Automatically Generated and Experimentally Validated System-Level Model of a Microelectromechanical RF Switch

the past decade, microelectromechanical systems (MEMS) have been extensively explored with a view to applications in the field of radio frequency (RF) circuits. Microelectromechanical (MEM) switches employed for the routing of RF signals, for instance, exhibit better performances compared to other concepts because of their low insertion loss and very good voltage standing wave ratio [1]. A key prerequisite for the routine use of RF MEM switches as standard circuit elements is the availability of computationally efficient, but yet physically-based and, thus, predictive simulation models that describe their operational behavior within a design framework which is easily accessible to circuit designers and enables them to include the models in the design process directly at circuit level. In this work, we present a mixed-level model of an electrostatically actuated and viscously damped ohmic RF MEM switch, which provides an accurate physical description of the device behavior and is suitable for direct implementation into standard circuit simulators. The coupled multi-energy domain model is derived on the basis of the hierarchical modeling approach as reported in [2], and applying a dedicated MATLAB-based toolbox for automatic model generation [3]. Starting point of the modeling procedure is the decomposition of the device into tractable subsystems in the case of the RF switch, this is the mechanical subsystem represented by the perforated membrane and the four flat suspension springs (see Fig. 1), the electrostatic subsystem, this is the electric field which is confined by the perforated membrane and the actuation electrode, and, third, the fluidic subsystem comprising the ambient atmosphere that exerts damping forces on the moving parts of the structure. In a second step, physically-based macromodels for the subsystems are formulated and calibrated with reference to measurements performed with a white light interferometer. The mechanical subsystem is initially modeled using finite elements in order to extract the basic eigenmodes and the mechanical parameters of the device. The residual stresses induced by the manufacturing process are taken into account by adjusting the simulated value of the fundamental eigenfrequency to the measured one of 14 kHz (see Fig. 3). Then, a reduced-order model of the mechanical subsystem is formulated in terms of modal coordinates by considering only those eigenmodes that are relevant for the adequate description of the system dynamics under regular operating conditions. For the compact model of the electrostatic subdomain, a capacitive function is calculated in terms of the respective modal amplitudes and, from this expression, an equivalent single lumped capacitance model is extracted. The electrostatic model has been validated by optical measurements and conforms well with the measured data (see Fig. 4). Gas film damping effects are modeled in the framework of the mixed-level approach described in [4], which makes it possible to properly include the effects of edges and perforations in the plate, and also the varying gap height due to the surface profile underneath the membrane (see Fig. 2). Finally, the three subdomain macromodels are interlinked to form a coupled system-level model of the device, represented as generalized Kirchhoffian network coded in one of the commonly used hardware description languages (e.g. Verilog-A), and implemented in a standard circuit simulator. The model has been validated by evaluating the measured and simulated responses of the RF switch to an electrostatic excitation (voltage step function of 25 V). The measured and simulated data show excellent agreement (see Fig. 5). Especially the frequency shift caused by an increase of fluidic damping and spring softening during actuation is correctly predicted, while models of RF switches without physically-based description of the gas film damping fail at this point [5]. This demonstrates the power of our modeling a...