What is meant by a "fast" pre amp


I have heard a pre amp described as "fast", what does that description mean?
brf
Agreed, Al's post was lucid & well-written for most people to understand this technical subject.
Just a small addendum - as far as specs are concerned, the higher the slew rate the better. Slew rate can also be thought of as the rate at which the amp can charge a capacitor i.e. besides the units of Volts/microsecond, slew rate has equivalent units of Amperes/Farad. Thus, slew rate can give you an idea of the robustness of the ampilifier's power supply. For difficult to drive speakers, amps with higher slew rates generally do better as their power supplies can provide more current.
(current is not the only requirement for hard to drive speakers, one also needs wattage which provides the max possible output voltage swing. So, one needs both watts & current for hard to drive speakers & that's what makes these amps very large chassis units).
Higher slew rate amps generally cost more as more robust power supplies are not cheap in parts or labour.

As alluded by Al, slew rate & bandwidth are inter-related: if you view slew rate in its dual definition as the ability to charge a capacitor, that current is related to gain of the amplifier stage & in turn, the gain of the amplifier stage & the total capacitance in that amplifier stage defines the bandwidth. So, higher slew rates, higher current generally yield wider bandwidth (or "faster") amps.
Interesting perspective, Bombaywalla, which I hadn't thought of or seen stated before. And it sounds right.

I (current) = C (capacitance) x dv/dt (change in volts per unit time)

Therefore,

dv/dt = slew rate = I/C = amperes/farad.

Thanks!

Best regards,
-- Al
I have been told that a fast preamp is one with good phase purity.
Supratek preamps sound very fast.
I also owned a Metaxas Marquis SS preamp which was fast.
These are the two best sounding preamps I have heard.

Once you get used to the speed there is no going back.
'good phase purity' comes from wide bandwidth/high slew rate.

In order to get to 20KHz without phase shift, the upper cutoff of the circuit needs to be 10X higher, IOW 200KHz. YOu can use that as a good rule of thumb for seeing a 'fast' preamp in its specs.

Mind you, 'fast' is not the same thing as 'bright', in fact brightness is often caused by phase shift issues due to poor bandwidth. Brightness is also caused by very minimal distortion of the 5th, 7th and 9th harmonics.
All of this can be summed up in one word, MUSIC.

A preamp could have all of the best specs in the world, but if it doesn't sound like music, you have nothing.

If you think your equipment sounds fast then it probably isn't.