Electronic – Why can an oscilloscope only find frequencies 1/10 of the sampling frequency, despite Nyquist


The oscilloscope at my university states both its sampling frequency and the maximum frequency that it can detect. However, the maximum frequency is just 1/10 of the sampling frequency! Nyquist's theorem states that all frequencies up to half the sampling frequency can be reconstructed.

What kind of problems are the oscilloscope constructors expecting?

Best Answer

There are a few reasons for this:

  1. Nyquist's theorem applies to reconstruction of sinusoidal signals of infinite duration from jitter-free, perfectly accurate samples. Real measurement device clocks have jitter and fixed frequencies, real samples have measurement error and real signals are not infinite sinusoids.

    • Jitter is the difference between a sample's recorded measurement time and the actual measurement time. When the display overlays several periods of a signal to create a picture, jitter makes the trace spread out or smear. Other factors will do this as well.
    • The period at which a device samples is not an exact half-multiple of the original -- it's the sampling frequency, and it's not going to change in relation to the input frequency.
    • Sinusoidal reconstruction is sensitive to measurement error and noise near Nyquist's rate. I'd really rather not do any \$\frac{d(freq.)}{dV}\$ right now, but there it is. This error is reduced by averaging samples, which reduces the effective sample rate.
    • Real signals are more than a single tone. They carry information, noise, and Christmas Spirit. A single-frequency sinusoid measurement is of little value, since that was never the original signal. It'd be like expecting anyone who looks at the Orion constellation to immediately interpret a hunter with a club.
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  2. The measurement device (DSO) uses several staggered-clock, lower frequency parallel processes to achieve its impressive sample rate. Not all steps can be done in parallel, however, which can introduce bandwidth bottlenecks. These are largely a thing of the past in high-end equipment with the development of special-purpose ASICs, and fast GPUs and memory.

  3. Several DSO manufacturers have found it more profitable to develop and manufacture a single or only a few high-end circuits, then introduce limitations such as lower frequency clocks and anti-aliasing filters for their mid and lower-end offerings, instead of developing and manufacturing a different design for each target consumer. The 'scope you were looking at may indeed be originally designed to measure higher maximum frequencies than stated, but is somehow handicapped.

Though I am far from an authority on the subject, I have heard the "10X" rule of thumb enough times to be repeating it here: an effective sample rate of at least 10X the signal frequency is required for intelligent reconstruction and analysis. As the listed sample rate on your school's 'scope is exactly that, I imagine the actual sample rate, taking into account the above considerations, is several times higher yet, but it all boils down to 10 samples of limited jitter and measurement error.