# An IoT Reader for Wireless Passive Electromagnetic Sensors
## 2 Materials and Methods
### Radiating Layer  
Regarding the radiating layer, it is fundamentally inspired on a bistatic system. The radiating layer schematic is shown in Figure 3. In the proposed scheme, four broadband patch antennas are used: two antennas for the reader (transmission and reception) pointed to two antennas connected to the sensor ports. Furthermore, a coupling level between the reader antennas lower than \(-30\) dB can be considered suitable for this application in order to reduce unwanted interferences between the signal generation and detection stages of the reader. Thus, a brass wall (8.15-cm height and 1.56-mm thickness) has been placed between the antennas of the reader, in order to increase their isolation. Besides, the reader antennas coupling can be further decreased if we choose an appropriate gap between them. Nevertheless, it is important not to oversize the system, and hence a trade-off gap is selected. We have optimized this gap through the software Computer Simulation Technology (CST) Microwave Studio, and we have obtainded a 28.1-cm gap between the metallic patches of the reader. Finally, we consider a distance of 11 cm between the reader antenna and the tag antenna, since this distance is useful in laboratory environments (short-range wireless communication). Four plastic cylindrical supports hold the reader during the measurement setup. A wireless line-of-sight (LoS) link is established between the four antennas. For simplicity, we consider two equal antennas for the reader and two equal antennas for the sensor. The gain of the reader and sensor antennas are \(G_{a_{s}}\) and \(G_{a_{s}}\), respectively. Moreover, the mispointing and polarization losses will be neglected in the present approach, since it is assumed that the antennas are perfectly pointed and have the same polarization. The thermal noise introduced by the channel, the external interferences, and the statistical nature of the detection process are also considered negligible; as well as other propagation effects. On the other hand, we have to take into account that the SRR-based sensor is passive and linear, and it can be characterized by its scattering parameters (\(\left[S\right]_{s}\)). Moreover, since it is reciprocal and symmetrical, we can consider that \(S_{21_{s}}=S_{12_{s}}\), and \(S_{11_{s}}=S_{22_{s}}\). The operation, according to Figure 3, is as follows: a signal generator is connected to the antenna 1, whose reflexion coefficient is \(S_{11_{a_{r}}}\). This signal is wirelessly transmitted from the antenna 1 to the antenna 2, which is connected to the input port of the sensor; then, the signal travels through the sensor, submersed in the LUT, to the output port where the antenna 3 is connected. The power transmission coefficient between the two antenna sensors is \(T_{s}\). Finally, the antenna 3 sends back the signal, modified by the sensor, to the antenna 4 and the signal is detected by the signal receiver. Then, the link budget (in power units), \(\left|S_{21_{nd}}\right|^{2}\), can be deduced from the Friis transmission equation [33] as:  
\[\left|S_{21_{nd}}\right|^{2}=T_{s}\left(\frac{\left(1-\left|S_{11_{a_{r}}} \right|^{2}\right)G_{a_{r}}G_{a_{s}}}{\left(\frac{4\pi r}{c_{0}}f\right)^{2}} \right)^{2} \tag{1}\]  
Figure 3: Bistatic system schematic. where \(c_{0}\) is the speed of light in vacuum, \(f\) is the working frequency, and \(r\) is the distance between the reader and the tag antennas. Equation (1) is valid because the antennas are operating in the far field region at this distance according to [33]. The transducer power gain equation demonstrated in [34] for arbitrary two-port networks, characterized by their scattering matrix [5], and with arbitrary source and load impedance, can be particularized for the proposed sensor system. In this scheme, the passive sensor is the two-port network and the two sensor antennas can be modelled as the source and load impedances, both with \(S_{11_{ss}}\) reflection coefficient.