Advances in nonlinear measurement & modeling of bulk acoustic wave resonators (invited)

Microwave acoustic filters operated at high power levels generate nonlinear mixing products necessitating improved nonlinear modeling. The latest communications protocols place strict limits on such mixing products including the generation of intermodulation distortion products, which desensitize a receiver, as well as second harmonic emissions. We extend the conventional nonlinear acoustic theory and practice into the microwave frequency range. We have developed a methodology for modeling the linear and nonlinear response of a resonator comprised of arbitrary piezoelectric and metal electrode layers and thicknesses. In this work we assume that the piezoelectric film is the dominant nonlinear source. An extended set of piezoelectric constitutive equations containing arbitrary nonlinear terms representing the behavior of the piezoelectric film is mapped into a general purpose nonlinear circuit, which is an extension to Mason´s original linear model of a resonator. A harmonic balance circuit simulator is used to solve this extended set of constitutive equations. We have fitted our model to a set of nonlinear two-tone resonator measurements by identifying four dominant nonlinear terms, by adjusting their corresponding scaling parameters such that the in- and out-of-band 2nd harmonic emissions and inter-modulation-3 products generated by the model is consistent with our measurements.