EZNEC doesn't do the transformation you describe.

The following description is a very simplified version of how NEC works.
I believe the whole NEC-2 manual is available on the web, for anyone who
wants a deeper and surely more accurate explanation.

First, an impedance is calculated for each segment of each wire, and a
mutual impedance for every segment relative to every other segment. This
is done in a rather complex way by assuming that each segment has sine,
cosine, and constant currents, calculating the field from each segment
arriving at each other segment, and evaluating the current induced on
the other segment by it. These impedances are put into a matrix, then
the currents on each segment are found by solving Ohm's law in matrix
form, where the E is provided by the specified sources. Once the
currents are found, the impedance at each of the sources is known. The
field from each segment is computed from the known current and assumed
current distribution along the segment with an approximate integral
equation that's solved numerically. The impedance of the medium (fixed
at free space in NEC-2 but user selectable in NEC-4) is of course
involved in this calculation, as it is for the mutual impedance calculation.

The fields are summed to obtain the overall field (both E and H) at any
point the user specifies. Both are reported in a near field analysis
output. In a far field calculation, the distance of the observation
point to all segments is assumed to be the same, and only the E field is
calculated.

An excellent and easy to follow description of the method of moments can
be found in Kraus' _Antennas_, Second Ed. I assume it's in the third
edition also, but it's not in the first. The NEC-2 manual recommends
R.F. Harrington, _Field Computation by Moment Methods_ (McMillan, 1968)
but I haven't seen this book.

I've tried to point out on this thread that although the feedpoint
impedance is an impedance with the units of ohms, and the impedance of a
plane wave in free space also has the units of ohms, they're not the
same thing. Feedpoint impedance is the ratio of a current to a voltage.
Wave impedance, or the intrinsic impedance of a medium, is the ratio of
an E field to an H field -- it's also the square root of the ratio of
the medium's permeability to its permittivity. An antenna converts
currents and voltages to E and H fields, it doesn't just transform one
impedance to another. Hence my insistence on calling an antenna a
transducer rather than a transformer.

Any explanation of an antenna as a transformer will have to include
parasitic array elements, which have zero feedpoint impedance, and array
elements that have negative feepoint resistances.

The answer to your last question is beyond my ability to answer. It's
discussed in great detail in most electromagnetics and antenna texts.

Roy Lewallen, W7EL

William E. Sabin wrote:
William E. Sabin wrote:

For example, consider an EZNEC solution to an antenna, say a 50 ohm
dipole. The far-field 377 ohm solution provided by the program is
precisely the field that I am thinking about. How does EZNEC, with its
finite-element, method-of-moments algorithm, transform a 50 ohm dipole
input resistance to 377 ohms in free space?

I don't want the equations, I want a word description (preferably
simple) of how EZNEC performs this magic.

The far-field E and H fields are different from the near-field E and H
fields. What is going on?

Bill W0IYH