## 3 Rectifier Design  
The rectifying circuit is an important part of the rectenna since it directly determines the performance of the rectenna. A good rectifier must have good power processing capacity. Generally, a rectifying circuit is composed of an impedance matching network, rectifying element (Schottky diode), and a DC-pass filter for smoothing waveform and the load. The full-wave voltage doubler rectifier is chosen mainly because it is simple and has a higher conversion efficiency than the traditional half-wave rectifier circuit in the application of 10 mW. Its efficiency compared with the traditional single series rectifier circuit is shown in Figure 10. The selection of diodes has a crucial impact on the performance of the rectifier since they bring the main loss. High series resistance (\(\mathrm{R_{S}}\)) and zero bias junction capacitance (\(\mathrm{C_{jo}}\)) of diodes will reduce conversion efficiency [1], while the reverse breakdown voltage (\(\mathrm{V_{br}}\)) of diodes will limit the maximum rectified power. Table 1 compares the important parameters of several commercial rectifying diodes. Finally, the HSMS2860 Schottky diode is selected, which has high voltage sensitivity at low input power. Figure 10: Conversion efficiency comparison between single series diode rectifier and full-wave voltage doubler rectifier. Figure 9: Simulated and measured gain of the proposed DRA array. The rectifier at the operating frequency is designed and optimized. For 10 mW applications, harmonic balance (HB) in ADS software is used for simulation. The final design is shown in Figure 11.  
The proposed rectifier is built on a Rogers 5880 dielectric substrate (h = 0.254, \(\varepsilon\) = 2.2, \(\delta\) = 0.0009). The capacitance value of the two capacitors is 100 nF. It is worth noting that for the rectifier circuit design, the impedance matching network can directly affect the performance of the rectifier circuit. In order to achieve good impedance matching in dual-band, a new type of impedance regulation stub (IRS) is proposed, as shown in Figure 12. The proposed IRS directly converts the impedance of the full-wave voltage doubler rectifier into a value that easily achieves dual-band impedance matching. The detailed impact of a matching network and IRS on RF-DC conversion efficiency has been simulated in Figure 13. It shows the following: Efficiency (00): the conversion efficiency of the rectifier when neither the matching network nor the IRS exist; Efficiency (10): conversion efficiency of the rectifier when only the matching network exists; Efficiency (01): conversion efficiency of the rectifier when only the IRS exists; Efficiency (11): conversion efficiency of the rectifier when both the matching network and the IRS exist. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Schottky Diode Model** & \(R_{S}\) **(\(\Omega\))** & \(V_{br}\) **(V)** & \(C_{j}\) **(pF)** \\ \hline SMS7630 & 20 & 2 & 0.14 \\ HSMS2820 & 7.8 & 26.7 & 0.65 \\ HSMS2850 & 25 & 3.8 & 0.18 \\ HSMS2860 & 6 & 7 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of several commercial Schottky diodes. The proposed rectifier is fabricated and it is shown in Figure 14. The conversion efficiency measurement setup is displayed in Figure 15. The power source is a 2-6 GHz signal generator; a multimeter is utilized to measure the \(DC\) voltage across the load, and the efficiency is calculated as:  
\[\eta=\frac{{{V_{DC}}^{2}}}{{{R_{L}}{P_{r}}}}\times 100\%, \tag{1}\]  
Figure 14: Fabrication of the proposed rectifier. Figure 13: The detailed impact in the four cases on conversion efficiency. Figure 15: Conversion efficiency measurement setups. Where V\({}_{\text{DC}}\) is the DC voltage across the load, R\({}_{\text{L}}\) is the load resistance value, and P\({}_{\text{r}}\) is the RF input power. The load resistance is 2 K\(\Omega\) since it is suitable for many small wireless devices. The input power level is selected as 10 dBm due to the good performance at this input level for signals of two frequencies in the simulation.