*3.2. Wireless Sensing Test*

Next, we tested the wireless strain sensing, and compared with simulations using electromagnetic simulator. Figure 8 compares the wireless sensing results from the measurement and simulation when the transceiver was 10 mm away from the sensor. Among the two peaks, the right peak was chosen as the resonant frequency of the transceiver, because the changes in frequency of the right peak showed a higher sensitivity than that of the left peak. The measured and simulated results show that the resonant frequency decreased as the sensor strain increased. Overall, the simulated impedance magnitudes were higher than the measured values. It appears to be due to the relatively high DC resistance of the sensor in measurements, caused by the serpentine shape, which however was not included in the simplified simulation model. Nevertheless, the degree of changes in the peak frequency of the simulation was similar to that of the measured results, so that the simulation results could be used to predict the maximum wireless working distance of the sensor.

**Figure 8.** Experimentally measured and simulated impedance magnitudes of the transceiver at 10 mm away from the sensor. The frequency of the right peak was shifted (**a**) from 15.01 MHz at 0% strain to 14.59 MHz at 100% strain in experiment, and (**b**) from 15.31 MHz at 0% strain to 14.47 MHz at 100% strain in simulation.

The shifted resonant frequencies and the gauge factors of strain sensing according to different strains and different distances are summarized in Figure 9. Figure 9a shows the measured resonant frequency modulation detected at the transceiver wirelessly, and Figure 9c shows the calculated gauge factors. As the strain of the sensor increased, the resonant frequency of the transceiver decreased gradually. This decreasing trend could be seen only up to 22.5 mm distance. When measured at farther distances, the frequency converged to the resonant frequency of the transceiver itself, indicating that no measurable changes were detected. At 100% strain, the gauge factor decreased from 0.028 to 0.011 at 10 mm to 22.5 mm distance, converging to 0 at farther distances. Figure 9b shows the simulated resonant frequency at the transceiver, and the calculated gauge factors are shown in Figure 9d. The simulated results also showed that as the distance increased, the frequency converged to the self-resonant frequency of the transceiver. The detectable distance was observed to be between 20 mm and 30 mm, in good agreement with the experimental results. However, unlike the measured results, the simulated results did not show that the resonant frequency first increased at strains up to 20% at distances greater than 20 mm. This appears to be because the simplified simulation model did not include the additional DC resistance caused by the serpentine pattern and therefore did not fully reflect the decrease of inductive coupling. Nonetheless, the simulation results showed that the used FEM model could predict the wirelessly measurable distance reasonably well.

**Figure 9.** Experimentally measured and simulated results of wireless strain sensing. (**a**) Measured and (**b**) simulated resonant frequency modulation as the strain applied to the sensor increased, and the gauge factor of the transceiver calculated based on (**c**) the measured and (**d**) simulated resonant frequency.
