Excitation of Two Adjacent Resonances with a Chosen Frequency Separation in a Ceramic Piezoelectric Resonator

Abstract

Abstmct-In the crystal class Car (piezoelectric ceramics) the excitation and propagation of elastic waves in arbitrary directions are theoretically investigated. It is shown that among other modes a transverse wave and a quasi-transverse wave may be excited piezoelectrically. Accordingly, resonators with two adjacent resonances are possible. Conditions for the simultaneous excitation of these two mode6 are derived. The frequency separation of these two resonances may be controlled by the angle between the direction of polarization and the wave normal while the amplitude ratio is governed by the direction of the applied ac field in the resonator. An experimental verification of the theoretical results is presented for piezoelectric ceramics. H Is~rl~oI~L~~~rto s PI; conventiorlal 1)iezoclcctric ceramic rcso~~ators the direction of the e~cit~ing electric ac field is eit,ller perpet~licular or parallel to the direction of the permanent polarizatio~~. To our knon-ledge, little use is made of oblique cuts. In a Japanese patent’ [l] oblique cuts have been proposed to reduce the effective coupling coefficient of resonators being employed as F11 discriminators. 111 a paper on thin-film transducers, Foster et al. [2] use a special oblique cut for the excitation of only one mode. This paper deals with the simultaneous excitation of two thickness modes that are not, mechanically coupled. This is made possible by an appropriate choice of the direction of the ac field.