# RF Energy Harvesting
## 5 Estimated Power Available in the Harvester from LTE Base Stations  
Equation (5) presented above can be used to calculate the power available to a receiver in a field generated by an LTE base station. The following devices have been selected as reference devices to assume the parameters of the wireless channel. The parameters of the LTE 800 MHz band are: an Ericsson 1001 1 L 0 M 2.3 m antenna is selected as a reference for source simulation purposes. It has a gain of up to 20.5 dBi according to its data sheet [24]. A 38 dBm transmitter power in accordance with the 3 GPP documentation TS 136.104 is assumed [25]. The parameters of a Signaflex THUNDER antenna are taken to simulate the receiver. It has a gain equal to 20 dBi [26]. The above configuration gives the power available at the receiving antenna as ca. 21 dBm according to Equation (5) at a distance of 20 m, which gives approximately 1.83 V at the output of the antenna when loaded with characteristic impedance. More detailed calculations are given in Table 1.  
A range of 20 m around the source of the beam seems to give satisfying conditions for rectifier construction; however, such a distance is problematic in practise. Definitely more realistic are distances of dozens of meters and an induced voltage of fractions of 1 V, which leads to more advanced difficulties for designing the harvester. The basic issue is that the most popular elements of rectifiers, Schottky diodes, consume some amount of voltage. Therefore, some solutions are needed to increase the voltage.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Distance [m]** & **Receiving Power [dBm]** & **Receiving Voltage [V]** \\ \hline
10 & 27.99 & 3.66 \\
15 & 23.77 & 2.44 \\
20 & 21.27 & 1.83 \\
50 & 13.31 & 0.73 \\
100 & 7.28 & 0.37 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution of power available at the receiver antenna (gain = 20 dBi) vs. the distance from the sending antenna (gain = 20.5 dBi) for 868 MHz (\(\lambda=35\) cm) frequency band and emitted power equal to 38 dBm. Impedance of the antennas: 50 \(\Omega\).  
A popular method involves an L-type circuit with a capacitor and a coil. Both elements, if ideal, do not consume energy, so they seem to be perfect for mediation in energy transfer. When there is a need to increase the voltage during a transfer, series LC resonance is helpful.  
The power received by the load is equal to: \(P_{R_{load}}=V_{R_{load}}^{2}/R_{load}\). The maximum value of the transferred power determines (2). So, the optimum case describes the condition (7).  
\[\frac{V_{ant}^{2}}{4\cdot R_{ant}}=\frac{V_{R_{load}}^{2}}{R_{load}} \tag{7}\]  
Hence, the Formula (8) shows a relation between the voltage gain \(k_{u}=V_{R_{load}}/V_{ant}\) of the circuit and the resistances \(R_{load}\) and \(R_{ant}\):  
\[k_{u}=\frac{V_{R_{load}}}{V_{ant}}=\sqrt{\frac{R_{load}}{4\cdot R_{ant}}}= \frac{1}{2}\cdot\sqrt{\frac{R_{load}}{R_{ant}}}, \tag{8}\]  
which assures keeping the maximal transfer of energy. The efficiency of the circuit \(\eta\) (9)--denoted as the maximum possible power to transfer from the antenna \(P_{ant}\) (2) to the power received by the load \(P_{load}\)--is:  
\[\eta=\frac{P_{load}}{P_{ant}}\cdot 100\%, \tag{9}\]  
and in this case, it is equal to 100 %.