Determination of d₃₁ Piezoelectric Constant via Lumped Element Analysis

Characterizing piezoelectric materials is paramount for optimizing their design for sensing application. While multiple techniques target the determination of the d₃₁ piezoelectric constant, this work spotlights the lumped element modeling for this determination. By examining the observed impedance of sensors with predefined dimensions, the study extracts values closely tied to both material and sensor attributes. Utilizing the analogies between mechanical and electrical domains, this technique underscores the evaluation of input impedance, distinguishing itself through its accuracy and efficiency. Significantly, this method delivers precise measurements without the usual requirement for bias conditions or any other sample preparation, representing a notable advancement in the field of piezoelectric material characterization. Applied to a 120 μm-thick PZT thin film, the method demonstrated congruency with established techniques. Its unique capability to glean multiple parameters, notably d₃₁ , without the usual biases, accentuates its promise. Impedance measurements were utilized also to estimate the mechanical load on a piezoelectric sensor using corresponding electrical impedance measurements. The value obtained was compared to alternative characterization methods, demonstrating that our proposed approach had the least error when compared to the manufacturer's provided value. Additionally, the lumped element model was employed to determine the force exerted on the piezoelectric sensor, with the estimated force closely matching the measured applied force.