How much amplifier power do you really need?

[David A]

In an earlier post you compared reproduction of a single tone at 40 Hz with reproduction of a single tone at 1000 Hz and observed that it takes much more power to reproduce the 40 Hz tone at a level that sounds as loud to us as the 1000 Hz tone and it does, but when both tones are present it takes virtually no more power to produce both tones at the same perceived loudness level as it takes to produce the 40 Hz tone at that perceived loudness level on it's own because what is causing the power requirement is not our perception of how loud each frequency in the signal is when there's more than one frequency present, it's the actual SPL of the bass frequencies that is the prime determinant of the power requirement. That's because the SPLs of the bass frequencies are much higher than that of the mid and high frequencies present in the music and the total SPL of the music is not much higher than that of the bass frequencies because of the way in which SPL levels which are measured in dB, a logarithmic scale add together.

If we have 2 tones, 40 hz and 1000 Hz, and they both have an SPL of 60 dB, the total level will be 63 dB. If we have a 40 Hz tone of 60 dB SPL and a 1000 Hz tone that we perceive as being equally loud, it will have an SPL of around 20 db and the total SPL will be around 60 dB. It's the low frequencies which dominate the total SPL, the mid range frequencies add very little to the total SPL when the bass frequencies are present at a level which we perceive as equally loud as the mid frequencies because our ears are more sensitive to the mid frequencies. Our ears are also less sensitive in the high frequencies so they will only sound as loud as the mids when they are at higher SPLs as the mids but there's no instrument producing a fundamental higher than 7 kHz or so and while they produce overtones, those overtones are lower in SPL than the fundamentals. Our ears have a very similar sensitivity at 7 kHz as they do at 1 kHz so it takes roughly the same amount of power to reproduce a 7 kHz tone at the same perceived level as a 1 kHz tone and since overtones in music are almost always lower in level than the fundamental the overtones, reproduction of high frequencies above 7 kHz contribute less to overall power requirements because they're being reproduced at much lower levels.

Because musicians balance the levels of their respective instruments so the overall sound of all notes being produced by the group has a balance where the bass is present at levels we perceive as being close to that of the mid tones, sometimes softer when the mids are what's important to the music and sometimes louder when the bass is important and sounding louder than the mids, the bass is always going to be generating higher SPLs than the mids and higher frequencies, the total SPL is going to largely track the SPL of the bass frequencies, and it's reproduction of the bass that's going to contribute to how much power you need to reproduce music. OK, there's more notes present in the mid range of music than there are in the bass where there's usually only a couple of notes present at once, but you need a lot of notes in the mids to raise the SPL of the mid range to that of the bass notes so the bass is always going to be the dominant factor in determining how much power you need if there is low bass present in the music.

That means that reproduction of an electronic track with "epic levels of infrasonic bass" is going to take a lot more power to reproduce at a given perceived level (ie how loud it sounds to us rather than what the actual SPL is) than a solo acoustic instrument such as a piano or a small classical ensemble playing a sonata where there's less bass present and what bass there is at frequencies much higher than infrasonic frequencies. Even reproducing the sonata at a level higher than the level at which most people would play it could easily require a magnitude less power than playing the electronic track with infrasonic bass at the same level. Let's say you're playing the electronic track at a total SPL of 90 dB, a 40 Hz tone of equal perceived loudness is going to be around 65 dB in level and the mids much much lower again. Pretty much all of the power you're using is going to the 20 Hz tone. Genuine infrasonic tones are lower than 20 Hz and require more power again if they're going to be loud enough for you to feel them rather than hear them because they may be below the lower limit of audibility.

The take away from all of this: the lower the bass notes present, the more the power you're using to reproduce the music at a given level is being devoted to reproducing the bass and the less power is being used to reproduce the mid range and higher. The less bass there is, there of the music will fall into the area where our ears are more sensitive, the louder it will sound to us than bass at the same SPL, and the softer we're likely to reproduce the recording because so we're likely to use less power to reproduce music with little bass content at a level we like than we are to reproduce music with a lot of bass, especially very low bass, at a level that's equally satisfying.

