On the Signal Filtering Property of CT Incremental Sigma–Delta ADCs

In this brief, the calculation of the signal behavior and the achievable signal-to-quantization-noise ratio of continuous-time (CT) incremental sigma-delta (I-SD) analog-to-digital converters (ADCs) is described. The presented method allows for the analysis of I-SD ADCs in frequency domain, including the specific non-idealities of the CT modulator. In the state-of-the-art, it is described that the omission of the preceding sample-and-hold for the I-SD ADC alters the transfer characteristic compared to a Nyquist-rate converter. So far, for CT I-SD ADCs this behavior is only investigated via simulations. In this brief, the model of a discrete-time I-SD ADC is generalized and adapted for the CT case. This allows to analytically obtain the signal and noise transfer function of the I-SD ADC in frequency domain in combination with arbitrary reconstruction filters due to the utilization of the lifting method in a fast and accurate way.