Analysis of the transfer function for layered piezoelectric ultrasonic sensors

We model theoretically the voltage response to an acoustic pulse of a multilayer system forming a low noise capacitive sensor including a Polyvinylidene Fluoride piezoelectric film. First we model a generic piezoelectric detector consisting of a piezoelectric film between two metallic electrodes that are the responsible to convert the acoustic signal into a voltage signal. Then we calculate the pressure-to-voltage transfer function for a N-layer piezo-electric capacitor detector, allowing to study the effects of the electrode and protective layers thickness in typical layered piezoelectric sensors. The derived transfer function, when multiplied by the Fourier transform of the incident acoustic pulse, gives the voltage electric response in the frequency domain. An important concern regarding the transfer function is that it may have zeros at specific frequencies, and thus inverting the voltage Fourier transform of the pulse to recover the pressure signal in the time domain is not always, in principle, possible. Our formulas can be used to predict the existence and locations of such zeroes. We illustrate the use of the transfer function by predicting the electric signal generated at a multilayer piezoelectric sensor to an ultrasonic pulse generated photoacoustically by a laser pulse at a three media system with impedance mismatch. This theoretical calculations are compared with our own experimental measurements.