My 140 Pro sounds great with a pair of Focal Sopra 2s but I don't play Kraftwerk :-)

[David A]

@Confused ,

An addition to my post above:

To illustrate what I was saying about the bass frequencies driving the power needs, take a look at the amplifier arrangement for Devialet's active setup for the Vivid Audio G1 Spirit speaker system. It's a 4 way speaker with drivers covering 29 to 220 Hz, 220 to 880 Hz, 880 to 3.5 kHz, and 3.5 to 33 kHz. The overhead slide from Guillaume's post about the Devialet presentation at Munich 2018 indicates 2 x 1000 watts being devoted to the lower 2 driver ranges and 2 x 250 watts being devoted to the upper 2 driver ranges. That's 4 times the power being used to cover from 29 to 880 Hz as is needed to cover the range from 880 to 33 kHz in what one would assume is an equally satisfactory manner since they don't seem to have been constrained by a need to stint on the number of amplifiers being used. Judging by the slide, it actually looks as if that is the number of amps being allocated to each of the 2 speakers.

As I said, it's the low frequencies where the biggest demand on amplifier power gets made. That setup is using 2000 watts to cover an 851 Hz range from 29 to 880 Hz and 500 watts to cover a bit over a 32 kHz range from 880 Hz to 33 kHz. I suspect that the reason for using that much power for the range from 880 Hz on up is that the total arrangement simply uses a stack of 250 Pros and they wanted to use the same amps throughout the the whole arrangement in order to ensure that the volume control worked identically across all of the amps and they didn't have to come up with some complicated arrangement of matching the output levels of amps with different peak outputs for a given volume setting on a single remote. I think they might well have been able to give less power to the upper range than the 2 x 250 watts and still had ample power reserves while matching the peak output from the 2 lower frequency ranges.

[David A]

Resurrecting a "somewhat finished" thread to some degree.

I just came across an online calculator which allows you to calculate the peak SPL you can get from a given amp and speakers. It takes into account both amplifier power and speaker sensitivity, the 2 big elephants in the room, and it also takes into account the number of speakers and the room itself to some degree (listening distance and a rough estimate of speaker location relative to the walls which affects the support the room gives). I tried it with my details and it gave an answer which was pretty close to the results of the calculation I did for peaks of 95 dB with my speakers in post #66. I said there that I would need roughly 12.6 watts to deliver 95 dB peaks and the calculator came up with 12.6 watts delivering 94.6 dB peaks which is pretty close since I was fudging my calculations a bit with some rough guesses.

The calculator also says that I can expect to achieve 105.1 dB peaks from 140 watts output, the rated output of my 140. We could add a bit to that because my speakers are 4 Ohm rather than 6 Ohm and the amp will deliver a little more into 4 Ohms than 6 Ohms and we could adjust for that if we had figures for the 140's output into resistances other than 6 Ohms.

So, for those inclined to crunch the numbers and wanting an easy way to do it, here's the link to the calculator: https://myhometheater.homestead.com/splcalculator.html

Have fun crunching numbers.

[Confused]

David - Thanks for the link, both interesting and potentially useful.

I thought it would be fun, and perhaps informative, to put whatever information we can glean from the video linked in the OP into the calculator, to see what number come out.

Some factors we know quite well, per the Stereophile measurements posted earlier in the thread, the Harbeth's have a sensitivity of about 84.5dB/1w/m. From the video, it is also clear that the speakers are within 4 feet of the back wall, but not within 24 inches of the corners of the room. It is also clear that there are two speakers. This much is good data. Of course, we also know that the amps were peaking at over 750w, and regularly running at over 500w.

The listening distance is a trickier one. To me it looks like they are listening from about 12 to 15 feet, but later in the video they move to within about 2 feet of one speaker, so listening distance clearly varies. Another unknown figure is what the SPL's are in the room. Back in post #63 I speculated, or perhaps guesstimated, a figure of 90dB with 95dB peaks, to me it is just not credible that it could be any louder than this if three guys could happily approach to within 2 feet of one speaker.

Putting these numbers into the calculator gives these results:

Assuming 84.5 efficiency, 750w, 12 feet distance, within 4 feet of wall, not in corner. Putting these numbers in the SPL calculator gives a result of 108dB. To me, this cannot be accurate. If the SPL was 108dB, then it would not be comfortable in the room, you would not hear the attendees voices over the music, and for sure nobody would move to within one or two feet of the speaker.

So lets do the calculation backwards, how much power would you need to achieve the 95dB peak I estimated earlier? According to the calculator, 40 watts. 40 watts is a full 710w less than the amps in the video were displaying.

