Testing of a one dimensional model for Field II calibration

Field II is a program for simulating ultrasound transducer fields. It is capable of calculating the emitted and pulse-echoed fields for both pulsed and continuous wave transducers. To make it fully calibrated a model of the transducer’s electro-mechanical impulse response must be included. We examine an adapted one dimensional transducer model originally proposed by Willatzen [9] to calibrate Field II.

This model is modified to calculate the required impulse responses needed by Field II for a calibrated field pressure and external circuit current calculation. The testing has been performed with Pz27 piezoceramic discs from Ferroperm Piezoceramics A/S, Kvistgaard, Denmark. The transmitted acoustic pressures from two sets of each five disc samples with 10.08 mm diameters were measured in an automatic water bath needle hydrophone setup together with the current flow through the driving circuit.

Resonance frequencies at 2.1 MHz and 4 MHz were applied. Two types of circuits were considered, one circuit with a simple resistance load of 47.5 Ohm and one with an example of a LR tuning circuit typically found in commercial transducers. The measurements were averaged 128 times and afterwards compared to the calibrated Field II program for 1, 4, and 10 cycle excitations.

Two parameter sets were applied for modeling, one real valued Pz27 parameter set, manufacturer supplied, and one complex valued parameter set found in literature, Alguer´o et al. [11]. The latter implicitly accounts for attenuation. Results show that the combination of the model and Field II can calculate the pressure within −15 % to 5 % RMS error for long excitation bursts and 7 % to 23 % for short excitation bursts.

Furthermore it is shown that current simulations can be done within 1 % to maximum 33 % RMS error, where best current simulations are found for 4 MHz long burst simulations and worst case is found for 2.1 MHz short bursts. Finally it is shown that maximum pressure deviation for the real parameter set and the complex parameter simulation is 3 % for pressure and 5.3 % for current.