Design method of large-interval low-sidelobe uniform array
By optimizing the position of the movable phase center in a large-pitch array antenna, the problems of increased cost and complexity in existing technologies are solved, and the sidelobe level is reduced and the cost is saved.
Patent Information
- Application Number
- CN202411422904.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-12
- Publication Date
- 2025-11-11
- Estimated Expiration
- 2044-10-12
AI Technical Summary
Existing technologies for reducing sidelobe levels in large-pitch array antennas require changing the excitation amplitude of each element in the array or configuring additional components, which increases implementation cost and complexity.
A movable phase center antenna element is adopted, and the phase center position of the array element is optimized by a genetic algorithm. The structure of the antenna element is changed to reduce the sidelobe level, thus avoiding changes to the excitation amplitude and the array element spacing.
Reducing the sidelobe level in a large-pitch uniform array lowers the array complexity and implementation cost, and eliminates the need for additional T/R components.
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Figure CN119378232B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array antenna technology, specifically relating to a design method for realizing a large-spacing, low-sidelobe uniform array based on the phase center of a moving antenna element. Background Technology
[0002] Antennas have wide applications in mobile communications, wireless measurement, radar, satellite and navigation. As an important research area in antenna design, array antennas have developed rapidly because they can obtain specific radiation characteristics.
[0003] The phase center of an antenna element is the location of a point related to the antenna. If this point is taken as the center of the equiphase sphere of the far-field radiation, then the phase of a given field component on the far-field sphere should be approximately constant. Adjusting the phase center of the antenna element can change the far-field radiation pattern, thus affecting the radiation performance of the array antenna. In the construction of an array antenna, element spacing is a fundamental parameter. Arrays with element spacing greater than one wavelength are generally called large-pitch array antennas. Compared to a full-array antenna with half-wavelength spacing, large-pitch array antennas can achieve the same gain using fewer elements, significantly reducing array implementation costs. However, due to the larger element spacing, undesirable grating lobes will appear in the array's radiation pattern, requiring related techniques to reduce grating lobes and improve array performance. Furthermore, the sidelobe level of the array antenna is also an important parameter affecting antenna performance. In practical applications, the lowest possible sidelobe level is generally required to improve the directivity and accuracy of the array antenna. In addition, a lower sidelobe level can suppress interference from irrelevant signals, improving the system's signal-to-noise ratio and performance, which is of great significance for production and daily life applications.
[0004] There are multiple ways to reduce the sidelobes of an array antenna. Common methods mainly involve changing the excitation amplitude weights of each element in the array, such as array synthesis methods like Taylor distribution or Chebyshev distribution. In addition, the distance between the elements in the array can be changed, i.e., a non-uniform array can be constructed to reduce the sidelobe level. With the rapid development of computer technology, many intelligent global optimization algorithms have emerged, such as genetic algorithms (GA) and particle swarm optimization (PSO). By performing random search optimization on the excitation of the array elements and the spacing between the elements, the sidelobes of the array can also be reduced.
[0005] While the above methods can effectively reduce the sidelobe level of the array, they also have some problems: changing the excitation of each element in the array requires additional T / R components, which will greatly increase the implementation cost of the array; non-uniform arrays are more complex to design, manufacture and test due to the different spacing between each element, which increases the difficulty of array implementation.
[0006] In recent years, some foreign scholars have proposed changing the far-field radiation pattern of an array by moving the phase center of each element, thereby reducing the array's sidelobe level. The specific method for moving the element's phase center involves designing a dual-feed port antenna element capable of operating in two modes, and moving the phase center by changing the excitation amplitude ratio between the two feed ports. This method can reduce the far-field sidelobe level of a uniform array, but it requires additional T / R components to change the excitation amplitude ratio between the two feed ports of each element, increasing implementation costs and hindering large-scale array applications. Summary of the Invention
[0007] To address the shortcomings of existing technologies, the present invention aims to provide a design method for a large-spacing, low-sidelobe uniform array. This method utilizes movable phase center antenna elements as array elements, and can reduce the far-field sidelobes of the array in a uniformly spaced array distribution without changing the excitation amplitude and phase of each element.
