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

frequencyoscilloscope

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?

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.