Cecil, et al:

I think the real key to this mystery is to consider the
wave velocity in the loading coil. Admittedly at the
beginning of this debate (I have been following the
debate since the big W8JI / K3BU shootout on the
Topband email reflector) I was squarely in the lumped
element camp, but Cecil Moore's thought provoking
arguments have begun to give me reason for pause.
Here's why:

Under the lumped circuit view of things, there is no
delay between current going into the inductor and the
current coming out the other terminal. There is a 90
deg phase shift between the inductor current
and its terminal voltage, but there is no need to introduce
the notion of a delay between the input and output currents
in order to account for an inductor doing inductor like
things. All one needs to get inductor like behavior is a
two-terminal black box whose terminal voltage is equal
to L times the derivative of the current passing thru it
(e.g. L = di/dt). If one could build such a black box
(unfortunately, I am afraid it is akin to building an isotropic
radiator), it could be used in place of a real inductor in all
manner of tuned circuits and impedance matching
applications. In fact, we routinely use such a black box to
simulate real inductors in programs like Spice, EZNEC,
Touchstone, etc. And in many of these applications, the
ideal inductor is a reliable proxy for a real inductor.

Now let's consider a parallel two-wire transmission line.
If I have such a line with a Zo of say 450 ohms, and I
open circuit one end of the line and drive the other
end with an RF generator, I will get a nice sinusoidal
standing wave pattern along the length of the line that
bears a striking resemblance to the current distribution
on a linear antenna element. At 1/4 wavelength from the
open end of this line, I will be at a current maximum where
the input impedance is very close to a short circuit (
I am assuming a low-loss line with minimal radiation).
If I now break this 1/4 wavelength long line in the middle
and remove a section of line and replace it with a pair
of my black box ideal inductors (one ideal inductor
in series with each leg of the transmission line), I should
be able to adjust the value of the inductors such that I
can replace the missing section of line and achieve a
current maximum/short circuit condition at the input of
the line (e.g. resonance).

At this point, I should look at the knobs on my two black
box ideal inductors, read off the inductance values, and
note the readings for future reference. Now, given that my
inductors are ideal, there will be no current taper across
them as there was in the transmission line section
that they replaced. You can verify this with a circuit
simulator, like Serenade, Touchstone, or Superstar. This
derives from the fact that there is no propagation delay
through an ideal inductor. The current going into an ideal
inductor is always in-phase (and of equal magnitude) with
the current leaving it.

Okay now that we have dealt with the ideal case,
let's remove the black boxes and replace them with a
pair of parallel ganged roller inductors (actual real parts
you can buy on Ebay!). As with the black box case, I
should be able to adjust the inductance values of the
ganged inductors until I achieve resonance (maximum
current/minimum impedance) at the input to the parallel
wire transmission line. Again, I will note and record the
readings on the calibrated turns counters for future
reference. Now let's take a close look at the setup. I now
have two roller inductors with their axis parallel to the
longitudinal axis of the transmission line. The centerlines
of the two roller inductors are some distance "d" apart
from each other. If I just consider the 4 terminal
network formed by these two inductors, it begins to
look an awful lot like a parallel two-wire delay line of
length, L and some unknown characteristic impedance,
Zd and unknown velocity of propagation, Vp.

Uh oh!! now we have some delay associated with our
"loading coils". A TEM mode wave impinging on the
input to this 4 terminal "delay line" network will propagate
at some finite Vp. Thus if I terminate the output of the
real inductor network with the proper Zo, the input current
will be equal to the output current, but with some finite
delay between the input current and the output current.

Now if I reinsert this delay contraption back into my
450 ohm two-wire line, it will still produce the same
resonant condition as before (I didn't change the
inductance settings), but now that I know it has some
delay associated with it, I should expect to see some
taper in the current along its length. Of course, the fact
that the Zd of the "delay line" doesn't necessarily match
the Zo of the 450 ohm line probably complicates
matters. I'll most likely generate reflections at the
input to the inductor assembly, and re-reflections at
the output (reward traveling wave). Still, I have satisfied
the condition for generating a taper across these real
inductors. After all, borrowing from Cecil Moore's
argument, the delay along a linear mismatched
transmission line is what is responsible for the
observed taper in the current (e.g. standing wave).

Now for the $64,000 dollar question. What is the Zd
and Vp of the ganged roller inductor assembly. Will
the Vp necessarily bear some fixed relationship to
the inductive reactance of the inductors, or will this
depend on the form factor of the inductor assembly.
Will the length of the inductor assembly divided by
the wave velocity, Vp be equal to the delay of the line
section that it replaced, or will this delay depend on
the form factor of the inductor assembly (using ferrites
versus air core inductors, I can easily envision two
pairs of parallel inductors with the same inductive
reactance, but very different form factors). Will the
value of inductive reactance needed to "resonate" my
loaded transmission line vary with the delay and or
form factor of the parallel loading inductors, or will
this value be fixed and equal to the value of inductive
reactance required when I was using the ideal "black
box" inductors?

Hopefully you alll see where I am going with
this. What say, Gents?

73 de Mike, W4EF.....................................

"Cecil Moore" wrote in message

Jimmy wrote:
lumped inductance = lumped change in current.

Actually, I think the assertion was that
lumped inductance = no change in current.
--
73, Cecil http://www.qsl.net/w5dxp