S. Y. Parameters Method for Accurate Measurements of Bulk Wave Crystal Resonators at Frequencies Up to 2 GHz,

Bulk wave quartz crystal resonators with very-high Q factors or of very high frequencies have received great attention in recent years and they do require new methods of characterization. A general method allowing accurate measurements of high Q or high frequency crystal resonators is described. The basic idea is the use of the admittance matrix of the resonator. For low frequency resonators f or 200 MHz, the transmission method through the classical I EC pi network leads to the determination of Y12 f and gives accurate results of motional parameters and frequency. For VHF crystals up to 2 GHZ the Y matrix is computed from the four S parameters. The equipment used the basic steps of the method and the calibration and measurement procedures are described. Typical results are presented. Accuracy and reproducibility of measurements are discussed for both high Q and VHF crystals.