Analysis of electrical equivalent circuit elements of piezo-tuning forks by the finite element method

A finite element method (FEM) employing three-dimensional (3D) linear piezoelectric solid elements is used to analyze the vibrational characteristics of piezo-tuning forks. From this information, the equivalent circuit elements such as equivalent inductance, capacitance, mass and capacitance ratio can be calculated. Stable piezo-tuning forks can easily be adapted as mechanical filters by addition of couplers. Besides the aforementioned equivalent elements, it is necessary in filter design to ascertain the ideal transformer ratios which relate to the coupling between the tuning forks forming the filter. A method for estimating these ratios is presented. An example of a particular tuning fork using two candidate materials, quartz and lithium tantalate, is given to illustrate the finite element analysis and the calculations of the equivalent circuit elements.