Modeling the quantizer in higher-order delta-sigma modulators

Existing design methodologies do not provide adequate insight into the cause of instability in higher-order delta-sigma modulators (DSMs) used for digital-to-analog and analog-to-digital conversion. The authors present a quasistatic approach to modeling the quantizer as a method for determining DSM loop stability. Signals in the DSM loop are separated into low-frequency (signal-related) and high-frequency (loop-noise-related) components. The quantizer is modeled as a memoryless sigmoidal nonlinearity whose shape depends on the high-frequency noise components. Stability of the DSM is determined by linearizing the quantizer at a particular DC input level. The shape of the quantizer nonlinearity, the probability density function (pdf) of the high-frequency noise components, and the range of stability for DSM loops were determined both by simulation and by experimental measurements. The range of stability determined by the quantizer model was shown to accurately predict the actual stability range.<>