Fundamental limitations of switched-capacitor sigma-delta modulators

In recent years oversampling techniques have become very popular for implementing high resolution analogue-to-digital (A/D) convertors. To obtain high resolution the order of the modulator L and the oversampling ratio M are commonly seen as degrees of freedom since no theoretical limit exists for the maximum achievable signal-to-quantisation-noise ratio (SNR). However, in practical cases two fundamental constraints need to be considered in the design of the modulator, namely the thermal noise generated by the switches and the amplifiers and the settling error due to finite values of the gain-bandwith product and the slew rate. The paper presents a closed form relation for the SNR performance of generic L-order N-bit modulators designed with switched-capacitor (SC) techniques. The relation takes into account all the above constraints. One of the major conclusions is that state-of-the-art 2nd-order SC modulators are sufficient to achieve competitive SNR performance.