Taylor-Weighting Ridge Gap Waveguide Feed Network for Low-Profile Fully Metallic Array Antennas

This letter showcases advancements in metallic array antennas tailored for millimeter-wave (mm-Wave) applications, supported by novel highly compact unbalanced dividers conceived in ridge gap waveguide technology. This innovative approach streamlines the feeding network by enabling high-weight-ratio dividers without adding design complexity. The study presents an 8 × 8 Ka-band antenna array employing Taylor amplitude tapering and featuring a compact corporate-fed design that effectively mitigates coupling effects between the feeding network and radiating elements. Experimental results highlight promising characteristics, boasting a matching better than <inline-formula><tex-math notation="LaTeX">$-$</tex-math></inline-formula>10 dB across the entire band of interest [(29 to 31) GHz] and secondary lobes below <inline-formula><tex-math notation="LaTeX">$-$</tex-math></inline-formula>20 dB while achieving a radiation efficiency exceeding 82%.


I. INTRODUCTION
T HE increasing demand for bandwidth in wireless commu- nications has spurred the rapid development of satellite networks.A prevailing trend in the space sector is the deployment of numerous satellite constellations that allow for increasing user bandwidth [1], [2].With the electromagnetic spectrum becoming more crowded, antennas for these links must meet various specifications, such as high efficiency, robust designs in hostile environments, compact size, or reduced sidelobes.Fully metallic antennas have a significant advantage over other types due to their high efficiency and power handling, mechanical robustness, and ease of design.Gap waveguide (GW), a technology with demonstrated potential [3], [4], [5], [6], has made significant advancements in the past decade and is presented as a good solution for these types of antennas.The nature of the technology brings numerous advantages, such as preventing field leakage, a common problem in waveguide (WG) arrays, Damián Pla-Herliczka is with the Institut d'Electronique et des Technologies du numéRique (IETR), 35708 Rennes, France (e-mail: Damian.Pla-Herliczka@insa-rennes.fr).
Digital Object Identifier 10.1109/LAWP.2024.3404998or providing flexibility for manufacturing through milling or additive processes.In this context, antenna arrays with low sidelobe level (SLL) are highly sought after because they minimize interference.While various techniques are employed for SLL control, applying a specific amplitude distribution scheme to each array element is prevalent.In this context, the Taylor distribution [7] is a well-known and widely used option.The vast majority of works rely on substrate-based designs due to the maturity of printed circuit board (PCB) technology and its ease of design and production [8].However, such arrays struggle with efficiency, power handling capability, and problems in harsh environments [9], [10].Other works based on WG technology also address the SLL issue.However, WGs tend to be bulky and heavy or require several layers, and the manufacturing process often constrains the design [11], [12], [13], [14].In the GW field, this specific amplitude distribution is usually achieved by designing appropriate corporate feeding networks [15], [16], [17], [18], [19].In this approach, a careful design of the dividers plays the most crucial and sensitive role within the feeding network as they create the amplitude taper.Different types of dividers can be distinguished based on whether a ridge gap waveguide (RGW) or groove gap waveguide (GGW) is used.While the dividers proposed in the literature serve their purpose, they come with certain drawbacks, including high complexity, tolerance sensitivity, need for multiple layers, bulkiness, or a low weight ratio among the outputs.
This letter introduces a novel unbalanced divider design utilizing RGW technology for constructing corporate feeding networks with controlled amplitude tapering.Overcoming the limitations of prior designs, this compact and versatile divider allows easy control over the output ports' amplitude with a uniform phase, while enabling a straightforward manufacturing process.To substantiate the advantages of the proposed divider, an 8 × 8 RGW array antenna, seen in Fig. 1, has been experimentally validated.The feeding network, exclusively built with RGW, directly powers each radiator without requiring a coupling cavity, facilitating miniaturization with a single-layer approach.Experimental results confirm the antenna's high efficiency, significant improvements in SLL, and robust manufacturing characteristics.

