Mesh Horn Antennas by Additive Manufacturing

Additively manufactured antennas with strategically placed holes address the inefficiencies of traditional manufacturing by reducing mass and maintaining performance, enabling efficient and reliable production.

JP7824740B2Active Publication Date: 2026-03-05THE BOEING CO
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Patent Information

Application Number
JP2021151261
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Priority Date
2020-09-30
Filing Date
2021-09-16
Publication Date
2026-03-05
Estimated Expiration
2041-09-16

AI Technical Summary

Technical Problem

Traditional manufacturing methods for antennas are time-consuming and expensive, and additive manufacturing processes face challenges with unsupported structures collapsing, lack of precision in fine details, or developing distortion or cracks, necessitating new designs for efficient fabrication.

Method used

The development of additively manufactured tubular antennas with strategically placed holes to reduce mass while maintaining electromagnetic wave transmission characteristics, achieved by modifying conventional designs to increase thickness and incorporating holes that are sized and positioned to be electromagnetically opaque within the operating frequency range.

Benefits of technology

The solution allows for efficient, reliable, and cost-effective production of antennas with reduced mass and improved structural integrity, compatible with existing systems, while maintaining electromagnetic performance.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

To provide an efficient mesh horn antenna manufactured through a time- and cost-saving process, and a manufacturing method thereof.SOLUTION: An antenna device 210 includes an additively manufactured tubular body (a rectangular waveguide portion 216 and a pyramidal horn portion 218) having a wall 228 and a wall 230 provided with a plurality of holes. The tubular body transmits electromagnetic radiation in a selected operating frequency range, and has a mass below a maximum mass threshold. The holes reduce the mass of the tubular body to less than the maximum mass threshold without significantly adversely affecting electromagnetic radiation transmission capability of the tubular body in the selected operating frequency range.SELECTED DRAWING: Figure 3
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Description

[Technical Field]

[0001] The present disclosure relates to additively manufactured mesh horn antennas and methods for making same. [Background technology]

[0002] Antennas are essential components in wireless communication technology for transmitting and receiving radio signals. The conductive material in an antenna acts as an interface between the electrical current in the communication circuit and the electromagnetic waves in space. The shape and material of an antenna determine its characteristics, such as impedance, directivity, and bandwidth. Appropriate characteristics can vary depending on the antenna's location and application. For example, civil frequency modulation (FM) radio uses monopole omnidirectional antennas to receive signals from any direction, while Global Positioning System (GPS) satellites use highly directional antennas for ground-directed transmission. In many applications, creating efficient antennas requires the precise formation of complex shapes. Traditionally, such antennas have been manufactured using a time-consuming and expensive process of manually assembling multiple individually machined parts.

[0003] Additive manufacturing (AM) is rapidly gaining popularity across many industries as a relatively low-cost, high-speed manufacturing method. Additive manufacturing, also known as 3D printing, is a technology used to create solid objects from 3D models by additively building the object. Additive manufacturing typically involves laying down raw material and selectively bonding or fusing it to create the desired object. The raw material is often laid down in layers, with the thickness of each layer depending on the technology used.

[0004] The raw material, typically in particulate or powder form, is laid down in layers and then selectively melted by a heat source. Often, the top surface of the material bed is melted, and then the workpiece being built is slightly lowered. A new layer of raw material is then laid on top of the material bed and fused to the previous layer as the next layer. Examples of particulate raw materials include thermoplastic polymers, metal powders, metal alloy powders, or ceramic powders, all of which can be melted using a computer-controlled heat source, such as a scanned laser or scanned electron beam. Typical methods include selective laser melting (SLM), direct metal laser sintering (DMLS), selective laser sintering (SLS), fused deposition modeling (FDM), and electron beam melting (EBM).

[0005] Traditional part designs intended for use with machining or other subtractive manufacturing methods are inefficient, or in some cases impossible, with additive manufacturing. Depending on the process and materials used, they can collapse when unsupported, lack precision in fine details, or develop distortion or cracks. New part designs are needed that can be efficiently fabricated using additive manufacturing methods while maintaining the functionality of traditional parts. Summary of the Invention

[0006] The present disclosure provides systems, devices, and methods for additively manufactured antenna devices. In some embodiments, the antenna device can include an additively manufactured tubular body having a wall with a plurality of holes formed therein. The tubular body is configured to transmit electromagnetic waves in a selected operating frequency range and to have a mass below a maximum mass threshold. The plurality of holes are configured to reduce the mass of the tubular body below the maximum mass threshold without substantially adversely affecting the electromagnetic wave transmission characteristics of the tubular body in the selected operating frequency range.

[0007] In some embodiments, an antenna device can include an additively manufactured tubular body having a plurality of holes, the antenna device having a given operating frequency range, the plurality of holes being sized and positioned such that the plurality of holes are substantially opaque to the operating frequency range.

[0008] In some examples, a method for additively manufacturing an antenna can include receiving an antenna design for traditional manufacturing and identifying a portion of the antenna design that is below a minimum size printable on a selected additive manufacturing device. The method can further include modifying the antenna design, including increasing the size of the identified portion and adding a plurality of holes. The method can further include additively manufacturing the antenna according to the modified design.

[0009] The features, functions, and advantages may be realized individually in various embodiments of the present disclosure, or may be combined with one another in other embodiments. Further details will become apparent from the following description and by reference to the drawings. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a schematic diagram of an exemplary antenna apparatus according to some aspects of the present disclosure. [Figure 2A] 2 is a schematic diagram showing a first embodiment of a cross section of a hole in the antenna device of FIG. 1. FIG. [Figure 2B] 1. FIG. 4 is a schematic diagram showing a second embodiment of a cross section of a hole in the antenna device of FIG. [Figure 3] FIG. 1 is an isometric view of an exemplary mesh horn antenna described herein. [Figure 4] FIG. 4 is a front view of the antenna shown in FIG. [Figure 5] FIG. 4 is a side view of the antenna shown in FIG. [Figure 6] FIG. 4 is a top view of the antenna shown in FIG. [Figure 7]4 is a detailed view of some of the holes in the antenna shown in FIG. 3. FIG. [Figure 8] 1 is a flowchart illustrating steps of an exemplary additive manufacturing method. [Figure 9] FIG. 1 is a schematic diagram of an exemplary additive manufacturing apparatus. [Figure 10] 1 is a flowchart illustrating steps of an exemplary antenna additive manufacturing method according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0011] Various aspects and embodiments of additively manufactured mesh antenna devices and related methods are described below and illustrated in the accompanying drawings. Unless otherwise specified, antenna devices and / or various components of such devices according to the present disclosure may, but need not, include at least one of the structures, components, functions, and / or variations described, illustrated, and / or incorporated herein. Furthermore, unless specifically excluded, method steps, structures, components, functions, and / or variations described, illustrated, and / or incorporated herein in connection with the subject matter of the present disclosure may be included in other similar devices and methods, including those that are compatible with embodiments of the present disclosure. The following description of various embodiments is for illustrative purposes only and is not intended to limit the present disclosure, its applications, or uses. Furthermore, while advantages achieved by the embodiments are described below, these are merely examples, and not all embodiments necessarily achieve the same or similar advantages.

