and is arranged by a 4*4 array to form the required dielectric layer, and the design variable is b, and the initial volume fraction V can be obtained by formula (1) Figure 5 (a) "cross" cell and is arranged by a 4*4 array to form the required dielectric layer, and the design variable is b, and the initial volume fraction V can be obtained by formula (1) Nylon :V air = 0.43:0.57, and the initial value of b is 0.73 mm, and the value range is still taken as [0.5, 2] to ensure the process feasibility of the designed material. Further, by solving the optimization model (4), when b = 1.1 mm, the dielectric constant is 1.57, and the loss tangent is 0.02, and the solving result is shown in Figure 5 (b).

[0041] Figure 6 The configuration design of the antenna dielectric layer 2 in the embodiment, since the metal radiation layer needs to be processed on the upper and lower dielectric layers, when designing the cell, it is necessary to consider that there is enough material to arrange the metal radiation layer in the plane, and the 3D printing precision cannot be met by continuing to use the cell design, therefore, the dielectric layer configuration shown in Figure 6 is proposed, and the optimization variables include d, e, f, and g. The antenna unit configuration is formed by matching the above-mentioned "cross" matching layer and the dielectric layer 1, and by optimization and solving, when d = 2.2 mm, e = 4.6 mm, f = 1.53 mm, and g = 10.2 mm, the radiation performance of the antenna can meet the requirements that the normal VSWR < 2, the E-plane scanning to 60° VSWR < 2.5, and the H-plane scanning to 60° VSWR < 2.5.

[0042] Figure 7 The overall scheme of the antenna after optimization in the embodiment is composed of the dielectric layer designed based on the above-mentioned design process.

[0043] Figure 8 The comparison and analysis result of the standing wave ratio of the antenna and the reference antenna in the embodiment, the reference antenna is an antenna with a nylon material as a dielectric substrate without microstructure design; compared with the reference antenna, the weight of the optimized antenna dielectric layer is reduced by 47.89%; and the design antenna can meet the X-band (8-12 GHz) VSWR wide-angle scanning characteristics, which is obviously better than the reference antenna;

[0044] Figure 8 (a) is the normal standing wave ratio of the overall scheme of the antenna after optimization in the embodiment and the reference antenna at different frequencies, and it can be found that the reference antenna only meets VSWR less than 2 at 2-9.75 GHz, and the VSWR reaches 15 at 10.5 GHz, while the design antenna can meet X-band (8-12 GHz) VSWR less than 2.

[0045] Figure 8 (b) is the E-plane scan standing wave ratio of the overall scheme after the antenna is optimized in the embodiment and the reference antenna at different frequencies. It can be found that the standing wave ratios of the reference antenna at scan angles of 30°, 45° and 60° are all greater than 2.5, and the standing wave ratio is slightly improved as the scan angle increases. The standing wave ratio of the designed antenna at scan angles of 30°, 45° and 60° is less than 2.5.

[0046] Figure 8 (c) is the H-plane scan standing wave ratio of the overall scheme after the antenna is optimized in the embodiment and the reference antenna at different frequencies. It can be found that the standing wave ratios of the reference antenna at scan angles of 30°, 45° and 60° are all greater than 2.5, and the standing wave ratio deteriorates more obviously as the scan angle increases. The standing wave ratio of the designed antenna at scan angles of 30°, 45° and 60° is less than 2.5.

[0047] Figure 9 is the E-plane and H-plane pattern of the antenna optimized in the embodiment. It can be found that for all sampling frequencies, the gain of the designed antenna decreases by less than 2dB within the range of ±45°, and the gain decreases by less than 4dB within the range of ±60°. In terms of cross-polarization range, whether in E-plane or H-plane, the cross-polarization of the designed antenna is below -35dB within the range of ±90°, which has good polarization purity.

