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Speaker Sensitivity, Dynamic Range, and Amplifier Output

I’m not convinced that you can have too much love, sex, money, or power. Especially amplifier power. Even if you don’t need it, exactly, it’s nice to have. But much of the time, it’s a must have.

I think this is one of the least-well understood things about high-end audio. At some point, in the search for perfect sound, inevitably the beleaguered audiophile will look again at amplifiers. Big amps don’t necessarily mean the highest fidelity, and in fact, many argue that seeking out the very best sound will eventually take you into a discussion of low powered amps. Very low powered.

The problem? As power output goes down, fidelity may go up, but dynamics will go down. That is, low power hampers the ability for a speaker to recreate the dynamic swings in reproduced music. The way this works, as I understand it, is as follows.

Your speakers are rated as having a certain sensitivity. This means that with 1 watt of power, they will create sound at some SPL when measured at a distance of 1 meter. An 85dB speaker, then, will make sound at 85dB with a single watt of power. This is actually pretty loud, so you’re all done, right?

Wrinkle #1

Well, not exactly. Sound falls off pretty quickly the farther away you move from your speakers. If you’re sitting near-field, or about 1m, then the stated sensitivity of your speakers is where you start. But, if you happen to sit a bit farther back, say 2 meters or 3 or 4m, you need to expect (at most) a 6dB falloff every time you double the distance. That is, if you listen 4m away, then, that single watt on those 85dB speakers is only going to make about 73dB.

Okay, a caveat. This 6dB/doubling-distance is for open-air, anechoic rooms or rooms that are wildly damped. Most rooms will drop off a bit less than this, maybe quite a bit less, but still, the number is a good rule of thumb. And remember, if it’s too loud, you’re too old! Ah, hmm … or you could just turn it down? Yeah, that works, too.

Now, speaking of old, I actually don’t tend to listen much to music at volumes much above 80dB, nominal. So, let’s set that as a threshold. Given that I sit ~3m back, that means that I need to be able to do 90dB at 1m because I need to add back ~10dB to account for the fall off that my 3m of distance introduces. Good so far?

Wrinkle #2

Music isn’t test tones, that is, loudness varies in real music. It swells, it wanes, it swells again. There are loud bits and not-so-loud bits. How much those vary is (more or less) the “dynamic range” of the music. More properly, this is the variance from baseline to the highest peak that is found in the music, and is commonly measured in dB. This is where the debate around the “Loudness Wars” comes in. It’s pretty common for popular music to be heavily compressed during post-production to make the track sound louder (where it’s assumed that louder = better). Now, some compression is required — without it, drums and vocals can sound really out of whack. The issue is how much is enough. As Bob Katz has mentioned, a peak-to-average range of 20dB is great, but precious few recordings go there — or anywhere near there. Most recordings have a much smaller range, something closer to 8dB — and some go lower! Audiophile recordings can vary, too, but I think it’s pretty safe to assume that most of your music will have less than 15dB of variance, so let’s use that as our number. Specifically, your amp must be able to not only produce a tone at a nominal listening value — 80dB in our example — but be also able to support well-produced/well-recorded music that includes transient swings of up to ~95dB at the listening position. Quiet … to VERY LOUD. If your amp can do that, you are covered. The question is, can your amp do that?

Wrinkle #3

Amps need to double their output for every 3dB of gain. That means that to go from 1 watt to 2 watts only gets you an additional 3dB of volume. We need 95dB-ish, so 2wpc isn’t going to get us there. Here’s a quick rule of thumb for amplifier gain:

  • 1wpc = 0dB
  • 10wpc = 10dB
  • 100wpc = 20dB
  • 1000wpc = 30dB

Our goal is the ability to create 95dB on demand, at the listening position, should the music require it. Our speaker’s sensitivity is 75dB (actually, it’s 85dB at 1m, but this is ~10dB down at 3m, so we’re now at 75dB), so we need the ability to pull an additional 20dB (to get us to a peak of 95dB) of dynamic, instantly available, gain from the amp.

Assuming that I haven’t screwed my math up, 20dB takes about 100wpc.

If your amp can’t put out 100wpc, you’re likely to clip the amp with your fancy-pants audiophile music. Remember, some music can open up an even larger swing, so it’s always wiser to go higher rather than lower. Of course, you could just go buy all your music compressed … or just turn it down. Not happening? Right ….

Anyway, to recap: if we’re shooting for an optimal SPL average of 80dB (which is loud) and we want to reproduce music with 15dB swings from average-to-peak, we target 95dB as a max output.

