What is the basic equation to calculate a -rough- number for maximum SPL output based on a driver's sensitivity and maximum rated power specs?
driver specs: _____WRMS max; _____dB sensitivity @1w/M; QTY____ speakers; = _____ dB max SPL at 1 meter
For example:
If I want to use qty=4 Acme model #1 speaker which the manufacturer says handles 100 WRMS, offers 95 db SPL @ 1W/M, what would the output SPL be at 1 meter for these if I provided 400W to the whole group of them wired together in series/parallel so that they offer the same impedance as a single one?
..Todd
driver specs: _____WRMS max; _____dB sensitivity @1w/M; QTY____ speakers; = _____ dB max SPL at 1 meter
For example:
If I want to use qty=4 Acme model #1 speaker which the manufacturer says handles 100 WRMS, offers 95 db SPL @ 1W/M, what would the output SPL be at 1 meter for these if I provided 400W to the whole group of them wired together in series/parallel so that they offer the same impedance as a single one?
..Todd
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Wow, there's too much information on that website. Let me see if I have this correct for my example above.
4 speakers with 100db sensitivity each would result in 112db sensitivity combined given 1 W of power (2x the +6db doubling of sensitivity per coherent pair).
400 watts would provide 26db power gain over the initial 1W. (10 × log 400/1 = 26.1 dB)
This results in a total of 112 + 26 = 138db SPL at 1 meter.
That looks about right intuitively. Is it correct?
[edit: I said 95db in the first message then I used 100 here. Oh well, same calc applies. just different results.]
[edit#2] Running this through the calculator listed in the first link gives the same results, so I believe I have it correct.]
..Todd
4 speakers with 100db sensitivity each would result in 112db sensitivity combined given 1 W of power (2x the +6db doubling of sensitivity per coherent pair).
400 watts would provide 26db power gain over the initial 1W. (10 × log 400/1 = 26.1 dB)
This results in a total of 112 + 26 = 138db SPL at 1 meter.
That looks about right intuitively. Is it correct?
[edit: I said 95db in the first message then I used 100 here. Oh well, same calc applies. just different results.]
[edit#2] Running this through the calculator listed in the first link gives the same results, so I believe I have it correct.]
..Todd
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Note that half of the +6dB sensitivity increase comes from the fact that most speaker designers think of amplifiers as perfect voltage sources, for two drivers in parallel the power is doubled because the load impedance is halved. You also get an additional +3dB (double) acoustical sensitivity due to acoustical coupling between the drivers.
If you are wiring the speakers in series parallel AND the effective load impedance is the same as for a single driver then you only get the acoustical sensitivity increase which is +3dB for each doubling in the number of drivers.
So in your case given both the 4 speaker set up and the single speaker set up have the same load impedance amplifier power does not change therefore you get +6dB acoustical gain in sensitivity.
You would theoretically get 132dBSpl @ 1M for a maximum input of 400W, note that there may also be room boundary reinforcement of >3dB at low frequencies depending to some extent on placement.
RANT: I've always thought factoring in the effect of twice the available power due to halving the load impedance as an increase in driver sensitivity along with the acoustical sensitivity increase due to two coherent acoustical sources coupling was kind of bogus - and note that it only applies in the world of solid state power amplifiers because simplistically tube amplifiers deliver the same output power regardless of load impedance because a different tap on the output transformer must be used to minimize distortion and maximize power output. /RANT
If you are wiring the speakers in series parallel AND the effective load impedance is the same as for a single driver then you only get the acoustical sensitivity increase which is +3dB for each doubling in the number of drivers.
So in your case given both the 4 speaker set up and the single speaker set up have the same load impedance amplifier power does not change therefore you get +6dB acoustical gain in sensitivity.
You would theoretically get 132dBSpl @ 1M for a maximum input of 400W, note that there may also be room boundary reinforcement of >3dB at low frequencies depending to some extent on placement.
RANT: I've always thought factoring in the effect of twice the available power due to halving the load impedance as an increase in driver sensitivity along with the acoustical sensitivity increase due to two coherent acoustical sources coupling was kind of bogus - and note that it only applies in the world of solid state power amplifiers because simplistically tube amplifiers deliver the same output power regardless of load impedance because a different tap on the output transformer must be used to minimize distortion and maximize power output. /RANT
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I understood the acoustic output was always +6db for coherent pairs (half of that for incoherent signals). The speaker impedance impacts how I generate/provide that 400W to the 4 speakers (from an amplifier load perspective), but I didn't think it impacted the output SPL once I delivered that power. No doubt I am confused.
Also, I used a power calculation (10log) rather than a voltage (20log) calculation since that is a more intuitive value to me. I haven't seen an amplifier that amplifies pure voltage.
..Todd
Also, I used a power calculation (10log) rather than a voltage (20log) calculation since that is a more intuitive value to me. I haven't seen an amplifier that amplifies pure voltage.
