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Digital-to-Analog Conversion

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Analog-to-Digital Conversion

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Abstract

The two most important architectures for constructing a digital-to-analog converter are the unary and binary approach. Both approaches have their merits. Next to the architecture, the second choice is the domain in which the converter is realized: voltage, current, charge or time. Realizations in all these domains are discussed and their specific behavior is analyzed. The resistor string is an important conversion element as it constitutes the digital-to-analog function in a flash converter. Its dynamic behavior is essential for reaching high-speed performance. The binary counterpart of this converter is the R-2R architecture. The current-steering topology is the dominant realization for fast stand-alone digital-to-analog conversion. The properties of this converter are described and analyzed. Charge domain converters are mostly applied in lower-performance, low-power applications. Various topologies allow to choose between low area or better performance. A special section is dedicated to error sources and methods to improve the performance. The dynamic element matching, current calibration, and data weighted averaging methods are explained. A number of examples detail the design considerations and choices. Lay-out examples of commonly used structures are presented.

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Notes

  1. 1.

    Many more representations exist, this table only lists the ones used in this book.

  2. 2.

    In this section the effect of statistical errors is examined. In the following chapters compensation and calibration techniques are discussed.

  3. 3.

    Formally the more correct approach involves starting with DNL = 2N(y 1 − y 2)∕(y 1 + y 2) − 1.

  4. 4.

    When counting elements and nodes of a series string, there is ambiguity: a string of 2N elements has 2N + 1 nodes if the outer connecting nodes are counted. So 1024 resistors give 1025 node voltages. In this book the number of elements is a power of 2, and the highest tap is left unused.

  5. 5.

    It is convenient to look in literature for solutions of the “Heat equation” problem with your specific boundary conditions and rewrite them to voltage equations.

  6. 6.

    It seems that a shortcut is possible by using the string of M resistors, however this string shares m resistors with R 1 and the covariance has to be included, which is a possible route, but not pleasant.

  7. 7.

    Explanation from Colin Lyden (ADI).

  8. 8.

    Also known as Kelvin-connection and four-point sensing.

  9. 9.

    Diffused resistors are a preferred alternative in more advanced processes.

  10. 10.

    The main remaining gradient in processes with an epitaxial layer is caused by the temperature differences in the die and voltage drops over the wiring.

  11. 11.

    Think of all the energy your tweeter loudspeakers would have to consume.

  12. 12.

    The ratio between signal power and the power of the harmonics of a perfect block wave is 1∕(π 2∕8 − 1) = 4. 27 or 6.31 dB.

  13. 13.

    Assuming only one edge is jittering.

  14. 14.

    From a discussion with Lucien Breems for the AACD 2016 pannel.

  15. 15.

    Two sources are available as the originator of DWA: Michael Story [174] and Maloberti [175].

  16. 16.

    Odd value: to stay away from idle patterns at this stage of the explanation.

  17. 17.

    In Chap. 10 “idle patterns” are discussed. The patterns in data-weighted averaging bear a lot of resemblance but come from a completely different origin.

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  1. HELMOND, Noord-Brabant, The Netherlands

    Marcel Pelgrom

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Pelgrom, M. (2017). Digital-to-Analog Conversion. In: Analog-to-Digital Conversion. Springer, Cham. https://doi.org/10.1007/978-3-319-44971-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-44971-5_7

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