Designing and optimizing of a novel sigma-delta modulator using PSO algorithm

Chi Xu1, Yu Jin2, Duli Yu3

1, 2College of Information Science and Technology, Beijing University of Chemical Technology,
Beijing, China

3Advanced Innovation Center for Soft Matter, Beijing University of Chemical Technology, Beijing, China

2Corresponding author


Received 5 September 2017; accepted 11 September 2017



Abstract. The performance of the conventional Sigma-Delta modulator can be improved by cascading electrical integrator behind the mechanical sensing element. In this paper, a novel Sigma-Delta modulator with a fractional-order controller is proposed and thus extending the traditional Sigma-Delta modulator to a new fractional-order in the Sigma-Delta ADC design field. The fractional-order controller allows fine tuning accuracy in seeking the coefficients for the proposed Sigma-Delta modulator and provides the robust stability in the placement of poles and zeros for compensating the phase delays. The parameters of the proposed fractional-order Sigma-Delta modulator is designed by using swarm intelligent algorithm, which offers opportunity to simplify the process of tuning parameters and further improve the noise performance. Simulation from the proposed fractional-order Sigma-Delta modulator, results of SNR > 134 dB and the noise floor under 170 dB are obtained in frequency range of [5-150 Hz].

Keywords: fractional-order system, sigma-delta modulator, system stability, pso algorithm.


[1]        Kajita T., Un Ku M., Temes G. C. A two-chip interface for a MEMS accelerometer. IEEE Transactions on Instrumentation and Measurement, Vol. 51, Issue 4, 2002, p. 853‑858.

[2]        Kraft M., Redman White W., Mokhtari M. E. Closed loop micromachined sensors with higher order-modulators. Proceedings 4th Conference on Modeling and Simulation of Microsystems, 2001, p. 100-103.

[3]        Dong Y., Kraft M., Gollasch C. O. A high performance accelerometer with fifth order-modulator. Micromechanics and Microsystems Europe workshop, Leuven, Belgium, 2004, p. 41-44.

[4]        Lang C., Tielert R. A low noise accelerometer with digital PID-type controller and multibit force feedback. Proceedings of the 25th European Solid-State Circuits Conference, Duisburg, Germany, 1999, p. 250-253.

[5]        Luo X. C., Feng J. A monolithic MEMS gyroscope interface circuit in 0.35 μm CMOS. Tien Tzu Hsueh Pao/Acta Electronica Sinica, Vol. 42, Issue 9, 2014, p. 1868‑1872.

[6]        Caputo M. Distributed order differential equations modeling dielectric induction and diffusion. Fractional Calculus and Applied Analysis, Vol. 15, Issue 4, 2001, p. 421‑442.

[7]        Chen Y., Ahn H., Xue D. Robust controllability of interval fractional order linear time invariant systems. 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Long Beach, USA, 2005, p. 1‑9.

[8]        Moze M., Sabatier J. LMI tools for stability analysis of fractional systems. 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Boston, USA, 2005, p. 1-9.

Cite this article

Xu Chi, Jin Yu, Yu Duli Designing and optimizing of a novel sigma‑delta modulator using PSO algorithm. Vibroengineering PROCEDIA, Vol. 14, 2017, p. 358‑363.


JVE International Ltd. Vibroengineering PROCEDIA. Oct 2017, Vol. 14. ISSN 2345-0533