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Abstract
The article delves into the design and implementation of a 3 dB coupler using Half-Mode Groove Gap Waveguide (HM-GGW) technology, centered at 77.5 GHz. It begins by discussing the importance of beamforming techniques and hybrid couplers in modern communication systems, particularly in 5G and beyond. The authors explain the principles of Gap Waveguide (GWG) and HM-GGW, highlighting their advantages such as manufacturing tolerance and compact design. The proposed design utilizes an E-plane Riblet topology, which is compatible with various waveguide-based technologies. The article provides detailed simulation results using Ansys HFSS, demonstrating the coupler's performance under ideal conditions and with a bed of nails (BoN) implementation. It also discusses the design of transitions from standard WR-10 waveguides to HM-GGW, ensuring seamless integration. The prototype manufacturing process and measurement results are presented, showcasing the coupler's performance in real-world conditions. The authors analyze the effects of surface roughness and manufacturing tolerances on the coupler's performance, providing insights into the practical considerations of implementing such technologies. The article concludes with a comparison of the proposed coupler with other similar designs, emphasizing its advantages in terms of operating frequency and compactness. This comprehensive exploration of HM-GGW technology and its application in designing a 3 dB coupler offers valuable insights for professionals in the field of high-frequency communication systems.
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Abstract
In this paper, a 3 dB coupler implemented using half-mode groove gap waveguide (HM-GGW) technology operating on the W-band is presented. The coupler is manufactured using CNC machining, achieving a good performance in terms of amplitude and phase. The resulting coupler exhibits phase difference and power imbalance values compared to other implementations in lower frequency bands, while benefiting from the advantage of HM-GGW and CNC machining. It is verified that, despite the relatively poor performance of the CNC machining technique used, a good result has been achieved and the differences between simulation and measurements are explained due to manufacture tolerances.
1 Introduction
Beamforming techniques are gaining interest in communication systems due to its capability to dynamically steer radiation patterns [1], which is especially valuable in 5G and beyond communication systems [2], where the demand for high data rates and efficient spectrum utilization is increasing. To implement these techniques, beamforming matrix networks are recognized as a fundamental component. Among these matrices, Blass, Nolen, and Butler matrices are commonly employed to distribute signals across various paths with controlled phase shifts and amplitudes [3, 4]. Such configurations enable the creation of directional beams, which can be steered electronically without physically moving the antennas, thereby improving the flexibility of the system.
Hybrid couplers are key elements in feeding networks, playing a pivotal role in power distribution and phase adjustment. By splitting the input signal into multiple output paths with precise control over phase differences, hybrid couplers enable the formation of well-defined beams. This capability is crucial in many communication, radar, and imaging systems.
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Gap waveguide (GWG) offers an excellent alternative to design radio frequency components [5, 6]. This technology uses artificial magnetic conductor (AMC) boundary condition generated by using a periodic structure, for example, a bed of nails (BoN), between parallel plates to confine the electromagnetic field in a specific direction. One of the significant advantages of GWG technology is its manufacturing tolerance, allowing the use of screws to attach the parallel plates, thus simplifying the assembly process and ensuring robust component construction. Half-mode groove gap waveguide (HM-GGW) builds on the principles of GWG, employing the AMC boundary condition to create a mirror-like impedance on one plane. This concept can be applied to guiding schemes [7], resonators [8], and more complex circuit elements, as in [9], from which we have adopted the “half-mode” terminology used in this work. This feature enables the reduction of one structural dimension by half, either in width (H-plane) or height (E-plane). The result is a more compact design that maintains excellent performance [9‐11]. In addition, the generated BoN is not component dependent and can be reused for other implementations on the same technology and band.
The proposed design in this work is a 3 dB coupler with an E-plane Riblet topology [12], based on the HM-GGW concept and centered at 77.5 GHz. E-plane Riblet topology can be used in any waveguide-based technology as long as it maintains even-mode symmetry, making it compatible with HM-GGW technology. This coupler will be manufactured using an inexpensive CNC machining techniques, to prove the limitations on high-frequency bands such as the W-band. The utilization of HM-GGW in this design not only enhances the compactness of the component, but also maintains high performance, making it suitable for various high-frequency applications.
