You're getting there Mark. 
Displacement doesn't matter here for the simple reason that a signal peak at 0dBFS is going to be the same voltage coming out of the amplifier whether it's at 32Hz, 320Hz or 3200Hz. All the same voltage - and if the speaker impedance is the same the same amount of current will flow thru the voice coil, meaning the amount of power.
What skews all that is the fact the woofers are often less sensitive than mids and tweeters (or horns). So for the same SPL out of the speaker different drivers will need different voltages. If the driver is flat across its bandwidth, a given voltage will produce the same SPL within it's range, no matter the frequency. But different section in an active crossover speaker may need different voltage to hit the same SPL.
Getting back to the original question, how much power does each section need? I think that's the wrong way to look at it. What's more important is ask "What peak levels are likely in each range?" The peak values in the recording do start dropping off above 2-4K. You can study the graphs for that. How much power on average is dependent on the band in which the section is operating, but that's more to do with heat sinks and power supplies. The average power of each section is always going to be much less than peak.
Plan for the peaks.
Displacement doesn't matter here for the simple reason that a signal peak at 0dBFS is going to be the same voltage coming out of the amplifier whether it's at 32Hz, 320Hz or 3200Hz. All the same voltage - and if the speaker impedance is the same the same amount of current will flow thru the voice coil, meaning the amount of power.
What skews all that is the fact the woofers are often less sensitive than mids and tweeters (or horns). So for the same SPL out of the speaker different drivers will need different voltages. If the driver is flat across its bandwidth, a given voltage will produce the same SPL within it's range, no matter the frequency. But different section in an active crossover speaker may need different voltage to hit the same SPL.
Getting back to the original question, how much power does each section need? I think that's the wrong way to look at it. What's more important is ask "What peak levels are likely in each range?" The peak values in the recording do start dropping off above 2-4K. You can study the graphs for that. How much power on average is dependent on the band in which the section is operating, but that's more to do with heat sinks and power supplies. The average power of each section is always going to be much less than peak.
Plan for the peaks.
Hello
Easiest thing to do in my mind is look at your woofers first to make sure you can hit your Max SPL number at your listening distance. I have a 4 way active system and my E-145's 98 dB 1 watt @ 1 meter was the key setting the power needs for the system. My max SPL target was 115 dB clean so no depending on amp headroom. This guarantees you will not be clipping your amps under any normal listening conditions.
So 98 db plus 3 db is 101 for the pair and with 100 watts add another 20 db so 121 at 1 meter minus 6 db for listening distance and it's close to the target. My other drivers also get 100 watts per with 2123H @ 101 dB 1 meter and compression drivers as well over 100db on the horn.
These are all JBL Pro drivers and for Pro use they would be underpowered. Don't fall into the more power is better all the time trap. I don't need peaks in excess of 115 dB in my room. Adding more power would just drive up the cost with negligible if any improvement. Once you get significant power into a driver you start fighting power compression with just robs you of extra headroom gained using more powerful amps.
So enough power to meet your needs and you scale using the drivers sensitivity differences.
Rob
Easiest thing to do in my mind is look at your woofers first to make sure you can hit your Max SPL number at your listening distance. I have a 4 way active system and my E-145's 98 dB 1 watt @ 1 meter was the key setting the power needs for the system. My max SPL target was 115 dB clean so no depending on amp headroom. This guarantees you will not be clipping your amps under any normal listening conditions.
So 98 db plus 3 db is 101 for the pair and with 100 watts add another 20 db so 121 at 1 meter minus 6 db for listening distance and it's close to the target. My other drivers also get 100 watts per with 2123H @ 101 dB 1 meter and compression drivers as well over 100db on the horn.
These are all JBL Pro drivers and for Pro use they would be underpowered. Don't fall into the more power is better all the time trap. I don't need peaks in excess of 115 dB in my room. Adding more power would just drive up the cost with negligible if any improvement. Once you get significant power into a driver you start fighting power compression with just robs you of extra headroom gained using more powerful amps.
So enough power to meet your needs and you scale using the drivers sensitivity differences.
Rob
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Hi Chris, thanks for joining in and trying to straighten me out.
There's many things i don't get
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.....
The hypothetical linear driver was there to make the point that displacement isn't just correlated with power - there's a frequency component, too.
ie, with the hypothetical driver, 2mm p/p travel will be a lot louder at 20kHz than 20Hz, and the power input to reach that excursion will also be much larger at 20kHz than 20Hz.
