Abstract
The Navy is constantly developing new materials for use as the active element(s) in high-performance underwater projectors. One such class of materials is the electrostrictive ceramics such as lead magnesium niobate/lead titanate (PMN/PT). These materials are characterized by high strain per unit electric field, high permittivity (ε = 12000), and a low Curie temperature. These ceramics must be used in their unpoled state in contrast to other classes of ceramic, such as lead zirconate titanate (PZT) ceramics that are usually poled before use.
For PMN/PT, the strain as a function of electric field is an almost perfect square-law, s = kE2, over a large range of voltages, neglecting higher-order effects such as hysteresis and saturation. This response suggests that a transducer made of PMN/PT should be driven by superimposing an ac signal upon a large bias voltage. The bias voltage is needed to achieve a large effective strain/volt (d33) in response to the ac signal. If the ac signal amplitude is greater than a few percent of the bias voltage, significant distortion appears in the output due to the material’s nonlinear response (Fig. 1). Further, when this material is incorporated into an electromechanical transducer the transducer’s transient response is a complex combination of the material’s nonlinearity and the poles and zeros of the mechanical system. If the output displacement of the transducer is to be a large fraction of the maximum possible displacement, a method must be found to overcome the effects of nonlinearity and transient response.
The goal of this work is to generate an output signal that is a near-perfect replica of a desired signal (e.g., a sinusoid that is turned on at t = 0) by driving the transducer with an “inverse” signal derived from a nonlinear model of the transducer. The nonlinear model used for a PMN/PT transducer is the Hunt electrostatic model, modified to include both polarization in the PMN material and the effects of radiation loading on the transducer. The model is presented in the form of coupled ordinary (but nonlinear) differential equations. Parameters for the model are estimated by fitting the model to actual data obtained by driving a PMN stack. Results for the parameters and for the goodness-of-fit of the model are presented. The model and its associated parameters for the stack are then effectively inverted by calculating the drive voltage required to produce a given sinusoidal displacement at the face of the transducer. Finally, the transducer is driven by the calculated drive and the resulting waveform is compared with the desired sinusoidal output. Measures of harmonic distortion reduction for a given output amplitude are presented.
