Skin Effect... and More(croft

Subject:  Skin Effect... and More(croft)
       Date: Sun, 27 Apr 1997 12:38:54 -0700
       From: Bert Hickman <bert.hickman-at-aquila-dot-com>
Organization: Stoneridge Engineering
         To: Tesla List <tesla-at-pupman-dot-com>

Malcolm, Alfred, and all,

There's even more wierdness associated with Skin Effect! It turns out
that some current actually does penetrate the conductor's interior. With
increasing depth, the magnitude of this current decreases, AND the phase
is continually retarded. What this really means is that it's possible
that after a certain depth of penetration, current may actually be
flowing in a direction OPPOSITE to that on the surface(!). In such a
case, the effective AC resistance of the conductor would be decreased by
removing the inside part of the conductor - a copper tube will show less
AC resistance than a solid copper rod! This effect _actually occurs_ in
high current busbars coming off the generators at 60 Hz in big power
plants - these are typically very heavy copper "pipes" with high
pressure gas flowing through the center for cooling. This interesting
tidbit comes from the very excellent book "Principles of Radio
Communication" 3rd Edition, by John Morecroft, John Wiley & Sons, 1943,
pages 177-178. I just ran into this "little" 1084 page gem at a local
used/out-of-print bookstore yesterday. Definately worth getting if you

There's lots of other interesting things in this book as well...
excellent explanations of proximity effect, "resistance" of sparks and
arcs, "best form" for a single-layer solenoid (Diameter = 2.45 x Length
for maximum inductance), spark-gap oscillator characteristics, and a
whole lot more. 

For example... on page 302, Morecroft references work done by Zenneck
and J. S. Stone which confirms Malcolm's observation that the decay of
current is, indeed, linear when a spark gap is used in an RLC circuit.
He presents a formula for the tank circuit current which is a function
of the maximum current multiplied by the factor (1-Rt/2L) where R is the
initial resistance of the spark gap, t = time, and L is the tank

Morecroft also covers disruptively excited coupled tuned circuits and
their behavior versus k in one of the most lucid manners I've seen thus
far. He also covers the case of "impulse excitation" with a relatively
low-inductance primary - this interesting variation results in  a
single, unidirectional pulse in the primary (NO oscillations!), causing
the secondary to ring at its characteristic frequency. Sort of like a
Marx-excited primary circuit. He also show an interesting variation
where the initial energy is stored in the primary inductor, instead of
the capacitor, and the input DC current supply is suddenly openned. 

I'll follow-up on some of the other interesting things in this book in a
later post (once I've had a chance to really read more of it!). Add this
book to your list of Tesla Coiling references - its a definate winner!

Anyway... safe skinnin', quenchin', and coilin' to you all!

-- Bert H --

Tesla List wrote:
> Subject:       Re: Using skin effect
>        Date:   Tue, 22 Apr 1997 08:03:26 +1200
>        From:   "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
> Organization:  Wellington Polytechnic, NZ
>          To:   tesla-at-pupman-dot-com
> HI Alfred, all,
>                 One skin depth in copper is 66/SQRT(f) mm. 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.
> 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. And it stilll
> requires enough conducting cross-sectional area to carry the current
> without significant heating (resistance).
> Malcolm