The "real-world" system I outlined was to bring it back around to my point that LF devices tend to be lower sensitivity, and we typically listen to program material with more LF energy than HF.
Displacement isn't the driving factor - it's a correlated result of the other forces at play.
Chris
You're getting there Mark.
Displacement doesn't matter here for the simple reason that a signal peak at 0dBFS is going to be the same voltage coming out of the amplifier whether it's at 32Hz, 320Hz or 3200Hz. All the same voltage - and if the speaker impedance is the same the same amount of current will flow thru the voice coil, meaning the amount of power.
What skews all that is the fact the woofers are often less sensitive than mids and tweeters (or horns). So for the same SPL out of the speaker different drivers will need different voltages. If the driver is flat across its bandwidth, a given voltage will produce the same SPL within it's range, no matter the frequency. But different section in an active crossover speaker may need different voltage to hit the same SPL.
Getting back to the original question, how much power does each section need? I think that's the wrong way to look at it. What's more important is ask "What peak levels are likely in each range?" The peak values in the recording do start dropping off above 2-4K. You can study the graphs for that. How much power on average is dependent on the band in which the section is operating, but that's more to do with heat sinks and power supplies. The average power of each section is always going to be much less than peak.
Plan for the peaks.
Hi again Pano, thank you
i feel fortunately beyond 'getting there', but thx again nonetheless
I made a mistake suggesting displacement as a method of considering power required across the spectrum.
It's too gross a simplification that undercuts too many downstream variables for decent general discussion.
I still do rightly or wrongly believe however, that displacement vs frequency is at the very roots of understanding a speaker's acoustic output and efficiency,.... mainly from charts like this based on the equations already posted.
As you point out, different sections in an active xover section may need different voltage to hit the same SPL. (I'd say almost invariably will need).
And also that woofers skew things because they are often less sensitive.
Well, that different (increased) voltage the woofer needs equates to different (increased) wattage, no?
And cool, back to the original question, how much power does each section need?
I totally agree we have to plan for peaks......
and I must add, plan for average too.
Neither alone is sufficient, ime/imo.
Pano, you say "How much power on average is dependent on the band in which the section is operating, but that's more to do with heat sinks and power supplies."
Aren't heat sinks and power supplies the really big thing behind power capability, behind wattage ratings? ???
I don't see how you can brush that off so easily....
Sure, by all means plan for voltage peaks....
make sure the amp's voltage rails cover them.
But like said earlier, also plan for current, for wattage, ..plan for average power consumption.....
make sure the heat sinks and power supplies can do the job ...
Thx Chris, as you might see in previous post to Pano, i'm currently of the view the other forces at play are what correlates to 'displacement vs frequency', which i see as the driving factor.
(I've needed to add 'vs frequency', for fullness of conceptualization)
I am not brushing it off easily. Let's think it thru.
Say you have somehow determined that you need a 100 watt amp for your woofers. An amp rated at 100 watts into 8 ohms should be able to supply 28.3 volts RMS without clipping or significant distortion. Or about 40 volts peak. If the amp is tested under FTC code part 432, it can do this for no less than 5 minutes.
Today you are listening full blast and just hitting those 40V peaks. What is your RMS voltage going to be on music? On highly compressed music RMS will be about 12 below peak. (14 to 18 is typical for older mixes). 40V -12dB puts you at 10 volts RMS, or 12.5 watts into 8 ohms. Even with a compressed peak to average of 10dB, your average power level would be 20 watts.
Can your 100 watt rated amp pump out 20 watts average all day long without overheating or stressing the PSU? I don't know. It's important to know that, but you still want to plan for the peaks.
You also might want to look at typical RMS to peak values within the bandwidth you'll be amplifying. It's likely your tweeter amp won't be working hard, even if it hits a few peaks from time to time.
Pano,
I think your maths is out.
-10dB = 1/10th power, so a 100w amp at the onset of clipping a signal with 10dB of dynamic range will be delivering 10w on average.
40Vpk, -12dB = 10Vpk, or 7.07Vrms. -6dB = half voltage, so -12dB must be 1/4.
The point you're making is good, though.
I think knowing the average music spectrum and peak-to-average ratios in different frequency bands would help to figure out the (peak) amplifier requirements.
Chris
Thanks for checking on me Chris. The different numbers come from this:
I started with 40 volts peak, and and counted a typical RMS value 12dB below that, or 40/4=10 volts.
