1968
DOI: 10.1121/1.1910967
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Analysis of Elastically Coupled Piezoelectric Resonators

Abstract: This paper presents an analysis of an elastically coupled piezoelectric resonator system consisting of a linear array of two or more counter electrode pairs placed on the major surfaces of a quartz crystal plate. Each pair of counter electrodes establishes resonator having a transverse thickness mode of motion. The equations describing this system are derived and applied to an array of n coupled resonators and specific numerical computations are made for the cases where n is equal to 2, 3, and 6. These results… Show more

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Cited by 39 publications
(14 citation statements)
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“…We also note that the interference between resonators decreases with increasing electrode separation as expected. This result was demonstrated early in quartz research using Mindlin's theory for arrays of electrodes of identical size [11].…”
Section: Introductionmentioning
confidence: 80%
“…We also note that the interference between resonators decreases with increasing electrode separation as expected. This result was demonstrated early in quartz research using Mindlin's theory for arrays of electrodes of identical size [11].…”
Section: Introductionmentioning
confidence: 80%
“…If the spacing between the electrodes is sufficiently large (usually greater than the thickness of the resonator), than each pair of electrodes can be regarded as constituting an independent energy trapped energy resonator, with there being no interaction or coupling between the two resonators. The spacing required for there to be no interaction is determined by the rate of decay of the evanescent waves in the region between the electrodes [2]. As the spacing between of the electrode pair is reduced, at some stage the evanescent wave associated with one resonator will extend into the region occupied by the other and vice-versa.…”
Section: Monolithic Filter Design Parametersmentioning
confidence: 99%
“…This is complicated and sometimes it can be impossible, especially when there are two or more pairs of electrodes. Theoretical results on crystal filters are few and scattered [21][22][23][24][25], and they were either for modes varying in one of the two in-plane directions of a plate only, or were with various approximations.…”
Section: Introductionmentioning
confidence: 99%