one for the theorist

Martin Czech martin.czech at intermetall.de
Wed Jul 14 16:36:02 CEST 1999


:::Is this anything to do with the "skin effect" theory? This is where 
:::it is believed that electrons tend to flow on the outside (skin) of a 
:::wire rather than straight down the centre,hence the theory of 
:::loudspeaker cables made from lots of small strands as opposed to a 
:::solid core.....
:::

This is not believed, but measured in accordance with theory:

For a cylindrical copper wire with radius r0 we can set

x=r0/2*SQRT(pi*sigma*u)*SQRT(f)

with 

u=0.4*pi*10e-6 V/(A*s*m)
sigma=57 m*A/(mm**2*V)

x=r0*0.0075/(mm*SQRT(Hz)*SQRT(f)

R0 is the dc resistance, R the ac resistance of the wire due to skinn effect.

Then :

R/R0 ~ 1+1/3x**4        for x<1
R/R0 ~ x + 0.25 +3/64*x for x>1

This means the resistance will double if x ~ 2

This resistance doubling for copper wire with diameter d will happen at


d        Frequency

0.2 mm   7.1   MHz
0.4 mm   1.7   MHz
1.0 mm   284   kHz
2.0 mm   71.1  kHz
4.0 mm   17.7  kHz

This means thick wires are useless for large frequencys (also non isolated
bunches of wires).

But: the dc resistance is still very small, so doubling won't hurt.
I still don't believe that any audible effects may happen with normal
lenght cable.

m.c.







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