3D printed variable aperture horn with modular ridges

3D printing technology has significant potential to modernize the student laboratory experience in the area of electromagnetic wave propagation and scattering. In this contribution, a fast and low-cost method to 3D print and metallize a variable aperture horn and waveguide launcher are presented. The launcher converts a SubMiniature version A (SMA) coaxial connector to WR 187 waveguide (standard size of waveguide for 3.95 GHz to 5.85 GHz) and is printed from plastic while being metallized with aluminum tape. The launcher provided similar performance to an off the shelf launcher at one 40th the cost. As a teachable extension to this launcher a variable aperture horn is 3D printed and metallized with aluminum tape. The aperture area of the horn is changed by rotating the E⃗ walls of the horn away from each other by use of pivot in the transition between the launcher and the horn. This horn showed the expected decrease in beamwidth and increase in peak gain as the aperture area was increased while maintaining a usable impedance match. Modular center ridges were also printed to demonstrate the utility of center ridges in a horn antenna without H⃗ walls. Overall, a modular, inexpensive, and easy to construct waveguide system is presented that is useful for teaching electromagnetics specifically the relationship between aperture area and antenna gain, as well as providing a platform for waveguide experiments.


Introduction
While 3D printing is well-known as a powerful technique to build objects with complex geometries that are difficult, costly and sometimes not even possible to manufacture with conventional machining methods, it is comparatively recently that 3D printing has started to be used for high-frequency electromagnetic (EM) structures such as waveguides and antennas−an area where which precision machining of metal stock using computer numerically controlled (CNC) drills and lathes is widespread. Thus, 3D printing also has significant potential to help modernize and transform the laboratory experience in undergraduate courses on classical electrodynamics because it is now possible to fabricate many parts at low cost and, more importantly, it is now possible to easily make reconfigurable components to demonstrate advanced concepts in EM education. Waveguide components and antennas are convenient for demonstrating such concepts.
Recently, multiple examples of inexpensive fused deposition modeling (FDM) 3D printed from plastic and metalized using metallic tapes [1,2], conductive paints [3,4], plastics with conductive additives [5], or by metallic printing [6] have been seen that drastically reduce the cost of the waveguide feed structures and antennas. However, these structures still require a waveguide launcher to be useable with the types of inexpensive vector network analyzers (VNAs) with coaxial connections. Methods for designing cost-reduced waveguide launchers have been proposed such as coaxial probe feeds to excite a wave on dual ridged horns in 3D printed structures [7][8][9] or machined structures [10]. This probe feed can be adapted to end-launch waves into center of circular waveguide [11] for TM01 mode propagation or rectangular structures can add dielectric materials to improve the match [12]. Septum structures can also be made inside the waveguide to provide a coaxial end launch [13] Other feed topologies use a microstrip probe to feed into a tapered or stepped waveguide section as the feed [14,15]. Planar circuit board structures can also be used as low-profile end-launch waveguide launchers by coaxially probe feeding [16] or edge feeding a patch to excite the propagating wave inside the waveguide [17]. Besides 3D printing and machining, coaxial waveguide launchers and waveguide structures have been made by soldering sheets of copper clad glass-reinforced epoxy laminate called FR4 to make the waveguide structure and probe launchers [18].
Center ridges are a useful technique in waveguide antennas for improving the radiation characteristics of the antenna by focusing the radiated power to the center of the horn. Dual and quad ridge horns are common based on the number of feeds, where normally the ridges are located on the E  walls of the horn in the linearly polarized cases. Often these ridges are incorporated into the feed of the horn to simplify the feed process so only the pin from the coaxial connection is needed to excite the horn [7,8,10,19,20]. Ridged horn antennas have been previously 3D printed and metallized to simplify the manufacturing process [7,8,19] or by soldering sheets of copper clad FR4 [18] to improve the peak gain or reduce side lobe levels (SLLs). These types of manufacturing methods allow for a greater variety of ridge geometry or the ability to include dielectric filling to better match to the radiating environment [7]. Horns have also been made with modular ridges [20] to experimentally verify the performance of the horn with different ridge topologies. From an educational perspective, modular ridges on a horn antenna would be useful for showing the purposed of ridges in a horn antenna.
The relationship between aperture area and directivity is well understood but can be difficult to demonstrate since it requires changing the size of the antenna's aperture. Designing a horn antenna and choosing the pitch of the horn walls can be done in theory or simulation to design a horn for a desired input match and peak gain [21] but this does not lend itself to hands-on adjustable horns. Other designs have made variable horns to vary the beamwidth to be able to change the coverage area by having a design with metal shutters around the aperture that could be moved to change the effective aperture area [22] to adjust the beamwidth of the horn in the H  plane of the antenna. These flaps were used as shutters to shorten or lengthen the aperture in the H  direction. Another horn antenna used two metal sheets inside a machined housing that could be variably pitched to provide a small amount of gain tuning by changing the aperture size for 35 GHz to 40 GHz 5G communications [23]. Each of these provide a mechanically adjustable aperture area but are either complex to manufacture, or hard to visualize for teaching applications.
