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arXiv · 2311.06983

A Different View of Sigma-Delta Modulators Under the Lens of Pulse Frequency Modulation

Victor Medina·Pieter Rombouts·Luis Hernandez
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Abstract

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.

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Victor Medina, Pieter Rombouts, Luis Hernandez. 2023-11-12. A Different View of Sigma-Delta Modulators Under the Lens of Pulse Frequency Modulation. https://doi.org/10.1109/mcas.2024.3352552

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