[0012] The Detailed Description herein includes the following sections: (1) Overview; (2) Examples, Components, and Alternatives; (3) Exemplary Combinations and Additional Examples; (4) Advantages, Features, and Benefits; and (5) Conclusion, as set forth below. The Examples, Components, and Alternatives section is further divided into subsections A through C, and is labeled accordingly. <Summary>

[0013] Generally, an antenna device can include a conductive material structure fabricated by additive manufacturing. The antenna device may also be described as an antenna component. The antenna device is configured to transmit and receive radio signals and may function as part of a conventional antenna, such as a command horn antenna, a cup dipole antenna, or a waveguide antenna. Additionally or alternatively, the antenna device may function as an antenna without additional components.

[0014] FIG. 1 is a schematic diagram of an antenna device, generally designated 110. The antenna device includes a body 112 having a wall 113 and a plurality of mesh through holes 114. The body may be, for example, tubular, elongated, and / or hollow. The body may be configured to form a channel for transmitting and receiving radio frequency signals and / or to transmit electromagnetic waves within an operating frequency range. For example, a satellite antenna may be configured to operate at a radio frequency of approximately 8 gigahertz to 18 gigahertz.

[0015] The antenna device 110 further includes one or more internal structures shaped to facilitate transmission and reception of radio frequency electromagnetic waves. These one or more structures may be configured for a selected polarization, resonant frequency band, radiation pattern, and / or any functional antenna characteristic. Examples of internal structures include, but are not limited to, a septum, an iris, a dipole, a tuning screw, a post-filter, and / or combinations thereof. The internal shape of the wall 113 may also be configured for a selected polarization, resonant frequency band, radiation pattern, and / or any functional antenna characteristic.

[0016] The antenna device 110 includes a conductive material, such as a laser-sintered metal. In some embodiments, the device may include aluminum, copper, titanium, and / or alloys thereof. The device may include multiple materials or may be formed of a single material. The material or combination of materials for the antenna device 110 may be selected based on a variety of factors, including electrical conductivity, elasticity, density, and temperature sensitivity. Suitable or desirable materials depend on the application of the antenna device and the additive manufacturing method selected.

[0017] The antenna device 110 has a manufacturing orientation defined by a build axis, which may coincide with the longitudinal axis of the body portion 112. The antenna device may be constructed from multiple layers generally perpendicular to the build axis, each layer being thin and planar and capable of being fused or otherwise bonded to adjacent layers.

[0018] The amount of variation between adjacent layers can be limited; that is, the dimensions of the antenna device 110 vary gradually along the build axis. The antenna device does not include any abrupt protrusions that create downwardly facing surfaces at angles greater than about 45 degrees or greater than about 50 degrees relative to the build axis. Thus, all portions of the antenna device 110 can be printed without the need for secondary supports.

[0019] In some embodiments, the antenna device 110 is fabricated by post-processing an additively manufactured blank. Horizontal holes, threads, and / or other features not suitable for additive manufacturing can be formed by machining. In such embodiments, the additively manufactured blank does not include any sharp protrusions and is printable without the use of additional supports.

[0020] The thickness of any structural portion of the antenna device 110 may also be limited by the additive manufacturing method and / or equipment used to fabricate the device. More specifically, a lower thickness limit may be imposed. A structural portion below this limit may be non-uniform, deviate from desired specifications, and / or crack during printing or subsequent cooling stages.

[0021] Conventional antenna designs may include walls or other structural features that are thinner than practical manufacturing limits. Therefore, such designs can be modified to allow for additive manufacturing. More specifically, structural features that are thinner than practical manufacturing limits are modified to increase their thickness. However, increasing the thickness can increase the overall mass of the antenna assembly. Increased mass also increases material costs and printing time, which is particularly disadvantageous for antennas used on satellites or other spacecraft.

[0022] The increased mass due to the increased thickness can be partially or completely offset by providing the holes 114 in the antenna device 110. In other words, the holes 114 are configured to reduce the mass of the antenna device 110 without substantially affecting the functionality of the antenna device.

[0023] The modifications required to conventional designs, including increasing thickness and adding holes, depend on the printing resolution limitations of the selected additive manufacturing method and / or device. In some embodiments, antenna device 110 can be additively manufactured according to conventional designs with little or no modification to increase the thickness of the structure. In such embodiments, the inclusion of multiple holes 114 can reduce the weight of antenna device 110 relative to a corresponding antenna device design fabricated using conventional methods.

[0024] Some of the holes 124 in the plurality of holes 114 are arranged in a regular, repeating pattern, which may be referred to as an array. In general, the holes 124 may be arranged in any suitable regular or irregular pattern. The holes 124 may be referred to as open areas, circular openings, and / or voids, and / or the material between the holes may be referred to as forming a mesh. The antenna device 110 may include an array of holes 124 arranged in a continuous line, in spaced-apart rows, and / or in any effective grouping. The holes may be uniform and consistent, or may vary in size, shape, and / or shape.

[0025] The holes 124 have a size and / or shape that allows for additive manufacturing without the use of auxiliary supports. In the illustrated example, the holes 124 are hexagonal, but have a small size that allows them to be printed without buckling. In some embodiments, the holes have a shape and orientation that allows them to be freestanding, such as a rectangle or diamond with each side angled at 45 degrees or less relative to the build axis.

