Sources of Third–Order Intermodulation Distortion in Bulk Acoustic Wave Devices: A Phenomenological Approach

Acoustic devices like Bulk Acoustic Wave (BAW) resonators and filters represent a key technology in modern microwave industry. More specifically, BAW technology offers promising performance due to its good power handling and high quality factors that make it suitable for a wide range of applications. Nevertheless, harmonics and 3IMD arising from intrinsic nonlinear material properties (Collado et al., 2009) and dynamic self-heating (Rocas et al., 2009) could represent a limitation for some applications. Driven by the need for highly linear devices, there is a demand for further development of accurate models of BAW devices, capable of predicting the nonlinear behavior of the device and its impact on a circuit. Many authors have attempted to model the nonlinearities of BAW devices by using different approaches, mostly involving phenomenological lumped element models. Although these models can be useful because of their simplicity, they are mainly limited to narrow-band operation and they usually cannot be parameterized in terms of device-independent parameters (Constantinescu et al., 2008). Another approach consists of extending all the material properties on the constitutive equations to the nonlinear domain and introducing the nonlinear relations to the model implementation, which leads to several possible nonlinear sources increasing model complexity (Cho et al., 1993; Ueda et al., 2008). On the other hand, (Feld, 2009) presents a one-parameter nonlinear circuit model to account for the intrinsic nonlinearities. Such a model does not include the self-heating mechanism and can underestimate the 3IMD by more than 20 dB. In this work, a model that uses several nonlinear parameters to predict harmonics and 3IMD distortion is presented. Its novelty lies in its ability to predict the nonlinear effects produced by self-heating in addition to those due to intrinsic nonlinearities in the material properties. The model can be considered an extension of the nonlinear KLM model (originally proposed by Krimholtz, Leedom and Matthaei) (Krimholtz et al., 1970) to include the thermal effects due to self-heating caused by viscous losses and electrode losses. For this purpose a thermal domain circuit model is implemented and coupled to the electro-acoustic model, which allows us to calculate the dynamic temperature variations that change the material properties. In comparison to (Rocas et al., 2009), this work describes the impact that electrode losses produce on the 3IMD, presents closed-form expressions derived from the