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[FAQ] BQ76952: How can I calculate the coulomb counter current error in the BQ769x2?

Part Number: BQ76952
Other Parts Discussed in Thread: BQ76972, , BQ769142, BQ76942

I want to know how can I calculate the worst-case current measurement error when using any of the BQ769x2 devices (BQ76952, BQ76942, BQ769142, BQ76972).

Can you explain how this is done?

  • The accuracy of the current measurement can be conceptualized as the averaging of multiple measurements, then comparing the average against the ideal expected result. This does not consider the noise in a measurement result.

    A worst-case error in whole range of the current measurement can be calculated by adding up the individual worst-case offset, gain, DNL and INL errors.

    These limits are provided in the datasheet Electrical Characteristics, as seen in Figure-1.

    Figure-1. Coulomb Counter datasheet specifications.

    All of the limits which affect accuracy are specified in terms of ADC resolution as LSB’s, where. Let’s calculate each individual error:

    • Worst-case Offset Error
      • The worst-case offset error is the offset plus drift error calculated over a change in temperature
        • Assuming a drastic temperature change, from 25C (nominal) to -40C. The worst-case offset would then be:
    • Worst-case Gain Error
      • The worst-case gain error (assuming we ignore their sense resistor) is the difference between the typical gain value and the worst-case gain factor over a particular gain range
        • Using the typical gain vs. the worst-case gain at the full 200-mV range, we get:
          •  
          • This error will decrease when a smaller range is used (E.g. if only 50-mV of the range is used, the worst-case gain error would be 44.05-LSB)
    • Worst-case DNL
      • This error is very small, and can be neglected. Datasheet only specs a typical value of 0.1 LSB
      • For worst-case-scenario calculation, we could assume 1-LSB
    • Worst-case INL
      • Given in the datasheet as 3-LSB

    Adding up all of these factors together, we get a worst-case error of 202.45-LSB. Which would correspond to a voltage of:

    Assuming a 1-mΩ sense resistor, this corresponds to an error of 1.539-mV/1-mΩ = 1.539-A at the 200-mV input (Which would correspond to 200-A of current across 1-mΩ). So, the percentage error would then become 1.539-A/200-A = 0.77%.

    Notes:

    1. This still assumes the sense resistor is ideal, and that the sense resistor value matches the calibrated values entered for Calibration:Current:CC Gain and Calibration:Current:Capacity Gain in the BQ769x2.
    2. These examples assume the worst-case scenario for each error factor of each specification, which means that this is the worst-case current measurement error. In real applications this error is unlikely to be as large.
    3. There are also multiple digital filters available that further filter the signal to provide optimized measurements. The BQ769x2 provides optimized measurements for the instantaneous, averaged, and integrated current. To read more information on the different types of current measurements available, see Section 4.3 Coulomb Counter and Digital Filters of the Technical Reference Manual.

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