Employing multi-stage sigma–delta modulators has provided an effective means of eliminating stability problems while achieving highresolution analog-to-digital conversion. However, component matching has become more stringent than a single-stage modulator. Mismatches cause loss in the modulators signal-to-noise ratio (SNR), but to a certain class of multi- stage modulators, discontinuity is also apparent in its SNR characteristics. This class of modulators employs a first-order modulator in its first stage. The discontinuity is caused by the nonlinearity of a first-order modulator’s noise, which is related to the minimum input requirement for the first-order modulator. This brief includes the formulation of the firstorder modulator’s minimum amplitude, nonlinear characteristics, and its effect on multi-stage modulators.