Publications Details

Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance

Martin, S.J.; Bandey, Helen L.; Cernosek, R.W.

We derive a lumped-element, equivalent-circuit model for the thickness shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of {pi}/2 radians. This model predicts accurately the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. The elements of the model are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and the Sauerbrey models.