Measurement sensitivity analysis of one port BAW resonators

Equivalent circuit model parameters for both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators are usually extracted from measured S-parameter data. All S-parameter measurement systems ultimately introduce random perturbations which result in uncertainties in the extracted parameters. This stochastic behavior is best understood by performing a sensitivity analysis. A theoretical first order analysis was found to be very accurate for high figure of merit resonators, where the static capacitance does not contribute significantly to the overall admittance at series resonance. A more accurate measurement sensitivity analysis for single port quartz resonators was also developed. This technique did not disregard the effect of the static capacitance, as the first order approximation did. The result was a sensitivity analysis model which accurately predicted the uncertainty in measured data. This paper presents the results of the sensitivity analysis which accurately predicts the standard deviation to mean ratio of the motional arm resistance for any one port resonator, showing the effects of both magnitude and phase of the input reflection coefficient.