# Integration of Microstrip Slot Array Antenna with Dye-Sensitized Solar Cells
## 2 Integrated Design Array Antenna and Solar Cells
According to Figure 2 and Table 1, for the antenna structure shown in Figure 1, the following two spectral domain integral equations can be obtained by using the boundary condition that the total electric field tangential direction of the antenna surface is 0:  
\[\iint\left[\widetilde{\mathrm{G}}_{\mathrm{ox}}\widetilde{\mathrm{J}}_{ \mathrm{x}}+\widetilde{\mathrm{G}}_{\mathrm{xy}}\widetilde{\mathrm{J}}_{ \mathrm{y}}\right]\exp\left\{-\mathrm{j}(\mathrm{k}_{\mathrm{x}}\mathrm{x}+ \mathrm{k}_{\mathrm{y}}\mathrm{y})\right\}\mathrm{d}\mathrm{k}_{\mathrm{x}} \mathrm{d}\mathrm{k}_{\mathrm{y}}=\iint\widetilde{\mathrm{G}}_{\mathrm{ox}} \widetilde{\mathrm{J}}_{\mathrm{z}}\exp\left\{-\mathrm{j}(\mathrm{k}_{\mathrm{ x}}\mathrm{x}+\mathrm{k}_{\mathrm{y}}\mathrm{y})\right\}\mathrm{d} \mathrm{k}_{\mathrm{x}}\mathrm{d}\mathrm{k}_{\mathrm{y}} \tag{1}\]  
\[\iint\widetilde{\mathrm{G}}_{\mathrm{yx}}\widetilde{\mathrm{J}}_{\mathrm{x}}+ \widetilde{\mathrm{G}}_{\mathrm{yy}}\widetilde{\mathrm{J}}_{\mathrm{y}}\right] \exp\left\{-\mathrm{j}(\mathrm{k}_{\mathrm{x}}\mathrm{x}+\mathrm{k}_{ \mathrm{y}}\mathrm{y})\right\}\mathrm{d}\mathrm{k}_{\mathrm{x}}\mathrm{d} \mathrm{k}_{\mathrm{y}}=\iint\widetilde{\mathrm{G}}_{\mathrm{yz}} \widetilde{\mathrm{J}}_{\mathrm{z}}\exp\left\{-\mathrm{j}(\mathrm{k}_{\mathrm{ x}}\mathrm{x}+\mathrm{k}_{\mathrm{y}}\mathrm{y})\right\}\mathrm{d} \mathrm{k}_{\mathrm{x}}\mathrm{d}\mathrm{k}_{\mathrm{y}} \tag{2}\]  
where \(\widetilde{\mathrm{G}}_{\mathrm{ox}}\), \(\widetilde{\mathrm{G}}_{\mathrm{xy}}\), \(\widetilde{\mathrm{G}}_{\mathrm{yz}}\), \(\widetilde{\mathrm{G}}_{\mathrm{yz}}\), \(\widetilde{\mathrm{G}}_{\mathrm{yy}}\) are the components of [PERSON]'s function in the electric field spectral domain, \(\widetilde{\mathrm{J}}_{\mathrm{x}}\) and \(\widetilde{\mathrm{J}}_{\mathrm{y}}\) are the x and y spectral components of the unknown current on the surface, and \(\widetilde{\mathrm{J}}_{\mathrm{z}}\) are the spectral components of the feed current of the coaxial probe. The antenna is covered with \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Dielectric Constant** & **Conductivity** \\ \hline Polyimide & 3.4 & \(3.92\times 10^{-15}\) S/m \\ Pt & 1 & \(9.3\times 10^{6}\) S/m \\ Dye-sensitized layer & 90 & \(1.51\times 10^{-2}\) S/m \\ TiO\({}_{2}\) & 86 & 100 S/m \\ Ti & 1 & \(1.82\times 10^{6}\) S/m \\ SiO\({}_{2}\) & 4 & 0 S/m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Solar cell material properties. Figure 2: Component of the integration of a circularly polarized microstrip slot antenna with a dye-sensitized solar cell. multi-layer dielectric plates, where each layer of the dielectric plate is a lossy medium, their relative dielectric constant is \(\varepsilon_{\rm ri}\), the thickness of each covering layer is \(\rm h_{i}\) and the permeability of each layer of the medium is \(\rm\mu_{0}\). According to reference [23], the analytical calculation formula of spectral domain Green's functions of the electric field on the antenna surface can be obtained as follows:  
\[\rm\widetilde{G}_{xxi}(k_{x},k_{y})=k_{0}\eta_{0}[B^{h}k_{y}^{2}/k_{t}^{2}+B^{e} k_{x}^{2}/k_{t}^{2}] \tag{3}\]  
\[\rm\widetilde{G}_{xyi}(k_{x},k_{y})=k_{0}\eta_{0}k_{x}k_{y}/k_{t}^{2}[B^{e}-B^ {h}] \tag{4}\]  
\[\rm\widetilde{G}_{yyxi}(k_{x},k_{y})=\rm\widetilde{G}_{xyi}(k_{x},k_{y}) \tag{5}\]  
\[\rm\widetilde{G}_{yyi}(k_{x},k_{y})=k_{0}\eta_{0}[B^{h}k_{x}^{2}/k_{t}^{2}+B^ {e}k_{y}^{2}/k_{t}^{2}] \tag{6}\]  
\[\rm\widetilde{G}_{xxi}(k_{x},k_{y})=jk_{0}\eta_{0}B^{e}k_{x}/\gamma^{2} \tag{7}\]  
\[\rm\widetilde{G}_{yzi}(k_{x},k_{y})=(k_{y}/k_{x})\rm\widetilde{G}_{xzi}(k_{x},k_{y}) \tag{8}\]  
where:  
\[B^{h}=(A^{h}_{11}+A^{h}_{21})/U^{h} \tag{9}\]  
\[\rm\left[ \begin{array}{cc}(A^{h}_{11})&(A^{h}_{12})\\ (A^{h}_{21})&(A^{h}_{22})\end{array} \right]=\prod_{i=1}^{N}\frac{1}{1+R^{h}_{i }}\left[ \begin{array}{cc}\rm e^{j_{i}\gamma_{i}h_{i}}&R^{h}_{i}e^{j_{i}h_{ i}}\\ \rm R^{h}_{i}e^{-j_{i}\gamma_{i}h_{i}}&e^{-j_{i}h_{i}}\end{array}