Aperiodic Rules of Thumb

I've been reading as much as I can on aperiodic enclosures lately but there are still some unanswered questions I have. I'm sure there are articles and threads I've missed but thought I would start a fresh thread in case others are interested.
I'm using the term 'aperiodic' in its widest possible sense at this stage.

First here's what I think I know.
There are three basic approaches to aperiodic design.

A. The stuffing a port approach. Take a vented box (e.g. bass reflex) and put some stuffing in it. The effect will be less bass output around the port tuning frequency. This would create an alignment between a BR and sealed. The roll off would approach 3rd order, again between vented and sealed. This might help to tune such an enclosure should the bass be too boomy in a given placement near walls or a small room.

B. Introduce a leaky vent into a sealed box approach. This would achieve a lower Qts (as measured by a lower magnitude impedence peak) and therefore lower group delay and better transient response. Or you can achieve the same Q as a sealed box but in a smaller volume.
What I'm not sure is what happens below tuning. If you model a large closed box (compared to a standard 0.707 box) you can see that the F3 rises in frequency because the roll off starts higher up but it is more gradual and therefore the F10 might be lower in frequency, i.e. it has lower reach. However if you start with a 0.707 box and introduce some leakiness resulting in lower Q what happens lower down, do we get the same reach as the same Q of a large sealed box or do we loose some reach?
Practical question: If we design a box for a typical woofer of say Qts 0.35 and we put it in a small enclosure that results in a Q of 1.0 would could the lowest Q be reasonably achieved by introducing an aperiodic vent?

C. Stuffed Transmission Line - I think this can be described as a Classic TL where the goal is maximally flat impedance. From what I've read this is the best way to achieve that compared to a leaky conventional box.
Similar question to the sealed what happens lower down below where the Z peak was?

The other thing I think I know is that if we achieve maximally flat Z the resulting Q approaches that of the bare driver.

I'm mostly interested in what happens in B and C above.
 
The first two are more or less the same thing from an operational and physics perspective, it's just that you've taken a different box as your starting assumption. Both are boxes with resistively damped vents (or leakage if you prefer). The alignment will in most cases track a larger sealed with similar internal damping, potentially with a slightly better damped impedance characteristic, but will at some point unload and transition to a 4th order. This is usually at a very low frequency & amplitude so rarely an issue / often not even realised. Since there is no standard definition for, size or resistance / damping of an 'aperiodic' (i.e. resistive) vent, there isn't a single answer for your question about driver & enclosure Q -it will depend on the size & damping behaviour of the vent.

A max-flat impedance TL will have the flattest impedance characteristic of anything other than a full-sized reactance-annulled horn, with the entire LF impedance range heavily damped / linearised.
 
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The first two are more or less the same thing from an operational and physics perspective, it's just that you've taken a different box as your starting assumption. Both are boxes with resistively damped vents (or leakage if you prefer). The alignment will in most cases track a larger sealed with similar internal damping, potentially with a slightly better damped impedance characteristic, but will at some point unload and transition to a 4th order. This is usually at a very low frequency & amplitude so rarely an issue / often not even realised. Since there is no standard definition for, size or resistance / damping of an 'aperiodic' (i.e. resistive) vent, there isn't a single answer for your question about driver & enclosure Q -it will depend on the size & damping behaviour of the vent.

A max-flat impedance TL will have the flattest impedance characteristic of anything other than a full-sized reactance-annulled horn, with the entire LF impedance range heavily damped / linearised.
Thanks for the reply Scott, so I'm thinking from your reply that you can indeed emulate a larger sealed box by introducing a resistive vent?
 
As part of a re-envision of the A26 plans, there is a note section that touches on aperiodic. Coming soon.

dave

Look forward to it.

I'm looking for people's practical experience on these things. e.g. if one were to start with a sealed alignment of 1.0 and introduce a resistive vent and wanted to achieve a 0.7 or less, is this easy to do, what are the practical limits?
 
Keep in mind 'Q[tc]' is only applicable to sealed boxes, not vented, even resistively vented, which as noted above can initially ~mimic the response shape of a sealed enclosure, but will at some point ultimately unload 4th order, albeit usually at a very low level. So the concept is not a direct equivalent.

Be that as it may, you're unlikely to be able to achieve an initial response shape ~mimicking a sub-Butterworth alignment using a baseline Vb & internal damping derived from a sealed box with a Qtc of 1.0. You might be able to get it somewhere just above Butterworth, but you'll be walking a tightrope between high levels of vent damping, and having so much that it ends up acting like a solid mass.
 
Stal, contained in my submission to a previous thread is a formula which constitures an 'aperiodic rule of thumb'. I'll copy it here for your interest.

Here is information from an article by Steve Hutton published by Hi-Fi News & Record Review in December 1974 which refers to the distributed port (DP) enclosure which was a type of aperiodic enclosure famously employed by Gilbert Briggs of Wharfedale fame. The DP consisted of a series of narrow slits or small holes in the rear of the enclosure which were covered internally by a thin, felt like cloth to form a resistive vent.

The article states that, as the DP area increases from zero, the Q and resonant frequency fall. However, after the Q has reached unity it starts to rise again with the figures becoming multi-valued, hence unpredictable, below Q = 1.

Most interestingly, the author gives an empirical formula for calculating the DP or resistive vent area:

A = 5.5 x V [0.818 (Fs/25) + 0.182]

Where A is the vent area in sq in, V is the enclosure volume in cu ft and Fs is the resonant frequency of the driver in free air.
The Wharfedale cabinet construction leaflet shows that the total area, A, can be made up of the appropriate number of 12" x 0.25" slots, placed 2" apart. Each slot can be replaced by fifteen holes of 0.5" diameter if preferred.
 
Thanks GM - stuffing and aperiodic combined should make for a nice small box.

:up: 😀 Certainly worked for me back when my driver options were mostly from old mono audio consoles/huge HIFI speakers, but needed them compact enough to fit in small bedrooms, college dorms and newly weds' closet sized rentals, winding up with pipe TLs to fit available corners.