Electrical behaviour of AT-cut quartz crystal resonators as a function of overtone number
Résumé
An investigation on the electrical behaviour of quartz resonators with fundamental frequencies up to 10MHzwascarried out by impedance analysisonseveral overtones. The values of the equivalent electrical components of these acoustic sensorsweredetermined and revealed to correctlymatchthose obtained for theoretical one-dimensional crystals. The study on different harmonics allowed to evaluate the variation of the effective vibrating area of each crystal and the effect of energy trapping intrinsic to a crystal of finite surface was then emphasized. It was also shown that the impedance behaviour is affected by the piezoelectric stiffening and the boundary conditions of real quartz resonators. These perturbing effects have a significant magnitude on the fundamental harmonic mode, and to a lesser extent on the third and fifth overtones. Besides, the theoretical models established for viscoelastic analysis of coated layers are based on the assumption that the quartz crystals are ideal with an infinite surface. For this purpose, a model was proposed for different crystals to take into account the various effects influencing both resonance frequencies and bandwidths of quartz resonators.
Mots clés
AT-cut quartz crystals
Coated layers
Electrical components
Energy trapping
Finite surface
Fundamental frequencies
Fundamental harmonic
High frequency HF
Impedance analysis
One-dimensional crystals
Piezoelectric sensors
Quartz crystal
Quartz resonators
Resonance frequencies
Theoretical models
Viscoelastic analysis Engineering controlled terms: Acoustic impedance
Crystals
Electric impedance
Electric sensing devices
Natural frequencies
Oxide minerals
Piezoelectric transducers
Piezoelectricity
Quartz Engineering main heading: Crystal resonators