[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0009] A design method for a large-spacing, low-sidelobe uniform array includes the following steps:
[0010] Step 1. Design the initial structure of the movable phase center antenna element;
[0011] Step 2. Acquire far-field data of the movable phase center antenna element;
[0012] Step 3. Using the movable phase center antenna element as an array element, determine the number of array elements N and the uniform array element spacing d according to the array antenna design specifications, and construct the array antenna; obtain the array far-field radiation pattern based on the constructed array antenna and the far-field data of the movable phase center antenna element; use the sidelobe level of the array antenna as the optimization target, and use a genetic algorithm to optimize the phase center of the array element to obtain the phase center position distribution of each array element;
[0013] Step 4. Change the structure of each array element so that the phase center of each array element moves to the optimized result obtained in Step 3;
[0014] Step 5. Perform simulation verification on the array antenna after the phase center of the moving array element to obtain the far-field pattern sidelobe level of the array antenna; if the far-field pattern sidelobe level meets the design specifications, the design is completed; if not, return to step 3 to re-optimize the position distribution of the phase center.
[0015] Preferably, in step 3, the basic parameters of the genetic algorithm are set, including: the population size is set to a range of 200 to 600, the maximum number of iterations is set to a range of 200 to 500, the crossover probability is set to a range of 0.25 to 0.9, and the mutation probability is set to a range of 0.01 to 0.1; the objective function is set to objv = |SLL - SLL0|, where SLL is the array sidelobe level in a certain iteration, and SLL0 is the expected array sidelobe level.
[0016] Preferably, the initial structure of the movable phase center antenna unit includes: an upper dielectric substrate, a parasitic metal patch on the top of the upper dielectric substrate, a lower dielectric substrate, a metal plate at the bottom of the lower dielectric substrate, and three metal patches arranged parallel and equally spaced between the upper and lower dielectric substrates; the parasitic metal patch coincides with the center of the upper dielectric substrate; the three metal patches are divided into a left metal patch, a middle metal patch, and a right metal patch, with a PIN diode loaded above and below the left and right metal patches respectively, and the middle metal patch connected to a coaxial feed port;
[0017] By changing the position of the parasitic metal patch and simultaneously changing the on / off state of the PIN diodes loaded on the left and right metal patches, the structure of the movable phase center antenna element is changed, thereby changing the phase center of the antenna element.
[0018] Preferably, in step 2, the far-field data of the movable phase center antenna element is acquired while the PIN diode is in the on state.
[0019] Preferably, the upper dielectric substrate and the lower dielectric substrate are square dielectric substrates with the same side length; the metal plate is a square metal plate with a side length greater than that of the lower dielectric substrate.
[0020] Preferably, the size of the parasitic metal patch is 11mm × 24mm;
[0021] The dimensions of the left and right metal patches are both 2mm × 34mm, and the dimensions of the middle metal patch are 2mm × 30mm. The distance between the left and right metal patches and the middle metal patch is 10mm. Symmetrically, a gap of 1.45mm is left at a distance of 1.8mm from the upper and lower edges of the left and right metal patches to install PIN diodes. All PIN diodes are of the same model.
[0022] The coaxial feed port is 12.5mm away from the upper edge of the middle metal patch, and the interface impedance of the coaxial feed is 50Ω.
[0023] Preferably, both the upper and lower dielectric substrates are Roger s5880 dielectric substrates with a relative permittivity of 2.2 and a size of 60mm × 60mm, wherein the upper dielectric substrate has a thickness of 10mm and the lower dielectric substrate has a thickness of 6mm.
[0024] Preferably, the metal plate is made of copper, a metallic conductor, with dimensions of 96.78mm × 96.78mm and a thickness of 0.035mm.
[0025] Compared with the prior art, the beneficial effects of this invention are as follows:
[0026] 1. This invention proposes a design method for a large-pitch, low-sidelobe uniform array, which changes the radiation pattern of the antenna elements by moving the phase center of the antenna elements, thereby reducing the sidelobes of the entire array pattern;
[0027] 2. This invention can reduce far-field sidelobes by changing only the phase center distribution of the antenna elements in a large-pitch uniform array, without changing the element spacing or the excitation amplitude and phase of the antenna elements, thus reducing the array complexity and implementation cost.
