Bulk acoustic wave mode shaping using a transversely graded electrode

This paper presents the basic principles of the transverse graded electrode (TGE) for the tailoring of BAW transverse modes. The theoretical basis and equations are summarized and the stacked matrix theory for solutions of the mode profiles is introduced for the BAW structures. The stacked matrix approach, well known from optics and electromagnetics, is powerful since it allows for easy solution of an arbitrary number of one dimensional waveguide sections. The results assume an isotropic substrate in the transverse propagation directions for solutions of the number of modes, the mode profiles, the mode velocities, and mode coupling. Different theoretical mode profiles are presented for various electrode weighting schemes.