Re: NEC-LIST: thin-wire general EM equations

There is an answer to yuour question of sorts. The problem is some of your assumptions. First,
the answer is given in the book by Jordan & Balmain, "Electromagnetic Waves and Radiating
System," 1968, Prentice-Hall. They address the formulas in Chapter 14 and have answers in
terms of sine and cosine integrals (tabulated functions). You should also be able to find
information in the book by R.W.P. King, "Linear Antennas," 1956, a bible on linear antennas
that people have compared to for years.

The assumptions I was talking about have to do with "any length" and an assumed length greater
than lambda/2. The problem is that as the wire gets long, the sinusoidal nature of the current
dies out and you have a traveling wave current instead, except near the ends. Basically you
are seeing continuous radiation along the wire and a corresponding reduction in the end
interaction. This is similar to the current distribution you find on a helix with a standing
wave toward the feed and tip, but a traveling wave between them.

Also, the "any length" issue has a problem whenever a multiple of a wavelength is approached
since the sine assumption is reasonable for the current distribution, but not with respect to
the input impedance that is approaching infinity based on the sine assumption (0 current point
at the feed).

The references may not have a basic single equation for the result, but do have the basic
forms that should do the job. These books were written before the large use of computers that
started in the mid to late 60s. Thus they focused on basic concepts and simple formulas, but
with limitations that they typically reviewed.

Bill

> Gentlemen: it seems that all textbook introductory treatments of freespace
> dipole impedance and EM fields limit themselves to dipole lengths less than
> about a half wavelength. This is related to the simplifying assumptions
> made when defining the Hertzian dipole. I am looking for a general set of
> equations, assuming sinusoidal current distribution on thin wires, for the
> input impedance seen by a source located at the center of the dipole. I am not
> interested in any MoM approaches, just the plain old CI and SI expressions,
> requisite integrations, etc. Surely there must be a general equation for
> this that is valid for any length of dipole?
>
> PS: when i say thin wires, i do not necessarily mean infinitesimally thin
> wires. g
>
> Grant W. Bingeman, P.E.

-- 
Dr. William A. Davis, Director of VT Antenna Group 
(Wireless @ VT)
The Bradley Dept of Elec & Comp Engr, Virginia Tech
Blacksburg, VA 24061-0111  [(540)231-6307, 231-3362FAX]
http://antenna.ece.vt.edu
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