So there are clearly other factors involved here. Earlier posts covered the power required to produce powerful bass heavy music, and the whole system of music production is complex and dynamic. I think these calculators are a useful guide, but there is a more complex picture to consider.

[thumb5]

I expect the calculator is basing its power calculations on sine wave inputs, which might not be a good guide to perceived sound levels for music (depending on the type of music, usual caveats apply, etc.).

At least, it would be helpful if the calculator explained what it was assuming about the input, and whether it takes things like Fletcher-Munson into account - presumably it must do otherwise it wouldn't seem to be particularly useful in practice.

Having downloaded the spreadsheet that the on-line calculator uses, it seems not to "know" anything about music or Fletcher-Munson. The spreadsheet calculation is simply taking the speaker sensitivity and amplifier power and making a correction for listening distance and number of speakers.

On reflection, I suppose if you're interested what an SPL meter might read then this calculation should work if the speakers have a reasonably flat frequency response. But does it tell us much about perceived volume when listening to music? Not sure that I can convince myself that it does...

[David A]

@thumb5 ,

I don't think the calculations are based on sine wave inputs. I think they're straight SPL calculations based on the number of watts the amp can deliver and the sensitivity rating of the speaker. The addition for multiple speakers assumes that each speaker is delivering the same SPL, the adjustment for listening distance is based on SPL falloff over distance, and the adjustment for speaker placement is a rough estimate of the support the room gives to a speaker placed in different positions. Ultimately the reliability of the result is going to depend on how the speaker sensitivity is measured, including the relevance of whatever is used for a test signal to situations involving music signals which could be quite different in frequency content, and the accuracy or otherwise of the sensitivity rating and amplifier output specification, both of which can often be wildly optimistic and owe more to marketing considerations than actual measurement. The calculator is simply basing its calculations on the data you enter and the usual GIGO rule (garbage in, garbage out) applies. I can't see anyone coming up with a better approach to the calculation method, anything more reliable is going to require more reliable data for input rather than a different approach to the calculation.

It definitely doesn't take Fletcher-Munson into account and it doesn't have to. What the Fletcher-Munson curves tell us is something about how frequency affects our perception of loudness. In music the level of the sound of different frequencies being played at the same time isn't uniform, the musicians adjust the level from their different instruments/voices to produce the sound balance they want the listener to hear. What the calculator calculates is what the SPL of that recorded sound balance is going to be at the listening position for a speaker of given sensitivity and a specified amplifier output. The relative levels of the different instruments/voices in the music will be preserved provided the speaker has a wide enough frequency response to produce all of the frequencies involved while preserving their relative levels accurately and the amplifier can deliver enough power to allow the speaker to do so.

I think it is quite useful in practice for the purpose for which it is intended. It's not perfect but the problems aren't problems with the calculator, they're problems with the accuracy of the speaker and amplifier specifications that are entered and the fact that music signals can be quite complex and there is no standard test signal that would be equally accurately represent every sort of music signal we send to our speakers. The things that would improve the accuracy of the result have nothing to do with what the calculator is doing and everything to do with the accuracy of the speaker and amplifier data we input.

[thumb5]

@David A I agree with you about Fletcher-Munson, if the purpose of the calculator is to tell you the sound pressure level for a given power input (which, to be fair, is all it claims to do). However I think it's still true to say that that doesn't tell you everything you might need to know about the perceived sound level.

I do still maintain that the result of the calculation is based on an assumption of sine wave input, though, because (as I understand it) that is how loudspeaker sensitivity is measured - the sensitivity is quoted for sine wave input at one or more specific frequencies so the calculator will only produce accurate results for that input.

[David A]

@Confused,

Take a look at Stereophile's speaker test reports, especially the impedance and phase plots at low frequencies. There's huge variations there from speaker to speaker and that affects the load the speaker places on the amp with some speakers being easy to drive, others hard to drive. There's going to be variations in power draw from speaker to speaker and there's no way any calculator can take that into account unless you can enter that kind of data into the calculator also. I don't know of any calculator that lets you do that.

