# Zero Energy IoT Devices in Smart Cities Using RF Energy Harvesting
## 3 Materials and Methods
### Testbeds Studies
#### 3.3.6 Optimal Points/Area for Sensor Devices  
When the charger is at point 1, the theta is 60 degrees, and the maximum distance is dependent on the charger to send the signal, as Powercast 35903 has a range of 80 feet, so when the charger transmits the energy in a circular form, as shown in Figure 3, the points are 1 foot from each other. This means that the lines are uniform, and one foot away, they intersect the circle (see Figure 4). At point 2 when the transmitter transmits the energy, it intersects the previous lines at any point, as shown in Figure 4, and we want to find the intersection points. Let lines intersect each other at points \(\mathrm{p_{s1}}\) and \(\mathrm{p_{s2}}\) then we can find the location of intersection points by the intersection formula. In the end, we can obtain the desired intersection points. The area between these intersection points is called the optimal area, and the points are optimal points to place the charging devices. We have presented two algorithms for our solution. Algorithm 1 is designed by keeping the dipole antenna range in mind, and Algorithm 2 is designed by keeping the patch antenna range in mind. Our main purpose is to find the optimal charger placement  
Figure 4: Optimal Points Algorithm Phases. Figure 3: Circular Charger Placement. points and optimal points for sensor placement by keeping in mind the constraints of the transmitter at 60 degrees. IP refers to intersection points by inscribed angles (IA), while 120\({}^{\circ}\) + \(\varepsilon\) is the angle of the patch antenna with some area of the charger because we have observed that the patch range is 120 degrees but also that it can take some benefits from the charger range to sense a large area. ```
Input Set of Sensor v\({}_{\text{k}}\) ={1,2,3..}, Charger Points M\({}_{\text{kp}}\) = {M\({}_{\text{k1}}\) M\({}_{\text{k2}}\), M\({}_{\text{k3}}\),...,360\({}^{0}\)},  Distance d\({}_{\text{k}}\) = {1,2, M\({}_{\text{k}}\)\({}^{\text{r}}\)}, Tx value Output Output Points/area for charger tour, IA, \(\theta\), IP
1. For every point M\({}_{\text{M}i}\)\(\in\) M\({}_{\text{kp}}\)
2. IP = \(\phi\), \(\theta\) = \(\phi\), AT = \(\phi\)
3. If P\({}_{\text{K}i}\)\(\
eq\)\(\phi\)then
4. Select the P\({}_{\text{K}1}\) point for mobile charger. 5. AT \(\leftarrow\) An inscribed triangle start from point P\({}_{\text{K}1}\) with d\({}_{\text{k}}\) = 1 ft
6. \(\Theta\) = as Equation (13)
7. Start Moving of charger from point P\({}_{\text{K}1}\) to P\({}_{\text{K}i}\)
8. Add AT
9. \(\Theta\) = as Equation (13)
10. IP = as Equation (16)
11. Repeat
12. Select IP
13. Until P\({}_{\text{K}i}\)\(\leq\) 360
14. Return IP, P\({}_{\text{K}i}\)
15. end If
```  
**Algorithm 1**Charger Placement Strategy for Dipole antenna. ```
Input Set of Sensor v\({}_{\text{k}}\) ={1,2,3..}, Charger Points M\({}_{\text{kp}}\) = {M\({}_{\text{k1}}\) M\({}_{\text{k2}}\), M\({}_{\text{k3}}\),...,122\({}^{0}\)},  Distance d\({}_{\text{k}}\) = {1,2, M\({}_{\text{k}}\)\({}^{\text{r}}\)}, Tx value Output Optimal Points/area for charger tour, IA, \(\theta\), IP
1. For every point M\({}_{\text{M}i}\)\(\in\) M\({}_{\text{kp}}\)
2. IP = \(\phi\), \(\theta\) = \(\phi\), AT = \(\phi\)
3. If P\({}_{\text{K}i}\)\(\
eq\)\(\phi\)then
4. Select the P\({}_{\text{K}1}\) point for mobile charger. 5. AT \(\leftarrow\) An inscribed triangle start from point P\({}_{\text{K}1}\) with d\({}_{\text{k}}\) = 1 ft
6. \(\Theta\) = as Equation (14)
7. Start Moving of charger from point P\({}_{\text{K}1}\) to P\({}_{\text{K}i}\)
8. Add AT
9. \(\Theta\) = as Equation (14)
10. IP = as Equation (16)
11. Repeat
12. Select IP
13. Until P\({}_{\text{K}i}\)\(\leq\) 120\({}^{0}\) + \(\varepsilon\)
14. Return IP, P\({}_{\text{K}i}\)
15. end If
```  
**Algorithm 2**Charger Placement Strategy for Patch Antenna.