Nonlinear Programming Approach for Design of High Performance Sigma–Delta Modulators

  • Valeri Mladenov
  • Georgi Tsenov
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 109)


In this chapter we present a nonlinear programming approach to the design of third-order sigma–delta modulators with respect to maximization of the signal-to-noise ratio, taking into account the modulator’s stability. The proposed approach uses an analytic formula for calculation of the signal-to-noise ratio and an analytic formula for stability of the modulator. Thus the goal function becomes maximization of the signal-to-noise ratio and constraints come from stability issues and bounds of the modulator noise transfer function coefficients. The results are compared with the optimal third-order modulator design provided by DStoolbox. The proposed procedure has low computation requirements. It is described for third-order modulators with one real pole of the loop filter transfer function and can be extended easily and generalized to higher-order modulators.


Sigma-delta modulators Digital signal processing Stability Analog-to-digital conversion Signal-to-noise ratio 



This work is supported by N.W.O. visitor travel grant Nr. 040.11.493 for 2015.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Theoretical Electrical EngineeringTechnical University of SofiaSofiaBulgaria

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