Analysis of capacitive sensing for 2D-MEMS scanner laser projection
Typical applications for resonantly driven vacuum packaged MEMS scanners including laser projection displays require a feedback signal for closed-loop operation as well as high accuracy angle synchronization for data processing. A well known and widely used method is based on determining the angular velocity of the oscillating micromirror by measuring the time derivative of a capacitance. In this work we analyze a capacitive sensing approach that uses integrated vertical comb structures to synchronize the angular motion of a torsional micromirror oscillating in resonance. The investigated measurement method is implemented in a laser display that generates a video projection by scanning a RBG laser beam. As the 2D-micromirror performs sinusoidal oscillations on both perpendicular axes a continuously moving Lissajous pattern is projected. By measuring the displacement current due to an angular deflection of the movable comb structures an appropriate feedback signal for ac tuation and data synchronization is computed. In order to estimate the angular deflection and velocity a mathematical model of the capacitive sensing system is presented. In particular, the nonlinear characteristic of the capacitance as a function of the angle that is calculated using FEM analysis is approximated using cubic splines. Combining this nonlinear function with a dynamic model of the micromirror oscillation and the analog electronics a mathematical model of the capacitive measurement system is derived. To evaluate the proposed model numerical simulations are realized using MATLAB/Simulink and are compared to experimental measurements.