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Old April 9th 09, 03:28 PM posted to rec.radio.amateur.antenna
Cecil Moore[_2_] Cecil Moore[_2_] is offline
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First recorded activity by RadioBanter: Mar 2007
Posts: 3,521
Default colinear representation in NEC

Tom Donaly wrote:
You and Gene also got the formula wrong, or at least you
didn't get the complete formula for two waves passing in opposite
directions deep in the night.


What I posted was the equation for a pure standing wave.
What you may be referring to is the omission of the
real world traveling wave component that gets radiated.
Since the radiated component amounts to only about
10% of the wave energy on a standing-wave antenna, it
can be considered to be mostly negligible. The phase
of that small traveling wave is completely swamped
by the 90% wave energy that is in the standing wave
on the 1/4WL standing-wave monopole.

The components of a pure standing wave are two equal
amplitude traveling-waves moving in opposite directions.
Their phasors are equal in magnitude and opposite in
direction of rotation.

What is the phase of the sum of two equal amplitude phasors
moving in opposite directions? Assuming each phasor has an
amplitude of 1.0, here are some points in 1/4WL:

Ifor + Iref = Itot
1.0 at 0 deg + 1.0 at 0 deg = 2.0 at 0 deg
1.0 at -15 deg + 1.0 at +15 deg = 1.9 at 0 deg
1.0 at -30 deg + 1.0 at +30 deg = 1.7 at 0 deg
1.0 at -45 deg + 1.0 at +45 deg = 1.4 at 0 deg
1.0 at -60 deg + 1.0 at +60 deg = 1.0 at 0 deg
1.0 at -75 deg + 1.0 at +75 deg = 0.5 at 0 deg
1.0 at -90 deg + 1.0 at +90 deg = 0.0 at 0 deg

In 90 degrees of wire, the phase of the total
(pure standing wave) current doesn't change.
This makes the phase of the total current on a
standing-wave antenna invalid for measuring
the delay through the wire or through a coil.

Note how the above values roughly correspond
to the current amplitude and phase distribution
on a 1/4WL monopole. From "Antennas" by Kraus:

"It is generally assumed that the current distribution
of a (thin wire dipole) is sinusoidal, and that the
*phase is constant over a 1/2WL interval* ..."

All illustrated on page 464 of the 3rd edition.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com