[0026] Each hole 124 has a maximum dimension 126 and, in some embodiments, a minimum dimension 127. The maximum dimension can refer to the maximum opening width of the hole, and the minimum dimension can refer to the minimum opening width of the hole. For hexagonal holes, as shown, the maximum dimension 126 is the distance between opposite corners, and the minimum dimension 127 is the distance between opposite sides. For circular holes, the maximum and minimum dimensions correspond to the diameter of the circle. The maximum dimension 126 can be limited by manufacturability and / or electromagnetic effects. The minimum dimension 127 can also be limited by manufacturability, for example.

[0027] The minimum dimension 127 may be limited to a dimension greater than the minimum printable hole size. The maximum dimension 126 may also be limited to a dimension less than the maximum self-supporting size. These limitations may be determined, for example, by the selected additive manufacturing process and equipment, as well as the selected hole shape and placement. For example, a diamond-shaped aperture will have a significantly larger maximum self-supporting size than a circular aperture. In another example, the smaller the layer thickness a printer can print, the smaller the minimum printable hole size.

[0028] The antenna device 110 may be configured to transmit and / or receive radio signals in a given wavelength range. In other words, the antenna device 110 is configured to transmit electromagnetic waves in a selected frequency band. In other words, the antenna device can be said to have a predetermined operating frequency range.

[0029] The maximum dimension 126 of each hole 124 may be limited to the shortest expected wavelength 128. Figure 1 shows a schematic, not to scale, representation of an electromagnetic signal at wavelength 128. By limiting the maximum dimension 126, the holes 124 have a negligible effect on the electromagnetic properties of the antenna device 110. That is, the holes 124 can be said to be electromagnetically opaque for the desired operating frequency range of the antenna device.

[0030] For example, maximum dimension 126 is less than 10% of wavelength 128. In some embodiments, maximum dimension 126 is selected so that the impact of hole 124 on the operation of antenna device 110 is below an acceptable threshold. The smaller the hole, the less impact it will have, and if hole 124 is sufficiently smaller than expected wavelength 128, impact on antenna performance can be avoided. In some embodiments, maximum dimension is less than 5% or less than 2% of the expected wavelength.

[0031] The size, spacing, and / or placement of the holes 124 may be determined according to the structural requirements of the antenna device 110. That is, the holes 124 may be configured to provide the antenna device 110 with sufficient structural strength, rigidity, and / or other structural properties. For example, the holes 124 may be spaced away from joints, corners, and / or critical structural features. In other embodiments, the holes 124 may be positioned such that they do not occupy more than a selected percentage of the surface area of ​​the wall 113 of the antenna device. For example, the holes 124 may occupy less than half of the surface area of ​​the wall 113 of the antenna device, i.e., the ratio of the hole area to the wall area is greater than 1.

[0032] Each hole 124 has a center 129, and the holes are spaced apart relative to a center-to-center distance 130. The distance 130, maximum dimension 126, and shape of the holes 124 determine the surface area of ​​the walls 113 or other structures between the holes 114. In some embodiments, the shape of the holes 124 is selected to allow for efficient dense spacing of the holes and to reduce the wall surface area corresponding to a given center-to-center distance 130.

[0033] As outlined above, the holes 114 can be configured to reduce the mass of the wall 113 and thus the overall mass of the antenna device 110. The size, number, and / or spacing of the holes 124 can be selected to provide a sufficient mass reduction. In some embodiments, the extent of the holes through the wall 113 can also be configured to contribute to the mass reduction. Figures 2A and 2B show two example cross-sectional shapes of the holes 124 taken along a plane perpendicular to the wall 113.

[0034] Figure 2A shows a linear depth-shaped hole 124, a configuration that is particularly suitable for embodiments where the minimum dimension 127 is close to the smallest printable hole size due to ease of printing. Figure 2B shows a butterfly or yo-yo depth-shaped hole that is largest on both sides of wall 113 and decreases in size toward the interior of the wall. This configuration further reduces the mass of wall 113 while maintaining the desired electromagnetic opacity.

[0035] In some embodiments, the antenna device 110 further includes a base for connection to electronic circuitry. For example, the antenna device may include a hole for attaching a coaxial adapter. The antenna device may be configured to be connectable to other antenna components, such as a reflector dish or dipole. In some embodiments, the design of the antenna device 110 is designed to provide functionality similar to existing antenna designs and is configured to be connectable to common electrical systems compatible with existing antenna designs.

[0036] The antenna device 110 may be partially or entirely one-piece. In other words, the body 112, any internal structure, any base, and / or any other portion of the antenna device may be a single structure. The antenna device may be additively manufactured in a single process without the need for separate assembly of other components. Additionally, the antenna device may be manufactured without the use of auxiliary supports that require removal after manufacture.

[0037] The integrated construction of the antenna assembly 110 allows for greater reliability because failure modes associated with component connections and interactions are eliminated. For example, the antenna assembly does not include bolts that can loosen due to vibration, shims that can move due to load, or tuning screws that can become out of tune during shipping. In general, an antenna with fewer components has fewer opportunities for operational problems. [Example]

[0038] In the following sections, several aspects of an exemplary antenna device and related systems and / or methods will be selectively described. The examples shown in the following sections are for illustrative purposes only and are not intended to limit the scope of the entire disclosure. Each section may include one or more distinct embodiments and / or descriptions of background information or related information, functions and / or structures. <A. Exemplary Mesh Horn Antenna>

[0039] As shown in FIGS. 3 to 6, an exemplary mesh horn antenna 210 will be described in this section. Antenna 210 is an example of the above-described antenna device. The illustrated additive manufacturing antenna is designed to replace the function of a pyramidal horn antenna fabricated by conventional traditional manufacturing methods. Conventional antennas include a plurality of separate machined parts joined by screwing, adhesion, or other methods. For example, a stepped septum for circular polarization of the antenna is joined inside a separately fabricated hollow rectangular waveguide, and this waveguide is also fixed to a plurality of separate horn portions.

[0040] The dimensions and arrangements of each component of the conventional antenna are calculated to obtain desired functional characteristics such as polarization characteristics, resonance frequency, directivity, etc. However, some of the surfaces and structures are important for electromagnetic wave characteristics, and some are important structurally and mechanically.

[0041] In the configuration of the additive manufacturing antenna 210, the electromagnetic and functionally important parts of the conventional antenna are maintained as they are, and changes are made to the structurally and mechanically important parts to enable additive manufacturing. Also, the antenna 210 can be configured to be compatible with electronic components that can be used in conjunction with the conventional antenna.

