Roy Lewallen wrote:
I feel strongly that if you really understand what you're talking about,
you should be able to express it mathematically as an equation or
equations. I haven't seen any evidence of this.

Taking a look at just the loading coil, the math is very simple.
Since a loaded mobile antenna is a standing wave antenna, there
exists a forward current through the coil. Balanis labels that
current as 'If'. There also exists a reflected current flowing
backwards through the coil. Balanis labels that current as 'Ib'.
The current at any point in the coil is the superposed sum of
If + Ib. The net current within the coil is approximately a section
of a cosine function.

On my web page is a mobile antenna modeled with EZNEC using a
segmented octal shaped coil.

http://www.qsl.net/w5dxp/octcoil.gif

EZNEC reports that the current at the bottom of the coil is
0.9956 amps and the current at the top of the coil is 0.5326.
Assuming the current is approximately a cosine function through
the coil, the approximate number of degrees occupied by the coil is:

arccos(0.5326/0.9956) = ~58 degrees

The other eight feet of antenna is equal to about 42 degrees
at 13.5 MHz.

58 + 42 = 100 degrees is within 10% of being 90 degrees and
seems reasonable for a ballpark estimate. This seems to be
a clue that a loaded mobile antenna is electrically slightly
longer than 90 degrees.

The forward current and reflected current magnitudes through the
coil are probably within 90% of each other for a mobile antenna.
Kraus considers them to be equal for a dipole discussion
in his book. Considering them to be equal introduces a small error
but is good enough for a reasonable estimate.

The point is that the difference in the net current at each
end of a coil gives us a rough estimate of the number of electrical
degrees that the coil occupies in the antenna. The whip above the
coil can be considered as a load on the source energy at the top
of the coil. It is unlikely that the coil is capable of changing
the characteristics of the load which would be necessary if Tom
were right.

If the coil occupies zero degrees, as implied by Tom, W8JI, then
the other 8 feet of the antenna would have to occupy 90 degrees
to make the feedpoint impedance resistive. I would say that shoving
90 degrees into 8 feet of whip at 13.5 MHz is impossible. That 8
feet of antenna would have to have a velocity factor of 0.46 which
is unlikely. At 4 MHz, that 8 feet of antenna would have to have a
velocity factor of 0.137 to occupy 90 degrees. That's seems obviously
impossible. Tom's requirement that a wire change velocity factor with
frequency is really hard to accept.
--
73, Cecil http://www.qsl.net/w5dxp


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