Loudspeaker cable: what to keep in mind
 Dr. Peter Strassacker Loudspeaker design since 1977 Books on material research and field theory Design of loudspeakers like Lagrange 98, Laplace XT, Pascal, Sub 10-60

Which aspects with regard to loudspeaker cable are important?
Peter Strassacker interviewed by
Dennis Frank (12/2005).

Dennis:
Peter, which loudspeaker cable properties are important?

Peter:
The properties of a loudspeaker cable could be described in explicit detail. Let me give you a simplified overview, describing loudspeaker cable sufficiently enough from a physics point of view:

 Picture 1: cable equivalent circuit with input left and output right.

- die ohmic serial impedance Rs
- the serial inductance Ls
- the ohmic parallel impedance Rp
- the parallel capacitance Cp
- the current proximity at higher
frequencies (skin effect)
- audiophile properties

Dennis:
Let's start with an easy aspect: the ohmic serial impedance. What are the implication? What do we have to keep in mind?

### The Serial Impedance Rs

Peter:
The ohmic serial impedance causes loss in the cable, i.e. the power supplied by the amplifier doesn't reach the loudspeaker.

Conductance of a copper cable at 20 degrees centigrade

 Diameterin mm2 Cable lengthin m Resistancein Ohm Conductance lossinto 4 / 8 Ohm *) Speaker output lossinto 4 / 8 Ohm **) Damping ***)into 4 / 8 Ohm 0,75 1 0.045 1.1% / 0.56% 2.2% / 1.1% 89 / 179 0.75 2 0.089 2.1% / 1.1% 4.3% / 2.2% 45 / 89 0.75 4 0.179 4.3% / 2.2% 8.4% / 4.3% 22 / 45 1.5 2 0.045 1.1% / 0.56% 2.2% / 1.1% 89 / 179 1.5 4 0.089 2.1% / 1.1% 4.3% / 2.2% 45 / 89 1.5 8 0.179 4.3% / 2.2% 8.4% / 4.3% 22 / 45 2.5 2 0.027 1.33% / 0.67% 0.67% / 0.33% 149 / 299 2.5 4 0.054 2.67% / 1.33% 1.33% / 0.67% 75 / 149 2.5 8 0.108 5.3% / 2.7% 2.7% / 1.3% 37 / 75 4.0 4 0.0336 1.66% / 0.83% 0.83% / 0.42% 119 / 238 4.0 8 0.067 3.2% / 1.67% 1.67% / 0.84% 60 / 119

*)     Power loss caused by cable.
**)   Loudspeaker power loss with impressed voltage
comprising cable loss and power loss due to less current.
***) Damping = cable resistance/loudspeaker resistance,
total damping = 1 / (1 / cable damping + 1 / amplifier damping)

Even more details are supplied by our Cable Calculator.

Dennis:
What are these figures telling us? The power loss is surely not worth mentioning, isn't it?

Peter:
That's right; even a loss of 8% due to a 4 metre cable with 0.75 mm2 diameter into 4 Ohm speakers doesn't cause any sound problems; 8% represent only a 0.7 dB volume drop. The real problem is more the movement control of the drivers, for this we often use the measurement "damping". This subject was discussed in a previous interview: "How big should the damping factor of an amplifier be", where we stipulated that the cable into 8 Ohm speakers shouldn't have more than 0.1 Ohm serial resistance (into 4 Ohm the resistance shouldn't be more than 0.05 Ohm).

The power that can be transmitted by the cable is usually also not a problem. We've proved this on our automotive hi-fi pages ; a 1.5 mm2 cable, is capable (according to DIN VDE 0298, Part 2) of carrying 20 ampere, i.e. the cable is capable of carrying a sinus signal of P = I*I*R = 3200 Watt to an 8 Ohm speaker.

Dennis:
In a nutshell, the cable connected to an 8 Ohm speaker should have less than 0.1 Ohm resistance. This means:
- a 0.75 mm2 cable is suitable for up to 2 metres
- a 1.5 mm2 cable is suitable for up to 4 metres
- a 2.5 mm2 cable is suitable for up to 7 metres
- a 4.0 mm2 cable is suitable for up to 12 metres

### Serial Inductance Ls

Peter:
It sounds simple, but that's the way it is. Let's move on to the serial inductance Ls. The serial inductance is design related and can be easily influenced by geometry.

A conductor with 2 mm diameter and its feedback in 5 mm distance (axial distance) possesses an inductance L of 0.6045 uH per metre; a conductor with 10 mm axial distance possesses an inductance L of 0.929 uH (calculated according to formulas from /1/). The resistance Z of a cable with 10 mm axial distance per metre is therefore
Z = jωL = 0.116 Ohm
The cable's diameter is 3.14 mm2, possessing a resistance of 0.0066 Ohm, that's 18 times less than the inductive reactance at 20 kHz

Twisted wires where several wires are carrying the signal, on the other hand, show a lower inductance L:

2x four-core Kimber cable 4 VS e.g. has an inductance L = 0.24 uH (at 20 kHz) per metre, representing a resistance Z = jωL = 0.03 Ohm at 20 kHz. That's more than double the ohmic resistance of 0.013 Ohm.

2x eight-core Kimber cable 8 VS e.g. has an inductance L = 0.15 uH (at 20 kHz) per metre, representing a resistance Z = jωL = 0.019 at 20 kHz. That's more than double the ohmic resistance of 0.008 Ohm.

Summed up:
At 20 kHz cable doesn't conduct as well as at lower frequencies. Depending on the cable geometry, the conductance due to serial inductance at 20 kHz is approximately 10 to 20 worse (standard cable), or 2 to 2.5 worse (Kimber Cable) than at lower frequencies.