Then there's the room response. We both know that lots of speakers, including the Harbeths, roll off at lower frequencies. Room response is even more uneven at low frequencies than speaker response and we've got no idea what the room response was like. I was once told by a dealer that his best showroom started rolling off at 100 Hz because of openings to other areas. I was once in a showroom where I could not hear a prominent bass line from a speaker at the listening position the dealer had set up but that bass line became very audible and in balance with the rest of the music if I stood up and took one or two steps forward so we're talking about what was probably a measurable SPL difference in the room of 30 dB or possibly more in a space of less than 3 feet. Where was the mic placed for the video? Was it in a null position for the bass or in a pressure zone for the bass notes? If it was in a null, was the volume level set for a balanced sound somewhere around where the mic was in which case the amp would have to have been delivering a lot more power in order to deliver the level heard at the mic position but the level of the voices of people near the mic wouldn't have to have been anywhere near the output from the speakers at the speaker location because most of that output of the speaker would have been disappearing at the mic position because of the null. Add to those issues a pile of people in the room with their clothes adding to the absorption of the room furnishings/carpet/curtains etc and whatever acoustic treatments are present and the absorption they provide.

As I said in my response to @thumb5 above, the problem isn't with the calculator, it's with the data we enter and the data we've got for entry is very limited. I have no idea what the acoustics of the room were like but I do know from experience that you can pour huge amounts of power into trying to get decent listening levels in one position in a room and much less power into getting similar results in another position. The calculator makes limited provision for speaker placement but that's a rough estimate which won't be accurate for every room, and no provision apart from for listening distance for room effects at the listening position. Most of us, probably nearly all of us, don't have that sort of data for our rooms and I hate to think what the calculator would look like if it allowed us to enter that sort of information.

I think the calculator is quite accurate for the sort of input data it uses but I can also envisage situations in which the 40 watts you calculated for a 95 dB level at a given distance could easily end up actually being an order of magnitude higher depending on whether or not the listening position was in a null for the bass frequencies and the listener was adjusting the volume level to compensate for the null, especially with a speaker that was difficult to drive.

It would be great if someone came up with a calculator that took more things into account. Then we'd find people complaining that the calculator was useless because they couldn't provide all of the data it asked for. There's no perfect solution here, and there's no way of avoiding the sort of difference in result shown by your video example and the situation in my room with the sort of calculator that we can find online. If we want anything more than that, then we're probably going to have to look for something that starts out with a professional level room analysis tool, speaker measurement tool, and a amplifier measurement tool which measures amplifier performance to a greater degree than even the Stereophile test reports do and they're more detailed than any other reports I've seen that are generally available. If we had that then we'd see a pile of complaints that the damn thing was too complex for anyone to use.

We've got what we've got, it's better than nothing, and it works better in some situations than it does in others. In the end, if you can't get the levels you want in your room with an amp of a certain size then you need a bigger amp or more sensitive speakers. The only simple and reliable test available for any one of us is to grab an amp and speaker combination, stick them in our room, and see whether we're happy with the result. The best the calculators we've got can do is give us an idea of what a starting point for amplifier power and speaker sensitivity should be. Sometimes, probably a lot of the time, that starting point will work but sometimes it won't.

[Confused]

Picking up on David A's point above re speaker impedance and phase plots, Archimago published an article on speaker measurements this week, see link below.  For me, some of the links from the article are more interesting than the article itself, in particular the Audioholics article re impedance curves and phase angles, see the third link below.  It is quite technical, but for those who are less technically minded it does include the phrase "Things are far more complicated than saying “Speaker X is 100dB sensitive, so you could power it with a potato!"

The curious use of a root vegetable as an amplifier analogy apart, this statement does seem to be consistent with the conclusion of the last few posts in this thread.

https://archimago.blogspot.com/2019/08/m...art-1.html

https://www.audioholics.com/loudspeaker-...ical-phase

https://www.audioholics.com/loudspeaker-...ase/page-2

@David A - Picking up on one point in your post above, we do actually know where the microphone is located in the video in the OP.  It is a built in microphone in the video camera, this point was stated on the Harbeth forum from where the video originates.  As you might expect, and consistent with what you wrote in the post above, you can clearly hear the sound change as the camera moves around the room.

[RebelMan]

As I pointed out before, for a sine wave the peak power is exactly twice the RMS power, because the (peak) amplitude is the square root of 2 times the RMS value of the signal and power depends on amplitude squared.

A lot of heavy weather seems to be being made of this...

This statement contradict's itself.  Peak power "by definition" is the √2 (which is 1.414) times the RMS power as you say but is NOT twice RMS power as you also say. Calculus proves this, what math are you using?