Hoffman Strikes Again: Passive Radiator VS Adding Another Speaker?

I'm working on a set of bookshelf speakers (2 way) and keep running up against hoffman's iron law. I also read recently about purifi's SPK16 reference design, and they were able to get down to about 32hz, but that also had a lot of design choices that were based on the fact they have a facility to design all of these things in and a budget much larger than mine. Additionally, I'm going to use a hypex fusion amp, which means I will have an active implementation as opposed to a passive one which also opens me to much greater tuning options including things like a linkwitz transform.

With all of that said, purely from a performance perspective, would it be more advantageous to use passive radiators, or just add subwoofers on the sides and make the design a 3 way?
 
I did a bunch of these sims recently. I noticed that optimum box needs to be much larger for two of the same drivers to get a similar response to only one of those drivers with PR. But eq can fill up that missing low end with the two drivers in the smaller box. But to my untrained eye it appears that using eq like that eats up the headroom available. Eg, when the rest of the subwoofer bandwidth is idling with decent SPL 10w, a 10dB boosted low end part is actually drawing 100w (If my understanding of such things is improving)
 
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I did a bunch of these sims recently. I noticed that optimum box needs to be much larger for two of the same drivers to get a similar response to only one of those drivers with PR. But eq can fill up that missing low end with the two drivers in the smaller box. But to my untrained eye it appears that using eq like that eats up the headroom available. Eg, when the rest of the subwoofer bandwidth is idling with decent SPL 10w, a 10dB boosted low end part is actually drawing 100w (If my understanding of such things is improving)
That would be where something like a linkwitz transform comes in. It Changes the power target for different frequencies in order to compensate for spikes and roll-offs. You do bring up a very good point about enclosure size. If there's no place for the energy to go those subs will rattle the hell out of the enclosure. Although, it does also make me think of one design that is an exception to that rule; the Devialet Phantom. But those speakers are designed more around bass response than anything else (that and they're weird in general).
 
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With all of that said, purely from a performance perspective, would it be more advantageous to use passive radiators, or just add subwoofers on the sides and make the design a 3 way?
Performance perspectives:
Efficiency-PR wins over Sealed subs
Sound quality-adding subwoofers reduces the excursion required from the woofers, reducing IM distortion for a given SPL.
Frequency response- Sealed subs can go lower, PR are limited by the tuning frequency chosen
Transient response- Sealed subs win
Output potential-Depends on excursion potential
 
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Performance perspectives:
Efficiency-PR wins over Sealed subs
Sound quality-adding subwoofers reduces the excursion required from the woofers, reducing IM distortion for a given SPL.
Frequency response- Sealed subs can go lower, PR are limited by the tuning frequency chosen
Transient response- Sealed subs win
Output potential-Depends on excursion potential
All terrific points. That and since I'm using a DSP I can tune the whole thing so that any bass response won't go into excess. If that's the case I guess I can start looking into small subwoofers that won't eat up too much real estate.
 
Big
and more speakers / cone area

Sealed

10" is " small"
12" about right

Otherwise tall is the answer for space
because footprint is the same.

2x8 mid and tweet
all done.
Shelf filter works great.
Otherwise known as a bass knob

Big subs can go in corners.
Because nobody does anything in a corner.
No space lost.
Corner loading needs no " EQ"
unless your a bass head.

"Small Sub"
somewhere , somehow is a 4 letter word
and just not allowed

2 cubic feet aint too big
and a little 12" fits in there.
Hoffman will loose
 
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With all of that said, purely from a performance perspective, would it be more advantageous to use passive radiators, or just add subwoofers on the sides and make the design a 3 way?
Depends on your outright goal. PBRs are (mostly) an alternative to ports for acoustically small enclosures, when you'd struggle to balance air velocity in the duct as against excessive self-harmonics. There are some other reasons for using them, but that's the main one. So the main question you have for yourself is whether you want an acoustically (and physically) small box, and are okay with the reduced power-handling etc., or if you require something potentially a bit larger and / or more complex with greater LF reach & dynamic range.
 
Depends on your outright goal. PBRs are (mostly) an alternative to ports for acoustically small enclosures, when you'd struggle to balance air velocity in the duct as against excessive self-harmonics. There are some other reasons for using them, but that's the main one. So the main question you have for yourself is whether you want an acoustically (and physically) small box, and are okay with the reduced power-handling etc., or if you require something potentially a bit larger and / or more complex with greater LF reach & dynamic range.
@weltersys I believe brought up the best point: including a sub in an enclosure is a good way to cut down on IMD. I want the signal to be as clean as possible. The main challenge there is just making sure the cavity inside is inert and the sub doesn't rattle the thing apart.
 
Then you know the route to follow for your needs. (y);)

Right, although assuming a given enclosure, partitioning will automatically increase rigidity relative to the full void (as well as potentially raising the frequency of any eigenmodes present, making them easier to damp out), so you're inherently in the right direction on that front. Beyond that -usual measures apply.
 
partitioning will automatically increase rigidity relative to the full void
Actually something I was thinking about trying is using hexagonal aluminum sheets as dividers between each section. I read a while ago in vance's book about how hexagonal aluminum was used to inert an enclosure (I believe it was by Celestion). Magico seems to use this technique in their higher end models as well, but I'm not going that advanced. I figure if I can use them as separating partitions, any acoustic energy will be split off and, therefore, easier to dissipate (assuming stuffing, something like rock wool).
 
SL600 used Aerolam. It worked, but ideally needed the whole (or most of the) structure to be made from it for best effect. Might be possible to key it into a wooden structure, but how much of an advantage over wood-based under those conditions -no idea. Interesting option though.
Paper Nomex, hexcel and alloy honeycomb will provide great benefits when used between two plywood skins