WO2019034119A1 - 一种超轻人工介质多层圆柱透镜 - Google Patents
一种超轻人工介质多层圆柱透镜 Download PDFInfo
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- WO2019034119A1 WO2019034119A1 PCT/CN2018/100882 CN2018100882W WO2019034119A1 WO 2019034119 A1 WO2019034119 A1 WO 2019034119A1 CN 2018100882 W CN2018100882 W CN 2018100882W WO 2019034119 A1 WO2019034119 A1 WO 2019034119A1
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- cylindrical lens
- dielectric constant
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
- H01Q15/02—Refracting or diffracting devices, e.g. lens, prism
- H01Q15/08—Refracting or diffracting devices, e.g. lens, prism formed of solid dielectric material
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08L—COMPOSITIONS OF MACROMOLECULAR COMPOUNDS
- C08L23/00—Compositions of homopolymers or copolymers of unsaturated aliphatic hydrocarbons having only one carbon-to-carbon double bond; Compositions of derivatives of such polymers
- C08L23/02—Compositions of homopolymers or copolymers of unsaturated aliphatic hydrocarbons having only one carbon-to-carbon double bond; Compositions of derivatives of such polymers not modified by chemical after-treatment
- C08L23/04—Homopolymers or copolymers of ethene
- C08L23/06—Polyethene
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08L—COMPOSITIONS OF MACROMOLECULAR COMPOUNDS
- C08L25/00—Compositions of, homopolymers or copolymers of compounds having one or more unsaturated aliphatic radicals, each having only one carbon-to-carbon double bond, and at least one being terminated by an aromatic carbocyclic ring; Compositions of derivatives of such polymers
- C08L25/02—Homopolymers or copolymers of hydrocarbons
- C08L25/04—Homopolymers or copolymers of styrene
- C08L25/06—Polystyrene
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08L—COMPOSITIONS OF MACROMOLECULAR COMPOUNDS
- C08L27/00—Compositions of homopolymers or copolymers of compounds having one or more unsaturated aliphatic radicals, each having only one carbon-to-carbon double bond, and at least one being terminated by a halogen; Compositions of derivatives of such polymers
- C08L27/02—Compositions of homopolymers or copolymers of compounds having one or more unsaturated aliphatic radicals, each having only one carbon-to-carbon double bond, and at least one being terminated by a halogen; Compositions of derivatives of such polymers not modified by chemical after-treatment
- C08L27/04—Compositions of homopolymers or copolymers of compounds having one or more unsaturated aliphatic radicals, each having only one carbon-to-carbon double bond, and at least one being terminated by a halogen; Compositions of derivatives of such polymers not modified by chemical after-treatment containing chlorine atoms
- C08L27/06—Homopolymers or copolymers of vinyl chloride
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08L—COMPOSITIONS OF MACROMOLECULAR COMPOUNDS
- C08L2203/00—Applications
- C08L2203/14—Applications used for foams
Definitions
- the present invention relates to the field of antenna engineering technologies, and in particular, to an ultra-light artificial medium multilayer cylindrical lens.
- antennas As wireless gateways.
- the antenna In order to meet the requirements of high gain, low side lobes, narrow beam, wide beam coverage, etc., it is also necessary to increase the network speed and consider the cost and environment. The most important of these is that the antenna must be able to carry large information capacity without increasing its quantity, weight and site.
- Multi-beam antennas developed in recent years are a solution.
- Conventional multi-beam antennas are constructed using a multi-beamforming network (BFN) to excite a planar array of radiating elements, or a multi-stage Butler matrix or the like.
- BFN multi-beamforming network
- the traditional Longbo ball lens technology has the potential to carry multiple antennas and multiple beams.
- due to the heavy weight of the Longbo lens and the extremely complicated manufacturing process it has long been used as a target for radar passive target detection, airport runway blind drop, etc. Application, it is difficult to enter the civilian field.
- the traditional Longbo ball antenna is mainly made by two processes of punching and foaming, and the process is time consuming and the product quality is too heavy.