[0048] In summary, the embodiment first finds the optimal material properties and size parameters through medium layer parameter optimization, then designs the medium layer unit cell or structure based on the scattering parameter inversion method, and comprehensively considers the 3D printing accuracy and the implementability of the metal layer process, finally obtains specific medium layer size and dielectric parameters, and realizes the manufacturability of the medium layer and the good matching characteristics and good polarization purity of the designed antenna, thereby verifying the effectiveness of the proposed method.

Claims

1. A dielectric layer design method for enhancing the performance of a phased array antenna, characterized in that: It involves two steps: Step 1 is to establish an optimization model for the dielectric layer material properties and metal layer size parameters suitable for stacked antennas based on the wide bandwidth and angular scanning characteristics of phased array antennas; and obtain the optimal design parameters by solving the optimization model. Step 2 is to design a unit cell or structure of the dielectric layer based on the scattering parameter inversion method according to the optimal parameter result of step 1, so as to design a dielectric layer with optimal dielectric properties, thereby achieving the expected wide bandwidth angular scanning characteristics; Step 1: establishing an optimization model for dielectric layer material properties and metal layer size parameters based on the wide bandwidth and angular scanning characteristics of the phased array antenna, and obtaining the optimal dielectric constant and metal layer size parameters by solving the optimization model; Step 2: Based on the optimal result in step 1, the unit cell or structure of the dielectric layer is designed based on the scattering parameter inversion method. According to step 1, it is necessary to comprehensively consider the 3D printing accuracy and the feasibility of the metal layer process. Specifically, the design scheme of each dielectric layer is first determined by analyzing the hierarchical relationship and design points of each dielectric layer. Then, the initial volume ratio of the material is determined according to the optimal dielectric constant according to the empirical formula (1): ; Among them, ε reff is the optimal dielectric constant, ε i is the dielectric constant of the i-th type material, V i is the volume of the i-th type of material; the initial size parameters of the designed dielectric layer microstructure are determined based on the above volume ratio; then, the dielectric properties of the designed dielectric layer material are evaluated based on the scattering parameter inversion method; The scattering parameter inversion method is based on the equivalent medium theory, which treats the actual artificial medium as a homogeneous medium and analyzes the scattering parameter S 11 and S 21 To determine key parameters such as equivalent relative permittivity, equivalent relative permeability, refractive index and wave impedance; The scattering parameter inversion method mainly involves four parameters: equivalent relative dielectric constant ε eff , equivalent relative permeability μ eff , refractive index n and wave impedance z; the above four parameters are expressed by the scattering parameter S 11 and S 21 Based on formula (2), we can get: ； Finally, taking the optimal dielectric constant value as the optimization target, the microstructure size as the design variable, and the 3D printing accuracy as the constraint condition, an optimal dielectric layer microstructure optimization model is established. The dielectric layer material microstructure with a specific dielectric constant can be obtained by solving it through an intelligent optimization algorithm.

2. The dielectric layer design method for enhancing the performance of a phased array antenna according to claim 1, characterized in that: In step 1, the optimization model is designed to achieve the wide-bandwidth angular scanning characteristic requirements of the stacked antenna, and the dielectric properties and thickness of the dielectric layer constituting the stacked antenna and the size parameters of the radiation patch are used as optimization variables. The optimal result is solved by the optimization algorithm, wherein the wide-bandwidth angular scanning characteristic is evaluated by a standing wave ratio less than a specified value.

3. The dielectric layer design method for enhancing the performance of a phased array antenna according to claim 1, characterized in that: In step 2, the implementation of the method for designing a unit cell or structure of a dielectric layer based on the scattering parameter inversion method requires first analyzing the characteristics of the designed dielectric layer and the design factors that need to be considered, and then determining the material design scheme, and then determining the initial volume ratio of the dielectric layer required to have optimal material properties based on an empirical formula, and then determining the initial configuration of the unit cell and performing parametric modeling, and then evaluating the dielectric constant of the dielectric layer based on the scattering parameter inversion method, and obtaining the optimal dielectric layer unit cell or configuration by establishing an optimization model, and finally solving the dielectric layer microstructure with optimal dielectric properties through an intelligent optimization algorithm; wherein, in the process of designing the dielectric layer unit cell, 3D printing accuracy and the feasibility of the metal layer process are focused on to ensure that the designed dielectric layer has manufacturability.

