Finite element prediction of Q and equivalent electrical parameters of quartz resonators

The equivalent electrical parameters C₀, C₁, L₁ and R₁ can be calculated in an eigenvalue analysis. For high Q resonators, the motional capacitance C₁ and inductance L₁ can be calculated from the short and open circuit resonant frequencies. The prediction of Q due to power loss via the mounting supports is demonstrated. For accurate prediction of the energy loss via the mounting supports it is important to provide an energy sink such as a large base. The Q estimated from an eigenvalue analysis can be used in a forced vibration model to calculate equivalent electrical parameters C₀, C₁, L₁ and R₁.