Static and dynamic aspects of an air gap capacitor

This paper deals with the theory of an air-gap capacitor used as a micromechanical resonator. Both static and dynamic aspects are discussed. A single-element approach for the electrostatic excitation and capacitive detection of the vibrational motion of the resonators is described. The non-linear character of the electrostatic force is accounted for in the static analysis. The behaviour of the air-gap capacitor is modelled as a lumped spring-mass system and its limitations are discussed. Also an equivalent electrical one-port network is derived, which can be used in a circuit simulation to account for the mechanical behaviour of the resonator. The results obtained from the spring-mass system are compared with the results obtained from a more elaborate numerical analysis of the air-gap capacitor. The lumped spring-mass system is adequate for modelling the air-gap capacitor.