- the punching method is very difficult to operate in hole positioning and processing, and because of the large number of holes, there are problems such as deformation and mechanical strength during the manufacturing process, and the robustness between the parts is low, and this design can only be realized.
- the macroscopic dielectric constant is equivalent. In fact, the efficiency of the lens antenna is very low.
- the dielectric constant of the material obtained by the conventional foaming method is hard to exceed 1.4, and then it is desired to upgrade.
- the density of the material is bound to be large, increasing the weight.
- the density of the foamed material is difficult to precisely control, and the foamed beads are liable to undergo secondary foaming or shrinkage, resulting in a gap between the materials, the dielectric constant is difficult to precisely control.
- the researchers have worked hard for decades. Recently, the multi-beam Longbo ball lens antenna used in the field of mobile communication has been seen on the market (Matsine Ball, US20110003131A1 used in the millions of mass rally in the US President Trump's inauguration in 2017).
- the inventor introduced Matsine.
- Longbo ball is 8 times lighter than natural media material (PTFE) and 3-4 times lighter than the artificial media Longbo ball on the market. It is the lightest artificial medium Longbo ball, and the antenna gain is 21dBi. .
- the Matsine ball antenna is also equipped with a complex vertical beam downtilt mechanism due to the narrow beamwidth of the vertical plane, which increases the operational difficulty, complexity and cost of the application.
- Chinese invention patent (201511027751.3: a lightweight medium filled multi-beam cylindrical Longbo lens antenna) discloses a three-layer cylindrical Longbo dielectric lens antenna, the invention mainly through a low dielectric constant disc-shaped base material The upper opening is filled with a high dielectric constant dielectric material to achieve the desired graded dielectric constant, and the density of the holes above the three-layer lens is densely packed from the outside to the inside.
- this method it is difficult to control the dielectric constant of each lens layer, and it is difficult to obtain the specific dielectric constant value of each layer, and the dielectric constant can only be changed macroscopically.
- the process of opening holes in the base material is cumbersome, the drilling process is difficult, and the number of holes is large, and the deformation and mechanical strength of the material need to be considered.
- the lens antenna is flat, and there is no advantage in vertical plane radiation.
- Chinese invention patent discloses a manufacturing method of a Longbo lens antenna, comprising the following steps: pre-expansion treatment of a foaming raw material; according to the design of each lens layer of the Longbo lens antenna The foaming raw material after pre-expansion is arranged to obtain a foaming raw material particle combination, and a corresponding mold is produced; the foaming raw material particle combination is added to a corresponding mold to be molded, and each lens of the Longbo lens antenna is obtained. Layer; each lens layer is assembled.
- the invention can improve the accuracy of the dielectric constant of each lens layer of the Longbo lens, the performance of the Longbo lens antenna can be improved.
- the production process is cumbersome, and the use of the mold is complicated, and the temperature and reaction time are controlled very accurately, and it is difficult to mass-produce.
- the Aerospace Special Materials and Process Technology Institute applied for a series of patents related to the Longbo lens antenna, including spherical and hemispherical Lombor lenses, which are similar in structure and manufacturing methods.
- a hemispherical lens antenna consisting of n hemispherical layers with different dielectric constants, which are manufactured using additive materials (usually It is produced by means of 3D printing.
- the lens produced includes cavities of various shapes and sizes, and finally the gradation of the dielectric constant is achieved.
- the lens prepared by this method does not require a mold, and the dielectric constant of each layer can be accurately controlled.
- the use of the additive manufacturing method to manufacture the lens has certain limitations in material selection, and it is impossible to use a foam material having a very low density.
- PLA or ABS used in the embodiment of the present invention has a large density of materials, and even if a lens is included in the prepared lens, the total apparent density of the lens is difficult to reach a very low level, and the lens weight is made. It is still difficult to have a big breakthrough. When used in the civil field, the quality is still not dominant.
- Chinese invention patent (200580038415.7: Luneberg dielectric lens and its manufacturing method) discloses a hemispherical dielectric lens comprising a plurality of concentric hemispherical layers, each layer being a thermoplastic resin expanded bead containing 0 to 80% by weight of ceramic Foam moldings.
