A Volterra Series Nonlinear Model of the Sampling Distortion in Flash ADCs Due to Substrate Noise Coupling

This brief presents a Volterra series model to evaluate the impact of substrate noise on Flash analog-to-digital converters. The proposed approach first relates substrate noise to the induced timing uncertainty of the comparator by means of an analytical linear model. The analysis then expresses the resulting sampling distortion power by also considering the comparator´s nonlinearities and thus models the signal-to-noise-and-distortion ratio (SNDR) of the converter. In particular, it is shown that substrate noise causes an FM modulation of the clock, and the resulting timing error is a joint effect of AM-FM modulation of the input signal and the coupled noise. The derivation of the analytical expression is also valid for any multitone ground perturbation and is validated on a high-resolution Flash converter. The developed nonlinear model for the SNDR is found to almost double the noise amplitude range compared with the linear model, thus predicting the impact of realistically large noise signals.