# Dual-Circularly Polarized 60 GHz Beam-Steerable Antenna Array with 8 \(\times\) 8 Butler Matrix
## 2 Design of Antenna Array System
\[\left[S\right]_{Hybrid}=-\frac{1}{\sqrt{2}}\left[ \begin{array}{cccc}0&j&1&0 \\ j&0&0&1\\ 1&0&0&j\\ 0&1&j&0\end{array} \right] \tag{1}\]  
The crossover is formed by cascading two quadrature hybrid couplers. Figure 5 shows the simulated S-parameters of the crossover when port 1 is excited. It can be seen that the return loss (S\({}_{11}\)) and isolation (S\({}_{21}\) & S\({}_{41}\)) are lower than \(-\)15 dB over the frequency range of 57.41 GHz-64.12 GHz. The insertion loss (S\({}_{31}\)) is calculated as \(-\)0.25 dB at 60 GHz. These results coincide with the theoretical scattering matrix, as follows. \[\left[S\right]_{Crossover}=\left[ \begin{array}{cccc}0&0&j&0\\ 0&0&0&j\\ j&0&0&0\\ 0&j&0&0\end{array} \right] \tag{2}\]  
Note that the branch-line coupler has a high degree of symmetry so that any port can be used as an input port. The simulated averaged insertion losses for the excitation from port 1 to port 4 of the \(8\times 8\) Butler matrix are shown in Figure 6a, and the simulated output phases of the Butler matrix for excitation of port 4 is shown in Figure 6b. The calculated phases of S\({}_{94}\), S\({}_{10,4}\), S\({}_{11,4}\), S\({}_{12,4}\), S\({}_{13,4}\), S\({}_{14,4}\), S\({}_{15,4}\), and S\({}_{16,4}\) are \(-\)117\({}^{\circ}\), 127\({}^{\circ}\), \(-\)71\({}^{\circ}\), \(-\)163\({}^{\circ}\), \(-\)40\({}^{\circ}\), \(-\)138\({}^{\circ}\), \(-\)11\({}^{\circ}\), and \(-\)101\({}^{\circ}\) at 60 GHz, respectively. When the phase of S\({}_{94}\) is regarded as a reference (0\({}^{\circ}\)), the phases of ports can be written as 0\({}^{\circ}\), \(-\)116\({}^{\circ}\), 46\({}^{\circ}\), \(-\)46\({}^{\circ}\), 77\({}^{\circ}\), \(-\)21\({}^{\circ}\), 106\({}^{\circ}\), and 16\({}^{\circ}\), respectively. On the other hand, as shown in Table 1, the desired output phases for excitation of port 4 are 0\({}^{\circ}\), \(-\)90\({}^{\circ}\), 45\({}^{\circ}\), \(-\)45\({}^{\circ}\), 90\({}^{\circ}\), 0\({}^{\circ}\), 135\({}^{\circ}\), and 45\({}^{\circ}\), respectively. The deviations between the calculated phases and desired ones for each output port are 0\({}^{\circ}\), 26\({}^{\circ}\), \(-\)1\({}^{\circ}\), 1\({}^{\circ}\), 13\({}^{\circ}\), 21\({}^{\circ}\), 29\({}^{\circ}\), and 29\({}^{\circ}\), respectively. In general, the deviation below \(\pm\)30\({}^{\circ}\) in the Butler matrix does not significantly affect the performance of the array antenna [12]. Figure 4: Simulated S-parameters of the quadrature hybrid coupler: (**a**) amplitude and (**b**) output phase. The configuration of the transition part to connect to the stripline-type Butler matrix with the microstrip patch antenna array is illustrated in Figure 7. The 0.17 mm widths of the stripline and microstrip line are chosen to be the same. The stripline and microstrip line share the bottom ground. The top ground of the stripline is cut out into a triangular shape at the interface between the stripline and microstrip line to obtain a good impedance matching. The series via array is also added for proper impedance matching. The radius of each via is 0.1 mm and the via array spacing is 0.5 mm. Figure 8a shows the comparison between the simulated transmission coefficients (S\({}_{21}\)s) of the designed transition part with and without the via array. For the case with a series via array, unlike the case without a series via array, it can be seen that there are no resonances and large ripples on the S\({}_{21}\) curves over the frequency range of 50 GHz-70 GHz. The calculated characteristic impedances of the stripline and microstrip line are 50 \(\Omega\) and 73 \(\Omega\), respectively, as shown in Figure 8b. Figure 9 shows the geometry of the designed 1 x 4 patch antenna array. The proposed antenna array has four inset-fed stacked patch antenna elements with wideband characteristics. The antenna elements are designed on two stacked substrates with three layers. Each substrate has a thickness of 0.127 mm.