Metasurface antenna based on third-order Hilbert fractal structure and design method of antenna

Abstract

The invention relates to a metasurface antenna based on a third-order Hilbert fractal structure. The metasurface antenna comprises a first substrate, a second substrate, a fractal patch, an air layer, a corner cut patch, a metal ground plane and a coaxial feeder line. The first substrate and the second substrate are separated by an air layer, the thickness of the first substrate is greater than that of the second substrate, and the first substrate and the second substrate are fixed together at an interval; a fractal patch is arranged on the front face of the first substrate, a corner cut patch is arranged on the front face of the second substrate, a metal ground plane is arranged on the back face of the second substrate, and the pair of coaxial feeder lines are used for feeding the whole antenna. By utilizing the self-similarity and space filling capability of the Hilbert fractal structure, the length of a current path is increased through fractal iteration, the bandwidth is expanded, the metasurface unit arrangement and the feed structure are optimized at the same time, a simulation result shows that the antenna has 19.5% broadband performance and good gain within the working frequency range from 4.86 GHz to 5.91 GHz, and the antenna has wide application prospects. And the antenna has the characteristics of low profile, wide band and miniaturization, and is suitable for various application scenes.

Description

Technical Field

[0001] The present invention relates to a metasurface antenna and an antenna design method, and in particular to a metasurface antenna based on a third-order Hilbert fractal structure that utilizes its self-similarity and space-filling capability to increase the current path length and expand the bandwidth through fractal iteration. Background Art

[0002] Against the backdrop of the rapid development of wireless communication technology, the rapid advancement of 5G-A technology and the vigorous development of fields such as the Internet of Things, satellite communications, and radar systems have placed higher demands on the bandwidth, gain, and miniaturization of antennas. On the one hand, multi-band communications, high-speed data transmission, and stable operation in complex electromagnetic environments require antennas to have a wider operating bandwidth to cover a wide frequency range; on the other hand, with the trend of miniaturization and integration of electronic devices, antenna size is strictly limited, and miniaturization is urgently needed. Although traditional microstrip antennas are widely used due to their simple structure and ease of integration, their narrowband characteristics severely limit their application in broadband systems. Methods of expanding bandwidth, such as increasing the thickness of the dielectric layer or using low-dielectric-constant materials, will result in an increase in antenna size or a decrease in radiation efficiency, making it difficult to balance miniaturization and broadband requirements. Fractal geometry, with its self-similarity and space-filling capabilities, provides new ideas for broadband and miniaturized antenna design. Summary of the Invention

[0003] In response to the above problems, the main purpose of the present invention is to provide a metasurface antenna based on a third-order Hilbert fractal structure, which utilizes its self-similarity and space-filling ability to increase the current path length and expand the bandwidth through fractal iteration.

[0004] The present invention solves the above-mentioned technical problems through the following technical solutions: a metasurface antenna based on a third-order Hilbert fractal structure, wherein the metasurface antenna based on the third-order Hilbert fractal structure comprises: a first substrate, a second substrate, a fractal patch, an air layer, a cut-angle patch, a metal ground plane, and a coaxial feed line; the first substrate and the second substrate are separated by an air layer, the thickness of the first substrate is greater than that of the second substrate, and the first substrate and the second substrate are fixed together with a gap; a fractal patch is provided on the front side of the first substrate, the fractal patch includes multiple groups, and is evenly distributed on the front side of the first substrate; a cut-angle patch is provided on the front side of the second substrate, and a metal ground plane is provided on the back side; a pair of coaxial feed lines is used to feed the entire antenna.

[0005] In a specific implementation example of the present invention, a pair of coaxial feed lines pass through the second substrate, the inner core of the coaxial feed line is connected to the feeding point of the corner patch, and the outer layer of the coaxial feed line is welded to the ground plane of the second substrate and fixed by a welding process to form an integrated feeding structure.

[0006] In a specific embodiment of the present invention, the thickness of the first substrate is 3.408 mm, and the thickness of the second substrate is 0.813 mm.

[0007] In a specific embodiment of the present invention, the first substrate and the second substrate are fixed together using nylon screws located at four corners of the first substrate and the second substrate.

[0008] In a specific embodiment of the present invention, the first substrate and the fractal patch are integrated by a printed circuit etching process; the second substrate and the corner-cut patch are integrated by a printed circuit etching process.

