If the output of your source(s) is double the input sensitivity of your power amp you wouldn't need an active preamp
is there a formula to calculate this?
You compare the specs of the pieces in question. For example the specifications of the DAC section of the micro iDSD show the output voltage to be >2V. The manual for my power amp shows the input sensitivity to be 600mV (rms input for rated output power which is 35wpc for this particular amp).
This means the DAC is capable of putting out more than three times what the amp needs to reach full power. The reason you want the source (DAC, CD player, phono amp, etc) to put out more than the amp needs is to allow for loss. The longer the interconnects, the more loss there will be.
The other thing to look out for is that there will not be an impedance mismatch between the source and the amp. Again, this information can be found in the specifications section of the pieces in question. You want the input impedance of the power amp to be at least 10 times the output impedance of the source. In the example above, the output impedance of the micro iDSD is <240 Ohms. The input impedance of the power amp is 100 kOhms. Since that's way more than 2.4 kOhms (240*10) There would not be an impedance mismatch.
So since the output voltage of the DAC is more than twice the input sensitivity of the power amp (>2V vs 600mV) and the input impedance of the power amp is more than 10 times the output impedance of the DAC (100 kOhm vs <240 Ohm) I can connect the micro iDSD DAC directly to my power amp and control the volume from the DAC.
In my office this works fine because the micro iDSD DAC is the only source and it is sitting right on the desk within arms reach. However, in my main system, even though the DAC and power amp are just as compatible, I have two other sources, an AVR and a phono preamp, and they are all on the other side of the room from my chair. So I need to be able to switch between three sources, and, because I'm lazy, I wnat remote volume control.
The reason for needing an active preamp (adds gain) would be if one or more of your sources did not put out enough voltage to drive the power amp. Since all of my sources do put out enough voltage to drive the power amp in this system I do not need an active preamp. I only need to be able to switch between inputs and control the volume. That's why I use a passive buffer (0 gain).
Just because I don't need an active preamp doesn't mean I can't use one. It wouldn't damage the system or anything, I just prefer the way the passive sounds and since I can use it, I do.
Mike