A linear systems model of the thickness mode piezoelectric transducer containing dual piezoelectric zones

The 'inversion layer' transducer (ILT), incorporating oppositely polarised piezoelectric zones across the thickness, has attracted recent interest. Such devices offer interesting properties particularly with regard to harmonic generation and the potential for wideband behaviour. This paper attempts to investigate the fundamental physical mechanisms that take place, through the creation of a 1D, linear systems model of the thickness mode ILT that incorporates two oppositely polarised zones of piezoelectric polarisation. Closed form solutions are obtained for the operational impedance, in addition to the transmission and reception transfer functions when the device is interfaced to an arbitrary electrical load. By representing device behaviour in a block diagram, of systems feedback format, cause and effect relationships are readily identified and the underlying differences between the ILT and conventional thickness mode transducer are demonstrated clearly. Examples are provided for a range of operating configurations, materials and external load parameters.