Lots of really great discussion and comments here about measuring scope bandwidth!
We get so many questions about this topic, I actually made a video explaining the basic concepts of "bandwidth" in oscilloscopes. Probably a bit too introductory for most of the people posting here, but it does cover a few things discussed in this thread such as calculating BW from rise time, the different frequency responses (Gaussian vs. flat), etc.
One thing I didn't cover is how to measure the bandwidth of an oscilloscope (i.e. procedures, techniques), but it seems like this might be a good topic for a future video. I've already learned a few things from this thread myself
Yes that is the way i have been doing it, sweeping a sine was up in frequency until you see the amplitude drop to 1/sqrt(2) which is the -3db point.
Since to do this test for a higher frequency scope like 100MHz you have to have a signal generator that can produce sine waves up to at least 100MHz. I did not have that for testing a scope that was said to be 100MHz but was really 30MHz but my frequency gen only goes up to 24MHz anyway, so i had to use the pulse method and assume that the pulse rise time was what the spec said it would be, and calculate the 90 percent threshold for the rise time of the scope given a first order LP filter front end.
You can get this number by noting the charge time for an R and C filter:
1-e^(-t/RC)
and note that the 3db cutoff point for an RC LP filter comes from:
w=1/RC
which is:
2*pi*f=1/RC
and solving for RC i get:
RC=1/(2*pi*f)
then substitute that into the charge time above:
1-e^(2*pi*f*t)
and then given your frequency f and equating that to 0.9 the equation becomes:
1-e^(2*pi*f*t)=0.9
and solving that for any 'f' we get approxmately:
t=0.366/f
and many people use t=0.35/f which is ok too really because it's just an estimate anyway.
It is possible that the 0.35/f formula comes from the 10 percent and 90 percent thresholds but i did not look into it, but since the time comes out slightly shorter i would think it was because of that.
However, since the rise time of the test pulse is never perfect and often more like 3ns, i like the longer time of 0.366/f as that helps a little to include the rise time of the input test pulse which of course makes the rise time on the scope slightly longer. The development of the formula for that is slightly more complicated because then we can not use a pulse with 0 rise time we have to use a ramp with whatever rise time we assume we will be working with. Some here use 2ns i think from a digital logic circuit.