Analytical modeling of the harmonic distortion caused by squeeze film damping in MEMS-based acoustic transducers

Miniaturized microelectromechanical system (MEMS) microspeakers are currently trending in the development of acoustic transducers. When a transducer is scaled down to fit on a microelectronic chip, its physics differ from the macroscopic world, and some common modeling assumptions become invalid. One of the effects observed in MEMS microspeakers is nonlinear squeeze film damping. Understanding this effect is crucial as non-linearities in the speaker can result in harmonic distortion, which is highly regulated in audio applications. In this study, we analyze the influence of squeeze film damping on harmonic distortion using a lumped parameter model of a MEMS microspeaker. This leads to a nonlinear ordinary differential equation, and an approximate analytical solution for moderate non-linearities is obtained using homotopy. We present our solution strategy, including the resulting closed-form expression, and verify our findings against numerical solutions.