A new factor affecting the acceleration sensitivity of the resonance frequency of quartz crystal resonators

A theory is presented showing that the acceleration sensitivity degradation of quartz crystal resonators due to a coupling of elastic and electrical properties in the crystal mounting structure and associated electrical paths can have magnitudes of 10^-10 per g. The exact electrical impedance of a lossless single thickness mode piezoelectric resonator with a series electrical inductance and a shunt electrical capacitance is discussed. All overtones are included in the derived impedance equation. A computer algorithm for calculating the exact electrical impedance of a lossy single thickness mode piezoelectric resonator with a series electrical inductance and a shunt electrical capacitance is discussed. Some calculations of the resonance frequency (reactance=0) of the single thickness mode piezoelectric resonator with series electrical inductance and shunt electrical capacitance are given. Some calculations of the movement of crystal blanks inside a package and the resonance frequency shifts associated with the resultant changes in the series electrical inductance and electrical shunt capacitance are given. Experiments which include cable effects and resonator orientation show that in a simple fixture a quartz SC blank can be made to have a reproducible 10^-11/g acceleration sensitivity