## 4 Rectenna Performance  
### Rectenna Measurement  
The receiving antenna and rectifying circuit make up the rectifying antenna. \(P_{r}\) is the input power received by the antenna; \(P_{r}\) can be calculated by the Friis transmission equation:  
\[P_{r}=\left(\frac{\lambda}{4\pi r}\right)^{2}P_{t}G_{t}G_{r}, \tag{2}\]  
In this paper, \(\lambda\) is the wavelength of the operating frequency, \(r\) is the distance between the transmitting antenna and the proposed DRA array, \(P_{t}\) is the transmission power. \(G_{t}\) is the gain of the transmitting antenna, and \(G_{r}\) is the gain of the proposed DRA array. Figure 19 shows the conversion efficiency measurement setups of the proposed rectenna. The microwave power output from a signal generator is amplified by an amplifier with a gain of 42 dB. A broadband horn is used to transmit energy signals. The receiving antenna is at the distance r from the horn. The measurement procedure is as follows:  
1. Measuring the gain of the standard broadband horn antenna: a vector network analyzer is used to measure the insertion loss of the coaxial line which is used to connect the DRA array and the rectifier circuit in the experiment;
2. Add a 3 dB coupler behind the signal generator; one port is connected to the power probe, and the other port is connected to the broadband horn. On the premise of meeting the dual frequency far-field conditions, the distance between the broadband horn and the proposed DRA array is fixed as \(r\); measure the input power at the broadband horn;
3. The receiving power at 2.45 GHz and 5.8 GHz is calculated according to the Friis transmission equation;
4. The voltage across the load resistance is measured with a multimeter, and the efficiency of the rectenna is calculated.  
The measured results are given in Table 2. The conversion efficiency of the proposed rectenna reaches 47.7% at 2.45 GHz and 40.3% at 5.8 GHz. The results show that the proposed rectenna can efficiently harvest RF energy. Compared with the performance of the rectifier, the conversion efficiency decreases. This could be caused by two things. On one hand, due to the error of the power probe, there may be measurement error in the transmission power. On the other hand, the DRA array and rectifier circuit are integrated  
Figure 18: Measured conversion efficiency (load resistance is 2 K\(\Omega\)).  
on different dielectric substrates; the RF adapter connecting the proposed DRA array and the rectifier circuit have unavailable parasitic behavior.  
To highlight the advantages of the proposed design, a few up-to-date reported rectennas have been compared with the proposed rectenna in Table 3. The gain of our design at 5.8 GHz is superior. Thanks to the novel IRS-loaded impedance matching network, the RF-DC conversion efficiency of our rectifier is significantly higher than other dual-band designs. Furthermore, the DRA matches well with the rectifier, and we achieve a superior conversion efficiency of the rectenna. The rectenna has a good performance in reported letters, so it is a good solution for RF energy harvesting in practice.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**f (GHz)** & **\(G_{\mathbf{t}}\)(dBi)** & **\(G_{\mathbf{r}}\)(dBi)** & **\(r\)** & **\(V_{\mathbf{DC}}\)(V)** & **Efficiency (\%)** \\ \hline
2.45 & 9.6 & 5.5 & 2 & 3.09 & 47.7 \\
5.8 & 9.8 & 12.9 & 2 & 2.84 & 40.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measured results of the rectenna performance.  
Figure 19: The conversion efficiency measurement setups of the proposed rectenna.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Frequency (GHz)** & **Gain (dBi)** & **Maximum** & **Maximum** \\  & & & **Conversion** & **Conversion** \\
2.45 & 9.6 & 5.5 & 2 & 3.09 & 47.7 \\
5.8 & 9.8 & 12.9 & 2 & 2.84 & 40.3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the proposed rectenna and similar reported designs.