# Measuring Torque and Temperature in a Rotating Shaft Using Commercial SAW Sensors
## 2 Materials and Methods
### RF Couplers  
A dipole antenna is the simplest solution for establishing communication at 434 MHz band. However, in the present case, this solution would compromise the line of sight, so a large diameter microstrip coupler [18] was implemented.  
The stator and rotor couplers were fabricated using FR-4 epoxy laminate. This material has a copper conductive layer and a dielectric constant of 4.5 and is available in plates of different thickness. On the top layer, micro strip transmission lines were patterned by selectively removing the copper layer, while the back surface remained covered with a copper layer, behaving as a ground plane. The length of the stator line was chosen to meet one wavelength \(L_{S}=\lambda\)--under these conditions, the travelling wave regime minimizes the amplitude variation of the signal along the stator circumference. The length of the rotor line was \(L_{R}=\frac{\lambda}{4}\). The possible combinations for the length \(L\) and width \(W\) of the stator and rotor lines were calculated as a function of the thickness \(W\) of commercially available FR-4 substrates using TX-Line by AWR transmission line design tool--Table 2. \(L\) remains almost unchanged while \(W\) changes significantly with the thickness of the FR-4 substrate. To keep the largest \(L\)/\(W\) ratio, FR-4 substrate with a thickness of 0.8 mm was chosen. The inner diameter of the couplers was \(\approx\)80 mm (to fit the external diameter of the load cell), which corresponds to a minimum perimeter of \(\approx\)250 mm, and the outer diameter was 110 mm. The \(\frac{\lambda}{4}\) rotor line was obtained with a curved line while the stator line had a zigzag shape (Figure 3a). The fabricated couplers can be seen in Figure 3b.  
The stator coupler was fixed with screws to an L-shape metallic piece mounted directly on the table; the transmission line was terminated with 50 \(\Omega\) and was connected to the interrogation unit with a coaxial cable. The rotor coupler was mounted directly on the shaft. The rotor was designed in a way that its inner diameter meets the external diameter of the load cell. After inserting the shaft through the coupler's hole, it was further fixed to the load cell with epoxy. This guarantees that shaft and rotor coupler behave as one single body once the system is rotating. The transmission line was short-circuited and was connected to the SAW sensors with W.FL cables. The scattering  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \multicolumn{3}{c}{**Rotor (\(\lambda\)/\(\lambda\))**} & \multicolumn{3}{c}{**Stator (\(\lambda\)/\(\lambda\))**} \\ \hline H (mm) & 0.80 & 1.00 & 1.60 & 0.80 & 1.00 & 1.60 \\ L (mm) & 93.86 & 93.86 & 93.85 & 375.44 & 375.46 & 375.42 \\ W (mm) & 1.50 & 1.88 & 3.01 & 1.50 & 1.88 & 3.01 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Length \(L\) and width \(W\) of the micro strip transmission lines calculated as a function of the thickness \(H\) of the FR-4 substrate.  
Figure 3: (a) Diagrams of rotor coupler line (longer line) and stator zigzag-shaped coupler line; (b) fabricated couplers.  
parameters of the implemented couplers (Figure 3b) were measured with a PNA E8361C network analyzer (Santa Rosa, CA, USA).