zac850 said:
Now, say you were thinking of putting the amps 75 feet or so away from the speakers, would that be OK or not?
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