# Efficient Wireless Charger Deployment for Wireless Reshapeable Sensor Networks
## 6 Experiments and Simulations  
### Experiments  
In this subsection, we show results of extensive experiments in indoor environments for modeling the RF charging efficiency (i.e., the received energy or received power). The devices used in the experiments are Powercast TX91501-3W-ID wireless charger [21] and P2110-EVAL-02 power harvester [22], as shown in Figure 13. The former is a wireless charger with a patch directional antenna with 8 dBi gain and 60\({}^{\circ}\) beamwidth in both horizontal and vertical directions. It is a 915 MHz transmitter with 3 Watts equivalent isotropically radiated power (EIRP). The latter is a power harvester with a dipole omni-directional antenna with 1 dBi gain. It can harvest energy from RF waves, provide intermittent/pulsed power output up to 4.21 V, and connect to rechargeable batteries. Figure 12: Illustration of two circles both of the radius \(r\) intersecting at two points \(a\) and \(b\). As shown in Figure 14, a wireless charger and a power harvester are set up. The distance \(D\) between the two devices is set to be 0.5 m, 1.0 m, \(\dots\), or 4.5 m for experiments. As shown in Figure 15, the orientation of the charger's patch antenna is specified by two angles, the horizontal angle (azimuth) \(\Phi\) and the vertical angle (elevation) \(\theta\). Either angle is set to be \(0^{\circ}\), \(15^{\circ}\), \(\dots\), or \(90^{\circ}\). Figure 16 illustrates the distance and the angle settings. In Figure 16, the charger is assumed to be at the origin and the harvester is assume to be on the \(x\)-axis and be \(D\) apart from the charger. Moreover, the charger's antenna direction is indicated by vector \(\overset{\rightharpoonup}{N}\) with the horizontal angle \(\Phi\) and the vertical angle \(\theta\) relative to the \(x\)-axis. By a multimeter, we measure the voltage (\(V\)) and current (\(I\)) of the output of the harvester 10 times for every distance \(D\) = 0.5 m, 1.0 m,..., and 4.5 m, every horizontal angle \(\Phi\) = 0\({}^{\circ}\), 15\({}^{\circ}\),..., and 90\({}^{\circ}\), and every vertical angle \(\theta\) = 0\({}^{\circ}\), 15\({}^{\circ}\),..., and 90\({}^{\circ}\). We average the measured data and then apply the average data to derive the received power (i.e., received energy). Table 1 (respectively, Table 2) shows the experimental results of the received power in the unit of mW for different distances and horizontal (respectively, vertical) angles with the vertical (respectively, horizontal) angle is 0. Note that 0.01 V and 0.01 mA are the smallest measurable voltage and current, respectively. Therefore, the voltage values smaller than 0.01 V or the current value smaller than 0.01 mA are not measurable and such cases lead to \"not available\" (i.e., \"-\") symbols shown in the Tables. By experimental data in Table 1, Table 2 and the specification [13] stating that the charger has a beamwidth of 60\({}^{\circ}\) in both horizontal and vertical directions, we model the charging space of a wireless charger as a cone with the opening angle of 60\({}^{\circ}\) and the generatrix length of \(D\). We perform power regression on the data to obtain an exponential function taking \(D\) as the independent variable (i.e., \(x\)) and \(P\) as the dependent variable (i.e., \(y\)) for every vertical and horizontal angle of 0\({}^{\circ}\), 15 \begin{table}
\begin{tabular}{c c c c c c c} \hline \(D\backslash\Theta\) & **0\({}^{\circ}\)** & **15\({}^{\circ}\)** & **30\({}^{\circ}\)** & **45\({}^{\circ}\)** & **60\({}^{\circ}\)** & **75\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline
0.5 m & 17.63 & 13.52 & 9.07 & 5.55 & 2.78 & 0.92 & 0.26 \\
1.0 m & 6.3 & 5.23 & 2.65 & 1.26 & 0.79 & 0.41 & - \\
1.5 m & 1.93 & 1.52 & 1.02 & 0.56 & 0.29 & - & - \\
2.0 m & 1.39 & 0.95 & 0.87 & 0.34 & 0.18 & - & - \\
2.5 m & 0.84 & 0.61 & 0.76 & 0.28 & - & - & - \\
3.0 m & 0.47 & 0.42 & 0.36 & 0.15 & - & - & - \\
3.5 m & 0.28 & 0.21 & 0.19 & - & - & - & - \\
4.0 m & 0.21 & 0.14 & - & - & - & - & - \\
4.5 m & 0.14 & 0.12 & - & - & - & - & - \\ \hline \end{tabular}
\end{table}