Richard Harrison wrote:
Roy, W7EL wrote:
"When asked for the justification of the "cosine rule", he never offered
any, so its origin remains obscure."

Roy, I posted a reference for the cosine rule weeks ago. Perhaps you
missed it. If you had read it, you wouldn't have wasted your time
measuring the phase angle of the net current through a loading coil.
My "odd theory" is based on Kraus' treatment of the cosine rule.
See below:

It comes from the similarity of a standing wave antenna to a
transmission line. It isn`t a prominent feature of antenna texts because
energy isn`t confined to an antenna as it is to a transmission line.

Kraus says that at the center of a 1/2-wavelength dipole, the effect of
wave cancellation is least and radiation is maximum perpendicular to the
wire at the center of the dipole, or words to that effect.

The reference for the cosine rule is from _Antennas_For_All_Applications_,
by Kraus & Marhefka, 3rd edition, pages 463-465, section 14-3, Current
Distributions, Figure 14-2, Relative current amplitude and phase along a
center-fed 1/2WL cylindrical antenna.

This is where my "odd theory" comes from. Kraus says: "It is generally
assumed that the current distribution of an infinitesimally thin antenna
is sinusoidal, and that the phase is constant over a 1/2WL interval, changing
abruptly by 180 degrees between intervals."

Kraus is making the assumption that the forward current is equal to the
reflected current such that their superposition sum has constant phase.
Setting the center of the dipole as the origin and normalizing the
feedpoint current to 1.0, the current at any point on the dipole can
be calculated as the cosine of 'x' where 'x' is degrees away from the
center. Thus, if one knows the normalized current at any point on the
dipole, one can calculate the number of degrees one is away from center
using ArcCos(I). This is how I calculate the number of degrees associated
with a loading coil. Assuming the input current is 1.0 and the output
current is 0.95, ArcCos(0.95) = 18 degrees.

All this "odd theory" is based on Kraus. I suggest anyone who thinks
this is "odd theory" take time out and read Kraus.
--
73, Cecil http://www.qsl.net/w5dxp



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