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handbook of modern sensors

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References 119<br />

specified and three equations <strong>of</strong> motion derived. By applying the equation <strong>of</strong> constraint<br />

i 1 − i 2 − i 3 = 0, it has been possible to condense all three equations <strong>of</strong> motion into a<br />

single expression. Note that each element in this expression has a unit <strong>of</strong> current (A).<br />

3.14.4 Analogies<br />

Earlier, we considered mechanical, thermal, and electrical elements separately. However,<br />

the dynamic behavior <strong>of</strong> these systems is analogous. It is possible, for example,<br />

to take mechanical elements or thermal components, convert them into an equivalent<br />

electric circuit, and analyze the circuit using Kirchh<strong>of</strong>f’s laws. Table 3.4 gives the<br />

various lumped parameters for mechanical, thermal, and electrical circuits, together<br />

with their governing equations. For the mechanical components, Newton’s second<br />

law was used, and for thermal components, we apply Newton’s law <strong>of</strong> cooling.<br />

In the first column <strong>of</strong> Table 3.4 the linear mechanical elements and their equations<br />

in terms <strong>of</strong> force (F ) are given. In the second column are the linear thermal elements<br />

and their equations in terms <strong>of</strong> heat (Q). In the third and fourth columns are electrical<br />

analogies (capacitor, inductor, and resistor) in terms <strong>of</strong> voltage and current (V and i).<br />

These analogies may be quite useful in a practical assessment <strong>of</strong> a sensor and for the<br />

analysis <strong>of</strong> its mechanical and thermal interface with the object and the environment.<br />

References<br />

1. Halliday, D. and Resnick, R. Fundamentals <strong>of</strong> Physics, 2nd ed. John Wiley &<br />

Sons, New York, 1986.<br />

2. Crotzer, D.R. and Falcone, R. Method for manufacturing hygristors. U.S. patent<br />

5,273,777; 1993.<br />

3. Meissner, A. Über piezoelectrische Krystalle bei Hochfrequenz. Z. Tech. Phys.<br />

8(74), 1927.<br />

4. Neubert, H. K. P. Instrument transducers. An introduction to their performance<br />

and design, 2nd ed. Clarendon Press, Oxford, 1975.<br />

5. Radice, P. F. Corona discharge poling process, U.S. patent 4,365, 283, 1982.<br />

6. Southgate, P.D., Appl. Phys. Lett. 28, 250, 1976.<br />

7. Jaffe, B., Cook, W. R., and Jaffe, H. Piezoelectric Ceramics. Academic Press,<br />

London, 1971.<br />

8. Mason, W. P. Piezoelectric Crystals and Their Application to Ultrasonics. Van<br />

Nostrand, New York, 1950.<br />

9. Megaw, H. D. Ferroelectricity in Crystals. Methuen, London, 1957.<br />

10. Tamura, M., Yamaguchi, T., Oyaba, T., and Yoshimi, T. J. Audio Eng. Soc. 23(31)<br />

1975.<br />

11. Elliason, S. Electronic properties <strong>of</strong> piezoelectric polymers. Report TRITA-FYS<br />

6665 from Dept. <strong>of</strong> Applied Physics, The Royal Institute <strong>of</strong> Technology, Stockholm,<br />

Sweden, 1984.<br />

12. Piezo Film Sensors Technical Manual. Measurement Specialties, Inc., Fairfield,<br />

NJ, 1999; available from www.msiusa.com.

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