System Efficiency when using multiple drivers

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Hi, I realise that this is probably a rather naive question but as my background is primarily electronics and not audio I will ask it anyway.

If you have 1 driver and run 1watt thru it, i realise that at 1m the SPL is equal to the efficiency of the driver (subject to the usual conditions that can change this of course)..... if you then have say 2 'identical' drivers and feed 1watt total thru them is the efficiency still the same as with 1 driver? each driver is getting 1/2watt so will be 3db down which i would have thought would give the same overall SPL @ 1m as in example 1 but something in the back of my mind is telling me different........

Could someone please set the matter straight for me.

Well, things are not so simple - as usual ;-)

At low frequencies, using two drivers results in better efficiency, because of increase in acoustical impedance. This is right as long as the distance between the radiating cones is small in comparison with the wavelenght. The theoretical increase of 3 dB is never reached, ususal values are 1.5 to 2 dB.

At high frequencies (1000 Hz and up) drivers must be considered as two sources, causing mutual interference, and the measured efficiency is depending on the location of the microphone. The efficiency is thus increased in the axis, but the total radiating power is the same as with one driver.

This directivity is a good thing in spacious places such churches, but not in a living-room...

Regards, P.Lacombe
Well I've found that the +3db acoustical gain isn't all that 'theoritical'. That's why it's a good idea to use higher efficiency tweeters in a MTM design :)

Regarding the amp power, use this example: 1 driver=8ohm load, 2 drivers=4 ohm load. If it's a good amp the power output doubles when the impedance/load halves.
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This is as good a place as any to bring up my related question. I have had my eye for some time on Universal Electronics' 24 inch driver. It's special order, not on the website. Fs=20, Vas=1 cu. meter, (37 cu. ft), Qts=.5, SPL=100 db@1Meter/Watt.

I have noticed that very large drivers have high sensitivities. However, other threads on this forum have opined that multiple smaller drivers give better bass than one big one. But smaller drivers have lower sensitivities.

The 24 inch Universal, while impressive, seems to be a large PA speaker-smaller voice coil, smaller "linear" excursion-though PA speakers routinely travel far outside the "linear" region. I was wondering what would happen to the overall sensitivity 1)below 100 Hz, and 2)below 50 Hz, if I placed 4 12" speakers of 90 dB @ 1Meter/Watt with longer voice coils in the following two arrangements:

A) Two vertical pairs placed directly next to each other. In other words, the four speakers would would be inside a square that is 24" across by 24" high, placed on a wall

B) Vertical alignment. The four speakers would be placed on a wall, one atop another to form a line 48" high by 12" across.

I remember once that I put two speakers right next to each other and at a bass frequency they seemed to go up between 2 and 3 dB in sensitivity, but it was a haphazard experiment.

I like the high efficiency of the 24", but if the 4 12 inchers raise their sensitivity 5 db or so because of their proximity to each other, that might change things.

Is there some kind of chart-or even some rough rule of thumb-that would give me some idea what will happen in those two configurations?

Thanks for any help with this question.

[Edited by kelticwizard on 11-30-2001 at 06:20 PM]
Four identical bass drivers placed in a 2X2 array will have approx +6db more acoutical output compared to just one of the drivers

Depending on the frequencies being reproduced, a line array of 4 bass drivers will have the same acoustical gain as the 2X2 array.
I'm in the process of building a system with 4 12" woofers a side, (kinda WWMTMWW config). They will all be driven independently, I will measure them and let you know. They won't be finished for at least a month, (I like to take my time and often go through many generations).

I have used EVM18s before, (both ported and sealed) they were impressive, kicked like a mule. Not a natural sounding system but for PA use they were ideal. I have found that it is harder to control large drivers, even 12" units. For HIFI use I wouldn’t use any thing larger than 12” if quality is the main goal, unless the amp has very low output impedance and doesn’t rely on lots of feedback to achieve it.
24” drivers scare me, I would use the under 50Hz, maybe.

