A new approach to analysis of residue probability density function in pipelined ADCs

• A new approach to analysis of residue pdf in pipelined ADCs is presented.
• It was performed based on the fundamental theorem for function of a random variable.
• It will be shown that residue pdf converges to uniformity.
• In the half-bit redundant structure, 6 dB of extra resolution can be gained.
• The appropriate backend to maintain the most extra resolution is proposed.

This paper presents a new approach to analysis of residue probability density function (pdf) in pipelined ADCs. This work was performed based on the fundamental theorem for function of a random variable to map stage input pdf to its output density. It will be shown that residue pdf converges to uniformity. For the stages with half-bit redundancy, this uniformity is accompanied with an extra bit of resolution. Also, the minimum number of stages required to achieve a given value of resolution improvement are studied. Investigating the impact of backend stage on this extra resolution, the appropriate backend to maintain the most extra resolution is proposed. Examining the allowable comparator offsets in different stages, we can see that with decreasing the offset errors in final stages, offset errors impact of the first stages on the final residue pdf and the total converter resolution can be eliminated.