Quote:
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Originally Posted by zac850
Now, say you were thinking of putting the amps 75 feet or so away from the speakers, would that be OK or not?
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It depends a lot on how much power you're trying to push through what size wire, and the speaker impedance.
Even the best wire has some resistance. For
FOH speakers, I like to use #12
AWG or better and keep the wires as short as possible. I cringe when I see #22 AWG being used as speaker cable at any length.
Let's do a little math (now you're the one to cringe
). Let's say your speaker is 4 ohms, a common value for fairly-high-power boxes, and your amplifier is rated to put 500 watts into a 4 ohm speaker. The first thing we need to know is how many
volts the amplifier will put on the speaker wire. We can figure it out.
We know power in watts = volts X amps: P=ExI. E stands for Electromotive Force, a fancy name for volts. Don't ask me why "I" was chosen to represent amps.
Ohm's Law tells us that amps is volts divided by ohms: I=E/R. If we plug Ohm's Law into the power formula, we get P=ExE/R... we've gotten rid of amps. Simple algebra tells us we can do almost anything to an equation if we do exactly the same thing to both sides of the equation. Let's multiply both sides by R. We wind up with RxP = RxExE/R. The two Rs on the right side of the equation cancel each other out, so we end up wit RxP=ExE, or RxP=E squared. So E is the square root of RxP. Plugging real numbers in, E is the square root of 4x500 = square root of 2000, so E is about 44.72 volts.
Stay with me on this. We're going to use that voltage to figure out how much power is actually getting to the speaker and how much is being wasted in the wire.
Let's assume your 75 feet of speaker wire is the cheap #22 AWG zip-cord a lot of places sell by the spool for home-stereo installations. I have a table that tells me the resistance per foot of various wire sizes. 22 AWG copper is .0165 ohms per foot. Doesn't sound like much, but we've got 150 feet of it, 75 from the amplifier to the speaker and another 75 back to the amplifier. 150x.0165=2.475 ohms! That's in series with the 4 ohms of the speaker, so what the amplifier sees is 6.475 ohms instead of the 4 ohms it was expecting.
What effect will that have on the amplifier? Amplifiers are generally voltage devices. That's why most amplifiers are rated for different power levels with different speaker impedances - the amplifier's fairly steady voltage output will push more power through a lower resistance. Now we're showing it a higher resistance.
44.72 volts will push 500 watts through 4 ohms, but what will it push through 6.475 ohms? Back when we were massaging the power formula, we got to a variation that said P=ExE/R. Let's plug the numbers in: P=44.72x44.72/6.475 = 2000/6.475 = 308 watts. We're only getting 308 watts out of our 500
watt amplifier.
But it gets worse. Let's go back to Ohm's law for a moment. How much current is the amplifier pushing through the speaker (and wire)? I=E/R = 44.72/6.475 = 6.9 amps. That,in turn, lets us figure out the voltage that the speaker sees and the voltage that shows up across the wire. Another form of Ohm's law is E=IxR. The speaker is still 4 ohms, so it sees about 27.6 volts (6.9x4). The rest of the 44.72 volts, 17.12 is spent on the wire.
Now, let's go back to our original power formula, P=IxE, and plug those numbers in. The power the speaker actually sees is 6.9x27.6, or 190 watts. About 118 watts (6.9x17.12) is being wasted in the wire. Because we used long speaker wires of a small AWG size, our 500 watt amplifier is only putting out 308 watts, and of that 308 watts, only 190 is actually getting through to our speaker. We're wasting 118 watts just heating up the cable.
A lot of ready-made speaker cables sold at Guitar Center, Sam Ash and other music stores are 14AWG. It's resistance is .00258 ohms per foot, so our 75-foot cable (150 feet of wire) is now just .387 ohms. I'm not going to show all the math again, but the result is that the amplifier sees 4.387 ohms and puts out about 456 watts. Of that, about 415 watts gets to the speaker and only about 41 watts are wasted in the wire.
In my own system, my amplifiers are right at the speakers. The cables are 5 feet long. The cable is #12 AWG, at .00162 ohms per foot. The cable resistance, then, is only .0162 ohms. The amplifier sees 4.0162 ohms and actually puts out 498 watts. Of that, about 496 watts actually get through to the speakers and only two watts are wasted in the cable.
Bottom line is that long speaker wires are NOT a good idea. Small speaker wires are NOT a good idea. Long, small speaker wires are a very BAD idea. Short, big speaker wires are a very GOOD idea.
John