isobaric bookshelf?

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Isobaric arrangement requires half the volume of a single driver, that's about it, very minimal reduction in distortion, in fact if you use the two drivers normally the distortion will be less due to less excursion

That's incorrect.

SPL is determined by displacement and stroke. (Similar to how a car engine works.)

Because SPL is determined by displacement and stroke, a "conventional" woofer and an isobaric pair of the same woofer will have identical maximum output if they're displacement limited.

This is because the bore and the stroke have not changed.

Now this might seem counter-intuitive, because the isobaric pair is less efficient. But, again, output is determined by bore and stroke. So the iso pair will reach the same output, they'll just need more power to get there.

Now the place where isobaric shines is that the smaller box size means that excursion is lower for the iso pair. This reduction in box size will generally mean that the iso pair can get louder than a single driver.

Also, note that you have two voice coils in an iso pair. So you may need to double the power to reach your SPL goals, but that power is being dissipated by twice the voice coils. So you would expect power compression to be comparable.

Having said all that, it's pretty hard to get excited about isobaric. That's a lot of hoops to jump through just to raise your output by a decibel or so.

Now if you require a very small box, it starts to look good.

Also, if you absolutely want the very best and you're prepared to pay for it, isobaric starts to look good, because being able to cram about four woofers into the space of two can yield some beastly designs.
 
Now the place where isobaric shines is that the smaller box size means that excursion is lower for the iso pair.
For the same input power, excursion is lower for isobaric than a single driver. That is basically the definition of sensitivity - isobaric is 6dB less sensitive. It's not an advantage because both configurations have the same amount of cone area exposed outside the box and SPL is a function of area and displacement/excursion as you point out. In practice you'll just increase the input power of the isobaric config to make up for the lack of sensitivity, getting you back to exactly the same amount of SPL/excursion as a single driver, however with the advantage that the box only needs half the internal volume.

Since the excursion vs SPL is the same for both configurations (since exposed cone area is the same) so you expect non-linear distortion to be about the same at the same SPL. The isobaric config needs twice the amount of power per driver (four times the power overall) to achieve the same SPL, so you expect to hit power compression issues earlier than a single driver.
 
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isobaric is 6dB less sensitive
Isobaric takes the same power per woofer, so it is 3 dB less sensitive. [For a given cut off frequency] efficiency is linearly related to box volume. Halving box sizes requires the force on the cone to be doubled. In an isobaric configuration two voice coils are acting on the same (compound) cone, so each coil still applies the same force so it must be getting the same power.


Since the excursion vs SPL is the same for both configurations (since exposed cone area is the same) so you expect non-linear distortion to be about the same at the same SPL
A cone-to-cone mounted isobaric pair reduces even harmonics by cancelling non-symmetries, as compared to a single woofer. Theoretically they can be fully cancelled. Odd harmonics are not affected for a given output level.
 
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