# A Quad-Band RF Circuit for Enhancement of Energy Harvesting
## 3 System Modeling  
The output voltage is one of the critical parameters in electronic circuits, especially in energy harvesting circuits. However, the generated output voltage in RF energy harvesting systems is tiny, mainly in using traditional rectifiers. As presented in [59], the output voltage (\(V_{out}\)) range was reported between 0.38 to 0.75 V. Small value of the output voltage, such as 0.75 V, is insufficient to meet the practical applications' needs to power up electronic devices. Hence, the voltage doubler circuits are the optimal way for RF energy harvesting applications to overcome the generated output voltage's limited values. The voltage doubler serves as a rectifier circuit to convert the alternative current (AC) signal into DC power. Furthermore, it multiplies the input signal's voltage thanks to the doubler's capacitors. For instance, the output voltage is twice of the input voltage (\(V_{in}\)), i.e., \(V_{out}=2V_{in}\) in the voltage doubler. However, we should consider that increasing the number of the voltage doubler stages reduces the generated output power, which is not favorable in RF energy harvesting systems. Besides the above-mentioned, it should be noted that the voltage doubler does not increase the output power since the output power totally depends upon the receiving antenna. In this model, a single-stage voltage doubler was connected to an RF source. The applied input power level (\(P_{in}\)) varied between \(-20\) dBm to \(+10\) dBm, whereas the frequency was extended between 0.5 GHz to 2.5 GHz. The equivalent circuit of the single-stage voltage doubler is shown in Figure 1. In this circuit, \(C_{\text{$\text{$\text{$\text{$\text{$\text{$\text{$\text{$\text{$ \text{$\text{$\text{$\text{$\text{$\text{$}}$}$}$}$\text{$0}}}\), \(R_{\text{$\text{$1\text{$\text{$2\text{$\text{$3\text{$\text{$4\text{$\text{$5 \text{$\text{$6\text{$\text{$7\text{$\text{$8\text{$\text{$9}}}}$\text{$0}$\text{$1}}}\), and \(R_{\text{$\text{$2\text{$\text{$3\text{$\text{$4\text{$\text{$5\text{$\text{$6 \text{$\text{$7\text{$\text{$8\text{$\text{$9\text{$\text{$0}}}$\text{$1}$\text{$2}}}$\text{$3\text{$\text{$4\text{$\text{$5\text{$\text{$6\text{$\text{$7\text{$\text{$8\text{$\text{$9\text{$\text{$0\text{$\text{$1\text{$\text{$2}}}$\text{$3}$\text{$4}}}}}}}$\text{$5}}\), \(R_{\text{$\text{$6\text{$\text{$7\text{$\text{$8\text{$\text{$9\text{$ \text{$0 \text{$ \text{$1\text{$ \text{$2\text{$ \text{$3\text{$ \text{$4\text{$ \text{$5}}}}$ \text{$6}}}}}}}}$ \text{$7}}\), and \(R_{\text{$ \text{$8\text{$ \text{$9\text{$\text{$0\text{$\text{$1\text{$\text{$2\text{ $\text{$3\text{$\text{$4\text{$\text{$5\text{$\text{$6\text{$\text{$7 $\text{$8}$\text{$9}}$}}}\), are the diode junction capacitance, the series resistance, and the internal diode junction resistance, respectively of the second diode (\(D_{2}\)) in the same circuit. The two diodes' parameters are the same since the two diodes belong to the same model, HSMS-2852. Assuming that the wave has an amplitude (\(V_{Max}\)), and frequency (F) is applied to the voltage doubler circuit in $\text{$0 This figure also depicts a single cycle of the applied RF wave to the voltage doubler. Based on the diode theory with the threshold voltage (\(V_{th}\)) and according to the single cycle of the applied RF wave in this figure, it can be concluded that there are two operation states in the circuit. The first case when \(D_{1}\) is forward biased and then switched-on during the period (\(t_{1}\): \(t_{2}\)) of the negative half while the other diode \(D_{2}\) is reverse biased and switched-off. During the positive half at (\(t_{3}\): \(t_{4}\)) the situation is changed so \(D_{1}\) becomes switched-off while \(D_{2}\) goes to be forward biased and switched-on. The circuit impedance at this condition is mentioned as (\(Z_{in,F}\)). The second case covers the rest periods of the cycle since both the diodes are reverse biased and switched-off. In this state, the circuit impedance is indicated by (\(Z_{in,R}\)).