Inner Transfer Functions in Incremental ΔΣ ADCs

In this brief the transfer functions from inner nodes of incremental Delta-Sigma (I-DS) analog-to-digital converters (ADCs) are analyzed. Such transfer functions are needed in order to predict the attenuation of error sources like noise and distortion from within the loopfilter (LF). In the state of the art, I-DS ADCs are often designed based on the theory of their free-running counterparts. However, the applied reset and reconstruction filter change the behavior of the incremental system and thus also alter its behavior with respect to inner error sources. A recently introduced methodology to describe I-DS ADCs in the frequency domain allows to analytically derive the internal transfer functions of I-DS ADCs. This enables the formulation of approximate error attenuation at inner nodes of I-DS ADCs and a comparison in form of a generalized noise-penalty factor to the known behaviour in their free-running counterparts.