Modeling, Identification and Operation of Air-Coupled PMUTs in Non-Linear Regime

When Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) are used for air-coupled applications, nonlinear effects (hardening spring behavior) cause saturation in the emitted sound pressure level as the input voltage increases. This is due to the non-constant mode stiffness that depends on the displacement. Here, we adopt the Duffing Equation as a lumped-elements model of the hardening spring behavior, i.e. we consider an harmonic oscillator equation, where stiffness
$k(x)= k(1+\beta x + \gamma x^{2}$
) is a polynomial function of displacement
$x$
. We face the problem of non-linear model identification and leverage the non-linearity to maximize the emitted power. We developed a method based on real-time experimental measurements to: express the non-linear parameter ϒ as function of ß, reducing the unknowns of the Duffing oscillator from two to one; identify the value of the parameter ß, based on a pre-trained neural network, fed with a ring down acquisition; find in real-time an optimal excitation frequency, where the emitted power is significantly increased respect to the (linear) resonance frequency. We used a custom-designed microcontroller-based hardware platform and PMUTs with 70kHz nominal frequency. We achieved good agreement between the measurements of a ring down signal and the numerical solution of the considered model computed with the estimated parameters. By exciting the transmitter at the optimal frequency, we improved the maximum range of a ranging system from 2.0 meters to 3.4 meters.