[0009] In a specific embodiment of the present invention, the first substrate is a Rogers RO4003C substrate; the second substrate is a Rogers RO4003C substrate.

[0010] In a specific implementation example of the present invention, the third-order Hilbert fractal metasurface effectively achieves bandwidth expansion by utilizing the multi-frequency characteristics generated by the self-similarity of the fractal iterative structure; and achieves antenna miniaturization by utilizing the space filling ability of the fractal iterative structure.

[0011] In a specific implementation example of the present invention, the corner-cut patch optimizes the radiation pattern by cutting the four corners, reduces the main lobe width or improves the control of the side lobes, and makes the radiation more concentrated or more directional.

[0012] A design method for a metasurface antenna based on a third-order Hilbert fractal structure, characterized in that the design method comprises the following steps:

[0013] Step 1: Metasurface Antenna Structure Design

[0014] A Rogers RO4003C substrate with a dielectric constant of 3.55 was selected, consisting of a 3.048mm thick first substrate and a 0.813mm thick second substrate, separated by an air layer. The top metasurface utilizes a 3×3 array of third-order Hilbert fractal elements, effectively expanding the bandwidth through the multi-frequency characteristics generated by the self-similarity of the fractal structure. The spatial filling capability of the fractal iterative structure is utilized to increase the current path length, thereby achieving antenna miniaturization. A cut-angle patch is designed on the surface of the second substrate as an excitation source, and a ground plane is provided at the bottom, providing dual-polarization excitation via dual coaxial feed lines.

[0015] Step 2: Metasurface Unit Fractal Structure and Optimization

[0016] Based on the self-similarity and space-filling capability of the Hilbert curve, the system was iterated according to the "half-size + rotation-fill" rule: the 0th order was a square patch, and the 3rd order structure was formed by 2nd order scaling and rotation. Unit geometry parameters were optimized, and structural irregularities were adjusted through electromagnetic simulation to ensure that the electrical length matched the operating frequency.

[0017] Step 3: 3×3 metasurface array construction

[0018] The optimized third-order Hilbert fractal units are deployed on the top layer of the first substrate 1 in a matrix of 3 rows and 3 columns to form a periodic metasurface structure. The overall size is maintained at 30 mm × 30 mm. The uniformity of electromagnetic coupling is ensured by arranging the units at equal intervals.

[0019] Step 4: Electromagnetic simulation verification

[0020] Using CST Studio Suite, we modeled 0th-, 2nd-, and 3rd-order Hilbert fractal metasurface antennas and analyzed their reflection coefficients and radiation patterns. We compared the impedance bandwidths of different orders: the 0th-order bandwidth was 9%, the 2nd-order bandwidth increased to 16.1%, and the 3rd-order bandwidth reached 19.5%. We also verified the 3rd-order radiation performance: the 3rd-order antenna exhibited a mainlobe gain of 6.93 to 7.40 dBi in the 4.9 to 5.8 GHz frequency band.

[0021] Step 5: Result analysis and performance summary:

[0022] The increase in fractal order significantly expands the impedance bandwidth, which is attributed to the enhanced multi-frequency characteristics; without increasing the size of the structure, the bandwidth is increased from 9% to 19.5%, and the maximum main lobe gain is 7.4dBi, meeting the application requirements of the 4.0-8.0GHz band.

[0023] The positive progressive effect of the present invention is that the metasurface antenna based on the third-order Hilbert fractal structure and the antenna design method provided by the present invention have the following advantages: the present invention proposes a metasurface antenna based on the third-order Hilbert fractal structure, which utilizes the multi-frequency characteristics generated by the self-similarity of its fractal structure to effectively achieve bandwidth expansion, and increases the current path length by utilizing the space filling ability of the fractal iterative structure, thereby realizing antenna miniaturization; simulation results show that the antenna has 19.5% broadband performance and good gain in the operating frequency range of 4.86GHz to 5.91GHz, and its low profile, broadband and miniaturization characteristics make it suitable for various application scenarios in the C band. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1-1 It is the Hilbert fractal curve iteration process (0th order) in the present invention.

[0025] Figure 1-2 It is the Hilbert fractal curve iteration process (1st order) in the present invention.

[0026] Figure 1-3 It is the Hilbert fractal curve iteration process (2nd order) in the present invention.

[0027] Figure 2 This is the geometric structure of the antenna in the present invention (side view).

