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I would figure that if a scope has a sample rate of 200 MSa/s, it should be able to measure signals up to its Nyquist frequency, 100 MHz. But there are a lot of scopes whose max bandwidth do not match their Nyquist frequency. For instance, the Agilent 54621A lists a sample rate of 200 MSa/s, and a frequency of only 60 MHz. Why is this?

Best I can figure, there's some parasitic capacitance in there that filters your input signal, and "that's what you get for that pricepoint."

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    \$\begingroup\$ Why use oversampling in any application? \$\endgroup\$
    – The Photon
    Jul 11, 2023 at 16:10
  • \$\begingroup\$ Why do you think so? Has someone managed to build infinitely steep ideal brick-wall filters? \$\endgroup\$
    – Justme
    Jul 11, 2023 at 16:30
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    \$\begingroup\$ If you measure a signal with a frequency of 20 MHz, you may get 10 samples of a period. You may see if your signal is a sinus, a squarewave or a triangel and the high and low time at least approximately. If you measure two signals, you see a phase shift with a resolution of 5 ns. \$\endgroup\$
    – Uwe
    Jul 11, 2023 at 16:44
  • \$\begingroup\$ @Justme Yes, if you wanted to get right up to the nyquist frequency, you would need perfect step function filters, I agree. But there are definitely filters that can do much much better than 60% of nyquist, and I'm curious if it's a case of the manufacturer not removing parasitic capacitances, or if they intentionally install a filter to damp those higher observable frequencies. \$\endgroup\$
    – fpf3
    Jul 11, 2023 at 17:09

6 Answers 6

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The frequency given is the cut frequency of the analog input (I suppose defined at -3dB, but to be confirmed). This means that there is still some analog signal at higher frequencies, just attenuated.

If you had the sampling frequency "just" twice the analog frequency, you would not get "clean" results, as you have still some higher frequency components in your analog signal after filtering.

The Nyquist frequency is only valid if you either have a pure sine wave, or a signal with no components above the limit (so in practice, you need to either filter at a far lower frequency, or at a somewhat lower frequency with a high order filter (to cut abruptly)).

So if you only care about perfect sines, then you could have a scope with 200MSa/s and 100MHz analog bandwidth. But as soon as you care about other signals (for example square signals), you want some margin.

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  • \$\begingroup\$ I agree with everything you write. I'm still confused as to what is actually meant by the manufacturer in this case, though. For instance, the scope I mentioned has a sister (Agilent 54622D), which has the same rate of 200 MSa/s, but lists a bandwidth of 100 MHz. So, are we intentionally filtering out the top of the observable sinusoids? I'm not sure why you would want to do that. If you're looking at a square wave @ nyquist for instance, there is no confusion as to why you are seeing a sine wave. \$\endgroup\$
    – fpf3
    Jul 11, 2023 at 17:03
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    \$\begingroup\$ If the 5422D is 100MHz for 200MSa/s, then it is really on the edge, and will behave in strange ways if you approach the 100MHz with non sine signals. They probably kept the same circuit, just changing the cutting frequency of the analog circuit. If you want to observe high frequency sines, then it is slightly better than the 60 MHz version. But for other signals, you might get some more aliasing. Of course, from a marketing point of view, 100MHz sells better. But I'm not sure I would prefer the 100MHz version to the 60MHz one: more risk of artifacts, even worse if you don't know what to expect \$\endgroup\$
    – Sandro
    Jul 11, 2023 at 17:46
  • \$\begingroup\$ @fpf3 why would you want to do that? cheaper analog circuit for a cheaper product \$\endgroup\$
    – slebetman
    Jul 12, 2023 at 4:59
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    \$\begingroup\$ @slebetman in this case it's more like "I'm going to stick a capacitor in this one and call the other one premium to create an artificial value differential", though as others have pointed out, there are valid engineering reasons to do it. If I ran a biology lab or similar, I suppose I would go for the filtered ones too, just so I could be sure my researchers who aren't familiar with signal processing know what they're seeing. \$\endgroup\$
    – fpf3
    Jul 12, 2023 at 13:54
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    \$\begingroup\$ @fpf3 The 54622 model's 100 MHz analog bandwidth is for repetitive signals. Later in the manual you'll find a mention that one-shot sampling bandwidth is up to samplerate/4. \$\endgroup\$
    – jpa
    Jul 12, 2023 at 20:09
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I would figure that if a scope has a sample rate of 200 MSa/s, it should be able to measure signals up to its Nyquist frequency

This works in principle, but in practice it's not so easy. If you have a sinusoid sampled just at its Nyquist rate, you might get samples only at the 0 crossings and not actually see the signal at all. Even if you sample off of the 0 crossings you won't be able to estimate the signal amplitude if you don't know the phase of the samples relative to the original signal. To make it easier to reconstruct the signal, we use oversampling in oscilloscopes just as we do in other applications like audio.

That said, there are also scopes, called equivalent time scopes (often with trade names like "digital communication analyzer" or something) that use sampling rates far below the signal frequency, but by carefully keeping track of the sample delay relative to the trigger and assuming some repetitive features in the signal can give useful measurements of very fast signals with relatively low sample rates. For example measuring 50 GHz signals with 45 kSa/s.

