# Computational Analysis of a 200 GHz Phased Array Using Lens-Coupled Annular-Slot Antennas
## 3 Simulation Results
### A 1 \(\times\) 3 ASA Array Analysis
In addition to the antenna gain, Figure 3c shows the antenna SLL as a function of \(\beta\) for different configurations. For \(L/R=0\), \(L/R=0.1\), and \(L/R=0.2\), SLL increases gradually with \(\beta\) when \(\beta\) increases from 0\({}^{\circ}\) to 120\({}^{\circ}\). When \(\beta\) approaches 180\({}^{\circ}\), the SLL increases rapidly due to the emerging grating lobes for a large \(\theta\), as suggested by ref. [14]. For the case of \(L/R=0.3\), the SLL becomes very high for all \(\beta\) (e.g., \(-2\) dB when \(\beta=150^{\circ}\), see the H-plane pattern in Figure 3c inset), since the large extension length of 1500 um significantly bends the antenna rays and raise the antenna directivity for both the main beam and sidelobes. Therefore, a smaller extension length (e.g., \(L<1500\) um) is preferred for designing a 1 \(\times\) 3 lens-coupled ASA array to achieve a reasonably low SLL. Figure 3: (**a**) The feeding phase difference \(\beta\) versus scanning beam angle \(\theta\) (the 1 \(\times\) 3 array configuration is shown as inset), (**b**) the radiation gain versus scanning beam angle \(\theta\) and (**c**) the sidelobe level versus phase difference \(\theta\) at different extension lengthes \(L\) for a 1 \(\times\) 3 array (the H-plane radiation pattern for an \(L/R=0.3\) at \(\beta\) of 150\({}^{\circ}\) is shown as inset). As discussed above, for a lens-coupled phased-array design, a larger extension length (for the same lens radius) typically leads to a higher gain improvement, but at the same time results in a narrower beam scanning range and higher SLL. As a compromise, for the configuration studied here, the extension lengths of 500 \(\upmu\)m and 1000 \(\upmu\)m with which both high antenna gains and low SLLs can be achieved are adopted for designing and demonstrating a lens-coupled 1 \(\times\) 3 ASA array. For the two designs (\(L\)/\(R\) = 0.1 and \(L\)/\(R\) = 0.2), the simulated H-plane (i.e., the beam scanning plane) radiation patterns at different scanning angles (\(\beta\) = 0\({}^{\circ}\), \(\pm\)60\({}^{\circ}\), and \(\pm\)120\({}^{\circ}\)) are plotted in Figure 4. Figure 4 shows that for \(L\)/\(R\) = 0.1, the main beam of the 1 \(\times\) 3 array scans from \(-\)22\({}^{\circ}\) to \(-\)11\({}^{\circ}\), 0\({}^{\circ}\), +11\({}^{\circ}\), and +22\({}^{\circ}\), as \(\beta\) changes from \(-\)120\({}^{\circ}\) to \(-\)60\({}^{\circ}\), 0\({}^{\circ}\), +60\({}^{\circ}\), and +120\({}^{\circ}\), respectively. The 3-dB beamwidth of the main beam for this design is estimated to be \(\sim\)21\({}^{\circ}\). For \(L\)/\(R\) = 0.2 (see Figure 4), the main beam is steered in a smaller range, i.e., from \(-\)17\({}^{\circ}\) to \(-\)7\({}^{\circ}\), 0\({}^{\circ}\), +7\({}^{\circ}\), and +17\({}^{\circ}\) when \(\beta\) changes from \(-\)120\({}^{\circ}\), to \(-\)60\({}^{\circ}\), 0\({}^{\circ}\), +60\({}^{\circ}\), and +120\({}^{\circ}\), respectively. As expected, the 3-dB beamwidth reduces to \(\sim\)15\({}^{\circ}\). In summary, the designed lens-coupled 1 \(\times\) 3 ASA phased array offers a high gain improvement while sacrificing the beam scanning range.