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

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.