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Sigma-delta Modulation

  • Chapter
Analog-to-Digital Conversion

Abstract

The sigma-delta modulator is a specific algorithm to convert low-bandwidth signals into a digital data stream. In the first section the effects of oversampling are described both for the analog-to-digital converter as well as for the analog-to-digital converter.

The next step is the noise-shape topology. The feed-back mechanism that is applied to the quantization errors, allows to free a fraction of the bandwidth of this error energy. The basic mechanisms in the noise-shaper are applied to show the effects of increasing the oversample rate and increasing the order of the feed-back filter.

A similar approach is adopted to deal with the sigma-delta topology. The time-discrete implementation allows to design first and second-order modulators. The main extension towards higher orders is found in the cascaded sigma-delta modulator.

The time-continuous sigma-delta modulators use simple transconductance-capacitor filters and their properties differ in a number of aspects from the time-discrete variants. Some implementation aspect are given. The discussion on the advantages of multi-bit conversion is summarized.

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Notes

  1. 1.

    Is the term “sigma-delta” or “delta-sigma” more correct? Inose [213] uses in 1962 delta-sigma. The other argument is that the basic form was originally a delta-modulator which was extended with an summing function: a sigma-delta modulator.

  2. 2.

    More language issues: “modulator” or “converter”. In this book the circuitry around the quantizer is referred to as the modulator. The same circuit is called a converter if its system function is the dominant feature.

  3. 3.

    Normally a designer will try to use maximum signals throughout the entire circuit. In case scaled signals are used in some part of the circuit the value of V i must be scaled as well.

  4. 4.

    In the audio range these components are audible and are called “whistles”. Trained listeners can hear idle tones down to 100 dB below full-signal.

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  1. NXP Semiconductors, HTC-32, Eindhoven, 5656AE, The Netherlands

    Marcel J. M. Pelgrom

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Pelgrom, M.J.M. (2010). Sigma-delta Modulation. In: Analog-to-Digital Conversion. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8888-8_9

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  • DOI: https://doi.org/10.1007/978-90-481-8888-8_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8887-1

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