So, at 3m (-10dB), we have:

  • 82dB speaker sensitivity = 200+wpc amplifier
  • 85dB = 100wpc
  • 88dB = 50wpc
  • 91dB = 25wpc
  • 94dB = 12wpc
  • 97dB = 6wpc
  • 100dB = 3wpc

At 2m (-6dB), we have:

  • 82dB speaker sensitivity = 100+wpc amplifier
  • 85dB = 50wpc
  • 88dB = 25wpc
  • 91dB = 12wpc
  • 94dB = 6wpc
  • 97dB = 3wpc
  • 100dB = 1.5wpc

If you want it louder, you need more power. If you want it quieter, you need less.

Also, if your music is heavily compressed, or you listen at low volumes, or listen closer (as in “near field”), you can get by with a lot less power. But for normal folks in normal situations, the guidelines I just laid out should be useful.

Which brings me to …

Wrinkle #4

Max output = major distortion. Unfortunately for our math here, your amp will probably sound best somewhere south of max output. Take a sec and go look at the amplifier reviews on Stereophile. Pick one. I think you’ll find that it — that is, most of them — tend to head toward heavy distortion as they approach their max rated output. So while, yes, it’s true, that EL84-based amp can hit 15wpc of output, it’s also hitting a 10% THD at that point, too. That much distortion is … ah … suboptimal. Yes, fine — tube amps may well “sound great” right up to clipping (and beyond) because of their design and the harmonic structure and how gracefully they fail … blahblahblah.

Distortion, even if pleasant, isn’t what we’re after — it’s fidelity. Fidelity = avoid distortion. So, here is an interesting thing about tube amps — they tend to have a max power output rating that corresponds to a pretty high level of THD. Solid state amps, by contrast, tend to under-state their power ratings, so the rated power output tends to still have a rather low THD.

So, here’s the lesson: got a low power amp? Plan on an even higher sensitivity speaker in order to get the optimal match.

And (another) besides, if you push your amp that hard for any serious length of time, you’re going to kill it or your speakers — and your system will probably sound like ass in the meantime. Dude. Just back it off, maybe even quite a bit off, and you’ll be joyously in the “sweet spot” for the amp. Said another way, if you want your amp to sound as it was designed for normal use, as opposed to what it sounds like when it’s getting its ass handed to it on a platter, you’re going to want to target the optimal output in your calculations, and not the max output. Don’t know where that knee is in the THD curve for your amp? Well, if it’s a tube amp, you can safely assume that it’s rather below max output (like halfway), and have done. How do you bake that in to your speaker match-ups? Add at least an extra 3dB of “head room” into our equation to account for … low-power amp irregularities.

But … I forgot something! If you’re talking about a two-channel setup, you’ve got [gasp!] two speakers throwing sound out there. Which brings me to ….

Wrinkle #5

Multiple speakers reinforce each other at the sweet spot. This is a freebie that we get when we talk about multiple speakers, but the long and short of it is this — if you have two speakers, you get an extra 3dB of “free” gain at the listening position. Add three more speakers to fill out your 5-channel rig and you’ll get a total of 7dB of gain “summing”. Add more speakers, get more gain.

Stew Nellness, from the recently relaunched Affordable Audio team, sent me a handy-dandy link to a calculator that sorts many of these parameters out. Thanks, Stew!

For those of you with tube amps, though, I’d keep that free-3 in reserve. That is, if you’re using a low-power amp (think SET with <15wpc), then play it safe and go with the chart numbers above. Remember, the amp will perform its best when it’s not pushed up to and past its max output. Call this your “headroom” and just keep it in your back pocket.

Bottom Line

Power is good, but more power is always better.

Are you screwed if you blow it? No, of course not! If you pull a Robb Stark and fall in love with a low-powered amp, just remember to avoid dinner at the Towers, regardless of how compelling the invite might read. Ahh, that is, remember that every halving of the power rating (200wpc to 100wpc, 50wpc to 25wpc) takes only 3dB off the max SPLs, which is actually not always easy to hear (every 10dB of gain is about perceived as twice as loud), so if you’re supposed to be shooting for 100wpc and buy an amp that maxes out at 50wpc, don’t sweat it. Just don’t expect the best sound if you try and mate that 85dB speaker with a 12wpc SET amp — unless you’re sitting with the speaker in your lap. If you’re not, your Norah Jones CD may sound just fine, even when you turn it up for your friends. But … the Philharmonic may sound flat … or confused … and your imaging and transient response and bass … well, they may go to shit. If so, it’s not your speakers. It’s not your amp. It’s the fact that the music, with those speakers when driven by that amp, simply equals civil unrest. Break up the band before someone goes postal.

