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Electromechanical modelization of cantilever-driver transducers

Four different models have been developed in order to describe the electromechanical behaviour of a resonating Cantilever excited electrostaticaly by a parallel Driver electrode (CD). All these models can describe the capacitive current signal provided by the cantilever-driver system, when the oscillation of the cantilever is excited by an AC voltage, and a DC voltage is applied between driver and cantilever.

Starting from the most simple, we describe the main characteristics of the electromechanical models:
- Linear RLC//C model: The model provides values of the discrete elements of a resonating equivalent circuit RLC in parallel with the static cantilever-driver capacitance. It is an small signal model, which is only valid for small amplitude oscillations of the cantilever.

- Non-linear parallel plate approximation model: This is a large signal model valid for large amplitude oscillations. Approximations are made on considering that cantilever deflects parallel to the driver and that cantilever dynamics are reduced to a spring-mass system.

- Non-linear linear cantilever deflection approximation model: It is also a large signal model that only differs from the previous one on considering that cantilever deflects with a straight profile. This approximation gives a more realistic collapse prediction and allows analysing the effects on the position, shape and length of the driver coupling.

- Non-linear real curved cantilever deflection approximation model: It has the same characteristics of the two previous models but it gives a more real deflection profile of the cantilever and, as consequence, it describes more accurately both the static and dynamic behaviour of the cantilever-driver transducer.

In general, the first model is valid for stiff cantilevers which will vibrate with small amplitudes. The second and the fourth Models are specially appointed for soft cantilevers. All the models describe the capacitive current provided by the CD. Besides, last three models give information on mechanical magnitudes as cantilever deflection, electrostatic force or velocity, predicts non-linear effects like collapse or electrostatic spring constant softening and can be implemented on a SPICE-like simulator, giving the opportunity to simulate the behaviour of the CD transducer together with electronic circuitry.

Related information

Reported by

Department of Electronic Engineering
Universitat Autònoma de Barcelona. Edifici Q. Escola Tècnica Superior d’Enginyeria
08193 Bellaterra (Barcelona)
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