How can I determine the necessary bandwidth and sample rate for my oscilloscope given the data rate of my system under test?

First, determine the fundamental frequency of the data signal. As an example, consider a 2.5 Gb/s non-return-to-zero (NRZ) serial data stream. If the data changes in a consistent 1-0-1-0 pattern, you essentially have a square wave whose frequency is half the data rate (1.25 GHz). So the fundamental frequency is 1.25 GHz.

Keysight recommends that you use a scope whose bandwidth is at least 3 to 4 times your signal´s fundamental frequency. This guarantees that the first and third harmonics will be represented. Given our 2.5 Gb/s example, the "bare minimum" scope for the job would have a 3.75 GHz bandwidth (3 * 1.25 GHz). A better choice would be a scope with a 5 GHz bandwidth (4 * 1.25 GHz). Bandwidth higher than 5 GHz would provide even better measurement results.

You can more precisely estimate your bandwidth requirement if you know your signal´s rise time and you know how much rise time error your application can tolerate. To learn more about the differences between today´s higher bandwidth "flat response" oscilloscopes and the more traditional "Gaussian response" type, including bandwidth and sample rate calculations for each, see Understanding Oscilloscope Frequency Response and Its Effect on Rise-Time Accuracy

Oscilloscopes are designed with maximum sample rates adequate to support their rated bandwidth without alias errors. For "flat response" scopes such as Keysight´s 5485xA models, a good general rule of thumb is that the sample rate must be no lower than 2.5 times the scope bandwidth.

Often scope users must sacrifice sample rate for the ability to acquire longer record lengths. For best results, choose a sample rate that is about four times the required bandwidth. This will ensure reasonably good amplitude and rise time accuracy. Keep in mind that Infiniium´s sin(x)/x interpolation filter limits the bandwidth of the scope to (sample rate/4) when the sample rate is less than 20 GSa/s. You may disable this filter to improve the accuracy, although you must be careful to avoid alias errors.