Fig. 1
HM-GGW 3 dB coupler with PMC boundary condition. a Schematic and dimensions. b Simulated S-parameters and phase difference between direct and coupled ports
First, a HM-GGW E-Plane Riblet coupler based on [12] was designed. An ideal perfect magnetic conductor (PMC) boundary condition was applied to enforce the half-mode operation. For all the full-wave simulation results included below, the Ansys HFSS software package was used [13]. The topology and its dimensions are shown in Fig. 1a. The feeding used for the structure are WR-10 standard waveguides, which are cut in half along its E-plane by the PMC plane.
In Fig. 1b, the simulated S-parameters of the coupler using a PMC boundary condition are shown. The transmission coefficients to the direct and coupled ports, \(|S_{21}|\) and \(|S_{31}|\), are around \(-\)3 dB \(\pm 1\) dB, while the phase difference between these same ports is around \(90\pm 5^\circ \). The isolation and matching are below \(-\)15 dB in the whole band. These results validate the correct operation of the coupler in an ideal PMC condition.
Fig. 3
HM-GGW E-plane 3 dB coupler with bed of nails. a Exploded view and dimensions. b Coupler closed with ports. c Simulated S-parameters
For the design of the coupler utilizing HM-GGW, the unit cell responsible for synthesizing the PMC boundary condition must be analyzed. A BoN, as described in [9], is employed for this purpose and is presented in Fig. 2, along with the corresponding generated dispersion diagram. A zero-gap implementation was chosen for the BoN. This guarantees lateral propagation blockage even when very small gaps between the individual pillars and the lid exist, furthermore offering robust mechanical support of the latter on the bottom piece as described in [14]. The results of the propagation constant in the \(\Gamma X\) direction indicate the half-mode TE\(_{10}\) like propagating within the structure, which is similar to a TE\(_{10}\) mode in a standard rectangular waveguide (RGW, also shown in the dispersion diagram) in the frequency range between 70 and 80 GHz, covering our band of interest.
Using the proposed unit cell and the design guidelines for HM-GGW [12], a first design of the E-Plane HM-GGW 3 dB coupler is shown in Fig. 3. In Fig. 3c, the simulated S-parameters results are shown. The magnitude of the transmission coefficients, \(|S_{21}|\) and \(|S_{31}|\), is around \(-\)3 dB ± 1 dB in the band of interest, while their phase difference \(\angle S_{21}-\angle S_{31}\) is around \(90 \pm 5^\circ \) in the assessed band. These results confirm that the use of BoN is suitable for the coupler implementation.
3 WR-10 Transition to HM-GGW
To implement the device, the transitions required to vertically feed the coupler using standard WR-10 rectangular waveguides must first be included. A transition from the standard waveguide WR-10 (\(2.54 \times 1.27\) mm) to HM-GGW was designed. This transition is based on the use of bends and tapering, as shown in Fig. 4, where all the sections are color-coded in Fig. 4a, which presents a side (cross-sectional) view. The tapering section (TS) ensures a gradual impedance transformation, while the squarely cut bend (SCB) and the corner section (CS) manage the waveguide direction changes with minimal reflection. Figure 4b provides a perspective schematic view, offering a clearer spatial understanding of the full 3D structure, including the arrangement of the pin bed and the integration of the transition with the waveguide interface.
In Fig. 5, the results of a back-to-back simulation are shown. The transition exhibits good performance in the operating band, with the reflection coefficient (\(|S_{11}|\)) remaining below \(-\)19.5 dB throughout the entire frequency band of interest, while the transmission coefficient (\(|S_{21}|\)) reaches values close to 0 dB.
Fig. 4
Schematic view of the WR-10 transition. a Cross-sectional side view. b Oblique view
The final design for the prototype including transitions is shown in Fig. 6. The device was finally manufactured using CNC electrical discharge machining (EDM) in aluminum, which assures a surface roughness \(Ra=3.2\, \mu \text {m}\) and a dimension tolerance of \(\pm 0.05\) mm according to the parameters provided by the manufacturer for their standard process. The fabricated device is shown in Fig. 7a. Regarding the measurements, they were performed using a VNA with W-band frequency extenders and termination loads as shown in Fig. 7b.
