First harmonic (2f) characterisation of resonant frequency and Q-factor of micromechanical transducers

Abstract

In this paper, the response to the first harmonic component (2f) of the electrostatic force in single terminal driven electrostatic comb-drive and parallel-plate drive was used as a signal to extract device parameters, namely, the Q-factor and resonant frequency instead of the fundamental (1f) resonance response. It is shown that the difficulty in motional measurement due to electrical cross-talk (parasitics) using 1f measurement can be overcome with a higher signal-to-noise ratio of the 2f signal. Both atmospheric (low-Q) and reduced pressure environment were investigated using off-chip electronics and lock-in amplifier. The measurements were done on the electrostatic comb-drive and capacitive parallel plate sensing plates that form the two core modules of a yaw rate sensor (dual-axis resonator). The effects of AC and DC bias voltages on the measured response have been investigated. Experimental amplitude and phase response data have been analysed using the Lorentzian curve-fit, Resonance Curve Area (RCA) method, the half-power bandwidth method (3 dB) and the Nyquist plot for data fitting and determination of the Q-factor and resonance frequency.