[0028] 3. This invention moves the phase center by changing the structure of the antenna element. Compared with foreign scholars who move the phase center by changing the excitation amplitude ratio of the two feed ports, this invention does not require additional T / R components, thus reducing the array implementation cost. Attached Figure Description
[0029] Figure 1 Flowchart of a design method for reducing sidelobes of a large-spacing uniform array to achieve phase center of a mobile antenna element;
[0030] Figure 2 This is a three-dimensional structural diagram of the initial structure of the movable phase center antenna unit in an embodiment of the present invention;
[0031] Figure 3 This is a three-dimensional structural perspective view of the initial structure of the movable phase center antenna element in an embodiment of the present invention;
[0032] Figure 4 This is a top view schematic diagram of the initial structure of the movable phase center antenna unit in an embodiment of the present invention;
[0033] Figure 5 This is a side view of the initial structure of the movable phase center antenna unit in an embodiment of the present invention;
[0034] Figure 6 This is a schematic diagram of the three metal patches and the loaded PIN diode between the upper and lower dielectric substrates of the initial structure of the movable phase center antenna unit in an embodiment of the present invention.
[0035] Figure 7 The S11 parameters are the initial structure parameters of the movable phase center antenna element in the embodiments of the present invention.
[0036] Figure 8 This is a two-dimensional radiation pattern of the far-field E-plane and H-plane of the initial structure of the movable phase center antenna element in an embodiment of the present invention;
[0037] Figure 9 The far-field E-plane and H-plane two-dimensional radiation patterns of the movable phase center antenna unit in this embodiment of the invention when PIN diodes 154 and 155 are in the on state and PIN diodes 156 and 157 are in the off state.
[0038] Figure 10 The far-field H-plane two-dimensional radiation pattern is shown when the PIN diodes 154 and 155 of the movable phase center antenna unit in the embodiment of the present invention are in the on state and the PIN diodes 156 and 157 are in the off state, while the parasitic metal patch 11 on the top of the upper dielectric substrate is moved to different distances along the positive half axis of the x-axis of the plane rectangular coordinate system xoy.
[0039] Figure 11 This is a top view of a large-spaced uniform array after moving the phase centers of each antenna element in an embodiment of the present invention.
[0040] Figure 12 This is a comparison of the far-field two-dimensional radiation patterns of a large-spaced uniform array behind the phase center of a moving antenna unit and behind the phase center of a stationary antenna unit in an embodiment of the present invention.
[0041] In the figure: 10. Initial structure of the movable phase center antenna element; 11. Parasitic metal patch; 12. Upper dielectric substrate; 13. Lower dielectric substrate; 14. Metal plate; 15. Three metal patches; 16. Coaxial feed port; 151. Left metal patch; 152. Middle metal patch; 153. Right metal patch; 154. PIN diode loaded above the left metal patch; 155. PIN diode loaded below the left metal patch; 156. PIN diode loaded above the right metal patch; 157. PIN diode loaded below the right metal patch. Detailed Implementation
[0042] The technical solutions of the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0043] like Figure 1 As shown, the design method of a large-pitch, low-sidelobe uniform array in this embodiment includes the following steps:
[0044] Step 1. Design the initial structure of the movable phase center antenna element.
[0045] In this embodiment, the designed movable phase center antenna element operates within the 3.03-3.12 GHz frequency band, and its initial structure is as follows: Figures 2-6 As shown, it includes: an upper dielectric substrate, a parasitic metal patch on the top of the upper dielectric substrate, a lower dielectric substrate, a metal plate at the bottom of the lower dielectric substrate, and three metal patches arranged parallel to each other and at equal intervals between the upper and lower dielectric substrates.
[0046] Both the upper and lower dielectric substrates are square Rogers 5880 dielectric substrates with a relative permittivity of 2.2, and each has a size of 60mm × 60mm. The upper dielectric substrate has a thickness of 10mm, and the lower dielectric substrate has a thickness of 6mm.
[0047] The metal plate at the bottom of the lower dielectric substrate is made of copper, which forms the ground of the antenna. It measures 96.78mm × 96.78mm and has a thickness of 0.035mm.
