Selecting a loudspeaker cable

Many people spend a lot of money on buying expensive speaker cables, trusting that sound quality can be improved by them. The speaker cable is a simple part (at least in the audio frequency range), it's described by the following parameters: resistance, capacitance and inductance. Besides I would say a few words on skin effect, which also plays a role. Let's see, which of these parameters can affect sound quality.

Capacitance

Power amplifiers can be designed so they can tolerate the capacitive load presented by cables. The capacitance of the loudspeaker cable can normally in no way affect the sound quality or frequency response of the loudspeaker hooked up to it.

Inductance

Due to inductance, the impedance of the cable increases with increasing frequency, therefore the voltage delivered by the amplifier is partially lost on the cable. This phenomenon is measurable in the audio frequency range, but with traditional cable structures (parallel pair or coaxial) the inductance is so low (0.3…0.6 µH/m), that it doesn't cause audible decrease of high frequency sound in case of usual cable lengths. Just think about it: the voice coil inductance of conventional dynamic tweeters is usually 50…100 µH, many times higher than the inductance of a simple 5 meter long common "electric wire". Yet, the inductance of tweeters doesn't bother anyone, though it reduces the highest frequencies much more than the speaker cable. The insufficiency of high frequency sound can't be solved by an expensive low-inductance cable, it can be solved by turning up the treble tone control or by the redesign of the crossover or selecting a more suitable tweeter.

Resistance

The resistance of the cable and the impedance of the loudspeaker constitutes a voltage divider, and so the voltage delivered by the amplifier is divided between the cable and the loudspeaker, and part of the delivered power is dissipated on the cable. This in itself is not a great disadvantage, the loudspeaker will be driven with a few percentage power loss. The problem may lie in that the impedance of loudspeakers is usually not constant with respect to frequency, therefore the resulting voltage division is also frequency dependent and this changes the the frequency response curve of the loudspeaker. So if the impedance of the loudspeaker if not flat and the resistance of the cable is too high, then an even audible change in tonality can occur compared to an ideal (very low) cable resistance. Besides, there is another problem with high resistance cables, which presents itself especially in ported enclosure loudspeakers. The resistance of the cable increases the Qes of the woofer, this causes its Qts to rise, and this practically means that the system will become somewhat mistuned. With the usual cable lengths and diameters however, this phenomenon results in max. 0.5...1 dB change in the low frequency range of ported enclosure speakers, which is below audible level. Nevertheless, these phenomenon indicate that resistance is the most important parameter of loudspeaker cables, which in worst case may as well cause audible differences in the frequency response (tonality) of loudspeakers.

Recommended cable cross section

The table below contains my recommended minimum cable cross sections for 4 Ω and 8 Ω loudspeakers, for different lengths of copper clad aluminum (CCAW) cables. If you choose cable cross section according to the table, then the voltage drop on the cable will not cause higher than 0.5 dB sensitivity loss on the loudspeaker, and the chances of audible deviations in the frequency response due to cable resistance will be negligible.


8 Ω loudspeaker

4 Ω loudspeaker

Cable length up to 5 m

0.75 mm2

1.5 mm2

Cable length 5...10 m

1.5 mm2

2.5 mm2

 

Decreasing the resistance

The specific resistance of copper is about 40% lower than aluminum, therefore a fully copper cable of the same cross section has about 40% lower resistance than a CCAW cable. Oxid free copper has not much lower resistance than plain copper, in my opinion it doesn't worth the higher price. I regard silver plated copper an even more superfluous waste. The cheapest and most obvious way of reaching lower cable resistance is using a thicker cable.

Low contact resistance of connections

The minimal resistance of loudspeakers generally falls in the 3...8 Ω range, relative to that the resistance of connectors may be significant. Therefore it is important for both the amplifier output and the loudspeaker connectors to have low contact resistance. If you connect a bare cable end, fasten the screw tightly. Gold plated connectors are not luxurious here, but they really make sense, only if both the male and the female ends of the connectors are gold plated. Don't use those run-of-the-mill spring loaded loudspeaker connectors in quality loudspeakers. The Speakon connector type, mainly used in pro audio equipment can be a good choice even for home audio speakers and amplifiers.

Damping factor

The resistance of loudspeaker cable deteriorates the effect of one of the amplifier parameters, the so-called damping factor. Many people don't know that in the crossover of passive loudspeakers, usually there is coil serial to the woofer that in general has resistance ranging 0.3…0.6 Ohm. This decreases the effective damping factor just as cable resistance does. It is very doubtful anyway if damping factor, unless it is very low  ̶  like <20, has any sensible meaning regarding sound quality.

The skin effect

In cables, a phenomenon called skin effect is observed as frequency increases. With increasing frequency, the current is more and more "squeezed out" to the outer parts of the conductor. Since the inner parts of the conductor carry little current at high frequencies, the effective cross section of the cable is reduced, its resistance increases. This has similar effect as cable inductance: at higher frequencies more and more voltage drops on the cable and less on the loudspeaker. The skin effect "hits", thicker cables more severely than thinner ones. The material dependent parameter of skin effect is the skin depth, which specifies the distance from the surface at which the current density is reduced to its 1/e (0.37) proportion. The skin depth for metallic conductors to a good approximation is:

\delta=\sqrt{{2\rho }\over{\omega\mu}}

ρ = specific resistance of conductor

ω = circular frequency of current = 2π × frequency

μ = absolute magnetic permeability of conductor

The skin depth in copper is 0.46 mm at 20 kHz, in aluminum, it's 0.58 mm. Using a skin effect calculator, one gets that the resistance of an aluminum cable of 2.5 mm2 cross section (1.8 mm diameter) at 20 kHz is 11% higher than at low frequencies. In case of a 0.75 mm2 cable, the increase in resistance is negligible, approx. 1%. This 11% seems like a big deviation, but keep in mind that the resistance of tweeters is typically 4...8 Ω, while the resistance of loudspeaker cables with usual lengths and cross sections is max. a few tenths of an Ω. For example, the there-and-back resistance of a 5 meter CCAW cable with 2.5 mm2 cross section is 0.1 Ω. A 11% increase of this resistance causes such a negligible drop of sound pressure on a 4...8 Ω tweeter, even at 20 kHz that is inaudible for human hearing. So I have to conclude that the practice of interwinding many thin, insulated wires to lessen the influence of skin effect is plainly a waste of time and money.

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