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    \$\begingroup\$ Pet peeve: The Nyquist rate is above twice the bandwidth, a sinusoid at exactly half the sampling frequency breaks the limit - as you have demonstrated in this answer. \$\endgroup\$
    – pipe
    Jul 11, 2023 at 16:48
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    \$\begingroup\$ @ScottSeidman That is the generally accepted definition, sampling rate must be above twice the bandwidth of the sampled signal, because exactly twice is not enough as then you can't know what you sampled and can't play it back. \$\endgroup\$
    – Justme
    Jul 11, 2023 at 17:34
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    \$\begingroup\$ @ScottSeidman, if the signal frequency is (strictly) less than the Nyquist frequency, then perfect reconstruction is in principle possible using a raised cosine filter. I don't know if it's a definition, but it's one of the properties of the Nyquist frequency. \$\endgroup\$
    – The Photon
    Jul 11, 2023 at 18:30
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    \$\begingroup\$ @ScottSeidman, BTW, notice I didn't say anything about the Nyquist frequency of a signal. I agree that's not correct. The signal has a Nyquist sampling rate (the minimum sampling rate to be able to reproduce it exactly), and a sampling system has a Nyquist frequency (the maximum signal frequency it can sample and reproduce exactly). \$\endgroup\$
    – The Photon
    Jul 12, 2023 at 17:28
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    \$\begingroup\$ @ScottSeidman, Yes, mathematically it should be an infimum rather than a minimum, but I've never heard an engineer use the word infimum in the real world. Or we could contort the definition to say "the maximum sampling rate that isn't sufficient to perfectly reconstruct the signal". \$\endgroup\$
    – The Photon
    Jul 12, 2023 at 23:25
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As well as only allowing for sine waves at the maximum frequency, for that to work well you'd need an anti-aliasing filter with extremely sharp cutoff or signals that have much frequency content in excess of Nyquist would alias badly and produce misleading waveforms. Ideally you'd like to have a sample rate 10x or more, not 2x, which makes everything better.

There is also sometimes some tricky specsmanship with multi-channel scopes where the sample rate per channel is less if more than one channel is used, so read the user manual carefully and with a suitably jaundiced eye.

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Sample rate and bandwidth are two different things. The bandwidth may be limited by the vertical input section to less than the ADC is capable of. It's not like the signal is going straight into the ADC, there are the attenuators and vertical amplifiers that take a signal ranging from generally 1 mV to several hundred volts and scale it to the range the ADC can accept, as well as position and trigger circuits, and these can limit the bandwidth. Up until the ADC it's still basically an analog scope. Here's a tech brief with some information on oscilloscope performance.

A manufacturer may make versions of a scope for different price points that use the same ADC, but different front ends. Some also make one basic scope and release it at different price points by limiting features for the lower priced ones in firmware, and then offering upgrades for a fee. For example, here's a software upgrade for a scope that takes it from 500 MHz to 1 GHz bandwidth.

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If a scope can sample at 200 MHz, and you want to measure signals up to 100 MHz, you need to pass signals below 100 MHz with 100% amplitude to ADC and you need to filter out signals above 100 MHz to zero amplitude so they don't get aliased by the ADC sampling.

This means you need to design a brick-wall filter with infinitely narrow transition band from 100% to 0%, and as with most infinities, it's just physically impossible to realize with components.

So, having a transition band from 60 MHz to 100 MHz to filter away only the required amount of frequencies to have only enough attenuation at 100 MHz and beyond is doable. The scope may show frequencies above 60 MHz but attenuated so it's beyond the measurements are not within manufacturer specs.

Some manufacturers may just artificially limit the specs even if it could perform higher, for example the scope can be manufactured and tested faster to lesser bandwidth and maybe even with cheaper parts with more tolerances. Or just that you have different models and can get a cheap model with low bandwidth or expensive model with high bandwidth, even of the scopes are essentially identical.

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1. Nyquist frequency does not consider measurement accuracy

Nyquist frequency is the limit at which the frequency gets folded, so that you cannot distinguish signals at 0.4x samplerate from signals at 0.6x samplerate.

The measurement accuracy of amplitude and phase suffers long before that. For practical oscilloscope use, you would aim for 10x samplerate compared to signal frequency.


2. Repetitive signals can be sampled multiple times

Oscilloscope analog bandwidth can be higher than Nyquist frequency for repetitive signals. This is called equivalent-time sampling. The oscilloscope will interleave samples from multiple repetitions of the signal to achieve higher effective samplerate, while the analog system must be able to pass the frequency in question.


3. The 54621A is an entry-level model

The sister model 54622A boasts 100 MHz bandwidth at 200 MSa/s samplerate:

Screenshot from manual

But later in the manual you'll find a note that "single shot BW = sample rate/4 or bandwidth of scope, whichever is less", i.e. 50 MHz. The higher analog bandwidth is there for equivalent time sampling.


4. Oversampling provides graceful degradation of signal quality

In modern entry-level scopes, it is typical to have 1 GSps sampling with 100 MHz -3 dB analog bandwidth, and no equivalent time sampling functions. These scopes can usually display even 200 MHz signals with little distortion other than decreased amplitude.

Compared to this, the 54621A requires more care from its operator. The manual does warn that aliasing and distortion can occur as signals get near or exceed the Nyquist limit at the active samplerate. The analog bandwidth limit is not there to avoid aliasing, it is just the best bandwidth that the analog circuit in this scope is capable of.

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  • \$\begingroup\$ Equivalent-time sampling deserves more visibility than it's getting. Early digital 'scopes could and did display (for one example) 400 MHz signals with only 500 KHz sampling--as long as the signal was repetitive. \$\endgroup\$ Jul 14, 2023 at 16:39

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