[0042] As shown in FIG. 3 , the antenna 210 is a one-piece construction. That is, the antenna is constructed in one piece and requires no assembly other than connecting a feed line, such as a coaxial adapter. The one-piece construction of the antenna can improve reliability and / or reduce failures. The antenna is designed to be fabricated without a secondary support. In other words, the support does not need to be removed after fabrication of the antenna. In the illustrated embodiment, fabrication of the antenna 210 requires minimal post-processing, such as drilling fastener holes in the bottom of the antenna, as described in more detail below. The antenna can be configured such that the as-fabricated surface is limited to a sufficient surface roughness without requiring a full surface finish.

[0043] Antenna 210 is designed for fabrication by direct metal laser sintering (DMLS). In this example, the antenna is made from a laser-sintered aluminum alloy, specifically AlSi10Mg Type II. This alloy offers high strength, hardness, and load-bearing capacity, as well as being lightweight. Any metal or alloy with similar suitable properties can be used in any available additive manufacturing process.

[0044] Antenna 210 has a central axis 214, which is also referred to as the fabrication and / or build axis of antenna 210. The antenna is fabricated such that central axis 214 is parallel to the vertical or z-axis of the fabrication equipment, for example. In this case, antenna 210 is constructed from multiple flat layers that are perpendicular to central axis 214.

[0045] As shown in FIG. 3 , antenna 210 includes a rectangular waveguide portion 216 and a multi-section pyramidal horn portion 218 having multiple wall sections. The rectangular cross-section 250 of each portion 216 and 218 is more clearly shown in FIG. 6 . Waveguide portion 216 and horn portion 218 may be described as forming a body portion of antenna 210, which is an example of body portion 112 described above. And / or each of the waveguide portion and horn portion may be described as an example of body portion 112. In this embodiment, horn portion 218 includes a tapered section 220, a mode suppressor section 222, and a flared section 224. Antenna 210 may be, for example, a Potter horn antenna, a command horn antenna, and / or a feed horn antenna.

[0046] The waveguide 216 is a cylindrical body having an internal cavity 226 and four flat walls 228 (e.g., wall surfaces) linearly connected at four corners. The walls 228 are an example of the wall 113 described above. In this embodiment, the waveguide has a rectangular cross section, and each wall 228 has the same dimensions. The internal cavity 226 has a constant cross-sectional dimension along the central axis 214. The waveguide 216 further includes a stepped septum 234 therein, as shown in FIGS. 4 and 5, configured to achieve circular polarization of the radio signal. The septum is a thin plate-like member extending between the two opposing walls 228 of the internal cavity 226.

[0047] Referring again to FIG. 3 , the horn portion 218 is composed of a plurality of flat walls (e.g., wall sections) 230 and can be said to have an internal cavity 232. The walls 230 can also be said to be an example of the wall 113 described above. Each of the sections 220, 222, and 224 that make up the horn portion includes four walls 230. Some of the flat walls 230 are inclined with respect to the central axis 214, and some are parallel to the central axis. The internal cavity 232 of the horn portion 218 communicates with the internal cavity 226 of the waveguide portion 216, and each wall 230 of the tapered section 220 in the horn portion is connected to a corresponding wall 228.

[0048] In general, antenna 210 can include any structure and / or feature found in conventional antenna designs and / or have electromagnetic functionality equivalent to structures or features found in conventional antenna designs. For example, antenna 210 can include a circular waveguide, a conical horn, and / or one or more ridges, fins, and / or corrugations.

[0049] A base plate 236 is formed at the lower end of waveguide 216. The base plate partially fills internal cavity 226 and is bonded to three of walls 228. The base plate has multiple holes extending vertically therethrough for receiving fasteners that can be used to secure base plate 236 and antenna 210 to other structures. These fastener holes can be machined or milled into base plate 236. Additionally, the surface of the base plate can be precision-finished by machining after additive manufacturing of antenna 210.

[0050] As shown in Figures 4 and 5, a feed interface portion (e.g., a feed interface adapter) 238 is formed in one of the walls 228 and is located adjacent to a base plate 236 at the lower end of the waveguide portion 216. The interface portion includes a rectangular raised boss with openings at either end that extend horizontally through the feed interface portion and the wall 228. The boss and openings are configured to connect a coaxial feedline and / or any antenna feedline. These connector openings can be machined or milled into the feed interface portion 238. Additionally, the surfaces of the feed interface portion can be precision-finished by machining after additive manufacturing of the antenna 210.

[0051] In some embodiments, command horn antenna 210 is configured to be connected to another support or electronic component. Base plate 236 and / or power feed interface portion 238 can include any suitable connection feature. In some embodiments, openings in the base plate and / or power feed interface portion can be formed as part of an additive manufacturing process. In such embodiments, these openings are formed as diamonds or other free-standing shapes rather than circles.

[0052] Antenna 210 has a plurality of holes 240 penetrating walls 228, 230. Holes 240 can also be referred to as mesh holes. Each of walls 228, 230 includes an array 242 of holes 240. The holes in each array are regularly arranged in a pattern suited to the shape and structural function of the respective wall. Holes 240 are an example of holes 124 described above, and array 242 is an example of holes 114 described above.

[0053] As shown more clearly in Figures 4 and 5, the holes 240 in each array 242 in this embodiment are arranged in a plurality of regularly spaced rows, with the rows staggered so that the holes in each row align with the gaps between the holes in the two adjacent rows. This row arrangement allows for a desired density of holes. In this embodiment, the holes 240 occupy approximately 60% of the surface area of ​​the walls 228, 230. The appropriate pattern for achieving the desired density depends on the shape of the holes 240, as will be described below with reference to Figure 7.

[0054] The holes 240 in each array 242 are spaced away from the edge of each wall, thereby providing additional structural strength at corners where the walls meet. The holes 240 and / or arrays 242 are also spaced away from and / or aligned to avoid other connections. For example, as shown in FIG. 5, the array 242 in wall 228 has a section without holes, where the holes 240 are spaced away from the junction between the wall and the inner septum 234.

[0055] 6, the walls 228, 230 of the antenna 210 all have a uniform thickness 244. In some embodiments, the thickness 244 can vary from wall to wall or within a single wall. Whether the thickness 244 is constant or varies from section to section, the thickness 244 is equal to or greater than the minimum printable hole thickness throughout the entire antenna 210. In other words, the antenna 210 is designed according to the constraints associated with the selected additive manufacturing process and / or equipment, and the walls of the antenna are thick enough to be fabricated by printing.

