UChicago Instructional Physics Laboratories

Now, there's a bit of an issue we have to deal with when we're trying to deal with measurements from the oscilloscope. What's the uncertainty on them? The device can't have infinite resolution, so how do we figure out what to use?

For that we'll go and Read The Friendly Manual (RTFM)! And in this case, it isn't the general user manual but the Specifications and Performance Verification technical reference that we need.

We'll start with static DC measurements. If we scroll through the document until we fine DC Voltage Measurement Accuracy, Average Acquisition Mode it gives us three specifications:

• Vertical position = 0
  • ±(3% of |reading| + 0.1 div + 1 mV)
• Vertical position ≠ 0 and vertical scale = 2 mV/div to 200 mV/div
  • ±[3% of |reading + vertical position| + 1% of |vertical position| + 0. 2 div + 7 mV
• Vertical position ≠ 0 and vertical scale > 200 mV/div
  • ±[3% of |reading + vertical position| + 1% of |vertical position| + 0.2 div + 175 mV]

So, let's try the most basic measurement: Nothing.

What is the uncertainty of this measurement?

Now let's zoom in to the 100 mV scale.

Now let's get as close in as we can, the 2 mV scale

Everything is within uncertainty of zero.

Now let's go back to that pesky case where there's an offset. Change the vertical scale back to 5V and position to 3 divisions.

Take the position down to zero again, zoom into the 100 mV scale, and then put another 3 division offset on the signal.

Takeaway here is that the scope isn't the best tool for measuring small, static DC values but it is plenty accurate. Also, don't add an offset if you don't need it.

9V battery

On 1V scale and -5 division offset:

reading of 8.05 V Uncertainty should be $0.03 * (8.05 + 4) + 0.01*4 + 0.2*1 + .175 $V = $ 0.36 + 0.04 + .2 + .175$ V = $0.78 $ V

handheld DMM says 8.12V

Okay, as you probably noticed the values you read out don't always change continuously, they're quantized to certain amounts. What amounts you say? Let's check the documents again! The Number of Digitized Bits indicates that the scope has 8 bits of voltage resolution everywhere except the smallest scale. But, what does that mean? Well, note that it also says that the scope has 10 divisions dynamic range. Taken together, this indicates that the smallest increment we can measure is the size of ten divisions divided by $2^8$. So, for the 5V range, we would have a resolution of $50 V / 2^8 = 195$ mV $\approx 200$ mV

Let's test this trend by using the amplitude cursors and seeing what the smallest increment they'll measure is.

Takeaway: If you're using cursors their resolution of around 4% of the scale will dominate your measurements.

Time uncertainty

Sometimes the quantity we're interested in is a time difference or interval. For that, we'll need to look at the Delta Time Measurement Accuracy information

Thankfully this is much more straightforward than voltage, as the uncertainty in a time interval is given as $\pm$(1 Sample Internal + 0.0001 * |reading| + 0.6 ns)

Averaging can knock the constant factor down to 0.2 ns, but that will rarely be relevant. Looking down to Table 3 there's a column for Sample interval in waveform record we can use! But, it is in a table form. Quite inconvenient. But! There's a consistent pattern to be seen there. The time interval is always 0.4 % of the Sec/Div reading. So, we can change our formula to

$\delta t = 0.004 * $horizontal scale$ + 0.0001 * |$reading$| + 0.6 $ns

Since you'll usually want to zoom in enough that your time intervals cover a few horizontal divisions, we'll usually need both parts of this. How about the fixed portion, when might we be able to ignore that?

Well, if we use the rule of thumb that we can neglect an uncertainty that's less that 10% of the contribution, that suggests that we could ignore the constant factor whenever 0.004 * scale $\ge$ 6 ns

Now, the cursors are quantized to 4% of the time scale, so if we're trying to use them then we can ignore that constant offset unless we're measuring on scales less than 100 ns. There are only 4 timescales faster than that, so not usually an issue.