: The frequency-temperature (f-T) behavior of a crystal resonator depends upon temperature, and its spatial and temporal gradients. For quasi-isothermal changes the static f-T curve can be used to determine frequency shifts that occur, e.g., in oven-controlled units. The frequency then depends upon the parameters of the static f-T curve, the temperature range over which the oven cycles, and upon the oven setting point. The maximum frequency excursion has been computed for the AT and SC cuts of quartz in terms of these parameters as a function of the orientation angle. When thermal-transient-compensated cuts are not utilized, oven cyclings or other temperature perturbations introduce an additional nonnegligible component of the frequency shift. This effect is quantified by means of a simple mathematical model. The model is capable of predicting the thermal transient effects for AT cuts appearing in the literature. Simulations, using the model, disclose that sinusoidal temperature variations with periods of hours can readily lead to frequency instabilities much larger than would be expected using the static f-T curve for the AT cut. This effect should be greatly diminished in the vicinity of the SC cut.

Static and Dynamic Behavior of Quartz Resonators

1 SUMMARY Frequency fluctuations of 5-m~ 5th-overtone plano-convex, AT-cut and IT-cut, quartz crystal oscillators, held in a temperature-stabilized oven, were measured with reference to a CS oscillator (HP 5061A); temperature fluctuations were measured simultaneously using a Pt resistor The power spectral density of the temperature fluctuation was proportional to l/f2 , where f is Fourier frequency The power spectral density of the frequency fluctuation was separat d into three parts; one being proportional to l/>, one to l/f and the third being frequency independent The l/f part and the frequency independent part were in quantitative agreement with the power spectral density estimated from the temperature fluctuation A coherence function between the frequency and temperature fluctuations was calculated The frequency fluctuation is correlated with the temperature fluctuation in the l/$ and frequency independent regions However, the coherence is lower in the range where the l/f spectrum is observed The observed l/f fluctuation is larger than the instrumentation noise, and hence is not electric noise but is attributed to the frequency fluctuation itself

http://ieeexplore.ieee.org/iel5/10315/32748/01537456.pdf

1/f Frequency Fluctuation of a Quartz Crystal Oscillator and Temperature Fluctuation

This article discusses regularity between the temperature fluctuation of environment, in which operates the transmitting device, and a random frequency shift of a carrier. Shows how frequency stability over temperature of reference oscillators of transmitting devices influences the probability of packet loss as a result of collisions in asynchronous radio system without feedback. The analytical expressions that allow calculating the probability aliasing signals resulting from of random frequency shift, which takes into account the probability density function of the distribution of temperature fluctuations and temperature-frequency characteristic of the reference oscillator.

Investigation of the influence of frequency stability over temperature on the probability collisions in low-speed asynchronous radio system without feedback

This article discusses regularity between the temperature fluctuation of environment, in which operates the transmitting device, and a random frequency shift of a carrier. Shows how frequency stability over temperature of reference oscillators of transmitting devices influences the probability of packet loss as a result of collisions in asynchronous radio system without feedback. Particular solutions for the uniform and Gaussian distribution of random frequency shift are presented.

Probability of the Spectrums Overlap in Case of Carrier Frequency Random Shift in Asynchronous Radio System without Feedback

http://ieeexplore.ieee.org/iel5/10313/32746/01537263.pdf

T. Musha

Papers

Frequency Response of a Quartz Oscillator to Temperature Fluctuation