One-parameter nonlinear mason model for predicting 2nd & 3rd order nonlinearities in BAW devices

Accurate modeling of the nonlinearities in BAW duplexers is important since handset manufacturers employing BAW duplexers at the handset ANT port desire low levels of 2nd harmonic emissions and intermodulation distortion. There are numerous papers describing ways in which non-linear behavior in BAW resonators can be modeled and it is generally agreed upon that it is the piezoelectric AlN that gives rise to this non-linear behavior. Little attention has been given to the generation of third order non-linear products and their impact on system performance. In this paper we present a non-linear model in which we assume that the piezoelectric constant is strain dependent. This second order model gives rise not only to second order mixing products but also to third order products. We show that this can happen through a process of re-mixing in which second order mixing products are initially generated in the piezoelectric AlN, and are subsequently remixed with the applied fundamental thus generating third order products. In this paper we compare measurements of second and third order behavior in duplexers and resonators to our model.