Skin depth... was Re: Balancing L/C Sizes

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-uswest-dot-net>" <jimlux-at-earthlink-dot-net>

It's important to remember a few things when talking about skin depth:

1)The skin depth in an infinite flat plate is NOT the same as in a round
conductor or tube.  In a round conductor, there is current flowing on the
other side of the tube, for one thing.

2) The skin depth is the depth at which the current density is 1/e (i.e.
1/2.71828...) of that at the surface. It's not like it abrubtly stops at
some depth.  Interestingly, if you integrate over the entire infinite slab
of infinite thickness, the resistance number you get is the same as if you
did have a uniform slab of that thickness at DC.  So, for computation, it
is a useful concept.

For these reasons, the AC resistance of a small (compared to "skin depth")
diameter conductor is tough to calculate analytically.  For a large round
conductor (T <<D/8), approximating the current carrying cross section as
circumference*skin depth is valid. Typically, one uses a variety of tables
to approximate the correction factors.

Also, if there are other current carrying conductors near the conductor of
interest, they will have an effect as well.

Some numerical examples...(sorry for non-SI units)
f(kHz)	AWG (diam)	Rac/Rdc Rdc (ohm/1000ft)
50	10(0.1")	2.48	1.037
100	10(0.1")	3.26		
200	10(0.1")	4.52

100	20(0.0316")	1.25	10.38
200	20(0.0316")	1.64	
	



Tesla list wrote:
> 
> Original poster: "Michael Rhodes by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <rhodes-at-fnrf.science.cmu.ac.th>
> 
> For the groups' information in case it hasn't been posted here
> is the relationship of frequency to skin depth.
> 
> In a copper wire at 100°C, this depth (in centimeters) is 7.5/sqr(f) where
> f is the frequency in Hz.  Don't know what it is at other temperatures,
> perhaps
> someone out their can let  us know.  The following is a table of frequencies
> appropriate for TC work.
> 
> Table 1-Skin-effect penetration depth
> Frequency(kHz)    Depth(cm X 10-3)   AWG gauge
> 50                          33.5                         27
> 100                        23.7                         31
> 200                        16.8                         33
> 300                        13.7                         35
> 400                        11.9                         36
> 500                        10.6                         38
> 750                        8.7                           39
> 
> So if you take the radius (not diameter) of #22 AWG wire (.032cm)
> that would suggest a frequency of 55kHz before the skin effect is totally
> negligible?  If I have time I'll try to write a program that correlates
> the frequency with the cross sectional area that the electrons will
> travel per gauge of wire.  That would reflect the current handling
> capability and loses.
> 
> Found this information at
> http://www.ednmag-dot-com/ednmag/reg/1999/012199/02df1.htm
> while researching for losses in magnets.
> 
> Would be interested in any comments on this.
> 
> -- Michael
> 
> ----- Original Message -----
> From: "Tesla list" <tesla-at-pupman-dot-com>
> To: <tesla-at-pupman-dot-com>
> Sent: Tuesday, May 01, 2001 9:00 PM
> Subject: Re: Balancing L/C Sizes
> 
> > Original poster: "William Swanson by way of Terry Fritz
> <twftesla-at-uswest-dot-net>" <swansontec-at-yahoo-dot-com>
> >
> > smaller wire does have greater losses. However, as
> > somebody else pointed out, after a certain point the
> > skin effect takes hold and causes the decrease in
> > resistance for a given wire size to decrease only
> > linearly. Once this limit is reached, wire size
> > becomes unimportant, but below this limit, it is
> > important. Perhaps this is the reason for the rule of
> > that says you should stick with 22 gauge wire for your
> > secondary...
> >
> > Sorry for the goof up.
> >
> > -William