K7ITM wrote:
Steve, this is fine for a base loading coil, but I'd suggest you try
your experiment with a loading coil well up the antenna, where the
coil is significantly larger diameter than the straight conductor in
which it's placed. The same size coil you described (though
presumably a different number of turns), placed at least half way up
something like a 15 or 20 foot long thin wire, should illustrate the
point. Is the EZNEC model then in such good agreement with placing a
reactive load at that point in the antenna, where the reactance is
from ON4AA's online calculator?

The key to understanding this question and its logical
answer lies in the phase shift that occurs at impedance
discontinuities.

For a base-loading coil, there is only one impedance
discontinuity in the system, a hi-Z0 coil to a low-Z0
stinger. That single discontinuity provides a positive
phase shift at the '+' junction of the coil and stinger.

coil stinger
FP//////////+-------------------

When a straight shaft section is installed under the
coil, it introduces one additional impedance discontinuity
at 'x' in addition to the '+' top of coil to stinger
discontinuity.

base coil stinger
FP-------x////////////+---------

Because the impedance discontinuity between the base
section is a low-Z0 to hi-Z0 transition, the phase shift
is negative, i.e. the antenna *loses electrical degrees*
at that junction.

Therefore, more turns must be added to the inductor
to supply the number of negative degrees lost at the
base section to coil impedance discontinuity.

This might best be illustrated with pieces of transmission
line. Please reference my web page at:

http://www.w5dxp.com/shrtstub.htm

The following concepts apply to the above antennas but
may be easier to understand using transmission lines.

Here is a dual-Z0 stub that is physically 44.4 degrees
long but is 90 degrees (1/4WL) long electrically, i.e.
it is functionally a 1/4WL open-circuit stub.

---22.2 deg 300 ohm line---+---22.2 deg 50 ohm line---

The Z0=300 ohm to Z0=50 ohm transition provides for
+45.6 degrees of phase shift. This is akin to the base-
loaded antenna above.

Here is a dual-Z0 stub with 11.1 degrees (half) of
the 50 ohm line moved to the left. (The words are
abbreviated because of space on the line.)

--11.1 deg 50--+--22.2 deg 300--+--11.1 deg 50--

Who can tell me how long electrically is this stub
using the identical feedlines from the above example?

This reconfigured stub with half of the 50 ohm feedline
moved to the bottom is now electrically only ~80.6 degrees
long. What has happened? The new impedance discontinuity
from the base section at the bottom of the coil has cost
us electrical degrees by providing a *negative phase shift*.

How do we solve the problem? Add some length (degrees) to
the Z0=300 ohm section. If we make the 300 ohm section
38.5 degrees long, the stub will be electrically 90 degrees
long once again.

This is conceptually the same problem we encounter when
we move the loading coil from the base location to the
center location. When we move the coil up the shaft, we
introduce a negative phase shift at the bottom of the
coil. Therefore, we must increase the number of turns
to make the loading coil electrically longer.

Incidentally, w8ji knows about the coil to stinger
positive phase shift and describes it on his web page.
He apparently doesn't know about the opposite negative
phase shift at the bottom of the coil where the shaft
attaches.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com