Isobaric frequency limits?

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As Don said, the chamber has compliance. It's a spring. The bigger the volume the weaker the spring. But the different in displacement between the front and rear drivers is not an error. It is the necessary difference to compress or stretch the spring the generate the required forces on the drivers. A weaker spring must be compressed or stretched more than a stiff spring to generate the same force.

I did an analysis of the isobaric system years ago. Isobaric
 
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No, they are not. The pressure in the isobaric chamber varies as the pressure would vary if the front driver were mounted in a box twice the size of the rear box. Think about the mechanics. When you mount a driver in a box the trapped air pressure in the box is a force against which the driver moves. If the front driver in an isobaric system is to move with a similar motion the pressure in the isobaric chamber must vary in the same manner and with the same magnitude. Otherwise the alignment would be different. F=ma

I looked at your paper, and we seem to be talking about two different systems.

The Linn Isobariks are not push-pull; both drivers point to the front, and are in-phase. The rear driver compresses the air behind it. If the rear driver were able to follow the music signal 100% faithfully, then the front driver would not compress the air between them at all. However, as the air in the rear chamber dampens the rear driver to some extent, the front driver must compress the air in the middle chamber by the difference between the signal and the rear driver's actual movement. The two drivers are not aligned; the front driver's motion will more closely follow the signal than the rear's.
 
I looked at your paper, and we seem to be talking about two different systems.

The Linn Isobariks are not push-pull; both drivers point to the front, and are in-phase. The rear driver compresses the air behind it. If the rear driver were able to follow the music signal 100% faithfully, then the front driver would not compress the air between them at all. However, as the air in the rear chamber dampens the rear driver to some extent, the front driver must compress the air in the middle chamber by the difference between the signal and the rear driver's actual movement. The two drivers are not aligned; the front driver's motion will more closely follow the signal than the rear's.

Whatever. The analysis I did is not dependent on push-pull or push-push. That only matters when asymmetries (suspension nonlinearities) are considered. Remember, the pressure in the isobaric chamber acts on both drivers. The rear driver feels a pressure force of Pbox - Pchamber where as the front driver only feels Pchamber. Both drivers follow the same motion but one has slightly greater excursion which is how Pchamber is generated.

If you read my article closely you would have noted that for the first isobaric case there is no nonlinearity considered. So push-pull or push-push is irrelevant. The drivers behave identically in either direction. Note in the first figure there is no distortion. Thus both drivers are following the input signal exactly.
 
Interesting point regarding extra excursion. I do agree that once the front driver's excursion exceeds the rear driver's, it's back to compressing the chamber(s). I guess this is where the twice-as-large-a-box rule comes in.

The first half of the excursion is still relatively distortion-free, though, even if the second half isn't. No?
 
let me summarize my article. For ordinary woofers, single woofer in single box, if there are closely spaced and radiating al low frequency the conventional wisdom is that when in a push-pull configuration even order distortion cancels. It does. It does so because the radiated SPL contains even order distortion components which are 180 degrees out of phase. That idea has been incorrectly carried over to the isobaric case where it has been claimed that mounting isobaric drivers in a push-pull format will also result in cancelation of the even order distortion. In general it does not. The reason is because in the conventional woofer case if is the distortion in the radiated SPL that sums to zero. In the isobaric case, the problem is that the distortion in the rear driver motion generates a distortion in the pressure force acting on the front driver, and vice versa.

Now what I have done in the isobaric analysis is to start with two perfectly linear drivers. That is, if the input is a sine wave, the driver motion is also a sine wave. No distortion can occur. In such a case there is no such thing as push-pull as it makes not differences which way the drivers are mounted. In that case the only difference in the motion between front and rear drivers is the magnitude of the excursion required to generate the pressure variations in the isobaric chamber.

The nesx thing I dis was to introduce nonlinear, but symmetric suspension characteristics. Since they are symmetric, again, there is not such thing as push-pull, etc. The results show that in such a case what you have is a response for both drivers where only odd order distortion is present. For the case I considered the distortion was greater for the front driver, which is understandable since the front driver undergoes slightly greater excursion, thus deeper into the nonlinearity of the suspension.

Then I introduce asymmetry in the suspension. This means, for example, that the variation in BL(x), Cms(x), Rms(x), etc is different in one direction of excursion compared to the other direction. I then looked at the result for the push-push configuration. As expected, the results now show the addition of even order distortion is the driver motion, again, with the front driver having slightly higher distortion for most harmonics.

The next thing I did was to repeat the above case (asymmetric suspension) with the drivers in push-pull format. Remember, with separate woofers in their own boxes, mounted push-pull, even order distortion cancels in the radiated SPL. But in the isobaric case my simulations show that both the front and rear driver of the isobaric system retain even order distortion in their motion. Since sound is radiated only by the motion of the front driver, the radiated SPL must therefore also contain both odd and even distortion.

you can not say 1/2 the motion has distortion and the other 1/2 doesn't. It's distortion. The output doesn't follow the input.

Look at it this way. If the front driver were perfectly distortion free, then for an input I=sin(wt) all the forces on the driver, would have the same form. So when you write F=ma you would have F =A sin(wt) - B sin(wt) - Csin(wt) where A would represent the motor force, B the suspension compliance force, C the mechanical resistance, etc. So, F = ma becomes [(A-B-C) sum(wt)]/m = a. That is, the driver acceleration, and motion in general, is distortion free XF = sin(wt). But now consider that the front driver is still perfect but that the rear driver has distortion. It's motion might be XR = X1 sin(wt) +x2 sin(2wT) + x3 sin(3wt) + .... where x2 and x3, ... are the distortion components. Now, since the pressure force in the isobaric chamber is proportional to the changes in volume of the chamber, which is due to the difference in motion between the front and rear driver, we can see that the pressure force is proportional to XF - XR =( X - X1) sin(wt) - x2 sin(2wt) - x3 sin(3wt) - ... So this pressure force which acts on the back sideof the front driver has distortion components in it. If we put that in the equation for the front driver motion we would have [(A-B-C + Xf-XR)) sum(wt) - x2 sin(2wt) - x3 sin(3wt) - ... ]/m = a and we see that even if the front driver is perfectly linear, it will have distortion in its motion because the pressure force from the isobaric chamber will impose a nonlinear force on it.

It's more complicated that that, but I hope it makes the point. As to which driver would have more distortion in its motion you can really say off hand. It will depend on how much distortion is present in the suspension and motor of each driver. There are never going to be exactly the same. But in general I would suspect that the front driver would have greater distortion simply because its excursion will be slightly greater than the rear driver, thus moving further into the nonlinearities of the suspension/motor. It's probably all pretty insignificant anyway. But the even order distortion canceling mechanism that you can get with two separate woofers just isn't present in a push-pull isobaric system.

I really don't have anything else to add.
 
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To be honest I lack the skills for that. If there was a way of adding a passive EQ circuit to work with an existing amp, I'd be really interested.
But yes, using two or even 1 of these drivers in a sealed with enough EQ to hit 40hz f3 would be amazing. They only need around 25 litres each.
 
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There is such a thing as a passive line level crossover which could be an option, it still requires a separate amp for the woofers. TLS.org | Passive Line-Level Crossover
Ah I just figured out that's Kate Bush in your avatar!
Thanks for the help and the link. I suppose a separate sub amp would be an option. Ive got a Line Magnetic amp coming, so I kind of blew my budget..
 
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