I wouldn't bring Hofman's Iron Law (the equation you are referring to) into the discussion. It doesn't say that doubling Vas doubles efficiency. (If it did it wouldn't give the physical cause). Hoffman's law is about the tradeoffs between efficiency, box volume and lower cuttoff. If you change one or the other then you would also have to change many of the woofer parameters to get back to a redesigned system of the same desired Q. If you double box size, and double the number of woofers to go with it, then you might have higher efficiency, but only if you redesigned woofers to retain the same woofer cut off and corner Q.
You can double the box size and not add an extra woofer. Conversely you could double the number of woofers and not double the box size.
It is a red herring.
Efficiency doubles with two woofers in close vicinty due to the change in acoustic loading as commonly refered to as mutual coupling. It has nothing to do with cabinets. The woofers can both be squeezed into the same cabinet and it still applies.
Regards,
David S.
You can double the box size and not add an extra woofer. Conversely you could double the number of woofers and not double the box size.
It is a red herring.
Efficiency doubles with two woofers in close vicinty due to the change in acoustic loading as commonly refered to as mutual coupling. It has nothing to do with cabinets. The woofers can both be squeezed into the same cabinet and it still applies.
Regards,
David S.
Indeed, the doubling of efficiency with two woofers still applies to an infinite baffle (or large open baffle) where there isn't even a box volume, (well technically infinite volume) to be applied to Hofmans Iron law.
Err, are you sure about that ? Any time I've simulated two woofers sharing the same box, if the box volume is doubled from the single woofer case an identical alignment is achieved with the same cutoff frequency and corner Q, using the same driver parameters, but resulting in higher efficiency...
No need to redesign the drivers to get the same alignment when using two drivers - just double the box volume. Still kind of irrelevant to where the efficiency gain comes from though...as you say its the mutual coupling between the drivers that is giving the efficiency increase - the double size box just allows you to maintain the same alignment with the much larger combined Vas.
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Yes, you are correct, two woofers and two boxes would bring the automatic efficiency doubling and an unchanged allignment. I went a little too far in making a point about Hofman's Law, that changing box volume doesn't inherently change efficiency (much as changing from acoustic suspension to vented, on its own, doesn't change efficiency). Doubling the box volume allows you to double efficiency and retain the same bass extension, but only if you thoroughly redesign the woofer to do so. It does turn out that one "redesigned" woofer that works would be 2 woofers, if you know what I mean.
David S.
David S.
Heh, as a longtime speaker engineer let me say this is one of the MOST confusing topics.
1st off, very very few amps actually double their power at clipping into half the impedance. Even if they are rated to do so, every amp me or my coworkers measured was actually underrated at the higher impedance just to give the appearance of doubling the power. Anyway, no speaker efficiency is added by doing anything from the amp side.
Then, two woofers in parallel should give an extra +6 dB in the "midrange" if I remember the math correctly: 20log(2) where the 2 represents the pressure doubled due to the directivity increasing. That is a SENSITIVITY gain, but not really an EFFICIENCY gain. At the lowest frequencies then you get a change in radiation resistance due to mutual loading or whatever you like to call it. That actually increases the efficiency...but usually at frequencies where the woofer is rolling off! You get the same effect, which Allison Acoustics and a lot of concert arrays exploit, by mounting near a wall.
And then there was the AES paper that said all the above was wrong, that it's actually the superposition principle that yields the +6 dB! Could be; I couldn't quite grasp what they were writing about.
By the way, Vas has nothing do with efficiency. At least not as a cause. Suspension stiffness does not affect the midband efficiency; that's up to the coil impedance + magnet + moving mass. Vas only appears in efficiency equations as a kind of side effect.
Those equations relating box size vs. efficiency vs. rolloff are NOT about transducers. They are about boxes, presuming you could magically conjure a series of perfect transducers for each box volume as just noted by speaker dave.
(Now, the suspension does of course affect the bass rolloff and thus the efficiency at the very low frequencies, but that's not what is usually referred to by "efficiency")
1st off, very very few amps actually double their power at clipping into half the impedance. Even if they are rated to do so, every amp me or my coworkers measured was actually underrated at the higher impedance just to give the appearance of doubling the power. Anyway, no speaker efficiency is added by doing anything from the amp side.
