# Predicting Electromagnetic Performance Under Wrinkling in Thin-Film Phased Arrays
## 4 Discussion
### Phased Array Antenna Analysis  
We now vary the values of \(c_{fz1}\) and \(c_{fz2}\) to predict the electrical performance of the phased array antenna; when \(c_{fz1}\) = 0.001 and \(c_{fz2}\) = 0.0012, the resulting structural deformation of the array layer most closely matches that shown in Figure 4.  
The unit performance variations are shown in Figure 13. When studying the effects of the structural parameters \(c_{fz1}\) and \(c_{fz2}\) on the unit antenna gain, gain-versus-angle curves were plotted for the E-plane (\(\phi\) = 0\({}^{\circ}\)) and H-plane (\(\phi\) = 90\({}^{\circ}\)) for different \(c_{fz1}\)-\(c_{fz2}\) combinations. The analysis indicates that variations in \(c_{fz1}\) mainly affect the main lobe level of the radiation pattern; variations in \(c_{fz2}\) primarily influence the pattern shape and sidelobe levels, with only a minor effect on main lobe gain. In Figure 13's four non-normalized unit gain plots, the first and third correspond to the E-plane, while the second and fourth correspond to the H-plane. Overall, when \(c_{fz1}\) or \(c_{fz2}\) increases, the main lobe gain typically fluctuates between 5 and 8 dB, but the sidelobe and null depths exhibit significant variation with parameter changes. In the E-plane (Figure 13, first and third plots), the main lobe gain at \(\theta\approx 0^{\circ}\) mostly remains at the 6-7 dB level, although in some cases, the gain decays more sharply (\(c_{fz1}\) = 0.001, 0.002), and the sidelobes are mainly concentrated near \(\theta\approx\pm 50^{\circ}\) and \(\pm 100^{\circ}\). As the parameter increases, some curves exhibit a 2-3 dB gain increase at those sidelobe positions or a shift in null locations, indicating that local film deformation or patch translation leads to an uneven current distribution, which, in turn, affects the E-plane sidelobe characteristics. If significant differences exist between elements, array synthesis may suffer amplitude and phase inconsistencies, raising the overall sidelobe level. In the H-plane (Figure 13, second and fourth plots), the main lobe gain also lies between 5 and 8 dB, but the curves are more sensitive to changes, and certain parameter combinations (e.g., \(c_{fz1}\) = 0.003 or \(c_{fz2}\) = 0.002-0.003) cause only minor shifts in the main lobe peak, yet produce higher sidelobes near \(\theta\approx\pm 70^{\circ}\) or deeper nulls near \(\theta\approx\pm 100^{\circ}\). Other combinations (\(c_{fz2}\) = 0.002) lead to severe fluctuations, blurring the distinction between main and sidelobes. Compared to the E-plane, the H-plane patterns oscillate more strongly, showing that film deformation and local patch displacement more significantly modulate polarization and current distribution in this plane. In phased array applications, such inconsistencies accumulate as amplitude and phase errors in beamforming, degrading beam pointing and sidelobe performance. In summary, variations in \(c_{fz1}\) and \(c_{fz2}\) lead to differing degrees of change in the main lobe, sidelobes, and null depths of the gain patterns in the E- and H-planes. While the main lobe gain remains generally stable, the sidelobe levels and null depths are more sensitive to film deformation, whereas copper foil deformation causes more pronounced attenuation of the main lobe. This implies that large \(c_{fz1}\) and \(c_{fz2}\) deviations between elements can degrade the phased array's overall sidelobe-suppression capability and beam scanning accuracy. Therefore, in high-precision antenna design and fabrication, \(c_{fz1}\) and \(c_{fz2}\) must be strictly controlled or calibrated to ensure consistent element gain characteristics and maintain excellent radiation pattern performance. The apparent discontinuity at \(\theta=\pm 90^{\circ}\) is a numerical artifact of discrete sampling and mesh-cell stitching at the spherical coordinate poles; it does not represent a physical gap and does not affect the main and side-lobe metrics.