In this paper, a closed-form expression for the pull-in voltage of fixed–fixed beams and fixed–free beams is derived starting from the known expression of a simple lumped spring-mass system. The effects of partial electrode configuration, of axial stress, non-linear stiffening, charge re-distribution and fringing fields are all included in the final expression. Further, the results obtained are summarized and validated with other existing empirical and analytical models as well as with finite element simulation results. The model agrees well with finite element simulation results obtained with COVENTORWARE software.

In this paper, the design, modelling and performance characteristics of electrostatically driven vacuum-encapsulated polysilicon resonators are addressed. A one-port configuration is preferably employed for excitation and detection of the vibration. Mechanical instability (pull-in) is discussed on the basis of the energy minimum principle. An expression for the pull-in voltage of a beam is given. The electromechanical behaviour in a limited frequency regime around the fundamental resonance is accurately modelled by an electric circuit consisting of a (static) capacitor shunted by a series (dynamic) RLC branch. The d.c. bias dependence of the circuit components and of the series resonance frequency has been experimentally investigated and is compared with the theory. The large-amplitude behaviour is discussed as well. The plate modulus and residual strain of boron-doped polysilicon are estimated from the resonance frequencies of microbridges of varying lengths. The feasibility of their application as resonant strain gauges is investigated. The 210 m long beams typically have an unloaded fundamental frequency of 324 kHz, a gauge factor of 2400 and an uncompensated temperature coefficient of-135 ppm 'C-'.

Lumped-parameter 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. Elementary electrostatic, electromagnetic, and electrodynamic transducers are used to illustrate the basic theory. Exemplary devices include electro-acoustic receivers (e.g., a microphone) and actuators (e.g., a loudspeaker), electromechanical filters, vibration sensors, devices employing feedback, and force and displacement sensors. This paper forms part I of a set of two papers. Part II extends the theory and deals with distributed-parameter systems.

A review of micro resonant force gauges IS presented A theoretlcal descnptlon IS aven of gauges operahng m a flexural mode of vlbratlon, mcludmg a dlscusslon of non-hnear effects Gauge factor and quahty factor are defined and their relevance IS dIscussed Performance Issues such as sensltlvlty, stablhty and resolution are addressed Design aspects, mcludmg the means for excltahon and detection of the vlbratron, and examples of slhcon mlcrofabncatlon technolo@es are described

Wireless communication has led to an explosive growth of emerging consumer and military applications of radio frequency (RF), microwave and millimeter wave circuits and systems. Future personal (hand-held) and ground communications systems as well as communications satellites necessitate the use of highly integrated RF frontends, featuring small size, low weight, high performance and low cost. Continuing chip scaling has contributed to the extent that off-chip, bulky passive RF components,

Basic design issues and a fabrication process based on surface-micromachining 'techniques for electrostatically driven vacuumencapsulated polysilicon resonators are presented. A novel freeze-drying method that does not require vacuum equipment is presented. Reactive sealing with LPCVD silicon nitride is used to create the evacuated cavity, resulting in cavity pressures close to the deposition pressure. Design issues regarding choice of materials, technology and layout are discussed, First experimental results, including an admittance plot of the one-port resonator and a plot indicating the dependence of the Qfactor on the resonator geometry and ambient pressure, are presented.

The mechanisms causing stiction of polysilicon structures fabricated by surface micromachining techniques have been investigated. It is found that during drying from rinse liquids attractive dynamic capillary forces are responsible for bringing micromechanical structures into contact with the underlying substrate. Measured adhesion energies of sticking microbridges indicate that van der Waals forces are responstble for the stiction of hydrophobic surfaces and that hydrogen bridging is an additional adhesion mechanism for hydrophilic surfaces. Methods to reduce the stiction problem are indicated.

Several errors occurred in the tables and equations of this article. The corrected versions are reproduced below.   Table 1. Constitutive and transfer equations of the lumped-parameter transducers shown in figure 3, completed with a stabilization spring k at the mechanical port (as illustrated by figure 4). The matrix equations describe the relations between the phasor quantities of the sinusoidal signals. The meaning of the symbols is explained in appendix B and in table 2.   Table 2. Parameters used in table 1, expressed in terms of the dimensional parameters, the bias conditions, and physical constants.   Table 3. Direct electromechanical analogies for lumped translational systems [1,2].