DIY CBT Design: (i) The Story So Far & (ii) A Question Unresolved...

Hi all,

I'm looking at building a straight delay-curved CBT (Constant Beamwidth Theory) line array (a la Keele), using 24 3.5” full-range drivers (Vifa TC9FD18-08 (apparently aka: Peerless FR35/8); sensitivity's ok-ish at 86dB, but good power handling for a small driver (50W/100W) with good wide-range performance 110Hz-15K. Qts = 0.72). CBT arrays look VERY promising; just Google CBT & Keele for more info, but to sum up, much better dispersion than std line-array; less vertical lobing, more consistent & homogeneous sound field near & far field.

However, I have a question re acoustic outputs & driver-group sensitivities for mixed parallel/series combinations of drivers that I’m hoping someone could please help me with, but see Keele's .pdf presentation on CBT's & then read on for the context first:

(Incidentally, I'll stress; all my efforts are for a PERSONAL system; in no way am I attempting to build a commercial unit. I'd also encourage all who follow to observe & respect the patents that JBL & Keele have on CBT technology). Right: now that the legal caveat is out of the way...

So far, I’ve established the appropriate Legendre shading amounts for each of the drivers (like I said, see Keele's preso'!), which I’ve then grouped around -3dB increments (ie, 0dB, -3dB, -6dB etc) to simplify the amplification logistics. My shaded groups end up looking like this:

Qty . . . . . Shading (dB)
1 . . . . . -18dB
1 . . . . . -12dB
1 . . . . . -9dB
2 . . . . . -6dB
3 . . . . . -3dB
4 . . . . . 0dB (ie, no attenuation)
4 . . . . . 0dB
3 . . . . . -3dB
2 . . . . . -6dB
1 . . . . . -9dB
1 . . . . . -12dB
1 . . . . . -18dB

Those of you who understand the maths may notice that I’m actually one driver short; there should be a 9th driver at 0dB in the middle, but I’ve decided to omit it for each of amplification (8 x 8ohm drivers: yeah! But 9 x 8ohms drivers… hmmm…). I’m hoping the fact that I’m roughly approximating the curve using the 3dB increments will allow a degree of fudging.

Re the amplification: Rather than try & driver the entire lot of one amp (which I think would involve having to come up with some very strange combinations of drivers to ultimately establish a workable end impedance (ie, 16 >= Z >= 4ohms)), I’ve decided it’s probably easier to use a small number of multiple amps to drive select combinations of the groups above that naturally occur -6dB apart in relation to each other (although see the caveat below before you jump on any errors in my assumptions), ie:

Group . . . . . Qty . . . . . Shading (dB)
C2 . . . . . 1 . . . . . -18dB
C1 . . . . . 1 . . . . . -12dB
B2 . . . . . 1 . . . . . -9dB
A2 . . . . . 2 . . . . . -6dB
B1 . . . . . 3 . . . . . -3dB
A1 . . . . . 8 . . . . . 0dB (I’ve added the two 0dB groups together)
B1 . . . . . 3 . . . . . -3dB
A2 . . . . . 2 . . . . . -6dB
B2 . . . . . 1 . . . . . -9dB
C1 . . . . . 1 . . . . . -12dB
C2 . . . . . 1 . . . . . -18dB

Ignoring the symmetrical layout & combining group numbers for simplicity, this should result in the following:

Group . . . . . Qty . . . . . Shading (dB)
A1 . . . . . 8 . . . . . 0dB
B1 . . . . . 6 . . . . . -3dB
A2 . . . . . 4 . . . . . -6dB
B2 . . . . . 2 . . . . . -9dB
C1 . . . . . 2 . . . . . -12dB
C2 . . . . . 2 . . . . . -18dB

Factoring in series/parallel (S/P) combinations, I hope to achieve the following (once again, see the caveat below before you jump on any errors in my assumptions):

Group . . . . . Qty . . . . . Shading (dB) . . . . . Combo impedance (ohms)
A1 . . . . . 8 . . . . . 0dB . . . . . 4ohms (straight 1-2-4-8 parallel/series combo)
B1 . . . . . 6 . . . . . -3dB . . . . . 5.33ohms (3 paralleled sets of series-pairs)*
A2 . . . . . 4 . . . . . -6dB . . . . . 8 ohms (straight 1-2-4 parallel/series combo)
B2 . . . . . 2 . . . . . -9dB . . . . . 4ohms (parallel pair)**
C1 . . . . . 2 . . . . . -12dB . . . . . 16ohms (series pair)
C2 . . . . . 2 . . . . . -18dB . . . . . 16ohms (series pair)**

Or, when viewed in their groups:

Group . . . . . Qty . . . . . Shading (dB) . . . . . Combo impedance (ohms)
A1 . . . . . 8 . . . . . 0dB . . . . . 4ohms (straight 1-2-4-8 parallel/series combo)
A2 . . . . . 4 . . . . . -6dB . . . . . 8 ohms (straight 1-2-4 parallel/series combo)

B1 . . . . . 6 . . . . . -3dB . . . . . 5.33ohms (3 paralleled sets of series-pairs)*
B2 . . . . . 2 . . . . . -9dB . . . . . 4ohms (parallel pair)**

C1 . . . . . 2 . . . . . -12dB . . . . . 16ohms (series pair)
C2 . . . . . 2 . . . . . -18dB . . . . . 16ohms (series pair)***

* No, I’ve no idea if the B1 combo will naturally yield a group sensitivity that’s -3dB with respect to A1; that’s yet to be established & may need a little cut/boost if required. But I’m estimating that it’ll be close.
** B2 will require an extra -3dB attenuation to bring them to the -9dB target
*** C2 will require -6dB of extra attenuation to bring them to the -18dB target

I’ll add the group pairs as follows:

A1 + A1 = series (Z = 12 ohms)
B1 + B1 = series (Z = 9.33 ohms)
C1 + C1 = parallel (Z = 8 ohms) – this may require an overall C-group attenuation if the parallel-config’ raises the sensitivity, but I didn’t want to series them due to the 32ohm impedance that would result.


So, in essence, I’m hoping to achieve the shading for all six groups by running them in relative +-6dB pairs off three amplified channels, with a little extra attenuation where required.

HOWEVER, here’s the main caveat (and the point of my post’s question):

Am I correct in my assumptions about the combination in Group A achieving a -6dB difference between the two sub-group pairs? I’ve taken into account gain due to both current draw as well as driver numbers, rather than just driver numbers, so, looking at Group A:

Group . . . . . Qty . . . . . Shading (dB) . . . . . Combo impedance (ohms)
A1 . . . . . 8 . . . . . 0dB . . . . . 4ohms (straight 1-2-4-8 parallel/series combo)
Connected in series to:
A2 . . . . . 4 . . . . . -6dB . . . . . 8 ohms (straight 1-2-4 parallel/series combo)

Given that A1 has twice the drivers as A2, and that A1 will draw twice as much current than A1 (due to half the impedance), is it correct to say that the overall difference in sub-group sensitivities will be 6dB? Or will it only be 3dB? And does connecting them in series help/hinder this?

I hope that all makes sense; can anyone please assist me with this?

Thanks heaps!

Paul