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Unformatted text preview: J. Micromech. Microeng. 7 (1997) 285–309. Printed in the UK PII: S09601317(97)837011 Equivalent circuit representation of electromechanical transducers: II. Distributedparameter systems Harrie A C Tilmans † CP Clare NV, Bampslaan 17, B3500 Hasselt, Belgium Received 25 April 1997, accepted for publication 29 August 1997 Abstract. Distributedparameter electromechanical transducers are examined theoretically with special regard to their dynamic electromechanical behaviour and equivalent circuits used to represent them. The circuits are developed starting from basic electromechanical transduction principles and the electrical and mechanical equations of equilibrium. Within the limits of the assumptions on boundary conditions, the theory presented is exact with no restrictions other than linearity. The link with lumpedparameter transducers, that were the subject of a previous publication will be indicated. Elementary electrostatic, electromagnetic, electrodynamic and piezoelectric transducers are used to illustrate the basic theory. Exemplary devices include a capacitive force (displacement) sensor, several types of a mechanical resonator, electromechanical filters, a piezoelectric thickness monitor and a piezoelectric acceleration sensor. 1. Introduction The advantages of using equivalent circuit representations for the smallsignal time and frequency analysis of electromechanical systems has been extensively explained and illustrated with examples in part I [1] of this paper. Summarizing, it can be said that equivalent circuits (1) provide a single representation of a system operating in more than one energy domain (e.g., electric, mechanical and acoustical), (2) give a better understanding and visualization of the system, (3) facilitate further analyses of the system in order to investigate the effects of connecting subsystems, or of making modifications to the system, and, moreover, (4) allow system analysis using the powerful methods of electrical network theory, for instance by using circuit simulation software such as SPICE. In part I [1], the analysis has been limited to lumpedparameter electromechanical systems. In this paper, the theory will be extended to include distributed (or continuous) parameter systems. In a distributed parameter system, as opposed to lumpedparameter systems, the mass, compliance, capacitance etc are not easily identifiable as lumped elements at individual points, but instead, are continuously distributed throughout the system [2–4]. It has been indicated in part I [1] that in lumpedparameter systems the wavelength of the signal is (much) greater than all physical dimensions of the system. In situations, however, where the dimensions of † Tel.: + 32 11 300 887. Fax: + 32 11 300 882. Email address: [email protected] the physical device are comparable or greater than the wavelength, the problem must be solved using the general theory of the threedimensional propagation of waves in solids (and fluids).solids (and fluids)....
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This note was uploaded on 01/17/2011 for the course EEE 5225 taught by Professor Dr.arnold during the Fall '10 term at University of Florida.
 Fall '10
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