Re: NEC-LIST: newbie question: split sources

Bibby wrote:

> Dan, in your reply to Andrew you refer to a "built-in Leeson correction
> algorithm". I have always understood that this is/was something that was
> arrived at empirically, not something that was derived from rigorous
> analysis. Perhaps you could comment on this issue.
>
> Malcolm M Bibby

The goal is to find the dimensions, meaning diameter and length, for a
constant diameter wire that is electrically equivalent to the set of
stepped diameter wires that make up a given element. Leeson developed
an algorithm, based on work by Schelkunoff (based on earlier work by
Lawson), that does this. This algorithm is available in a Fortran
implementation (Efflen.for) that is bundled with the 19th edition of the
ARRL Antenna Book (second printing or later). It is also available as
an Excel spreadsheet from somewhere on the ARRL web site, although I
can't find the exact url at the moment.

To answer your question, I believe (but am not positive) that the
algorithm was developed using a combination of analysis followed by
empirical fitting to the "known" target characteristics. I'm afraid the
math is over my head, but looking at the Fortran code reveals
calculations for equivalent lengths and cross section areas for the
individual stepped diameter wires, followed by some final code that
includes several constants that appear to be "adjustment factors." I
further believe that the target was to have a wire of diameter and
length such that the impedance calculated by NEC-2 for this single wire
matched that given by MININEC for the original set of stepped diameter
wires. That is, the MININEC results were taken as "truth" as opposed to
actual measurements, of course with MININEC having been earlier verified
against measurements. Perhaps a more knowledgeable list member can
comment on that.

Regardless of how it was derived, the algorithm is now available such
that you can "plug in" a set of lengths and diameters and "get back" an
equivalent single diameter and length. But the real trick is knowing
when to apply the algorithm in the first place. It can only be used in
limited circumstances, namely when the original element is linear, has
sources, loads, or transmission lines only at its center (or end for a
monopole), and has a total length within about 15% of resonance. That
sounds easy enough at first, but remember that the element is composed
of many individual wires in the original model specification, not
necessarily defined in any particular order, not necessarily centered
about an axis, and not necessarily parallel with any axis of the XYZ
coordinate system. Knowing if the element is then "straight" with a
source/load/TL (if any) that is "centered" is a bit trickier.

To my knowledge, only EZNEC and NEC-Win Plus have implementations of the
Leeson algorithm that also include program logic to determine just when
the algorithm can be used. The two implementations are similar but not
identical. For example, in EZNEC the algorithm will be applied in all
cases where it is appropriate to do so, unless the user has explicitly
requested otherwise. In NEC-Win Plus, the user must request that the
algorithm be applied and then inspect a report file to make sure the
application was successful.

My response to Andrew was meant to imply that if he already owned EZNEC
he could continue to use it in his desired "automatic modify and re-run"
environment, by making use of a wrapper program that shall now be left
unnamed. <g> This would not be necessary for some models, but would be
very convenient for models with stepped diameter wires.

I believe that both Roy Lewallen and Joe Finnerty monitor this list, I
hope they will jump in with additional comments.

Dan

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