# Integration of Microstrip Slot Array Antenna with Dye-Sensitized Solar Cells
## 2 Integrated Design Array Antenna and Solar Cells
\right] \tag{10}\]  
\[\rm R^{h}_{i}=(\gamma_{i}-\gamma_{i-1})/(\gamma_{i}+\gamma_{i-1}) \tag{11}\]  
\[\rm R^{e}_{i}=(\varepsilon_{ri}\gamma_{i+1}-\varepsilon_{ri+1}\gamma_{i})/( \varepsilon_{ri}\gamma_{i+1}+\varepsilon_{ri+1}\gamma_{i}) \tag{12}\]  
\[\rm U^{h}=\left\{j\gamma\cot y(\gamma h)\rm\left[(A^{h}_{11})+(A^{h}_{21}) \right]-\gamma_{1}[(A^{h}_{11})-(A^{h}_{21})]\right\} \tag{13}\]  
\[\rm U^{e}=\left\{j(k^{2}_{0}\varepsilon_{r}/\gamma)cot y(\gamma h)\rm\left[(A^{e}_{11})+(A^{e}_{21}) \right]-(k^{2}_{0}\varepsilon_{r}/\gamma)\rm\left[(A^{e}_{11})+(A^{e}_{21}) \right]\right\} \tag{14}\]  
\[\rm\gamma=\sqrt{\varepsilon_{r}k^{2}_{0}-k^{2}_{t}} \tag{15}\]  
\[\rm\gamma_{i}=\sqrt{\varepsilon_{r}k^{2}_{0}-k^{2}_{t}} \tag{16}\]  
\[\rm k_{t}=\sqrt{k^{2}_{x}+k^{2}_{y}} \tag{17}\]  
Replace the superscript 'h' in Equations (9) and (10) with 'e' to obtain the expressions for each component of \(B^{e}\), \(A^{e}_{11}\), \(A^{e}_{12}\), \(A^{e}_{21}\) and \(A^{e}_{22}\). \(k_{0}\) is the free space wave number, and \(\eta_{0}\) is the free space wave impedance. Equations (3)-(8) are the new analytical calculation formulas for the spectral domain Green's function of the microstrip slot antenna structure covered by the multilayer dielectric. After obtaining the calculation formula of Green's function in the spectral domain, the solution of integral Equations (1) and (2) can be discussed, as below. Assuming that the coaxial probe is fed at point (\(\rm x_{p}\), \(\rm y_{p}\)) and there is a constant current \(\rm I_{0}\) on the probe, the formula for calculating the spectral domain of the current on the probe can be obtained as follows:  
\[\rm\widetilde{J}_{z}=I_{0}\exp[j(k_{x}x_{p}+k_{y}y_{p})] \tag{18}\]  
Let the unknown current on the antenna surface be:  
\[\rm\widetilde{J}_{s}(x,y)=J_{x}(x,y)\rm\widetilde{x}+J_{y}(x,y)\rm\widetilde{y} \tag{19}\]\(\rm J_{x}(x,y)\) and \(\rm J_{y}(x,y)\) are expanded by a set of basis functions, and then Fourier transform is used to obtain the spectral domain expression:  
\[\rm\widetilde{J}_{x}(k_{x},k_{y})=\rm\sum_{n=1}^{N_{x}}C_{xn}\rm\widetilde{J}_{xn }(k_{x},k_{y}) \tag{20}\]  
\[\rm R^{e}_{i}=(\varepsilon_{ri}\gamma_{i+1}-\varepsilon_{ri+1}\gamma_{i})/( \varepsilon_{ri}\gamma_{i+1}+\varepsilon_{ri+1}\gamma_{i}) \tag{12}\]0  
\(\rm\widetilde{J}_{xn}(k_{x},k_{y})\) and \(\rm\widetilde{J}_{yn}(k_{x},k_{y})\) in Equations (20) and (21) are the spectral domain expressions of the selected basis functions. By introducing Equations (18), (20) and (21) into Equations (1) and (2), the integral Equations (1) and (2) can be solved using the [PERSON] method to obtain the current coefficients \(\rm C_{xn}\) and \(\rm C_{yn}\). Then the relevant characteristic parameters of the antenna can be further calculated. The electromagnetic simulation software ANSYS HFSS is used to obtain the relevant electromagnetic parameters of the antenna [24]. The center frequency of the antenna is set to 5.8 GHz and the polarization mode is right-handed circular polarization. The microstrip slot antenna and the microstrip slot antenna integrated with dye-sensitized solar cell are simulated separately, and the related reflection coefficient and radiation efficiency are shown in \[\rm R^{e}_{i}=(\varepsilon_{ri}\gamma_{i+1}-\varepsilon_{ri+1}\gamma_{i})/( \varepsilon_{ri}\gamma_{i+1}+\varepsilon_{ri+1}\gamma_{i}) \tag{12}\]1 It can be seen that the solar cell has little influence on the impedance matching of the antenna, and the microstrip slot antenna integrated with dye-sensitized solar cell has an impedance bandwidth of 2.33 GHz, from 4.23 to 6.56 GHz. After the integration of the dye-sensitized solar cell, the radiation efficiency of the antenna decreases from 76.1% to 68.9% when the operation frequency is 5.8 GHz. The radiation efficiency of the antenna decreases slightly, which indicates that the dye-sensitized solar cell has little influence on the circular polarization radiation characteristics of the antenna.