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I am trying to calculate the energy delivered by a short electrical pulse. I am using an oscilloscope to capture the waveform and then exporting it to a CSV file. My scope took measurements at a rate of once every 8 microseconds which means that each time time value could potentially vary by plus or minus 4 microseconds. The manual of my scope gives no mention of uncertainties whatsoever, but it says that the maximum capture rate that can be used is once very 1 microsecond. My question is whether my uncertainty should be taken as half of the time increment I am using (± 4 microseconds) or half of the smallest possible time increment the scope can capture (± 0.5 microseconds).

Here comes the real issue, to calculate energy, we must square voltage to get power, and add up power values multiplied by how long each power value lasted for (energy=timestep*SUM(powers)). We are dealing with the error of the oscilloscope's time resolution. To get the final uncertainty we must add up the relative uncertainties of the timestep and uncertainty of the sum of powers. If I am to say that the error in the time resolution is ±4 microseconds, then I necessarily must have a relative error of at least 4μs/8μs=0.5 which is tremendous. That does not seem right, so which method of estimating uncertainty is correct here?

Thank you all

Smitty Flufferson
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    >My scope took measurements at a rate of once every 8 microseconds which means that each time time value could potentially vary by plus or minus 4 microseconds.- What makes you assume that? – John D Sep 14 '22 at 21:39
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    What is the typical duration of the "short electrical pulse"? Is the 8 uS sample rate significant compared to the pulse duration? – Peter Bennett Sep 14 '22 at 21:46
  • @JohnD I will explain my logic. I am assuming this because the scope has a threshold of 4 microseconds in each direction before the resolution forces it to label the value differently. If a time value is equal to 16μs and time resolution is 8μs, then it could be actually be anywhere from 12.1μs to 19.9μs because either of these values will be rounded up or down respectively. If the actual time was 11.9 μs then it would have to be rounded down to 8μs by my logic. This applies to Voltage measurements, so I assume it applies to the time axis too. Please let me know of any flaw in my reasoning, – Smitty Flufferson Sep 14 '22 at 21:54
  • @PeterBennett Hello Mr. Bennett. The pulse duration here is 250μs. I am not sure how pulse duration will affect the uncertainty values, can you please explain? Thanks – Smitty Flufferson Sep 14 '22 at 21:58
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    If the typical pulse duration is 250 uS, a 8 uS uncertainty in measurement times is only 3% - is that significant for your application? In any case, I think you are misunderstanding the sample rate spec. The scope will take a measurement every 8 uS (possibly +/- a few nanosec). There is no +/- 4 uS uncertainty of the sample timing. There may be a +/- 1 sample variation depending on when the pulse starts and ends relative to the scope sample timing. – Peter Bennett Sep 14 '22 at 22:13

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The real issue is how quickly your real signal changes relative to the sampling rate. DSO's often operate at GHz rates just to deliver 256 levels at 100 MHz BW. This is to prevent aliasing distortion error.

If you measured an 80 us pulse with 4us samples, OK thats 5% but not if the pulse was only 8us wide, that's 50%.

You have a stable sample interval with an uncertainty in between. The most accurate will be with the shortest interval. Thus your present uncertainty is 4 us.

The relative uncertainty depends on the actual pulse width and risetime. Normally you would use a sample interval less than 1/3rd the risetime, but there may be higher frequency content and you have high amplitude resolution.

There is uncertainty for amplitude depending on the scope bandwidth and risetime.

For a 1st order approximation, we can estimate the half-power bandwidth. 10% to 90% Tr=0.35/f-3dB If you have N=10 bit or 1024 quantization levels then you may want a greater sampling rate to determine the values with greater accuracy.

If you show more details, I can help make more suggestions, but it seems you need to sample faster if the pulse width is small.

Tony Stewart EE75
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