# Review of Substrate Integrated Waveguide Circuits for Beam-Forming Networks Working in X-Band
## 3 Components for the Beam-Forming Network
### Four-Port Directional Coupler  
One of the basic building blocks of a BFN is the four-port directional coupler. There are many examples of SIW couplers made using quite expensive substrates, such as Rogers RT/duroid@5870/5880 [19; 20; 21; 22; 23; 24; 25; 26]. The main goal of using a Rogers RT/duroid@substrate is to reduce as much as possible the dielectric losses. However, an antenna for a DVB-S signal is quite big, i.e., comparable with the size of a commonly used dish antenna, and should be low-cost. In order to accomplish these specifications, a less expensive substrate was used for this study. In particular, the chosen substrate was the Taconic RF-35 (\(\varepsilon_{r}\) = 3.5), which exhibits a nominal loss tangent equal to 0.002. Moreover, the higher dielectric permittivity compared to Rogers RT/duroid@substrates can be exploited to reduce the size of the circuits. The coupling coefficient of a directional coupler can be different depending on the application. For example, prototypes with a coupling of 3 dB, 6 dB, and 10 dB have been realized [19]. The most common coupler structure used for SIW realization is the Riblet coupler [27]. This device is very simple since it can easily be built using a single dielectric layer. The coupler in [19] was a good example, but it operated in K band. In [28; 29], an in-depth investigation of directional couplers made with RF-35 substrate was done. The study analyzed state-of-the-art existing devices available in the literature. It adapted the results to the new substrate and improved the frequency response in order to obtain the desired coupling coefficient over a bandwidth from 10.5 GHz to 12.5 GHz. In [29], this was done by first scaling the device in order to have a TE\({}_{10}\) cut-off frequency at nearly 9 GHz, then, by changing the shape of the waveguide walls in order to improve the matching and adjust the coupling. In the aforementioned study, eight different couplers were designed using two different thicknesses of the substrate. The first group of four couplers used a 0.5 mm-thick substrate, whereas the second group used a 1.52 mm-thick substrate. For both groups the starting point was a coupler with straight lateral walls, as the one proposed in [19]. The best results were obtained for the second group. Three prototypes were built (Figure 2) corresponding to coupler #6, #7, and #8, as described in the article [29]. They exhibited the best performances in terms of bandwidth, return loss, and coupling balance. These results have been obtained by tapering the shape of the lateral walls of the couplers in different ways. As can be seen by the photos, the connection between the devices and the SMA connectors was made by using an SIW-to-microstrip transition, as the one proposed in [1; 30; 31]. The experimental scattering parameters of the couplers are shown in Figure 3. All the measurements of scattering parameters were done using a Keysight PNA E8361C with TRL calibration. The results showed a low return loss and flat coupling coefficients over the band 10.7-12.7 GHz. Another approach to the design was used in [32]. In this case, a 3 dB directional coupler was designed starting directly from the Riblet theory. In the coupling zone, i.e., the area where the aperture was between the two adjacent waveguides, the width of the coupler was usually lower than double the width of a single waveguide. The reason was that, in the coupling region, only two modes (TE\({}_{10}\)  
Figure 3: Experimental responses for the couplers shown in Figure 2[29]. (**a**) Coupler #6; (**b**) Coupler #7; and (**c**) Coupler #8. Figures adapted from [28; 29]. Figure 2: Examples of a four-port directional coupler designed in [29]. (**a**) Coupler #6; (**b**) Coupler #7, (**c**) Coupler #8; and (**d**) Photographs of the prototypes. Figures adapted from [28; 29]. and TE\({}_{20}\)) must be above cutoff in the passband of the device.