Hardware implementation of an electrostatic MEMS-actuator linearization

In this paper, an electrostatic actuator linearization will be introduced, which is based on an existing hardware-efficient iterative square root algorithm. The algorithm is solely based on add and shift operations while just needing n/2 iterations for an n bit wide input signal. As a practical example, the nonlinear input transformation will be utilized for the design of the primary mode controller of a capacitive MEMS gyroscope and an implementation of the algorithm will be instantiated in the Verilog hardware description language. Furthermore, an implementation of an improved version of the algorithm will be given reducing the number of needed iterations to n/2 − 1 for an n bit wide input signal while just requiring an acceptable additional amount of hardware resources. Finally, measurement results will validate the feasibility of the presented control concept and its hardware implementation.