Headroom is completely arbitrary. When you look at an amp, the power rating is based on either voltage limitation or current limitation. In most cases, you can't exceed the former. With the latter, you can usually run the amp short-term past its thermal operating limits but it's never a good idea to do so (unless you're a pro audio tech knowing what they're doing, I suppose). Either way, it's best just to figure out how loud you want your peaks (with an allowance for power compression at the speaker/driver) and determine your amp power requirements based on that.
Let's say you have a movie soundtrack that, at some arbitrary SPL (100 dBA at listening position), is causing the sub to move 4 mm peak-to-peak because of an explosion that just happened. The sound then transitions to gunfire, still at 100 dBA at the listening position, but with much more midrange energy and almost no bass. The power requirements would be the same, given the same sensitivity for all the speakers/drivers, but there is comparatively way less excursion now. So really, where the energy is in your music/soundtrack is a big factor.
However, when you talk about low bass, the Thiele-Small parameters will end up governing the response and power requirements and it's not all about displacement (it is, but not really). Shrink the enclosure and you need more power to get the same displacement. Provide impedance matching between the driver and the air (e.g. put it in a horn) and you get more sensitivity without necessarily increasing your displacement.
What do you think would happen if you listen to a flute solo at 120 dBA at listening position? It's loud as ****, will take tons of power, and your sub still won't budge. On the other hand, if you listen to a 100 dB sine wave at 40 Hz, you might be almost bottoming out your sub driver, but it wouldn't necessarily take any more power to do that than to get 100 dB with a 4 kHz sine wave if the sub had the same in-room sensitivity as your tweeter/speaker (quite feasible). Put simply, "bass needs more power because you need more displacement for bass" is sort of correct but it is an oversimplification.
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Good stuff 
Although i haven't found headroom to really be arbitrary...it's work to measure for sure, but i've had some fairly decent attempts at mapping it out. (while learning to set peak and rms limiters in conjunction with am output capability)
And sure, an amps peak voltage will be set/limited by its rails, and then power will be limited by how much current for how long, can the amp deliver its full rail voltage. (This is my simplified amp novice take anyway.)
I've watched voltage on a rolling scope trace, to see just when the rails sag, under increasing levels and signal duration. It ain't easy work, but it gets pretty clear, pretty fast, amps don't begin to hold their rail voltages for anything other than very short bursts...particularly not long enough for some bass transients.
I think the movie soundtrack explosion is an example of a particular waveform, and trying to extrapolate a speaker's power or voltage needs from that particular signal.
But what if i use a different example to extrapolate from. I mean, try a youtube Falcon Heavy launch or landing (be careful if you don't have any excursion limiting).
Or more benignly, the drops like in Lindsey Sterling's Crystallize.
We all know tracks that ring our system's bells or show us where it poos out, huh?
These are cases where the simplification that bass capability ultimately equals displacement capability has more weight than any other criteria, i think.
In any system, it's almost always the extremes, the very lows (and often the very highs), that ends up defining what the system can faithfully reproduce.
Oh, i've been finding small signal T/S to fail to hold up at higher power levels for subs (and sometimes mids).
I don't know if it's all due to thermal compression or what...any ideas?
Although i haven't found headroom to really be arbitrary...it's work to measure for sure, but i've had some fairly decent attempts at mapping it out. (while learning to set peak and rms limiters in conjunction with am output capability)
And sure, an amps peak voltage will be set/limited by its rails, and then power will be limited by how much current for how long, can the amp deliver its full rail voltage. (This is my simplified amp novice take anyway.)
I've watched voltage on a rolling scope trace, to see just when the rails sag, under increasing levels and signal duration. It ain't easy work, but it gets pretty clear, pretty fast, amps don't begin to hold their rail voltages for anything other than very short bursts...particularly not long enough for some bass transients.
I think the movie soundtrack explosion is an example of a particular waveform, and trying to extrapolate a speaker's power or voltage needs from that particular signal.
But what if i use a different example to extrapolate from. I mean, try a youtube Falcon Heavy launch or landing (be careful if you don't have any excursion limiting).
Or more benignly, the drops like in Lindsey Sterling's Crystallize.
We all know tracks that ring our system's bells or show us where it poos out, huh?
These are cases where the simplification that bass capability ultimately equals displacement capability has more weight than any other criteria, i think.
In any system, it's almost always the extremes, the very lows (and often the very highs), that ends up defining what the system can faithfully reproduce.
Oh, i've been finding small signal T/S to fail to hold up at higher power levels for subs (and sometimes mids).
