Frequency-dependent equivalent modelling of broadband air-coupled transducers

Abstract

Electrical impedance is an essential parameter for characterizing the performance of transducers during manufacturing and application phases. The conventional method to model the electrical impedance is based on Butterworth–Van Dyke (BVD) model with constant equivalent parameters, which is valid only in the neighborhood of resonance frequency. In this study, we present a method for modelling the electrical impedance over broadband featuring an improved BVD model with frequency-dependent equivalent parameters. In order to obtain frequency-dependent parameters from the measured impedance, estimation is performed in a constrained piecewise and stepwise manner. Firstly, a concise calculation method to obtain initial values of equivalent parameters is presented. Then, the original impedance is equally divided into multiple segments and the resonant segments containing the resonant frequencies are located. New impedance data is reconstructed with one of non-resonant segments and the resonant segments. Finally, with the initial values refined by genetic algorithm (GA), equivalent parameters are obtained from the reconstructed impedance based on GA. The estimation results are assigned to the central frequency point of the non-resonant segment. A new segment is generated by shifting the last non-resonant segment one frequency interval, and data reconstruction and estimation process are repeated till all parameters at each frequency are gained. Frequency-dependent parameters are obtained by the combination of a series of constant parameters at each frequency. The proposed method is verified with good accuracy in modelling of electrical impedance and transmitting response of broadband air-coupled transducer used for gas flow measurement which are difficult to be accurately modelled by the traditional method.