Symbolic statistical analysis of SNR variation for delta-sigma modulators

Traditional methods for statistical analysis of Delta-Sigma (ΔΣ) modulators are based on Monte Carlo analysis to iteratively change the design parameters and evaluate the histogram of signal-to-noise ratio (SNR). But Monte Carlo analysis is time-consuming, especially when a number of candidate designs need to be considered. In this brief, a systematic symbolic formulation of statistical SNR variation is made so that variations of capacitors are directly translated to SNR variation. In addition, the symbolic formulation is derived from a generic ΔΣ modulator topology, so that the derived symbolic formulation is applicable to any topology that is covered by the generic topology. Experiments have shown the symbolic formulation can provide fast and reasonably accurate estimation of statistical SNR variation, especially for high-order modulators.