"Mark Keith" wrote
I beat Reg's vertload program to death
finding the best overall coil height for my mobile antenna. Basically
I ended up putting it as high as I could. Which ended up a center load
at 5 ft up, with a 10 ft whip.

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There are 3 losses - coil loss resistance, ground loss resistance and
radiation resistance.

To calculate and maximise efficiency all 3 values must be transformed to a
common point - the base feedpoint.

The length of radiator between coil and base behaves is a transmission line
transformer which transforms the coil loss resistance (XL/Q) to another
value at the base. Would-be modellers should take this into account.

The Cosine current distribution along the radiator is a direct consequence
of its behaviour as a lossy line. (Actually, it is not an exact cosine shape
because of end-effect)

Efficiency = Rrad / ( Rrad+Rcoil+Rground ).

Rground is constant. For short antennas Rrad is the smallest of the 3
resistances.

As the coil is moved further up the antenna both Rrad and Rcoil increase.

But even if the coil is located at the extreme top of the antenna, radiation
resistance cannot increase to more than 4 times the radiation resistance
when the coil is located at the base feedpoint. Usually it is considerably
less than 4.

So the rapidly increasing coil loss resistance very soon overtakes the
increase in radiation resistance. Even if coil Q remains constant, coil
loss resistance increases just by virtue of its necessary increase in
inductive reactance.

To maintain resonance coil inductance increases inversely proportional to
the length of the whip above it. So when the coil is located 95% of the way
to the top of the antenna its loss resistance is TWENTY times greater than
that of a base loading coil even when Q is unchanged. In practice, a coil
having 20 times the inductance but with the same overall dimensions will
very likely have a lower Q and an even higher resistance.

Its easy to see the fixed value of Rground in the above efficiency formula
has the following effects -

When coil loss is less than ground loss, higher radiating efficiency is
achieved by placing the coil nearer to the top of the antenna.

And vice-versa.

When ground loss is very small (zero if antenna is a pair of two
back-to-back radiators to form a dipole) efficiency is relatively high
anyway, maximumum efficiency perhaps occurring with the coil located in the
lower half of the antenna. The slight improvement relative to base loading
(as part of a tuner) may not then be worth the mechanical inconvience of
fitting a coil in the antenna anyway.

An important factor, not considered quantitatively by anybody, is that a
mobile antenna is not just a loaded vertical - the vehicle body, just by
looking at it, obviously forms the major portion of the antenna and is
floating above ground. The vehicle body plus loaded whip should be
considered to be an off-centre-fed, short, 1/2-wave resonant vertical dipole
and modelled as such.

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Regarding antenna modelling - program LOADCOIL considers all 3 parts parts
of the antenna, the mast, loading coil and whip, as consecutive lengths of
transmission line each with its own Zo and loss resistance. It is obliged to
do this because it covers actual antenna heights approaching 1/4-wavelength
as may be erected in your backyard.

And it continues to do this for very short antennas with very short loading
coils even where there would be negligible error by assuming the current
going into one end of the coil is the as what comes out of the other.

There's a companion program TOPHAT2. There's no coil in it.
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Regards from Reg, G4FGQ
For Free Radio Design Software
go to http://www.g4fgq.com
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