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

A theoretical analysis based on the Johnson noise equation and an established transducer model has revealed a simple mathematical expression for the minimum signal force detectable in air with an open-circuit piezoelectric plate transducer operating in its thickness mode. A significant finding is that, except for any frequency dependence associated with a transducer's intrinsic losses, the minimum detectable signal force is independent of frequency. By contrast, the sensitivity (e.g. volts per unit signal force) is known to be a strong function of frequency, with the principal peak being at the plate's fundamental thickness resonance. The results are explained by showing 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 generalized theory of thermal noise, which is sometimes referred to as the fluctuation-dissipation theorem. It is now evident that the mechanical equivalent of the Johnson noise equation provides a useful starting point from which many other device-specific MDF equations may be derived with relative ease. This approach is not restricted to piezoelectric transducers and can be applied regardless of whether the device is intended for operation in a solid, liquid or gaseous medium.