Assessment of Electromechanical Coupling Coefficient for a Completed PIN-PMN-PT Array

The calculation of electromechanical coupling coefficient (EMCC)used in KLM models of fully assembled transducers is generally an imprecise estimate which is derived from standardized element geometries and assumptions regarding ideal boundary loading and coupling conditions. With applicability to a fully assembled transducer, we propose a new closed form expression to calculate an effective coupling coefficient, or kEFF. An example 1-3 composite array design at 3.75MHz using PIN-PMN-PT single crystal material has been measured on the bench to demonstrate the method which utilizes the effective accuracy and economy of the 1D KLM model. To permit more comparisons between model and lab, the array was also heated in an oven at 160 °C for 15 minutes which produced reductions in EMCC of 5%, mechanical Q of 39%, clamped dielectric constant of 7.9
^%
, and effective transducer longitudinal velocity of 2.7
^%
. Utilizing the pre-and post-heating array impedance data, we found the aggregate predicted EMCC values using the new closed form expression exhibited half the error as compared to the traditional formula. In addition, in silico predictions using our full KLM model as the standard were performed which showed that our new method, using array designs with various matching layers, performed in a similar trend showing half the error of the traditional formula.