Determination of Parameters of the Equivalent Electrical Circuit of the Sensitive Element of a Piezoresonance Sensor Based on Measuring the Zero Phase Frequency

In the presented work, a new technique for determining the parameters of the equivalent electrical circuit (EEC) of the piezoresonator based on the Butterworth-Van Dyke (BVD) model, which relies on the measurement of zero-phase frequencies, is proposed. The proposed technique is developed for use with available laboratory equipment, significantly simplifying and reducing the cost of the measurement process. Analytical expressions are presented that allow determining the parameters of the EEC of the piezoresonator without the use of approximate calculation methods. This expands the applicability of the proposed method in various sensor applications, including quartz microbalances, as well as pressure, temperature, and acceleration sensors, among others. The method's accuracy has been confirmed by numerical analysis performed using the Wolfram Mathematica software package, as well as by computer modeling in the Advanced Design System (ADS). The results obtained showed a high degree of agreement with the reference values provided by the manufacturer, with a maximum parameter deviation of no more than 0.037%. An experiment is described for determining the parameters of the equivalent electrical circuit of the piezoelectric resonator, conducted using the newly developed methodology.