On Tue, 15 Sep 2009 16:53:55 -0700 (PDT), Richard Fry
wrote:

On Sep 15, 5:44*pm, Richard Clark wrote:
To cut to the chase: *The full length of the radiator contributes to
radiation and the evidence of this is found in any characteristic lobe
displayed in the far field.

In practical and provable terms, how much of that characteristic, far-
field radiation pattern can be attributed to the linear, unloaded,
center-fed dipole radiator lengths as exist less than ~10% distant
from the endpoints of that dipole?

The math behind this has been terribly abused by Cecil in the past,
but we shouldn't let that poison the well. It is based in optics, a
field that predates RF by several centuries.

"... S1 and S2 are two point sources of light each
emitting a sinusoidal wave of the same angular
frequency omega. They have position vectors r1
and r2. The field point P where we evaluate the
intensity [flux density] has position r. The electric
field at P resulting from the two sources is assumed
to be of the form....
"The total relative phase Psi0 between the two waves
at P thus consists of two parts: a part Phi2 - Phi1
coming from the relative phases at the two sources,
and a part -Dell coming from the different
retardation in phase suffered by the two
beams resulting from the propagation
from S2 to P and from S1 to P.
"An important special case occurs when
A1 == A2. Then we can write
I = 2·I1·(1 + cos(phi2 - phi1 - Dell))"

Every point along the radiator is considered to be a point source with
the same frequency. However, each point is not at the same phase by
virtue of its distance from the feedpoint and its distance from other
points. Each point is not at the same distance from P (a point in the
far field) which gives rise to a retardation of that altered phase.
Thus the phase accumulates over two distances: one from the excitation
source to the point on the radiator; and, two, from the point on the
radiator to the point of the lobe where we are observing all of the
effects of the combined illumination from all point sources along the
length of the radiator. The extract above speaks to the contributions
of only two points, an antenna comprises many, many more.

I will add here that the intensity variable now draws in the
discussion of the superposed forward and reflected currents. This is
the remaining part of the analysis which is more instructive for your
very simple example. Clearly, from a very small dipole to a half
wave, there is little variation in the far field pattern and it is
appealing to infer that the differences in length suggest that that
additional length suggests nothing is going on in the ends. However,
when we add only a slightly longer length (by proportion*), this
negates the appealing suggestion. The superposed current distribution
change accounts for this and we are still talking about simple linear
elements (and there is still zero current at the ends).

If we were to succumb to the argument of "length efficiency" as
offered in the practice and Art of Antenna Bris, then the additional
gain of that proportionate smaller length addition would have been
lost to that invalid proposition.

The NEC method of moments is by definition the application of the
formula above to the middle of EVERY segment to EVERY point in three
space. The resulting curve is an abstraction of that fog of numbers
that is reduced to a planar curve (or to a solid model in the 3D
representation).

[* What is this proportional and proportionate mean? For a dipole of
0.05 WL to a dipole of 0.5WL, the far field change for that 10:1
variation is negligible. However, for a dipole of 0.5WL to a dipole
of 1.25WL, the far field change for that 2.5:1 (a smaller proportion)
variation is very noticeable.]

73's
Richard Clark, KB7QHC