## 3 Technical Background  
Over the years, research on enabling the battery aided electrical devices to consume less power for their operation and making them to be small have called for new sources of energy to recharge the battery. In this context, recently, RF has been viewed as the main source of energy to charge the batteries residing in electrical devices. Consequently, wireless charging has gained widespread research attention both in academia and industry communities. One of the commercially present evaluation kits that allows wireless energy transmission is the Powercast kit. Powercast P2100 uses radio frequency transmission and its transmitter comprises of an oscillator and an antenna, both operating at 915 MHz. The intensity of the wave decreases as a function of distance and as the wave reaches the receiver side it is collected by the antenna and the RF energy is translated to DC power, which is then used to charge the capacitor until a threshold voltage is reached. Following this, the voltage booster and voltage monitor circuits yield an output pulse. The general process of energy harvesting process is depicted in Figure 1[29]. In order to understand the theoretical background pertaining RF-based wireless charging technology, it is fundamental to realize first how energy is transferred from the transmitter, propagated into the space, and received by the receiving antenna. Therefore, a technical summary about the wave propagation concept is provided. At the transmitter side, considering an isotropic antenna that emits the electromagnetic wave in all directions, the power density measured in \(W/m^{2}\) (\(P_{d}\)) at a distance (\(d\)) from the radiating antenna is given by Equation (1)[30]:  
\[P_{d}=P_{t}\cdot G_{t}/4\pi\cdot d^{2} \tag{1}\]  
where \(P_{t}\) is the transmitter emitted power, and \(G_{t}\) is the antenna transmitter gain. The amount of received power \(Pr_{d}\) at the receiving antenna with an effective aperture (\(A_{e}\)) (\(m^{2}\)) is calculated using Equation (2):  
\[Pr_{d}=P_{d}\cdot A_{e}. \tag{2}\]  
Then, the received power \(Pr_{d}\) can be written as shown in Equation (3):  
\[Pr_{d}=\frac{P_{t}\cdot G_{t}\cdot A_{e}}{4\pi\cdot d^{2}}. \tag{3}\]  
Figure 1: Energy harvesting process simplified. Note, that the denominator of Equation (1) represents the area of a sphere of radius \(d\). The receiver antenna \(A_{e}\) is related to the antenna receiver gain (\(G_{r}\)) using Equation (4) [31]:  
\[G_{r}=\frac{4\pi\cdot A_{e}}{\left(\lambda\right)^{2}} \tag{4}\]  
where \(\lambda\) is the wavelength of the signal. Therefore, the amount of received (harvested) power (\(P_{r}\)) at the receiver antenna at distance \(d\) from the transmitter can be calculated theoretically by using Equation (5):  
\[P_{r}(d)=P_{r-f_{8}}(d)=P_{t}\cdot G_{t}\cdot G_{r}\cdot\lambda^{2}/(4\pi\cdot d )^{2}. \tag{5}\]  
This equation represents the simple free space (\(P_{r-f_{8}}(d)\)) wave propagation, which is well known as the Friis wireless transmission equation [12]. However, in the real world, the wireless signal is prone to more attenuation due to the surrounding environment, and hence, more advanced models have been proposed in the literature such as the two-ray model [32], where the received power \(P_{r-nf_{8}}\) is estimated using Equation (6) [32]:  
\[P_{r-nf_{8}}(d)=\frac{P_{t}G_{t}G_{r}(h_{t}h_{r})^{2}}{d^{4}} \tag{6}\]  
where \(h_{t},h_{r}\) are the transmitter and receiver antenna heights, respectively. Furthermore, it is important to use the suitable wireless propagation model to estimate the amount of the received energy at the receiver side.