[0048] The parasitic metal patch measures 11mm × 24mm, and its center coincides with the center of the upper dielectric substrate.
[0049] The three metal patches are divided into a left metal patch, a middle metal patch, and a right metal patch, with a spacing of 10mm. The dimensions of the left and right metal patches are both 2mm × 34mm. Symmetrically, a gap of 1.45mm is left at 1.8mm from the top and bottom edges of the left and right metal patches to accommodate PIN diodes. The dimensions of the middle metal patch are 2mm × 30mm. The feed point of the coaxial feed port is 12.5mm from the top edge of the middle metal patch, and the interface impedance of the coaxial feed is 50Ω.
[0050] By changing the position of the parasitic metal patch and simultaneously changing the on / off state of the PIN diodes loaded on the left and right metal patches, the structure of the movable phase center antenna element is changed, thereby changing the phase center of the antenna element.
[0051] Figure 7 The figure shows the S11 parameters of the initial structure of the movable phase center antenna element. As can be seen from the figure, the S11 parameters are less than -10dB in the frequency range of 3.03-3.12GHz, which shows the resonance characteristics.
[0052] To facilitate the description of the position of the phase center of the parasitic metal patch and antenna element, a Cartesian coordinate system xoy is introduced here, such as... Figure 4 As shown, in the initial structure of the movable phase center antenna element, the center of the parasitic metal patch is located at the origin of the plane rectangular coordinate system xoy.
[0053] Step 2. Set all PIN diodes in the movable phase center antenna element to the ON state and acquire the far-field data of the movable phase center antenna element.
[0054] Figure 8 The figure shows the two-dimensional far-field E-plane and H-plane radiation patterns of the initial structure of the movable phase-center antenna element. As can be seen from the figure, when operating at 3.1 GHz, the main lobe beam of the H-plane radiation pattern of the movable phase-center antenna element points to 0 degrees. Through far-field data processing, it can be found that the phase center of the movable phase-center antenna element is located at x = 0 in the x-axis component of the Cartesian coordinate system xoy.
[0055] Step 3. Using the movable phase center antenna element as an array element, determine the number of array elements N and the uniform array element spacing d according to the array antenna design specifications, and construct the array antenna. In this embodiment, the number of array antenna elements N = 8, and the uniform array element spacing d = 96.78 mm, which is exactly one wavelength when operating at 3.1 GHz, forming a 1×8 large-spacing uniform array. Based on the constructed array antenna and the far-field data of the movable phase center antenna element, obtain the array far-field radiation pattern.
[0056] A genetic algorithm is used to optimize the phase center of each array element, resulting in the phase center position distribution for each element. In this embodiment, the basic parameters of the genetic algorithm are set as follows: population size of 500, maximum number of iterations of 300, crossover probability of 0.7, mutation probability of 0.05, and the objective function is objv = |SLL - SLL0|, where SLL is the array sidelobe level in a certain iteration, SLL0 is the expected array sidelobe level, and the expected sidelobe level is set to -15dB.
[0057] The steps involved in optimization based on genetic algorithms include:
[0058] Step 1. Set the number of array antenna elements N=8, the array spacing d=96.78mm, and the basic parameters of the genetic algorithm: population size is 500, maximum number of iterations is 300, crossover probability is 0.7, and mutation probability is 0.05;
[0059] Step 2. Read the far-field amplitude and phase pattern of the movable phase center antenna element;
[0060] Step 3. Write the objective function of the genetic algorithm based on the expected array sidelobe level to constrain the array sidelobe level. The objective function is: objv=|SLL-SLL0|;
[0061] Step 4. Run the genetic algorithm to obtain the uniform array antenna after the phase center of each antenna element has been moved;
[0062] Step 5. Calculate the far-field radiation pattern and sidelobe level of the array antenna after each antenna element moves its phase center, and calculate the objective function value, which is the difference between the array sidelobe level in the current iteration and the expected array sidelobe level.
[0063] Step 7. Repeat steps 5 and 6 until the maximum number of iterations is reached. At this point, the optimal solution is obtained, that is, the difference between the array sidelobe level after iteration and the expected array sidelobe level is minimized, resulting in the final low sidelobe uniform array antenna.
