Detection of cyclic-fold bifurcation in electrostatic MEMS transducers by motion-induced current

This paper presents a new detection method of cyclic-fold bifurcations in electrostatic MEMS transducers based on a variant of the harmonic detection of resonance method. The electrostatic transducer is driven by an unbiased harmonic signal at half its natural frequency, omega(a) = 1/2 omega(o). The response of the transducer consists of static displacement and a series of harmonics at 2 omega(a), 4 omega(a), and so on. Its motion-induced current is shifted by the excitation frequency, omega(a), to appear at 3 omega(a),5 omega(a), and higher odd harmonics, providing higher sensitivity to the measurement of harmonic motions. With this method, we successfully detected the variation in the location of the cyclic-fold bifurcation of an encapsulated electrostatic MEMS transducer. We also detected a regime of tapping mode motions subsequent to the bifurcation.