An analysis of sinusoidally excited delta-sigma modulators

This paper introduces a new method of analysis for Delta-Sigma Modulators based on modeling the nonlinear quantizer with a linerized gain, obtained by minimizing a mean-square-error criterion[7], followed by an additive noise source representing distortion components. In the paper, input-signal amplitude dependencies of Delta-Sigma Modulator stability and signal to noise ratio are analyzed. It is shown that due to the nonlinearity of the quantizer, the signal-to-noise ratio of the modulator may decrease as the input amplitude increases prior to saturation. Also, a stable third-order Delta-Sigma Modulator may become unstable by increasing the input amplitude beyond a certain threshold. Both of these phenomenon are explained by the nonlinear analysis of this paper. The analysis is carried out sinusoidal excitations.