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The volume knob adjusts gain - power is determined by the signal amplitude and the load being driven.
Pardon me while pick this nit.
Typically, gain is fixed. The volume knob just attenuates the incoming signal, and the amplifier's fixed gain is applied to that.
Yeah that's what I thought too. Usually the gain is fixed at, say 2.5x in the Objective 2. Adjusting the volume knob wouldn't adjust the 2.5x gain, but the gain switch will. So now I'm a bit confused when cjl says the volume knob adjust the gain.
Vout/Vin = gain
Volume knob in a low position:
2.5 V / 1.0 V = 2.5
Volume knob in a higher position:
5 V / 2.0 V = 2.5
5 V > 2.5 V = more power
2.5 == 2.5 same gain
Volume knob in a low position, low gain:
2.5 V / 1.0 V = 2.5
Volume knob in the same low position, high gain:
5.0 V / 1.0 V = 5.0
5.0 > 2.5 V = more power
5.0 > 2.5 = more gain
I almost never touch the gain button/switch on an amplifier; usually the lowest gain setting on a given setup is all that I need.
I do see the point cjl is trying to make though. If I play a loud song and switch to a quiet song, the song itself is quieter, so the input signal to the amp, and thus the output, will be smaller accordingly.
The question is then, how can I predict how much I would need to turn the volume knob to output the same power, and thus SPL from the used speakers/headphones, to match that of the louder track (without using ReplayGain)? Earlier I modeled a specific situation for the OPPO HA-2 driving a HiFiMAN HE-560 in a practical scenario. My preliminary calculations seemed to fit my subjective testing, but the model may have been incorrect from the start since I assumed that with a given volume knob position, the amp would output the same power regardless of the input signal (loud to quiet track in this case).