Roy Lewallen wrote:
Now explain how you'd do it with a box having only two terminals -- and
assuming the box is very small compared to a wavelength.

Assume a one-wavelength dipole off-center fed 1/4WL from
one end. Using EZNEC with 60 segments, feeding at segment
number 15 is 24.2% from one end and that's close enough
for this example. This is actually done in EZNEC with a
130 ft. dipole on 7.2 MHz and I'll email out that file
upon request. I'm going to describe the current
distribution in the following diagram with 60 segments
running from left to right in *fixed font*. Eash dash
corresponds to a segment in EZNEC and F is the feedpoint.

seg L L seg
1 v v 60
--------------F---------------------------------------------
^ ^ ^
N N N

The current distribution is sinusoidal. N stands for 'node'
which is a current minimum point. L stands for 'loop' which
is a current maximum point. Since I'm limited to ASCII, the
reader will need to imagine a current envelope drawn from
seg 1 up to 'L', down to seg 30, back up to 'L', and back
down to seg 60. I'll follow this posting up with actual
EZNEC graphics posted to my web page.

Now we are going to replace part of that wire with a 6" long
coil. A 6" long coil on 7.2 MHz is about 1/3 of one percent
of a wavelength so that should qualify as 'very small'. And,
to illustrate another fact, I'm going to make the coil from
1/4 wavelength of wire, 33' on 40m, and try to model that
using the helical coil feature of EZNEC. That may or may not
violate an EZNEC design rule - I just don't know yet. But
it doesn't change the concepts being presented here.

Let me say this is a very rough approximation to what happens
in the real world. The concepts are accurate. The values may
be off by a relatively large percentage. The coil certainly
distorts the current away from that near-perfect sinusoid and
certainly doesn't radiate like the wire it replaces. But roughly,
here will be the results of placing the bottom of the coil at
seg 30:

seg L L seg
1 v v 46
--------------F---------------////----------------
^ ^ ^
N N N

The current at the left end of the coil will be low because
that is roughly the location of a current node (minimum). The
current at the right end of the coil will be high because that
is roughly the location of a current loop (maximum). If one
considers the current flowing from left to right, more current
will be flowing into the coil than is flowing out of it, like
the current at:

http://www.qsl.net/w5dxp/qrzgif35.gif

This is a standing-wave antenna so the standing-wave current
displayed by EZNEC is flowing hardly at all. That standing-
wave current consists of two component phasors, rotating in
opposite directions. That's why the phase of the standing-wave
current is relatively constant. The standing-wave phasor, the
superposition of the forward and reflected current phasors,
rotates hardly at all, usually by just a few degrees from end
to end in a 1/2WL dipole. If the dipole is made of 'thin wire',
the phase of the standing-wave current is fixed at zero degrees.
(Can a phasor that doesn't rotate be called a phasor?)

Taking 1/4WL of the antenna wire and winding it into a high-Q
coil above replaces *roughly* 90 degrees of the antenna. The
radiation pattern certainly changes because the coil doesn't
radiate much. But we are not concerned about radiation patterns
in this discussion. We are concerned about the current at each
end of the coil, the same current that we measure and the same
current reported by EZNEC. That current is certainly not constant
through the coil and THE DIFFERENCE IN THE MAGNITUDE OF THE
CURRENT AT EACH END OF THE COIL DEPENDS UPON WHERE IT IS PLACED
IN THE STANDING-WAVE SYSTEM.

The traveling-wave current through a coil is close to equal at
each end. The standing-wave current at each end of a coil is
NOT equal unless we locate the center of the coil at a current
node or at a current loop. In a bottom-loaded mobile antenna,
the coil is located very near a current loop where the slope
of the current is near zero. In fact, the net current peaks
inside the bottom-loading coil.

So the concept that net current at each end of a coil installed
in a standing-wave environment is equal is just a myth, an old
wives' tale that needs to be banned from ham radio.

The coil does indeed cause considerable distortion away from the
perfect cosine current wave exhibited by a thin wire. But the
macro effects of that cosine wave still exist when a coil is
installed. The current at each end of a coil installed in a
standing-wave antenna depends upon its location in the system.
--
73, Cecil http://www.qsl.net/w5dxp