A co-worker asked me a question tonight and I was unable to answer it.
He has a 1000 watt subwoofer and a 1000 watt amplifier. For purposes of discussion, assume we are not applying maximum power to a maximum spec. speaker.
His question: how to calculate which size wire to use. He assumes it's 1000 watts divided by 12 volts equalling 83 amps.
I guess this has been a variation of my curiosity. I've been curious what calculations are used to spec an amplifier of being 1000 watts.
I understand a home speaker is 8 ohms. Using P= I^2(R) gives a current of
12 amps.
Is this a safe calculation for maximum current?????
The question to ask you colleague is: what measurement system is used to come up with 1000 watts. Many amplifiers use some 'interesting' measurement system which seems to be based on "think of a number and multiply it by another number" to get the wattage.
Why 12v? is it an in-car system? If it really was providing 1000w then you'd need a 100A supply to the amplifier.
You really ought to be asking on a hifi newsgroup - when it comes to things like speaker wire, decisions are rarely made on mere engineering prinicples and logic.
However, let's look at some of those boring principles..
If the power output really is 1000W rms, which it mostly isn't and the speaker impedance at that frequency really is 8 ohms, which it won't be, then the current would be about 12A.
However, not only does P=I^2 x R, .....P=V^2 /R. Hence V will not be
12v, but nearer 90.
Which all ties together, because P = I x V.
Where does that 90v come from in a car? Simple, one of the biggest and most expensive part of a car high power amplifier is nothing to do with the audio - it is the converter that steps the 12v supply up to a suitable higher voltage at high power. Useful to know, poking around in a running "12v" amplifier could easily connect you to a high enough voltage with enough power to kill.
Now, when it comes to sizing the speaker wires, audio purists wouldn't dream of using cable designed to handle *mains* at 12A, for that distance. An electrical engineer might, because it would be perfectly safe and putting in anything better would not be cost effective.
However, the audio guy would point out that *there* would be power lost in the wire. That audio signals cover a far higher frequency range and so it isn't merely a problem of dc resistance. That impurities in the copper can produce both a non-linear response and non-linear current distibution..
So, rather than use 12A mains cable, he will use something akin to 200A welding cable composed of thousands of strands of extremely high purity copper wire, individually silver coated and Litz woven...
I remember reading an article in "Wireless World", now known as "Electronics world", by no less an authority than Douglas Self, about why he uses "Woolworths" mains cable to wire up his loudspeakers! [1]
He is the designer of a number of high performance amplifiers, author of any number of papers and articles on audio amplifier design and his website can be found at:
It's not quite *that* silly to use larger wire. The amplifier has quite a lot of feedback, and acts as a (controlled) voltage source with very low impedance. If the damping factor is 100 with an 8 ohm load, the amp output impedance is 0.08 ohm, and that helps to control the cone in the speaker (which is not a resistive load, but closer to a permanent magnet DC motor). Any speaker cable resistance is in series with the amplifier output impedance, and degrades the damping correspondingly.
How much resistance you can tolerate is a matter of argument.
For that matter, someone wiring 12 V auto electrics will use a larger diameter wire to carry 12 A than you'd use for 12 A at household line voltages. A 5 V drop in the wires is not a big deal when the supply voltage is 120 V or 240 V, but it's a big deal when the supply is only
12 V. So even if you're only talking about DC, and only resistive loads, you use heavier wire for the same current at lower voltage.
Except for monstrously large amplifiers, speaker circuits are lower voltage than line voltage.
Dave (who, I must admit, uses 16 or 18 gauge speaker wires)
Absolutely. They are attempting to calculate speaker wire as if it were a power cord. But as you point out there is much more to it than that. While there is also a sort of religion about speaker wires amongst the audiophools, generally speaking the rule is that you should use as heavy a conductor as you can practically use/afford/ install etc.
Yes it is. Some people argue like mad that you can't hear any difference. But they are Phools. Virtually ANYONE can hear the difference between super heavy braided speaker wire and say 22 gauge bell wire found on some cheapo players. Now exactly how much copper you need until you can no longer hear any difference is a matter of argument and does depend on how long the wire runs are. Sure, you COULD "wire" your speakers with 1" copper tubing and they'd sound great, but it makes it hard to move the speakers around! And on the other hand wiring expensive components with the ever-popular lamp cord is sure to make your system sound like you spent a lot less money than you really did!
Bottom line: Just get as big a wire as you can practically use. Be it heavy duty power too extension cord, special speaker wire (I've got some that is rubber covered flat braid...VERY nice and was cheap too). or anything else you pick up cheap. Don't believe all the crap about oxygen free, virtually all electrical wire is oxygen free so the wire remains flexible and won't work-harden.
Usually for shorter runs 16 gauge is getting pretty close to where you can't hear much of a difference. For longer runs on high-end gear, I would consider heavier wire.
| Absolutely. They are attempting to calculate speaker wire as if it | were a power cord. But as you point out there is much more to it than | that. While there is also a sort of religion about speaker wires | amongst the audiophools, generally speaking the rule is that you | should use as heavy a conductor as you can practically use/afford/ | install etc.
The big issue as I understand it is that an "8 ohm" speak is not really
8 ohms across the whole range of audio frequencies. Things are supposed to be designed so that a consistent voltage at any frequency gives a consistent level of sound. Maybe the high end speakers actually achieve that. The problem is, adding a resistance in the line will reduce those frequencies that the speaker has a lower impedance for more so than the the ones it has a higher impedance for. So, the less resistance in the wire, the better ... but only worth it for the high end speakers that do achieve a more accurate sound ... so you don't ruin that sound.
Maybe they should have used a higher standard speaker impedance :-)
A speaker is generally a pure resistance at its free-air resonance frequency. Below that, it is inductive, above it is capacitive. The impedance at resonance is generally quite high relative to its nominal impedance and enclosures, etc. are often designed to lower the resonant frequency so as to extend the speaker's useful lower range. Above resonance, the impedance tends to be fairly uniform out to some higher frequency, where it again rises and may even develop another resonance.
Applying Phil's analysis, adding a series resistance then will have less effect on the lower and higher frequencies (where the impedance is above the nominal impedance) and relatively greater effect on the wide band of frequencies in mid-range at which the speaker is rated. Still, it is difficult to see how a small fraction of an ohm can significantly affect the loudness of an 8 ohm speaker, even in mid-range.
Some interesting plots of speaker impedance can be found here:
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