Auto-Resonance - A New Paradigm for Driving Linear and Nonlinear Electrostatic Resonators

For the first time ever, we experimentally demonstrate auto-resonance driving of an electrostatic resonator. This simple driving scheme, instantaneously locks on to the resonance frequency from the very first cycle, and the amplitude of the harmonic oscillation rapidly converges to the stable, fully-developed response. We demonstrate that even if the resonator is nonlinear and its resonance frequency is affected by motion amplitude, the auto-resonance driving scheme naturally tracks the nonlinear backbone of the dynamic response. We demonstrate that auto-resonance driving eliminates the bifurcation instability, which appears when a nonlinear resonator is driven in frequency sweeps. This means that nonlinear resonators can be operated at large amplitudes without any concern of instability. Auto-resonance is therefore a simple and practical alternative to phase-lock-loop driving of resonators.