Shown above is the -55oC to +85oC to -55oC frequency vs. temperature characteristic of an SC-cut resonator when the temperature was measured with a quartz thermometer external to the resonator.  When, during the same temperature cycle, the temperature was measured by means of the self-temperature sensing method, no hysteresis could be detected when observed on the scale shown above (for a discussion of the self-temperature sensing method, see  “Effects of Harmonics on f vs. T” later in this chapter, and “Resonator Self-Temperature Sensing” in chapter 2).
	The apparent hysteresis shown above is due to the thermal lag between the resonator and thermometer during the temperature cycle (the rate of change of temperature was ~0.25oC/min).  The left to right shift between the two curves is an indicator that one is observing apparent, rather than real hysteresis.  Real hysteresis usually shifts the curves vertically, i.e., in real hysteresis, at the same temperature, there is a frequency difference between the two curves.  In apparent hysteresis, the thermal gradients dominate the f vs. T results.
	The apparent hysteresis would have been much greater if the resonator had been, e.g., an AT-cut, because of the thermal transient effect (see “Warmup of AT- and SC-cut Resonators,” earlier in this chapter).
	R. L. Filler, “"Measurement and Analysis of Thermal Hysteresis in Resonators and TCXO's" Proc. 42nd Ann. Symp. On Frequency Control, pp. 380-388, 1988.
	J. A. Kusters and J. R. Vig, "Thermal Hysteresis in Quartz Resonators - A Review," Proc. 44th Annual Symposium on Frequency Control, pp. 165-175, 1990, IEEE Catalog No. 90CH2818-3.
	R. Filler and J. Vig, "Resonators for the Microcomputer-Compensated Crystal Oscillator," Proc. 43rd Annual Symposium on Frequency Control, pp. 8-15, 1989, IEEE Catalog No. 89CH2690-6.