II. RGW DIVIDERS
Dividers are the most critical elements when designing corporate feeding networks for low sidelobe arrays.The topology used affects the space to be occupied, the coupling with adjacent network and radiating elements, and the overall performance of the divider.In a uniform array, every divider must distribute waves with the same amplitude and phase to each output, thus facilitating their design.In the case of unbalanced dividers, however, an asymmetry in the structure must be introduced to induce a power difference between the output ports.In GW technology, several unbalanced GGW dividers have been proposed [15], [16], [17], [20].However, few solutions can be found in RGW technology, and they tend to be bulky and contain many tuning elements, significantly complicating corporate feeding network design.A higher number of tuning elements slows the optimization task, hinders the manufacturing process, and compromises the required fabrication tolerances.This work proposes the novel unbalanced RGW divider shown in Fig. 2(a).As can be seen, the structure is straightforward.Two notches at the top of the output ridges allow for control of the impedance and propagation constant, i.e., power ratio and phase delay, by only using four variables (l 1 , l 2 , h 1 , and h 2 ).This fact significantly reduces the design complexity while providing the desired response in amplitude and phase.Obviously, in balanced dividers, both notches will be symmetrical.In the case of an unbalanced divider, the notches are designed independently with the help of an optimizer until the desired output weights are achieved.The proposed approach enables high output weight ratios with a seamless modification of a conventional splitter.One of its most appealing advantages is its natural ability to be integrated into the distribution network, avoiding tapers or pedestals.Moreover,  thanks to such design simplicity, the construction is an additional advantage, allowing for the possibility of manufacturing with 3-D printing technologies.
For example, Fig. 2(b) and (c) shows the performance of 3 dB and 6 dB unequal power dividers.The S-parameters, weight error in amplitude, and phase difference between outputs are depicted.These dividers exceed 35% bandwidth (S 11 ≤ − 10 dB).However, only a fraction of this bandwidth will be used for antenna design, covering the (29 to 31) GHz SATCOM transmission band.As it can be seen, aside from the good matching level in both cases, the power ratio between outputs is easily attained, resulting in a very low drift, less than 0.03 and 0.05 dB (for the 3 dB and 6 dB dividers, respectively).Regarding the output phase difference, since the proposed dividers allow tuning the zero phase at the center of the band, the maximum phase drift is reduced, achieving very low phase differences between output ports (0 ± 0.8 • and 0 ± 1.7 • , for each divider).Table I contains the physical dimensions of the dividers and the bed of nails (BoN) where they are hosted.These pins' dimensions create an appropriate stopband, in which no mode propagates in our band of interest, from 29 GHz to 31 GHz.
Table II is provided for the sake of comparison with available dividers in the literature.It can be seen how, in all cases, the phase difference between output ports is 3 • at best, while in the proposed designs, it is decreased to less than 0.9 • , in the case of the 2:1 divider, and 1.8 • for the 4:1 divider.In addition, the weight error is almost negligible, lower than 0.1 dB for both dividers, while compared to other cases, it can even reach 0.9 dB.These errors are negligible in arrays with a small number of radiating elements.However, in the case of large arrays, the phase and amplitude error is accumulated for each divider traversed, greatly increasing the effect on the final radiator.Therefore, the error produced in power weight and phase must be as small as possible.

