Modeling of bulk acoustic wave devices built on piezoelectric stack structures: Impedance matrix analysis and network representation

The fundamental electro-acoustic properties of a solid layer are deduced in terms of its impedance matrix (Z) and represented by a network for modeling the bulk acoustic wave devices built on piezoelectric stacked structures. A piezoelectric layer is described by a three-port equivalent network, a nonpiezoelectric layer, and a short- or open-circuit piezoelectric layer by a two-port one. Electrical input impedance of the resonator is derived in terms of the Z-matrix of both the piezoelectric layer and an external load, the unique expression applies whether the resonator is a mono- or electroded-layer or a solidly mounted resonator (SMR). The loading effects of AZ-electrodes on the resonating frequencies of the piezoelectric ZnO-layer are analyzed. Transmission and reflection properties of Bragg mirrors are investigated along with the bulk radiation in SMR. As a synthesizing example, a coupled resonator filter (CR.F) is analyzed using the associated two-port equivalent network and by calculating the power transmission to a 50 Omega-load. The stacked crystal filter is naturally included in the model as a special case of CRF. Combining a comprehensive matrix analysis and an instructive network representation and setting the problem with a full vectorial formalism are peculiar features of the presented approach.