Those transition times (~250 ps) seem rather long for a 2 GHz bandwidth scope. I saw that the spec is 230 ps, but the 1 GHz version of the scope is 350 ps. Whatever they are doing to get the extra bandwidth is not helping the risetime nearly as much.
Higher bandwidth oscilloscopes often lack a Gaussian or simple transition band response so they do not follow the 0.35 relationship between rise time and bandwidth.
Exactly. And just this is case here and based to hard facts. Rejecting aliasing is much more important than this rise time. We have here maximum sampling frequency 5GHz, so fNyquist is 2.5GHz. If with this sampling frequency we want BW 2GHz (and this mean allways pure sinewave) there is really small room before Sinc reconstructions start problems and also only 0.5GHz to Nyquist. If there is some kind of "Gauss" type analog BW before ADC it may aliase lot with fast edges. We need cut these harmonics what reduce edges time.
Band width MHz is 350/risetime (ns) is really only old and bit "simply" thumb rule. It was somehow ok thumb rule in old analog oscilloscopes times tens of years ago. Now need think lot of more. In old times with discrete components made oscilloscope typically have gaussian type BW shape from input to tube cathode ray Y deflection. Today we need care aliasing, least with serious instruments.
No one can make real analog brick wall filter but theoretically we can still think it. Think about its risetime and frequency -3dB corner.
Usually "flat top" type BW (also some times called as "brick wall" type) in higher freq oscilloscopes may have this "thumb rule" number not 350 but 400... 450 and even more, depending how steep BW rejecting filter is and and other features of this LP filter (what is always compromise between many things).
Only way to measure oscilloscope BW is sinewave generator and signal level controlled for oscilloscope input, not generator output alone - if accuracy is important.
Oscilloscope risetime can measure using known fast edge what ends to known real flat top without overshoot.
This is a good example of how some and many peoples imagine that measuring the rise time can calculate the BW of an oscilloscope. It is for the most part a misunderstanding when understanding is poor and applied incorrectly. It’s an old and partly outdated rule of thumb that, however, is spreading everywhere on the internet as if it were some sort of de facto. Yes it is an ok rule of thumb for a 60 year old Tektronix oscilloscope. It was just okay when Tek published this rule of thumb in history. We have to walk out of that religion.
Here some bottom basics what everyone need know and also understand.
https://www.keysight.com/zz/en/assets/7018-01129/application-notes/5988-8008.pdf