I've been trying to find a reliable formula to calculate the total group sensitivity of a relatively odd configuration and number of LF drivers. They would be arranged as close as possible to each other.
In my own personal scenario ->
- 3 identical 12" LF drivers, wired in parallel, individual base sensitivity of 87 dB/2.8V/1M per driver, arranged in a triangle.
- what would the total sensitivity be of all 3 drivers playing together at frequencies lower than the equivalent of 1/2 WL?
With an even number of 4 drivers connected 2 in series, then the 2 groups paralleled, we'd theoretically observe a 3dB gain from doubling the driver count and another 3dB from doubling the cone area, but lose 3dB from cutting the drive voltage to each woofer of the series connections. That leaves us with a total net gain of only 3 dB if we only count the frequency range that falls in the 1/2 WL CTC driver spacing.
With an abnormal quantity of drivers, CTC spacing and adding in series.resistance from a thinner awg, it becomes a bit more complicated to figure all this out. Short of putting it in a software sim, which isn't always accurate, there has to be a better way to get a closer answer.
In my own personal scenario ->
- 3 identical 12" LF drivers, wired in parallel, individual base sensitivity of 87 dB/2.8V/1M per driver, arranged in a triangle.
- what would the total sensitivity be of all 3 drivers playing together at frequencies lower than the equivalent of 1/2 WL?
With an even number of 4 drivers connected 2 in series, then the 2 groups paralleled, we'd theoretically observe a 3dB gain from doubling the driver count and another 3dB from doubling the cone area, but lose 3dB from cutting the drive voltage to each woofer of the series connections. That leaves us with a total net gain of only 3 dB if we only count the frequency range that falls in the 1/2 WL CTC driver spacing.
With an abnormal quantity of drivers, CTC spacing and adding in series.resistance from a thinner awg, it becomes a bit more complicated to figure all this out. Short of putting it in a software sim, which isn't always accurate, there has to be a better way to get a closer answer.
CTC spacing has nothing to do with it. You get 6dB from two drivers even if they're at opposite ends of the room. It just limits where you can sit to get that, and related spatial effects.
3 drivers is 9.5dB.
Halved voltage is -6dB
3 drivers is 9.5dB.
Halved voltage is -6dB
Assuming identical, parallel-connected drivers and coherent acoustic summing, the sensitivity gain in dB is
20×log10(N), where N is the number of drivers. Efficiency gain in dB is 20×log10(N/sqrt(N)) → 10×log10(N)
This is interesting because a while ago I had 6 woofers rewired to 24R, mainly give better handling with a particular amplifier I had that didn't like low impedance speakers but was [ for the time] quite powerful.
Boxes fell apart but the rescued woofers are still in the stash.
Boxes fell apart but the rescued woofers are still in the stash.
@AllenB Shouldn't the gain be based off log10 (wattage) and not log20 (voltage)?
I understand the relationship regarding power, which is a 3 dB gain when doubling it. With doubling voltage, it ends up being a 6 dB gain.
The reason why I mentioned WL is that the calculated gain is only effective throughout the entire listening space if the driver CTC distance is less than the equivalent of double the WL being reproduced. If you're on axis with all drivers and the sound is relatively in phase from them, you'll also have the same gain, but that is with the drivers playing at higher frequencies.
I understand the relationship regarding power, which is a 3 dB gain when doubling it. With doubling voltage, it ends up being a 6 dB gain.
The reason why I mentioned WL is that the calculated gain is only effective throughout the entire listening space if the driver CTC distance is less than the equivalent of double the WL being reproduced. If you're on axis with all drivers and the sound is relatively in phase from them, you'll also have the same gain, but that is with the drivers playing at higher frequencies.
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log10 typically refers to logarithm base 10. The 9.5dB figure for sensitivity gain given by @AllenB (and @hifijim) is correct:
20×log10(3) = 9.542...dB.The efficiency gain, as stated before, is
10×log10(3) = 4.771...dB. Given a constant input voltage, the total electrical power is multiplied by the number of drivers (since the drivers are connected in parallel), so sensitivity gain is then 10×log10(3×3) = 20×log10(3) = 9.542...dB.
Pressure is proportional to density. Consider that two drivers which are being crossed, sum at 6dB.
Why only the highs?
If you are equidistant and on axis to each driver, they sum constructively regardless of frequency and CTC distance.
I even did series and parallel measurements which proved that in real life, back when life seemed more real 😉
In parallel, disregarding any wire losses (which you can, if not using long lengths of wimpy wire), as per the formulas in post #7 :
1=0 dB (individual cabinet SPL)
2 +6.02 dB
3 +9.54 dB (+ 3.52 dB more than 2 cabinets)
4 +12.04 dB (+ 2.5 dB more than 3 cabinets)
5 +13.98 dB (+ 1.94 dB more than 4 cabinets)
6 +15.56 dB (+ 1.58 dB more than 5 cabinets)
7 +16.9 dB (+ 1.34 dB more than 6 cabinets)
8 +18.06 dB (+1.16 dB more than 7 cabinets)
9 +19.08 dB (+1.02 dB more than 8 cabinets)
10 +20 dB (+ .92 dB more than 9 cabinets)
11 +20.827 (+.83 dB more than 10 cabinets)
12 +21.583 (+. 76 dB more than 11 cabinets)
13 +22.278 (+.69 dB more than 12 cabinets)
14 +22. 922 (+.64 dB more than 13 cabinets)
Note that the gain is with multiple cabinets, or in your case, tripling the volume of the cabinet the three drivers would use compared to one- the LF sensitivity depends on the cabinet the driver is in, the base sensitivity is usually well above the LF range.
Art
RPTFLOL
I guess you'd get a heart attack with these huh? 😉
I honestly don't remember any speaker brand with more drivers... try the ones with berillium!
They seem to be a love it or hate it.. If I had space for more speakers, I'd get them...
https://tektondesign.com/products/full-range-speakers/flagship/
@tonyEE Yes, I'm aware of those. They do project effortless dynamics in the mids on up with all that tweeter surface area. I've heard them once and it wasn't a matter of good or bad, just different. They can play loud though. Not my taste in a speaker and certainly not an accurate sounding speaker.
The circular driver array isn't anything new, but it has its benefits. The way B&O does it is clever. Thats really the design to emulate if you have the DSP for it. A large tweeter array crossed at 1k can sound alot like a large biradial JBL horn and driver combination. I used to mix alot on 4430s. Those are my reference for a coherent, large 2 way.
The circular driver array isn't anything new, but it has its benefits. The way B&O does it is clever. Thats really the design to emulate if you have the DSP for it. A large tweeter array crossed at 1k can sound alot like a large biradial JBL horn and driver combination. I used to mix alot on 4430s. Those are my reference for a coherent, large 2 way.
So those sensitivity, either measured and not then fudged/lied about by Marketing, or calculated from Thiele-Small parameters,* have little to do with actual sensitivity at very low frequencies. For that you need to run a good simulator. The +6 dB for a pair comes from superposition and you get more sensitivity on-axis but less elsewhere, there's no free lunch, except at the very low frequencies where you get some mutual loading upping the resistive part of the coupling to the air or something like that (it's been a long time since I messed with that!). But at very low frequencies the room is affecting things...I'm not feeling you just get endless boost. We need someone who does research on PA systems to bless us with some knowledge here.
*Richard Small's thesis specifically calls this out as essentially a midrange quantity (passband).
@head_unit This is exactly what I'm getting at with my situation. Mutual coupling is bandwidth limited by CTC spacing and driver count, but also room loading.
