Nonlinear lumped electrical model for contour mode AlN resonators

This paper presents a lumped electrical model to simulate the nonlinear behavior of aluminum nitride contour mode resonators. The model is derived from the Duffing equation and validated through experiments. Amplitude-frequency (A-f) and third order intermodulation distortion (IMD3) measurements were performed to extract an equivalent nonlinear coefficient α. The two experiments yield the same results when the system is dominated by thermally-induced nonlinearities. In case of high frequency modulations, purely mechanical non-linearity can also be extracted.