A quartz crystal, when coupled to conventional oscillator circuitry by replacing its resonant tank circuit, results in an oscillator whose frequency is controlled by the crystal as shown schematically in Fig. 5.33. The precise control depends on the crystal geometry and orientation with respect to the crystallographic axis referred to as a cut. The AT cut, for example, is used in very stable frequency oscillators.
In a quartz thermometer, the transduction mechanism consists of the changes in the elastic and piezoelectric properties of the crystal as a function of temperature.
These changes result in corresponding changes of the oscillator frequency. The frequency of an oscillator can be represented by a third-order polynomial in temperature t80 and is expressed with reference to 25°C, as shown below.
where A, B, C are the temperature coefficients of frequency, f25 is the oscillator frequency at 25°C, and t is the temperature to be sensed. Hammond discovered a crystal cut where A was large and B, C were simultaneously zero, designated as the linear coefficient (LC) cut. This cut is used as a transduction element in quartz thermometers. Figure 5.33 shows an oscillator using the LC cut.
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| Fig 5.33 Crystalline quartz thermometer. |
Its output is a voltage whose frequency changes linearly with temperature. The outputs from the two oscillators are mixed, and the output of the mixer is a much lower frequency but retains the linear relationship between frequency and temperature. The quartz thermometer measures temperatures in the range -80 to 250°C with an accuracy of ±0.075°C. The sensitivity is 1000 Hz/°C and the corresponding resolution is 0.0001°C.
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