Skin Effect Re: Why do primaries get hot?

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

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



Tesla list wrote:
> 
> Original poster: "Terry Fritz" <twftesla-at-qwest-dot-net>
> 
> Hi Ralph,
> 
> Skin depth is a big deal at work where we pump hundreds of CW amps at
> 13.56MHz...
> 
> Any college level electromagnetics book will have the gory details but the
> web has them too:
> 
<SNIP>
> 
> I really could not find a "nice" web page to explain the details in a
> straight forward way...

That's because it's a "secret of the guild"...

Actually, the easiest way to do skin effect stuff is to have one reference
number and then just remember how it scales.. square root of frequency,
square root of permeability, inverse square root of conductivity etc.

That is.. the effective resistance (of an infinite sheet) goes up as the
square root of frequency (i.e. 4 times the frequency, twice the AC resistance)

the effective resistance goes up as the square root of permeability
(i.e. AC resistance of silicon steel with relative permeability=100 is 10
times that of comparable conductivity metal with permeability 1)

The effective resistance goes down as the square root of bulk specific
resistance (sigma)

More properly... surface impedance is Zs=Rs+jXs = sqrt( (j *
omega*mu)/(sigma+j*omega*epsilon)) where
mu is absolute permeability
epsilon is absolute permittivity (dielectric constant)
sigma is specific resistance
omega is radian frequency (2*pi*f)
j = sqrt(-1)


The wrench in the works in practical terms is that the "idealized" skin
effect is for an infinite sheet of metal.  Edges (and circular cross
sections) have a noticeable effect, especially if the skin depth is a
significant fraction (>1/10th) of the diameter.  

The skin depth is the depth at which the field has fallen off to 1/e (37%),
but the current still penetrates deeper. This is what causes the problems
when looking at round conductors, and why there are all of those tables.
(why 1/e?  because if you integrate the effective resistance all the way to
infinity, it is the same as if you had a uniform layer the same thickness)

Other problems crop up in the real world.. particularly in magnetic
materials (comes up in shielding problems), the propagation into the
conductor takes some time. When the conductor's length starts to get close
to a wavelength (not an issue for tesla coils, but is a problem for
antennas and waveguides), the assumption of identical currents everywhere
breaks down.