# Low-Profile High-Efficiency Transmitarray Antenna for Beamforming Applications
## 3 Beamforming Partial H-Plane Waveguide Slot Array Antenna  
To design the FSS for the proposed beamforming slot array antenna, a square patch array is presented in this paper. The unit cell is based on a metallo-dielectric FSS [21] and formed by three dielectric layers with equally spaced capacitive square-printed patches, as shown in Figure 4. The patch array FSS has the characteristic of a low-pass filter and can have a transmission phase variation of \(2\pi\), which can be controlled by the dimension of a patch in the passband. If the TA has multi-array sources, both spillover and taper efficiencies are inversely proportional to \(F/D\) ratio. When distance (\(F\)) between the FSS and the slot array antenna becomes narrow, the aperture efficiency is improved. However, the fabricated FSS has to be integrated with the 2D partial H-plane waveguide array antenna, and a minimum space for the supporter is required. As a result, the distance (\(F\)) is chosen as 2.5 mm (0.1\(\lambda_{0}\) at 12 GHz). Figure 5 shows the simulation setup to obtain the transmittance response in the commercial ANSYS Electronics desktop software. The operation frequency of the FSS is 12 GHz, and the utilized substrate for the FSS is TLY-5 (\(\epsilon_{r}\) = 2.2 and tan \(\delta\) = 0.0009). The thickness of one substrate (\(hm\)) and the dimension (\(wm\)) of the unit cell are 0.8 mm and 14.43 mm, respectively. The transmittance can be obtained by 1-\(\Gamma^{2}\) (\(\Gamma\) = reflection coefficient at port), and the transmission phase can be calculated by the difference in the transverse electric field through the FSS. The unit cell is symmetrically located above the slot, and the dimension of the unit cell is designed to be equal to the slot periodicity to obtain the same transmission characteristics for the slot source. Table 2 shows the transmittance response of the optimized FSS against patch dimension. When the dimension of a patch is larger than 7 mm, the transmittance is less than 0.9 and poorer than those of others. Thus, as \(pw_{2}\) is larger than 7 mm, we simulated and computed transmittances and transmission phases by changing \(pw_{1}\) with fixed \(pw_{2}\), where \(pw_{1}\) is the dimension of the first and fourth patches, and \(pw_{2}\) is the dimension of the second and third patches. As a result, the unit cell has a good transmittance (>0.9) and a full transmission phase variation of about 530\({}^{\circ}\) by changing the dimensions of the patches, as shown in Table 2.  
Figure 4: Unit cell of the designed frequency selective surface (FSS). Figure 5: Simulation setup for the transmittance response of the unit cell of the FSS. Figure 6 shows the structure of the proposed beamforming partial H-plane waveguide slot array antenna. The distance between the FSS and the 2D partial H-plane waveguide array antenna is 0.1\(\lambda_{0}\). The overall dimension of the proposed beamforming array antenna is 120.44 mm (width) \(\times\) 261.45 mm (length) \(\times\) 9.43 mm (height). To achieve the 1D beamforming in the \(x\)-\(z\) plane, the array factor (AF) of a uniform amplitude and spacing can be considered because the magnitudes of the incident field at the unit cell of the FSS are nearly identical. When the array distance is \(d_{x}\) in the \(x\)-axis, the AF of the array is expressed as  
\[\text{AF}=\sum_{n=1}^{N}exp\{j(n-1)(kd_{x}cos\theta+\beta_{x})\} \tag{4}\]  
where \(N\) and \(\beta_{x}\) are the number of arrays and the phase difference between the adjacent units in the \(x\)-direction, respectively [24]. The phase difference for radiating toward a specific angle can be calculated from Equation (4) and controlled by the designed FSS. The dimensions of the cells of the FSS for eight rows against the beamforming angle of 0\({}^{\circ}\), +20\({}^{\circ}\), and +40\({}^{\circ}\) are listed in Table 3. Similarly, the dimensions of the cells of the FSS for \(-20^{\circ}\) and \(-40^{\circ}\) are symmetrical to the \(y\)-axis.