In Fig. 8, the measured S-parameters of the prototype are shown and compared with the simulation results, which account for the expected surface roughness of \(3.2\, \mu \text {m}\) and the conductive losses introduced by the aluminum. This was modeled using a “Finite Conductivity” boundary condition in Ansys with \(\sigma =3.8\cdot 10^7 \text { S/m}\) and the Huray model for the surface roughness, being the nodule radius \(3.2\, \mu \text {m}\) and the Hail-Huray surface ratio, 2.9. It has been verified that, when compared to the ideal case (lossless and without surface roughness), an additional transmission loss is observed. This loss is primarily attributed to the extension of the feeding lines and the transitions. However, good agreement is observed with the full-structure simulation results, which take into account manufacturing characteristics. Regarding the phase difference between the direct and coupled ports (\(\angle S_{21} - \angle S_{31}\)), it is around 100\(^\circ \pm 5^\circ \) in the assessed band.
To explain this phase variation, a study was carried out by varying the width of the waveguide a within the tolerance declared by the manufacturer, which is 0.05 mm. First, using a section of length \(L=19.45\) mm, which corresponds to the nominal length of the feeding arm, and a nominal width of \(a_r=1.27\) mm. Then, a variation of a within the tolerance is performed to obtain the new phase constant of the waveguide section, and the phase difference is then calculated using \(\phi = (\beta _{a_r}-\beta _a)L\) for a frequency of 77.5 GHz.
Figure 9 presents the results of the phase difference as a function of the variation in a within the tolerance range specified by the manufacturer. It can be seen how a phase difference of 10\(^\circ \) corresponds to a width difference around 0.015 mm. Therefore, it becomes clear that the slight variations in the groove depth of the long feeding lines used, attributed more to the feeding lines themselves than to the coupler, are responsible for the observed phase error.
Fig. 9
Phase variation tolerance study. a Feeding arm length. b Waveguide depth variation. c Simulated phase results with respect to the variation of the width a
Delving deeper into this idea, 200 simulations of the two output lines were performed (from the coupler output to the final waveguide transitions) to evaluate potential impact of systematic errors in the groove depth of the output waveguides due to the mentioned tolerance. A uniform distribution of groove depth errors was considered to this aim. The phase difference between the two paths modified by these errors was then estimated, yielding a standard deviation of approximately \(30^\circ \). Therefore, the \(10^\circ \) phase error observed in our case can reasonably be attributed to this type of effect.
5 Study of Surface Roughness Effect
To understand the effect of surface roughness on the propagation losses in the HM-GGW structure, a waveguide was modeled using the “Finite Conductivity” boundary condition in Ansys with the same parameters used in Sect. 4. The transmission was evaluated as a function of the waveguide length in HM-GGW, with the corresponding number of pins included to achieve the required lengths. The \(|S_{21}|\) parameter was obtained at a single frequency—the center frequency—as a function of guide length, as shown in Fig. 10. To quantify the loss per unit length, a first-order linear regression was applied, revealing an attenuation of approximately \(-\)0.21 dB per centimeter of HM-GGW.
Fig. 10
Surface roughness effect study. a HM-GGW section with roughness. bS-parameter results
The measurement results make the performance of this device comparable to other \(3 \text { dB}\) couplers in GWG technologies, having the advantage of being implemented in W-band and in the half-mode version. Table 1 presents a comparison with devices similar to the one proposed in this work. In all reported cases however, the operating frequency is lower than the one considered in this study. It is also important to clarify that the first case in the table (cite [15]) corresponds to a solution that employs a dielectric substrate, which contributes to increased losses, whereas all other cases, including the one presented in this article, are all-metal solutions.
Table 1
Comparison of 3 dB couplers in different technologies: PRGW (printed ridge gap waveguide), RGW (ridge gap waveguide), GGW (groove gap waveguide), HM-GGW (half-mode groove gap waveguide)
The symbol (\(^{*}\)) indicates only simulated results, being the estimated BW larger than 7% in this case
7 Conclusion
The 3 dB coupler in HM-GGW technology that was designed, fabricated, and measured exhibited good performance within the band of interest. Considering the manufacturing limitations, the discrepancies between the measured and simulated results were not significant, as noted in the measurement section. This technology presents opportunities for reducing testing costs, as the test bed can be reused, and it also offers the potential to create more compact components.
Declarations
Ethical Approval
Not applicable
Conflict of Interest
The authors declare no competing interests.
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