# Predicting Electromagnetic Performance Under Wrinkling in Thin-Film Phased Arrays
## 3 Structural-Electromagnetic Coupling Model
### Patch Electro-Magnetic Performance Simulation
As shown in the S-parameter (S11) curves in Figure 10, when \(d_{pch}\) = 0 mm, the antenna achieves its best match around 1.28 GHz, with the minimum S11 reaching approximately \(-12\) dB, indicating optimal resonance and impedance matching. As \(d_{pch}\) is reduced in 0.2 mm steps from 0 to \(-1\) mm, the resonant frequency first shifts downward to 1.24 GHz, then returns to the 1.28-1.30 GHz range. Over this range, the S\({}_{11}\) minimum oscillates between \(-9\) dB and \(-16\) dB, showing that matching gradually degrades as the patch is translated downward. Moreover, at \(d_{pch}\) = \(-0.4\) mm, a small additional dip appears near 1.6 GHz, suggesting the excitation of a parasitic mode and potential multi-band behavior that could interfere with single-band operation in the 1.24-1.30 GHz band. Figure 9: Electrical performance of an ideal patch antenna. In the gain radiation patterns shown in Figure 10, \(d_{pch}\) = 0 mm yields the highest main lobe gain of about 6.5 dB, with low sidelobe levels and a symmetric pattern. As \(d_{pch}\) decreases from \(-0.2\) mm to \(-1\) mm, the main lobe gain drops noticeably, falling to around 5 dB at \(d_{pch}\)= \(-1\) mm and shifting off-axis from \(\theta\) = 0\({}^{\circ}\). At the same time, the sidelobe levels around \(\theta\approx\pm 150^{\circ}\) rise by about 0.2 dB, and the pattern's symmetry degrades. This indicates that shifting the patch alters the current distribution and thereby distorts the far-field radiation pattern, affecting both the main and sidelobes. In a phased array application, such unit-level misalignments can degrade overall beam-scanning accuracy and increase sidelobe interference. Based on the phase change analysis theory [28], the phenomenon of the gain main lobe splitting into two in Figure 10 can be explained by the following process. When each patch is laterally translated by \(d_{pch}\), its radiated field acquires an extra path-length phase shift \(\Delta\phi(\theta)=kd_{pch}\cos\theta\). For \(d_{pch}\) = 0, the aperture phase front remains planar, yielding a single boresight beam. As soon as \(d_{pch}\
eq 0\), this uniform phase ramp tilts each element's pattern off broadside. If the phase gradient places a null at \(\theta\) = 0, the main beam splits into two symmetric lobes. Since every element undergoes the same translation, the array reproduces two lobes around broadside for all non-zero \(d_{pch}\). According to the equivalent-circuit model [29], a slight variation (\(\pm 1\) mm) in the probe-to-ground-plane spacing significantly alters the probe's series inductance, causing shifts of tens of ohms in both the real and imaginary parts of the input impedance. This leads to a sudden rise in VSWR and severe mismatch, ultimately distorting the patch current distribution and producing beam splitting with a dual-peak radiation pattern. Furthermore, [PERSON] et al. [30] emphasize that minute perturbations in feed-geometry parameters such as probe length and substrate thickness can excite parasitic modes or feedline radiation, thereby elevating sidelobe levels and flattening the main beam. In summary, as the patch position shifts from 0 mm to \(-1\) mm, not only does the resonant frequency oscillate and matching degrade, but the main lobe gain also falls, and the radiation pattern deteriorates. Therefore, in phased array antenna design and fabrication, patch-position deviations must be tightly controlled to ensure uniform matching and gain across all elements, thereby achieving optimal beam patterns and array performance. As shown in the S-parameter (S11) curves in Figure 11, as \(d_{zm}\) increases, the antenna's matching characteristics change noticeably. At \(d_{zm}\) = 0 mm (no translation), the resonant frequency is near 1.28 GHz with S11 \(\approx-12\) dB, indicating good matching. However, when \(d_{zm}\) increases to \(-5\) mm, the resonant frequency shifts toward 1.30 GHz, and S11 becomes smaller.