Double 136a's with single 2118?

[tagerbaek]

Hello Lansingheritage,

I started building speakers just 3 years ago, so I'm still a rookie struggling with the basics. Here's two interrelated questions:

Q1. I've got four 136a's and a pair of 2118J, all in good shape. I plan to do a 3- or 4-way, active x-over. In your experience, will a single 2118's cut it in terms of power handling, output, etc, the double 136a's having a efficiency of 93+3=96dB (see Q2) vs the 97dB of the 2118, or should I lose them and get 2123's?

Q2. About dual drivers, there seems to be general agreement that if one uses two drivers in parallel, eg two 136a's, each with a sensitivity of 93dBspl/2.83Vrms/1m, one will get +6dB more output, eg 99dBspl, than with a single driver (with the same rms voltage drive). Fine, the 3dB are because you deliver twice the power to the drivers, but I cannot grasp why each driver apparently becomes twice as efficient (ie, the remaining 3 dB) just because it's now working in tandem. Taking the argument ad absurdum and doubling the number of drivers - and therefore also the efficiency - over and over, one eventually arrives at a situation where the drivers would apparently be delivering more acoustic power than they are receiving in the form of electric power. That was a long question, I hope someone knows a shorter answer!

Thanks in advance, Thomas

[edgewound]

The quick answer is because you are doubling the cone area with two drivers... that gives you the second additional 3dB of output.

The first additional 3dB of output is by halving the impedance or doubling the load to 4 ohms from 8 ohms.

[macaroonie]

The efficiency of the bass drivers is irrelevant --- since you plan to go fully electronic the overall system efficiency is that of the least efficient diver.
As an example lets say your tweet was a ribbon with effficiency of 86dB therefore to even begin to sound correct everything else will have to come down to that level either by padding or by gain reduction at the amp. stage.

[toddalin]

The quick answer is because you are doubling the cone area with two drivers... that gives you the second additional 3dB of output.

The first additional 3dB of output is by halving the impedance or doubling the load to 4 ohms from 8 ohms.

If you think about it, I don't think that is quite right.

First, lets assuming that the amp can deliver the current so that the voltage doesn't sag and the power does truely double when halving the impedience.

Now assume that at 1 watt the driver would have a peak to peak excursion of 0.1" producing 90 dB.

Add the second driver and the power goes to 2 watts. But each driver is still receiving just 1 watt so still has a p-t-p excursion of 0.1". You are now moving exactly twice the air (and that's what is actually making the sound regardless of the watts involved), so the sound should twice the power, or 3 dB louder so now 93 dB.

Now lets say that the amp has a max of 100 watts RMS (then it blows up) and each speaker can hold 100 watts (then they blow up). So, the amp would run out of power before you ever got the additional 3 dB would would only be possible at maximum cone excursion for both drivers.

I don't think it works like that.

What I've been able to deduce is that when you add the second speaker and halve the impedience you pick up 3 dB by virtue of doubling the power and moving area.

The other 3 dB comes from the "acoustic coupling" of the speakers. Assuming the speakers are in phase, each speaker produces as much sound as the single speaker did. But the acoustic peaks of the sound waves are additive and this is where the other 3 dB come from.

This is the case at any and all volume levels.

I've never read this anywhere, but having a grasp of acoustics, this is really the only way I can reconcile it in my mind.

[edgewound]

Todd,

Here's the deal....theoretically, anyway. He wanted the short answer.

If you have a 130A(8 ohm) 1 watt/ 1 meter...you have 97dB sensitivity.

If you have (2) 130B(16 ohm) 1 watt/ 1 meter...now you have 100dB sensitivity...twice the radiating cone area....coupling if you will.

Now...(2) 130A @ 97dB 1 watt/ 1 meter each....now pulling 2 watts with double the cone area and double the power...

You now have 103dB sensitivity...twice the speaker, twice the power.

To get there with one 130A, you would need 4 watts or four times the power for a 6dB increase in SPL to make up for half the cone radiating area.

[toddalin]

Todd,

Here's the deal....theoretically, anyway. He wanted the short answer.

If you have a 130A(8 ohm) 1 watt/ 1 meter...you have 97dB sensitivity.

If you have (2) 130B(16 ohm) 1 watt/ 1 meter...now you have 100dB sensitivity...twice the radiating cone area....coupling if you will.

Now...(2) 130A @ 97dB 1 watt/ 1 meter each....now pulling 2 watts with double the cone area and double the power...

You now have 103dB sensitivity...twice the speaker, twice the power.

To get there with one 130A, you would need 4 watts or four times the power for a 6dB increase in SPL to make up for half the cone radiating area.

Nope, still don't see it.