Then, two woofers in parallel should give an extra +6 dB in the "midrange" if I remember the math correctly: 20log(2) where the 2 represents the pressure doubled due to the directivity increasing. That is a SENSITIVITY gain, but not really an EFFICIENCY gain. At the lowest frequencies then you get a change in radiation resistance due to mutual loading or whatever you like to call it. That actually increases the efficiency...but usually at frequencies where the woofer is rolling off! You get the same effect, which Allison Acoustics and a lot of concert arrays exploit, by mounting near a wall.
And then there was the AES paper that said all the above was wrong, that it's actually the superposition principle that yields the +6 dB! Could be; I couldn't quite grasp what they were writing about.
By the way, Vas has nothing do with efficiency. At least not as a cause. Suspension stiffness does not affect the midband efficiency; that's up to the coil impedance + magnet + moving mass. Vas only appears in efficiency equations as a kind of side effect.
Those equations relating box size vs. efficiency vs. rolloff are NOT about transducers. They are about boxes, presuming you could magically conjure a series of perfect transducers for each box volume as just noted by speaker dave.
(Now, the suspension does of course affect the bass rolloff and thus the efficiency at the very low frequencies, but that's not what is usually referred to by "efficiency")
This is conventional wisdom for 2 8ohm woofers wired in parallel vs a single 8 ohm woofer.
What happens if it is 2 4ohm woofers wired in series compared to a single 8 ohm woofer.
if "Eff=(27E-6 x (Fs^2))/Qes" then how is Vas related to Eff? 😕
Not really. Compare 2 8" 8ohm woofers working in the same box as a single 8" 8ohm woofer. The single woofer system will have a different Qtc. So if one really wants to have a full 6db increase one needs to also double box volume so Qtc remains the same.
Exactly. Which is why I was considering using 3 4ohm woofers to make 12 ohms. My assumption was that 3 4 ohm woofers rated as 90db/2.83V or 87db/1W would end up producing 87db/1W (3.46V) but only (87-1.74)
85.25db/2.83V. Hence if you are mating these 3 woofers to a 8ohm midrange, the midrange need only have a sensitivity of 85db (after baffle step compensation).
The maths is below:
Say each woofer is 90db/2.83V @ 4ohms so 90db/2W = 87db/1W.
When the amplifier is pushing 2.83V into 3 woofers (hence 12ohms) each woofer will see only 0.94V (which is 0.89/4 = 0.22W). At 0.22W each woofer will produce only 87-6.5db or 80.5db. I can follow the logic this far....now is the confusing part...
Since 3 woofers are in close proximity what will be the gain from mutual coupling? WIll it be +3db or 10log3 (+4.77db). Hence will be senstivity of the 3 woofe system be 83.5db or 85.27db? Do we loose 1.73db or 3.5db in sensitivity compared to a single woofer system?
The three series woofers will have exactly the same sensitivity as a single woofer. The efficiency gained by mutual coupling is exactly negated by the higher impedance.
I recently did a test which proved just that.
http://www.diyaudio.com/forums/subwoofers/204472-multiple-cabinet-combined-response.html
Wired two monitors (each containing 2x8" eight ohm speakers in series) in series (32 ohms nominal), then four monitors in series, (64 ohms nominal impedance) and the resulting SPL was identical.
Had originally planned to do eight monitors in series (128 ohms) too, but ran out of clip leads.
Art
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Yes, the voltage division and the pressure summation exactly compensate. This holds true as long as the units can all add coherently and until the increasing efficiency makes the acoustic resistance air load big enough to start shifting the impedance curve. Then it breaks down (wouldn't do to allow over 100% efficiency!).
I did a lot of line array modeling back at McIntosh. Assuming that you were adding independent pressure vectors gave a reasonable model that seemed very accurate.
David S.
I did a lot of line array modeling back at McIntosh. Assuming that you were adding independent pressure vectors gave a reasonable model that seemed very accurate.
David S.
Actual efficiency will of course never reach 100%, but large frontal area arrays can achieve sensitivity in excess of 6 dB per doubling of speakers and power due to the higher directivity.
The large array front effectively becomes a plane, turning 1/2 space into 1/4 space.