[0064] The final distribution of the phase centers of each unit is shown in Table 1.
[0065] Table 1
[0066]
[0067] Here, the distribution of the phase center position only considers the distribution on the x-axis of the Cartesian coordinate system xoy, and it is the offset distance relative to the geometric center of each antenna element. Each antenna element establishes a separate Cartesian coordinate system xoy at its geometric center. Positive numbers represent the positive half-axis of the phase center on the x-axis of the antenna element, negative numbers represent the negative half-axis of the phase center on the x-axis of the antenna element, and zero represents the phase center at the geometric center of the antenna element.
[0068] Step 4. Change the structure of each array element so that the phase center of each array element moves to the optimized result obtained in Step 3.
[0069] The specific method for changing the structure of the movable phase center antenna element is as follows: First, change the conduction state of the PIN diodes, put PIN diodes 154 and 155 in the conduction state, and put PIN diodes 156 and 157 in the off state, while keeping the position of the parasitic metal patch unchanged. Figure 9 The image shows the two-dimensional radiation patterns of the far-field E-plane and H-plane of the antenna element in this state. As can be seen from the figure, when operating at 3.1 GHz, the main lobe beam of the H-plane radiation pattern of the movable phase-center antenna element in this state no longer points to 0 degrees, but to 5 degrees. Through far-field data processing, it can be found that the phase center of the movable phase-center antenna element is located at x = 6.63 mm on the x-axis component of the Cartesian coordinate system xoy, that is, the position of the phase center has changed.
[0070] Then change the position of the parasitic metal patch. Here, PIN diodes 154 and 155 are still in the on state, and PIN diodes 156 and 157 are in the off state. Move the parasitic metal patch along the positive half-axis of the x-axis of the Cartesian coordinate system xoy by moving distances of 0mm, 5mm, 10mm, 15mm and 20mm respectively. Figure 10 The far-field H-plane two-dimensional radiation pattern of the antenna element at different moving distances is shown. As can be seen from the figure, when operating at 3.1 GHz, the pointing angle of the main lobe beam in the H-plane pattern of the antenna element gradually increases as the parasitic metal patch moves further along the positive x-axis. Through far-field data processing, the x-axis components of the phase center of the movable phase center antenna element in the Cartesian coordinate system xoy are x = 8.25 mm, x = 12.24 mm, x = 15.82 mm, x = 17.44 mm, and x = 18.03 mm, respectively. It can be observed that the phase center of the antenna element can gradually change along the positive x-axis.
[0071] Because the structure of this movable phase center antenna element is symmetrical, if PIN diodes 154 and 155 are in the off state and PIN diodes 156 and 157 are in the on state, and the parasitic metal patch is moved along the negative half-axis of the x-axis of the Cartesian coordinate system xoy, then the phase center of the antenna element can gradually change along the negative half-axis of the x-axis.
[0072] To move the phase center of each antenna element to the optimized position of the genetic algorithm, the structure of each antenna element needs to be adjusted. The final structure of each movable phase center antenna element that meets the requirements is shown in Table 2. A positive movement distance of the upper parasitic metal patch indicates movement towards the positive x-axis, a negative movement distance indicates movement towards the negative x-axis, and a movement distance of zero indicates no movement.
[0073] Table 2
[0074]
[0075] Figure 11 The diagram shows a top view of a large-spaced uniform array after the phase centers of each antenna element have been moved.
[0076] Step 5. Perform simulation verification on the array antenna behind the phase center of the moving array element to obtain the far-field radiation pattern sidelobe level of the array antenna.
[0077] Figure 12The image shows a comparison of the far-field two-dimensional radiation patterns of a large-spaced uniform array with a movable antenna element phase center and a fixed antenna element phase center. As can be seen from the image, the sidelobe level of the uniform array is -13.7dB with the movable antenna element phase center distribution, which is close to the expected sidelobe level of -15dB. Compared with the uniform array with a fixed antenna element phase center, the sidelobe level is reduced by 5.6dB, which is a significant improvement.
