Ian White GM3SEK wrote:
In practical terms, a lumped-inductance model will take you straight to
a buildable prototype."

If you are a technician or a hobbyist, by all means
use the shortcuts. If you are an engineer or physicist,
to do so will lead your concepts astray.

Take the use of standing-wave current to try to measure
the delay through a 75m mobile loading coil. The results
of using the lumped-inductance model are off by a magnitude.
A 75m mobile loading coil is a distributed network that
is an appreciable percentage of a wavelength. As such, the
lumped inductance model is inadequate for analysis.

Here is a quote from my web page:

Many experiments and measurements have been made on loading
coils using net standing wave current. A lack of understanding
of the nature of standing wave current has resulted in some
strange and magical assertions about current through a loading
coil. The equation for standing wave current is of the form:

I(x,t) = Imax sin(kx) cos(wt)

For any point location 'x', it can be seen that the standing
wave current is not "flowing" in the ordinary sense of the word
but rather, is just oscillating in place at that fixed point.
EZNEC confirms that the phase of standing wave current is essentially
constant all up and down a typical HF mobile antenna and therefore
cannot be used to make a valid measurement of the phase shift (delay)
through a loading coil (or even through a wire.) The validity of that
statement is obvious if one understands the implications of the
standing wave current equation above. In fact, we can just as easily
write the standing wave current equation as:

I(x,t) = Imax sin(kx) cos(-wt)

We can reverse the direction of rotation of the standing wave
current phasor and still have the same value of current. Standing
wave current really doesn't have a direction of flow.
--
73, Cecil http://www.w5dxp.com