Coefficients quartz resonator, frequency

A filter is required to pass a certain selected frequency band, or to stop a given band. The passband for a piezoelectric device is proportional to k2, where k is the appropriate coupling coefficient. The very low k value of about 0.1 for quartz only allows it to pass frequency bands of approximately 1% of the resonant frequency. However, the PZT ceramics, with k values of typically about 0.5, can readily pass bands up to approximately 10% of the resonant frequency. Quartz has a very high Qm (about 106) which results in a sharp cut-off to the passband. This, coupled with its very narrow passband, is the reason why the frequency of quartz oscillators is very well defined. In contrast PZT ceramics have Qm values in the range 102—103 and so are unsuited to applications demanding tightly specified frequency characteristics. 

Quartz Crystal Thermometer. The temperature coefficient of the resonant frequency of quartz (14-20 MHz), using the piezoelectric effect, is a function of temperature (1 kHz per degree). In the temperature range -80°C to 230°C, an electronically controlled quartz crystal thermometer can be accurate to 0.02°C and has a sensitivity of 10 microdegrees centigrade in temperature difference measurements. 

Another resonant-frequency thermometer is the quartz crystal resonator (Benjaminson and Rowland, 1972), which, if the crystal is properly cut, is quite linear from about 190 to 525 K. Although this thermometer has excellent resolution, it does exhibit hysteresis and drift. The principle of quartz crystal thermometry is based on the temperature dependence of the piezoelectric resonant frequency of a quartz crystal wafer of a given dimension. The angle of cut of the quartz crystal is selected to give as nearly a linear and yet sensitive correspondence between resonant frequency and temperature as possible. This angle of cut is referred to as an LC (linear coefficient) cut. The temperature sensitivity of the quartz crystal thermometer is about 1000 Hz/°C. 

In its original application as timing reference, special care has been taken to minimize the perturbations on frequency of the selected mode of vibration caused by unavoidable variations in the environment, first of all temperature and acceleration. The breakthrough of quartz crystal resonators in timekeeping is very much correlated to the existence of a specific crysfal cuf, at which the device resonance frequency provides a zero temperature coefficient of frequency at 25 °C and a remarkable temperature stability around room... 

Figure 6b and c shows the dynamic compliance and corresponding phase shift of the indenter (uncorrected for electronics). The response was fit to the model in Fig. 6a for this indenter the damping coefficient, Q is 0.008 Ns/m, resonance frequency, Q)o is 110 Hz, indenter mass, m is 236 mg, and spring constant, Ki is 116 N/m. A Berkovich diamond indenter with a tip radius of -200 nm was used for all experiments. Tip shape calibration and machine compliance were determined by standard techniques (14) using electropolished indium and quartz. 

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