- the hemispherical dielectric lens disclosed in the invention can overcome the disadvantages of the conventional antenna to achieve greater gain and lighter weight, the lens manufacturing process needs to mix the ceramic with the foam expansion beads and then use the mold for foaming. The requirements are high and it takes a long time to prepare the mold.
- the total apparent density of the hemispherical lens provided in the examples is between 0.17 and 0.27 g/cm 3 , although this density is already lower than that of most lenses in the prior art, there is still the possibility of continued optimization.
- the technical problem to be solved by the present invention is to provide a simple processing, an ultra-light quality, and an ultra-wide frequency for the defects of the existing spherical or hemispherical lens, which are difficult to process, excessive in quality, and narrow in beam width on the vertical plane.
- an ultra-light artificial medium multilayer cylindrical lens comprising n concentric layers having different dielectric constants, and the central cylindrical layer is represented as a first layer, which is a solid cylinder;
- the second to nth layers are sequentially arranged around the central cylindrical layer, which are respectively n-1 concentric rings, and the n concentric layers are assembled into a multi-layered cylinder, characterized in that the n concentric layers are The electric constant is reduced layer by layer from the first layer to the nth layer, specifically between 2.05 and 1.05;
- each of the n concentric layers includes a substrate having a low dielectric constant and a high dielectric constant, low specific gravity addition a material;
- the substrate is a light foaming dielectric material, specifically a material having a density of 0.02-0.03 g/cm 3 ; wherein the content of the added material in the n concentric layers per unit volume is from the first layer to the n-th layer gradually decreases.
- the light foaming medium material is polystyrene, polyvinyl chloride or polyethylene.
- the additive material comprises one or more of ceramic powder, aluminum silver powder, and metal wire.
- the dielectric constant of each concentric layer is determined by the electromagnetic response and density of the additive material contained in each layer.
- the dielectric constant values of the n concentric layers in the cylindrical lens are determined by testing by a dielectric constant tester.
- n-1 concentric rings are formed, and the first layer is nested into the cylindrical lens, and the stacking is ensured to be tight between the layers. Gap.
- the structural parameters and performance parameters of the cylindrical lens are determined according to the actual working needs of the antenna.
- the structural parameter comprises a diameter, a height, and a number of layers of the cylindrical lens
- the performance parameter includes a dielectric constant value of each concentric layer.
- the cylindrical lens has a diameter of 20-90 cm and a height of 20-70 cm.
- the cylindrical lens has a total apparent density of 0.08-0.095 g/cm 3 .
- cylindrical lens provided by the present invention can also be used to construct an ultra-wideband multi-beam antenna in an antenna system, and the ultra-wideband refers to a frequency of 0.6 GHz to 28 GHz.
- the ultra-light artificial medium multilayer cylindrical lens provided by the invention comprises the following steps:
- step (4) uniformly magnifying the sample of each layer in step (4), forming the 2-n layer into a concentric ring, and assembling the first concentric layer into an n-layer concentric cylinder as a crude cylindrical lens. ;
- the ultra-light artificial medium lens provided by the present invention changes the dielectric constant of different layers of the lens by adding a high dielectric constant material to the low dielectric constant substrate, and the manufacturing process is simple, convenient, and quick.
- the dielectric constant of each layer of material can be accurately measured by measurement, which overcomes the problem of mechanical deformation and inaccurate dielectric constant caused by punching in the conventional process, and does not cause secondary foaming which may occur in the foaming process. Or the shrinkage of the material causes a gap between the layers.
- the artificial medium multilayer cylindrical lens provided by the invention has a simpler manufacturing process, and adopts a cylindrical shape instead of a spherical or hemispherical shape for the antenna, and has multiple beams and vertical The characteristics of the plane pattern width.
- the artificial medium multilayer cylindrical lens provided by the invention can be made according to the specific needs of the antenna index, and most importantly, the lens produced is ultra-light, ultra-low density, and the total table is The apparent density is only 0.08-0.095 g/cm 3 , which is lower than all artificial medium lenses in the prior art, and has ultra-wideband (even applicable to frequencies above 28 GHz). This will greatly expand the application of the lens in the fifth generation (5G) civil and military fields, and combine with antenna technology to form an artificial medium lens antenna, especially for crowded areas and large data traffic areas.
