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Author Topic: SPL calculation  (Read 563 times)

Tim Hite

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SPL calculation
« on: May 15, 2019, 10:48:29 pm »

Suppose I'm running 6x 8Ω  identical subs with 3x 8Ω per channel at 2.7Ω on two separate amp channels.

Now suppose an amp channel goes down during a gig, and I repatch a single 8Ω sub to the good channel now presenting a 2Ω load across 4x 8Ω subs on one amp channel.

Assume the amplifier has enough power to drive the repatched load.

I know that losing half the subs would net me -6dB SPL, but how do I figure the repatched output? What is the calculation for SPL loss in dB?

I want to say that the repatch would net -4dB, because I'm losing 1/3 of the total, but I'm guessing that's probably incorrect. . .
« Last Edit: May 15, 2019, 11:01:09 pm by Tim Hite »
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Joe Pieternella

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Re: SPL calculation
« Reply #1 on: May 15, 2019, 11:13:36 pm »

Assuming the Amp is current limited....

Short answer: you'll lose 1,7dB <-- this was wrong I used random phase addition in my first calculation.

Edit: based on the assumption that the amplifier is current limited we can use P=I^2/R to determine max amperage.
To make the calculations easier we will make P 1000w.
I^2= 2,7 x 1000w=2700

In the first situation where you had both channels running you had ~333 watts running to each speaker. Netting 40,8dB of gain over 1watt/1speaker

Next you have 2 ohms so we get P=2700/2=1350w so ~337watts per speaker netting 37.3dB of gain.

So indeed a difference of 3,5 db, however this is all pure theory the true load presented to your Amp will almost never be the nominal value of the speaker.
Also when you start considering that to keep the same output you had before you would need 1,5 times the excursion per driver and that you would need more than double the power to do so while adding power compression making your net gains lower.
But if you look at it the other way around you did make the first three speakers' life easier by about 25% by adding the fourth.

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« Last Edit: May 16, 2019, 12:53:59 am by Joe Pieternella »
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Russell Ault

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Re: SPL calculation
« Reply #2 on: May 15, 2019, 11:58:35 pm »

I want to say that the repatch would net -4dB, because I'm losing 1/3 of the total, but I'm guessing that's probably incorrect. . .

For simple math, 20*log(4/6) (i.e. the 20 times the logarithm of the ratio of remaining subs to total subs) = ~-3.5 dB, which is basically the -4 dB you mentioned.

That being said, the simple math only applies if all six subwoofers occupy the exact same physical space (which, of course, is impossible). IRL the six subwoofers are interacting with each other, and reducing them down to four will inevitably change those interactions, so the actual changes in SPL will be location-specific.

On the average, though, it should be about 3.5 dB down.

-Russ
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Chris Grimshaw

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Re: SPL calculation
« Reply #3 on: May 16, 2019, 03:59:35 am »


Edit: based on the assumption that the amplifier is current limited we can use P=I^2/R to determine max amperage.

P=(I^2)*R, or P=(V^2)/R.


If all the cabinets are receiving the same power before/after (ie, the amplifier can source all of the current required), then there'll be 3.5dB difference in running 6x subs vs running 4x subs.

That's assuming that your subs are all acting as coherent sources and they're in-phase across their operating band. For subs, this is generally correct until you get to very large sub arrays.


If your amplifier is current-limited, it's a bit more complicated. You'll get 0.74x the power output at 2ohm (since P is proportional to R when we're at the current limits).

0.74x power = -1.3dB.

So, if you're up against current limiting and an amp goes down, swapping to 2R/ch with a reduced number of cabs will result in a 4.8dB drop in available level.

Chris
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Ivan Beaver

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Re: SPL calculation
« Reply #4 on: May 16, 2019, 08:17:28 am »

Just to add to the complexity of the situation.

Are you going to leave the "undriven subs" in place? Or are you going to take them to the truck?

If you leave them in place, not only are they not adding to the sound, they are TAKING AWAY from what the other subs are doing.

At some freq more than others.

When you have undriven or non shorted loudspeakers near others, they will cause notches in the freq response.

That is why whenever I bring a system into a venue, I ask the venue guy to turn on the amps, but make sure there is no input to them.

That way the amps are acting as a "brake" to the cone movement that the unused subs are trying to do.

Yes, it would be better to remove them or short them out, but that is not usually possible.

So, as usual, the correct answer gets a bit deeper than the "simple math" might suggest.  And it is also freq dependent.
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Tim Hite

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Re: SPL calculation
« Reply #5 on: May 16, 2019, 01:26:16 pm »

Thanks for the answers guys. This is coming from me examining wiring amp racks for regular use on tours and festivals.

It's been a rule of thumb to leave the shop with everything wired up at 4Ω or 2.7Ω so that if something goes down on the road you are carrying some 'overhead' amplifier capacity to give you options for repatching and keeping things rolling. This is as opposed to heading out the door with your system running at 2Ω, which doesn't really allow for a repatch and would require carrying spare amplifiers or going without.

I was giving it a deeper thought and seeing if there's a way to quantify the difference in output. I suppose it would also be salient to examine the effects of running a high current load in relation to amplifier reliability.

I get that it's a big, complex subject. I was just looking for some clarity.
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Re: SPL calculation
« Reply #5 on: May 16, 2019, 01:26:16 pm »


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