Simply putting half a sheet of plywood (4x4 foot) either side of a speaker will give nearly 3 dB of LF gain outdoors.
Even though amps are getting pretty cheap, doubling power with a sheet of plywood is still a better bargain 😀.
Art
Sorry for the confusion by mistyping the formula, small print and old eyes, should have been
Eff=(27E-6 x (Fs^3*Vas))/Qes ( in%)
Argument still holds. We are not talking enclosure size here, but the Vas of the driver. By taking two identical drivers, Vas is doubled, but Fs and Qes remain unchanged. Result is doubling of efficiency.
On top of the 6dB sound power increase this delivers, there might be further gains from a tightening of the radiation pattern, because stacked speakers have a larger frontal area, so the baffle keeps radiation in 2pi longer than in the case of single speaker. But, this is on top of the 6dB.
Yes, it is all superposition. There is no significant increase in radiation impedance. I have worked through the math of this independently.
Please explain! My memory is too hazy and as I said I didn't really follow what they were getting at...
As for mutual coupling and Vas and all that confusion, let me say again:
1) Mutual coupling only has an effect at LOW frequencies. Like subwoofer frequencies!
2) Above that, there is NO efficiency gain. There is a sensitivity gain due to increased directivity.
3) Don't wire woofers in series, it's just a bad idea. They don't all have the same resonance so it becomes a mess. If you don't believe me, look up Richard Greiner's AES paper that has all the math (which was borne out in practice by observation)
4) Don't compare an 8 ohm woofer to "2 4 ohm woofers in series." I can easily understand why someone would say that, it's OK. The point you're missing is that those woofers will NOT be equivalent in all their other parameters.
5) Vas DOES NOT AFFECT EFFICIENCY. Or, to put it another way, Vas DOES NOT AFFECT EFFICIENCY.
It DOES show up in efficiency equations because it is a factor which transforms physical parameters like moving mass into the electrical analogy domain. But Vas (=suspension) cannot change the electric-to-acoustic efficiency*-how could it possibly? Seeing efficiency proportional to Vas is a kind of mathematical accident. It is the magnet and coil and cone that affect efficiency.
(*Meaning midband efficiency and excluding array or horn or corner effects; efficiency at subwoofer frequencies is affected by cabinet and suspension and just about everything)
1) Mutual coupling only has an effect at LOW frequencies. Like subwoofer frequencies!
2) Above that, there is NO efficiency gain. There is a sensitivity gain due to increased directivity.
3) Don't wire woofers in series, it's just a bad idea. They don't all have the same resonance so it becomes a mess. If you don't believe me, look up Richard Greiner's AES paper that has all the math (which was borne out in practice by observation)
4) Don't compare an 8 ohm woofer to "2 4 ohm woofers in series." I can easily understand why someone would say that, it's OK. The point you're missing is that those woofers will NOT be equivalent in all their other parameters.
5) Vas DOES NOT AFFECT EFFICIENCY. Or, to put it another way, Vas DOES NOT AFFECT EFFICIENCY.
It DOES show up in efficiency equations because it is a factor which transforms physical parameters like moving mass into the electrical analogy domain. But Vas (=suspension) cannot change the electric-to-acoustic efficiency*-how could it possibly? Seeing efficiency proportional to Vas is a kind of mathematical accident. It is the magnet and coil and cone that affect efficiency.
(*Meaning midband efficiency and excluding array or horn or corner effects; efficiency at subwoofer frequencies is affected by cabinet and suspension and just about everything)
Is sensitivity measured as db/1w or db/2.83V? So are the 3 woofers (12 ohms) producing 90db@1W or 90db@2.83V (which at 12 ohms is 0.67W)?😕
If it is "db/1w" then 1W @ 12 ohms=3.46W. Hence a 90db/1W 8 ohm midrange (crossover over to the woofers) would be actually producing almost 92db@3.46V (1.5W @ 8 ohms).
You are still misusing a formula that has no bearing on the arguement. There is no linkage between Vas and woofer efficiency! I can increase Vas by using a softer spider but efficiency does not change. I can remove the spider entirely and efficiency does not change!
The equation is the long form of Hofman's Iron Law. He stated that the 3 factors of system cuttoff, system efficiency, and box volume are tied together, that efficiency is proportional to box volume time f3 cubed.
