Non-linear dynamics of an electrothermally excited resonant pressure sensor

Non-linear dynamics of a resonant silicon bridge pressure sensor with electrothermal excitation has been investigated. Non-linear vibration model of the bridge resonator in the pressure sensor is developed by Euler–Bernoulli beam modeling. Besides non-linear geometric effect, the model also takes into account the measured pressure, the heating effect of the electrothermal excitation, and the residual internal force in the bridge. An approximate solution for this model is found via Galérkin procedure and the multiple scales method. From the solution, a bending parameter is extracted to quantitatively evaluate the bending of the bridge amplitude–frequency response. Dependence of the bending parameter on the sensor operating conditions is examined analytically and experimentally. Analytical calculations and experimental observations show good agreement qualitatively. An improved prediction for the critical vibration amplitude of the bridge is proposed, beyond which frequency hysteresis occurs. The critical vibration amplitude presented in this work is compared with those in other literatures. Moreover frequency output error of the sensor due to non-linear vibration is also examined. And finally several suggestions on resonant sensor design and operation with respect to non-linear effects are proposed.