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.