Parametric anti-phase excitation of resonant MEMS mirrors for fast start-up

This paper analyzes anti-phase parametric excitation for a resonant MEMS mirror by independently driving two out-of-plane electrostatic comb-drive actuators positioned at the left and right sides of the MEMS mirror, enabling a fast and reliable start-up from zero amplitude. Both the angular derivative of the comb drives' capacitance and the square wave driving signals are approximated by complex Fourier series, leading to a nonlinear model that describes the slow evolution of the amplitude and the phase of the MEMS mirror. The proposed model is validated through measurements, demonstrating strong agreement with the analytical results. A detailed discussion on injected and dissipated energy provides an intuitive understanding of the response curve for in-phase and anti-phase excitation signals with various duty cycles. Additionally, the initial start-up behavior of conventional in-phase parametrically excited MEMS mirrors is analyzed and compared to that of MEMS mirrors operated with anti-phase excitation, revealing an improvement of the start-up time by a factor between 8 to 50, depending on the operating point and condition.