Conversion of 1/f fluctuations in crystal resonator within an interresonance gap

摘要

This paper presents general relationships for transformationncoefficients of BAW or SAW crystal resonator amplitude and phasenfluctuations through the 1/f flicker noises of its motional and staticnequivalent parameters within the resonator inter resonance gap.nApproximate functions of phase and amplitude power spectral densitiesnare found based on Leeson's oscillator open loop model and are givennwith detailed consideration of Butler and Colpitts modes of operationnwith the assumption of full and zero inter noise correlation. It is alsonsubstantiated that a low-noise frequency region of crystal resonatornoperation exists in which the fluctuation influence of its motionalninductance and capacity tend to zero in oscillators. Five examples arengiven as an illustration of a good agreement of the measured data withnthe prediction curves, giving a possibility of resonator power phase andnamplitude spectral densities valuation at an arbitrary offset frequencynfrom the carrier through the 1/f flicker noises of resonator parameters.nEmphasis is laid in conclusion on the possible way of parameter spectralndensities definition