Roy Lewallen wrote:
John Popelish wrote:

. . .
I think I agree with just about every conclusion you are making about
treating coils as slow wave transmission lines. . .


A coil itself isn't a slow wave transmission line.

Not at all? It seems to me that any real, physical inductor must have
some lumped properties and some transmission line properties, and it
is the balance of these that must be considered in any particular case
to decide which analysis is the more accurate way to deal with it in a
circuit. Solenoidal air core inductors have a lot of transmission
line properties if the frequency is high enough. If this were not so,
they would look exactly like fixed capacitors above self resonance,
instead of having multiple impedance peaks and valleys.

In conjunction with
shunt C, it can be analyzed as a transmission line, but only in
conjunction with shunt C.

But any real, physical inductor has shunt capacitance to its
surroundings. So if you neglect this without considering whether or
not this is reasonable, you are going to be blindsided by its effects,
eventually.

Remove the shunt C and it ceases looking like
a transmission line.

How do I remove the shunt C of an inductor? With an active guarding
scheme?

The earlier example of the modification to Cecil's
EZNEC model illustrated this -- when the ground (the other side of the
shunt capacitor) was removed, the current drop across the coil disappeared.

So whether or not this coil is acting as a slow wave transmission line
in addition to being inductive depends on the surrounding fields and
connections? I have no trouble with that.

As far as considering a coil itself as a "slow wave structure", Ramo and
Whinnery treat this subject. It's in the chapter on waveguides, and they
explain how a helix can operate as a slow wave waveguide structure. To
operate in this fashion requires that TM and TE modes be supported
inside the structure which in turn requires a coil diameter which is a
large part of a wavelength. Axial mode helix antennas, for example,
operate in this mode. Coils of the dimensions of loading coils in mobile
antennas are orders of magnitude too small to support the TM and TE
modes required for slow wave propagation.

I'll have to take your word for this limitation. But it seems to me
that the length of the coil in relation to the wavelength and even the
length of the conductor the coils is made of are important, also.