Sampling and the fastest rate

A digital scope does not watch a signal continuously. It measures the voltage many times a second, the sample rate, and joins the dots.

Half the sample rate

To show a wave faithfully, the scope needs more than two samples in every cycle. So the fastest signal it can show is just under half the sample rate, the Nyquist frequency. With 20 000 samples a second, that is just under 10 000 Hz.

Samples a cycle

Half the sample rate is the limit, not a goal. What a reading needs is enough samples in each cycle of the signal (the sample rate divided by the signal’s frequency). We measured how many, with the scope’s own measurements, on signals sampled at many speeds, including the worst case where the samples fall on the same points of every cycle:

Samples a cycle	What you can trust
4	The frequency, within 0.2 %, whatever the shape. Not the shape or the peak to peak.
10	A sine’s shape, and its peak to peak within 5 %.
20	A square that looks square, with its duty cycle within 5 points.
50	Precise readings: a sine’s peak to peak within 1 %, a triangle’s within 5 %, duty cycle within 2 points.

Two things surprise people:

• A square wave’s peak to peak is right at any speed, because its flat tops are always sampled. Its shape is what needs the samples: the edges and the harmonics that make them sharp.
• A triangle needs more samples than a sine, not fewer. Its harmonics are weak, but its peaks are sharp points, and the samples rarely land exactly on them, so it reads low.

With few samples a cycle the scope draws the wave with sin(x)/x (see Drawing), which is right down to 2.5 a cycle, and takes the frequency from the spectrum, which crossings miscount below 4. The peak to peak still needs the samples above.

What this means for each board is in Accuracy and limits. While it runs, the scope says so under the measurements when a signal has fewer than 10 samples a cycle.

Aliasing

A signal faster than that does not vanish: it shows up as a false, slower wave. This is aliasing, the same effect that makes wheels on film seem to turn backwards. If a trace looks slower than you expect, raise the sample rate and see whether it changes.

More samples, less time

Each capture holds a fixed number of samples. A higher rate shows finer detail but covers less time; a lower rate covers more time with less detail. The board’s fastest rate is listed on Connect a board.