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

All closed form analyses of dipole input impedance require simplifying
assumptions since the underlying equations can't be solved in closed
form, and each has its limitations. The task of developing useful
approximations consumed the effort of numerous people for several
decades. You might start with Middleton & King, "The Thin Cylindrical
Antenna: A Comparison of Theories", J. of Appl. Physics, Vol. 17, April
1946. This compares analysis methods developed by Hallen, Bouwkamp,
Gray, King, Middleton, and Schelkunoff and with some experimental
results. It points out the strengths and weaknesses of each
approximation. If you want a transmission line analogy type of
approximation (using Si and Ci functions), see Schelkunoff, "Theory of
Antennas of Arbitrary Size and Shape", Proc. of the I.R.E., Sept. 1941.
This development also appears in his _Advanced Antenna Theory_ (Wiley,
1952.) Like all other approximations, it does better over some ranges of
length and diameter than others. Some other papers on the topic:

King, Ronold and Blake, "The Self-Impedance of a Symmetrical Antenna",
Proc. of the I.R.E., July 1942.
Brown and Woodward, "Experimentally Determined Impedance Characteristics
of Cylindrical Antennas, Proc. of the I.R.E., April 1945.
King, Ronold and Middleton, "The Cylindrical Antenna: Current and
Impedance", Quarterly of Appl. Mathematics, Jan 1946.
King, D.D., "The Measured Impedance of Cylindrical Dipoles", J. of Appl.
Physics, Oct. 1946.
King, Ronold, "Self- and Mutual Impedances of Parallel Identical
Antennas", Proc. of the I.R.E., Aug. 1952.
King, Ronold, "An Improved Theory of the Receiving Antenna", Proc. of
the I.R.E., Sept. 1952.
King, Ronold, _The Theory of Linear Antennas_ (Harvard U. Press, 1956).
King, Ronold and Harrison, _Antennas and Waves: A Modern Approach_ (MIT
Press, 1969), Chapter 3.

Of course, the fundamental equations can now be solved numerically in a
tiny fraction of a second to nearly arbitrary accuracy with a computer
and codes like NEC, giving far better results than the best efforts of
these brilliant people.

Roy Lewallen

GrantBingeman_at_cs.com wrote:
> 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.
>

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