The underlying assumption is that you will appropriately redesign the woofer to get an apples and apples comparison of two systems. For example if you double box volume and want to take the bonus as efficiency, you need to adjust the woofer spec to do so. If you want to take the bonus as response extension (1/3 Octave) you need to again adjust the woofer spec (different adjustments this time) to do so.
Small expanded the equation to include Vas and Qes to better cover the cases where you didn't fully adjust the woofer specs.
Vas has no effect on efficiency!
David S
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Regarding the frequency range of mutual coupling, it applies for any wavelength where the multiple sources add predominantly in phase at all angles. The rule of thumb is that its good for frequencies up to a half wavelength of the spacing. So a pair of 10" woofers can easily have a real efficiency gain up to several hundred Hz.
Until we are talking about very large arrays and efficiencies approaching 50% we can assume a frequency invariant axial gain of 6dB for every doubling of source numbers. For low frequencies it will be an efficiency increase, for upper frequencies it will be a directivity index increase. The two curves will add to give a constant 6 dB.
David S
Until we are talking about very large arrays and efficiencies approaching 50% we can assume a frequency invariant axial gain of 6dB for every doubling of source numbers. For low frequencies it will be an efficiency increase, for upper frequencies it will be a directivity index increase. The two curves will add to give a constant 6 dB.
David S
How does all of this come into play when designing an enclosure for multiple drivers? For example, when using two woofers in a sealed box design, does one simply double the volume of the box as compared to a single-driver enclosure, or is it best to mount each driver in its own sealed chamber, with each chamber at the normal single-driver volume?
I imagine that it becomes more complex with a vented design. Again, if one is using two woofers, this time with a vented alignment, does one build two single-driver bass reflex boxes with identical volume and tuning, or is it possible to get good results with two identical drivers in one vented enclosure? How would the proper tuning be accomplished?
Lastly, could some one elaborate on the problems with connecting identical woofers in series? I am considering building a speaker with small drivers hooked up in a series/parallel arrangement (that is, two drivers hooked up in series, then two of those dual units hooked up in parallel, for a total of four woofers for each cabinet). I am assuming an increase in efficiency with maintenance of the original driver's impedance and inductance, but I don't know how to apply the T/S parameters of the combined drivers units to the cabinet design.
I performed a search on these concerns but could not find answers specific to my questions. If anyone can supply a link or point me to a helpful reference it would be much appreciated. My apologies if this is too much off topic.
I imagine that it becomes more complex with a vented design. Again, if one is using two woofers, this time with a vented alignment, does one build two single-driver bass reflex boxes with identical volume and tuning, or is it possible to get good results with two identical drivers in one vented enclosure? How would the proper tuning be accomplished?
Lastly, could some one elaborate on the problems with connecting identical woofers in series? I am considering building a speaker with small drivers hooked up in a series/parallel arrangement (that is, two drivers hooked up in series, then two of those dual units hooked up in parallel, for a total of four woofers for each cabinet). I am assuming an increase in efficiency with maintenance of the original driver's impedance and inductance, but I don't know how to apply the T/S parameters of the combined drivers units to the cabinet design.
I performed a search on these concerns but could not find answers specific to my questions. If anyone can supply a link or point me to a helpful reference it would be much appreciated. My apologies if this is too much off topic.
Originally Posted by weltersys
The three series woofers will have exactly the same sensitivity as a single woofer. The efficiency gained by mutual coupling is exactly negated by the higher impedance.
2.83 v is often used, as it results in one watt used in an 8 ohm load, though 2.83 v drops 1/2 watt in a 16 ohm load, two watts in an 4 ohm load, and 8 watts in an 2 ohm load.
A measure using "one watt" at one meter implies the speaker is actually one impedance throughout it's bandwidth, which it is not.
Art
The three series woofers will have exactly the same sensitivity as a single woofer. The efficiency gained by mutual coupling is exactly negated by the higher impedance.
Sensitivity is the sound pressure level a speaker, or combination of speakers, put out when a specific voltage is applied at a specific distance.
2.83 v is often used, as it results in one watt used in an 8 ohm load, though 2.83 v drops 1/2 watt in a 16 ohm load, two watts in an 4 ohm load, and 8 watts in an 2 ohm load.
