Post History

Your question is ambiguous.

First, you need to define "rise time".  That applies to a step, not a periodic signal.  Let's say you have a 0 to 5 V digital signal.  The rise time is how long it takes to go from the low state to the high state.

However, that is still ambiguous.  Let's say the signal goes thru a single-pole filter, like a resistor followed by a capacitor to ground.  In theory, the output never fully gets to the 5 V level.  Do you need it to get 90% of the way?  99%?  99.99%?

For a digital signal, you might consider the rise time to be from when the signal first exceeds the maximum guaranteed logic low input level to when it first reaches the minimum guaranteed logic high input level.  In other cases, "rise time" might mean the time to get from 10% to 90% of the final value, or some other fixed thresholds.  It depends on the application and what characteristics of the signal you actually care about.

Your question is further confusing because it wants to relate this to frequency.  Rise time is a single step-response event.  Frequency implies something periodic.  It's not clear what you are envisioning.

For a pure frequency, which is a sine wave, you could argue that the "rise time" is the part of the waveform where the signal is rising.  That's half the period, so 1/2f in seconds when f is the frequency in Hz.

A more reasonable question would be how rise time relates to bandwidth, but that's not what you asked.  Or, you could ask about the xx% to yy% rise time of a step after a single-pole filter of a particular rolloff frequency.  That can actually be answered and the result meaningful, but it is also getting rather far from what you asked.