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However, transfer functions for the two-port delay line configuration may be generalized. One such transfer function used for rapid simulation tools is as follows11:
where where f is the frequency, k is the piezoelectric coupling coefficient, τ is the delay between IDTs in wavelengths, CS is the capacitance for an IDT digit pair per unit length, NP is the number of IDT digit pairs, and X is defined as:
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| Physical quantity | Linear coefficient |
|---|---|
| Temperature | up to 100 ppm*/K |
| Pressure, stress | 2 ppm/kPa |
| Force | 10 ppm/kN |
| Mass loading | 30 ppm/μg·cm2 |
| Voltage | 1 ppm/V |
| Electric field | 30 ppm/V·μm−1 |
Figure 68: Linear coefficients for physical effects on SAW sensors6. *ppm = parts per million. For example, when measuring pressure, a change in SAW frequency of 2x10-6 corresponds to a change in pressure of 1 kPa.
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| Substrate material | Crystal cut | Linear TK* |
|---|---|---|
| Lithiumniobate LiNbO3 | rotated 128 Y/X cut Y/Z standard cut | 72 ppm**/K 92 ppm/K |
| Lithiumtantalate LiTaO3 | X/112Y 36 Y/X rotated cut | 18 ppm/K 30 ppm/K |
| Quartz (SiO2) | ST-X cut | 0 ppm/K |
Figure 79: Temperature coefficients at room temperature for SAW substrate materials. *TK = temperature coefficient. **See note on figure 6 8 above for explanation of ppm.
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10C.K. Campbell (1989), “Applications of Surface Acoustic and Shallow Bulk Acoustic Wave Devices,” Proceedings of the IEEE, Vol. 77, Issue 10, Oct 1989.
11W11W.C. Wilson, G.M. Atkinson (2007), “Rapid SAW Sensor Development Tools,” NASA Langley Research Center.