# An IoT Reader for Wireless Passive Electromagnetic Sensors
## 2 Materials and Methods
### Radiating Layer
From the S-parameters of the SRR-based sensor and the sensor antennas reflexion coefficient, \(T_{s}\) can be computed as:  
\[T_{s}=\left(|S_{21s}|\frac{\left(1-|S_{11_{s}}|^{2}\right)}{\left|\left(1-S_{1 1_{s}}S_{11_{ss}}\right)^{2}-S_{21_{s}}^{2}S_{11_{ss}}^{2}\right|}\right)^{2} \approx\ |S_{21s}|^{2} \tag{2}\]  
since the sensor antennas and the two-port SRR-based sensor are designed to be matched to the system reference impedance (50 \(\Omega\)) within the working bandwidth, as it will be shown in the system implementation. Hence, from Equation (2) and considering that the reader antennas are matched to the reference impedance as well, Equation (1) reduces to:  
\[|S_{21 rad}|^{2}\ \approx\ \left(|S_{21s}|\frac{G_{a_{s}}G_{a_{s}}c_{0}^{2}}{ \left(4\pi rf\right)^{2}}\right)^{2} \tag{3}\]  
From Equation (3), it can be seen that the transmission coefficient of the whole radiating layer is directly proportional to the transmission coefficient of the SRR-based sensor. Thus, the frequency notch produced in \(|S_{21s}|^{2}\) are appreciated as well in \(|S_{21 rad}|^{2}\), allowing the detection of different LUTs. Regarding the antennas implementation, the same design has been used for the four antennas. They have been designed to cover the whole working bandwidth of the sensing system. Patch antennas have been chosen because they are easy to manufacture and low-cost. Moreover, their radiation characteristics (broadside pattern and gain) are suitable for the application. However, conventional patch antennas are resonant antennas. For this reason, the antennas used in this paper are based on the broadband design proposed in [35]. These antennas are based on a microstrip patch using L-probe feeding system, achieving the whole bandwidth of the system. On the other hand, we must also consider that the mentioned brass wall slightly influences the reader antenna gain, so it will not be exactly the same as the sensor antenna gain. In order to cover the desired bandwidth, the following antenna dimensions are determined from [35] (Figure 4): L = 62.5 mm, W = 41.6 mm, L\({}_{\text{h}}\) = 25 mm, L\({}_{\text{v}}\) = 16 mm, and H = 25 mm. Moreover, the antenna substrate is Rohacell 51 HF foam (\(\varepsilon\)r = 1.057 and tan \(\delta\) = 0.0002), covered  
Figure 4: Sketch of the proposed broadband patch antenna. Side view **(a)** and top view **(b)**. by a copper metallized 80-\(\upmu\)m thin-film of Kapton. In addition, the ground plane material is brass (1.56-mm thickness). The four antennas have been manufactured and placed in the measurement setup. Then, the measured reflexion coefficient of the reader antennas (Figure 5a) and sensor antennas (Figure 5b) are represented below. It can be observed that the four antennas achieve the matching criterion \(\left|S_{11}\right|_{dB}\leq-10\) dB within the system frequency range. Moreover, a satisfactory isolation level between the antennas of the reader has been accomplished because the coupling is below \(-30\) dB (Figure 5a). The final step is the demonstration that the proposed radiating layer can detect different LUTs, even with close values of relative permittivity. Figure 6 shows the simulations, performed in CST Microwave Studio (Transient Solver), and the corresponding measurements of the whole radiating system. The measurements have been taken with the Keysight N9918A Vector Network Analyzer (VNA) [36]. The objective of the simulations is to validate that the trend of the resonant frequencies is consistent to the measurements. There is a good agreement between both cases, although a frequency shift is observed between all the simulated and measured results. It is remarkable that these simulations require a high computational cost. Moreover, the simulator used is not optimum for highly resonant structures (like the SRR-based sensor) which might lead to undesired frequency shifts in the simulations. Moreover, there are additional factors in the measurements, such as interferences and multipath effects, which are neither contemplated in the simulations.