When you have both at 1 watt/1 meter, you've doubled the power (each gets 1 watt) so you can't double it again or you're double counting..., or each is only receiving 1/2 watt and moving half as far.

[edgewound]

Nope, still don't see it.

When you have both at 1 watt/1 meter, you've doubled the power (each gets 1 watt) so you can't double it again or you're double counting..., or each is only receiving 1/2 watt and moving half as far.

Ok....nevermind.

[Allanvh5150]

Here is a much easier way to look at it. The sesitivity of JBL's are generally measured with one watt input. If you have a speaker with a 97db sesitivity driven by 1 watt, adding a second speaker using the same test, i.e. 1 watt input, the sensitivity will increase to 100db. If the power input doubles, the figure will increase to 103db, double the power and add another 3db. The sensitivity figure is a baseline figure, the actual SPL figure when driven by, say, a one hundred watt amplifier will be much higher. So in general, if you add another speaker and your amplifier can run to twice the power with half the load, most amps cant do this, the output will increase by 3db. Make sense?

[pos]

Regarding mutual coupling and 3/6 db gains I think I just recently understood the whole thing, and it is quite simple in fact.
I will try to expose my point of view, but I hope the language barrier will not blur the message too much.

When you double the amplitude of the signal you get a 6db boost. You can try that on your soundforge or anything like this. That is also the reason why 16bit gives you a 96db dynamic range: 16*6=96.

So if you double the voltage, you double the amplitude of the electric signal, and so you double the amplitude of the cone motion, and you get 6db.

BUT to double the voltage you need to multiply the power by four!
this is given by these equations:
P = UI
and U = ZI

so P = U^2/Z

there is a power of two on the voltage!

So here is the deal:
If you want a 6db boost you have two choices:
- multiply the power by 4 => the cone amplitude will double => +6db
- take 2 amplifiers with the same power (ie mutliply the power by 2) and feed to different speakers => each cone will move the same, but the total cone area has double => the amplitude has double => +6db (with a cotion, see below)

these two things will give you your 6 db, but one case will need twice the power of the other

now there is a draw back, which is stressed by the mutual coupling "theorem" :

If you want two signal to sum perfectly and get your 6db boost, these two signals need to be in phase. If they are not in phase you will get less than your 6db (you can also try that with soundforge, ading sinusoid with a small time shift).
That is the reason why woofers have to be close together to get the "mutual coupling" thingy : The more their distance increases and the less "in phase" the summed signal will be on average (in fact if you stand exactly between the two speakers you will always get your 6db boost, up to a frequency were the distance between your hears starts to matter).
So the more you increase the distance, the longer the wavelength for which the summing will be good.
If you exeed a certain distance you only get a quadratic summation, with an average of 45° phase shift, and you only get a 3db boost...

So, to sum that up:

- IF you double your cone area and you are able to feed each cone with the same power (ie in practice if you have an amplifier that can put twice the power with half the load, OR if you use two amplifiers)

- AND if you seat directly in the middle of the two woofers OR if these woofers are close enough together for the highest frequency (ie the smallest wavelength) they have to reproduce

- THEN you will get a 6 db boost

If the first statement is not true you will not double the amplitude of your signal, so will get less than 6db of boost.
If the second statement is not true you will have a quadratic summation, and only get a 3db boost on average (and up to 6db for the lower frequencies)


The second statement is difficult to maintain, and that is the reason why we always tend to say that doubling the number of speakers and amplifiers gives us a 3db boost, but that is only due to the quadratic nature of the summation you get most of the time...

So when you double the number of speakers and amps (cone area and power) the theoritical gain is always 6db, but the partical gain is only 3db most of the time due to phase issues. "mutual coupling" is a special case where you can enter the theorical territory and get your 6db gain for real, because phase issues can be ignored.

I hope I made my point, sorry for my bad english

[Allanvh5150]

If the speakers are doubled, you get a 3db boost. If the power is doubled, you get a 3db boost. If the amplitude is doubled, you get a 6 db boost. Go back to the original example, 1W/m gives 97db so 2W/m gives 100db. If you put 1W/m on 2 speakers, i.e. .5W on each, it drops the sensitivity of the driver to 94db. The 1W/m rule always has to stay constant for measuring purposes. In the real world if you have 500 watts in to a 2225 for example, to get a 3db increase you would need to put in another 500 watts. This normally means another speaker and amplifier. Doubling the whole system still only yeilds a 3db increase. Look at the specs for the JBL 4430 at 93db and the 4435 at 96db.

[pos]

Doubling the whole system still only yeilds a 3db increase.

In pratcice that is often true, due to quadratic summation.
But you will get 6db on axis for most of the frequency range, and 6db everywhere for the bass frequencies (the closer the drivers, the higher the limit frequency).

