The effective coupling coefficient for a completed PIN-PMN-PT array.

The computation of the electromechanical coupling coefficient (EMCC) of a fully assembled medical ultrasound transducer array is directly computed with closed form expressions. The Levenberg-Marquardt non-linear regression algorithm (LMA) is employed to help confirm the EMCC calculated prediction (k) and provide statistical insights. The complex electrical impedance spectra of a 1-3 composite array with two matching layers operating at a 3.75 MHz center frequency using PIN-PMN-PT single crystal material is measured in air both before and after oven heating at 160 °C for 15 min. The oven heating produces changes in the EMCC of -4.9%, clamped dielectric constant of -11%, and effective transducer longitudinal velocity of -2.5%. Utilizing the pre- and post-heating array impedance data, the calculated EMCC values from the new closed form expressions agree well with the complete KLM model based LMA, and also exhibit approximately one tenth the error as compared to the formulas for a flat, unloaded transducer.