Replicating Spectral Baseline for Unambiguous Frequency Locking in Resonant Sensors

Abstract

Electrothermal piezoresistive resonant cantilever sensors have been fabricated with embedded actuating (heating resistor) and sensing (piezo resistors) parts, with the latter configured in a Wheatstone bridge circuit. Due to the close spacing between these two elements, a direct thermal parasitic effect on the resonant sensor during the actuating-sensing process leads to asymmetric amplitude and reversing phase spectral responses. Such a condition affects the precise determination of the cantilever’s resonant frequency, f0. Moreover, in the context of phase-locked loop-based (PLL) resonance tracking, a reversing phase spectral response hinders the resonance locking due to its ambiguity. In this work, a replica of the baseline spectral was applied to remove the thermal parasitic effect on the resonance spectra of the cantilever sensor, and its capability was simulated through mathematical analysis. This replica spectral was subtracted from the parasitized spectral using a particular calculation, resulting in optimized spectral responses. An assessment using cigarette smoke particles performed a desired spectral shifting into symmetrical amplitude shapes and monotonic phase transitions, subsequently allowing for real-time PLL-based frequency tracking.