A fractional-order zero-phase integrator for sigma-delta modulator
Abstract: In the system of MEMS digital geophone, the mechanical sensing element and post-stage detection circuit are combined to work as the Sigma-Delta (Sigma Delta) modulator. The performance of Sigma Delta modulator can be improved by cascading electrical integrators behind the sensitive structure. Thus, additional integrators are introduced in series with the mechanical sensing element to form the high order Sigma Delta modulator. In fact, the increase of the system order of Sigma Delta modulator is limited to maximum 5 or 6 order due to the system instability. In other words, the stability of Sigma Delta modulator system will be weaken caused by the phase loss from the additive integrators. This paper proposes a fractional-order zero-phase integrator (FOZPI) that in series with the 5th-order Sigma Delta modulator to effectively suppress the phase distortion in the noise-shaping process for MEMS digital geophone. The proposed Sigma Delta modulator with the FOZPI applies in MEMS digital geophone can better enhance the compromise capability between the high signal to noise ratio (SNR) and strong robust stability than the pure 5th-order Sigma Delta modulator does. The order of FOZPI is designed by using swarm intelligent algorithm, which offers opportunity to simplify the process of tuning parameter and further improve the noise performance. Finally, the simulation results show that the proposed Sigma Delta modulator with FOZPI scheme is an effective way to improve the performance and loop stability for Sigma Delta modulator.