*2.3. Finite Element Simulation of Wireless Sensing*

Before measuring the maximum distance that the sensor could operate wirelessly, finite element simulation using an electromagnetic simulator ANSYS HFSS (ANSYS Inc., Canonsburg, PA, USA) was performed to estimate the wireless working distance. Although the inductance of the sensor can be relatively easily calculated based on equations, it is not easy to mathematically derive the coupling coefficient between the sensor and the transceiver and thus, we simulated the wireless sensing using FEM. The simulation model is illustrated in Figure 5. The simplified geometry of the sensor was used, same as the model used in inductance calculation. Both the transceiver and the sensor were set to resonate at 13.56 MHz. The sensitivity of frequency shifting was defined as the gauge factor as follows:

$$\text{Gauge Factor} = \frac{\Delta f / f\_0}{\varepsilon} \tag{9}$$

where *f* <sup>0</sup> is the resonant frequency at 0% strain, Δ*f* is the difference between *f* <sup>0</sup> and the measured resonant frequency, and *ε* is the applied strain.

**Figure 5.** Simulation model of the sensor and the transceiver for wireless sensing. The distance between the sensor and the transceiver was changed from 10 mm to 50 mm, and the strain applied to the sensor was changed from 0% to 100%. In this figure, the transceiver is 20 mm away from the non-stretched sensor.
