Speaker sensitivity, impedance, and calculating amp power

"What role does impedance have, if any, alongside other factors in the calculation of how much power should be used to drive a speaker comfortably?"

Zero, because in my experience, the math is not complete. We don’t get damping factor for the amp, most of the time, and it too, is frequency dependent. In addition, my experience says that amps are more sensitive to impedance dips than the math would lead us to believe if we did know this.

The way to approach this is, for a given speaker, note where the impedance is worse, then listen to amps with music in that range and see if you hear or feel the deficiency in amplifier output.

One speaker I feel is notorious like this is Focal. They often have these narrow dips around 100 Hz and anything but the most robust amp will noticeably sag.

One decent indicator of an amp’s current drive (ability drive low impedance speakers) is how well it doubles power as impedance drops in half.

8 Ohms -> 100 W
4 Ohms -> 200 W
2 Ohms -> 400 W

But again, I feel noting the impedance dips and listening is a better indicator than this.

Best,

E

OP:

If you are interested in theory alone, start with understanding power and sensitivity (not efficiency) at 1 meter.

Assume the amplifier is a perfect voltage source, and the speaker an ideal 8 ohms. Then understand that you can use the power in dB to tell you the difference in speaker output.

dB louder = 10 log (power / 1 watt)

So, if you h ave an 89 dB sensitive speaker, and apply 100 watts, the output at 1 meter will be 109 dB.

The truth is that an ideal speaker with flat frequency response speaker has equal voltage sensitivity at all frequencies, but the power consumed at any frequency is proportional to the inverse of the impedance, so the idea of using power to determine output is a cheat. We’re really using the amps equivalent voltage difference.

So long as your speaker is exactly 8 Ohms, then we can use the power calculation (above) interchangeably with the voltage calculation, below:

db louder = 20 log ( voltage / 2.83V)

The real problem we have is that amps are not sold by voltage output, but by power, but in fact, power amps are not power amps at all, they are voltage amps with (ideally) zero output impedance. That is, a power amplifier does not multiply the input power. It multiplies the input voltage and produces whatever current, and therefore power, is needed.

I’m overfilling your bucket here because I want you to reconsider your question. :)

This handy Wikipedia entry may further confuse you:  https://en.wikipedia.org/wiki/Decibel


Best,

E

Honestly, as some one who does a lot of measuring and critical listening, this is difficult. It seems amps are more sensitive to speaker impedance than we think, so current is important, but the rated power at 8 Ohms is not really.  Usually 50-100 W is plenty for a modest listening area with your standard 2 or 3 way speaker.

Looking at the speaker impedance, look for dips below 4 Ohms, and that will tell you were it will challenge an amplifier, and what areas of music to listen for while buying.

Use your own ears. :)

Best,