Explaining Sigma-Delta Modulators with Pulse Frequency Modulation

A well established analysis technique of low-pass Sigma-Delta modulators is based on the white noise model, where quantization noise is assumed a uniformly distributed random signal. However, Sigma-Delta modulators exhibit numerous nonlinear effects that the white noise model fails to explain. Recently, a different way of describing low-pass Sigma-Delta modulators has been developed, establishing its similarities with VCO-based ADCs. A key idea in this new representation is the concept of the Pulse Frequency Modulation equivalent of a low-pass Sigma-Delta modulator. This paper reviews this new description with a simplified and intuitive approach and proposes new applications of the PFM analysis to other Sigma-Delta modulator architectures such as Band-Pass and Multistage modulators.