# Predicting Electromagnetic Performance Under Wrinkling in Thin-Film Phased Arrays
## 4 Discussion
### Phased Array Antenna Analysis
As shown in the S-parameter (S11) curves (Figure 14, first plot), when \(c_{fz1}\) varies between 0, 0.001, 0.002, and 0.003, the antenna's matching in the 1.2-1.4 GHz band undergoes significant drift and change. Initially (\(c_{fz1}\) = 0 mm), the resonant frequency is about 1.28 GHz, and the S11 minimum reaches approximately \(-12\) dB; as \(c_{fz1}\) increases to 0.003, the resonant point oscillates. Meanwhile, the S\({}_{11}\) matching depth also changes markedly, indicating that local film deformation shortens the effective electrical length and degrades matching. Furthermore, at \(c_{fz1}\) = 0.003, three resonant points appear, the strongest near 1.6 GHz, suggesting excitation of parasitic modes. At \(c_{fz1}\) = 0.002, a possible parasitic mode with about \(-5\) dB depth is also seen, though it has limited impact on the main operating band. As shown in the S-parameter curves (Figure 14, second plot), as \(c_{fz2}\) increases from 0 to 0.003, the antenna's resonant frequency and matching shift sequentially. According to the color legend, \(c_{fz2}\) = 0 (red line) shows a main matching dip of about \(-12\) dB near 1.28 GHz; at \(c_{fz2}\) = 0.0012 (orange line), the resonance shifts to \(\approx\)1.32 GHz, with a minimum of \(\approx\)\(-11\) dB; at \(c_{fz2}\) = 0.002 (blue line), the resonance shifts most severely to \(\approx\)1.45 GHz, with the lowest point of \(\approx\)\(-9\) dB; and at \(c_{fz2}\) = 0.003 (green line), the main resonance shifts back to \(\approx\)1.28 GHz, with a minimum of \(\approx\)\(-8.5\) dB. Secondary dips near 1.63, 1.83, and 1.95 GHz (\(\approx\)\(-6\) dB, \(-7\) dB, \(-10\) dB) appear at \(c_{fz2}\) = 0.0012 and 0.003, indicating that local patch deformation excites new parasitic modes. Overall, increasing \(c_{fz2}\) causes resonant-frequency oscillation, secondary dips, and a gradual weakening of matching. As shown in the gain radiation patterns (Figure 14, third plot), at \(c_{fz1}\) = 0, the main lobe gain peaks at 7.9 dB, with low sidelobe levels; when \(c_{fz1}\) increases to 0.003, the main lobe gain amplitude changes little, but the angle of maximum gain shifts away from \(\theta\) = 0\({}^{\circ}\), and sidelobes near \(\theta\approx\pm 50^{\circ}\) rise by about 2-3 dB, reducing pattern symmetry. This shows that local deformation alters the current distribution, boosting radiation at certain angles while causing sidelobe rise or shallower nulls. If such \(c_{fz1}\) variations occur between phased array elements, amplitude and phase inconsistencies in beamforming may result, degrading overall beam pointing accuracy and sidelobe suppression. When \(c_{fz1}\) = 0.001 mm and 0.002 mm, the gain curve shows significant attenuation at \(\theta=0^{\circ}\), with the peak gain still near \(\theta=0^{\circ}\), leading to poorer directivity. In the gain radiation pattern (Figure 14, fourth plot), the curves for different \(c_{f22}\) values show main lobe gains at \(\theta=0^{\circ}\) of roughly 5-7 dB: when \(c_{f22}=0.0012\) and 0.002 (orange and blue lines), the main lobe gain still reaches about 7 dB. However, when \(c_{f22}=0.003\) (green line), the main lobe gain only reaches 5-6 dB, and the sidelobes near \(\theta\approx\pm 50^{\circ}\) and \(\theta\approx\pm 100^{\circ}\) rise by 2-3 dB, causing noticeable distortion and null shifts in the pattern. This indicates that further increases in \(c_{f22}\) not only degrade matching but also alter the far-field current distribution, enhancing radiation at certain angles and increasing sidelobe energy. In a phased array antenna, if \(c_{f22}\) errors vary significantly between elements, amplitude and phase errors accumulate during beamforming, degrading overall beam pointing accuracy and sidelobe suppression. In summary, as \(c_{f21}\) increases from 0 to 0.003, the resonant frequency begins to oscillate around 1.28 GHz, and the matching performance degrades slightly, while the gain radiation pattern shows a modest increase in the main lobe level, accompanied by elevated sidelobes.