I don't know if it's all due to thermal compression or what...any ideas?
As Casull says displacement isn't the issue for amp. What is important is what voltage does it take to reach that SPL? In a linear driver, that's going to be the same voltage for anything within its bandwidth. Only when you have to apply EQ will that change. (and some active load related spikes.)
Power will be related to how much current is flowing. "Strong like Bull" power supplies can supply the current needed for long term loud.
Power will be related to how much current is flowing. "Strong like Bull" power supplies can supply the current needed for long term loud.
Hi Pano, i get all that in spades. But imo, you cannot simply say it's all about voltage.
The linear voltage gain needed across the bandwidth will sag at particular low regions of the impedance curve, when the amp cannot put out sufficient current long enough to sustain the required voltage duration.....even when well below the peak voltage capability of the amp.
I mean there's always the amplifier design consideration, what impedance to optimize to,.... which just distills down to a voltage vs current optimization imo.
As far as displacement, well...it's what moves air, what makes sound, right?
Do you disagree that 4x is needed per octave decrease for equal SPL? (setting efficiency aside)
Besides this is almost silly...you need more bass, you get more sub...
sounds like displacement to me
The linear voltage gain needed across the bandwidth will sag at particular low regions of the impedance curve, when the amp cannot put out sufficient current long enough to sustain the required voltage duration.....even when well below the peak voltage capability of the amp.
I mean there's always the amplifier design consideration, what impedance to optimize to,.... which just distills down to a voltage vs current optimization imo.
As far as displacement, well...it's what moves air, what makes sound, right?
Do you disagree that 4x is needed per octave decrease for equal SPL? (setting efficiency aside)
Besides this is almost silly...you need more bass, you get more sub...
sounds like displacement to me
How many different ways do you want to be told that it doesn't really matter? There are relationships, yes, but you cannot directly equate displacement to power.
Do not disagree, just know that it is not the issue
The cone will move, but the amplifier does not supply any more power, current or voltage. That's what we are talking about. You seem to have an idea that bass needs more power because the cone moves more. That is not the case. It's an easy confusion, so take time to think it through. If a driver has a flat FR, that means that it will produce the same SPL for at the same voltage, independent of frequency. If it did not, it would not have a flat frequency response.Pano said:
Ok, a few lines of thought i'd like to approach.
First, i don't have the idea bass necessarily needs more power because the cones moves more.
For any driver, yes it needs power to move more...i trust no one will dispute that.
But, we know you can increase power to a given driver, increase the size of the driver, or add more drivers, or add more drivers with more power.....to get more SPL....all equate to more displacement.
Truly i think, all roads to higher SPL lead to more displacement, even after efficiency gaining techniques such as horn loading etc,
Second line of thought.
Let's consider a single full range driver ..a super-duper that covers the whole span.
How much SPL do you think it can/will generate?
I don't think much at all, or that is all we would own.
It's not about IMD or any other spec other that might preclude a full range driver, other than the simple need to move air, imo. (ignoring directional issues, always something to ignore huh
Continuing with the need to divide the spectrum to achieve decent SPL...
what size are tweeters, what's their excursion, what's their power requirements?
Same for mids? their typical size? their excursion? their power?
And woofers...of course the set of same questions..all getting bigger answers.
How can that not be displacement...moving air....????
Active amps same thing...how are they sized power wise, W vs M, vs T?
Passive xovers too...what's the power handling requirements between WMT?
Sure voltage gain on a linear system is constant across the spectrum, but imho that has nothing to do with the power needs across the spectrum..
It ain't just voltage
Sigh. You are simply working yourself into a knot. Linear is linear
If an 8 ohm 92dB/watt tweeter has to hit 100dB @ 3kHz it will need exactly the same voltage, power and current as an 8 ohm 92dB/watt woofer does to hit 100dB @ 300 Hz.
(Yes we know driver impedance isn't flat)
The voltage and current needed by the driver to hit 100dB SPL have nothing to do with the peaks or average levels of music inside a given bandwidth. The amount of power at any given point on the spectrum has nothing to do with displacement - it has only to do with the recorded signal. The amplifier just amplifies the signal it gets. It knows nothing of displacement.
If an 8 ohm 92dB/watt tweeter has to hit 100dB @ 3kHz it will need exactly the same voltage, power and current as an 8 ohm 92dB/watt woofer does to hit 100dB @ 300 Hz.
