Roy Lewallen wrote:

no, you can't put a box around anything having any length and expect
the current in to equal the current out. And why should this be
surprising to anyone?

Possibly because radio amateurs are not taught well about what a "lumped
component" is. All lumped components are defined as having zero (or
negligible) physical dimensions relative to the wavelength at the
operating frequency. Similarly, lumped networks are defined as having
zero (or negligible) lead lengths relative to the operating wavelength.

In this idealized case, the current into and out of the two terminals of
a lumped inductor is always exactly the same. This remains true even if
that component is embedded into an antenna where current variations
along the length of the conductor do exist.

Because all practical components and networks have some finite physical
size, lumped-component behaviour is never absolutely perfect. In
principle, any real component must also show some "antenna-like"
behaviour, which does allow some variation of current between its
terminals... but in practice this effect is usually very small indeed.
For example, for physically small components the lumped-component
approximation works well in circuit simulations at frequencies up to
several GHz. (You may have to simulate each component as a small network
in order to account accurately for self-capacitance, self-inductance and
loss resistance, but these are still networks of idealized lumped
components.)


Yes, a solenoid produces a local (near) field in the direction of its
axis. The far field that remains depends on the size and aspect ratio
of the solenoid. Hence, we have solenoidal antennas that radiate
primarily axially and those which radiate primarily radially. It's not
clear to me how this bears on the topic.

Quite a lot, I think. At one extreme, a loading coil may be so small
that it behaves as a near-perfect lumped inductor. Such an inductor will
not radiate, and will have almost zero difference in current between its
two terminals. Those two properties - lack of radiation and no
difference in terminal currents - are locked together.

At the other extreme, you may have a long, skinny loading coil that has
significant antenna-like properties, radiating at right-angles to its
length like a "rubber-duck" (more formally known as a normal-mode
helix). In this case the coil does form part of the radiating structure,
so you do expect to see a variation in current along the length of the
coil, and hence a difference between the currents at its two ends. Once
again, the two properties of radiation and current variation are locked
together.

This brings us back to the question of practical loading coils, and how
much radiation (and therefore current variation along the length) we can
expect. I haven't ever tried to work it out, but my guess is that a
fairly short "square" coil that has been optimized for high Q is not
going to radiate much, and that we therefore shouldn't expect a large
difference in current between its two ends.

Let's see now... a 3.5MHz loading coil that is as much as 10 inches long
would scale down to 0.010 inches at 3.5GHz... at that frequency I'd
expect to be able to model such a tiny inductor very accurately as a
small network of lumped components with no radiating properties.

On the other hand, people who mistakenly believe that even an ideal
lumped inductor can have a difference between the currents at its two
terminals are rather unlikely to be convinced.



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