Study of intermodulation in RF MEMS variable capacitors

This paper provides a rigorous study of the causes and physical origins of intermodulation distortion (IMD) in RF microelectromechanical systems (MEMS) capacitors, its analytical dependence on the MEMS device design parameters, and its effects in RF systems. It is shown that not only third-order products exist, but also fifth order and higher. The high-order terms are mainly originated by the nonlinear membrane displacement versus applied voltage and, in the case considered in this study, with an additional contribution from the nonlinear dependence of the reflection coefficient phase on the displacement. It is also shown that the displacement nonlinear behavior also contributes to the total mean position of the membrane. In order to study these effects in depth, an analytical frequency-dependent IMD model for RF MEMS based on a mobile membrane is proposed and particularized to the case of a MEMS varactor-a device for which IMD can be significant. The model is validated, up to the fifth order, theoretically (using harmonic balance) and empirically (the IMD of a MEMS varactor is measured). To this end, a two-tone IMD reflection measurement system for MEMS is proposed.