My understanding of acoustic coupling is that THERETICALLY 2 drivers will give you +3dB, 4 drivers equate to +6dB, 8 will give +9dB and so on, (same power into each regardless of impedance). In practice I've got slightly less.
I agree that as the frequency rises, (greater than half a wavelength between drivers) things get more confusing, not for HIFI.

Don't confuse the power output increase with lower impedance connections with the acoustic gain you get with multiple drivers.

I don't believe that an amp connected to more than one driver has the same control over it as an amp connected to one driver.

Acoustic coupling better matches the drivers acoustic impedance with the air’s impedance, when they are equal you get the maximum efficiency, (not likely without massive cone areas). Horns achieve a better match but at the cost of sound quality, that’s why they’re used when SPL is the main goal.

The above rings true if my neurones serve me correctly:)

Regards WALKER
I will attempt to explain this with physics. As long as everything is playing within its linear limits in acoustics, Pressure is similar to voltage and the two are directly related in a moving coil system. i.e. a doubling of pressure = 6 dB increase in output SPL. There are a few ways to increase pressure in acoustics, 1 is to increase the number of drivers. So if you had 2 drivers getting one watt each, the SPL measured at a point equidistant from them would be 6dB higher than a single speaker with 1 watt. Next way is to increase the voltage applied to the speaker. This holds until x-max is reached. Doubling the voltage applied to the voice coil will cause the cone to move twice as far, giving double the pressure or a 6dB increase again.


16 watts into 4, 8 ohm speakers, 90db/w/m, wired for a final load of 8 ohms vs one 8 ohm driver, 90db/w/m with 16 watts applied. There are about 5.65 volts across each coil in the first setup, and 11.31V across the coil in the second setup.

so in the first setup each speaker is capable of producing 96dB on its own. Add 12 dB because there are 4 speakers. so with 16 total watts input option 1 plays at 108dB.

Option 2 has the lone speaker playing at 102dB. A difference of 6dB. as far as i know, this is true regardless of frequency as long as you are equidistant from all 4 drivers (can't really happen since you've got two ears, but you'd have to be playing a really high frequency from a large driver to notice i think.)

This brings me to a question. Why wouldn't you want "beaming" if you had a room devoted to your stereo and one chair. Couldn't you improve imaging as long as the beam width of all drivers was greater than the diameter of your head? I think you'd be able to remove room interactions much more effectively this way since: #1 the power radiated everywhere except towards the hotseat will be drastically reduced. #2, the power that is radiated will be easier to pinpoint and apply deadening materials to your walls and whatnot. I think this could provide far less interference from wall reflections which are oft neglected and can ruin an "image". #3, You could play your system quite loudly without annoying neighbors or your spouse. Clearly there are the problems of materials. Getting a 10 inch piece of thin aluminum(or even titanium) to move back and forth 20,000 times in a second without bending is quite a chore. How would this affect efficiency? I assume it would be quite a bit better since the same power radiated is the same, but is more concentrated. This could ease the stress on whatever materials used. I have to believe somebody has tried this somewhere, has anybody here heard of something like this? I am thinking it would be like having a big pair of headphones you didn't have to wear.

am I missing something important here ? Does distortion increase? If it does, what specifically causes it? Maybe the Frensel Diffraction effects would pose a large problem. My acoustics professor worked on or patented a method to greatly reduce these effects. He used it to make a more omnidirectional full range speaker though(70-16khz from a 4" speaker). They were impressive and i wish i would have spoken to him more about them. I think fewer than half a dozen pairs exist though :/

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I would like to thank all the people who responded.

So far, there seems to be general agreement that four woofers in a 2 X 2 arrangement, will go up 6 dB or close to it over that of a single woofer driven by the same power. Even P. Lacombe's "dissenting" opinion appears to allow for that, as the original post in this thread did not specify that the speakers would be abutting each other.

Just a couple of more questions.

A) Will the increase in efficiency apply to ported systems too? If these four drivers are mounted 2 X 2 in a closet door, will the output from the port be approximately 6 db higher as well? I want to make sure that the coupling applies to the back wave as well as the front.

B) Thomas W said that the vertical alignment would give 6 db improvement depending on frequency. Is there some relationship between length of the vertical alignment and the frequency?

