Modeling Frequency Fluctuations in Surface Contaminated Crystal Resonators
Abstract
Effects of adsorption and desorption of surface contaminant molecules on mean resonant frequency and frequency fluctuations are studied. A model based on mass-loading of contaminant molecules with adsorption and desorption rates is developed. Equations relating change in mean frequency and frequency fluctuations to adsorption and desorption rates are derived. Since the adsorption and desorption rates are functions of pressure and temperature, change in mean frequency and spectral density of frequency fluctuations are studied with respect to pressure and temperature. Calculations are performed for a 10 MHz and a 525 MHz thickness-shear resonator. Frequency-temperature and frequency-pressure curves are plotted for the 10 MHz resonator. The curves do not follow a cubic polynomial function and have a magnitude in the range of 10 ppm. The mean square of frequency fluctuations under multilayer contamination is significantly greater than that under monolayer contamination. The spectral density of frequency fluctuations at 1 Hz is quite constant in a wide range of temperatures (-50 to 100 C) when the values of heat of adsorption for the second and subsequent layers is close to that for the first layer. The magnitude of spectral density of frequency fluctuations is about -120 dBc (Hz2/Hz). The spectral density of frequency fluctuations is inversely proportional to the fourth power of the thickness if other parameters are held constant. Since the resonator frequency is inversely proportional to the thickness, the spectral density is, in effect, proportional to the fourth power of resonator frequency.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 23, 1990
- Accession Number
- ADA226019
Entities
People
- Yook-kong Yong
Organizations
- Rutgers School of Engineering