handbook of modern sensors

References 497
plate—the so-called angle of cut. Thus, by selecting a cut, a negligibly small temperature
sensitivity may be achieved (AT- and BT-cuts), or just the opposite—a cut with
pronounced temperature dependence may be selected. The temperature dependence
of the resonant frequency may be approximated by a third-order polynomial:
f
f 0
= a 0 + a 1 T + a 2 T 2 + a 3 T 3 (16.53)
where T and f are the temperature and frequency shifts respectively, f 0 is the
calibrating frequency, and a are the coefficients. The first utilization of temperature
dependence was made in 1962 by utilizing a nonrotated Y -cut crystal [22]. A very
successful development of a linear temperature coefficient cut (LC) was made by
Hewlett- Packard [23]. The second- and third-order coefficients had been eliminated
by selecting a doubly-rotated Y -cut. The sensitivity (a 1 ) of the sensor is 35 ppm/ ◦ C and
the operating temperature range is from −80 ◦ Cto230 ◦ C with a calibration accuracy
of 0.02 ◦ C. With the advent of microprocessors, linearity became a less important
factor, and more sensitive, yet somewhat nonlinear quartz temperature sensors had
been developed by using a slightly singly rotated Y -cut (Q =−4 ◦ C) with sensitivity
of 90 ppm/ ◦ C [24] and by utilizing a tuning-fork resonators in flexural and torsional
modes [25,26].
It should be noted that thermal coupling of the object of measurement with the
oscillating plate is always difficult and, thus, all piezoelectric temperature sensors
have a relatively slow response as compared with thermistors and thermoelectrics.
References
1. Benedict, R. P. Fundamentals of Temperature, Pressure, and Flow Measurements,
3rd ed. John Wiley & Sons, New York, 1984.
2. Callendar, H. L. On the practical measurement of temperature. Phil. Trans. R.
Soc. London 178, 160, 1887.
3. Sapoff, M. Thermistor thermometers. In: The Measurement, Instrumentation and
Sensors Handbook. J.G. Webster, ed., CRC Press, Boca Raton, FL, 1999, pp.
32.25–32.41.
4. Fraden, J.Atwo-point calibration of negative temperature coefficient thermistors.
Rev. Sci. Instrum. 71(4), 1901–1905, 2000.
5. Steinhart, J.S. and Hart, S.R. Deep Sea Res., 15, 497, 1968.
6. Mangum, B.W. Rev. Sci. Instrum. 54(12), 1687, 1983.
7. Sapoff, M., Siwek, W.R., Johnson, H.C., Slepian, J., and Weber, S. In: Temperature.
Its Measurement and Control in Science and Industry. J.E. Schooley, ed.
American Institute of Physics, New York, 1982, Vol. 5, p. 875.
8. Keystone NTC and PTC Thermistors. Catalogue Keystone Carbon Company, St.
Marys, PA, 1984.
9. Caldwell, F.R. Thermocouple Materials. NBS monograph 40. National Bureau
of Standards, Washington, DC, 1962.