[0056] In this embodiment, thickness 244 of walls 228, 230 is approximately 0.035 inches (35 mils or 0.09 cm). A pyramidal horn antenna fabricated using conventional manufacturing methods, which antenna 210 replaces, may include walls only approximately 0.15 inches (15 mils or 0.04 cm) thick. Thickness 244 of antenna 210 is designed to be twice or more the thickness of a corresponding conventional antenna. However, due to the presence of holes 240 in the antenna walls, the mass of antenna 210 is not twice that of a conventional antenna.

[0057] The mass of antenna 210 is below a maximum mass threshold. In other words, antenna 210 is designed so that the increase in mass due to the increase in wall thickness 244 is sufficiently offset by the decrease in mass due to the provision of holes 240 to maintain the mass of the antenna below a selected value. The maximum mass threshold is selected based on operational constraints, such as fuel capacity in a launch vehicle, or material costs. In this example, antenna 210 weighs approximately 0.15 pounds (2.4 ounces), which is designed to be below the selected maximum mass threshold of approximately 0.05 ounces per square inch. The weight of antenna 210 is only approximately 15 percent greater than the weight of a conventional antenna.

[0058] 7 shows some of the holes 240 in the array 242 in the wall 228 of the waveguide 216. In this embodiment, the array 242 is arranged in the same pattern, and the holes 240 have the same size and shape, throughout the antenna 210. It will be understood, therefore, that the following description applies to other arrays of holes as well. In some embodiments, the pattern of the array 242 and / or the size and / or shape of the holes 240 may vary from wall to wall, or may have different configurations within a single wall.

[0059] In this example, the holes 240 are circular and extend linearly through the wall 228, thereby forming a generally cylindrical cavity in the wall. Each hole has a diameter 246, which is an example of the maximum dimension 126 discussed above. The holes 240 in the array 242 are arranged in a staggered fashion in rows, as discussed above. Two adjacent holes in the same row can be described as having a center-to-center distance 248. That is, the center of one hole is spaced a distance 248 from the center of the adjacent hole.

[0060] In this embodiment, the diameter 246 of the holes 240 is approximately 0.08 inches (80,000ths of an inch (mils), or 0.2 centimeters (cm)), and the center-to-center distance 248 between adjacent pairs of holes in the same row is approximately 0.1 inches (100 mils, 0.25 cm). Therefore, adjacent holes are spaced at their closest points by approximately 0.02 inches (20 mils, 0.05 cm). In other words, there are no points where two holes 240 are closer to each other than 0.02 inches.

[0061] The diameter 246 and distance 248 can be selected according to printing limitations, structural considerations, and electromagnetic effects, as discussed above. The selection of the size and shape of the hole 240 can be interrelated; that is, the selected hole shape determines printing limitations, such as the maximum size that can be printed without requiring an auxiliary support.

[0062] In the illustrated example, diameter 246 is small enough to print a circular hole 240 without requiring an auxiliary support, and large enough to print at the resolution of the selected DMLS printer. Hole 240 is also small enough to provide adequate opacity to electromagnetic waves in the operating frequency range of antenna 210.

[0063] Antenna 210 is configured to perform wireless communication in a given frequency band. That is, this antenna is tuned to a given radio frequency band. In the illustrated embodiment, antenna 210 is tuned to the X-band including frequencies corresponding to wavelengths between approximately 3.75 and 2.5 cm. The diameter 246, which is the maximum dimension of hole 240, is less than or equal to about 8% of the expected shortest wavelength. Therefore, the influence of hole 240 on the electromagnetic function and characteristics of antenna 210 is negligible.

[0064] The shape of hole 240 and the pattern of array 242 are selected so that the holes can be arranged at a desired density. For example, in an embodiment where hole 240 is hexagonal, array 242 may be a honeycomb pattern. In an embodiment where hole 240 is square, array 242 may be a grid pattern. In some embodiments, it can be said that holes 240 are densely arranged and wall 228 is mesh-like. In some embodiments, the number of required holes is small, and it is possible to arrange holes 240 at a distance longer than the maximum hole dimension, that is, to make the distance between holes longer than diameter 246. <B. Exemplary Additive Manufacturing Method>

[0065] In this section, the steps of an exemplary additive manufacturing method 300 for fabricating a workpiece will be described. Refer to FIG. 8. In the method steps described below, the aspects of the exemplary additive manufacturing apparatus shown in FIG. 9 can be used. If necessary, components and systems that can be used for the execution of each step will be mentioned. However, such mentions are for illustrative purposes and are not intended to limit the modes capable of executing specific steps of the method.

[0066] In some embodiments, method 300 may be referred to as a 3D printing method. It is understood that additive manufacturing and 3D printing are both terms that encompass the process of creating an object by successively depositing layers of material. Additive manufacturing is a broader term that encompasses 3D printing. In some embodiments, additive manufacturing and 3D printing are used synonymously. In this disclosure, printing and / or printing steps are understood to include fabrication by any additive manufacturing method. Examples of additive manufacturing include, but are not limited to, material extrusion, powder bed fusion, material jetting, binder jetting, directed energy deposition, liquid vat photopolymerization, and sheet lamination.

[0067] 8 is a flowchart illustrating steps performed in an exemplary method, but does not necessarily depict a complete process or every step of the method. Although various steps of method 300 are described below and illustrated in FIG. 8, not all of these steps need be performed. In some cases, these steps may be performed simultaneously or in a different order than shown.

[0068] In step 310, digital information representing an ordered plurality of layers is received. The digital information is received by a computer controller 412 of an additive manufacturing device 410, shown in FIG. 9. An additive manufacturing device is also referred to as a printer or fabricator. The computer controller 412 may include any data processing system configured to receive the digital design information and control the functions of the printer 410. The computer controller illustrated in FIG. 9 includes a processor 414 that controls the functions of the printer and a memory 416 that stores the received data.

[0069] The received information includes geometric data and / or design details for multiple two-dimensional patterns that make up layers of a three-dimensional object, which is the workpiece 428 to be fabricated. These layers may be represented in cross sections or slices. The multiple layers may be ordered by numbering each layer or ordering them from first to last.