[0028] Figure 3-1 Schematic diagram of the corner-cut patch in the present invention.

[0029] Figure 3-2 Schematic diagram of the ground layer in the present invention.

[0030] Figure 4-1 It is the fractal iteration process of the hypersurface unit in the present invention (0th order Hilbert fractal).

[0031] Figure 4-2 It is the fractal iteration process of the hypersurface unit in the present invention (1st order Hilbert fractal).

[0032] Figure 4-3 It is the fractal iteration process of the hypersurface unit in the present invention (2nd order Hilbert fractal).

[0033] Figure 4-4 It is the fractal iteration process of the hypersurface unit in the present invention (3rd order Hilbert fractal).

[0034] Figure 5-1 This is one of the evolution processes of the Hilbert fractal metasurface arrays of different orders in the present invention ( Figure 4-1 extensions).

[0035] Figure 5-2 This is the second evolution process of the Hilbert fractal metasurface array of different orders in the present invention ( Figure 4-3 extensions).

[0036] Figure 5-3 This is the third evolution process of the Hilbert fractal metasurface array of different orders in the present invention ( Figure 4-4 extensions).

[0037] Figure 6-1 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 4.9 GHz in the YZ plane.

[0038] Figure 6-2 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 5.2 GHz in the YZ plane.

[0039] Figure 6-3 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 5.5 GHz in the YZ plane.

[0040] Figure 6-4 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 5.8 GHz in the YZ plane.

[0041] Figure 7is the S of the 0th, 2nd and 3rd order Hilbert metasurfaces in the present invention. 11 parameter.

[0042] The following are the names corresponding to the labels in the present invention:

[0043] Figure 2 Middle: first substrate 1, second substrate 2, fractal patch 3, air layer 4, cut-angle patch 5, ground plane 6, coaxial feed line 7. DETAILED DESCRIPTION

[0044] The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings to illustrate the technical solutions of the present invention in detail.

[0045] Figure 2 The geometric structure of the antenna in the present invention (side view), Figure 3-1 is a schematic diagram of the corner-cut patch in the present invention, Figure 3-2 This is a schematic diagram of the ground layer in the present invention, as shown in the above figure: the metasurface antenna based on the third-order Hilbert fractal structure provided by the present invention includes: a first substrate 1, a second substrate 2, a fractal patch 3, an air layer 4, a cut-angle patch 5, a ground plane 6, and a coaxial feed line 7; the first substrate and the second substrate are separated by an air layer 4, the thickness of the first substrate is greater than the thickness of the second substrate, and the first substrate and the second substrate are fixed together with a gap; a fractal patch is provided on the front side of the first substrate, and the fractal patch 3 includes multiple groups, which are evenly distributed on the front side of the first substrate; a cut-angle patch 5 is provided on the front side of the second substrate, and a metal ground plane 6 is provided on the back side, and a pair of coaxial feed lines are used to feed the entire antenna.

[0046] In the present invention, a pair of coaxial feed lines are used to pass through the second substrate. The inner core of the coaxial feed line is connected to the feeding point of the cut-corner patch. The outer layer of the coaxial feed line is welded to the ground plane of the second substrate and fixed by a printed circuit process (such as etching and then welding) to form an integrated feeding structure.

[0047] The thickness of the first substrate is 3.408 mm, and the thickness of the second substrate is 0.813 mm. The first substrate and the second substrate can be fixed together using nylon screws located at the four corners of the first substrate and the second substrate.

[0048] The first substrate and fractal patch are integrated through a printed circuit etching process without any additional mechanical fixing method. Generally, the substrate and the metal surface are produced as a whole, and then the fractal patch is etched on the metal surface.

[0049] The second substrate and the corner-cut patch are integrated through a printed circuit etching process, without the need for additional mechanical fixing parts. Generally, the substrate and the metal surface are produced as a whole, and then etched into shape on the metal surface.

[0050] In a specific implementation of the present invention, the first substrate is generally a Rogers RO4003C substrate; the second substrate may also be a Rogers RO4003C substrate.

[0051] In a specific implementation of the present invention, the third-order Hilbert fractal metasurface effectively achieves bandwidth expansion by utilizing the multi-frequency characteristics generated by the self-similarity of the fractal iterative structure; and achieves antenna miniaturization by utilizing the space filling ability of the fractal iterative structure.

