We’ve been talking about speaker cable and have covered resistance and capacitance in past columns, which are also posted in the Wired for Sound index page.
There was a little error in the previous column of Sept. 12. It was a Web address to a chart that shows cable distances and losses at standard speaker impedances and for 70-volt distributed systems.
The correct URL is http://bwcecom.belden.com/catalog/TechInfo/TechSpeaker.htm
Now let’s discuss inductance, impedance and skin effect.
Inductance
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Inductance is the ability of a wire to store the magnetic field of a signal. This is most important at low frequencies, because sending DC down a wire produces an electromagnet, with an unchanging field.
We are talking about music and voice signals, so these would be “changing” signals.
Inductance is the opposite of capacitance, so the effect on frequencies also is opposite. A capacitor running at a certain frequency produces “capacitive reactance.” The same frequency with an inductor produces “inductive reactance.”
Inductance can be affected by several factors. The first is the size of the wire itself – the bigger the wire, the larger the inductance. This is most often cited by those considering speaker cables.
As mentioned in a previous column, the most popular size, at least among the “high-end audio” crowd, is 10 AWG. This is a hefty wire size.
So inductance is a major consideration, right? Well, no.
If you’ve ever played around with inductors, coils and transformers, you will be aware that it takes a lot of wire to make even a small inductor. Even then, you have to wind the wire up to increase the inductive effect.
A straight conductor has only microscopic amounts of inductance. In fact, a 10 AWG wire, such as in 10 AWG zip cord, has only about 0.06 microhenries of inductance per foot. This is why you will never see the inductance listed in almost any wire and cable catalog.
The effect of capacitance, capacitive reactance, is much more prominent. Because inductive reactance and capacitive reactance cancel out, capacitance always is the winner.
This is why capacitance is more often mentioned in a wire and cable catalog and inductance is not.
Impedance
No subject is more misunderstood, especially among the high-end audio crowd, than impedance.
Impedance really is a combination of resistance, capacitance and inductance in a cable. So why isn’t the impedance of a cable, like a speaker cable, mentioned in any catalog?
All cable has an impedance. It’s just that, at analog audio frequencies, impedance is not important.
Veteran readers of this column will know where I am going next: to a discussion of wavelength. Unless a cable is a quarter of a wavelength at the frequency of interest, the impedance doesn’t mean anything.
For instance, the wavelength at 20 kHz, arguably the highest frequency you can hear, is 15,000 meters or nine miles. A quarter-wavelength is 2-1/4 miles. Even if you consider 1/8th wavelength to be the critical distance, that requires a cable over one mile.
You must also factor in the quality of the insulation or velocity of propagation. So let’s say you choose a very bad PVC, one that has a 50 percent velocity. You’re still talking about a cable that is over half a mile long before the impedance means anything!
The graph in Fig. 1 shows why. Resistance affects the total impedance until the cable gets to a frequency where resistance has no effect. Then only the inductance and capacitance are left, and this impedance is then stable out to the gigahertz.
The impedance of the cable, once it has settled into a single value, is called the “characteristic impedance.” This does not occur until one is well into the megahertz, so this does not apply to any analog audio cable.
But does audio cable have an impedance? Sure it does. But it is changing from a very high number (infinity at DC, 0 Hz), to the characteristic at 10 MHz or so. So, if someone says they have “8-ohm speaker cable,” you would really have to ask them, “At what frequency is it 8 ohms?” It’s a different value at a frequency above or below the one at which the calculations are made.
So why does resistance have an effect, but less and less as the frequencies on it get higher? The answer is something called “skin effect,” our next subject.
Skin effect
As frequencies go higher and higher, electronic signals begin to move from the whole conductor to the outer layer, the “skin” of a conductor. When you are in the megahertz, this can be a serious effect.
This is why, for instance, CATV/broadband cable has copper-clad steel center conductor. At Channel 2 (54 MHz) and above, only the skin of the conductor is carrying the signal. The rest of the wire can be anything: aluminum, steel – it could be empty! Steel is most commonly used because it is cheap and it is strong.
How much skin effect is there at analog audio frequencies? I used to say “none,” but that’s not completely true. After all, even Fig. 1 shows that there is a slope, meaning that less and less of the conductor is being used.
There is a simple formula for the skin depth (in inches) for copper conductors:
This is a rough formula, but is fairly accurate up into the gigahertz for copper conductors.
What does it tell us about speaker cable, such as a 10 AWG conductor? If you’re going to compare this to the diameter of a particular wire, you have to double the skin depth. The diameter is all the way across the wire, and the skin depth appears at “both ends” of the diameter as shown in Fig. 1.
What this means is pretty simple. At 20 kHz, small wires are used completely; that is, the skin depth is equal or greater than the diameter. For a large wire, such as a 10 AWG speaker cable (diameter 0.115 inches), the entire wire is used as a conductor until you get to 2 kHz.
At 2 kHz the signal begins to migrate to the outside of the wire. At 20 kHz, generally the analog audio frequency limit, 68 percent of that 10 AWG wire is being used.
Does that mean we should use hollow wires, or copper-covered base metals? No, in fact the reverse is indicated.
The majority of power going to a speaker is low-frequency power. Anyone who has played with multiple amplifier setups is aware of this. Much more power is used to drive low frequencies than high.
This table shows the approximate percentage of power:
Woofer (below 300 Hz) = 65 percent
Midrange (below 3 kHz) = 30 percent
Tweeter (above 3 kHz) = 5 percent
Therefore, the cable to the speaker must be all copper because most of the power (i.e., from 2 kHz on down) will want to flow down the entire conductor.
We’ll finish our look at speaker cable next time with more exotic specifications such as copper purity, and take a look at basic speaker wiring techniques.