[0070] Step 312 of method 300 includes depositing feedstock material on a build platform 418 disposed within a build environment 420 of printer 410. The build platform may include a support that is movable along a build axis 422 by computer control 412. The build platform may have, for example, a flat surface that is perpendicular to the build axis 422.

[0071] The feedstock may be any material suitable for additive manufacturing, typically a fluid or powder, including, but not limited to, photopolymer resins, thermoplastics, plasters, ceramics, and metals. Such feedstock is supplied from a material source 424, such as a hopper, tank, or powder bed. For example, a brush arm driven by computer controller 412 may sweep aluminum alloy powder from the powder bed onto build platform 418.

[0072] The feedstock material may be uniformly distributed on the build platform 418 or deposited in a selected pattern. Deposition is performed under the control of the computer controller 412. In some embodiments, the build platform 418 is positioned to be submerged in the feedstock material, and gravity or fluid pressure is used to deposit the feedstock material. In some embodiments, a print head 426 is connected to the material source 424 and deposits the feedstock material in a pattern corresponding to the first layer of a sequence of multiple layers.

[0073] In step 314, the deposited raw material is altered to create a first layer, i.e., physically altered according to the design information for the first layer of the ordered layers and according to instructions from computer controller 412, thereby forming the first layer as a physical object on the build platform.

[0074] A print head 426 of the printer 410 can act on the material under the control of the computer controller 412. For example, the print head can include a laser to harden a photopolymer by exposing it to light or sinter a metal powder by exposing it to heat. The print head can be guided by the computer controller 412 to follow a path specified in the received digital information for the first layer and / or a path calculated by the processor 414 based on the received digital information.

[0075] Step 316 includes repositioning the build platform. In some embodiments, the build platform 418 starts at a predetermined distance from the print head 426. This predetermined distance can be determined depending on the process being performed by the print head. After a layer is fabricated, the computer controller 412 repositions the build platform along the build axis 422 away from the print head 426 by the thickness of the fabricated layer. That is, the build platform is moved so that the top surface of the fabricated layer is located a predetermined distance from the print head 426.

[0076] In some embodiments, the build platform 418 may start in a position aligned with other elements of the printer 410, such as a feedstock dispensing component. As a layer is built, the computer controller 412 moves the position of the build platform along the production axis 422 so that the top surface of the built layer is aligned with the other elements of the printer 410. In some embodiments, in step 316, the position of the print head 426 may be changed instead of or in addition to the build platform 418. In some embodiments, step 316 may be omitted.

[0077] In step 318, a source material is deposited over an existing layer created in a previous step in method 300. The source material can be any suitable material and deposited by any suitable method, as described for step 312. In step 320, the source material is modified to create the next layer, as described for step 314.

[0078] Steps 316 through 320 are repeated to create each layer of the plurality of layers represented by the received digital information until the final layer is created. The first through final layers thus created form a workpiece 428 represented by the received digital information. The workpiece is then removed from the printer and optionally post-processed. For example, the formed workpiece may be machined off the build platform and then machined or otherwise processed to create details or a smooth surface finish.

[0079] The workpiece 428 fabricated by method 300 may have different structural characteristics from workpieces fabricated by traditional methods such as machining, casting, and / or assembly. For example, all parts and / or details of the workpiece 428 may be integral and / or monolithic. In other embodiments, the workpiece 428 includes a plurality of layers perpendicular to the shaping axis of the workpiece formed by melting a material. In other embodiments, the workpiece 428 includes microstructural anisotropy resulting from the orientation of the manufacturing process. <C. Exemplary Method>

[0080] In this section, the steps of an exemplary method 500 for fabricating an antenna will be described. Refer to FIG. 10. In the method steps described below, aspects of the antenna device, manufacturing method, and / or additive manufacturing device described above can be used. Components and systems that can be used for the execution of each step will be referred to as necessary. However, such references are for illustrative purposes and are not intended to limit the modes in which the specific steps of the method can be executed.

[0081] FIG. 10 is a flowchart showing the steps executed in an exemplary method. However, it does not necessarily show the complete process or all the steps of the method. Various steps of method 500 are described below and shown in FIG. 10, but not all of these steps necessarily need to be executed. Also, in some cases, these steps can be executed simultaneously or in an order different from the order shown here.

[0082] In step 510, the method includes receiving a conventional antenna design. The design may be for any type of antenna configured to transmit and / or receive electromagnetic signals, such as a command horn antenna, a cup dipole antenna, or a waveguide antenna. The conventional antenna design may be referred to as a design for conventional antenna manufacturing and may include multiple components fabricated by subtractive processes, such as machined parts that are then fastened, fused, bonded, and / or otherwise assembled.

[0083] Step 512 of the method involves identifying portions of the received design that are too thin to print. A desired additive manufacturing method and equipment is selected, and printing limitations to ensure the desired build quality are determined. Any available additive manufacturing method and / or equipment can be selected, such as the exemplary methods and additive manufacturing equipment described in Section B. A threshold thickness is selected below which printing is impossible and / or does not result in the desired build quality. Portions of the antenna design that are below the selected threshold thickness are identified as being too thin to print.

[0084] In some embodiments, the selected thickness varies depending on the orientation. For example, for a DMLS printer configured to deposit layers approximately 30 micrometers thick, a thickness of 0.03 inches (30 mils or 0.075 cm) or less is unprintable when measured perpendicular to the build axis, while a thickness of 0.02 inches (20 mils or 0.05 cm) or less is unprintable when measured parallel to the build axis. Each portion of the antenna design is evaluated for its thickness along the selected build direction or axis. In some embodiments, portions that are too thin to print are identified based on other factors, such as limitations inherent in the selected printing equipment or materials.

[0085] Step 514 of the method includes modifying the received conventional antenna design for additive manufacturing. Step 514 includes a sub-step 516 of modifying the identified portions to increase their thickness. In other words, portions of the conventional antenna design that are identified as being too thin to print are modified to be at or above a selected threshold thickness. The thickness may be increased uniformly for each identified portion, and / or may be increased uniformly across all identified portions, and / or a new printable thickness profile may be designed for each identified portion according to an optimal additive manufacturing approach. The newly designed printable thickness profile may vary in thickness according to a selected threshold thickness, vary in thickness according to the structural requirements of the antenna design, and / or vary in thickness in any suitable manner.

