January 10, 2020

Let’s start with the facts: Otii Arc has a sample rate of 4ksps for current and 1ksps for voltage. If you’re wondering how shorter pulses affect energy measurement accuracy, you’ve come to the right place!

We used pulses of 1us, 10us, 100us, 1ms, 10ms and 100ms. The current in these pulses was roughly 25mA. There was no current consumption between the pulses, except for a small leakage of single-digit nA. We’ll refer to it as zero-current consumption.

So, here’s what we did to verify Otii measurement accuracy for short pulses. Feel free to follow these steps and try it out for yourself:

- Measure the energy in the pulse with Otii
- Subtract the Otii zero-current energy measurement
- Use an oscilloscope to get the pulse width and voltage
- Calculate the current required to get the Otii measured energy, based on the oscilloscope data
*Checkpoint*: You now have a calculated Otii current for the pulse. - Based on 100ms and 10ms measurements, calculate the error created in the oscilloscope based current calculation
- Compensate the Otii calculated current with the oscilloscope error

*Checkpoint*: You now have an oscilloscope error compensated Otii measured current. Remember that the oscilloscope has also provided you with data concerning the pulse.

*Result*: You now know the error created from different pulses.

We repeated our measurement 10 times to find variations and to calculate an average error. We recommend that you do the same.

We used pulses of 100ms and 10ms to get a feeling of the error that occurs when we move from current measured with Otii to current calculated from energy. Why these pulses, you ask? We chose them because we can trust the Otii current measurements for these pulse lengths. As you might remember, we used oscilloscope data, i.e. pulse length and voltage, to calculate the current from energy. The reason is that, at shorter pulses, we don’t have voltage measurement samples from Otii.

Pulse | Current, calculated from energy | Current, measured with Otii | Error |

100ms | 24.85mA | 24.90mA | -0.2% |

When moving to shorter pulses, we cannot compare with Otii measured current. Instead, we need to compare the current calculated from energy with the current measured with the oscilloscope. Measure the voltage drop over a resistor in-line with the load, or – as we did – over a part of the load, since we have it divided into two parts. After this, you can calculate the current flowing through the load. If nothing else is connected to Otii Arc, Otii should give you the same value.

Pulse | Current, calculated from oscilloscope | Current, measued with Otii | Error |

100ms | 25.40mA | 24.90mA | 2.0% |

10ms | 25.40mA | 24.90mA | 2.0% |

When we use current calculated from oscilloscope values, we can see that the error is roughly 2 % compared to Otii measured current. As we use this knowledge and follow steps 1 to 7 above, we reach the following result:

Pulse | Current, calculated from energy | Current, calculated from oscillscope | Error, compensated with 2% oscilloscope error | Standard deviation for compensated error |

100ms | 24.85mA | 25.40mA | -0.2% | 0.5% |

10ms | 25.18mA | 25.40mA | 1.1% | 1.8% |

1ms | 23.36mA | 25.50mA | -6.4% | 2.0% |

100µs | 31.10mA | 24.50mA | 29.0% | 51.5% |

10µs | 24.51mA | 22.30mA | 11.9% | 7.4% |

1µs | 24.66mA | 24.10mA | 4.3% | 25.2% |

So, this is very interesting. Why does the error suddenly decrease when we go below 100us pulse? Our explanation: a switch between measurement ranges takes roughly 10us. For a 10us and 1us pulse Otii Arc has no time to switch. In other words, Otii Arc remains in high accuracy mode.

The increase in standard deviation between a 1us and 10us pulse shows that the individual error, for one pulse, is higher. We haven’t concluded that the error is normally distributed, so we only use this value as a comparison to show how much it varies from pulse to pulse. We’d also like to point out that, because the amount of energy in these pulses is so small, there are many other sources of inaccuracies that will have an impact on battery life.

Feel free to replicate our investigation to verify the results above and let us know your results. Want to achieve something specific? Interested in more details? Get in touch!

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