[0052] In a specific implementation of the present invention, the cut corner patch optimizes the radiation pattern by cutting the four corners, reduces the main lobe width or improves the control of the side lobes, and makes the radiation more concentrated or more directional.

[0053] Figure 1-1 is the Hilbert fractal curve iteration process (0th order) in the present invention, Figure 1-2 is the Hilbert fractal curve iteration process (1st order) in the present invention, Figure 1-3 This is the Hilbert fractal curve iteration process (2nd order) in the present invention. As shown in the above figure: Figure 1-1 This is a 0th-order Hilbert fractal: a basic structure, usually a simple line segment or initial geometric shape, which is the starting point of the fractal iteration. Its form is the most primitive unit and has not undergone fractal transformation. Figure 1-2 A 1st-order Hilbert fractal is generated by applying geometric transformations (such as folding or scaling) to a 0th-order structure. It begins to exhibit the fractal's "self-similarity"—the local shape is similar to the overall structure. At this point, the curve begins to fill space, but with lower complexity. Figure 1-3 It is a 2nd-order Hilbert fractal: further iterating on the basis of the 1st order, the number of folds of the curve increases, the space filling ability is enhanced, and the length of the line segment is significantly extended within a limited area. This order provides an intermediate transition form for the design of subsequent high-order fractals.

[0054] Figure 4-1 is the fractal iteration process of the hypersurface unit in the present invention (0th order Hilbert fractal), Figure 4-2 is the fractal iteration process of the hypersurface unit in the present invention (1st order Hilbert fractal), Figure 4-3 is the fractal iteration process of the hypersurface unit in the present invention (2nd order Hilbert fractal), Figure 4-4 It is the fractal iteration process of the hypersurface unit in the present invention (3rd order Hilbert fractal). Figure 4-1 As shown in the figure, the 0th-order Hilbert fractal in the present invention is the initial basic structure, showing a simple square metal patch unit, which is the starting point of the fractal iteration. At this time, the unit electrical length is the shortest, corresponding to a higher operating frequency.

[0055] like Figure 4-2As shown in the figure, the first-order Hilbert fractal in this invention is the first fractal iteration based on the zero-order structure, which fills the space with curved line segments to form a more complex path. Compared with the zero-order, its electrical length is increased, and the operating frequency can be reduced within the same area.

[0056] like Figure 4-3 As shown in the figure, the second-order Hilbert fractal in the present invention further fracts the first-order structure, increasing the number of line segment bends and the structural complexity. The electrical length is further increased compared to the first-order, and the frequency response shifts to a lower frequency band, laying the foundation for expanding bandwidth.

[0057] like Figure 4-4 As shown: The third-order Hilbert fractal in this invention is the highest-order fractal structure. By reducing the length and width of the second-order structure to half and rotating it before filling it, a denser meandering path is formed. Although the appearance appears irregular due to the optimization process, its electrical length is maximized, and its self-similarity effectively extends the antenna's impedance bandwidth to 19.5%.

[0058] Figure 5-1 This is one of the evolution processes of the Hilbert fractal metasurface arrays of different orders in the present invention ( Figure 4-1 extensions). Figure 5-2 This is the second evolution process of the Hilbert fractal metasurface array of different orders in the present invention ( Figure 4-3 extensions). Figure 5-3 This is the third evolution process of the Hilbert fractal metasurface array of different orders in the present invention ( Figure 4-4 The figure above shows: Figure 5-1 、 5-2 , 5-3 is the evolution process of Hilbert fractal metasurface arrays of different orders in the present invention. Figure 4-1 、 4-3 , 4-4 are fractal designs of a single unit, and Figures 5-1, 5-2, and 5-3 are based on Figure 4-1 、 4-3 , the unit structure in 4-4, Figure 5-1 、 5-2 ,5-3 is Figure 4-1 、 4-3 , 4-4 Structural expansion.

[0059] Figure 6-1 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 4.9 GHz in the YZ plane. Figure 6-2 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 5.2 GHz in the YZ plane. Figure 6-3 This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 5.5 GHz in the YZ plane. Figure 6-4This is the simulation result of the two-dimensional radiation pattern of the third-order Hilbert metasurface antenna in the present invention at a frequency of 5.8 GHz in the YZ plane.

