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
Another way to have asked the question would have been:

"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?"

In modern times speaker sensitivities are usually (although not always) based on the SPL produced at 1 meter in response to an input of 2.83 volts, rather than in response to an input of 1 watt. 2.83 volts into 8 ohms corresponds to 1 watt, so in the case of an 8 ohm speaker (that is truly 8 ohms) both numbers will be the same. However 2.83 volts into 4 ohms corresponds to 2 watts, which is 3 db greater than 1 watt. So 3 db should usually be subtracted from the specified sensitivity of a 4 ohm speaker to derive the SPL it will produce in response to 1 watt.

In the case of a 6 ohm speaker the corresponding figure to subtract is about 1.25 db.

Often such specs do not indicate whether they are based on 2.83 volts or 1 watt. In those cases it would be a good bet that they are based on 2.83 volts.

Note though, that since most solid state amplifiers can provide considerably more power into 4 ohms than into 8 ohms (sometimes as much as a factor of 2 more) that increase in amplifier power capability will partially or fully compensate for the 3 db subtraction. That would not be the case with tube amps, though, or with McIntosh solid state amps which have autoformers at their outputs. Tube amps and McIntosh solid state amps having autoformers are usually designed such that maximum power capability when a 4 ohm load is connected to their 4 ohm tap is essentially the same as when an 8 ohm load is connected to their 8 ohm tap.

On another note, the 80 db average and 100 db peak listening levels you mentioned are fairly similar to mine, my listening being mostly to classical music. Although I’ve found that some (relatively few) classical symphonic recordings that have been well engineered with minimal or no dynamic compression can produce 105 db peaks at my 12 foot listening distance while being listened to at average levels in the mid-70s.

Also, here is another SPL calculator you may find useful:

https://myhometheater.homestead.com/splcalculator.html

In contrast to the Crown calculator you cited this one adds 3 db if two speakers are specified, which is a reasonable approximation, and it attempts to address the effects of room reflections, i.e., what is sometimes referred to as "room gain."

Also, be aware that these calculators will significantly underestimate the resulting SPL in the case of planar speakers, such as electrostatics and Magnepans, for which SPL falls off much less rapidly as distance increases, compared to dynamic (box-type) speakers.

Finally, be aware that speaker sensitivity specs are frequently optimistic by a few db. Before using these calculators it would be prudent to Google the specific make and model of the speaker together with the word "measurements." If Stereophile, SoundStage, or some other publication has reviewed the speaker the measurements that may be presented in conjunction with the review will usually be much better to rely on than the manufacturer’s spec. And their measurements and the associated text will also often provide useful insight into the impedance of the speaker, how it varies as a function of frequency, and how accurate or inaccurate the specified number may be.

Regards,
-- Al
I was about to type Almarg's basical post.  That is solid advice.  Even was going to recommend the same calculator.

Good luck to you!


"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