(Yes we know driver impedance isn't flat)
The voltage and current needed by the driver to hit 100dB SPL have nothing to do with the peaks or average levels of music inside a given bandwidth. The amount of power at any given point on the spectrum has nothing to do with displacement - it has only to do with the recorded signal. The amplifier just amplifies the signal it gets. It knows nothing of displacement.
I’m getting the feeling that you’re asking questions that you think you already know the answers to.Ok, a few lines of thought i'd like to approach.
First, i don't have the idea bass necessarily needs more power because the cones moves more.
For any driver, yes it needs power to move more...i trust no one will dispute that.
But, we know you can increase power to a given driver, increase the size of the driver, or add more drivers, or add more drivers with more power.....to get more SPL....all equate to more displacement.
Truly i think, all roads to higher SPL lead to more displacement, even after efficiency gaining techniques such as horn loading etc,
Second line of thought.
Let's consider a single full range driver ..a super-duper that covers the whole span.
How much SPL do you think it can/will generate?
I don't think much at all, or that is all we would own.
It's not about IMD or any other spec other that might preclude a full range driver, other than the simple need to move air, imo. (ignoring directional issues, always something to ignore huh
Continuing with the need to divide the spectrum to achieve decent SPL...
what size are tweeters, what's their excursion, what's their power requirements?
Same for mids? their typical size? their excursion? their power?
And woofers...of course the set of same questions..all getting bigger answers.
How can that not be displacement...moving air....????
Active amps same thing...how are they sized power wise, W vs M, vs T?
Passive xovers too...what's the power handling requirements between WMT?
Sure voltage gain on a linear system is constant across the spectrum, but imho that has nothing to do with the power needs across the spectrum..
It ain't just voltage
THAT is exactly the point of this whole conversation---it's all about having enough power to AVOID CLIPPING in each driver's bandwidth. Hence the distinct advantage of bi (or tri, even quad) amping. Sure, you need enough muscle to achieve the desired SPL but it's the HEADROOM that will make or break your listening enjoyment. Typical music will have an rms-to-peak difference of ~14 db and that's what you need to take care of.
I have a question, especially for folks who already know (as opposed to looking it up).
What is the formula for the acoustic watt output of a driver of a given size at a given frequency at a given excursion?
E.g., move a nominally 15" driver 1/32" at 50 Hz, what is the acoustic watt output?
Thanks!
What is the formula for the acoustic watt output of a driver of a given size at a given frequency at a given excursion?
E.g., move a nominally 15" driver 1/32" at 50 Hz, what is the acoustic watt output?
Thanks!
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First: SPL vs. Frequency vs driver movement or Piston Excursion calculator
Then, second: Sound power level SWL and sound pressure level SPL distance compare acoustic power sound source noise Conversion of sound pressure to sound intensity conversion sound level energy level strength directivity factor coefficient sound intensity SIL - se
Note: Directivity factor Q is 1 for full-space radiation (i.e. sub suspended in air outdoors), 2 for half-space (i.e. flush-wall-mounted, or mid/tweet above baffle step transition), 4 for quarter-space (i.e. corner sub, assuming thick rigid walls)
Then, second: Sound power level SWL and sound pressure level SPL distance compare acoustic power sound source noise Conversion of sound pressure to sound intensity conversion sound level energy level strength directivity factor coefficient sound intensity SIL - se
Note: Directivity factor Q is 1 for full-space radiation (i.e. sub suspended in air outdoors), 2 for half-space (i.e. flush-wall-mounted, or mid/tweet above baffle step transition), 4 for quarter-space (i.e. corner sub, assuming thick rigid walls)
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Sure voltage gain on a linear system is constant across the spectrum, but imho that has nothing to do with the power needs across the spectrum..
It ain't just voltage
Sorry Mark, but it feels like you're not getting this. Your first sentence contradicts itself, since P=V*V/R.
If we take a magical 8" speaker that's 90dB@2.83V, 20Hz-20kHz and apply 2.83V RMS of 20Hz, then the cone will move 27.2mm p/p and produce 20Hz at 90dB.
If we take that same setup and change to 20kHz, the cone will move 0.0000272mm p/p, and produce 90dB.
Since it's a magic driver, the impedance curve is perfectly flat at 8ohm exactly.
In both cases, precisely 1W of signal is being applied. The conversion efficiency is identical, and 90dB is being produced in each case.
Next, we're going to make it a little bit more real-world. 15" 2-way PA speaker with a large-format HF unit. The assumption I'm going to make is this: the HF horn is a perfect 90x60 horn. At +/-45.1 degreesH, the SPL is zero. At +/- 30.1 degrees V, SPL is zero.
