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I'm after a stereo amp that can deliver ~50W into a 16-ohm load. What types of amplifiers work well with a 16-ohm load? AI tells me that amps with high-voltage rails and robust power supplies are better. Is it correct that the addition of post filter feedback opens up the TPA3255 chip amps as an option? And how would a well-designed Purifi amp work with this type of load?
If you look at this diagram you will work out the voltage needed to get to 50W into 16 Ohms is 28V and the current is 1.8A. So 16 Ohm speakers need relatively small current delivery and so are less dependent on cooling than 8 Ohms (20V and 2.5A) or even 4 Ohms (14V and 3.5A).
28V is not particularly large. I would expect most amplifiers would cope.
If you look at the specs for the Purifi modules you will see: 1ET400A and 1ET6525SA = 65V/25A, 1ET7040SA = 70V/40A, 1ET9040BA = 90V/40A. So they all exceed your requirements by a very large margin.
An amplifier that puts-out 100W int to 8 Ohms will provide (at least) 50W into 16-Ohms. Higher impedance is "easier" on the amplifier but you usually don't get as much power.
AI tells me that amps with high-voltage rails and robust
You (usually) won't find a voltage spec for an amplifier. Amplifiers are "voltage amplifiers" so the voltage is independent of the load impedance, up to its current limit.
Impedance (and resistance) is "the resistance to current flow". With lower impedance you get more current and more power, up to the point where the amplifier can no longer supply the current... If you try to drive a 2-Ohm load with a regular amplifier "bad things" can happen.
P.S.
In the chart that MaxwellsEQ linked to, E is voltage and I is current.
Simplified, power is inversely proportional resistance (or impedance), and proportional to the square of the voltage.