[0086] Step 514 includes sub-step 518 of adding holes to the identified portions. In some embodiments, the holes are added to other portions of the antenna design in addition to or instead of the portions identified in step 512 or the portions thickened in sub-step 518. The holes are configured to reduce the mass of the antenna below a maximum mass threshold. For example, the mass of the antenna design may be reduced to less than 120% of the mass of the original conventional antenna design, below acceptable material costs, and / or below an acceptable landing weight. The size, number, and / or spacing of the holes are selected to provide a sufficient mass reduction.

[0087] Modified antenna designs may include arrays of holes arranged in a continuous line, in spaced-apart rows, and / or in any effective grouping. The holes may be uniform and consistent, or may vary in size and / or shape. In other words, the holes may be described as openings, holes, and / or voids, and / or the material between the holes may be described as forming a mesh.

[0088] The additional holes have a size and / or shape that allows for additive manufacturing without a secondary support. For example, the holes are small enough to be printable without buckling. In other examples, the holes have a shape and orientation that allows them to be freestanding, such as a diamond shape with each side angled at 45 degrees or less relative to the build axis. The maximum and minimum dimensions of each hole may be limited by the manufacturability of the selected additive manufacturing method and / or apparatus.

[0089] The maximum dimension of each hole may be limited to the shortest expected wavelength in the antenna's operating range. That is, the antenna design is configured to transmit and / or receive signals in a given wavelength range, referred to as the operating frequency band. By limiting the size of the holes, the holes have a negligible effect on the electromagnetic properties of the antenna device. That is, the holes can be said to be electromagnetically opaque to the desired operating frequency range of the antenna device.

[0090] The size, spacing, and / or placement of the holes may be determined according to the structural requirements of the antenna design. That is, the holes are added to adequately maintain the structural strength, rigidity, and / or other structural properties of the antenna design. For example, the holes may be added to space the holes away from joints, corners, and / or critical structural features. In other embodiments, the holes are added so that they do not occupy more than a selected percentage of the surface area of ​​the designed antenna.

[0091] In addition to sub-steps 516 and 518, step 514 includes making any appropriate design modifications to achieve efficient and robust additive manufacturing of the antenna. For example, sections designed as separate components may be integrated into a single monolithic configuration. In other examples, corners, joints, and sharp edges may be beveled and / or rounded. In other examples, lattice structures and / or supporting buttresses may be introduced. In other examples, solid members may be replaced with a honeycomb structure surrounded by a shell. Generally, the design is modified to eliminate secondary supports, prevent warping and cracking, and adhere to design specifications.

[0092] Step 520 of method 500 includes additively manufacturing the antenna according to the modified design. Step 520 is performed by the additive manufacturing method and / or additive manufacturing equipment selected in steps 512 and 514, and can indicate areas identified as being too thin to print and areas where the design has been modified. Step 520 can be performed iteratively as necessary, thereby quickly and cost-effectively producing antennas that are electromagnetically and functionally equivalent to conventionally fabricated antennas according to traditional antenna designs, but with little or no mass and / or weight penalty. Exemplary Combinations and Additional Examples

[0093] In this section, additional aspects and features of the antenna device and the method for manufacturing the antenna device are described as appendices, which are not intended to be limiting. Note that some or all of the appendices are alphanumeric for clarity and efficiency. Each appendix may be combined in any appropriate manner with one or more other appendices and / or with the disclosure elsewhere in this application. Some of the appendices described below explicitly refer to and further qualify other appendices, but this is merely to provide some examples of suitable combinations and is not intended to be limiting. <Additional Notes>

[0094] A0. An additively manufactured tubular body configured to transmit electromagnetic waves in a selected operating frequency range and having a mass below a maximum mass threshold; The antenna device, wherein the cylindrical body includes a wall having a plurality of holes formed in the wall that reduce the actual mass of the cylindrical body below the maximum mass threshold without substantially adversely affecting the electromagnetic wave transmission characteristics of the cylindrical body in the selected operating frequency range.

[0095] A1. The antenna device of A0, wherein the selected operating frequency range includes radio waves.

[0096] A2. The antenna apparatus of A0 or A1, wherein the wall has a thickness of at least 5 mils.

[0097] A3. The antenna device according to any one of A0 to A2, wherein the wall has a thickness of at least 30 mils.

[0098] A4. The antenna device described in any one of A0 to A3, wherein each of the plurality of holes is sufficiently small so that the wall can be printed without the need for an auxiliary support.

[0099] A5. The antenna device according to any one of A0 to A4, wherein the maximum dimension of each hole is less than 100 mils.

[0100] A6. The antenna device according to any one of A0 to A5, wherein each hole has a center and the distance between the centers of adjacent holes is less than 200 mils.

[0101] A7. The antenna device according to any one of A0 to A6, wherein the cylindrical body is made of laser-sintered aluminum.

[0102] A8. The antenna device according to any one of A0 to A7, wherein each hole is circular.

[0103] A9. The antenna device according to any one of A0 to A8, wherein the selected operating frequency range is between 8 gigahertz and 40 gigahertz.

[0104] A10. An antenna device according to any one of A0 to A9, wherein the maximum mass threshold is 0.05 ounces per square inch of the wall.

[0105] A11. The antenna device according to any one of A0 to A10, wherein the cylindrical body has a rectangular cross section.

[0106] A12. An antenna device described in any of A0 to A11, wherein the cylindrical body has four sides, each side including a wall, and the wall has a plurality of holes that reduce the actual mass of the cylindrical body to below the maximum mass threshold without substantially adversely affecting the electromagnetic wave transmission characteristics of the cylindrical body in the selected operating frequency range.

[0107] A13. The antenna device according to any one of A0 to A12, wherein the plurality of holes form an array in which the holes are arranged.

[0108] B0. An antenna device, an additively manufactured tubular body having a plurality of holes; The antenna device has a given operating frequency range, and the holes are sized and arranged such that the holes are substantially opaque to the operating frequency range.

[0109] B1. The antenna device of B0, wherein each hole is a circular hole that penetrates a wall of the tubular body.

[0110] B2. The antenna apparatus of B1, wherein each hole has a diameter of less than or equal to 200 mils and greater than or equal to 30 mils.

[0111] B3. The antenna device according to any one of B0 to B2, wherein the plurality of holes form a regularly arranged array.

[0112] B4. The antenna device according to any one of B0 to B3, further including a power supply interface section, wherein the cylindrical main body section and the power supply interface section are integrally configured.

[0113] B5. The antenna device according to any one of B0 to B4, wherein the cylindrical main body is made of laser-sintered aluminum.

