PRAP Version 2.2

(Piezoelectric Resonance Analysis Program)

The electromechanical coupling of a piezoelectric resonator influences the impedance or admittance of the resonator as a function of frequency. By modelling the complex impedance or admittance, the complex elastic, piezoelectric, and dielectric properties of the resonator can be determined. Examples of piezoelectric materials are Quartz, PZT, PVDF, PVDF-TRFE, Odd Nylons, 1-3 or 0-3 piezo-composites. The use of complex material properties allow account to be taken of losses in the resonator. Complex constants are related to the traditional tand and Q through the relations;



PRAP runs under Windows 95, 98, Windows NT, and Windows 2000. The user-friendly interface of PRAP ensures expert analysis is maintained in your laboratory regardless of personnel changes.

The PRAP package accepts a variety of optional plug-in analysis modules and optional plug-in data acquisition modules.

PRAP Analysis Modules

PRAP Data Acquisition Modules

Included with the Basic PRAP Package is the 6mm Symmetry Analysis Module. This includes seven standard 1-dimensional resonance modes of the 6mm crystal symmetry. The optional Basic Data Acquisition Module allows resonance spectra to be acquired directly from a variety of impedance analysers under a variety of measurement conditions. Additional optional plug-in data acquisition modules require the Basic Data Acquisition Module.

The following provide overviews of analysis and data acquisition with PRAP. For details about specific analysis or data acquisition modules, see the above links.

Features of Analysis

After the analysis of any resonance spectrum, PRAP uses determined material properties to generate a fit over the analysed resonance spectrum. Conversely, any set of material properties can be used to generate a theoretical resonance spectrum. Aside from the visual confirmation of analysis provided by the fitted spectrum, a norm parameter is generated as an estimate of the 'goodness-of-fit'.

Analysis with PRAP is enhanced with the PRAP Compound file. The Compound file allows one or more related resonance spectra to be brought together in one document. This allows collective analysis of the spectra to be performed. Types of analysis include; determining the dependence of a material property on a measurement or process variable (such as d33 as a function of frequency or temperature), statistical studies on the results for a set of similar samples, or the computation of the complete piezoelectric matrix for a crystal symmetry supported by the existing PRAP installation.

Other features exploit the analytical capability of PRAP;

  • Display resonance spectra in a variety of representations

  • Evaluate dispersion in complex material properties

  • Easily zoom in on regions of your resonance spectra with a convenient mouse zoom feature

  • Quickly copy results to the Windows clipboard for use in other software packages

  • Determine the standard deviation in material properties for a set of similar specimens.

  • Study the dependence of material properties on aspect ratio, geometry, density, etc.

Features of Data Acquisition

Aside from the simplicity and speed of acquiring resonance spectra with the optional Basic PRAP Data Acquisition Module, the additional optional plug-in data acquisition modules of PRAP provide advanced analytical capability. Examples of capability added by these modules include;

  • Study time dependencies through ageing or time response on DC bias field.

  • Study temperature dependence of material properties.

  • Study the DC bias field of electrostrictive or ferroelectric materials.

Technical Information about PRAP

This web site provides a wealth of technical information about resonance analysis using PRAP. Please see the following link for details.

PRAP Technical Information

PRAP Tutorials

Users of PRAP can perform a variety of tutorials from this web site designed to familiarise them with the sequence of steps required to analyse resonance spectra. Please see the following link for details;

PRAP Tutorials

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