# Methodology for Improving Scanning Performance Loading an Array Element with a 3D All-Metal WAIM
## 3 WAIM Design Methodology
### Application of the Methodology  
The methodology is applied for a case where the array element is a metallic horn partially filled in with dielectric (Figure 7a). Thanks to this dielectric, the horn has a periodicity smaller than \(0.5\lambda_{0}\) at the design frequency, avoiding triggering of grating lobes at maximum angle of scanning.  
The active reflection coefficient of the array without the WAIM is shown in Figure 8 in black, and efforts are focused on matching the _H-plane_, as the matching becomes worse earlier in this scanning direction. The matching of the array is worse than \(-10\) dB for steering angles higher than \(\theta=45^{\circ}\) and \(\theta=55^{\circ}\) in the _H-_ and _E-plane_, respectively. Following the aforementioned design steps, the optimizable circuit elements for a slit \(w_{y}=0.15p\) are: \(d_{WAIM}=0.004\lambda_{0}\), \(l_{1}=l_{2}=0.176\lambda_{0}\) and \(Z_{x}=37j\ \Omega\). Figure 8 (red curve) shows the matching in _H-plane_ at \(\theta=55^{\circ}\) is improved by more than \(10\) dB. Note that the matching in _E-plane_ has been slightly degraded, but it was not considered in the optimization. Next, the load impedance has been synthetized using vertical columns with \(R=0.483\ \mathrm{mm}\) and \(A_{x}=0.633\ \mathrm{mm}\), and a full-wave simulation is performed, placing the WAIM as shown in Figure 7b, and yielding green curve in Figure 8. Unfortunately, the performance is not as good as expected, especially in the higher \(\theta\) angles. The main reason for the disagreement is the close proximity between the antenna and the WAIM (\(d_{WAIM}=0.004\lambda_{0}\)). This placement of the WAIM in the direct vicinity of the antenna results from the brute optimization process and further investigations demonstrated it was effectively the best solution. However, for such a reduced spacing, the EC is not so accurate due to tight coupling effects. Then, in order to overcome this limitation, a post-processing is applied. Indeed, starting from the EC result, a simple refinement in the radius of the columns is sufficient to improve the final response. By decreasing \(R=0.483\ \mathrm{mm}\) to \(R_{optim}=0.465\ \mathrm{mm}\), new full-wave results are obtained (blue curve in Figure 8a). These results show significant improvements in the _H-plane_ matching all \(\theta\) angles. Furthermore, there is an improvement of more than \(5\) dB, compared with the initial matching (black curve), in \(\theta=45^{\circ},\ 50^{\circ}\) and \(55^{\circ}\). Such an improvement is not reached in the _E-plane_.  
An additional validation is presented to demonstrate that the agreement between full-wave and EC is satisfactory in the case where \(d_{WAIM}\) is not as small as in the previous case. To do so, a re-optimization is conducted where the minimal value of \(d_{WAIM}\) is limited to \(0.1\lambda_{0}\).  
The recalculated circuit elements for the same slit size (\(w_{y}=0.15p\)) are now: \(d_{WAIM}=0.1\lambda_{0}\), \(I_{1}=l_{2}=0.1\lambda_{0}\) and \(Z_{x}=51j\,\Omega\). The corresponding results are shown in Figure 9 (red curve). As suggested before, the matching improvement in the \(H\)-_plane_ is not as good as in Figure 8 because \(d_{WAIM}\) is now limited. However, what is important is that the agreement with full-wave simulation (green curve) is now much better. This suggests the extremely low value of \(d_{WAIM}\) in the previous example was the main reason for a loss of accuracy in the EC prediction. Note that the agreement is quite sensitive to the used value of \(Z_{x}\) and, consequently, it might be improved by accounting for its variations with \(\theta\).  
This design can be compared with the literature in Table 1.  
Figure 8: Active reflection coefficient at \(f=18\) GHz without limiting \(d_{WAIM}\): **(a)**\(H\)-_plane_ and **(b)**\(E\)-_plane_; phased array (\(PA\)), full-wave (\(FW\)).  
Figure 9: Active reflection coefficient at \(f=18\) GHz limiting \(d_{WAIM}\): **(a)**\(H\)-_plane_ and **(b)**\(E\)-_plane_; phased array (\(PA\)) and full-wave (\(FW\)).