Nonlinear distortions caused by sigma‒delta analog-digital conversion of signals

Abstract

With the use of a linear approximation, the quantizer characteristics are defined by the stability conditions of the discrete models of the first- and second-order sigma‒delta analog-to-digital converters. The processes occurring in the nonlinear converter models are discussed at an arbitrary amount of digit positions in the representation of numbers under periodic external actions. An investigation method whereby stationary oscillations are represented as an invariant set of nonlinear discrete point mappings is employed. The spectral composition of the converter response and nonlinear signal distortions with an arbitrary period are calculated using the classical and modified discrete Fourier transformations. The dependences of the nonlinear- distortion coefficient of harmonic signals in the first- and second-order converters on the oversampling coefficient, the approximation method, the amount of digits in the representation of numbers, and the time constant of an integrating filter are presented.