# Measuring Torque and Temperature in a Rotating Shaft Using Commercial SAW Sensors
## 3 Results  
### RF Couplers  
The S parameters (S-parameters are used for the characterization of multi-port networks in the frequency domain. S-parameters are a measure of the reflected and transmitted energy arriving at each port of the network. In this sense, S-parameters encompass reflection coefficients as measure of each port impedance and transmission as a measure of the coupling between ports. Interested readers are referred to [19]) of the RF couplers at 433 MHz were measured with different terminations (50 \(\Omega\) and short-circuit) at different couplers relative orientation--Figure 6. The introduction of a 50 \(\Omega\) resistor in the second port of the stator coupler flattens the S\({}_{21}\) for all orientation angles (Figure 6a). On the other hand, short-circuit termination creates periodic negative peaks in the transmission response that repeat every \(L=\frac{\lambda}{4}\) (with \(L\) the length of the stator micro strip line). The influence of the termination of the rotor coupler is not so critical and best results are obtained with the rotor in short-circuit. The termination with a 50 \(\Omega\) load deteriorates S\({}_{21}\) in around 5 dB in comparison with short-circuit termination; however, it does not compromise the flatness of the response for all coupler orientations. Figure 6b shows S\({}_{11}\) for different terminations and orientation angles. When the stator is terminated with a short-circuit, the reflection at the stator is maximum, which means that the energy transferred to the rotor is minimum. On the other hand, termination of the stator with 50 \(\Omega\) load decreases the reflection and maximizes the energy transferred to the rotor. Again, best results were obtained with the rotor in short-circuit. Figure 6c shows the S\({}_{22}\) for different terminations and orientation angles. The minimization of the reflected energy at the rotor side happens when the rotor is terminated with a 50 \(\Omega\) load. The termination of the stator has little influence in the S\({}_{22}\).  
Figure 6: (**a**) S\({}_{21}\), (**b**) S\({}_{11}\) and (**c**) S\({}_{22}\) measured for different stator/rotor terminations and coupler orientations.  
Following the results obtained with this characterization, the stator was terminated with a 50 \(\Omega\) load and the rotor was kept in short-circuit. This minimizes the reflections at the stator port and guarantees the maximum flatness of the transmission with the rotation angle, which, in turn, reduces the parasitic frequency shift due to the angular variations of the coupling.  
A similar coupler was implemented by [PERSON] and his co-workers [PERSON] and his co-workers [PERSON] and [PERSON] (2016); however, they used a coplanar strip line coupler, the coupling elements were de-tuned and resonated at a higher frequency than the SAW device and the design approach aimed at minimizing the frequency pulling and providing 360\({}^{\circ}\) angular coverage of the sensor visibility by the reader. This strategy showed better stability of the transmission loss for different angular positions. In our case, both stator and rotor lines were matched to the SAW devices and the transmission loss obtained with the stator matched to 50 \(\Omega\) and the rotor in short circuit (Figure 6a) is similar to the transmission loss [PERSON] et al. obtained (Figure 10, [PERSON] and [PERSON] (2016)).