  The fact that VCO-ADCs produce noise-shaped quantization noise suggests that
a link between frequency modulation and Sigma-Delta modulation should exist.
The connection between a VCO-ADC and a first-order Sigma-Delta modulator has
been already explained using Pulse Frequency Modulation. In this paper, we
attempt to extend the theory based on Pulse Frequency Modulation to a generic
Sigma-Delta modulator. We show that this link between Sigma-Delta modulation
and Pulse Frequency Modulation relies in a sampling invariance property that
defines the equivalence between both entities. This novel point of view, allows
to go beyond the white quantization noise model of a Sigma-Delta modulator,
revealing the origin of some nonlinear phenomena. We first predict spurious
tones which cannot be explained by circuit non linearity. Multi-bit and single
bit modulators are shown to belong to a same generic class of systems. Finally,
quantizer overload is analyzed using our model. The results are applied to
Continuous-Time Sigma-Delta modulators of orders one, two and three and then
extended to a generic case.
