Re: Equivalent lumped inductance and toroidal coils

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

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 



 > Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk>
 >
 > [the R=0 problem]
 >
 >
 > Avoiding the center of the wire (or any other filament arrangement)
 > doesn't help because you must now take R to be the radius from
 > each filament, not from the wire centerline.  So you have an R=0
 > problem for each filament.

I suspected you would say that.  The same thought crossed my mind just as I
pressed the send key :-))  Here's an idea.  Use the filament as originally
intended with the differential current element, but stop the H field
sampling at the surface of the wire (or give the filiment thickness and stop
the sampling at the surface of the filament).  I suspect the reason you want
to simulate the current distributing in the wire is to get a good AC
inductance calculation.  What I don't know is how this distribution effects
the final answer.  I suspect the displacement current "bleed off" (ie, the
non constant current profile of the coil from bottom to top) is the main
contributor to Lres < Ldc.

 >
 >  > If one assumed that J was only a function of (r), would
 >  > this alter the answer that much?  I suspect not.
 >
 > Probably not, for TC secondaries and normal primaries where the
 > wire is relatively thin compared to overall dimensions.  I've tried
 > in tssp modelling to represent the wire with various arrangements
 > of filaments around the perimeter of the wire cross section, with
 > little effect on the inductance.  Now I just have one filament down
 > the center, which corresponds to what you say in
 >
 >  > ...stop the H field sampling at the surface of the wire since
 >  > the current density will drop off once the wire is "penetrated"
 >  > and not worry about the distribution of current within the wire.
 >  > For purposes of evaluating the differential current element,
 >  > assume the current is at the center of the wire...
 >
 > But if we start to look at inductors formed from thick tubes and
 > wide sheets, that's another story.   We reach a point where it *does*
 > make a difference where you choose to place the filament.  So then
 > you have to switch to multiple parallel filaments for the conductor,
 > which in turn forces you to a network solution to determine the
 > current branching, perhaps as you say by
 >
 >  > ...simulate the multiple current path problem in the past using
 >  > loop equations and iterating numerically until boundary
 >  > conditions were met.
 >
 >  > I'm assuming that the alternate paths you are describing are the
 >  > multiple current filaments that represent the wire and the varying
 >  > current density contained within the wire.  Is this complexity
 >  > really necessary?
 >
 > There are two levels at which this applies:-
 > 1) When a 'wide' conductor is represented by a bundle of filaments
 > connected in parallel;
 > 2) When we have more than one distinct conductor in parallel.
 >
 > We need a 'network' solution to decide the current branching,
 > between the filaments in (1) and between the conductors in (2).

Would it be reasonable to determine apriori the current branching and then
use that distribution thru out the winding.  Would certainly simplify
things.

Gerry R.