J. Phys. III France 4 (1994) 1305-1319
Application of the impedance transformation on transmission lines to electrochemical microbalanceM. Valentin and C. Filiâtre
Equipe de Physique et Electronique des Capteurs, ENSMM, 16 route de Gray, 25030 Besançon Cedex, France
(Received 15 November 1993, revised 28 February 1994, accepted 29 March 1994)
The purpose of this paper is to propose an analysis of stacked mechanical resonator designs in terms of microwave network approach. The application to electrochemical quartz crystal microbalance (EQCM) is achieved where we have priviliged the fundamental impedance transformation equation on transmission line relating the impedance at any point of the line to that at an other point of the line. From this systematic procedure applied to a quartz crystal with simultaneous mass loading and liquid loading we have derived the impedance expression and the near-series-resonance characteristics of the loaded crystal resonator by means of a multilayer model. The effect of thickness of a mass layer and of a contacting Newtonian liquid on real and imaginary parts of impedance is predicted for several deposited materials. A lumped equivalent circuit is obtained from this formulation and the proposed results are compared with recently published experiments. The analysis presented in the familiar context of distributed circuit theory make the formulation and the physical interpretation of various scattering problems easier.
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