# High-Efficiency Triple-Band RF-to-DC Rectifier Primary Design for RF Energy-Harvesting Systems
## 3 Results and Discussion  
The voltage-doubler input impedance for the dual-band design was computed using the S-parameters simulator of the Advanced Design System (ADS) software. The derived values before the impedance matching were \(11.42-j66.36\) and \(27.1-j65.4\) at 866 MHz \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Width/Length** \\ \hline TL11 & 3/39 \\ TL12 & 3/24.3 \\ TL13 & 3/25 \\ TL14 & 1/7.5 \\ TL15 & 48/18.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical dimensions of the microstrip lines for the impedance-matching network of Figure 5b: triple-band circuit (width/length values are expressed in mm). Figure 6: Basic topologies of two shunt combinations: (**a**) open-open; (**b**) open-shorted; (**c**) shorted-shorted. Figure 7: Flowchart for a typical genetic algorithm optimization. and 937 MHz, respectively. We considered a standard antenna port of 50 Ohm. The size of the impedance-matching circuits was optimized and adjusted to the input impedance of the overall system. The derived values after the impedance matching were \(44.3+j6.1\) and \(55.0+j8.5\) at the two frequencies of interest. To obtain the impedance matching of the overall system, a simple short-circuited stub was included, as depicted in Figure 5b. Additionally, the input impedance for the triple-band design was computed, and the derived values were \(53.48+j0.44\), \(48.81+j9.66\), and \(48.19-j1.6\) at 866 MHz, 948 MHz, and 2.423 GHz, respectively. Table 3 lists the previously mentioned input impedance values of the dual- and triple-band rectifier, with and without the impedance-matching network, at the frequencies of interest. We can derive that the percent deviation of the input impedance of the dual-band rectifying circuit, calculated using the gradient optimizer, was greater than 10%. Simultaneously, the percent deviation of the computed input impedance using genetic algorithm optimizer for the triple-band rectifying circuit was less than 7%. Figure 8 illustrates the S11 magnitude (reflection coefficient) of the proposed dual- and triple-band RF-to-DC rectifier versus frequency. From the presented graph, we can derive that the dual-band rectifying circuit operates satisfactorily in the European LoRaWAN frequency band (863-870 MHz), as well as in the GSM-900 mobile communication frequency band (880-960 MHz). The utilized rectifier has a dual-frequency operation (\(-21.89\) dB at 869 MHz and \(-20.87\) dB at 940 MHz) that falls into the previously mentioned frequency bands. It is also noteworthy that the \(-10\) dB bandwidth of the proposed rectifier extends to 121 MHz (846-967 MHz). Furthermore, we can observe that the triple-band rectifying circuit operates satisfactorily in the European LoRaWAN frequency band (863-870 MHz), the GSM-900 (880-960 MHz) mobile communication frequency band, and the WiFi 2.4 GHz wireless network frequency band. The proposed rectifier has a triple-frequency operation (\(-29.4\) dB at 866 MHz, \(-22.13\) dB at 948 MHz, and \(-32.75\) dB at 2.423 GHz) within the previously mentioned frequency bands. The \(-10\) dB bandwidth of the proposed rectifier in the three distinguished regions is 27 MHz (853-880 MHz), 29 MHz (933-962 MHz), and 33 MHz (2.406-2.439 GHz), respectively. We should also point out that, besides the third tuning operation achieved by the shunt stubs method along with the GA optimizer, the tuning operation in the first two frequency bands was improved by 7.51 dB and 1.96 dB, respectively.