III. ARRAY DESIGN
As an example of use, an 8 × 8 Ka-band array antenna with Taylor distribution has been designed.The corporate feeding network takes advantage of the above proposed dividers, allowing the design of a low-profile array that minimizes field Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.coupling between the feeding network and the radiating elements.The 1 × 1 cell can be seen in Fig. 3.The array has a periodicity between unit cells of 0.8λ 0 × 0.95λ 0 .Each output of the corporate feeding network feeds an open-ended ridge, which couples to an offset rectangular slot radiating into free space.
In a ridge WG, while the electric field maximum occurs at the center of the ridge, the longitudinal magnetic field has a component in the direction of propagation (x-axis in Fig. 3) which is maximum along the sides of the WG.Placing a slot parallel to this longitudinal direction allows the H-field to couple to the slot and produce efficient radiation.The slot dimensions, its distance to the ridge end, the offset from the center of the ridge, and the ridge height (l slot , w slot , x offset , y offset , and h ridge , respectively) are optimized to maximize both bandwidth and matching values.The slot's length tends to be around λ 0 /2, while the distance to the WG short, x offset , is around λ 0 /4 to maximize the field coupling.In this regard, it is noteworthy that if the ridge is close to the cover, the field will mostly be confined within the ridge width, making slot excitation much more difficult.Hence, optimizing the ridge height enables an effective magnetic field coupling to the slot for wideband free space radiation.Regarding the slot array lid, it is typical to introduce a waffle shape surrounding the slots to give the structure more rigidity and avoid material stress that could bend the metallic piece.It also acts as an interface between the slot and the free space, improving matching.Since the slot is not centered in the unit cell (see Fig. 3), the same offset has been applied to the cover waffle to avoid any asymmetry in the radiation pattern.
The corporate Taylor feeding network has been designed for a nominal SLL of 25 dB in both xand y-planes, resulting in three different values of weight ratios: 6 dB, 5.7 dB, and 1.46 dB.The distribution of these dividers along the feeding network can be seen in Fig. 4(a).Within the network, spanning from the input port to each radiating element, the field passes through six dividers in total.They are sequentially numbered, with first denoting the splitter immediately after the input port and the sixth positioned closest to the radiating slot.The resulting electric field at the design frequency across the array aperture can be seen in Fig. 4(b), where the amplitude tapering toward array edges is evident.
It is important to note that the ridge height along the entire corporate feeding network differs from that of the unit cell.Its height, h R2 , is 2.4 mm, greater than the ridge of the unit cell, h R1 =1.77 mm.Fig. 5 illustrates the field distribution along a   RGW for these two heights, surrounded by 1 row of pins.It is observable that the ridge with a height of 1.77 mm results in appreciable field leakage, potentially impacting the nearby elements within the feeding network.Specifically, this reduced height in the 2 × 2 unit cell enables the field to couple to the slot.Conversely, a height of 2.4 mm concentrates the field in the upper ridge, significantly reducing field leakage effects across the first stages of the network.
Considering that the ridge height for the radiating slots differs from that of the network, a stepped transition is employed to align these varying heights.The optimal placement for this transition is situated as close as possible to the radiating element, maximizing field confinement along the feeding network.Due to the compact nature of the network, there is limited space to position the transition immediately after the sixth-level divider or between the fifth and sixth-level dividers.Consequently, the transition is ultimately positioned right after the fourth-level divider.Note that this distinction is pivotal for the design's functionality and is advantageous.The cell combines unbalanced dividers with the high-to-low ridge transition, aiming to mitigate potential coupling effects from the proximity of slots, dividers, and transition components.This is demonstrated by the field behavior within the 2 × 2 unit cell, shown in Fig. 6.Despite minor leakiness, the magnetic field excites in phase the four slots, exhibiting a good reflection coefficient.

IV. EXPERIMENTAL RESULTS
The designed array has been fabricated using computer numerical control (CNC) machining.The resulting antenna covers a total surface area of 100 mm × 100 mm and only 9.7 mm height (equivalent to 10λ 0 × 10λ 0 × 0.97λ 0 ).Fig. 7 corresponds to the photographs of the manufactured prototype.Fig. 8 illustrates the measured and simulated matching at the input port.The reflection coefficient exhibits a consistent value lower than −10 dB across a bandwidth extending from 28.4 GHz to 31.7 GHz.The range for the intended application from 29   GHz to 31 GHz is shown.Fig. 9 illustrates the prototype's measured directivity, gain, and radiation efficiency across different frequencies.Notably, most of the band of interest exhibits a radiation efficiency above 85%.However, a slight reduction in this threshold is observed around a specific frequency (29.7 GHz).Nevertheless, overall, the antenna consistently maintains an efficiency level exceeding 82%.Fig. 10(a) and (b) depicts the simulated and measured co-and cross-polarized components in the XZ-and YZ-planes, corresponding to the E-and H-planes, respectively.A low SLL is found in the XZ-plane, better than −24.8 dB.The YZ-plane shows a slightly higher SLL than the XY-plane but is still below −20 dB.Both planes also have high cross-polarization discrimination, exceeding 40 dB in all planes, which is typical of rectangular slot arrays.Finally, Fig. 10(c) and (d) illustrates the copolarization pattern at the edges of the desired band (29 GHz and 31 GHz) in both main planes.It is important to note that the x-pol is intentionally omitted from the figures to enhance the clarity of the copolar patterns.The x-pol consistently performs better than −40 dB in both cases, as shown at the center frequency.Although the radiation patterns exhibit slight asymmetries, they are deemed acceptable and effectively fulfill the defined objectives.These asymmetries may stem from mutual couplings inherent in such a compact array, impacting the amplitude distribution.Nevertheless, the overall results remain highly satisfactory.
Finally, Table III shows key features of several antennas with low SLL available recently in the literature.The antenna demonstrates a significant improvement in efficiency, exceeding 82%, whereas the efficiencies of the antennas provided in Table III hover around 70%.Moreover, the proposed divider structure integrates naturally into the corporate feeding network, allowing for a very compact and simple design.Note that the proposed antenna requires only two pieces, keeping the antenna profile extremely low, below one λ 0 .Other works with a low profile characteristic exist, but in exchange for lower efficiency due to the use of dielectric substrates.Also, [11] and [22] are GW-based antennas that also seek reduced SLL with Taylor distribution.Nevertheless, in these examples, an intermediate coupling layer is needed due to the feeding network bulkiness, and hence, slots are not fed individually but in groups of four slots.As a consequence, a quasi-Taylor amplitude distribution is synthesized with a noticeable impact on the radiation patterns.

