# Predicting Electromagnetic Performance Under Wrinkling in Thin-Film Phased Arrays
## 4 Discussion
### Phased Array Antenna Analysis
During this increase in \(c_{f22}\), the resonant point oscillates, the primary matching dip shifts from \(-12\) dB to \(-8\) dB, and additional parasitic modes appear at the high-frequency end; at the same time, the main lobe gain rises slightly, but sidelobes also climb, degrading the antenna's directivity to some extent. In high-precision antenna or phased array applications, it is therefore critical to tightly control the \(c_{f22}\)-induced local patch deformation and to employ matching-compensation techniques to minimize cumulative errors, thereby preserving the antenna's operational bandwidth and radiation-pattern stability. Adjustments of the structural parameters \(c_{f21}\) and \(c_{f22}\) primarily affect the antenna's resonant frequency, input matching characteristics, and the sidelobe structure of the far-field radiation pattern. \(c_{f21}\) has a relatively small impact on the main lobe gain, whereas  
Figure 14: Variation of the antenna’s input reflection coefficient and E-plane gain with frequency (\(c_{f21}\) and \(c_{f22}\) variations). \(c_{f22}\) exerts a significant influence on it. In phased array applications, such variations can alter the phase relationships between elements and degrade beam-forming performance. Therefore, during the antenna design process, \(c_{f21}\) and \(c_{f22}\)--that is, the stiffness matching between the copper patch and the film--must be judiciously tuned to optimize sidelobe behavior while preserving good matching, ensuring element-to-element consistency, and enhancing overall array performance. In phased array antenna systems, element errors have a significant impact on the array's overall gain and radiation pattern characteristics. To investigate how variations in structural parameters \(c_{f21}\) and \(c_{f22}\) affect the phased array gain, simulations were performed, and the effects of different error values were analyzed in both the E-plane (\(\phi\) = 0\({}^{\circ}\)) and the H-plane (\(\phi\) = 90\({}^{\circ}\)), as shown in Figure 15. The results indicate that, although individual element gains do not always change dramatically under these errors, the array's overall sidelobe levels, null depths, and main beam direction are nonetheless influenced to some extent. In the four phased array gain plots--showing the \(\phi\) = 0\({}^{\circ}\) and \(\phi\) = 90\({}^{\circ}\) planes for various values of \(c_{f21}\) and \(c_{f22}\)--we observe the following: in the \(\phi\) = 0\({}^{\circ}\) plane, as \(c_{f21}\) or \(c_{f22}\) increases, the main beam gain around \(\theta\)\(\approx\) 0\({}^{\circ}\) remains largely unchanged, but sidelobe levels at \(\theta\)\(\approx\)\(\pm\) 60\({}^{\circ}\) and \(\theta\)\(\approx\)\(\pm\) 100\({}^{\circ}\) rise, and some nulls become shallower, reflecting cumulative phase and amplitude inconsistencies during array synthesis. In the \(\phi\) = 90\({}^{\circ}\) plane, these fluctuations are even more pronounced: increasing \(c_{f21}\) or \(c_{f22}\) not only raises sidelobes near \(\theta\)\(\approx\)\(\pm\)60\({}^{\circ}\) but also introduces additional peaks or dips around \(\theta\)\(\approx\)\(\pm\)120\({}^{\circ}\), indicating that local deformation of the patch or film has a greater impact on the high-off-axis radiation. Overall, the greater the deviation of \(c_{f21}\) and \(c_{f22}\) from their ideal values, the more prone the array's sidelobe distribution and null-positioning are to distortion--a phe  
Figure 15: Prediction of the phased array antenna’s electrical performance (\(c_{f21}\) and \(c_{f22}\) variations). nomenon that can degrade beam pointing accuracy and interference suppression in large-scale phased arrays. Therefore, to maintain both main-beam gain and sidelobe suppression, manufacturing and assembly processes must tightly control element deformation and patch-position offsets, and where necessary, employ amplitude- and phase-correction algorithms to mitigate the errors' impact on the overall radiation pattern.