On the monotonicity and linearity of ideal radix-based A/D converters

Both cyclic and pipelined analog-to-digital (A/D) converters are getting more and more popular, as they are relatively easy to design and either have a high throughput (pipelined converters) or small area- and power-consumption (cyclic/algorithmic converters). To avoid saturation and to ensure effective digital calibration, in the analog stage(s) of these converters, instead of the ideal two, often a smaller nominal gain (called radix number) is used. In this paper, it is shown that these radix-based converters have nonmonotonic output and finite linearity. The causes of these phenomena are discussed in detail. Fully digital method is suggested to remove nonmonotonic code transitions and estimation on the maximum differential nonlinearity of the ideal converter as a function of the number of cycles is presented.