# Passive Harmonic RFID System for Buried Assets Localization
## 3 Read Range
### Link Budget  
The read range in an RFID system can be limited by the uplink (reader to tag) or by the downlink (tag to reader) [49; 50]. In the uplink, the tag must receive enough power to be activated (\(P_{r,\,tag}>P_{th}\)),  
Figure 11: Simulated attenuation coefficient in dB/m calculated from Equations (2) and (3) as a function of the volumetric water content of the soil at 865 MHz and 1730 MHz for two soil cases.  
Figure 12: Simulated reflection attenuation in dB calculated from Equation (1) as a function of the volumetric water content of the soil at 865 MHz and 1730 MHz for two soil cases.  
whereas in the downlink, the backscattered power (\(P_{r,\,reader}\)) by the tag must be higher than the reader sensitivity (\(S_{min}\)).  
In a conventional UHF RFID system, as the reader's antenna interrogates the tag in the air, the main problem is the fading due to multipath interference from objects, especially in indoor environments. The read range is limited by the tag sensitivity as the propagation loss is the same in both directions.  
In this application, the reader antennas are close to the ground (for example, at 10 cm in order to avoid detuning by the proximity of the ground), and the main source of attenuation is the result of the loss of the soil that depends on its composition. Therefore, the read range is the maximum distance that complies with the two conditions (\(P_{r,\,tag}>P_{th}\) and \(P_{r,\,reader}>S_{min}\)). The main advantage of harmonic systems is that the receiver sensitivity in the reader may be noticeably better than in a conventional reader because the coupling interference between the reader transmitter and receiver can be filtered as the receiver is tuned at the second harmonic. As discussed previously in Section 2, the effect of residual coupling at \(2f_{0}\) can be reduced by improving the filters in the transmitter and receiver or by modulating the radar cross-section as in conventional tags. In this work, the second option is investigated.  
The power received at the tag from the reader can be calculated from the Friis equation, the reflection loss, and the attenuation [38], as follows:  
\[P_{r,tag}(dBm)=EIRP(dBm)-10 log\left(4\pi d_{S}^{2}\right)+G_{tag}(dB)+10 log \left(\frac{\lambda^{2}}{4\pi}\right)-L_{r}(dB)-L_{p}(d)(dB) \tag{4}\]  
where \(d_{S}\) is the distance from the reader antenna to the ground; \(\lambda\) is the wavelength at \(f_{0}\); EIRP is the equivalent isotropic radiated power of the reader (limited by the regulations); \(G_{tag}\) is the gain of the tag antenna; \(L_{r}\) and \(L_{p}\) are the reflection and propagation loss of the soil in dB, given by (1) and (3), respectively; \(L_{p}\) is a function of the underground distance; \(d\). \(G_{tag}\) is the gain of the tag antenna; and \(G_{R,\,reader}\) is the gain of the reader antenna in reception.  
The backscattered power in a harmonic tag is given by the following [38]:  
\[P_{r,reader}(dBm)=P_{r,tag}(dBm)-CL(dB)+G_{tag,2}(dB)-10 log\left(\frac{\lambda _{2}^{2}}{4\pi}\right)+G_{R,reader}(dB) \tag{5}\]  
where \(CL\) is the doubler conversion loss (including the modulation factor, that is a function of the \(P_{r,\,tag}\) power and is given in Figure 8), \(G_{tag,\,2}\) is the antenna gain at \(2f_{0}\), and \(\lambda_{2}\) is the wavelength at \(2f_{0}\) (=\(\lambda/2\)).