- 5G fifth generation
- the lens provided by the present invention can be applied to the field of antennas, and provides a practical carrier for constructing a multi-beam antenna.
- the antenna unit is usually fixed on the outside of the artificial medium multilayer cylindrical lens, which can be realized compared with the conventional electronically modulated antenna.
- the vertical surface lobes are wider and cover, and the field strength is fully dominant in most areas. Therefore, the traditional vertical lobe electric adjustment down-tilt mechanism can be omitted, and the traditional base station antenna (including the Longbo multi-beam antenna) can be used.
- the two-dimensional scanning in the fixed wide sectorization horizontal and vertical surface coverage simultaneously exist), saving a lot of energy and cost, saving site resources, especially suitable for crowded areas and big data traffic business areas.
- the artificial medium multilayer cylindrical lens provided by the present invention has a simple manufacturing process, and because the lens is small in volume, ultra-light in weight, and ultra-wide in frequency band, the antenna using the lens can be applied to the military and civilian fields, overcoming the conventional antenna being too bulky. Or the equipment is difficult to enter the shortcomings of the civilian sector.
- FIG. 1 is a perspective view of a 6-layer cylindrical lens of an artificial medium provided by the present invention.
- FIG. 2 is a cross-sectional view of a 6-layer cylindrical lens of an artificial medium provided by the present invention
- FIG 3 is a cross-sectional view of a 10-layer cylindrical lens of an artificial medium provided by the present invention.
- the invention provides an ultra-light artificial medium multilayer cylindrical lens comprising n concentric layers having different dielectric constants, the central cylindrical layer being represented as a first layer and being a solid cylinder; and sequentially arranged around the central cylindrical layer to the outer jacket
- the second to nth layers are respectively n-1 concentric rings, and the n concentric layers are assembled into a multi-layered cylinder, characterized in that the dielectric constants of the n concentric layers are from the first layer to the nth
- the layer is reduced layer by layer, specifically between 2.05 and 1.05; each of the n concentric layers comprises a low dielectric constant substrate and a high dielectric constant, low specific gravity additive material, by adding high in the substrate A dielectric constant material increases its dielectric constant.
- the substrate is a light foaming medium material, which can be made of the following materials: polyethylene, polystyrene, polytetrafluoroethylene, polypropylene, polyurethane and polyvinyl chloride, wherein the preferred density is 0.02-0.03.
- the material of g/cm 3 is more preferably polystyrene, polyvinyl chloride or polyethylene.
- the amount of the additive material contained in the n concentric layers per unit volume is gradually decreased from the first layer to the nth layer, and the additive material is a material having a high dielectric constant, and a substrate having a low dielectric constant With the cooperation, the n concentric layers can realize the dielectric constant gradation.
- the density and electromagnetic response should be considered.
- materials with lower density and higher dielectric constant should be selected.
- the additive material in the present invention is preferably one or more of ceramic powder, aluminum silver powder, and metal wire.
- the additive material may have a cylindrical shape, a powder shape, a block shape, a needle shape, and a spherical shape. Etc., preferably needle-like or spherical.
- the cylindrical lens of the present invention When preparing the cylindrical lens of the present invention, firstly, according to the designed dielectric constant value, an additive material selected according to density and electromagnetic response is added to the selected substrate, and a sample of each layer of the substrate is initially prepared. The amount of the additive material per unit volume in each layer is reduced from the first layer to the n-th layer layer by layer. Since the substrate used in the present invention is a low-k dielectric lightweight foam material, after adding a high dielectric constant additive material to the substrate, the dielectric constant value of each concentric layer of the cylindrical lens increases with the unit volume. The amount increases and increases. It should be noted that the outermost layer, that is, the amount of the additive material contained in the nth layer, should be extremely small or 0, to ensure that the outermost dielectric constant is closer to air.
- the dielectric constant value of each of the preliminary samples was tested using a dielectric constant tester, and the amount of the added material having a high dielectric constant added to each layer was adjusted according to the measured value of the dielectric constant equivalent of +/- 0.05, and Make a sample and retest until a final sample of each concentric layer of substrate meets the initial design requirements for dielectric constant.
