Electromechanical and electromagnetic analyses of two- and three-plate voltage-controlled oscillators (VCOs) with micromachined tunable capacitors

This work presents the simulation-based electromechanical and electromagnetic analyses of two-plate and three-plate CMOS voltage-controlled oscillators (VCOs). These oscillators, described in, use electromechanically tunable capacitors fabricated using the MUMPs process and integrated inductors. Numerical models for each capacitor design were constructed using appropriate dimensions and material properties. The effects of process-induced stresses and electrostatic fringing fields were incorporated in the design analyses of the capacitors. Coupled electromechanical analyses were performed to measure the behavior of the tunable capacitors as a function of the applied voltages. The two-plate capacitor has a nominal capacitance of 2.05 pF, is tunable to 3.08 pF, and has a Q-factor of 20 at 1 GHz and 11.6 at 2 GHz. The three-plate capacitor has a nominal capacitance of 4.0 pF, is tunable to 7.4 pF, and has a Q-factor of 15.4 at 1 GHz and 7.1 at 2 GHz. The electromagnetic analyses were performed using the Generalized Transverse Resonance-Diffraction (GTRD) method, a 3D integral equation approach well suited for quasi-planar structures involving thick conductors and dielectric discontinuities. Structures of this type usually prove to be challenging for standard 3D techniques (e.g. Finite Elements, Finite Differences, etc.) owing to their critical aspect ratio, while being ill-suited for the so-called 2.5 techniques, in which conductor thickness and dielectric discontinuities are hardly accounted for. The combination of electromechanical and electromagnetic simulations presented in this paper allows for complete analysis and optimization of RF MEMS devices to be performed at the simulation stage.