[0114] B6. The antenna device according to any one of B0 to B5, wherein the cylindrical main body is configured to transmit radio frequency signals.

[0115] B7. The antenna device according to any one of B0 to B6, wherein the operating frequency range is included in the X band, the Ku band, or the Ka band.

[0116] B8. The antenna device according to any one of B0 to B7, wherein the antenna device is a horn antenna.

[0117] B9. An antenna device described in any of B0 to B8, wherein the multiple holes are provided in the wall of the cylindrical main body, and the ratio of the area of ​​the area between the multiple holes in the wall to the area of ​​the multiple holes is between 1 and 2.

[0118] C0. A method for manufacturing an antenna, comprising: receiving an antenna design for traditional manufacturing; Identifying a portion of the antenna design that is below a minimum size that can be printed on a selected additive manufacturing device; modifying the antenna design, including increasing the size of the identified portion and adding holes; additively manufacturing the antenna according to the modified design.

[0119] C1. The method of C0, wherein the antenna design has a desired operating frequency range and the added holes are sized and positioned such that the holes are substantially opaque to the operating frequency range.

[0120] C2. The method of C0 or C1, wherein the traditionally manufactured antenna has a first mass and the additively manufactured antenna has a second mass, the second mass being no more than 20% greater than the first mass.

[0121] C3. The method according to any one of C0 to C2, wherein increasing the size of the identified portion is making the thickness of the identified portion equal to or greater than a selected threshold thickness.

[0122] C4. A method according to any one of C0 to C3, wherein adding a plurality of holes includes adding a plurality of holes to a portion of the antenna design other than the identified portion. <Effects, features, advantages>

[0123] Various embodiments of the antenna device described herein offer several advantages over known solutions for designing and fabricating antennas using additive manufacturing. For example, the exemplary embodiments described herein allow for antennas to be fabricated using additive manufacturing to replace antennas fabricated using traditional manufacturing methods.

[0124] Furthermore, exemplary embodiments described herein allow for the fabrication of antennas below mass limitations using additive manufacturing equipment that is limited by the minimum printable thickness.

[0125] Furthermore, according to the exemplary embodiments described herein, holes can be formed by additive manufacturing without the use of sacrificial materials or auxiliary supports.

[0126] Furthermore, the exemplary embodiments described herein enable highly reproducible additive manufacturing to create geometrically accurate antennas.

[0127] No known systems or devices are capable of performing these functions within stringent mass constraints. Accordingly, the exemplary embodiments described herein are particularly useful for satellite communication antennas and other space-based antennas. It should be noted that not all exemplary embodiments described herein may be equally effective or to the same degree. <Conclusion>

[0128] The above disclosure may encompass multiple individual embodiments with unique utility. While each embodiment is disclosed in a preferred form, many variations are possible, and the specific embodiments disclosed and illustrated herein should not be construed as limiting. Where section headings are used in this disclosure, such headings are for organizational purposes only. The subject matter of this disclosure includes all novel and non-obvious combinations and subcombinations of the various elements, features, functions, and / or properties disclosed herein. The following claims specifically set forth certain combinations and subcombinations that are deemed novel and non-obvious. Other combinations and subcombinations of features, functions, elements, and / or properties may be set forth in the claims of any application claiming priority from this or a related application. Such claims, whether broader, narrower, equivalent, or different in scope than the original claims, are deemed to be encompassed within the subject matter of this disclosure.

Claims

1. an additively manufactured tubular body configured to transmit electromagnetic waves in a selected operating frequency range and having a mass below a maximum mass threshold; the cylinder includes a wall having a plurality of holes in the wall that reduce an effective mass of the cylinder below the maximum mass threshold without substantially adversely affecting electromagnetic wave transmission characteristics of the cylinder in the selected operating frequency range; Each hole is circular.

2. 10. The antenna apparatus of claim 1, wherein the wall has a thickness of at least 30 mils.

3. 3. The antenna device of claim 1, wherein each of the plurality of holes is small enough to allow printing of the wall without the need for auxiliary supports.

4. A system including an additively manufactured tubular body configured to transmit electromagnetic waves in a selected operating frequency range and having a mass below a maximum mass threshold; the cylinder includes a wall having a plurality of holes in the wall that reduce an effective mass of the cylinder below the maximum mass threshold without substantially adversely affecting electromagnetic wave transmission characteristics of the cylinder in the selected operating frequency range; An antenna apparatus wherein the maximum dimension of each hole is less than 100 mils.

5. A method for transmitting electromagnetic waves in a selected operating frequency range, the method comprising: the cylinder includes a wall having a plurality of holes in the wall that reduce an effective mass of the cylinder below the maximum mass threshold without substantially adversely affecting electromagnetic wave transmission characteristics of the cylinder in the selected operating frequency range; The antenna apparatus, wherein each hole has a center and the centers of adjacent holes are spaced apart by less than 200 mils.

6. 6. The antenna device according to claim 1, wherein the cylindrical body is made of laser-sintered aluminum.

7. 6. An antenna arrangement according to claim 4 or 5, wherein each hole is circular.

8. An antenna arrangement according to any preceding claim, wherein the selected operating frequency range is between 8 GHz and 40 GHz.

9. The antenna device of any preceding claim, wherein the maximum mass threshold is 0.05 ounces per square inch of the wall.

10. 10. The antenna device according to claim 1, wherein the cylindrical body has a rectangular cross section.

11. A method for manufacturing an antenna, comprising: receiving an antenna design for traditional manufacturing; Identifying a portion of the antenna design that is below a minimum size that can be printed on a selected additive manufacturing device; modifying the antenna design, including increasing the size of the identified portion and adding holes; additively manufacturing the antenna in accordance with the modified design; The method, wherein adding holes includes adding holes to portions of the antenna design other than the identified portions.

12. 12. The method of claim 11 , wherein the antenna design has a desired operating frequency range, and the added holes are sized and positioned such that the holes are substantially opaque to the desired operating frequency range.

13. 13. The method of claim 11 or 12, wherein the traditionally manufactured antenna has a first mass and the additively manufactured antenna has a second mass, the second mass being no more than 20% greater than the first mass.

14. 16. The method according to any one of claims 11 to 13, wherein increasing the size of the identified portion comprises increasing the thickness of the identified portion to equal or exceed a selected threshold thickness.

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