A parametric electrostatic resonator using repulsive force

Abstract

In this paper, parametric excitation of a repulsive force electrostatic resonator is studied. A theoretical model is developed and validated by experimental data. A correspondence of the model to Mathieu's Equation is made to prove the existence and location of parametric resonance. The repulsive force creates a combined response that shows parametric and subharmonic resonance when driven at twice its natural frequency. The resonator can achieve large amplitudes of almost 24 m and can remain dynamically stable while tapping on the electrode. Because the pull-in instability is eliminated, the beam bounces off after impact instead of sticking to the electrode. This creates larger, stable trajectories that would not be possible with traditional electrostatic actuation. A large dynamic range is attractive for MEMS resonators that require a large signal-to-noise ratio.

A Tunable Electrostatic MEMS Pressure Switch

“…Previous experimental results showed the beam oscillating almost 25 µm peak-to-peak, with the tip repeatedly tapping on the center electrode. As reported by the authors in [17], the beam dynamics are heavily influenced by the air spring effect when the dynamic amplitude is large. The large oscillation at a high frequency creates a compressible cushion of air between the beam and substrate and significantly limits the dynamic amplitude, which is also affected by squeeze film damping.…”

“…Electrostatic levitation has a number of interesting attributes that are very useful for pressure sensing. Most importantly, it Table I. can produce very large oscillations over an order of magnitude greater than the anchor height of the beam [16], [17]. Previous experimental results showed the beam oscillating almost 25 µm peak-to-peak, with the tip repeatedly tapping on the center electrode.…”

Merging parallel-plate and levitation actuators to enable linearity and tunability in electrostatic MEMS

“…One alternative to parallel-plate actuation is electrostatic levitation [8][9][10][11][12][13] . The electrode configuration shown in Figure 1 creates an electric field that pushes electrodes apart instead of pulling them together.…”

A reliable MEMS switch using electrostatic levitation

“…Much effort has been placed in creating electrostatic MEMS designs that do not experience pull-in at all. One of these methods is by actuating a structure using electrostatic levitation [9][10][11][12][13][16][17][18][19][20][21][22][23] . This involves a slightly different electrode configuration than the standard parallel plate design, with two extra electrodes that help induce an effectively repulsive force instead of an attractive one.…”

“…The center electrode will not create any attractive electrostatic forces on the beam because they are both at the same voltage potential, and thus pull-in will not occur. The authors have previously demonstrated in experiment that when excited with a harmonic voltage signal, the beam can collide with the center electrode, but instead of sticking it simply bounces off 23 .…”