V. CONCLUSION
In conclusion, the 8 × 8 Ka-band antenna design represents a significant breakthrough in high-gain metallic arrays.The antenna achieves a commendable SLL in both main planes by implementing a corporate feeding network with Taylor amplitude tapering.The proposed approach mitigates the inner coupling effects and maintains phase and amplitude stability across the radiating elements.Moreover, implementing a stepped transition elegantly aligns ridge heights, gradually decreasing toward the network end to enhance the coupling to the radiating slots and reducing the risk of interference.Despite its apparent ease, the key and novel contribution lies in its ability to create a very lowprofile, entirely metallic antenna with highly compact splitters that can unbalance power distribution efficiently.It is verified that, to the best of the authors' best knowledge, this antenna exhibits the lowest layer requirement and superior radiation efficiency among antennas documented in the literature.
Taylor-Weighting Ridge Gap Waveguide Feed Network for Low-Profile Fully Metallic Array Antennas Damián Pla-Herliczka , Jose I. Herranz-Herruzo , Member, IEEE, Miguel Ferrando-Rocher , Senior Member, IEEE, and Alejandro Valero-Nogueira , Senior Member, IEEE Abstract-This letter showcases advancements in metallic array antennas tailored for millimeter-wave (mm-Wave) applications, supported by novel highly compact unbalanced dividers conceived in ridge gap waveguide technology.This innovative approach streamlines the feeding network by enabling high-weight-ratio dividers without adding design complexity.The study presents an 8 × 8 Ka-band antenna array employing Taylor amplitude tapering and featuring a compact corporate-fed design that effectively mitigates coupling effects between the feeding network and radiating elements.Experimental results highlight promising characteristics, boasting a matching better than −10 dB across the entire band of interest [(29 to 31) GHz] and secondary lobes below −20 dB while achieving a radiation efficiency exceeding 82%.Index Terms-Corporate feeding network, gap waveguide (GW), high efficiency, Ka-band, metallic array antennas, ridge gap waveguide (RGW), single layer, Taylor amplitude tapering, unbalanced power dividers.

Fig. 2 .
Fig. 2. (a) Schematic structure of the proposed RGW divider (ridge only).(b) S-parameters of 3 dB and 6 dB dividers.(c) Weight error and output phase difference of 3 dB and 6 dB dividers (solid and dashed lines, respectively).

Fig. 3 .
Fig. 3. H-field distribution in the unit cell at 30 GHz.

Fig. 5 .
Fig. 5. E-field distribution of a section of an RGW with different ridge heights.

Fig. 10 .
Fig. 10.(a) Measured normalized copolar and cross-polar radiation patterns at 30 GHz in XZ-plane and (b) in YZ-plane.Simulated normalized copolar also included.(c) Measured normalized copolar radiation patterns at 29 GHz and 31 GHz in XZ-plane and (d) in YZ-plane.

TABLE I (
A) DIMENSIONS OF THE BON; (B) DIMENSIONS OF THE 3 dB AND 6 dB DIVIDERS SHOWN IN FIG.2(A)

TABLE III COMPARISON
TABLE WITH LOW SLL ARRAY ANTENNAS IN THE LITERATURE Fig. 8. Simulated and measured reflection coefficient of the prototype.