[0060] Figure 6-1 The corresponding frequency is 4.9 GHz, and the antenna main lobe gain is 6.93 dBi. The radiation pattern shows typical radiation characteristics, with a clear main lobe direction and low side lobe levels, ensuring the directional radiation capability of the signal. Figure 6-2 The operating frequency is 5.2 GHz, and the main lobe gain is increased to 7.11 dBi. Compared with the 4.9 GHz frequency, the radiation main lobe directivity is further optimized, and the energy concentration is higher. Figure 6-3 At 5.5 GHz, the mainlobe gain reaches a maximum of 7.40 dBi, the peak value within the entire operating frequency band. At this point, the mainlobe width of the radiation pattern is narrow, and the sidelobe suppression is significant, demonstrating the antenna's optimal radiation performance at this frequency. Figure 6-4 At 5.8 GHz, the mainlobe gain is 7.24 dBi. Despite approaching the upper bandwidth limit, the radiation pattern maintains a relatively regular shape, with even mainlobe energy distribution, demonstrating the antenna's stability across a wide frequency band.

[0061] Figure 7 is the S of the 0th, 2nd and 3rd order Hilbert metasurfaces in the present invention. 11 parameter. Figure 7 Plotting the simulated reflection coefficients for the three structures together, the impedance bandwidth of the antenna increases as the Hilbert fractal order increases.

[0062] The present invention also provides a design method for a metasurface antenna based on a third-order Hilbert fractal structure, the design method comprising the following steps:

[0063] Step 1: Metasurface Antenna Structure Design

[0064] A Rogers RO4003C substrate with a dielectric constant of 3.55 was selected, consisting of a 3.048mm thick first substrate 1 (where the metasurface is deployed on the top layer) and a 0.813mm thick second substrate (where the excitation structure is deployed on the bottom layer), separated by an air layer. The top metasurface utilizes a 3×3 array of third-order Hilbert fractal elements, effectively expanding the bandwidth through the multi-frequency characteristics generated by the self-similarity of the fractal structure. The spatial filling capability of the fractal iterative structure is utilized to increase the current path length, thereby achieving antenna miniaturization. A cut-angle patch is designed on the surface of the second substrate as an excitation source, and a ground plane (GND) is provided at the bottom, providing dual-polarization excitation via dual coaxial feed lines.

[0065] Step 2: Metasurface unit fractal structure and optimization:

[0066] Based on the self-similarity and space-filling capability of the Hilbert curve, the system was iterated according to the "half-size + rotation-fill" rule: the 0th order was a square patch, and the 3rd order structure was formed by 2nd order scaling and rotation. Unit geometry parameters were optimized, and structural irregularities were adjusted through electromagnetic simulation to ensure that the electrical length matched the operating frequency.

[0067] Step 3: 3×3 metasurface array construction:

[0068] The optimized third-order Hilbert fractal units are deployed on the top layer of the first substrate 1 in a matrix of 3 rows and 3 columns to form a periodic metasurface structure. The overall size is maintained at 30 mm × 30 mm. The electromagnetic coupling uniformity is ensured by arranging the units with equal spacing (spacing parameters such as g1 = 0.8 mm and g = 0.6 mm).

[0069] Step 4: Electromagnetic simulation verification:

[0070] Use CST Studio Suite to model the 0th, 2nd, and 3rd order Hilbert fractal metasurface antennas and analyze the reflection coefficient (S 11 ) and radiation patterns; compared the impedance bandwidths of different orders: the 0th order bandwidth is 9% (4.97-5.44GHz), the 2nd order is increased to 16.1% (4.91-5.85GHz), and the 3rd order reaches 19.5% (4.86-5.91GHz); verified the 3rd order radiation performance: the 3rd order antenna has a main lobe gain of 6.93-7.40dBi in the 4.9-5.8GHz frequency band.

[0071] Step 5: Result analysis and performance summary:

[0072] Increasing the fractal order significantly expands the impedance bandwidth, attributed to enhanced multi-frequency characteristics. Without increasing the size of the structure, the bandwidth is increased from 9% to 19.5%, with a maximum mainlobe gain of 7.4dBi, meeting the requirements of C-band (4.0-8.0GHz) applications. This conclusion validates the effectiveness of the Hilbert fractal in miniaturizing, broadband, and low-profile antenna design.

[0073] The present invention proposes a metasurface antenna based on a third-order Hilbert fractal structure. Through a 3×3 array structure design, the impedance bandwidth is increased from 9% to 19.5%, and the maximum main lobe gain reaches 7.4dBi. It can be applied to C-band wireless communications, satellite communications or radar systems.

