Modeling of piezoelectric multilayer ceramics using finite element analysis

For medical ultrasound imaging, 2-D array transducers have greater versatility than linear arrays. Unfortunately, the tiny array elements in a 2-D array have poor signal-to-noise ratio (SNR). We have previously shown that SNR is increased in 2-D array transducers made from piezoelectric multilayer ceramics. Conventional one-dimensional models provide accurate results when comparing multilayer ceramic performance relative to single layer transducers. However, these models are not accurate when comparing simulations directly to measurements. Because multilayer ceramics have a complex structure, a 3-D model, such as finite element analysis, is needed for accurate simulations. We modeled four arrays that were previously fabricated: a single layer and multilayer 1 MHz, 2-D array element, and a single layer and multilayer 2.25 MHz, 1.5-D array element that can focus and steer in azimuth but only steer in the elevation dimension. We compared the simulated and measured impedance plots for each transducer. The finite element analysis plots accurately predicted the impedance for each vibration mode. On the other hand, the one dimensional KLM transmission line model could simulate only the thickness mode vibrations and the results were inaccurate compared to measurements. We also simulated the transmit output pressure for the 2.25 MHz arrays and compared the results to measurements. The simulated pressure vs. time plots and their spectra were accurate when compared to measurements. Finally, we obtained a series of images that show the impulse response vibrations for the 2.25 MHz, arrays. These animations show the vibration modes in the complex multilayer ceramic structure. Measurements were not available to confirm the animations. Our results show that finite element analysis in three dimensions is a valuable tool to predict the performance of multi-layer transducers.