Effect of electrode area on equivalent circuit of AT-cut quartz resonator

A quartz resonator can be modeled as a series circuit consisting of an inductance (L), a capacitance (C), a resistance (R) in parallel with a capacitor (C₀), which are related to the dimensions, density, electrode area and elastic, dielectric and piezoelectric constants of the quartz. In this paper, the derivation of the equivalent circuit of a quartz resonator is briefly discussed and results of extensive research on the relationship between electrode area and equivalent circuit is presented. The main purpose of this work is to make it more simple and easy for quartz circuit design and application. The experimental results show that when the dimensions of quartz are constant, C and C₀ are directly proportional to the electrode area, and L and R are inversely proportional to the electrode area.