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Temperature Compensation

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Book cover Mobility-based Time References for Wireless Sensor Networks

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

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Abstract

In Chap. 4, it has been shown that after a single-point trim at room temperature the output frequency of mobility-based oscillators is characterized by a strong temperature dependence, which is larger then ± 30% over the commercial temperature range from − 40 to + 85 ∘ C. However, if an ideal temperature compensation is applied, their inaccuracy is in the order of 1% over the same temperature range. As has been shown in Chap. 2, such inaccuracy is low enough for a large variety of applications, including Wireless Sensor Network (WSN) nodes. This chapter discusses how to keep such level of inaccuracy when going from an ideal to a practical temperature compensation scheme.

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Notes

  1. 1.

    In package datasheets the junction-to-ambient thermal resistance is also often reported, which for the simple model presented is equal to \({R}_{ja} = {R}_{jc} + {R}_{ja}\).

  2. 2.

    Throughout this chapter, the terms batch-calibration or correction (curvature correction, non-linear correction) refer to the procedure of estimating the average error of a production batch from the measurements of a limited number of samples from that batch, and by adjusting all individual samples in the same manner and by the same amount based on that estimate.

  3. 3.

    With reference to the symbols used in Sect. 5.6.4, for α = 18, the bs = 1 phase is the same as in the case α = 2, while the length in the bs = 0 phase has been assumed equal to \({T}_{1} + (\alpha - 1){T}_{2} = 50\,\mu \textrm{ s} + 17 \cdot 20\,\mu \textrm{ s} = 390\,\mu \textrm{ s}\).

  4. 4.

    A third or fourth-order polynomial would be sufficient to compensate for the third-order non-linearity of V be , which is usually the main residual non-linearity. A sixth-order polynomial is employed in this work to compensate the strong non-linearity at high temperature due to leakage.

  5. 5.

    Note that the order of the polynomials P 7( ⋅) and Q 4( ⋅) is the minimum required for the error due to the non-linearity of the compensation to be negligible compared to the spread among the samples.

  6. 6.

    The up-date rate of N { div} depends on the temperature variations rate in the chosen application.

  7. 7.

    Note that a faster sampling rate is adopted for the temperature sensor with respect to that (2.2 Sa/s) employed for the measurements presented in Sect. 5.7. Though this could result in a larger temperature error, it is allowed because, as shown earlier in this section, the full accuracy of the temperature sensor is not required for the reference’s compensation.

  8. 8.

    The time constant of the exponential settling is in this case τ2 = 180 s due to the lack of induced air flow on the sample and the consequent increase in thermal resistance R pkg .

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Authors and Affiliations

  1. NXP Semiconductors, High Tech Campus 32, Eindhoven, Netherlands

    Fabio Sebastiano & Lucien J. Breems

  2. Delft University of Technology, Mekelweg 4, Delft, Netherlands

    Kofi A. A. Makinwa

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  1. Fabio Sebastiano
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  2. Lucien J. Breems
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  3. Kofi A. A. Makinwa
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Sebastiano, F., Breems, L.J., Makinwa, K.A.A. (2013). Temperature Compensation. In: Mobility-based Time References for Wireless Sensor Networks. Analog Circuits and Signal Processing. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3483-2_5

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  • DOI: https://doi.org/10.1007/978-1-4614-3483-2_5

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