Page 230 - The Mechatronics Handbook

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when a pressure differential exists across the transducer, so that the impedances of the variable capacitors
change according to the displacement

dx
–
= ------------------------ and Z C = d + x
Z C ------------------------
db 8.854 jwA bc 8.854 jwA
and we obtain the following expression for the phasor output voltage, if we choose R 1 = R 2 .
 ------------------------ 
d +
x
R 2 

V out jw( ) = V S jw) -------------------------------------------------------- – -----------------
8.854 jwA
(
 d – x d + x R 1 + 
 ------------------------ + ------------------------ R 2 
8.854 jwA
8.854 jwA
R 2 

x
1
= V S jw( ) -- + ------ – -----------------
2  2d R 1 + R 2 
x
= V S jw( )------
2d
Thus, the output voltage will vary as a scaled version of the input voltage in proportion to the displacement.
References
Irwin, J.D., 1989. Basic Engineering Circuit Analysis, 3rd ed., Macmillan, New York.
Nilsson, J.W., 1989. Electric Circuits, 3rd ed., Addison-Wesley, Reading, MA.
Rizzoni, G., 2000. Principles and Applications of Electrical Engineering, 3rd ed., McGraw-Hill, Burr
Ridge, IL.
Smith, R.J. and Dorf, R.C., 1992. Circuits, Devices and Systems, 5th ed., John Wiley & Sons, New York.
1993. The Electrical Engineering Handbook, CRC Press, Boca Raton, FL.
Budak, A., Passive and Active Network Analysis and Synthesis, Houghton Mifflin, Boston.
Van Valkenburg, M.E., 1982, Analog Filter Design, Holt, Rinehart & Winston, New York.

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