[0078] The purpose of this invention is to optimize the design of the array antenna by moving the phase center of the antenna elements. By moving the phase center of the antenna elements, the radiation pattern of each antenna element can be changed, which can reduce the sidelobes of the radiation pattern of a large-spacing uniform array without changing the spacing between the array elements or the excitation amplitude and phase of the antenna elements, thus reducing the complexity and implementation cost of the array.
[0079] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A design method for a large-pitch, low-sidelobe uniform array, characterized in that, Includes the following steps: Step 1. Design the initial structure of the movable phase center antenna element; The initial structure of the movable phase center antenna unit includes: an upper dielectric substrate, a parasitic metal patch on the top of the upper dielectric substrate, a lower dielectric substrate, a metal plate at the bottom of the lower dielectric substrate, and three metal patches arranged parallel and equally spaced between the upper and lower dielectric substrates; the parasitic metal patch coincides with the center of the upper dielectric substrate; the three metal patches are divided into a left metal patch, a middle metal patch, and a right metal patch, with a PIN diode loaded above and below the left and right metal patches, and the middle metal patch connected to a coaxial feed port; Step 2. Acquire far-field data of the movable phase center antenna element; Step 3. Using the movable phase center antenna element as an array element, determine the number of array elements N and the uniform array element spacing d according to the array antenna design specifications, and construct the array antenna; obtain the array far-field radiation pattern based on the constructed array antenna and the far-field data of the movable phase center antenna element; use the sidelobe level of the array antenna as the optimization target, and use a genetic algorithm to optimize the phase center of the array element to obtain the phase center position distribution of each array element; Step 4. By changing the position of the parasitic metal patch and simultaneously changing the on / off state of the PIN diodes loaded on the left and right metal patches, the phase center of the antenna element is changed, so that the phase center of each element moves to the optimized result obtained in step 3. Step 5. Perform simulation verification on the array antenna after the phase center of the moving array element to obtain the far-field pattern sidelobe level of the array antenna; if the far-field pattern sidelobe level meets the design specifications, the design is completed; if not, return to step 3 to re-optimize the position distribution of the phase center.
2. The design method of a large-pitch, low-sidelobe uniform array as described in claim 1, characterized in that, In step 3, the basic parameters of the genetic algorithm are set, including: population size (range 200-600), maximum number of iterations (range 200-500), crossover probability (range 0.25-0.9), and mutation probability (range 0.01-0.1); the objective function is set as follows: objv =| SLL - SLL 0|, where SLL This refers to the array sidelobe level in a certain iteration. SLL 0 represents the expected array sidelobe level.
3. The design method of a large-pitch, low-sidelobe uniform array as described in claim 2, characterized in that, In step 2, with the PIN diode in the on state, the far-field data of the movable phase center antenna element is acquired.
4. The design method of a large-pitch, low-sidelobe uniform array as described in claim 3, characterized in that, The upper and lower dielectric substrates are square dielectric substrates with the same side length; the metal plate is a square metal plate with a side length greater than that of the lower dielectric substrate.
5. The design method of a large-pitch, low-sidelobe uniform array as described in claim 4, characterized in that, The size of the parasitic metal patch is 11mm × 24mm; The dimensions of the left and right metal patches are both 2mm × 34mm, and the dimensions of the middle metal patch are 2mm × 30mm. The distance between the left and right metal patches and the middle metal patch is 10mm. Symmetrically, a gap of 1.45mm is left at a distance of 1.8mm from the upper and lower edges of the left and right metal patches to install PIN diodes. All PIN diodes are of the same model. The coaxial feed port is 12.5mm away from the upper edge of the middle metal patch, and the interface impedance of the coaxial feed is 50Ω.
6. The design method of a large-pitch, low-sidelobe uniform array as described in claim 5, characterized in that, Both the upper and lower dielectric substrates are Rogers 5880 dielectric substrates with a relative permittivity of 2.2 and a size of 60mm × 60mm. The upper dielectric substrate has a thickness of 10mm and the lower dielectric substrate has a thickness of 6mm.
7. The design method of a large-pitch, low-sidelobe uniform array as described in claim 6, characterized in that, The metal plate is made of copper, a metallic conductor, and measures 96.78mm × 96.78mm with a thickness of 0.035mm.
Citation Information
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