# Broadband Flexible Microstrip Antenna Array with Conformal Load-Bearing Structure
## 2 Antenna Design  
### Antenna Element  
The overall geometry of the proposed antenna element is shown in Figure 2. Composed of three substrate layers (polyimide film, \(\varepsilon_{r}\) = 3.5, \(\tan\delta\) = 0.0027, thickness = 0.3 mm), four metallic layers, and two honeycomb core layers (\(\varepsilon_{r}\) = 1.1, thickness = 2 mm), the layered structure was depicted Figure 1 in perspective view. Specifically, the relative positions of these layers are as follows: (1) radiation patch on the top surface of the upper substrate layer; (2) ground plane with coupling aperture and microstrip line on the top and lower surface of the middle layer substrate, respectively; (3) metallic reflection surface on the back surface of the lower surface; and (4) honeycomb cores between the three substrate layers. The radiation patch is excited by a 50 \(\Omega\) microstrip feeding through a coupling aperture and the metallic reflection surface is used to reduce the SLL of the antenna element. Figure 2: The coordinate geometry and dimensions of the proposed antenna element: (**a**) explosion view of the layered structure, (**b**) honeycomb core structure, (**c**) side view of element, (**d**) top layer with radiation patch, and (**e**) middle layer with the microstrip feeding and ground with coupling aperture. Figure 2b,c shows the structure of the honeycomb core and the side view of the antenna element, respectively. The mixed equivalent permittivity of the upper layer of substrate (\(\varepsilon_{r}\)) can be expressed as:  
\[\varepsilon_{r}=\frac{h_{1}+h_{2}}{\frac{h_{1}}{\varepsilon_{1}}+\frac{h_{2}}{ \varepsilon_{2}}} \tag{1}\]  
Then, \(H_{p}\) is the mixed thickness of layers, the relationships between \(BW\), \(H_{p}\), and \(\varepsilon_{r}\) are described as [18]:  
\[H_{p}=h_{1}+h_{2}, \tag{2}\]  
\[BW\propto(1/\varepsilon_{r});\ BW\propto H_{p}, \tag{3}\]  
where \(h_{1}\) and \(h_{2}\) are the thickness of substrate layers and honeycomb core layers, \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are the equivalent permittivity of the substrate layer and honeycomb core layer. The \(BW\) of the microstrip antenna is proportional to \(H_{p}\) and is inversely proportional to \(\varepsilon_{r}\). Therefore, loading honeycomb layers plays two vital roles in the proposed element with a conformal load-bearing structure. For one thing, it takes the load-bearing function and stability for the antenna. For another, it broadens the BW through the increase in \(H_{p}\) and the decrease in \(\varepsilon_{r}\). Calculated by Formulaes (1) and (3), the bandwidth of the proposed antenna element is increased by the loading of the honeycomb core between the upper and middle substrate layer. From Figure 2d, the length and width of the radiation patch is \(L_{2}\times W_{2}\), which can be calculated by [18]:  
\[L_{2}=\frac{C}{2f_{r}\sqrt{\varepsilon_{e}}}-2\Delta L_{p},\ W_{2}=\frac{C}{2 f_{r}}\sqrt{\frac{2}{\varepsilon_{r}+1}}, \tag{4}\]  
\[\varepsilon_{e}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}\frac{ 1}{\sqrt{(1+12H_{p}/W)}}, \tag{5}\]  
\[\Delta L_{p}=0.412H_{p}\frac{\varepsilon_{e}+0.3}{\varepsilon_{e}-0.258}\frac {\frac{W_{p}}{H_{p}}+0.264}{\frac{W_{p}}{H_{p}}+0.800}, \tag{6}\]  
where \(f_{r}\), \(C\), \(\Delta L_{p}\), \(W_{p}\), \(\varepsilon_{e}\), and \(\varepsilon_{r}\) are the operating frequency point of the antenna, the speed of light, the amount of extension of the patch, the width of the 50 \(\Omega\) microstrip feeding line the mixed relative effective permittivity, and the mixed equivalent permittivity, respectively. In Figure 2e, the coupling aperture is implemented by etching a rectangular slot in the center of the ground plane, and its dimension is \(L_{3}\times W_{3}\). The dimensions of the 50 \(\Omega\) microstrip feeding line are \(L_{4}\times W_{4}\) which is printed on the lower surface of the middle substrate. Additionally, the overall size of three substrate layers is \(L_{1}\times W_{1}\times h_{1}\), and the overall dimension of two honeycomb cone layers is \(L_{1}\times W_{1}\times h_{2}\).