John R. Vig

Noise in microelectromechanical system resonators

Microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) based resonators and filters, ranging in frequencies from kHz to GHz, have been proposed. The question of how the stabilities of such resonators scale with dimensions is examined in this paper, with emphasis on the noise characteristics. When the dimensions of a resonator become small, instabilities that are negligible in macro-scale devices become prominent. The effects of fluctuations in temperature, adsorbing/desorbing molecules, outgassing, Brownian motion, Johnson noise, drive power and self-heating, and random vibration are explored. When the device is small, the effects of fluctuations in the numbers of photons, phonons, electrons and adsorbed molecules can all affect the noise characteristics. For all but the random vibration-induced noise, reducing the dimensions increases the noise. At submicron dimensions, especially, the frequency noise due to temperature fluctuations, Johnson noise, and adsorption/desorption are likely to limit the applications of ultra-small resonators.

Fundamental limits on the frequency stabilities of crystal oscillators

The frequency instabilities of precision bulk acoustic wave (BAW) quartz crystal oscillators are reviewed. The fundamental limits on the achievable frequency stabilities, and the degree to which the fundamental limits have been approached to date are examined. Included are the instabilities as a function of time, temperature, acceleration, ionizing radiation, electromagnetic fields, humidity, atmospheric pressure, power supply, and load impedance. Most of the fundamental limits are zero or negligibly small, a few are finite. We speculate about the progress which may be achievable in the future with respect to approaching the fundamental limits. Suggestions are provided about the paths that may lead to significant stability improvements.<<ETX>>

Resonator surface contamination-a cause of frequency fluctuations?

The mass loading effects of adsorbing and desorbing contaminant molecules on the magnitude and characteristics of frequency fluctuations in a thickness-shear resonator are studied. The study is motivated by the observation that the frequency of a thickness-shear resonator is determined predominantly by such mechanical parameters as the thickness of the resonator, elastic stiffnesses, mass loading of the electrodes, and energy trapping. An equation was derived relating the spectral density of frequency fluctuations to: (1) rates of adsorption and desorption of one species of contaminant molecules; (2) mass per unit area of a monolayer of molecules: (3) frequency constant; (4) thickness of resonator; and (5) number of molecular sites on one resonator surface. The induced phase noises were found to be significant in very-high-frequency resonators and are not simple functions of the percentage of area contaminated. The spectral density of frequency fluctuations was inversely proportional to the fourth power of the thickness if other parameters were held constant. >

Dual-mode oscillators for clocks and sensors

Frequency can be measured with far higher accuracy than any other quantity. Dual mode excitation of resonators allows the highly accurate measurement of, and compensation for, the effects of temperature, pressure, etc., by means of frequency measurements alone. In dual mode excitation, the two excited modes occupy the same volume of quartz, thereby eliminating gradients between the resonator and sensor. This paper reviews the dual-mode technique and its applications in oscillators, clocks and sensors.

Comments on the effects of nonuniform mass loading on a quartz crystal microbalance

The Sauerbrey equation can yield incorrect results when the mass and amplitude of vibration distributions are not uniform, and when the mass is not attached rigidly.

Hysteresis in quartz resonators-a review

The literature on the frequency versus temperature characteristics of quartz crystal resonators is reviewed. Three papers that deal with frequency versus pressure hysteresis are included, as these may possibly have relevance to frequency versus temperature hysteresis. It is seen that the causes of hysteresis are not well understood. The evidence to date is inconclusive. The mechanisms that can cause hysteresis include: strain changes changes in the quartz, contamination redistribution, oscillator circuitry hysteresis, and apparent hysteresis due to thermal gradients. The results to date seem to indicate that lattice defects are somehow related to thermal hysteresis. Stress relief in the mounting structure can also produce significant hysteresis. As crystal processing techniques have improved. contamination has become less of a problem.<<ETX>>

Modeling resonator frequency fluctuations induced by adsorbing and desorbing surface molecules

Resonator frequency fluctuations due to adsorption and desorption of molecules on plate electrodes are studied using the principle of mass-loading effects of adsorbed molecules. The study is based on a 525 MHz, AT-cut quartz resonator enclosed in a small crystal holder. Equations relating the surface adsorption rates of the crystal holder to pressure were derived and found to be quadratic polynomial functions of the adsorption rates. Calculations based on these equations show that a contaminant gas with a higher desorption energy creates larger changes in pressure when the temperature is varied. The function describing the frequency fluctuations due to any one contaminant site is a continuous-time Markov chain. Kolmogorov equations and an autocorrelation function for the Markov chain are derived. The autocorrelation and spectral density function of resonator frequency fluctuations are derived. The spectral density of frequency fluctuations at 1 Hz is studied as a function of pressure, temperature, and desorption energy of molecules. The noise levels for a contaminant gas with one type of molecules are found to be lower for lower desorption energies, and higher at lower pressures.<<ETX>>

Sensing the properties of liquids with doubly rotated resonators

Immersion of a resonator into a liquid results in changes in the resonators frequency and impedance. These changes have been used to characterize liquid properties. Frequency can be measured with far higher accuracy than impedance or any other quantity. The goal of the project described in this paper was to investigate whether or not it is possible to measure a liquids properties by means of frequency measurements alone. When a doubly rotated resonator (/spl theta//spl ap/35/spl deg/ and /spl phi/>0/spl deg/) is operated in a liquid, the displacement of the surface is partly out of the plane of the plate. By controlling the /spl phi/ angle, one may control the ratio of in-plane to out-of-plane displacements. The out-of-plane component of the displacement propagates a damped compressional wave into the liquid, while the in-plane component propagates a damped shear wave. The frequency changes of doubly rotated resonators have been measured in glycerol solutions of a variety of concentrations. At each concentration, the frequency change was found to increase with increasing /spl phi/ angle. A method is proposed for the determination of a fluids density, viscosity and acoustic wave velocity.

Doubly rotated resonators for sensing the properties of liquids

When a doubly rotated resonator is operated in a liquid, the displacement of the surface is partly out of the plane of the plate of the resonator. The out-of-plane component of the displacement propagates a damped compressional wave into the liquid, and the in-plane component propagates a damped shear wave. In this paper, we report the measurements of the series resonant frequency and the motional arm resistance of doubly rotated quartz resonators (/spl theta//spl ap/35/spl deg/ and /spl phi/=7/spl deg/) in liquids to compare with singly rotated AT-cut resonators (/spl theta//spl ap/35/spl deg/ and /spl phi/=0/spl deg/). A modified Butterworth-Van Dyke (BVD) equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading.

On acoustic sensor sensitivity

Acoustic sensor sensitivity expressed as frequency change per unit of measurand can result in the erroneous conclusion that higher-frequency sensors are superior to lower-frequency ones. It is argued that, when compared on the bases of reproducibility and resolution capability, good low-frequency sensors are superior to good high-frequency ones.<<ETX>>