In this work a 3D printable WR 187 waveguide (standard size of waveguide for 3.95 GHz to 5.85 GHz) launcher and variable aperture horn is presented that can be used to produce an inexpensive setup for teaching of electromagnetics or as a foundation for further experiments. Here a WR 187 launcher is FDM 3D printed from PLA and is metallized using aluminum tape to reduce cost of fabrication. The launcher is fed with a commercial-off-the-shelf (COTS) SMA probe and uses a standard quarter wavelength section with a back short to easily visualize the transition. This launcher is evaluated and compared to a COTS WR 187 and shows comparable performance at less than 40th of the cost, which is extremely useful for teaching as a large number of launchers can be produced at minimal cost. The launcher is used to feed a horn antenna that has E  walls that can be pivoted to increase the aperture area of the antenna and demonstrate the relationship between aperture area, half power beamwidth, and peak gain. Further demonstrations of a waveguide horn antenna are observed by adding E  wall center ridges that help improve the consistency of the pattern shape of the H  plane radiation patterns more consistent versus aperture area, while increasing the peak gain. Since this horn does not utilize H  walls it makes it obvious for students to visualize the change in aperture area and the edition of the E  wall ridges and how they help to center the fields. Overall, the horn and launcher here provide an inexpensive setup that can give students hands on experience with waveguide fed antennas and the relation between aperture area and peak gain.

Horn and launcher design
All components of this work were designed to be FDM 3D printed from polylactic acid (PLA) with no support material and to be modular to allow for further experiments or demonstrations. The method of metallizing plastic parts to create waveguide components using adhesive back metallic tapes has been established in prior works [1,2] to produce cost-effective waveguide components that preform similarly to simulation.
Launcher design-The launcher was designed to allow for ease of manufacture and to be significantly less expensive than off the shelf alternatives. This launcher used a probe feed and a back reflector like many off the shelf launchers. The design of the launcher was based around an Amphenol SV Microwave SF2950-6200 SMA connector with a long center pin and long Teflon dielectric. This combination allowed the SMA connector to be flange mounted to the top of the plastic housing, pass through the housing, and provide a place to mount the center probe. The Computer Aided Design CAD model of the launcher is shown in figure 1. The distance between the center pin and the back reflector was longer than seen in comparable commercial launchers to try and improve the performance at the lower end of the band to maximize the usable performance when this launcher was measured with a VNA (vector network analyzer) that had an upper frequency of 4.8 GHz. The body of the launcher was split down the center plane so that the launcher could be metalized around the cut-out for the dielectric. This allowed the coaxial feed to be continued through the body of the launcher to the inside of the waveguide to have a complete ground connection. The detentions of the probe cylinder were tuned for the best input match across the WR 187 band, especially below 5 GHz. The mounting holes on this launcher were located at the corners rather than the standard WR 187 flange to allow for the thicker walls of the launcher body which were necessitated since the SMA connector, and all parts of the launcher were screwed together. This combination of splitting the launcher into three parts allowed the launcher to be printed without the use of any support material. For this design, all screws to assemble the launcher were chosen as a #4-40 machine screw since it was small, but still had threads that could easily be taped into the PLA that was to be used to print the launcher. Thus, the thickness of the launcher needed to be such to support the threads tapped into the plastic and fully enclose any fastener heads that needed to be counter-sunk into the part.
Horn design-The horn was designed to maintain an electrical connection between the two walls of the pyramidal horn and the feeding waveguide through a wide range of aperture sizes. This was done by designing an adapter piece that attached to the waveguide launcher and acted as the pivot for the two walls of the horn. This adapter piece has a matching contour to the rounded ends of the horn walls so that they maintained contact regardless of the tilt angles of the horn walls. The assembled horn is shown in figure 2 for the horn with and without ridges and an exploded assembly. To aid in the positioning of the two walls, a sliding mechanism was designed that attached to the sides of the horn walls to help hold them in place. These sliding mechanisms incorporated a rudimentary protractor to help set the angles of the walls. Further, by keeping the sliding mechanisms normal to the direction of propagation, this forced the two walls of the horn to be an equal angle tilted away from the waveguide.