C) Walker mentioned half a wavelength. Am I correct in assuming that means that a vertical alignment will go up 6 dB for those frequencies that the line is less than half a wavelength, (for those with smaller wavelengths the effect rolls off gradually)? To complicate matters further, 4 12 inchers arranged vertically can be viewed as two pairs. The middle of each pair is located between the two speakers. Counting from the top, on a four speaker vertical line, the two centers will be between speaker 1 and 2, and between speakers 3 and 4. The centers will be located 24 inches, not 48 inches apart. What is the wavelength of this line-24 inches or 48 inches?

I don't mean to pepper the forum with a million questions. I just want to make sure what is going to happen if I convert a large closet to a subwoofer-not that I have such a project pending. Thank you for any information that can clear this up.
Extensive measurements done in large fields have gived results such +1.8 dB for two drivers, and 3.2 dB for four drivers, with constant power of 1 Watt *for the entire array* of 1, 2 or 4 drivers.

Drivers were mounted on a piece of 20 mm thick plywood, fastened in the embrasure of an open window. Measuring microphone (Bruel & Kjaer 4133) was disposed outdoor, at 1m in the axis. Measuring frequency : 50 Hz. Precision of the B & K microphone : +/- 0.1 dB. Drivers : Peerless L 825 WG 8 ohms, resonnant frequency 20 Hz or so.

Similar results have been found 50 years ago by G.A. Briggs, R.E. Cooke and many others. This loss over theoretical values is caused by incomplete acoustical coupling of the drivers, I presume.

Regards, P.Lacombe.
I tend to believe a measured effect over a calculated or perceived effect but what we are trying to do in the end is enjoy a perception, not get off on measurements. In the end the ears (and mind) must win.

P.Lacombe’s post is very interesting (thanks) in that the acoustic coupling was measured with reputable equipment. If it were in error it would not be the first time that extremely accurate equipment was used inappropriately. I tend to believe that it’s accurate but it is much lower than I have experienced. I’ve used quality microphones (not calibrated) and VU meters with signal generators when setting up PAs.
Note; you will NOT get +6dB with 4 drivers but something less.
He also lists more than one source, (the evidence mounts) it’s pretty compelling. I will measure the gains on my new system as soon as I can.

Kelticwizard, the effect works for ported systems, (the bass bins that I have used were often ported) as long as you increase the box and port size appropriately. The rear wave is in a small closed system (therefore impedance matching would be better) so I don’t believe the gains will be as great out the port. Hopefully some one can confirm this for us.

With regard to measuring the gain at different frequencies, at low frequencies the drivers can all coexist within the same part of the waveform so only one wavefront is produced. At higher frequencies this can not be achieved and more than one wavefront is produced. These mix and produce nodes and anti-nodes, nodes are where two high pressures mix to produce twice the pressure, anti-nodes are where a high and low meet and null out. The points in space where these nodes and anti-nodes exist are dependent on a number of parameters one of them frequency.
Two tweeters are fixed to an infinite baffle, driven with a signal generator, say 1kHz signals, (in phase) and measured at a distance of 1m on the centre line. The frequency is now varied at a constant voltage. As nodes and antinodes pass the microphone the SPL recorded will vary from +3dB (compared to a single driver) to zilch, (in practice you won’t get the extremes due to reflections and diffractions). See I told you it gets messy.

Why would anyone in their right mind manufacture a speaker with more than one tweeter? Because these nodes and antinodes always exist caused by, you guessed it, reflections and diffractions. Still I prefer one driver when high SPLs aren’t needed. I’m building a speaker with two tweeters, for most listening one tweeter will be shorted out, (only used at high volumes).

I know that this isn’t the whole story, hopefully it covers the salient points.

Regards WALKER

It's possible that poor power increase was caused by the drivers used for experiments. Peerless L825WG are cheap woofers with relatively small magnet, magnetic field is 9000 Gauss or so. This experiments have be done 20 years ago, perhaps it's time to start again...

Regards, P.Lacombe.
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