# A Power Processing Circuit for Indoor Wi-Fi Energy Harvesting for Ultra-Low Power Wireless Sensors
## 3 Analytical Analysis
### Rectifier Circuit Impedance Analysis  
For the bridgeless rectification, Schottky diode is preferred as the component for the rectification operation. The diode has a very fast switching action and activates with a low forward bias voltage. The illustration in Figure 5 shows the diode in a series configuration with a source \(V_{ac}\) and load. The source has an internal resistance \(R_{g}\), and the load consists of a resistor \(R_{L}\) in parallel with a capacitor \(C_{L}\).  
The rectifier input impedance can be calculated by applying circuit analysis for the given diode model employing commercially available software. For the analysis, the value of the load capacitor, \(C_{L}\) is assumed to be sufficiently large \((C_{L}\geq 0.1\)\(\mu\)F) for the frequency range between 0.1 GHz to 2.5 GHz. Hence, the load is assumed to be in short circuit condition. Table 2 lists different diode parameters that could be uses for simulating the diode performance for some commercially available Schottky diodes. Parameter \(n\) is the emission coefficient of the diode. The type of Schottky diode used in the proposed circuit is SMS7621 from SKYWORKS (Woburn, MA, USA).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Diode** & \(L_{\textit{fp}}\) **(nI)** & \(C_{\textit{f}}\) **(pP)** & \(C_{\textit{p}}\) **(pP)** & \(R_{\textit{s}}\) **(I)** & \(I_{\textit{s}}\) **(\(\mu\)A)** & \(n\) \\ \hline HSMS2850 & 0.4 & 0.18 & 0.09 & 25 & 3 & 1.06 \\ HSMS2860 & 0.4 & 0.18 & 0.09 & 6 & 0.05 & 1.08 \\ HBAT5400 & 2 & 3.0 & 0.08 & 2.4 & 0.1 & 1.00 \\ SMS7621 & 0.2 & 0.1 & 0.05 & 12 & 0.04 & 1.05 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters of Schottky diode.  
Figure 5: A series configuration with a source and load of a diode circuit model.  
As labelled in Figure 4, the input voltage \(V_{ac}\) follows from the relation between generator voltage and available incident power \(P_{inc}\). The input impedance for a different commercially Schottky diode is depicted in Figure 6. In the figure, the simulation result of the real and imaginary parts of the input impedance as a function of available power \(P_{inc}\) for the frequency of 2.45 GHz is illustrated. The figure demonstrates that the input impedance satisfies the conditions for high sensitivity and RF-to-DC power conversion as required by Equation (11). From the simulation, it has been found that the real part of the input impedance for the selected Schottky diode is low, and the imaginary part absolute value for all types of diodes is high except for the HBAT5400. The highest imaginary part value shown in the figure is for the SMS7621 diode. The input impedance of the rectifier/switching circuit is also simulated with different frequencies, as seen in Figure 7 the impedance real value is at a constant value throughout the simulated frequencies at 6.4 Ohm. The imaginary value is gradually increasing as the frequencies move closer to 3 GHz. In short, the simulation results demonstrate that the rectifier/switching circuit satisfies the requirements for obtaining a high sensitivity circuit.  
Figure 6: Radio frequency (RF) input impedance versus \(P_{inc}\) at \(f\) = 2.45 GHz for some commercially Schottky diodes.  
Figure 7: The input impedance of the rectifier/switching circuit versus frequencies.