The horn was designed with removable center ridges to demonstrate the effect of ridged horn antennas that do not have H  plane walls. The ridge is used to help concentrate the field intensity in the center of the aperture reduce help to maintain a consistent beam-shape in the H  plane regardless of opening angle. These ridges attached to the walls of the horn using screws that went through the walls of the horn and taped into the ridge. For this the, the ridge was designed to be attached with the same fasteners as the launcher which dictated the minimum width (RW in figure 2(b)). From this minimum width the ridge with was chosen in simulation along with the height of the ridge were chosen in simulation to maximize the indented field focusing effect of the ridge. Each of the ridges was a segment of a circle, with a maximum height RH less than half the narrow width b of the waveguide, so that when the walls of the horn were in plane with the walls of the launcher, the ridges would not touch in the middle. Having the modular center ridges also allowed each wall of the horn to be printed without any support material, resulting in a smooth inner surface.
Fabrication-The launcher and the horn were printed as separate components as visualized in figures 1 and 2. All components were FDM printed from PLA except for the off the shelf SMA connector and the probe cylinder which was printed using a stereolithography (SLA) printer. First the feed-probe was assembled as shown in figure 3. The feed consisted of an off the shelf SMA connector (Amphenol SV Microwave SF2950-6200) where the length of the Teflon dielectric was trimmed to match the top thickens of the launcher body DL = 10 mm as shown in figure 1. This allowed for the center pin of the SMA connector to stick out further from the dielectric and further into the probe cylinder to give a stronger mechanical connection. The end of the probe was formed by SLA printing a small cylinder that was then wrapped in adhesive backed copper tape and soldered to the center pin of the SMA connector. Copper tape (3M 1181) was used over aluminum tape for this probe so that it could be soldered to the pin to improve the electrical connection and more tightly attach the tape to the small probe cylinder. The probe cylinder was printed from a photo-curing SLA resin rather than FDM printed from PLA since it can better withstand the heat of soldering the copper tape to the center pin of the SMA connector. PLA was used for the remainder of the structure as it is easy to print, inexpensive, and can be thread tapped so that parts can be assembled without the need for embedding threaded inserts into the parts which reduces complexity. Since the PLA components were covered in conductive foil tape to form the waveguide feed and inner surface of the antenna, the electrical properties of the polymer used do not impact the design, thus allowing for the use of any polymer to print the structure of the device. Finally, the mounting holes of the SMA connector were reamed to a clearance fit for a standard #4 − 40 machine screw.
To form the launcher body, all parts were FDM printed from PLA and all holes that were to receive a screw were tapped. Each FDM printed part was designed and oriented so that it could be printed to minimize the use of support material. This was done to reduce waste and therefore cost, but to also reduce the post processing time required to sand the interface layers between any support material and the finished part. The inner surfaces of the launcher were covered with aluminum tape. Aluminum tape with non-conductive adhesive was used to reduce the cost of the assembly instead of using copper tape. Since the adhesive was non-conductive the tape was applied in such a way that there was never a current path that needed to travel through the adhesive of the tape and all matching surfaces mated aluminum side out. The same approach was taken for all the components of the horn. The aluminum foil tape used was thick-enough so that the wrapped PLA components behaved as if they were made from solid aluminum stock, from an electrical standpoint. The only portion of the horn not covered in aluminum tape where the side support arms as shown in figure 4, these were placed close to the feed of the horn so that they would not impact the radiation performance of the antenna. These were included in all simulation models with ò r = 2.7 and negligible loss-tangent [24]. The assembled horn and launcher were assembled using #4 − 40 cap-screws. All components are shown in figure 4. The final printed weight of the horn and launcher was 168 g without the ridges and 197 g with the ridges.  The joint between the waveguide feed and the walls of the horn needed to rotate to allow for adjustment of the aperture area. The electrical contact was made by having a foil coated cylinder on the launcher end of each wall that rolled against a mating surface on the waveguide feed. This made an electrical connection between the feed and horn walls as shown by looking down the horn in figure 4(c). To relieve friction and to force the feed point to be at the inner surface of the waveguide and horn a relief cut was made on the outside of the horn and waveguide, producing the gap shown in figure 4(d). Since a tight connection was maintained on the inner surface of the waveguide the horn was designed to have a minimal impedance discontinuity, as all currents would be flowing on the inner surface of the waveguide to the inner surface of the horn.

Measured results
To characterize the performance of the coaxial cable to waveguide launchers a 100 mm section of waveguide was 3D printed and metallized using aluminum tape, using the same method to 3D print waveguide discussed in [1,2]. The S-Parameters of this waveguide were measured with a COTS WR 187 launcher (PEWCA1057) and the printed launchers as seen in figure 5(a). These S-Parameters were measured using an Anritsu MS4644B VNA that was calibrated using a coaxial calibration to fully characterize the COTS and printed launcher. The measured S-Parameters for the COTS launcher and the printed launcher as well as simulated S-Parameters are presented in figure 5(b) and (c). Here the printed launcher shows comparable performance the COTS launcher across the full standard WR-187 band of 3.95 GHz to 5.85 GHz with better performance between the cut-off frequency and 3.95 GHz.
