How thick?

[icehockeyboy]

At high frequencies, any wire thicker than 1.0mm in diameter is largely wasted. (At 10kHz, the current density in a copper wire 1.0mm in diameter, is 97% compared with that at the edges. This is the 'skin' effect.)

However to maintain a decent damping factor ( control of the back EMF of the speaker), the loop resistance of the speaker cable should be no more than 5% of the nominal speaker impedance. So you do the maths - like mosts things in audio, it's all a bit of a compromise.

The back EMF?

You’re Unbelievable!


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[Barry]

The back EMF?

You’re Unbelievable!


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Uhh ?

[RMutt]

‘Uhh?’

https://m.youtube.com/watch?v=K5kr2OBhh4c

[Audio Al]

‘Uhh?’

https://m.youtube.com/watch?v=K5kr2OBhh4c

[Pharos]

I don't understand the first para by Barry;

"At high frequencies, any wire thicker than 1.0mm in diameter is largely wasted. (At 10kHz, the current density in a copper wire 1.0mm in diameter, is 97% compared with that at the edges. This is the 'skin' effect.)"

But the second part is correct IMO, although maybe not a brilliant description.

[Barry]

I don't understand the first para by Barry;

"At high frequencies, any wire thicker than 1.0mm in diameter is largely wasted. (At 10kHz, the current density in a copper wire 1.0mm in diameter, is 97% compared with that at the edges. This is the 'skin' effect.)"

But the second part is correct IMO, although maybe not a brilliant description.

Alternating current flows differently to direct current in a conductor. With DC, the current density is constant and uniform across the cross section of the conductor. With AC, the current density tends to be concentrated near the surface of the conductor. This effect depends on the frequency, and on the resistivity (and permeability) of the conductor. Current flow is thus likened to as flowing in a cylindrical sheath (or 'skin') at the surface. The actual behaviour is more complicated than this, but a parameter called the 'skin depth' is useful to give an idea of this variation.

Thus across the diameter of a circular wire, the current density will be 'U shaped'; being lower at the centre of the wire compared with that at the surface. At low frequencies the deviation of current density from uniformity is very small, at high frequencies the deviation is large. The variation is described by Kelvin's expression; an expression involving Bessel functions with complex argument. But as an example, consider a copper wire 1mm in diameter. At 10kHz the current density at the centre of the wire is 97% compared to that at the surface, so is virtually uniform. If the diameter is enlarged, the current density distribution becomes increasingly non-uniform, and the current density at the centre is small. As the diameter is further increases, the current density at the center of the wire will fall to near zero, thus the conductor material there is being unused.

The 'skin depth' in copper at 10kHz is 0.66mm, so for distances (r, measured in mm) away from the surface into the conductor, the current density falls off approximately as exp(-r/0.66). Worse still, the phase of the current increases by 1 radian per skin depth going into the conductor, so not all of the current is coherent in phase; leading to a 'time smearing' of the signal.

The 'ideal' speaker cable would thus consist of bundles of conductors having an effective diameter of no more than 1mm (preferably no more than 0.5mm) that are individually insulated so as to avoid this skin effect. The total number of bundles, and hence overall cross section will be chosen so the cable has a sufficiently low resistance per unit length.

Addendum
I ought to point out that the phase incoherence or 'time smearing' effect is very much overplayed by speaker cable manufacturers, and IMO the effect is very small, as it is only a small part of the signal current that is delayed. It is thus not essential that a speaker cable be made up of a bundle of individually insulated small diameter wires, only ideal.

The effect of using sensible stranded wire at audio frequencies will be an increase in the resistance per unit length over that for a direct current. The increase is by a factor of (1 + ((r/delta)²)/48), where r is the radius of the wire and delta is the skin depth (= 66/sqrt(F) , where F is the frequency in Hz). If you do the sums the increases are utterly negligable.

[icehockeyboy]

Alternating current flows differently to direct current in a conductor. With DC, the current density is constant and uniform across the cross section of the conductor. With AC, the current density tends to be concentrated near the surface of the conductor. This effect depends on the frequency, and on the resistivity (and permeability) of the conductor. Current flow is thus likened to as flowing in a cylindrical sheath (or 'skin') at the surface. The actual behaviour is more complicated than this, but a parameter called the 'skin depth' is useful to give an idea of this variation.

Thus across the diameter of a circular wire, the current density will be 'U shaped'; being lower at the centre of the wire compared with that at the surface. At low frequencies the deviation of current density from uniformity is very small, at high frequencies the deviation is large. The variation is described by Kelvin's expression; an expression involving Bessel functions with complex argument. But as an example, consider a copper wire 1mm in diameter. At 10kHz the current density at the centre of the wire is 97% compared to that at the surface, so virtually uniform. If the diameter is enlarged, the current density distribution becomes increasingly non-uniform, and the current density at the centre is small. As the diameter is further increases, the current density at the center of the wire will fall to near zero, thus the conductor material there is unused.

The 'skin depth' in copper at 10kHz is 21um, so for distances (r, measured in um) away from the surface into the conductor, the current density falls off approximately as exp(-r/21). Worse still, the phase of the current increases by 1 radian per skin depth, so not all of the current is coherent in phase; leading to 'time smearing' of the signal.

The ideal speaker cable will thus consist of bundles of conductors having an effective diameter of no more than 1mm (preferable 0.5mm) that are individually insulated so as to avoid this skin effect. The total number of bundles, and hence overall cross section will be chosen so the cable has a sufficiently low resistance per unit length.

Wot ‘e said!


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[Pharos]

Many thanks Barry, rather than my not understanding the principles of skin effect, which I studied in '69, it was your description I didn't get.