Introduction to Quartz Frequency Standards - Thermal Hysteresis and Retrace

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The f vs. T characteristics of crystal oscillators do not repeat exactly upon temperature cycling [27]. The lack of repeatability in TCXOs, "thermal hysteresis," is illustrated in Figure 23. The lack of repeatability in OCXOs, "retrace," is illustrated in Figure 24. Hysteresis is defined [28] as the difference between the up-cycle and the down-cycle f vs. T characteristics, and is quantified by the value of the difference at the temperature where the difference is maximum. Hysteresis is determined during at least one complete quasistatic temperature cycle between specified temperature limits. Retrace is defined as the nonrepeatability of the f vs. T characteristic at a fixed temperature (which is usually the oven temperature of an OCXO) upon on-off cycling an oscillator under specified conditions.

Figure 23. Temperature-compensated crystal oscillator (TCXO) thermal hysteresis, showing that the first f vs. T characteristic upon increasing temperature differs from the characteristic upon decreasing temperature.

Figure 24. Oven-controlled crystal oscillator (OCXO) retrace example, showing that upon restarting the oscillator after a 14 day off-period, the frequency was about 7x10^-9 lower than what it was just before turn-off, and that the aging rate had increased significantly upon the restart. About a month elapsed before the pre-turn-off aging rate was reached again. (Figure shows Df/f in parts in 10⁹ vs. time in days.)

Hysteresis is the major factor limiting the stability achievable with TCXOs. It is especially so in the MCXO because, in principle, the digital compensation method used in the MCXO would be capable of compensating for the f vs. T variations to arbitrary accuracy if the f vs. T characteristics could be described by single-valued functions.

Retrace limits the accuracies achievable with OCXOs in applications where the OCXO is on-off cycled. Typical values of hysteresis in TCXOs range from 1 ppm to 0.1 ppm when the temperature-cycling ranges are 0°C to 60°C, and -55°C to +85°C. Hysteresis of less than 1 x 10^-8 has been observed in a few SC-cut (MCXO) resonators [25]. The typical MCXO resonator hysteresis in early models of the MCXO was a few parts in 10⁸ [14]. Typical OCXO retrace specifications, after a 24 hour off period at about 25°C, range from 2 x 10^-8 to 1 x 10^-9. Low-temperature storage during the off period, and extending the off period, usually make the retrace worse [17].

The causes of hysteresis and retrace are not well understood; the experimental evidence to date is inconclusive [27]. The mechanisms that can cause these effects include strain changes, changes in the quartz, oscillator circuitry changes, contamination redistribution in the crystal enclosure, and apparent hysteresis or retrace due to thermal gradients.

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