Speaker sensitivity, impedance, and calculating amp power


This is an elementary question, but I'm not quite understanding how to match amp power to speakers. When I searched around on this forum, I found many discussions which went deep into the weeds. I am hoping for a way of calculating the level of amplifier power I need for speakers with different sensitivities and impedances.

If you have the patience, here's the basic question. So, I've learned that one must consider a number of factors to calculate the amount of amplifier power to drive the speaker:

Sensitivity of the loudspeaker
Loss of db at the listening position
SPL desired at listening position
Amount of headroom desired

Most discussion of the demands a speaker will make on an amp focus on the speaker sensitivity. But the speakers I'm considering vary also in their impedance. How would I use both of those factors to estimate necessary amplifier power to drive them with a comfortable amount of headroom?


128x128hilde45
Question 3 is about duty cycle....

is that “ word salad “ enough ?

its easy but math and science based...
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
Avoid any speaker that dips below 4 ohms through the bass section.Above 5-6 ohms is even better.The flatter the impedance curve the better.

For every 3db increase in SPL the amplifier power required doubles. 1 watt, 2 watts, 4 watts, 8 watts, 16 watts, 32 watts, 64 watts, 128 watts ... And a 10db increase in SPL (double the loudness) requires about 10X the power.
SPL isn't the only consideration when choosing an amp. Factors such as headroom for transient spikes and damping factor play key roles. I had an amp from a specific manufacturer that was rated at 200w into 4 ohms. I had a sense (how's that for a scientific analysis) that it just didn't seem to have enough power to control my speakers which are rated at 96db. I sold it and went for the same brand with an output of 370w into 4 ohms. My system improved because the sound was tighter and more detailed than previously. I wasn't listening any louder, that wasn't my goal. The larger amp was able to control my speakers much better and give me more detailed and cleaner performance. Again, power is not only about SPL.