[0074] The present invention deploys a 3×3 array of third-order Hilbert fractal elements on the top surface of the first substrate 1 to manipulate the direction of electromagnetic wave radiation and bandwidth expansion. "Deployment" here refers to deploying a 3×3 array of third-order Hilbert fractal elements on the top surface of the substrate 1 through a printed circuit etching process to manipulate the direction of electromagnetic wave radiation and bandwidth expansion.

[0075] A corner-cut patch is placed on the top surface of the second substrate 2, with the four corners cut to optimize the radiation pattern, and a ground layer is set at the bottom. Specifically, through a printed circuit etching process, a corner-cut patch is placed on the top surface of the second substrate 2, with the four corners cut to optimize the radiation pattern, and a ground layer is set at the bottom.

[0076] Both the first and second substrates are made of Rogers RO4003C material with a dielectric constant of 3.55. In this invention, the thickness of the first substrate 1 is 3.048mm, and the thickness of the second substrate 2 is 0.813mm, with an air space reserved between the two layers. In this invention, this thickness must be fixed; any deviation will affect the antenna's radiation characteristics. These are two typical Rogers RO4003C factory thicknesses.

[0077] The present invention uses a pair of coaxial feed lines to feed the entire antenna. The pair of coaxial feed lines passes through the second substrate, the inner core is connected to the feeding point of the corner patch, the outer shielding layer is welded to the ground surface of the second substrate, and is fixed by a printed circuit process (such as etching and then welding) to form an integrated feeding structure.

[0078] The structural advantages of the present invention are: low profile, miniaturization, fractal design with both self-similarity and space-filling capabilities, and optimized antenna performance.

[0079] Performance verification: 3D electromagnetic simulations conducted with CST Studio Suite demonstrated an S11 <-10dB impedance bandwidth of 4.86 to 5.91GHz (19.5%), mainlobe gain ranging from 6.93 to 7.40dBi at various frequencies, and a favorable radiation pattern, achieving broadband radiation within the C-band and meeting the requirements of wireless communications, satellite communications, and radar systems.

[0080] The key optimization parameters are shown in Table 1:

[0081] parameter L W <![CDATA[L r ]]> <![CDATA[W r ]]> <![CDATA[L e ]]> <![CDATA[L p ]]> <![CDATA[W p ]]> Unit (mm) 30 30 12 11 2 6.5 6.5 parameter g <![CDATA[g1]]> <![CDATA[g2]]> <![CDATA[h1]]> <![CDATA[h2]]> <![CDATA[h3]]> / Unit (mm) 0.6 0.8 0.83 3.408 1 0.813 /

[0082] Note: L and W are the length and width of the metasurface as a whole, Lr and Wr are the length and width of the radiation unit, Lc is the length of the cut corner, Lp and Wp are the length and width of the patch unit, g1, g2, and g correspond to the gap sizes at different positions, h1, h3, and h2 are the thickness of the first substrate, the thickness of the second substrate, and the thickness of the air layer, respectively.

[0083] As can be seen from the table above, the optimized geometric parameters of the metasurface antenna based on the third-order Hilbert fractal, including the overall size of the metasurface, fractal unit size, corner patch parameters, unit gap, feed structure size and substrate thickness, have been optimized through simulation to achieve a broadband performance of 19.5% and good gain in the frequency range of 4.86 GHz to 5.91 GHz.

[0084] The present invention proposes a metasurface antenna based on a third-order Hilbert fractal structure, which utilizes the multi-frequency characteristics generated by the self-similarity of its fractal structure to effectively achieve bandwidth expansion, and increases the current path length by utilizing the space-filling ability of the fractal iterative structure, thereby realizing antenna miniaturization; simulation results show that the antenna has a broadband performance of 19.5% and good gain in the operating frequency range of 4.86GHz to 5.91GHz, and its low profile, broadband and miniaturization characteristics make it suitable for various application scenarios in the C band.

[0085] The basic principles, main features and advantages of the present invention are shown and described above. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention, which is defined by the appended claims and their equivalents.

