#### dellphinus

##### Member

- Location
- Southern Illinois, USA

Stranded Litz"

Source 1:

THE SKIN EFFECT

From the book "Applied Electromagnetism", by Liang Chi Shen and

Ju Au Kong, PWS (ISBN 0-534-07620-3), we have:

Skin Depth (meters) = SQRT( 2 / (w * u * o) ),

where

w = 2 * pi * frequency

u = permeability in free space = 4 * pi * 10^-7

o = conductivity for copper = 5.9 * 10^7

At DC, we see by inspection that the skin depth is infinite (w = 0).

At 20 Hz, we see that

Skin Depth = SQRT( 2 / (2 * pi * 20 * 4 * pi * 10^-7 * 5.9 * 10^7) )

= SQRT( 2 / (8 * pi^2 * 20 * 5.9) )

= SQRT( 2 / 9316.906 )

= 14.65E-2

= 14.65 mm

At 20 kHz, we see that

Skin Depth = SQRT( 2 / (2 * pi * 20000 * 4 * pi * 10^-7 * 5.9 * 10^7) )

= SQRT( 2 / (8 * pi^2 * 20000 * 5.9) )

= SQRT( 2 / 9316906.6 )

= 4.6E-4

= .4633 mm

Now, 12 AWG wire has a diameter of 0.0808" (from "Handbook...",

REA, ISBN 0-87891-521-4), which is

0.0808" = 0.0808" * 25.4 mm/" = 2.052 mm dia

and a resistance of 1.619 ohms/1000', or roughly 0.0053 ohms/meter

So, at DC, the cable has infinite skin depth, thus uses the full diameter,

and results in a resistance of 0.0053 ohms/meter.

Also, at 20 Hz, we see that the skin depth is much greater than the diameter

of the wire; hence there is NO skin effect at 20 Hz.

Source 2:

Watch out here... we haven't really defined "skin" yet. The current being

conducted through the conductors drops off exponentially with depth, so

it's not as if it drops off discontinuously at some point. The skin effect

is defined at the point below which 1/e of the current is conducted (where

e is about 2.72). It's not any magic point, it just makes the math a lot

easier. It's possible for comparatively subtle effects to still exist

even if the cable is thinner than twice the skin depth,

Source 3:

Skin depth is the thickness of conductor where the majority of AC

current is concentrated. The AC resistance of a given conductor is

approximately the same as the DC resistance of a hollow tube having a

wall thickness equal to one skin depth. Skin depth is given by the

equation

skin depth (cm) = 5033 sqrt(p/uF) (Terman)

where p (rho) is in ohms/cm^3, and F is the frequency in Hertz. u

(mu) is the relative permeability of the conductor. For copper, the

formula reduces to

skin depth (inches) = 2.61 / sqrt(F)

[ March 01, 2003, 11:36 PM: Message edited by: dellphinus ]