Optimal Coefficient Quantization in Optimal-NTF ΔΣ Modulators

Strategies for the adaptation of ΔΣ modulators (ΔΣMs) to the embedding environment with respect to the ability of the latter to remove quantization noise have recently been introduced. They rely on formal optimization techniques to deliver finely tuned values for the coefficients of the ΔΣM internal filters. However, in digital ΔΣMs, coefficients will necessarily be quantized to short wordlengths, the shorter the better, cost-wise. Unfortunately, this can severely hinder optimality. In this brief, a strategy is proposed to re-use the very optimization framework to minimize the effects of coefficient quantization. The technique is discussed by a practical design example based on a ΔΣM for a wideband fractional-N phase locked loop (PLL).