Piezoelectric vibrators equivalent circuits

Fig. 6.3 (a) Equivalent circuit for a piezoelectric specimen vibrating close to resonance (b)... 

Piezoelectric crystals, notably quartz, are used to control or limit the operating frequency of electrical circuits. A well-known example is their use in quartz clocks . The fact that a dielectric body vibrating at a resonant frequency can absorb considerably more energy than at other frequencies provides the basis for piezoelectric wave filters. The equivalent circuit for a piezoelectric body vibrating at frequencies close to a natural frequency is given in Fig. 6.3. At resonance the impedance due to L, and C falls to zero and, provided that Rx is small, the overall impedance is small. 

The equivalent circuit for the piezoelectric acuator is represented by a combination of L,C and R. Figure 4.1.1 la shows an equivalent circuit for the resonance state, which has a very low impedance. Ca corresponds to the electrostatic capacitance, and the components La and Ca in a series resonance circuit are related to the piezoelectric motion. For example, in the case of the longitudinal vibration of the above rectangular plate through dji, these components are represented by... 

Piezoelectric MIcrodlspenser, Figure 1 Equivalent circuit modeling of (a) planar, thickness-polarized, thickness-vibrating piezoelectric transducers using (b) a simple lumped-element Van Dyke model and (c) a more complex transmission-line model. A model of a piezoelectric microdispenser (d) may be formed by connecting the output terminals to the equivalent circuit model of the remaining components (e)... 

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