Mass-Loading of Thickness-Excited Crystal Resonators Having Arbitary Piezo-Coupling.

摘要

The unbounded piezoelectric plate problem admits an exact solution for the case of thickness modes and may be represented rigorously by an equivalent electrical circuit containing lumped and distributed elements. Mass-loading effects arising from uniform surface coatings such as electrodes may be incorporated into the exact solution and represented by simple additions to the electrical schematic of the plate. The simplest useful case of this type is that of equal masses lumped at the surfaces of a plate which only a single mode is piezoelectrically excitable; this is also the most important practical situation. A single-mode plate with equal mass coatings on its surfaces and excited by an electric field in the thickness direction is examined. The usual restriction to low piezoelectric coupling coefficient is, however, not made. From simple considerations regarding the equivalent network, the exact equation for the critical frequencies of interest are shown to follow directly. These are used throughout without approximation. Use of the exact relations allow high coupling materials to be covered as easily as low. Families of curves showing the variations of the resonance and antiresonance frequencies over a wide range of values of mass-loading, coupling coefficient, and harmonic number are given. A new plate-back parameter, valid for all piezoelectric substances, is also introduced.