System-level post-optimization of Delta–Sigma modulators using finite difference stochastic approximation

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Traditional methods for system-level design of Delta–Sigma (∆Σ) modulators typically assume linear modeling of the modulator, in which quantization noise is modeled as additive independent white noise. But it is well known that the ∆Σ modulator is a non-linear system and linear modeling is only an approximation. Also, circuit-level non-idealities, which may greatly change the modulator behavior, are typically neglected at system-level design. As a result, system-level modulator designs obtained from traditional methods may not be realistically optimal. This paper presents a system-level post-optimization method for ∆Σ modulators so that modulator designs initially obtained from traditional methods are post-optimized considering non-linear and non-ideal characteristics of ∆Σ modulators including both quantization noise and circuit-level non-idealities. The post-optimization algorithm is based on Finite Difference Stochastic Approximation due to the stochastic nature of modeling of some circuit-level non-idealities in system-level design. During the post-optimization run, each candidate design is simulated for performance measures and stability has always been a must constraint. Results on two ∆Σ modulators have shown that post-optimized modulator designs outperform the original designs from traditional methods.

Original languageEnglish (US)
Pages (from-to)31-42
Number of pages12
JournalAnalog Integrated Circuits and Signal Processing
Issue number1
StatePublished - Jul 1 2016


  • Behavioral modeling
  • Circuit-level non-idealities
  • Delta–Sigma modulators
  • Noise
  • Post-optimization
  • Quantizer non-linearity
  • Stochastic optimization algorithms
  • System-level design


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