How to Understand Rise Time

Rise time is the time it takes for a signal to cross a specified lower voltage threshold and then follow the specified upper voltage threshold. It is an important parameter in both digital and analog systems. In digital systems, it describes the amount of time a signal spends in an intermediate state between two valid logic levels. In analog systems, it specifies the time it takes for the output to rise from one specified level to another when the input is driven by an ideal edge with zero rise time. This indicates the extent to which the system maintains fast transitions in the input signal.

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 select an oscilloscope with the same or greater system bandwidth and be confident that the oscilloscope will display the signal accurately. On the other hand, if we know the rise time of the signal, it is useful to know how much the oscilloscope will slow down the signal and thus increase its rise time.

The bandwidth BW, in Hertz, of an amplifier with a rise time t 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 0.35 in this equation is accurate if the oscilloscope's input amplifier has a simple frequency response similar to that of a single-pole RC filter. In practice, many oscilloscopes have faster roll-off speeds to provide a flatter frequency response in the passband, which can increase the numerator to 0.45 or even higher. The formula also assumes that the rise time is measured between 10% and 90% of the voltage level of the signal.

Example Calculations

When displaying a fast square wave signal on my oscilloscope, it appears to have a 10%-90% rise time of 1 ns. What is the approximate bandwidth of the oscilloscope?

Using the formula above, the system bandwidth of the scope (including the detector) is:

0.35 / (10-9s) = 0.35 x 109 Hz = 350 MHz