4. The dielectric layer design method for enhancing the performance of a phased array antenna according to claim 1, characterized in that: The typical structure of the X-band stacked phased array antenna has an overall unit size of 12mm×12mm and consists of a feed area, a radiation area, and a matching area. The feed area consists of a 50Ω coaxial cable, a signal hole, a lower metal ground layer, a two-way stripline, an upper metal ground layer with an I-shaped gap, two layers of Rogers RT / duroid 6002 dielectric board, and an intermediate bonding sheet. The 50Ω coaxial cable serves as the signal input channel, the signal hole transmits current to the stripline, and the stripline achieves impedance conversion by splitting the cable into two. The lower metal ground layer and metal shielding tape provide shielding and grounding, and the upper metal ground layer with an I-shaped gap couples the signal upward to the radiation area. The radiation zone is composed of a first metal radiation layer with a cut corner at the bottom, a second metal radiation layer with a cut corner at the top, a second dielectric layer between the first and second metal radiation layers, and a first dielectric layer between the upper metal ground and the first metal radiation layer at the bottom. The first and second metal radiation layers interact through the dielectric layer in between to generate a dual-frequency resonance mode, thereby achieving signal radiation. The matching area is composed of a matching dielectric layer and a foam layer, wherein the matching dielectric layer is used to adjust the matching characteristics of the antenna, and the foam layer is used to adjust the distance between the matching layer and the metal radiation layer; The X-band stacked phased array antenna is designed for wide bandwidth and angle scanning to achieve impedance matching performance of the phased array antenna at different scanning angles, with the difference between the normal standing wave ratio and the target value 2 f FX =VSWR-2, the difference between the E-surface scanning to 60° and the target value of 2.5 E =VSWR-2.5, H plane scan to 60° The difference between the VSWR and the target value of 2.5 is f H =VSWR-2.5 weighted sum is minimized as the objective function. At the same time, parameters that have a significant impact on the radiation mechanism and impedance matching characteristics of the antenna are selected, including the dielectric constant ε of the matching layer r1 and thickness h1, foam layer thickness h foam , the dielectric constant ε of the first dielectric layer in the radiation zone r2 and thickness h2, the dielectric constant ε of the second dielectric layer r3 The thickness h3, the dimensions x1, y1 of the first metal radiation layer (1), and the dimensions x2, y2 of the second metal radiation layer (2) are used as design variables, and the section height H<10 mm is used as a constraint to establish the following optimization model: ； The antenna is processed using powder 3D printing technology, and the material used is nylon PA12. The waveguide method is used to test the solid sample, and the specific values ​​obtained are a dielectric constant of 2.45 and a dielectric loss of 0.

017. Considering that the minimum size that can be achieved by 3D printing is 0.5mm, the lower bound lb = [1,1,1,1,1,1,1,7,8,4,7] and the upper bound ub = [2.45,3,3,2.45,3,2.45,3,9,10,6,9] of the above optimization model can be determined, and their initial values ​​are taken as X initial =[2.45,2,2,2.45,2,2.45,2,8,5,8]. Performance simulation was performed using high-frequency simulation software HFSS. The optimization model was solved using Matlab-HFSS-API combined with a genetic algorithm. The optimal solution is X = [1.9,1.77,2.21,1.49,2.53,1.57,2.20,7.85,9.23,4.71, 7.90]. At this point, the normal VSWR is less than 2, the E-plane scan to 60° VSWR is less than 2.5, and the H-plane scan to 60° VSWR is less than 2.

5. The dielectric layer design is based on the optimal solution of the above optimization. The following optimization model is established to design a dielectric layer with specific dielectric properties: ； in, is the optimization variable, lb is its lower bound, ub is its upper bound; f εr is the equivalent dielectric constant of the dielectric layer composed of a unit cell, f goal is the optimal value of the dielectric layer parameters.

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