Dennis:
At a glance that sounds terrible; but then many tweeters have dropping resistors of a few Ohm and maybe an additional resistance of 1 or 2 Ohm might not play such an important role. When using standard cable, however, the tops at 20 kHz are reduced by 0.5 bis 1.5 dB.

Peter:
Well, I have to admit that this effect is stronger than I imagined. Surely, here Kimber Cable has a distinctive advantage.

### The Ohmic Parallel Impedance Rp

Dennis:
Good quality cable has a leakage resistance of more than 100 000 000 Ohm; this should play a role at all, wouldn't it?

Peter:
That's right - even with a leakage resistance of only 10 000 Ohm there would be any influence.

### The Parallel Capacitance Cp

Dennis:
Parallel capacitance stresses an amplifier, but shouldn't otherwise affect much?

Peter:
Correct; standard cable has 10-200 pF per metre, that's negligible. But there are some exotic contenders: According to Stereoplay 1/2006 the MIT EXP 2 cable has a capacitance of more than 10 000 pF (by means of internally added parallel capacitors). There are also terminals with a sort of secret circuitry (= parallel capacitor) promising to improve on the liveliness of reproduction.

Dennis:
The sound liveliness is enhanced with terminals or cable, with built-in capacitors? How does it work?

Peter:
In both cases a capacitor is in parallel to the amplifier output putting a capacitive load onto the amplifier. Generally this is problematic, since the negative feedback of the amplifier - controlling the frequency response, the low output resistance and the low loss - is affected.

The capacitive load causes the amplifier to lose somewhat in stability, to exaggerate high frequencies and to capture more high frequency noise.

This leads to a more vibrant possibly more authentic sound. Nevertheless, I disapprove this vehemently, because:
a) the amplifier loses stability
b) the recording studio could have added this type of excitement with an aural exciter.
(the correct amount of "excitement" is important. If it's too much it's just horrible)
c) some amplifier might lose control and stability and consequently overheat the tweeters.

Dennis:
Sometimes the terms current proximity and skin effect come up. What's that?

### Skin Effect

Peter:
Current proximity, better known in the audio industry as skin effect, crops up in AC with increasing frequency. The current generates magnetic fields causing a higher reverse voltage within the conductor. Therefore, the inside of the conductor contributes less to the current flow than the outside (skin).

This effect is dependent on frequency. The outside area still carrying current can be calculated (refer to /1/).

 Skin effect table: This table shows how far down the conductor carries the current. Frequency 100 Hz 1 kHz 10 kHz 20 kHz 40 kHz 100 kHz Penetration Depth 6.0 mm 2.0 mm 0.6 mm 0.4 mm 0.3 mm 0.2 mm

If we have a cable with 1.8 mm diameter (2,5 mm2), then the wire conducts a frequency of 20 kHz only down to a depth of 0.4 mm. Conducted is at a radius r=0.9 mm:
altogether an area of π*r*r = 2.54 mm2
thereof with bad conductance (inside): π*(r-0.4 mm)*(r-0.4 mm) = 0.79 mm2
the good conductance area is therefore 2.54 mm2 - 0.79 mm2 = 1.75 mm2.
The impedance is increased only by a few umpteen percent. That's not vital (let's recollect: the inductance caused a deterioration by a factor between 15 and 18). At larger gauge wire, however, the effect will be stronger.

Here also, the stranded wire of Kimber cable has an advantage, since the individuals strands don't have a diameter of more than 0.4 mm causing the skin effect to occur at frequencies above 20 kHz.

### Audiophile Properties

Dennis:
Now I have the following question: What properties still need to be discussed, that have an influence the sound quality?

Peter:
Well, we haven't spoken about OPC cable, about mono-crystalline cable and about the difference between solid and stranded wire. Quite often it is said that the sound just "disappears" in stranded wire.

The law of physics doesn't support this opinion. Current chooses the shortest possible route according to the electrical field, it certainly doesn't disperse. Also, the opinion that the current continues to run through strands is not convincing: Current, traveling at almost the speed of light, causes wave length λ of around 15 000 000 - 15 000 m at audible frequencies (20 Hz to 20 kHz). To support this opinion of current dispersing in a strand, a strand without any contact to a neighbouring one - at the critical frequency of 20 kHz - needed to be λ/2, i.e. 7500 m longer than the neighbouring strand. Usually, an insulated strand is just a 1/1000 000 longer.

Dennis:
Are then some of the characteristics that are noticed by many customers just imagination?

Peter:
This is difficult to answer. We should try to find out,
- what is just imagination (if you are in doubt do a blind test)
- what is fraud (I know of an alleged cable test where the sound quality was changed with a remote control)

We suggest to use cable with a geometry that makes sense (e.g. braided strands like Kimber cable), made of (preferably) pure copper.

If you are still in doubt, just do a blind test at home with a friend.

In a nutshell,
- you should use cable with less than 0.1 Ohm resistance to drive 8 Ohm speakers and
- where the two conductors are not too far apart (causing inductance that leads to loss of high frequencies).
An excellent solution is cable with braided strands like Kimber cable. It also helps when the conductor is relatively clean (otherwise there could be lattice imperfection). Everything else is rather subjective.

### Suggested Literature:

/1/  G. Strassacker: Rotation, Divergenz und das Drumherum, Eine Einführung in die
Elektromagnetische Feldtheorie, 4th Edition, B.G. Teubner, 1999, page 130 et seq.