The minimum signal force detectable in air with a piezoelectric plate transducer

A theoretical analysis based on the Johnson noise equation and an establish ed transducer model has revealed a simple mathematical expression for the m inimum signal force detectable in air with an open-circuit piezoelectric pl ate transducer operating in its thickness mode. A significant finding is th at, except for any frequency dependence associated with a transducer's intr insic losses, the minimum detectable signal force is independent of frequen cy. By contrast, the sensitivity (e.g. volts per unit signal force) is know n to be a strong function of frequency, with the principal peak being at th e plate's fundamental thickness resonance. The results are explained by sho wing that the new equation for minimum detectable force (MDF) is equivalent to the mechanical version of the Johnson noise equation. Both the Johnson noise equation and its mechanical equivalent are consistent with a generali zed theory of thermal noise, which is sometimes referred to as the fluctuat ion-dissipation theorem. It is now evident that the mechanical equivalent o f the Johnson noise equation provides a useful starting point from which ma ny other device-specific MDF equations may be derived with relative ease. T his approach is not restricted to piezoelectric transducers and can be appl ied regardless of whether the device is intended for operation in a solid, liquid or gaseous medium.