# The First-Order Sigma-Delta Modulator

## Abstract

This chapter focuses on specific system-level simulations of the simplest Sigma-Delta modulator, to be referred as MOD1, formed by a first-order loop filter and a single-bit quantizer. The aim of this chapter is to help beginners make the important leap from theory to actually understand the significance of the subtle concepts that are essential to becoming confident in designing a successful modulator. As mentioned, MATLAB^{®} and Simulink^{®} are the tools used to explore the properties of MOD1. Therefore, after a brief description of the Simulink^{®} model provided in the Toolbox accompanying this book, a step-by-step set of practical exercises is proposed. Specifically, the reader will be able to observe the time domain waveforms of the modulator in response to both DC and sinewave inputs as well as noise shaping in the frequency domain via fast Fourier transform (FFT). A number of non-ideal effects are studied such as tones, dead zones, and saturation. Further, the prevention of the non-idealities discussed is investigated, mainly through the use of dither. Some simple mathematics is used as an aid in presenting the theoretical concepts, and for results evaluation, however, formula proofs are generally avoided in order to keep the focus on the results themselves and a rather practical approach to the subject. The interested reader is encouraged to consult the references for complete mathematical derivations.

## Supplementary material

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