OpAmp specs: slew rat vs. rise/fall time

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I had a question about normal opamp specs:

Why are slew rate and rise/fall time specified separately, and why are they not always in "agreement"?

For instance, slew rate is max rate of change in voltage vs. time.

Rise/fall time is usually the time it takes the opamp to go from most positive output (at clipping) to most negative output (at clipping).

==> If I know an opamp's slew rate, and I know the supply voltages I am operating from, I should be able to calculate the amount of time it would take the output to go from high to low or low to high:

[ (Vpos_supply_rail) - (Vneg_supply_rail) ] / (slew rate) = time

Yet, the answer to this equation does not always match the opamp's rise/fall time on its datasheet. What is in the descrephancy?
 
Rise time is for small signal, slew rate is for large signal.

If u test the opamp with a few hundred mV step pulse, u'll see the rise time.

As u increase the pulse amplitude, the rise time will stay relatively constant. That means the rate of change of voltage increases with signal amplitude.

Continue to increase the pulse amplitude until the rate of change hits the slew rate limit, the rising slope will start to decrease again.
 
You could answer this question by looking at some waveforms in datasheets. Unfortunately not all datasheets have waveforms for these tests. The rise/fall times are usually longer than what you would expect from a caculation based on slew rate, because the device doesn't slew at the maximum rate always. In particular, as the actual output gets closer to the intended output, the rate of change (slew) of the output usually slows down. If it didn't, then ringing would occur and the settling time would be awful. This slow down streches out the rise/fall time a little. There are probably other factors at play too. Also note that rise/fall times are usually measured between the 10% and 90% marks, not 0% and 100%.
 
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