# A Survey of NFC Sensors Based on Energy Harvesting for IoT Applications
## 2 NFC Energy Harvesting
### Tag Antenna Design Considerations  
In order not to decrease the voltage that reaches the IC, a matching network is not used in the tag (as it is in the reader) that will introduce a voltage divider. Several studies [32; 33] demonstrated that, for example, introducing a series capacitance for matching increases the backscattering modulated level but reduces the energy that reaches the IC. The tag design, therefore, consists of the design of the antenna and the adjustment of the tag resonance frequency with no matching network. From a system perspective, the analog RF performance of a batteryless transponder can be considered using a simplified equivalent circuit (shown in Figure 3b), where the IC chip is modeled as a parallel connection of a resistance (\(R_{IC}\)) and chip capacitances (\(C_{IC}\)). The tag's resonance frequency must be tuned to the central frequency of operation or slightly shifted to a higher frequency to avoid detuning caused by the presence of metallic materials or the reader's own loop. The tag's resonance frequency is approximately calculated using Equation (5). \[f_{r}=\frac{1}{2\pi}\sqrt{\frac{R_{IC}+R_{a}}{L_{a}\big{(}C_{IC}+C_{p}+C_{ tuning}\big{)}R_{IC}}}\approx\frac{1}{2\pi\sqrt{L_{a}\big{(}C_{IC}+C_{p}+C_{ tuning}\big{)}}}, \tag{5}\]  
where \(L_{a}\) is the tag's antenna inductance, \(C_{IC}\) is the internal IC capacitance, \(C_{p}\) is the layout parasitic capacitance (which includes the antenna capacitance and the parasitic capacitance due to the interconnections), and \(C_{tuning}\) is the capacitor used to adjust the resonance frequency to the operation frequency \(f_{c}\) (13.56 MHz). The antenna inductance, \(L_{a}\), can be calculated from compact analytical formulas [34], from numerical methods [35], or using full-wave electromagnetic simulators. The antenna losses are the result of conductor DC resistance, and the alternating current (AC) losses are due to the skin effect. Depending on the substrate material, additional (e.g., dielectric) losses may also be significant. Parasitic capacitance for planar loop coils is a function of the conductor area, the gap between turns, the dielectric substrate, and permittivity. This can generally be extracted from the antenna's resonance frequency. The losses in the dielectric are modeled with a resistance in parallel with the capacitor, \(R_{pa}\). This resistance can be neglected in antennas printed on low-loss substrates or in the air. A key decision when designing the antenna is the size of the loop. Although this is restricted by the application, this decision plays a key role in the read range. To investigate the importance of the size of the antenna, the coupling between two circular loop antennas is considered as an example. Using [PERSON]'s formula, mutual inductance \(M\) can be found as a function of the complete elliptic integrals (e.g., implemented in MATLAB using the _ellipke_ function). Analytical expressions can be derived for this case [36]. Figure 5a depicts the coupling factor \(k\) between two loop antennas of radius \(r_{1}\) and \(r_{2}\) as a function of the ratio between the two radii for different axis distances \(x\). It can be derived that there is an optimum ratio \(r_{2}/r_{1}\) that depends on the distance (see Figure 5b). The most widespread NFC readers are those integrated into smartphones. As the main application is for making payments, mobile antennas are often optimized to read payment cards (standard size = 85.60 \(\times\) 53.98 mm). The reader radius \(r_{1}\) is, therefore, on the order of 2-2.5 cm. The typical read range is on the order of 1 cm. Figure 5 shows that the optimum case is when the two loop antennas have the same size (\(r_{2}\approx r_{1}\)). Although this conclusion is derived for the special case of circular loop antennas, the result can be extended to other shapes. Modern mobiles often use metallic cases; thus, a special design is used to avoid any losses introduced by the metallic parts or batteries [37; 38; 39]. Some mobiles use ferrites to avoid this problem [40; 41].