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The authors propose a procedure to characterize the intrinsic nonlinearities of bulk acoustic wave resonators by performing one-port measurements of the second harmonic and second-order inter-modulation spurious signals. Closed-form expressions have been derived that relate the nonlinear stiffened elasticity with experimental observables. These formulas are valid in a wide range of frequencies around the resonance and have been verified with nonlinear circuit simulations. The measurement setup and its effects are also discussed in their approach. Measurements of a set of aluminum nitride-based devices from several manufacturers yield consistent model parameters and allow one to obtain a coefficient of the nonlinear stiffened elasticity intrinsic to this piezoelectric material.
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