Theoretical and Experimental Investigations of the PWM Frequency Effect on the Sensitivity of Thermal Expansion-Based Angular Motion Sensor

In this paper, we present a systematic study of the PWM frequency ( $f_{\text{PWM}}$ ) effect on the sensitivity of a thermal expansion-based angular motion (TEAM) sensor. An optimal $f_{\text{PWM}}$ of heaters was experimentally derived for each pair of temperature detectors to achieve the optimized sensitivity. Based on the time-dependent analysis of our $2\mathrm{D}$ PDE model and experiments, a semi-empirical formula has been proposed to relate the optimal $f_{\text{PWM}}\, (f_{\mathrm{o}})$ with the thermal time constant ( $\tau^{\ast}$ ). Moreover, a generalized ‘Phase Diagram’ of the TEAM sensor's normalized sensitivity ( $S^{\ast}$ ) was presented, for the first time, as a function of the $f_{\text{PWM}}$ and the normalized heater-to-detector distance $(D_{x}/L_{x})$ . Herein, an optimal region, where $S^{\ast}\geq 0.95$ , has been identified to enhance the sensor performance with the corresponding optimal $f_{\text{PWM}}$ range of $22\sim 26\text{Hz}$ and optimal $D_{x}/L_{x}$ range of 0. $42\sim 0.53$ . Thus, the diagram can be useful to guide the designing optimization of TEAM sensors.