Quartz resonators with load capacitance-problems of modelling and measurements

In most application circuits, a quartz resonator does not work at the series resonance frequency f_s. Typically, the quartz resonator is loaded with a series capacitance C_L. In most cases, only the frequency f_s of series resonance and the motional resistance R₁ of the resonator are measured. The considerations presented in this paper concern following problems: proper modelling (using equivalent network) of the resonator loaded with an application circuit of capacitive character; choosing and defining parameters useful for prediction of the properties of such a circuit; measuring these parameters; construction of test fixture with an electrically controlled load capacitance. The measurement of motional capacitance and parameters characterizing pullability of quartz resonator frequency is not a trivial task, especially for higher frequencies. Due to major influence of stray capacitances connected with the tested resonator, test fixture and application circuit, measured load resonance frequency, pulling range and pulling sensitivity can differ substantially from those which appear in application circuit