A variational analysis of cylindrically symmetric FBARs

The resonant modes of cylindrically symmetric film bulk acoustic resonators (FBARs) are found by variational analysis. The FBARs under consideration are fabricated by depositing gold, zinc oxide and aluminum films onto a membrane of fused quartz. The method of analysis allows the transducer and the membrane to have unequal diameters. The primary objective of this work is to investigate the effect of the transducer diameter on the mode spectrum, particularly the intermode spacing. Each trial function used in the analysis is a product of a radial and an axial function. It is desirable for the trial functions to have local support and a certain degree of smoothness. The Schoenberg cubic B-spline satisfies these criteria. Accurate eigenanalyses are available for several hundred angularly symmetric modes.<>