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Conventional Techniques for Maximizing Cycle Lengths

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Minimizing Spurious Tones in Digital Delta-Sigma Modulators

Part of the book series: Analog Circuits and Signal Processing ((ACSP))

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Abstract

In this chapter, we review conventional stochastic and deterministic techniques that guarantee long cycles. First we explain the dithering approach, which belongs to the class of stochastic techniques. Then, we explain two deterministic techniques, namely setting the internal registers to predefined initial values and using prime modulus quantizers. These techniques yield longer cycles and thereby reduce the undesirable tones in the spectrum that arise when the period of the quantization error signal is short.

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Notes

  1. 1.

    In practice, the “random” sequence might be generated by a pseudo-random or chaotic source.

  2. 2.

    Here, we refer to the quantization error of a quantizer in the DDSM that contributes to the output quantization noise.

  3. 3.

    The interested reader may consult with [9]. Here we summarize the key results.

  4. 4.

    The pmf is a function that gives the probability that a discrete random variable is exactly equal to some value. It differs from a probability density function (PDF) in that the values of a PDF, defined only for continuous random variables, are not probabilities as such. Instead, the integral of a PDF over a range of possible values (a,b] gives the probability of the random variable falling within that range.

  5. 5.

    q and d are discrete random variables; however, for simplicity we have assumed continuous random variables.

  6. 6.

    The reader can refer to [4, Chap. 3, 66] for a more comprehensive study of in-loop dithering in DSMs.

  7. 7.

    The detail of the quantizer implementation is not given in [58]. Here, we use a multi-level mid-tread quantizer of the type shown in Fig. 2.7 b to illustrate the point.

  8. 8.

    Order ≥ 3.

  9. 9.

    Continuous-amplitude.

  10. 10.

    In the case of DDSMs, the input is rational by definition.

  11. 11.

    \(X=2^8\) in the 9-bit case and \(X=2^{17}\) in the 18-bit case.

  12. 12.

    The results in [11] are for MASH and EFM topologies with order in the range 1–5; the analysis presented here covers only the MASH DDSM with order in the range 1–3. The interested reader may consult [72] for MASH DDSM with orders 4 and 5 and [73] for higher order EFMs.

  13. 13.

    This gives the exact power per tone in the spectrum of a periodic signal.

  14. 14.

    M is a power of two; therefore, the period cannot be odd.

  15. 15.

    Two integers a and b are said to be co-prime if they have no common positive factor other than 1.

  16. 16.

    Subtracting two odd integers results in an even integer.

  17. 17.

    See Appendix A for calculation of the variance.

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Authors and Affiliations

  1. Cypress Semiconductor, Cork, Ireland

    Kaveh Hosseini

  2. University College Cork, Cork, Ireland

    Michael Peter Kennedy

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  1. Kaveh Hosseini
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Correspondence to Kaveh Hosseini .

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Hosseini, K., Kennedy, M.P. (2011). Conventional Techniques for Maximizing Cycle Lengths. In: Minimizing Spurious Tones in Digital Delta-Sigma Modulators. Analog Circuits and Signal Processing. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0094-3_3

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  • DOI: https://doi.org/10.1007/978-1-4614-0094-3_3

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