..Todd
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Your understanding is only true if the device driving the coherent pair is a true voltage source and that is because the load impedance is halved - doubling the power delivered to the coherent pair, that is where half (3dB) of the 6dB comes from, the other half comes from the acoustical coupling between a coherent pair. If the power delivered to the coherent pair is the same power that was delivered to one driver then you get the sensitivity increase derived from a coherent pair acoustically coupling. Using constant power as the basis of comparison rather than voltage shows you what the actual gain in acoustical efficiency is.
Just because an amplifier can deliver power does not preclude its being categorized as a voltage source or amplifier. The ideal voltage source would deliver constant voltage into any load impedance connected to its output. Most voltage amplifiers approach an ideal voltage source only under narrowly defined conditions - i.e. from something approaching an open circuit to some minimum load impedance at which point the amplifier cannot safely deliver the current to the load required to maintain the required output voltage.
Using the power equation was the correct decision since it is power delivered to the voice coil that makes the noise you hear.
Is often undefined as far as it was taken, and is more or less meaningless for home hifi use.
dave
In my particular case, I am referring to pro audio (for which diyAudio has no separate forum, sadly). And I'm referring to drivers being used in a situation where excursion limits are probably not a huge concern. For example, an 8" pro audio midrange driver being HP crossed at about 700 Hz in a 4-way system. Or a compression driver HP crossed at 3-4KHz.
Kevin, I understand the power/load issue, but I'm trying to square the circle you've presented that arises from all the texts I've now found saying (I think) that acoustic coupling (alone presumably) results in a +6dB gain for coherent pairs.
So for example, if I provide 1W electrical power to 1 speaker (based on its load impedance) and get 100dB, I would get +6dB gain (106 dB SPL) by using 2 speakers (same signal and side-by-side to achieve coherence) with 1W for each (2W total) of electrical power. And +12dB (112 dB SPL) with 4 speakers and 4W total signal power.
At least that's what it seems to me the texts are saying.
..Todd
Kevin, I understand the power/load issue, but I'm trying to square the circle you've presented that arises from all the texts I've now found saying (I think) that acoustic coupling (alone presumably) results in a +6dB gain for coherent pairs.
So for example, if I provide 1W electrical power to 1 speaker (based on its load impedance) and get 100dB, I would get +6dB gain (106 dB SPL) by using 2 speakers (same signal and side-by-side to achieve coherence) with 1W for each (2W total) of electrical power. And +12dB (112 dB SPL) with 4 speakers and 4W total signal power.
At least that's what it seems to me the texts are saying.
..Todd
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Why do you say that? Most of the builds and discussions are using pro audio drivers lately.
As for your question, do you have measurement equipment? Just wire two drivers up and find out the exact truth. You have to figure out the sensitivity differences at some point in your build anyways.
I think your numbers look generally okay, you just have to measure to know each specific case what the total sensitivity will be.
What was posted before was important, you are going from 8 ohms to 4 ohms when wiring your drivers, if wire them different then you are going from doubling the ohms and not gaining +3dB. Two drivers alone double the surface area and give you a +3dB gain, they other gain is from the impedance change
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Which is exactly what Kevin is saying. You get 3dB from doubling the number of drivers, and 3dB from doubling the amplifier power (from 1 to 2 watts).
I expect that the real limit will more likely be how much real power you can deliver to the loudspeaker (i suspect that many of the very inexpensive, very high power pro amplifiers do not reach their rated power before clipping into a real load).
dave
Some do very well though. Even the Berhringer EP2500 bridged puts out almost 2000Watts which is close enough.
Here is a list of pro amps measured over on AVS
Measuring Amplifiers - AVS Forum
Btw, the new Peavy IRL-1600 amp has been measured, its 7 lbs!!!
Measuring Amplifiers - Page 56 - AVS Forum
Did the OP ever post what his max SPL needs are?
Nothing to do with drivers. The difference has to do with keeping the discussion relevant to the purpose and scope of the topic, reducing the noise/signal (oil/water) ratio, and most important to me; developing a community of like-minded people. The design requirements are so completely different. I enjoy designing speakers for home audio and pro audio purposes, but they are such different topics. Despite the science being common to both, the 'art' couldn't be further apart. It's probably difficult to understand what I mean without being involved in both areas. Trust me on this: home audio enthusiasts and music industry people are from different dimensions. Half of me from each.
I have measuring gear but I moved recently and am renovating, so my speaker/amp build stuff is all in storage. I can only plan, model and dream until the never-ending reno is finished.
..Todd
Thanks for all the feedback, guys. I think I have a better handle on the topic now.
I'm not too concerned with how the power is generated (which amplifiers) that's a side issue. My concern was more a matter of making sure compatible drivers were being spec'd for the appropriate purpose. I want to make sure the all the drivers melt/explode at the same point in the show. It's all about entertainment.
..Todd
I'm not too concerned with how the power is generated (which amplifiers) that's a side issue. My concern was more a matter of making sure compatible drivers were being spec'd for the appropriate purpose. I want to make sure the all the drivers melt/explode at the same point in the show. It's all about entertainment.
..Todd
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