This article discusses on the measured third-order intermodulation (IMD3) products and third harmonics (H3) appearing in a set of six different solidly mounted resonators (SMR) and bulk acoustic-wave (BAW) resonators with different shapes and stack configurations. The discussion is supported by a comprehensive nonlinear distributed circuit model that considers the nonlinear effects potentially occurring in any layer of the resonator stack. The aluminum-nitride (AlN) and silicon-dioxide (SiO2) layers are identified as the most significant contributors to the IMD3 and H3. The frequency profile of the third-order spurious signals also reveals that, in temperature-compensated resonators, where the SiO2 layers are usually thicker, the remixing effects from the second-order nonlinear terms are the major contributors to the IMD3 and H3. These second-order terms are those that explain the second-harmonic (H2) generation, whose measurements are also reported in this article. Unique values of the nonlinear material constants can explain all the measurements despite the resonators have different shapes, resonance frequencies, and stack configurations.

中文翻译：

---

体声波谐振器中的三次谐波和互调失真

本文讨论了测量的三阶互调 (IMD3) 乘积和三次谐波 (H3)，它们出现在一组具有不同形状和堆叠配置的六个不同的固体安装谐振器 (SMR) 和体声波 (BAW) 谐振器中。该讨论得到综合非线性分布式电路模型的支持，该模型考虑了谐振器堆栈任何层中可能发生的非线性效应。氮化铝 (AlN) 和二氧化硅 (SiO2) 层被确定为 IMD3 和 H3 的最重要贡献者。三阶杂散信号的频率分布还表明，在温度补偿谐振器中，SiO2 层通常较厚，二阶非线性项的再混合效应是 IMD3 和 H3 的主要贡献者。这些二阶项是那些解释二次谐波 (H2) 生成的项，本文也报告了其测量结果。尽管谐振器具有不同的形状、谐振频率和堆叠配置，但非线性材料常数的唯一值可以解释所有测量结果。