# Computational Analysis of a 200 GHz Phased Array Using Lens-Coupled Annular-Slot Antennas
## 3 Simulation Results
### A 1 \(\times\) 5 ASA Array Analysis  
In order to achieve a wider beam scanning range, larger arrays with more antenna elements can be used. As a prototype demonstration, a 1 \(\times\) 5 array is implemented (see Figure 5 inset) for full-wave simulation using ANSYS HFSS. The array size along the scanning plane (H-plane) is increased to \(\sim\)1200 \(\upmu\)m by adding two more antenna elements while keeping the same element spacing of 0.55A. Figure 5 plots the scanning beam angle \(\theta\) as a function of the feeding phase difference \(\beta\). Similar to that observed in Figure 3, \(\theta\) increases as \(\beta\) increases, and smaller \(L\) leads to larger beam steering angles for the same \(\beta\). The \(\theta\) achieved when \(\beta\) = 180\({}^{\circ}\) is increased from 31\({}^{\circ}\) to 41\({}^{\circ}\), 48\({}^{\circ}\), and 56\({}^{\circ}\) while the \(L\)/\(R\) decreases from 0.2 to 0.1, 0.05 and 0, respectively. In addition, the theoretical calculation for a phased array without lens using the array factor technique is plotted (same as the one in Figure 3). Finally, as compared to the lens-coupled 1 \(\times\) 3 arrays, the lens-coupled 1 \(\times\) 5 arrays show that improved beam scanning ranges, e.g., improvement of 15\({}^{\circ}\), 5\({}^{\circ}\), and 11\({}^{\circ}\) for \(L\)/\(R\) = 0, \(L\)/\(R\) = 0.1, and \(L\)/\(R\) = 0.2, respectively, have been achieved for \(\beta\) = 180\({}^{\circ}\). This indicates that using a larger array size allows a larger beam scanning range for applications such as wireless communications, wireless power transmission systems, and radar systems [20]. Figure 4: The radiation pattern of the H-plane for a 1 \(\times\) 3 array with (**a**) \(L\)/\(R\) = 0.1 and (**b**) \(L\)/\(R\) = 0.2 at different phase differences \(\beta\). Figure 5b plots the antenna gain as a function of \(\theta\) for different 1 \(\times\) 5 array configurations. Similar to the 1 \(\times\) 3 arrays, the antenna gain of a 1 \(\times\) 5 array increases when \(L\) increases. For example, the boresight gain raises from 13.92 dB to 15.27 dB, 16.63 dB, and 17.51 dB, while the \(L\)/\(R\) changes from 0, to 0.05, 0.1, and 0.2, respectively. Additionally, similar to the 1 \(\times\) 3 configurations with \(L\)/\(R\) = 0 and \(L\)/\(R\) = 0.3, it is also observed that the peak gain achieved for a 1 \(\times\) 5 array is not located at the boresight for all cases due to the more antenna elements at the off-axis positions. For a 1 \(\times\) 5 array without lens, a maximum gain of 8.49 dB at boresight can be seen, and the gain gradually decreases to -7.2 dB as the beam steers away from the boresight, i.e., from 0\({}^{\circ}\) to \(\pm\)55\({}^{\circ}\) (see the black curve in Figure 5b). In addition, a good gain improvement can also be achieved by using lens-coupled configurations. For the cases of \(L\)/\(R\) = 0 and \(L\)/\(R\) = 0.05, a gain improvement of 6.51 dB and 7.51 dB (compared to the 1 \(\times\) 5 array without the lens), and a beam scanning range of \(\pm\)56\({}^{\circ}\) and \(\pm\)48\({}^{\circ}\) (for \(\beta\) = \(\pm\)180\({}^{\circ}\)), respectively, can be realized. Although the gain improvement and the peak gain of the 1 \(\times\) 5 array are relatively smaller than those of the 1 \(\times\) 3 array with \(L\)/\(R\) = 0.1 or \(L\)/\(R\) = 0.2, the beam scanning range has been enormously increased by -40\({}^{\circ}\) when \(\beta\) = 180\({}^{\circ}\), approaching the theoretical maximum of the ideal phased array (i.e., \(\theta\) = \(\pm\)63\({}^{\circ}\) when \(\beta\) = \(\pm\)180\({}^{\circ}\)). This shows the great potential of the 1 \(\times\) 5 arrays for future wireless communications. The SLL was also characterized for the 1 \(\times\) 5 arrays. Figure 5c shows the SLL as a function of \(\beta\) for different \(L\)/\(R\) ratios. For \(L\)/\(R\) = 0, \(L\)/\(R\) = 0.05 and \(L\)/\(R\) = 0.1, the SLL varies from \(-\)9 dB to \(-\)6 dB as \(\beta\) increases from 0\({}^{\circ}\) to 180\({}^{\circ}\).