# SIW Cavity-Backed Antenna Array Based on Double Slots for mmWave Communications
## 2 Design
Otherwise, out-phase fields (phase difference of 180\({}^{\circ}\)) would be obtained at the output ports. The described feeding network was designed and simulated in CST Microwave Studio. The simulations were performed for a relative electrical permittivity of the substrate of 3.35,  
Figure 1: SIW antenna array design. The feeding layer is fed by a coaxial port and the radiating layer contains the cavity-backed antennas based on double slots. a loss tangent of 0.0009, and a substrate thickness of 1.524 mm. All these characteristics correspond to the 4003C Rogers material, which is commercially available. The simulated results of the magnitude of the scattering parameters are shown in Figure 2c. An input reflection coefficient below \(-10\) dB was obtained from 34.5 to 37 GHz with equally distributed magnitude coefficients (around \(-6\) dB). These transmission coefficients (\(|\text{S}_{\text{X1}}|\)) are slightly lower than expected due to the dielectric losses, since the loss tangent in simulation was set to 0.0009. The phase imbalance between output ports is illustrated in Figure 2d. In this figure, a phase error lower than \(2^{\circ}\) is achieved. This is a very low value for the phase imbalance, being almost negligible in the radiation pattern of the antenna array. The second SIW layer of the antenna array contains the four backed cavities and the radiating slots. The backed cavity is fed at its bottom side with a rectangular coupling aperture with the same dimensions as the one described in the corporate feeding layer. Figure 3a,b shows a planar view of the designed backed cavity where the rectangular coupling aperture, depicted using a yellow dashed line, is positioned at the center of the cavity to properly generate the fundamental mode of the cavity TE\({}_{320}\) (Figure 3c). Some additional vias, whose dimensions are indicated by the parameters s\({}_{\text{v1}}\), d\({}_{\text{v2}}\), and s\({}_{\text{v2}}\), were  
Figure 2: Planar view of the corporate feeding network and simulated results: (**a**) planar view, (**b**) electric field distribution at 36 GHz, (**c**) magnitude of the simulated reflection and transmission coefficients (\(|\text{S}_{\text{11}}|\) and \(|\text{S}_{\text{X1}}|\)), and (**d**) simulated phase shift among output ports (\(\angle\) S\({}_{\text{X1}}\)). The dimensions are: D\({}_{1}\) = 0.5 mm, D\({}_{2}\) = 1.67 mm, L\({}_{\text{H1}}\) = 13.55 mm, L\({}_{\text{H2}}\) = 4.5 mm, and L\({}_{\text{H3}}\) = 7.2 mm. introduced in the cavity design to improve the excitation of the cavity mode. This cavity mode is the one required to allow the radiation of the slots because the amplitude of the electric field and the orientation of the magnetic field produce an equal amplitude and in-phase radiation of the slots. In the designs illustrated in Figure 3a,b, a difference exists between both planar views, which lies in the introduction of an additional slot in the double slot design (marked by a blue solid line). All the slots are placed near the corners of the backed cavity, as these are the locations at which the electromagnetic field favors slots radiation, as depicted in Figure 3c. It is also necessary to consider that to enhance the power coupling between the substrate integrated waveguide (marked by solid yellow lines) and the cavity, it is required to introduce a coupling metallic via hole at a distance \(\mathrm{d_{p}}\) from the rectangular coupling aperture. This coupling via is not introduced in the corporate feeding network depicted above, but it is employed in the design of a single cavity-backed antenna to reduce computational effort since the input port is located at the beginning of the substrate integrated waveguide (marked in yellow). It is important to remember that the vias that form the waveguide turns of the T-type power divider emulate the effect of this coupling via in the corporate feeding network design.