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