# Skin effect

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#### dellphinus

##### Member
This is info collected from various sources on skin effect. Found with Google searches on "Skin Effect
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 ]

#### gwz2

##### Senior Member
Re: Skin effect

When I try your last formula for inches at 60 Hz, it seems the answer would be not probable.

20.20 - - - inches ???

#### dellphinus

##### Member
Re: Skin effect

Originally posted by gwz2:
When I try your last formula for inches at 60 Hz, it seems the answer would be not probable.

20.20 - - - inches ???
Sorry about that. I checked the equations I found at work, but I didn't bring them home. I thought I had found the same posts again, and copied them, but obviously the last one was a different one, and the division sign was left out. I fixed it.

And, these aren't mine, they came from several engineering and audio threads on Usenet.

Using both equations gives 8.5 mm or .337 inches at 60 Hz

[ March 02, 2003, 12:04 AM: Message edited by: dellphinus ]

#### luke warmwater

##### Senior Member
Re: Skin effect

I still concur that skin effect is on each strand of a multi-strand cable and not on the outside strands only, but this is just my opinion. I will try to research it farther unless someone can show me hard evidence otherwise.

#### don_resqcapt19

##### Moderator
Staff member
Re: Skin effect

Luke,
Look at this site on Litz wire . This is some good information about a woven insulated strand conductor to reduce the skin effect.
Don

#### luke warmwater

##### Senior Member
Re: Skin effect

Don, thanx for the good reading.

#### harryg

##### Member
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