# SIW Cavity-Backed Antenna Array Based on Double Slots for mmWave Communications
## 2 Design  
The complete antenna design is shown in Figure 1. The antenna consists of two SIW layers, where the first one implements the feeding network and the second one contains the cavity-backed slot antennas. The antenna is fed by a coaxial port and then the feeding layer distributes the incoming power to the four inputs of the cavity-backed antennas. The second SIW layer, which is stacked atop the previous one, implements the backed cavities that allow the equal distribution of the power among the slots through the existence of a cavity mode. Each backed cavity contains a subarray of four double slots arranged in a 2 \(\times\) 2 configuration. Therefore, the complete antenna is composed of 16 antenna elements configured in a square planar array to produce a pencil-shaped beam. Each SIW layer is composed of a substrate coated on the upper and lower sides with copper. Inside each layer, metallized via are inserted to implement the circuit based on substrate integrated waveguide. According to the design laws, these via can simulate a metallized wall in order to confine the electromagnetic fields inside the substrate through the walls made by metallized via-holes (sides) and the two copper layers (top and bottom sides of the substrate). Equation (1) specifies the maximum value of the periodicity of the metallic via (\(p_{v}\)), which depends on the diameter of these metallic vias (\(d_{v1}\)) [19]. This diameter should be as small as possible but it must satisfy Equation (2), which depends on the wavelength inside the substrate (\(\lambda_{g}\)). \[p_{v}<2\cdot d_{v1} \tag{1}\] \[d_{v1}<\frac{\lambda_{g}}{5} \tag{2}\]Values that do not satisfy the previous conditions would not allow a good confinement of the field, producing unacceptable values for the leaky-waves outside the structure. From a manufacturing point of view, mechanical limitations in the prototyping do not allow the distance between metallized via holes to be less than 0.3 mm, since lower values cause a failure in the manufacturing of the prototype. Thus, to prevent any of the above problems, the diameter of the vias and the period between them were set to 0.4 mm and 0.7 mm, respectively. This adjusts all values below the critical ones set by Equations (1) and (2) and the prototyping constraints. The planar view of the proposed corporate feeding network is illustrated in Figure 2a. The feeding port (labeled as 1) is a coaxial line in which the inner conductor has a diameter D\({}_{1}\) and the outer conductor has a diameter D\({}_{2}\). These dimensions are imposed by a commercial connector used in the measurement setup [20]. As shown in Figure 2b, the incoming power is distributed to the T-type power dividers once it exits the coaxial line. In addition, the output fields from the feeding port are in phase, which is an advantage regarding the conventional E-plane waveguide power divider, which introduces a 180\({}^{\circ}\) phase shift between outputs. In the T-type power dividers placed after the feeding port, the power is split and directed to the rectangular coupling apertures (labeled as 2, 3, 4, and 5), as shown in Figure 2a. The output waveguides of the T-type power divider is terminated at a short-circuited waveguide to favor the coupling to the rectangular apertures, which are the input ports to the backed cavities. Figure 2a shows the dimensions of the substrate integrated waveguides that form the power dividers. Due to the proximity between the outputs of the power divider and the coupling apertures, the vias that form the waveguide turn toward the outputs favor the coupling without the need to use additional vias. This setup provides a compact corporate feeding network design. Another important design aspect of the proposed corporate feeding network is the location of the rectangular coupling apertures at the end of the waveguide. In order to ensure an in-phase feeding of the output ports of the feeding network, all the coupling apertures should on at the same side of the waveguide because the surface currents have the same direction.