# Wide-Band Wide-Beam Circularly-Polarized Slot-Coupled Antenna for Wide-Angle Beam Scanning Arrays
## 4 Numerical Assessment
Moreover, a good polarization purity is yielded in the whole scan range as indicated by the plot of both the \(AR\) and the _XPD_ along the angular steering direction, since \(AR(\theta_{s},\ \varphi_{s})\leq 14.6\) [dB] and \(XPD(\theta_{s},\ \varphi_{s})\geq 3.3\) [dB] when \(|\theta_{s}|\leq 90\) [deg] and \(\varphi_{s}=\{0;\ 90\}\) [deg] [Figure 13b]. Finally, let us note that the _WASA_ properties of the array are confirmed within the frequency range of interest (Figure 14) where \(6.5\leq SL(f)\leq 15.1\) [dB] for \(f_{\min}\leq f\leq f_{\max}\) in both elevation planes. In addtion to the numerical assessment, a tolerance analysis has been carried out to give the interested reader some insights into the reliability and robustness on the fabrication tolerances of the proposed antenna layout both stand-alone and within an array arrangement. First, the height of the parasitic element, \(D\), has been supposed to deviate of \(\pm 5\%\) and \(\pm 10\%\) from the nominal value \(D^{(opt)}\)(Tab. 2) because of some manufacturing tolerances. Figure 15 summarizes the results of the tolerance analysis versus the frequency for the input reflection coefficient [Figure 15a], the broadside \(AR\) [Figure 15b], and the _HPBW_ along the \(\varphi=0\) [deg] [Figure 15c] and the \(\varphi=90\) [deg] [Figure 15d] planes. As it can be inferred, the proposed antenna layout turns out to be quite robust. More precisely, the wide-band [Figure 15a] and the wide-beam [Figure 15c,d] characteristics of the _WWCS_ radiator are confirmed regardless of the non-negligible fabrication tolerances on \(D\), the fractional bandwidth being equal to \(FBW=12.1\%\) in the worst case [i.e., \(D=D^{(opt)}-10\%D^{(opt)}\)--Figure 15a]. As a consequence, the scan loss value of the array, \(SL(f)\), within the working frequency range, \(f_{\min}\leq f\leq f_{\max}\), is quite stable in both elevation planes (Figure 16), as well. Similar conclusions can be drawn when taking into account fabrication tolerances on the width of the feeding line, \(W_{f}\), and the parasitic ring, \(W_{r}\), which have been varied according to the following rule: \(W_{f/r}=W_{f/r}^{(opt)}+(\xi\times\
u)\), \(\
u=0.35\) [\(\mu\)m] being the metallization thickness and \(\xi\in\{-1.0;-0.5;\,+0.5;\,+1.0\}\). The effects of such deviations are almost negligible on the features of both the elementary radiator and the array as one can derive from the analysis of the plots in Figure 17 and in Figure 18, respectively. Figure 16: _Numerical Assessment_ (\([f_{\min},\,f_{\max}]=[2.3,\,2.6]\) [GHz]—\(N=(50\times 50)\))—\(SL\) performance versus frequency when steering the beam towards \(\theta_{s}\in[0,\,90]\) [deg] and (**a**) \(\varphi_{s}=0\) [deg] or (**b**) \(\varphi_{s}=90\) [deg] and assuming that the height of the parasitic element, \(D\), is affected by manufacturing deviations of \(\pm 5\%\) and \(\pm 10\%\) from the nominal value \(D^{(opt)}\)(Table 2). Figure 15: _Numerical Assessment_ (\([f_{\min},\,f_{\max}]=[2.3,\,2.6]\) [GHz])—Behavior of the (**a**) reflection coefficient, \(\left|S_{11}^{(dB)}(f)\right|\), (**b**) axial ratio, \(AR(f,\,\theta=0,\,\varphi=0)\), and \(HPBW(f)\) along the (**c**) \(\varphi=0\) [deg] and (**d**) \(\varphi=90\) [deg] elevation planes of the _WWCS_ radiating element when the height of the parasitic element, \(D\), is affected by manufacturing deviations of \(\pm 5\%\) and \(\pm 10\%\) from the nominal value \(D^{(opt)}\) (Table 2).