A measure using "one watt" at one meter implies the speaker is actually one impedance throughout it's bandwidth, which it is not.
Art
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Eff=(27E-6 x (Fs^3*Vas))/Qes ( in%)
No, it is very relevant. Your example does not hold up. By using a softer suspension or leaving it out entirely, Vas goes up, but Fs goes down. End result is no change in efficiency. The above equition can also be rewritten by substituting Vas and Fs into their components, yielding
It is the same formula, just written down differently, and in my sense it is a less intuitive form to explain where the 6dB increase comes from. As you can see, Cms is not part of this equation, so changing the suspension stiffness does not have an impact on efficiency (but it will increase Vas and lower Fs at the same time).
Another way of putting it is that by taking double the number of identical drivers, you double Bl, Sd and Mms, which leads to a doubling of efficiency. It has nothing to do with radiation patterns of acoustic coupling, it just follows from the mathematical desription(s) of loudspeaker efficiency. Which I hold to correspond with the underlaying physical phenomena.
vac
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As Speaker Dave Puts it:
“Regarding the frequency range of mutual coupling, it applies for any wavelength where the multiple sources add predominantly in phase at all angles.”
Having done an outdoor test to confirm just that, the results are posted below.
The test used one and two full range cabinets, both placed on speaker stands , tweeters at about 2 meters high, pointed at a mic on a two meter high stand at two meters distant, the tweeters and the mic making a (roughly) equilateral triangle.
There was a 6 dB level increase using two cabinets up to 1.6 kHz, then the level increase drops to no increase at 7.26 kHz, and various amounts of gain or loss above.
The reason the summation was not 6 dB all the way out to 16 K is threefold:
1) The speaker stands were on uneven ground, resulting in slightly different angles and path length to the microphone.
2) The two speakers have minor deviations in tweeter frequency and phase response.
3) Wind plays havoc with high frequency response when the sources are separated as they were in this test.
Even with the above problems it is clear that mutual coupling, summation, or whatever one chooses to call it, works at all frequencies, and is not dependent on directivity, which can affect whether 6 dB per doubling of speakers occurs.
The results of the tests I made using Eminence Alpha 8 in series show none of the problems you mention regarding speakers in series.
http://www.diyaudio.com/forums/subwoofers/204472-multiple-cabinet-combined-response.html
The tests below were done with the same stage monitor cabinets. Each cabinet consists of two 8 inch woofers in series with a passive crossover and a tweeter between the woofers.
Cabinets were vertically stacked two and four high, 22.5” and 45” vertical height.
The same pink noise signal was applied in all tests, no level variation.
The difference in response above 300 Hz is due to directivity change from the vertical array, identical whether series or parallel.
The differences below 300 Hz are on the order of 1/4 dB, track the individual pairs of cabinet differences, and are virtually identical for both the parallel and series tests, proving that wiring in series does not cause frequency response aberrations.
The green trace is two cabinets in parallel, 8 ohms nominal.
The brown trace is four cabinets in parallel, 4 ohms nominal, trace lowered by 6 dB to show how frequency response is unchanged.
The blue trace is two cabinets in series, 32 ohms nominal, the lavender line is four cabinets in series, 64 ohms nominal.
If two (or more) speakers have grossly different response to start with, their combined response will generally be poor whether wired in series or parallel.
If speakers are reasonably matched, either wiring series or parallel (or series and parallel) can be equally useful.
Art Welter
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Post # 79 should answer your questions regarding series arrangements, they cause no problems in themselves as far as cabinet design (at least using Hornresp), but may require different passive crossover solutions dependant on impedance.
When using two woofers in a sealed box design, simply double the volume of the box as compared to a single-driver enclosure.
With a vented alignment, one can build two single-driver bass reflex boxes with identical volume and tuning, or combine them in one box using double the ports and box volume resulting in the same tuning.
In both cases there are slight advantages to having separate enclosures, which can be completely separate, or simply have a center wall.
If one driver were to fail, with separate chambers the alignment remains the same.
Separate boxes are stiffer, reducing resonances.
The differences are relatively minor, often the center wall is eliminated to save weight and material expense and reduce construction time.
Art