Transmission-Line Analogs for Stacked Piezoelectric Crystal Devices

摘要

An equivalent circuit consisting of transmission lines and lumped elements is shown to be the exact quasi-static representation of a stack of piezoelectrically driven thickness-mode crystal vibrators. The stack may consist of any number of layers, each of which may be arbitrarily anisotropic, but homogeneous. Thickness- or lateral-field excitation may be used to drive one or any combination of the plates. A canonic element, consisting of two layers, forms the basis for deriving the network representation, which is then generalized to stacks of any number of strata. In a vibrating system of this type, the crystal comprising each layer is represented, in the bulk, by three acoustic transmission lines. Each interface, however, appears as lumped transformer elements coupling together the six transmission lines incident upon that boundary from the media on both sides. Incorporation of the piezoelectric drive mechanism is shown to require an additional simple network and interconnection. The analysis brings under systematic treatment crystal resonators and filters, delay lines, and pulse and code generators. Some practical applications are illustrated by computer simulation of new device characteristics. (Author)