Admittance Bridge Determination of Quartz Vibrator Parameters Using Augmenting Immittance Elements

Bridge methods are the most accurate means of determining the parameters of quartz vibrators, particularly in the VHF region and above. Present and future crystal requirement specifications point to the increasing use of such methods to obtain the accuracy necessary for both filter and oscillator applications. A practical difficulty that arises is that the ranges of any given bridge are not compatible with every immittance characteristic encountered with the various crystal types in use, particularly if measurements are to be made over substantially different portions of the region of resonance. One means of obviating this difficulty is to augment the crystal with another impedance element in series or parallel so that the behavior of the combination is accommodated within the bridge ranges. A capacitance in parallel with the crystal is suitable for reducing the variation in impedance bridges that consider the unknown as a series combination of resistance and reactance; a series element reduces the variation in admittance bridges that represent the unknown as a conductance and susceptance in parallel. The purpose of this paper is to discuss the applicability and limitations of this latter procedure and to describe how the crystal parameters are extracted from measurements of this type.