So, the output voltage is not directly tied to transformer size?
Right. The VA gives us the power output of the transformer at maximum current draw, but any given VA rating can have different output voltages. What matters is what is called the winding ratio. For instance:
600 VA w/ 10:1 : Outputs 12 Vrms
600 VA w/ 5:1 : Outputs 24 Vrms
And watts are also not directly related to voltage?
For a load, they are proportional to the square of the voltage:
W = (V*V) / R
If the amp is 80wpc, the absolute maximize voltage is about 80volts?
Nope, not at all. The 80 Wpc is rated at 8 Ohms. It is really W(rms). I probably will miss a step here:
Sqrt(80 Wrms * 8 Ohms) = 25.3 Vrms
Vrms to Vpk = 25.3 * 1.4 = 35 V
That + and - Volts is what the power supply has to make available to the amplifier board, which is then going to swing back and forth between them to create the voltage at the speaker.
Assuming there were no losses (and there are always losses) the voltage the speaker would see would go from + 35V to -35V at maximum.
So, for an amp rated at 80 watts per channel an output winding of around 5:1 seems about right. The VA we can estimate at a minimum should be twice this, so 160 VA. However, there are losses AND .... no speaker is exactly 8 Ohms. As the impedance drops, more current must be drawn, so at 4 Ohms we must draw at least 320 VA.
The capacitance offsets limits in the ability of the transformer to recharge?
Yes. What comes out of the transformer and bridge rectifier is pulsing DC. From zero to some positive number on one side, and zero to some negative number on the other. The filter caps smooth this out. More capacitance, the closer the average V is to the peak voltage, and the stiffer it will seem while playing music.