## 4 RF Concepts and Principles
### Radio Frequency Energy Harvesting in the Far Field  
Antennas can receive EM energy in the form of RF signals, which can travel for several kilometers in the RF-EH far-field before being transformed to power by rectifier circuits [53]. The ambient far-field RF-EH and the dedicated far-field RF-EH are the far-field RF-EH [57].  
It is possible to charge a receiver's battery via a circular disk transmission model using an EM wave transmitter \(\mathrm{Tr_{s}}\) to transmit power to a receiver's \(\mathrm{R_{v}}\)s located within its charging range, \(\mathrm{R_{c}}\). The received power of omnidirectional antennas operating in free space varies inversely to \(\mathrm{d^{2}_{rt}}\), and it is assumed to be 0 when \(d_{rt}>\mathrm{R_{c}}\), where \(\mathrm{d_{rt}}\) is the distance between \(\mathrm{Tr_{s}}\) and \(\mathrm{R_{v}}\)s. The obtained power is provided by:  
\[P_{r}=P_{t}G_{t}G_{r}\bigg{(}\frac{\lambda}{4\pi d_{rt}}\bigg{)}^{2} \tag{1}\]  
where is the wavelength \(\lambda\), \(G_{r}\) is the sequential receiver gain, and \(P_{t}\)\(G_{t}\) is the power of the transmitted radio frequency signal multiplied by the linear transmitter gain. For lack of a better description, a transmitted power of 3 W will be received as 0.325 mW at a distance \(d_{rt}\) of 5 m for 0.328 m at 915 MHz and \(G_{r}\) = 3.98. The receiver converts the received power to a DC voltage and stores it in a capacitor after receiving the RF signal. As a result of the receiver, converter, and capacitor, a sensor equipped with these components can harvest energy and store it in a battery for later use. In practical terms, the amount of received power will be heavily influenced by the propagation properties of the environment [58]. A measure of power loss in space is free space path loss (FSPL), which is the loss of signal power during propagation in free space. For the far-field region, regarding the FSPL, PL is expressed as:  
\[P_{L}=\frac{P_{T}}{P_{R}}=\frac{\left(4\pi R\right)^{2}}{G_{T}G_{R}\lambda^{2} }=\frac{\left(4\pi fR\right)^{2}}{G_{T}G_{R}c^{2}}=\frac{4}{G_{T}G_{R}}{ \left(kR\right)^{2}} \tag{2}\]  
\[P_{L}=20\log_{10}(f)+20\log_{10}(R)+20\log_{10}\frac{4\pi}{c}-G_{T}-G_{R} \tag{3}\]  
where \(f\) is the frequency (MHz), \(R\) is the distance (km), and \(G_{T}\) and \(G_{R}\) are the gains (dBi).  
The Friis transmission and equivalent isotropically radiated power (EIRP) represent two crucial upper boundaries in the design of the RF-EH. Firstly, the available power at the antenna side should not ever go beyond the EIRP irrespective of the range. Secondly, when the power is determined at a distance, the power drops nearly below the power density of the Friis transmission except in distinctly reflective environments. The path loss is considered in the analysis to represent the power signal in the far-field region [59]. Although it is constantly available, radio waves pose a concern over the potential penetration of EMI/EMC through the human body, which the world health organization classifies as a potential risk [28; 60]. Nevertheless, RF-EH systems remain a reliable, robust, and feasible solution to address the increasing demands for low-powered devices for domestic and commercial purposes [61; 62; 63; 64].