# Predicting Electromagnetic Performance Under Wrinkling in Thin-Film Phased Arrays
## 3 Structural-Electromagnetic Coupling Model
### Patch Electro-Magnetic Performance Simulation  
The simulation analysis first focuses on a single antenna unit; the array antenna analysis is then conducted by exporting the data and performing superposition calculations in MATLAB based on formula (21) and patch results from HFSS. For a patch size of 98 mm \(\times\) 98 mm and a film spacing of 12.7 mm, analysis of a representative patch unit yields the antenna's reflection coefficient and its E and H plane gain patterns. Simulation was carried out using Ansys HFSS. A patch length of 98 mm was selected, corresponding to approximately 0.425A at the center frequency of 1.3 GHz. This dimension provides a practical trade-off between structural rigidity, radiation efficiency, and integration requirements within our deployable membrane antenna platform. It is also consistent with the patch configurations used in related institutional engineering projects. It is worth noting that several simplifications were adopted in the current electromagnetic simulation framework. First, mutual coupling effects between adjacent antenna elements were not considered in the array-level analysis. The radiation pattern was obtained through the superposition of isolated element responses, assuming negligible interaction. This approach is commonly used in preliminary parametric studies, but may overestimate the array performance in practical scenarios with strong inter-element coupling. Second, the structural deformation used in the electromechanical coupling model was derived under static assumptions. The influence of dynamic factors such as deployment vibrations, thermal-induced fluctuations, or time-varying disturbances was not incorporated. While the static assumption provides a tractable means of evaluating the deformation-induced gain degradation, it may not fully capture transient behavior encountered in orbit. Third, the material properties of the membrane and conductive layers were treated as ideal and invariant during simulation. Effects due to temperature variations, radiation aging, or material nonlinearity were not included. These assumptions simplify the model and reduce computational cost but may introduce discrepancies in long-term or extreme-environment conditions. Despite these simplifications, the current framework provides valuable insight into the sensitivity of antenna gain and beam steering to structural deformations. Future work will consider mutual coupling effects, dynamic structural responses, and realistic material behavior to enhance the fidelity of the model. The antenna model was constructed in HFSS with standard microstrip patch geometry using sheets and PEC (Perfect Electric Conductor) material for the patch and ground, along with a dielectric substrate modeled using the membrane with solids with polymide parameters. Radiation boundaries were applied to enclose the entire simulation domain, with a minimum distance of \(\lambda/4\) from the structure. A lumped port was used for excitation. The frequency sweep was set from 1.2 GHz to 1.6 GHz using a discrete sweep with a 10 MHz step. Regarding meshing, the default adaptive meshing strategy in HFSS was used. This includes a convergence criterion of \(\Delta\)S = 0.02 and a minimum of 2 and a maximum of 15 adaptive passes. Since the deformation was quite small compared with the patch length, no manual mesh operations were applied, and the software automatically refined the mesh near edges and the feed region. These settings were sufficient to ensure accurate convergence and are consistent with the best practices for planar antenna modeling. The simulation results are shown in Figure 9. It can be seen that the reflection coefficient S11 achieves a good matching depth at 1.3 GHz, with approximately \(-12\) dB. In both the E-plane and H-plane, the antenna attains a gain level of approximately 7.5 dB. Next, a hypothetical independent deformation analysis of the film and patch regions was performed, first identifying the extent to which each region impacts the electrical performance of the patch.