# A Quad-Band RF Circuit for Enhancement of Energy Harvesting
## 5 Simulation Results and Discussion
The output Voltage across all branches (\(V^{\prime}_{Out}\)) for the improved circuit in Figure 9 can be calculated according to [PERSON]'s theorem [77] as shown below:  
\[V^{\prime}_{Out}=\frac{\frac{V_{Branch1}}{R_{1}}+\frac{V_{Branch2}}{R_{2}}+ \frac{V_{Branch3}}{R_{3}}+\frac{V_{Branch4}}{R_{4}}+\frac{V_{Branch4}}{R_{L}}} {\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}+\frac{1}{R_{ L}}}, \tag{35}\]  
where \(V_{Branch1},V_{Branch2},V_{Branch3}\) and \(V_{Branch4}\) are the output voltage of the four channels of GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45, respectively. Applying Equation (35) to the case of 0 dBm input power, the expected output Voltage (\(V^{\prime}_{Out}\)) is 1.27 V. For the +10 dBm power level's variations, \(V^{\prime}_{Out}\) is expected to be 3.32 volt. The proposed modification to the quad-band circuit has little effect on the RF-DC conversion efficiency which is clearly illustrated in Figure 20. The peak efficiency of 70.4% was obtained at the 900 MHz band under 0 dBm power. Figure 17: Output voltage of the proposed quad-band circuit with four receiving antennas for the load of 5 k\(\Omega\). \begin{table}
\begin{tabular}{l c c} \hline \hline
**Frequency** & **RF-DC Conversion Efficiency (\%)** & **Output Voltage (V)** \\ \hline GSM-900 & 71.194 & 1.373 \\ GSM-1800 & 64.944 & 1.421 \\ UMTS-2100 & 62.363 & 1.594 \\ Wi-Fi 2.45 & 65.096 & 1.896 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Recorded results for the second scenario under 0 dBm. The results are summarized by Figures 21-23. Figure 21 shows the maximum received output voltage, output power, and conversion efficiency for the single four bands. Figure 22 describes the maximum received output power at single-band, dual-band, triple-band, and quad-band. Finally, the peak received conversion efficiency at single-band, dual-band, triple-band, and quad-band are depicted in Figure 23. Considering Figure 22, it can be observed clearly concerning the importance of the multi-band concept. In this work, 0.443 mW, 0.8 mW, 1.45 mW, and 2 mW are the highest DC power levels were harvested at the circuits of single-band, dual-band, triple-band, and quad-band, respectively, at the input power of 0 dBm. To study the effect of load variation on the RF-DC conversion efficiency, a range for the load varied between 1 k\(\Omega\) to 50 k\(\Omega\) was applied and simulated at three input power levels of \(-\)10 dBm, 0 dBm, and +10 dBm, respectively. The relevant results for this parameter are illustrated in Figure 24, which introduced conversion efficiency (\(\eta\)) greater than 40% under - 10 dBm at the range of 5 k\(\Omega\) to 50 k\(\Omega\), \(\eta>70\%\) under 0 dBm at the range of 5 k\(\Omega\) to 35 k\(\Omega\), and \(\eta>70\%\) under +10 dBm at the range of 1 k\(\Omega\) to 15 k\(\Omega\). However, 54.953%, 78.866%, and 78.527% were the optimal values that received at 15 k\(\Omega\), 20 k\(\Omega\), 5 k\(\Omega\) under input power levels of \(-\)10 dBm, 0 dBm, +10 dBm, respectively. Finally, Table 4 shows the results of this work compared to related published results. Figure 18: Output voltage of each channel under 0 dBm input power. (**a**) GSM-900. (**b**) GSM-1800. (**c**) UMTS-2100. (**d**) Wi-Fi 2.45. Figure 19: Output voltage of each channel under + 10 dBm input power. (**a**) GSM-900. (**b**) GSM-1800. (**c**) UMTS-2100. (**d**) Wi-Fi 2.45. Figure 20: RF-DC conversion efficiency vs. the input frequency of the improved quad-band circuit with four receiving antennas based on [PERSON]’s theorem for the load of 5 k\(\Omega\). Figure 23: A chart for the conversion efficiency for single band, dual band, triple band and quad band. Figure 21: A chart for the output voltage, output power, and conversion efficiency. Figure 22: A chart for the output power for single band, dual band, triple band and quad band. Based on the number of the utilized frequency bands, the proposed work harvests the number of bands more than the published results [3; 52; 55; 57; 58; 59; 61; 69; 74; 78].