After verifying the performance of the printer launched, it was attached to the printed variable aperture horn as shown in figure 4. The input reflection to the horn was measured using the same VNA calibration setup used previously. The measured input reflection is shown in figure 6 for the horn with and without ridges for various opening angles. For both horns, the measured and simulated input reflection is better than -10 dB across the WR-187 band for opening distances greater than 40 mm. For opening distances less than this these is a poor match to free space, especially for the ridged horn case where the ridges are touching at the smallest opening distance. Next for aperture spaces between 30 mm and 110 mm the radiation characteristics were measured across the band in the anechoic chamber at Queen's University. The setup was calibrated using a TDK HRN-0118 reference horn antenna with ISO17025 calibration accreditation to report realized gain. Figure 7 shows the measured and simulated realized peak gain for the horn with and without ridges at 4.7 GHz across the range of opening angles. The peak gain, radiation patterns, and half-power beamwidth (HPBW) are all plotted at midband which is 4.7 GHz. Each measurement was carried out a single time for these measurements, as such there is some uncertainty in the actual opening of the antenna. For each measurement the aperture space was set using a set of vernier calipers. As such the uncertainty should be less than ±1 mm. Regardless of the uncertainty in the aperture space, as the aperture space increases (the two walls of the horn are tilted apart) the peak gain increases with the increase in aperture area. Further, the peak gain of the horn with the center ridge is higher across all aperture spaces than the horn without the ridge, illustrating the purpose of a center ridge on a horn linear horn without conductive H  -walls. There is good agreement between the simulated and measured peak realized gain, especially for larger aperture spaces.    Figure 8(a) and (c) show the H  and E  plane patterns for the horn without center ridges, while (b) and (d) show the patterns for the horn with the center ridge. In the H  plane the effect of the ridge can be seen with how regardless of the aperture space the shape of the pattern is the same as opposed to the variation seen with the ridge-less horn. This again helps to illustrate the utility of a ridged horn. Whereas the E  plane patterns show how as the aperture space and thereby the aperture area of the horn is increased the pattern narrows and becomes more directive.
Finally, this narrowing of the radiation patterns in figures 8(c) and (d) is shown in figure 9 where the HPBW is plotted versus aperture space at 4.7 GHz. The reduction in the E  plane HPBW shows how the directivity increases as was seen in figure 8(c) and (d) and how the peak gain increased in figure 7. Additionally, as the aperture space increased and the E  plane HPBW decreased, the H  plane HPBW stayed the same regardless of the aperture space, especially for the horn with the center ridges.
All these measurements were taken using an anechoic chamber and bench top VNA, however, these types of measurements could also be realized with an open-air measurement and a portable VNA that would be more cost effective for a demonstration or laboratory experiment while teaching electromagnetic.

Conclusion
An inexpensive and easy to fabricate waveguide launcher and variable aperture horn was presented that is useful for the teaching of electromagnetics, specifically giving students hands on experience with waveguide components and providing physical validation of the relation between aperture area, beamwidth, and peak gain. As well as the utility of adding a center ridge to horns that do not use a H  walls. This work presented a WR 187 sized waveguide launcher that was inexpensively FDM 3D printed and metallized using aluminum tape and showed comparable performance to an off the shelf launcher costing many times as much. This type of launcher can be customized giving students experience with launcher design or could be used in conjunction with other waveguide experiments. Further, the horn design is the only example seen in the literature where the aperture area of a horn is changed by physically rotating the sides of the horn to change the characteristics of the horn. The horn maintained a good impedance match throughout its range of movement while demonstrating and increase in gain and decrease in beamwidth in the E  plane as the aperture area was increased. Modular center ridges could also be added to demonstrate the utility of ridged waveguide antennas and how the ridges can be used to improve the radiation patterns in the absence of H  walls. Overall, this system gives a foundation for a series of experiments that are inexpensive and easy to build and expand upon for the teaching of propagation electromagnetic waves. Acknowledgments I Goode is a recipient of the Ontario Graduate Scholarship from the Province of Ontario, Canada, the Ian M Drum Scholarship at Queen's University, and NSERC PGS-D from the Government of Canada. This work was supported, in part, by grant #RGPIN-2022-05204 from the Natural Sciences and Engineering Research Council of Canada (NSERC).

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.