[Prev][Next][Index][Thread]

Re: Using skin effect

Subject:  Re: Using skin effect
       Date:   Mon, 28 Apr 1997 20:18:06 -0700
       From:   Bert Hickman <bert.hickman-at-aquila-dot-com>
Organization:  Stoneridge Engineering
         To:   Tesla List <tesla-at-pupman-dot-com>
 References: 
            1


> > > HI Alfred, all,
> > >                 One skin depth in copper is 66/SQRT(f) mm.
> >
> > I had checked my notes and found the equation 2.6/SQRT{f} inches.
> > Which when multiplied by 2.54 to convert to mm. yields 66.04/SQRT{f}
> > mm. which compares favorable with your equation.
> >
> > > The definition of a skin depth is that distance inwards to the point
> > > where current has dropped to 1/e of its total value. The equation
> > > above has resistivity factored in so will be different for silver.
> >
> > Hmmm, in my notes the equation is listed as being independent of
> > materials or resistance.
> 
> >
> > > In fact, the skin depth on silver is not as deep due to the higher
> > > conductivity. If a silver film is not thick enough I have heard
> > > things could actually be worse than bare copper.
> >
> 
> Alfred,
> 
> It turns out it is a function of the resistivity AND the magnetic
> permeability (u) of the conductor. The latter is usually ignored, since
> u for silver or copper is very close to that of vacuum. A somewhat more > exact form of this equation is:
> 
>    x = Pi*D*SQRT(2*u*F/p)
> 
> where:  D = Diameter in cm
>         u = permeability of the conductor
>         F = Frequency (Hertz)
>         p = specific resistivity of conductor, ohm-cm^-3
>         x = penetration depth (cm)
> 
> Plugging in 1.724 X10^-6 ohm-cm^-3 for Cu and changing the units results
> in the shorthand form of the equation that Malcolm presented and you
> confirmed. Since silver has has greater p than copper, x is less.
> 
> <SNIP>
> 
> -- Bert --

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.

Safe coilin; to you!

-- Bert H --