- the concentric layer substrate samples were uniformly enlarged to obtain respective concentric layers.
- the 2-n layer is then formed into a concentric ring and assembled with the first layer enlarged into a solid cylindrical shape to form a rough product of an n-layer concentric cylindrical lens.
- the efficiency of the lens is affected by the gap between the layers, the more and the gap, the lower the lens efficiency. This is because when the gap is large, radio waves are unnecessarily reflected or refracted through the air-layer interface, which causes a decrease in antenna gain or an increase in side lobes. Therefore, when assembling n concentric layers into a cylindrical lens, it should be ensured that no gap is left and tightly bonded into a multi-layered cylinder.
- Each concentric layer substrate sample was re-prepared according to the determined addition amount, and enlarged, and folded into a desired cylindrical lens. Then, the combined cylindrical lens and the antenna unit are combined to form an antenna for measurement, and the gain and direction diagram of the antenna are tested to ensure that various index parameters meet the design requirements.
- the difference in the electromagnetic response of the added material should affect the value of the dielectric constant. Therefore, the amount of material added in each layer will affect the dielectric constant value of each layer. In essence, the electromagnetic response of the added material will affect the lens.
- the dielectric constant value of the layer. The influence of the electromagnetic response value of the added material on the performance of the lens is represented by the dielectric constant value tested by the dielectric constant tester and the final measured antenna measurement index. Therefore, it is necessary to comprehensively consider the lens index selection during the production process. Material and amount added.
- the number, height and diameter of the cylindrical lens used in the present invention, as well as the number of antenna elements, and the arrangement outside the cylindrical lens can be selected or produced according to the application scenario and the antenna index, and can be adapted to various application requirements.
- the cylindrical lens height provided by the present invention is preferably 20-70 cm, more preferably 25-60 cm, most preferably 30-50 cm, and the diameter of the cylindrical lens is preferably 20-90 cm, more preferably 30-, because satisfactory antenna performance and installation space requirements are required. 60 cm, most preferably 35-50 cm.
- the "ultra-light" in the ultra-light artificial medium multilayer cylindrical lens provided by the present invention is that after the final preparation of the lens, the total apparent density of the entire lens is 0.08-0.095 g/cm 3 , and the contrast polystyrene density is 1.05 g. /cm 3 can calculate that the ultra-light artificial medium multilayer cylindrical lens provided by the present invention is about 11 times lighter than polystyrene.
- the ultra-light artificial medium multi-layer cylindrical lens provided by the invention has the characteristics of ultra-wide frequency, in particular, the application frequency can exhibit almost the same performance (dielectric constant, low insertion loss) from 0.6 GHz to 28 GHz and above in mobile communication. ). It has an extremely broad prospect in the field of electromagnetic radiation and scattering.
- a 6-layer artificial medium cylindrical lens is provided, the lens height is 30 cm, and the diameter is 36 cm.
- Table 1 shows the specific parameters of each layer index of the lens, and finally The resulting lens has a total apparent density of only 0.092 g/cm 3 , an ultra-low density and an ultra-light quality.
- the cylindrical lens When the cylindrical lens is applied to a multi-beam antenna, due to the special action of its columnar structure on the elevation plane, a complicated electro-optic down-tilt mechanism can be omitted compared to a conventional spherical or hemispherical lens, such as the present invention.
- the provided 6-layer cylindrical lens when operating at 2500MHz, the antenna gain obtained by the unit antenna excitation can reach 18.39dBi.
- a 10-layer artificial medium cylindrical lens having a height of 50 cm and a diameter of 65 cm is provided.
- Table 2 shows specific parameters of each layer of the lens, and the final lens is prepared.
- the total apparent density is only 0.086g/cm 3 , the density is ultra-low, the quality is ultra-light, and the application range is wider.
- the cylindrical lens when applied to construct a multi-beam antenna in an antenna system, it can be combined with the antenna unit to construct a full-frequency 180° sector horizontal coverage antenna of the de-energizing down-tilt mechanism 10, which can save the traditional antenna.