The compression driver + HF horn combination can therefore be thought of as covering 1/6th of a hemisphere, or, alternatively, there's six of them radiating into a hemisphere. It's just we're only listening to one of them, in a fraction of the hemisphere.
I hope that makes sense.
We'll pull some numbers out of the air and say the 15" is 97dB@1w from 100Hz-1kHz, and drops to 91dB@1w @50Hz. Above 1kHz, the HF driver (with a 3" diaphragm) takes over, and it's 107dB@1w across the range.
If we EQ the bass driver flat, then a +6dB boost is required at 50Hz to manage that. The HF driver also needs to be operated at -10dB to match the sensitivities.
So, here's what we need to do if we want 97dB out of this speaker at any frequency:
- +6dB at 50Hz, so 4W applied
- 1W applied to the 15" for the rest of its range
- 0.1W applied to the HF driver for the rest of the range
We'll say the 15" can stand 1KW continuously, while the HF driver can only stand 80W continuously. That's real power.
As we push the fader and get close to the limits, the woofer gives up first, due to its low sensitivity at 50Hz.
1KW @50Hz = 121dB. To match that SPL at a higher frequency, the 15" would only need 250W. The HF driver is sitting pretty at 25W.
Let's say we apply a brick-wall highpass at 100Hz, so the 15" is now just 97dB@1w across its operating range.
We'll push the faders again. This time, if we max out the 15" at 1KW, the 3" HF driver will be exceeding its long-term thermal limits by 20W.
Remember, that's trying to produce 127dB at any frequency.
We can calculate the excursion requirements of the 3" diaphragm, and see how likely it is to mechanically survive.
This calculator: Piston Excursion calculator
Assumes the driver is operating omnidirectionally in half space. For a HF driver on a horn, this is not true. Scroll back up, and we noted that there are effectively 6x HF drivers covering the hemisphere.
So, 6x drivers, 3" diaphragm, 127dB, 1kHz.
We can see that 0.46mm of Xmax is required, or there'll be 0.92mm p/p travel.
That's probably as much as I'd ever ask of a compression driver. So, short-term it'll survive and probably won't hammer against the phase plug. Long-term, it'll overheat.
Using a narrower horn effectively means there are more drivers covering the hemisphere, so excursion decreases for a given SPL. What we tend to see is HF sensitivity rising as narrower horns are used. So, we're using the same excursion and getting more SPL. Same thing.
At the moment, then, if we wanted to produce any frequency over 100Hz at 127dB, the 15" will survive indefinitely at 1KW, while the 80W HF driver operated at 100W won't last long.
Side note: the 15" cone producing 127dB@100Hz would require an Xmax of 11mm to do so.
What factors in now is the program material. I expect someone has posted a load of graphs of this, but if there's 3dB more average power below 1kHz, then the tables have turned against the 15".
The HF unit is now being asked to run at an average power of 50W, and would survive that indefinitely. It'll still receive 100W peaks, but it has enough thermal mass and excursion to suck it up.
Another factor would be the house curve. If we were to call +6dB at/below 100Hz the "new flat", and run the 15" down to 50Hz, it'll be getting 10x power at 50Hz, 4x power at 100Hz, and 1x power for the rest of the range. The HF driver would have a very easy life indeed, reaching 10W while the 15" is receiving 1KW at 50Hz.
So, the following are important when it comes to determining the amount of power needed for each passband:
- Sensitivity of each driver
- House curve
- Program material
I can corroborate your observations that low frequency speakers tend to require more power. My conclusion is that the subwoofers have lower sensitivity, and are asked to play louder (LF haystack) with program material that features lots of LF to start with. Given all of those, it's hardly surprising that the sub amps might be screaming for mercy while the HF amps wonder why the mains supply is bouncing all over the place.
Apologies for the long post. I hope it was useful.
Chris
Hi JustDave,
From Electroacoustical Acoustic Reference Data, edited by Eargle
acoustical output
W=[Xpeak (f^2 * a^2)]^2/ 2.32 * 10^17
Spl output
Lp= 20 log [(Xpeak (f^2 * a^2)) / 1.18 * 10^3]
valid when wavelength is large with respect to piston diameter, and small with respect to baffle size
I had to look it up of course, and really glad you asked....because i was unaware how greatly frequency effects output, holding excursion and piston area constant.
I knew frequency had to come into play somehow, because otherwise we would see an increase in power needed to produce lower frequencies than higher, even with the same driver, .........which of course we don't.
I just had no idea output increases as a function of freq increase squared...
