# Dual-Circularly Polarized 60 GHz Beam-Steerable Antenna Array with 8 \(\times\) 8 Butler Matrix
## 2 Design of Antenna Array System  
The block diagram of the designed switching beamforming antenna array system is illustrated in Figure 1. The designed switching beamforming network is implemented based on a Butler matrix, and the antenna array is implemented using patch elements. The Butler matrix generates output signals with different phases and feeds the antenna array, which enables the beam-steering of the antenna in different directions. Figure 2 shows the configuration of the proposed antenna array system. The antenna array system is fabricated on a three-layer Taconic TLY substrate with a relative permittivity of 2.2, a loss tangent of 0.0009, and a thickness of 0.254 mm. The proposed antenna array system mainly consists of three parts, which include an \(8\times 8\) Butler matrix, a transition, and a stacked patch antenna array. The structure of the \(8\times 8\) Butler matrix is shown in Figure 3. The \(8\times 8\) Butler matrix, which is based on the design scheme suggested in [3], consists of two \(4\times 4\) Butler matrices and additional parts to obtain the desired output phase distribution, as listed in Table 1. Each Butler matrix and the additional parts consist of stripline-based quadrature hybrid couplers, crossovers, and phase-balancing dummy crossovers. The line width of the striplines in the Butler matrix design are set to 0.17 mm to obtain a 50 \(\Omega\) characteristic impedance. Figure 1: Block diagram of the switched-beam network. Figure 3: Structure of the \(8\times 8\) Butler matrix. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{8}{c}{**Output Phase [Degree]**} \\ \hline  & **Port 9** & **Port 10** & **Port 11** & **Port 12** & **Port 13** & **Port 14** & **Port 15** & **Port 16** \\ \hline Port 1 & \(0^{\circ}\) & \(-90^{\circ}\) & \(-45^{\circ}\) & \(-135^{\circ}\) & \(-90^{\circ}\) & \(-180^{\circ}\) & \(-135^{\circ}\) & \(135^{\circ}\) \\ Port 2 & \(0^{\circ}\) & \(-90^{\circ}\) & \(135^{\circ}\) & \(45^{\circ}\) & \(-90^{\circ}\) & \(-180^{\circ}\) & \(45^{\circ}\) & \(-45^{\circ}\) \\ Port 3 & \(0^{\circ}\) & \(-90^{\circ}\) & \(-135^{\circ}\) & \(135^{\circ}\) & \(90^{\circ}\) & \(0^{\circ}\) & \(-45^{\circ}\) & \(-135^{\circ}\) \\ Port 4 & \(0^{\circ}\) & \(-90^{\circ}\) & \(45^{\circ}\) & \(-45^{\circ}\) & \(90^{\circ}\) & \(0^{\circ}\) & \(135^{\circ}\) & \(45^{\circ}\) \\ Port 5 & \(0^{\circ}\) & \(90^{\circ}\) & \(-45^{\circ}\) & \(45^{\circ}\) & \(-90^{\circ}\) & \(0^{\circ}\) & \(-135^{\circ}\) & \(-45^{\circ}\) \\ Port 6 & \(0^{\circ}\) & \(90^{\circ}\) & \(135^{\circ}\) & \(-135^{\circ}\) & \(-90^{\circ}\) & \(0^{\circ}\) & \(45^{\circ}\) & \(135^{\circ}\) \\ Port 7 & \(0^{\circ}\) & \(90^{\circ}\) & \(-135^{\circ}\) & \(-45^{\circ}\) & \(90^{\circ}\) & \(180^{\circ}\) & \(-45^{\circ}\) & \(45^{\circ}\) \\ Port 8 & \(0^{\circ}\) & \(90^{\circ}\) & \(45^{\circ}\) & \(135^{\circ}\) & \(90^{\circ}\) & \(180^{\circ}\) & \(135^{\circ}\) & \(-135^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Phases associated with the selected port of the \(8\times 8\) Butler matrix. Figure 2: Configuration of the proposed antenna array system: (a) 3D-view and (b) side-view. The quadrature hybrid coupler is realized by two pairs of 50 \(\Omega\) and 35.35 \(\Omega\) quarter-wavelength striplines. Figure 4 illustrates the simulated S-parameters of the quadrature hybrid coupler when port 1 is excited. It can be seen that the return loss (S\({}_{11}\)) and the isolation (S\({}_{41}\)) are lower than \(-\)20 dB over the frequency range of 57.32 GHz-63.71 GHz. Further, the calculated S\({}_{21}\) and S\({}_{31}\) are \(-\)3.02 dB and \(-\)3.16 dB at 60 GHz, respectively. This shows that the transmitted power is well divided between the two output ports, port 2 and port 3. The calculated output phases of S\({}_{21}\) and S\({}_{31}\) are \(-\)9.76\({}^{\circ}\) and \(-\)99.69\({}^{\circ}\) at 60 GHz, respectively, with a phase difference of 89.93\({}^{\circ}\). These results agree with the theoretical scattering matrix as follows [21].