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Re: Using skin effect
Subject: Re: Using skin effect
Date: Sun, 04 May 1997 15:49:31 -0700
From: Bert Hickman <bert.hickman-at-aquila-dot-com>
Organization: Stoneridge Engineering
To: Tesla List <tesla-at-pupman-dot-com>
References:
1
Tesla List wrote:
>
> Subject: Re: Using skin effect
> Date: Sat, 3 May 1997 22:34:17 +0500
> From: "Alfred A. Skrocki" <alfred.skrocki-at-cybernetworking-dot-com>
> To: Tesla List <tesla-at-pupman-dot-com>
>
> On Mon, 28 Apr 1997 20:18:06 -0700 Bert Hickman
> <bert.hickman-at-aquila-dot-com> wrote;
>
> > All,
> >
> > Alas, the perils of an early morning post! The above gives the factor
> > (x) of AC resistance divided by DC resistance, not skin depth! Sorry
> > 'bout that!
> >
> > Skin depth = 1/SQRT(Pi*f*Uo*a) for a cylindrical conductor (meters)
> > where f = Hertz
> > Uo = 4*pi*10-7 Henry/meter
> > a = 5.80x10^7 mho/m (conductivity of copper)
> > = 6.17x10^7 mho/m (conductivity of silver)
> >
> > Copper skin depth = 66.1/SQRT(f) millimeters
> > = 2602/SQRT(f) mils
> >
> > Silver skin depth = 64.1/SQRT(f) millimeters
> > = 2523/SQRT(f) mils
> >
> > Comparing skin depths (in mils = 0.001") of the two metals at various
> > frequencies:
> > Skin Depth (mils)
> > f Silver Copper
> > ====== ====== ======
> > 10 kHz 25.2 26.0
> > 50 kHz 11.3 11.6
> > 75 kHz 9.2 9.5
> > 100 kHz 8.0 8.2
> > 200 kHz 5.6 5.8
> > 300 kHz 4.6 4.8
> > 400 kHz 4.0 4.1
> > 500 kHz 3.6 3.7
> > 750 kHz 2.9 3.0
> > 1000 kHz 2.5 2.6
> >
> > As can be seen, copper tubing is very hard to beat! At typical Tesla
> > Coil frequencies, smooth copper tubing is almost as good as it gets!
> > Only pure silver or relatively thick silver plating can beat it.
>
> Interesting equation Bert, where did you get it from?
>
>
> Sincerely
>
> \\\|///
> \\ ~ ~ //
> ( -at- -at- )
> -----o00o-(_)-o00o-----
> Alfred A. Skrocki
> alfred.skrocki-at-cybernetworking-dot-com
> .ooo0 0ooo.
> -----( )---( )-----
> \ ( ) /
> \_) (_/
Alfred and all,
This particular form, for a good cylindrical conductor, came from
"Engineering Electromagnetics, 2nd ed." by William H. Hayt, Jr.,
McGraw-Hill Book Co., 1967, page 344. This is the result of taking the
more complex equations for potential and current density (presented
earlier in the chapter), and solving for the depth at which the current
decreases to 1/e or 37% of the value seen at the outer surface of the
conductor. The only thing I've changed are the units to go to CGS or
English equivalents.
Skin depth REALLY means that the average power loss in a conductor with
skin effect is exactly the same as that if the total current flow was
uniformly flowing through a tube whose wall thickness was exactly one
skin depth.
Even at relatively low frequencies skin effect can still be significant.
For example, skin depth at 60 Hz for copper is about 8.53mm, or about
1/3 of an inch. A 4" x 2" high-current busbar in a power plant can be
made tubular, with only 1/2" wall thickness, and will still be virtually
as effective as a solid conductor.
-- Bert --