Prediction Of The H2 Response Of An Fbar Resonator Using Finite Element Method

Finite element method (FEM) is used to simulate the H2 and H3 emissions of FBAR resonators resulting from piezoelectric material nonlinearities [5]. The method incorporates both the linear and higher -order terms in the free energy state variable. The variational principle is applied to the Lagrangian, which includes the free energy state variable to obtain the weak form of the materials continuum of the resonator. The COMSOL FEM solver uses this weak form expression to find the H2 and H3 emissions solutions. The method is validated by comparing an H2 emissions simulation of a 1-D resonator simulated with: (1) the COMSOL FEM solver, and (2) Keysight's harmonic balance nonlinear circuit solver [2]. The method is further validated by comparing measured H2 emissions of a circular resonator with a 2-D COMSOL simulation of the same. In addition, spurious modes which are a solution of 2-D COMSOL, are shown to give rise to H2 "spike" emissions emissions which correlate with the peaks of time averaged elastic energy. 2-D COMSOL is also used to simulate the H2 emissions of a pair of resonators that are connected in an anti -parallel configuration.