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**9** 

 *Italy* 

**Dynamics of RF Micro-Mechanical** 

**in Coplanar Waveguide Configuration** 

Romolo Marcelli1, Daniele Comastri1,2, Andrea Lucibello1,

*2University of Roma "Tor Vergata", Electronic Engineering Dept., Roma,* 

Giorgio De Angelis1, Emanuela Proietti1 and Giancarlo Bartolucci1,2

Micro-electromechanical switches for Radio Frequency applications (RF MEMS switches)[1]- [4] are movable micro-systems which pass from an ON to an OFF state by means of the collapse of a metalized beam. They can be actuated in several ways but, generally, the electrostatic actuation is preferred because no current is flowing in the device nor power

The bias DC voltage signal is usually separated with respect to the RF signal for application purposes. Anyway, in the simplest mechanical model, a voltage difference *V* is imposed between the metal bridge, connected to the ground plane of a coplanar waveguide (CPW) structure, and the central conductor of the CPW, which also carries the high frequency signal. Under these circumstances, the switch will experience an electrostatic force which is balanced by its mechanical stiffness, measured in terms of a spring constant *k*. The balance is theoretically obtained until the bridge is going down approximately (1/3) of its initial height. After that, the bridge is fully actuated, and it needs a value of *V* less than the initial one to remain in the OFF (actuated) position, because contact forces and induced charging effects help in maintaining it in the down position. A general layout of the switch is diagrammed in Fig. 1a, with its simplified equivalent lumped electrical circuit. In Fig. 1b the cross-section of the device is shown, with the quantities to be used for the definition of the

The actuation as well as the de-actuation are affected also by the presence of a medium (typically air, or preferably nitrogen for eliminating humidity residual contributions in a packaged device) which introduces its own friction, causing a damping, and altering the speed of the switch [5]-[7]. Several models are currently available to account for a detailed treatment of the damping, including also the presence of holes in the metal beam [8]-[11]. Moreover, the damping modifies the natural frequency of oscillation for the bridge. In particular, the actuation and de-actuation mechanisms will be consequently affected, leading to *simple oscillations* (no fluid damping contribution) or *damped oscillations* (fluid contribution) up to *over-damping* for particular values of the bridge dimensions or material properties. Experimental problems related to the dynamic characterization of

**1. Introduction** 

absorption has to be involved in the process.

geometry and of the physical properties of the structure.

**Capacitive Shunt Switches** 

*1CNR-IMM Roma, Roma,* 
