# A Quad-Band RF Circuit for Enhancement of Energy Harvesting
## 5 Simulation Results and Discussion  
S-parameters (\(S_{11}\)) for the frequencies GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45 bands are shown in Figure 10. Excellent matching can be noticed from this figure, a very small \(S_{11}\) is found. Therefore, in light of S-parameters, the obtained RF-DC conversion efficiency has high values, as presented in Figure 11. The RF-DC conversion efficiency (\(\eta\)) can be calculated as follows:  
Figure 9: Improved quad-band circuit with the four series resistors. \[\eta(\%)=\frac{P_{out}(DC)}{P_{in}(RFpower)}\times 100=\left(\frac{V_{out}^{2}}{R_{L }}\times\frac{1}{P_{in}}\right)\times 100 \tag{34}\]  
where \(P_{out}\) is the harvested DC power across the load resistor. From Figure 11, maximum efficiencies of 82.345% at 6 dBm, 78.165% at 8 dBm, 75.72% at 8 dBm, and 74.622% at 9 dBm were obtained for the GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45 bands, respectively. The output voltage was 1.489 V, 1.276 V, 1.22 V, and 1.163 V, respectively, for the mentioned bands at 0 dBm. The highest output voltage obtained at 20 dBm for the Wi-Fi 2.45 band was 3.579. For the first scenario of the quad-band circuit with a single receiving antenna, Figure 12 shows S-parameters for the four bands. Figures 13 and 14 illustrate RF-DC conversion efficiency and output voltage versus the input frequency under the input power of 0 dBm. For this scenario, the recorded results for the RF-DC conversion efficiency and output voltage are presented in Table 2. The highest value for the output voltage that could be received was 3.648 V at the Wi-Fi 2.45 band under input power of +20 dBm for the first scenario. Figure 10: S-parameters for each single-band. (**a**) GSM-900. (**b**) GSM-1800. (**c**) UMTS-2100. (**d**) Wi-Fi 2.45. Figure 11: RF-DC conversion efficiency vs. the applied input power level at each single-band for the load of 5 k\(\Omega\). (**a**) GSM-900. (**b**) GSM-1800. (**c**) UMTS-2100. (**d**) Wi-Fi 2.45. Figure 12: S-parameters of the proposed quad-band circuit with a single receiving antenna. Figure 15 shows S-parameters vs. frequency regarding the proposed quad-band circuit with four receiving antennas as the second proposed scenario. It can be observed that the reflected power is as follows: \(-30\) dB, \(-24.5\) dB, \(-3.5\), and \(-30\) dB at the bands GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45, respectively. Figures 16 and 17, and Table 3 depict the conversion efficiency and output voltage vs. the second scenario's input frequency \begin{table}
\begin{tabular}{l c c} \hline \hline
**Frequency** & **RF-DC Conversion Efficiency (\%)** & **Output Voltage (V)** \\ \hline GSM-900 & 74.846 & 1.662 \\ GSM-1800 & 66.974 & 1.422 \\ UMTS-2100 & 64.486 & 1.333 \\ Wi-Fi 2.45 & 61.407 & 1.587 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Recorded results for the first scenario under 0 dBm. Figure 13: RF-DC conversion efficiency vs. the input frequency of the proposed quad-band circuit with a single receiving antenna for the load of 5 k\(\Omega\). for the input power of 0 dBm. The maximum output voltage of 3.66 V was noticed under input power of 20 dBm at the Wi-Fi 2.45 band for this scenario. Figure 16: RF-DC conversion efficiency vs. the input frequency of the proposed quad-band circuit with four receiving antennas for the load of 5 k\(\Omega\). Figure 15: S-parameters of the proposed quad-band circuit with four receiving antennas. (**a**) GSM-900. (**b**) GSM-1800. (**c**) UMTS-2100. (**d**) Wi-Fi 2.45. The output voltage of each channel is illustrated in Figures 18 and 19 under 0 and +10 dBm input powers at the case of connecting one channel and disconnecting the remaining channels. Under 0 dBm, the output voltage varied between 1.23 to 1.387, whereas it varied between 3.307 to 3.328 under +10 dBm.