You started with 40 volts peak and lowered that by 12 dB to get 10 volts peak. Then divided by square root of 2 to get 7.07 RMS.
I counted the RMS values as 12 dB below peak, you counted peak as 12dB below peak, and figured RMS from that. Thus a 3dB difference.
I started with 40 volts peak, and and counted a typical RMS value 12dB below that, or 40/4=10 volts.
You started with 40 volts peak and lowered that by 12 dB to get 10 volts peak. Then divided by square root of 2 to get 7.07 RMS.
I counted the RMS values as 12 dB below peak, you counted peak as 12dB below peak, and figured RMS from that. Thus a 3dB difference.
Hello
Back in the early 70's there were ridiculous ways you could advertise the power ratings of amplifiers. So some manufacturers took advantage of that and greatly inflated the power ratings. So the FTC stepped in and came up with the 1/3 power 1 hour preconditioning requirement prior to full power testing. BGW was OK with it Dynaco's position was that it was a little too much. Do a search I think these was an article in Audio Magazine that covered this issue with both manufacturers comments.
Rob
Article starts at page 81
Popular Mechanics - Google Books
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It *was* 1/3 power - but not anymore. And most amps don’t even carry an FTC rating anymore because they can’t even sustain 1/8 power for more than a minute or two. 1/8 power, BTW, is very loud and very distorted. But some of us have been known to run them that hard from time to time.
Good stuff Pano,
Sure, if you fully size an amp to peaks, such that its wattage rating covers the peaks, it's only logical it can handle average power needed. But I have to wonder how many will do that .
If i may ask, how would you go about determining a woofer needs 100 watts rms to cover peaks?
Here's mine.
If simply going by specs, I first take the 1 watt sensitivity and add however many dB's louder average SPL I want to make.
So e.g. if I have a 95 dB 1 watt subwoofer, and want to get to 116dB (+21 for ease of calc), I know i need 2^7th or 128 watts. So I have my max SPL, rms requirement.
Then for peaks I'd say i want at least 15dB headroom, which would be another 12dB rms or 2^4th.
So for loudest SPL with headroom, I'd say I need a total of 2^11th or 2048 watts to cover peaks fully.
In reality, i don't go by specs for the starting 1w rms sensitivity.
I measure bandpassed, EQ processing in place, pink noise ...rms vs spl on a simultaneous time averaged basis. (of course using 2.0v for 4 ohm, 2.83v for 8 ohm etc)
Then I do the same numerical extrapolation as above to determine rms wattage needed.
I use amps as big as those numbers imply, but I'm a bit of a basshead.
Say you dropped the max SPL down by 9dB to a more modest 107dB, it would still take 256 watts rms to cover peaks.
That's a pretty big amp still for home audio imo, especially if the sub is 8 ohms. And a passive with the same sub power would have to be a fair bit higher still, I'd think.
Maybe you see something amiss with my example/numbers....
1000% agree it would be nice to see/measure the crest factor on each bandwith. The closest I've come to that is watching the remaining headroom meters on the amp channels, how they compare peak, and then how they compare rms. But they bounce around so much, i'd be lying to say a know anything for sure.
This issue has always perplexed me a little...
..does peak to average mean just that, peak voltage to average rms voltage
..or does it mean rms peak to rms average ?
I've gotten where every time i forget i just measure a good signal generator's pink noise to see, ...you'd think i could remember lol
and reconfirm that 12 dB peak to average (RMS) (crest factor 4);
means peak voltage to rms voltage.
One good way has been pointed to for years in my signature line.
Do you really need 116dB average out of a domestic sub? Meaning peaks of 130dB or more? That's kinda nuts unless you have a really big room. Then you'd want multiple drivers anyway.
I can't see RMS as static unless we're talking periodic waveforms, it's certainly not for music or even pink noise.
So over some measured time interval, it will have an average value, a minimum value , and a maximum value which i was calling peak RMS.
I'll use the term maximum RMS from now on to avoid confusion.
I measure these three RMS values fairly often, for both music and pink noise.
I've found pink as dense as it is, can measure +3dB maximum RMS to averaged RMS over given intervals.
It's one of the issues I have with substituting a sine wave as a surrogate to determine amp voltage like in your test. Misses the temporal RMS maximums, I think.
The second is using a single frequency surrogate to represent the average of all the passbands' voltages.
In my world, all 0dBFS means is that I don't have any digital clipping; it doesn't have anything to do with the maximum output of any particular passband.
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