A fractional-order zero-phase integrator for sigma-delta modulator

  • Chi Xu
  • Yu JinEmail author
  • Duli Yu
  • Xin Wang


In the system of MEMS digital geophone, the mechanical sensing element and post-stage detection circuit are combined to work as the Sigma-Delta (ΣΔ) modulator. The performance of ΣΔ 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 ΣΔ modulator. In fact, the increase of the system order of ΣΔ modulator is limited to maximum 5 or 6 order due to the system instability. In other words, the stability of ΣΔ 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 ΣΔ modulator to effectively suppress the phase distortion in the noise-shaping process for MEMS digital geophone. The proposed ΣΔ 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 ΣΔ 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 ΣΔ modulator with FOZPI scheme is an effective way to improve the performance and loop stability for ΣΔ modulator.


Sigma-delta modulator Fractional-order zero-phase integrator Phase distortion Noise-shaping PSO algorithm 



This work was supported by the research fund to the top scientific and technological innovation team from Beijing University of Chemical Technology (No. buctylkjcx06).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Advanced Innovation Center for Soft MatterBeijing University of Chemical TechnologyBeijingChina

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