Closed Loop Micromachined Inertial Sensors with Higher Order Σ∆-Modulators

Micromachined inertial sensors are often incorporated in closed loop force feedback structures; a particularly advantageous approach is based upon the inclusion of the sensing element in a sigma-delta modulator (Σ∆M) type control structure. The order of the Σ∆M, and hence the noise shaping properties, is usually limited by the dynamics of the mechanical sensing element and may be insufficient for high performance applications. This paper presents a novel approach suggesting the use of a sigma-delta modulator with an order higher than the mechanical sensing element. This is achieved by a modified cascaded (or MASH) Σ∆M loop architecture. A model of the electromechanical MASH is presented and the quantisation noise analysis is derived. Simulation results indicate nearly 30 dB increase in signal to quantisation noise ratio.