Re: Current Distribution Re: Aluminium aka Aluminum Wire (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sun, 07 Oct 2007 10:05:29 -0300
From: Antonio Carlos M. de Queiroz <acmdq@xxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Current Distribution Re: Aluminium aka Aluminum Wire (fwd)

Tesla list wrote:
> ---------- Forwarded message ----------
> Date: Fri, 05 Oct 2007 21:08:28 -0700
> From: Barton B. Anderson <bartb@xxxxxxxxxxxxxxxx>
> To: Tesla list <tesla@xxxxxxxxxx>
> Subject: Re: Current Distribution Re: Aluminium aka Aluminum Wire (fwd)
>
>
> If we induce a current across an entire coil and mentally break up the 
> coil into several segments, the total inductance will be the net sum of 
> all segments. 
This, plus twice the sum of all the mutual inductances between the segments.
> Now imagine high frequency where the usable current carrying geometry of 
> the wire is changing and currents are disproportionate. Each segment 
> will have a different inductance than the next because the "property" or 
> "ability" to induce a voltage has been changed by the new geometry and 
> the time varying magnetic field is varying the distribution of current 
> within the conductor. The result is a decrease in the net inductance of 
> all segments. The inductance has decreased.
What happens in high frequency is a composition of two effects. Skin and
proximity effects can be considered as effect of the resistivity of the
wire material, pushing the current away from the more central parts of
the wires. If the wire is decomposed in a series of parallel segments
having resistance, inductance, and mutual inductance to the others, the
effect appears naturally when the frequency of the voltage applied over
the combination is increased.
Nonuniform current distribution along the wire is a consequence of the
existence of distributed capacitance. Some of the charge that enters the
wire is trapped in the capacitance instead of exiting trough the other
side. If the wire is decomposed in a series of segments in series, with
capacitors interconnecting the connection nodes and the ground, the effect
also appears naturally.
(Radiation is involved too in both models, and is more complicated to 
treat.)
Note that in both cases the equivalent circuit is not  a single inductor,
that is just an approximation at low frequency. At high frequency,
the model would be a complicated distributed RLCM network. Approximation
using a finite number of discrete fixed elements can be used to approximate
the distributed effects in a given frequency range. The most basic case is
to say that the secondary of a Tesla coil is a fixed series RL circuit
with a capacitor in parallel. This accounts for the first resonance only.
If you want the second resonance too, use two sections, and so on.

Antonio Carlos M. de Queiroz