# Broadband Flexible Microstrip Antenna Array with Conformal Load-Bearing Structure
## 3 Theoretical Analysis
### Principle for Wideband Operation  
In order to better reveal the broadband operation mechanism of the antenna, the characteristic mode analysis (CMA) theory of the antenna structure is carried out using a CST microwave studio (version 2016). The CMA theory was proposed by [PERSON] in the late 1960s, who suggested that the eigen currents could be determined by analyzing the scattering matrix. These characteristic currents are surface currents on the conducting body and depend only on the shape of the conductor without any external excitation. The model significance indicates the normalized magnitude of the eigen currents and the band with MS greater than 0.707 is the potential operating band of the antenna. Thus, the CMA analysis allows the analysis of the potential operating bandwidth of the antenna structure.  
Firstly, the CMA on the radiation patch and the top substrate is carried out, as shown in Figure 8. For these modes, only mode 1 and mode 2 have identical modal significance. It can be observed from Figure 8b,c that the modal currents of mode 1 and mode 2 show orthogonal characteristics. Due to the difference in the width and length of the radiation patch, the difference occurs in the resonant frequency points of mode 1 and mode 2. As illustrated in Figure 8a, the operating frequency band with an MS greater than 0.707 is  
Figure 7: The comparison of scattering parameters of the honeycomb core layer, cell EM equation, and layer EM equation in flat state and under different states, (**a**) planar, (**b**) 30\({}^{\circ}\) bending, (**c**) 60\({}^{\circ}\) bending, and (**d**) 90\({}^{\circ}\) bending.  
extremely narrow in both modes, and this structure for the antenna design is a hard strategy to implement a broadband operating frequency band. Initially, the CMA method is employed after the honeycomb core equivalent layer is added, as depicted in Figure 9. It is apparent that mode 1 is identical to mode 2 in the modal significance. In this case, the potential operating frequency band is wider than the previous structure which is shown in Figure 8a. Meanwhile, these results further support the concept in formulae (3) that the operating bandwidth of the microstrip antenna can be improved by adding a substrate layer with a low dielectric constant between the radiation patch and the ground.  
Finally, to further investigate the operating bandwidth stability under deformation, its structure utilizes the CMA method to analyze various bending states as shown in Figure 10a. Since prior cases indicate that mode 1 and mode 2 are degenerate modes, only one of them is needed for the analysis. In this case, mode tracing is performed for mode 1, and the modal significance has been shown in Figure 10b. Whether in a flat or deformed state, this structure maintains a wide operating frequency band. Although the deformable  
Figure 8: Modal behaviors of the top substrate and radiation patch, (**a**) modal significance, (**b**) the modal current and far-field radiation pattern of mode 1, and (**c**) the modal current and far-field radiation pattern of mode 2. Modal Significance.  
Figure 9: Modal behaviors of the top substrate, radiation patch, and honeycomb equivalent layer, (**a**) modal significance, (**b**) the modal current and far-field radiation pattern of mode 1, and (**c**) the modal current and far-field radiation pattern of mode 2.  
state will cause a partial shift in frequency, the primary operating frequency band is out of change.