Motional impedance of resonators in the nonlinear regime

We developed a model for the motional impedance Z
_m
of electrostatic resonators that operate in a nonlinear regime. The model predicts that the Z
_m
at resonance has the same expression as it has in the linear case. In addition, we developed a new measurement setup, which is based on a variable-phase feedback circuit. This setup enables the measurement of Z
_m
at operating points that are unobservable with a conventional impedance analyzer measurement. The estimation based on our model matches the measurement with errors less than 10% in the worst case.