If you’re looking for quick-and-dirty, then I think most speakers, with most music, will almost always be served very ably by an amp with 100wpc of output. But if your speakers have a really low sensitivity, or your amp has a really low power output, or it’s a tube amp … be concerned, do your homework, all that.

Or you could just turn it down, old man.

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About Scot Hull (979 Articles)

Founder, Editor and Publisher at Part-Time Audiophile and The Occasional Magazine.

11 Comments on Speaker Sensitivity, Dynamic Range, and Amplifier Output

  1. This helped me decide how loud my car stereo should be, and what characteristics of speakers and amps I should define to achieve that loudness. Thanks a heap. Hear are a few questions that come to mind:

    1) Maybe this is merely a matter of language and words and definitions, but what is the reason to start the analysis from the low end of the dynamic range? For example: “I actually don’t tend to listen much to music at volumes much above 80dB, nominal”, then you go on to describe ONLY about how to reach higher loudness.

    2) What about the volume ranges below the sensitivity rating of the speaker? 85db is loud and would drown out a conversation. To run a speaker (sensitivity 85db) at loudness of 80db, the amp is working at close to 0.25 watt. 80db is loud too. In fact, still much louder than a conversation. Can’t an amp operate at less than a watt?

    3) When you talk about loudness preference, why not mention the risk of hearing loss? You know, 80db is fine, but loudness above 85db over time can causes permanent damage, according to hearing health resources. I’m not a nanny, just trying to be careful, and if I take your advice that more power is better, I might be putting my ears at risk. Prudence requires a limit.

    Thanks. Good work. And Happy New Year!

  2. Mike in SC // April 5, 2012 at 2:55 PM //

    This should be a “Sticky” in every audiophile forum.

  3. Good point. McIntosh amps (tube or SS) deliver their rated power into 4, 8 or 16ohms.

    Which brings to mind a question about amp power and impedance…

    What drives the difference in stated power across impedances?

    — McIntosh claims one stated power across three impedances…

    — Plinus SA Reference on the other hand, claims 450 wpc at 4 ohms, 300 wpc at 8 ohms

    — Krell Evolution One…900wpc 4ohms, 450 wpc 8ohm

    I thought it was Ohm’s Law…based on the above, it seems more like Ohm’s Suggestion.

    Cheers

    Bill

    • Part-Time Audiophile // April 4, 2012 at 10:38 PM //

      It’s the transformers. My guess is that they do some rejiggering to keep the output stable regardless.

  4. Charlie // April 4, 2012 at 8:37 PM //

    No replacement for displacement applies to internal combustion engines – amplifiers and frankly speakers (box – planar – stats – horns) and flat panel screens as well. With amps, solid state watts are cheap these days buy as much as you can afford, tubes are another matter entirely…………..

  5. Ditto the above comments…

    So if I understand your table correctly, a speaker with 88db sensitivity (actually the exact specs are 88 dB SPL..2.83 V @ 1 M) requires a minimum of 50 wpc. So, in my case a McIntosh MC275 delivering 75 wpc into 4ohm would be fine…listening room is 20x18ish.

    Thanks for the scholarly legwork. Very helpful indeed.

    Cheers,

    Bill

    • Part-Time Audiophile // April 4, 2012 at 5:07 PM //

      “Requires 50wpc” is a strong way to put it — say rather, “You won’t be limiting your dynamics with 50wpc”. You can certainly do quite a bit with less, though.

      I did miss something, which I’ll go back and edit which is the summing effect that you get with two speakers — a “free” 3dB of gain! So, that could halve your output requirements — or, better still, allow your 50wpc amp to be run closer to it’s sweet spot and away from the high-distortion max output.

      • Yes, but are his speakers 4 ohm impedance? Or are they 8 ohm? He might be delivering substantially less power to his speakers if the speakers are rated at 8 ohm. Might need a little note about impedance in calculating these things.

      • Part-Time Audiophile // April 4, 2012 at 6:21 PM //

        Good point. Most amps don’t put out the same power into the same impedance. I mean, some do (say, McIntosh), but most don’t.

  6. Atlasiris // April 4, 2012 at 1:43 AM //

    Spot on once again!

  7. Thanks for putting this in easy to understand terms. Don’t think I’ve ever seen anyone else tackle this in anywhere this depth.

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