So why do we need to know the rise time of an oscilloscope?
The rise time of an amplifier is related to its bandwidth. If we know the bandwidth of the signal under test, we can choose an oscilloscope with an equal or greater system bandwidth and be confident that the oscilloscope will display the signal accurately. If, on the other hand, we know the rise time of our signal, it would be useful to know by how much the oscilloscope will slow down the signal and therefore add to its rise time.
The bandwidth BW in hertz of an amplifier with a rise time of tR seconds can be estimated as: BW ≈ 0.35 / tR
BW and tR can be scaled to more convenient units such as MHz and µs, or GHz and ns.
The numerator of 0.35 in this formula is accurate if the oscilloscope's input amplifier has a simple frequency response like that of a single-pole RC filter. In reality, many oscilloscopes have a faster roll-off to give a flatter frequency response in the pass band, and this can increase the numerator to 0.45 or even higher. The formula also assumes that the rise time is measured between the 10% and 90% voltage levels of the signal