Claims

1. A metasurface antenna based on a third-order Hilbert fractal structure, characterized by: The metasurface antenna based on the third-order Hilbert fractal structure includes: a first substrate, a second substrate, a fractal patch, an air layer, a cut-angle patch, a metal ground plane, and a coaxial feed line; the first substrate and the second substrate are separated by an air layer, the thickness of the first substrate is greater than that of the second substrate, and the first substrate and the second substrate are fixed together with a gap; a fractal patch is provided on the front side of the first substrate, and the fractal patch includes multiple groups and is evenly distributed on the front side of the first substrate; a cut-angle patch is provided on the front side of the second substrate, and a metal ground plane is provided on the back side; a pair of coaxial feed lines is used to feed the entire antenna.

2. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, characterized in that: A pair of coaxial feed lines pass through the second substrate, the inner core of the coaxial feed line is connected to the feeding point of the cut-angle patch, and the outer layer of the coaxial feed line is welded to the ground plane of the second substrate and fixed by a welding process to form an integrated feeding structure.

3. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, characterized in that: The thickness of the first substrate is 3.408 mm, and the thickness of the second substrate is 0.813 mm.

4. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, wherein: The first substrate and the second substrate are fixed together using nylon screws located at four corners of the first substrate and the second substrate.

5. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, characterized in that: The first substrate and the fractal patch are integrated through a printed circuit etching process; the second substrate and the cut-corner patch are integrated through a printed circuit etching process.

6. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, characterized in that: The first substrate is a Rogers RO4003C substrate; the second substrate is a Rogers RO4003C substrate.

7. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, characterized in that: The third-order Hilbert fractal metasurface effectively achieves bandwidth expansion by utilizing the multi-frequency characteristics generated by the self-similarity of the fractal iterative structure; and achieves antenna miniaturization by utilizing the space filling ability of the fractal iterative structure.

8. The metasurface antenna based on a third-order Hilbert fractal structure according to claim 1, characterized in that: The corner-cut patch optimizes the radiation pattern by cutting the four corners, reduces the main lobe width or improves the control of the side lobes, and makes the radiation more concentrated or more directional.

9. A method for designing a metasurface antenna based on a third-order Hilbert fractal structure according to any one of claims 1 to 8, characterized in that: The design method includes the following steps: Step 1: Metasurface Antenna Structure Design A Rogers RO4003C substrate with a dielectric constant of 3.55 was selected, consisting of a 3.048mm thick first substrate and a 0.813mm thick second substrate, separated by an air layer. The top metasurface utilizes a 3×3 array of third-order Hilbert fractal elements, effectively expanding the bandwidth through the multi-frequency characteristics generated by the self-similarity of the fractal structure. The spatial filling capability of the fractal iterative structure is utilized to increase the current path length, thereby achieving antenna miniaturization. A cut-angle patch is designed on the surface of the second substrate as an excitation source, and a ground plane is provided at the bottom, providing dual-polarization excitation via dual coaxial feed lines. Step 2: Metasurface unit fractal structure and optimization: Based on the self-similarity and space-filling capabilities of the Hilbert curve, the system was iterated using the "half-size + rotation-fill" rule: the 0th order was a square patch, and the 3rd order structure was formed by 2nd order scaling and rotation. Unit geometry parameters were optimized, and structural irregularities were adjusted through electromagnetic simulation to ensure that the electrical length matched the operating frequency. Step 3: 3×3 metasurface array construction: The optimized third-order Hilbert fractal units are deployed on the top layer of the first substrate 1 in a matrix of 3 rows and 3 columns to form a periodic metasurface structure. The overall size is maintained at 30 mm × 30 mm. The uniformity of electromagnetic coupling is ensured by arranging the units at equal intervals. Step 4: Electromagnetic simulation verification: Using CST Studio Suite, we modeled 0th-, 2nd-, and 3rd-order Hilbert fractal metasurface antennas and analyzed their reflection coefficients and radiation patterns. We compared the impedance bandwidths of different orders: the 0th-order bandwidth was 9%, the 2nd-order bandwidth increased to 16.1%, and the 3rd-order bandwidth reached 19.5%. We also verified the 3rd-order radiation performance: the 3rd-order antenna exhibited a mainlobe gain of 6.93 to 7.40 dBi in the 4.9 to 5.8 GHz frequency band. Step 5: Result analysis and performance summary: The increase in fractal order significantly expands the impedance bandwidth, which is attributed to the enhanced multi-frequency characteristics; without increasing the size of the structure, the bandwidth is increased from 9% to 19.5%, and the maximum main lobe gain is 7.4dBi, meeting the application requirements of the 4.0-8.0GHz band.

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