Cecil Moore wrote:
Ian White, G3SEK wrote:

Cecil Moore wrote:
OK, let's agree on that and take another look at the example I just
presented
on another thread involving half a dipole.

wire coil wire
---------------////---------------
22.5 deg ? deg 22.5 deg

Assuming a lumped inductance, presumably the current into the coil
will have the same phase as the current out of the coil. Zero phase
shift through the coil means this antenna has the same current
phasing
as a 40m dipole used on 75m, i.e. the feedpoint current is at a current
minimum point.
Sorry, I don't understand that last statement...

A 40m 1/4WL vertical used on 40m is 90 degrees long.

A 40m 1/4WL vertical used on 80m is 45 degrees long and we know its
characteristics.
If the coil above has zero phase shift, the antenna above is also 45 degrees
long and will exhibit the feedpoint characteristics of a 40m 1/4WL vertical
used on 80m but we know it doesn't exhibit those characteristics. ERGO,
the phase shift through the coil is not zero.

OK, I see what you're getting at, but by changing the frequency you are
losing sight of some important points. Let's stay on the *same*
frequency, halve the physical height of the antenna and insert a lumped
loading coil at the midpoint.

Instead of being 90deg tall, our vertical monopole is now only 45deg
tall (physically). Drawn on its side, and fed against ground at one end,
it now looks like:

wire coil wire
---------------////---------------
22.5 deg ? deg 22.5 deg

(just as you drew it)

Where you're going astray (I suspect) is in believing that the coil
literally "replaces" the 45deg of antenna that was lost when we halved
the height. It doesn't - the loading coil drastically changes the
current distribution.

Fed with 1.0A at the base, the original quarter-wave has a roughly
cosine-shaped current distribution, so the current at a point 22.5deg
from the top is 1A * cos(90-22.5) = 0.38A.

Now feed the loaded antenna with 1.0A at the base. The current
distribution is now radically different: in the bottom 22.5deg of the
antenna, the current hardly changes - let's say it's 0.9A at the bottom
of the loading coil.

Since we have assumed a lumped loading coil, the current at the top of
the coil is the same 0.9A. But now the current distribution in the top
22.5deg is very different from the full-size case: it tapers much more
sharply, from 0.9A down to zero at the very top.

This is all standard stuff. My reason for walking through it is to
emphasize that shortening the antenna and loading it changes many things
about the current distribution, both above and below the loading coil.
And here are two other important differences: the feed impedance of the
loaded antenna is much lower than that of the full-size; and the much
sharper reduction in current is associated with a much higher E-field
over the same length of top section.

To sum up, shortening and loading the antenna creates so many important
differences that you're misleading *yourself* if you say that the
loading coil simply "replaces" the missing length of antenna.


Two footnotes:

1. The diagram for current distribution with center loading in 'Low Band
DXing' is based on the same incorrect assumption that loading coil
somehow fully "replaces" the missing 45deg of antenna. (Fortunately the
method later in the same chapter for calculating the inductance of
loading coils is still OK, because it doesn't depend on any assumptions
about current distribution.)

2. I haven't thought about an answer to Cecil's problems of what happens
to the "missing" 45deg, and what happens to the forward and reflected
waves of voltage and current. Since it's Cecil who chooses to think
about antennas in such ways, he'll have to solve his own problems!

My only point is that a correct solution can *not* involve a difference
in the currents at the two ends of an idealized lumped inductor. Such a
difference simply cannot be... so the true solution will be that bit
harder for Cecil to find.



--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek