dellphinus
Member
- Location
- Southern Illinois, USA
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 ]
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 ]