Sigh. You are simply working yourself into a knot. Linear is linear
If an 8 ohm 92dB/watt tweeter has to hit 100dB @ 3kHz it will need exactly the same voltage, power and current as an 8 ohm 92dB/watt woofer does to hit 100dB @ 300 Hz.
(Yes we know driver impedance isn't flat)
The voltage and current needed by the driver to hit 100dB SPL have nothing to do with the peaks or average levels of music inside a given bandwidth. The amount of power at any given point on the spectrum has nothing to do with displacement - it has only to do with the recorded signal. The amplifier just amplifies the signal it gets. It knows nothing of displacement.
Hi Pano, yes it does get easy to get tied in knots on this stuff..
Your example above, which is obviously true, put me to bed thinking i needed to look up how frequency comes in to play....because clearly SPL can't just be about how much air is moved.
And as you might have read in what i posted to JustDave, i found out that output increases as a squared function of frequency, displacement held constant.
Anyway, it seems to me adding freq into the discussion clarifies even further why tweeters are normally smaller than mids, which are normally smaller than woofers, ...and how increased excursion and Sd are needed to counter a decreasing frequency effect on output.
That's part of what i needed to clarify further in my mind, from this discussion.
Another part, is why we are seeing things so differently in terms of amplifier power needs...
I think the reason is probably our starting perspectives....
it appears your view is that it is most likely our systems do have linear output at whatever level being listened to, and there isn't any SPL constraint across the bandwidth. Pls correct me if i'm wrong.
My view is that it is most likely our systems do not have linear output at whatever level being listened to...because most systems do have SPL constraints across the bandwidth, or simply not enough amp to maintain headroom thru the spectrum.
I feel this is especially true for most traditional home audio speakers using passive crossovers, which are probably most speakers. Sensitivities are just too low, amps too small, and bass drivers too little, for folks not to run into occasional spl limitations and non-linearities..
But maybe nobody cranks it up anymore and i"m just full of bull...i dunno...
Anyway, all i think i know from a pragmatic point of view, is there aren't many ideal linear systems without likely SPL constraints somewhere in the spectrum...usually down low.
And we often see multi-amped speakers use amps of decreasing wattage as frequency icreases.
An interesting example however, of a full range 4-way speaker that uses four internal amps with the exact same wattage and voltage gain, is the Meyer MTS4a.
On it's back side, it has four limit indicator lights: high, mid, low, and sub for a 4" CD, 12", 15" and 18" drivers.
I've never seen the high or mid lights, low light blinks a fair amount, sub alot. It's reputed to have excellent high spl linearity...fwiw
Anyway again, thx for continued discussion
Hi Chris, thanks for joining in and trying to straighten me out.
There's many things i don't get
..... but i'm one of those hard-headed-gotta-simplify and get down to grass roots, nutcases ...almost always oversimplifying for the purpose of gaining true understanding..I am a bit puzzled by the points you were making though...
The first case seemed to be about showing a hypothetical linear driver where power is indeed constant across the spectrum,
and the second case a real word speaker where it isn't.
My whole point all along, is that real speakers most often have different power needs across the spectrum. The whole thing about displacement was just to help illustrate that.....
Speakers stay mostly linear as volume increases up until they hit a bottleneck. That bottleneck could be from driver excursion limits, voice coil thermal limits, distortion tolerance, vent chuffing, amplifier thermal limits, amplifier clipping, etc. etc. With the exception of extreme cases of power compression (this comes before the voice coil's thermal limit is reached), the shape of a driver's or speaker's frequency response curve (dB per X volts at some reference distance vs frequency) does not change with respect to power input.Anyway again, thx for continued discussion
No one is disputing this. In fact, we all agree that this is true. It's just that it's not directly relating to the need for more displacement (where the frequency response curve is still flat), but more because of how the power is distributed across the spectrum in actual music. Output where the sub rolls off (at the longest wavelengths) is a special case, controlled by the T-S parameters as previously mentioned.
Sure, so many ways linearity can fall apart...
Have you spent any time at Josh Ricci's data-bass site ? dB v2
It's only for subs, but he does the best testing i've seen re how compression and distortion rise with output..
I've seen many pro sub builders comment that T/S paramenters are low signal, use them as starters for a build, but go to large level signals to make final tunings..
But again, maybe our differnet perspectives are simply about how clean do you want to stay at what SPL....???
Me? very clean, very loud, particularly with bass
I understand the rationale for looking at the spectral content of music for power distribution...
I guess a point i tried to make earlier is, i prefer a system that is linear no matter what the spectral distribution..
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