structural:reformatting, quality:corruption
Bandwidth

As with all practical instruments, oscilloscopes do not respond equally to all possible input frequencies. The range of sinusoid frequencies an oscilloscope can usefully display is referred to as its bandwidth. Bandwidth applies primarily to the Y-axis, though the X-axis sweeps must be fast enough to show the highest-frequency waveforms.

The bandwidth is defined as the frequency at which the sensitivity is 0.707 of the sensitivity at DC or the lowest AC frequency(a drop of 3 dB). The oscilloscope's response drops off rapidly as the input frequency rises above that point. Within the stated bandwidth the response is not necessarily exactly uniform (or "flat"), but should always fall within a +0 to −3 dB range. One source says there is a noticeable effect on the accuracy of voltage measurements at only 20 percent of the stated bandwidth. Some oscilloscopes' specifications do include a narrower tolerance range within the stated bandwidth.

Probes also have bandwidth limits and must be chosen and used to handle the frequencies of interest properly. To achieve the flattest response, most probes must be "compensated" (an adjustment performed using a test signal from the oscilloscope) to allow for the reactance of the probe's cable.

Another related specification is rise time. This is the time taken between 10% and 90% of the maximum amplitude response at the leading edge of a pulse. It is related to the bandwidth approximately by:

Bandwidth in Hz × rise time in seconds = 0.35.

For example, an oscilloscope with a rise time of 1 nanosecond would have a bandwidth of 350 MHz.

In analog instruments, the bandwidth of the oscilloscope is limited by the vertical amplifiers and the CRT or other display subsystem. In digital instruments, the sampling rate of the analog-to-digital converter (ADC) is a factor, but the stated analog bandwidth (and therefore the overall bandwidth of the instrument) is usually less than the ADC's Nyquist frequency. This is due to limitations in the analog signal amplifier, deliberate design of the anti-aliasing filter that precedes the ADC, or both.

For a digital oscilloscope, a rule of thumb is that the continuous sampling rate should be ten times the highest frequency desired to resolve; for example a 20 megasample/second rate would be applicable for measuring signals up to about 2 MHz. This lets the anti-aliasing filter be designed with a 3 dB down point of 2 MHz and an effective cutoff at 10 MHz (the Nyquist frequency), avoiding the artifacts of a very steep ("brick-wall") filter.

A sampling oscilloscope can display signals of considerably higher frequency than the sampling rate if the signals are exactly, or nearly, repetitive. It does this by taking one sample from each successive repetition of the input waveform, each sample being at an increased time interval from the trigger event. The waveform is then displayed from these collected samples. This mechanism is referred to as "equivalent-time sampling". Some oscilloscopes can operate in either this mode or in the more traditional "real-time" mode at the operator's choice.