- the complex vertical beam ESC down-tilt mechanism is installed.
- the antenna operates at 850MHz/1920MHz, the low-frequency antenna gain can reach 14.6dBi and the high-frequency antenna gain can reach 20dBi.
- the artificial medium multilayer cylindrical lens provided by the invention has the layer number, the height, the diameter and the dielectric constant of each layer are designed according to the actual needs of the antenna index, and the preparation method is simple, and the obtained dielectric constant value of the lens is more ideal. design. The most important thing is that the lens produced is ultra-light, ultra-low density and ultra-wide application frequency, which will greatly expand the application of the lens in the military and civilian fields, especially in crowded areas and big data traffic areas.
- the lens provided by the present invention When the lens provided by the present invention is combined as a carrier and an antenna unit, a wider vertical coverage can be achieved, and it is no longer necessary to install a complicated vertical beam down-tilt mechanism, which is not available in the conventional Longbo ball antenna. It is also one of the biggest highlights of the present invention.
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Abstract
Description
层 | 1层 | 2层 | 3层 | 4层 | 5层 | 6层 |
设计介电常数值 | 1.85 | 1.6 | 1.45 | 1.3 | 1.15 | 1.08 |
最终介电常数值 | 1.85+/-0.05 | 1.6+/-0.05 | 1.45+/-0.06 | 1.3+/-0.07 | 1.15+/-0.03 | 1.08+/-0.03 |
内径(mm) | — | 95.5 | 156.4 | 208.6 | 256.9 | 311.4 |
外径(mm) | 95.4 | 156.3 | 208.4 | 256.8 | 311.2 | 360.2 |
Claims (10)
- 一种超轻人工介质多层圆柱透镜,包括n个介电常数不同的同心层,中心圆柱层表示为第1层,为一个实心圆柱体;围绕中心圆柱层依次向外套叠排列第2至第n层,分别为n-1个同心圆环,n个同心层被装配成一个多层圆柱体,其特征在于,所述n个同心层介电常数由第1层至第n层逐层降低,具体在2.05至1.05间变化;所述n个同心层中每层都包括低介电常数的基材和高介电常数、低比重的添加材料;所述基材为轻型发泡介质材料,具体为密度0.02-0.03g/cm 3的材料;其中,每单位体积所述n个同心层中添加材料的含量从第1层至第n层逐渐减少。
- 如权利要求1所述的圆柱透镜,其特征在于,所述轻型发泡介质材料为聚苯乙烯、聚氯乙烯或聚乙烯。
- 如权利要求1所述的圆柱透镜,其特征在于,所述添加材料包括陶瓷粉、铝银粉、金属丝中的一种或几种。
- 如权利要求1所述的圆柱透镜,其特征在于,各同心层介电常数由各层中包含所述添加材料的电磁响应和密度决定。
- 如权利要求1所述的圆柱透镜,其特征在于,所述圆柱透镜中n个同心层的介电常数值通过介电常数测试仪测试确定。
- 如权利要求1所述的圆柱透镜,其特征在于,所述第2至第n个同心层制备完成后形成n-1个同心圆环,并与所述第1层套叠成所述圆柱透镜,套叠时应保证各层之间紧密无缝隙。
- 如权利要求1所述的圆柱透镜,其特征在于,所述圆柱透镜的结构参数和性能参数根据天线的实际工作需要确定。
- 如权利要求7所述的圆柱透镜,其特征在于,所述结构参数包括所述圆柱透镜的直径、高度、层数,所述性能参数包括各同心层的介电常数值。
- 如权利要求1-8中任一项所述的圆柱透镜,其特征在于,所述圆柱透镜的总表观密度为0.08-0.095g/cm 3。
- 将权利要求9所述的圆柱透镜应用于天线系统中构造超宽频多波束天线的应用,所述超宽频是指频率为0.6GHz-28GHz。
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US16/491,157 US11145987B2 (en) | 2017-08-18 | 2018-08-16 | Ultralight artificial medium multilayer cylindrical lens |
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US20190393614A1 (en) | 2019-12-26 |
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