In phase summation => +6db
quadratic summation => +3db

this is also why some filters are disigned with a -3db gain at the cutoff frequency, whereas others give you -6db. You choose the filter that gives you a flat summation depending on your specifiaction (on axis or out of axis, frequency range, driver distance, etc.)

and this is also why drivers are directive: the larger the cone the higer the directivity, because when you move off axis signals from the left and the right side of the cone will be delayed, and that phase shift will cause high frequencies to sum in a quadratic manner (the larger the cone, the lower that frequency)

Look at the specs for the JBL 4430 at 93db and the 4435 at 96db.

That is something else, entierly. The 2234H is 96db sensible by itself. The second 2234 is an helper woofer, and the rolloff and tuning is calculated to get a flat curve with the help of mutual coupling in the bass.
The 4355 is a better exemple of mutual coupling. Here you get 96db with two 93db drivers, but in the bass (maybe under 150hz) you really get 99db and that is the reason for the low tuning of the cabinet.

The two designs have a similar frequency response and sensitivity at the end, but the 4435 design is much clever because you have virtually no phase issue (quadratic summation is not something desirable).

[tagerbaek]

Thanks for the answers, but, no, I still don't get it.

Exemplifying again: take a 90dB/1W driver, feed it 2W, you get 93 dB. Take two drivers, feed them 1W each (coherent) and you get 96dB for the same 2W total power input.
That is strange. It is also absurd, in its extension, because if you keep doubling up, then the cluster of drivers would eventually output more acoustic power than they are receiving from the amplifier. Could it be that the efficiencies of multiple drivers in fact do not add up linearly, but merely appear to do so as long as the efficiencies are far below 100 %?

Thomas

[Mr. Widget]

That is strange. It is also absurd, in its extension, because if you keep doubling up, then the cluster of drivers would eventually output more acoustic power than they are receiving from the amplifier.

No, because in this example you also doubled the electrical input. If both woofers are getting a full watt, you are supplying twice the initial power of 1 watt for 1 woofer.

As was also pointed out above, since you are planning an active system it is mostly an academic exercise.

Back to your original question, the 2118 can work. It will be the limiting factor as far as maximum SPL.


Widget

[pos]

Exemplifying again: take a 90dB/1W driver, feed it 2W, you get 93 dB. Take two drivers, feed them 1W each (coherent) and you get 96dB for the same 2W total power input.

Yes, you get 96db IF the drivers are close enough for an inphase summing of the considered frequencies.

That is strange. It is also absurd, in its extension, because if you keep doubling up, then the cluster of drivers would eventually output more acoustic power than they are receiving from the amplifier.

It can appear to be strange, but it is not: when you double the power you do not double the amplitude (voltage), because P = U^2/Z.
You need to multiply the power by 4 to multiply the amplitude by 2.
You can see that if you have a speaker simulation software that shows driver excurtion: simulate 1W input and look at the excurtion at a given frequency, that simulate it with 4W and you will see that the excurtion only doubles.

So by adding more speakers and amps you gain more than just adding amps.

But, again, this is only true for in phase signal summing

[toddalin]

POS is basically saying the same thing that I am and there is an easy way to demonstrate it.

You pick up 3 dB by having the two speakers of equal volume level adding their respective "tones." You pick up an additional 3 dB if the tones are the same and in phase because of the way waves (be they sound or water, or ???) add together.

When two wave crests/troughs come together simultaneously, they are additive and this is acounting for the other 3 dB.

OK, the test:

Take two woofers in small enclosures so they can be placed very close or moved apart.

Connect a stereo amp, one channel to each woofer. Play a pure sine wave through each channel (one at a time) and calibrate the sound level using a real sound level meter to some level (e.g., 90 dBL).

(If the mono amp driving two woofers can truly double its power into half the load, then the use of stereo amps of equal power is warranted for this test. But a true mono amp driving both speakers would be better because there could be small phase/delay/frequency issues between the two channels that would alter the wave form and test slightly.)

Now play them simultaneously and observe the new volume level. Is it 3, 6, or some other dB level louder???

Move the speakers apart. Does the addition value change? Bet is does as the wave crests/troughs become less additive.

Now run the speakers out of phase. If is was just a matter of power and cone movement and not the physics of wave addition, the volume level should be no different than if they are in phase. But I bet it is considerably different as the crests/troughs are now canceling each other out, at least to some extent.

Now for the coup de gras.

Use two signal generators, one on each channel. Set one at 60 Hz and the other at 100 Hz, each at 90 dBL. Run them together and observe the volume level. Now sweep the frequency of one to the other and observe the volume level when the wave become additive. I would bet that it gets louder at that point. But the waves must be exactly in phase so as to be purely additive. (I don't know how this would be accomplished with separate signal generators.)