John Popelish wrote:
Roy Lewallen wrote:
. . .
In
my modification to Cecil's EZNEC file I showed how the coil behaves
the same with no antenna at all, just a lumped load impedance. As long
as the load impedance and external C stay the same, the coil behavior
stays the same.

Excellent. As long as there is external C, the coil acts in a non
lumped way, regardless of whether its current passes to an antenna or a
dummy load. This is the same result you would get with any transmission
line, also, except that the C is inside the line, instead of all around it.

No, the coil is acting in a lumped way whether the C is there or not. A
combination of lumped L and lumped C mimics a transmission line over a
limited range. But neither the L nor C is acting as more or less than a
lumped component. All the "transmission line" properties I listed in my
last posting for the LC circuit can readily be calculated by considering
L and C to be purely lumped components.

Well, not a "slow wave" transmission line.

Its propagation is a lot slower than a normal transmission line based on
straight conductors, isn't it?

There's more L per unit length than on an equal length line made with
straight wire, so yes the propagation speed is slower. But there's
nothing magic about that. A lumped LC circuit can be found to have
exactly the same delay and other characteristics of a transmission line,
and it can do it in zero length.


We shouldn't confuse an ordinary lumped LC transmission line
approximation with a true slow wave structure such as a helical
waveguide (next item).

Heaven forfend. ;-) I am not clear on the difference.

A slow wave structure is a type of waveguide in which the fields inside
propagate relatively slowly. Ramo and Whinnery is a good reference, and
I'm sure I can find others if you're interested.

The propagation velocity of the equivalent transmission line is
omega/sqrt(LC), so the speed depends equally on the series L and the
shunt C.

Per unit of length in the direction of propagation. Helical coils have
a lot of L in the direction of propagation, compared to straight wire
lines, don't they?

Yes indeed, as discussed above. And as I said above, you can get plenty
of delay from a lumped L and C of arbitrarily small physical size.

. . .
So what can we conclude about inductors from this similar behavior?
Certainly not that there's anything special about inductors
interacting with traveling waves or that inductors comprise some kind
of "slow wave structure". The duality comes simply from the
fundamental equations which describe the nature of transmission lines,
inductances, and capacitances.

The question, I think is whether large, air core coils act like a single
inductance (with some stray capacitance) that has essentially the same
current throughout, or is a series of inductances with distributed stray
capacitance) that is capable of having different current at different
points, a la a transmission line. And the answer must be that it
depends on the conditions. At some frequencies, it is indistinguishable
from a lumped inductance, but at other frequencies, it is clearly
distinguishable. You have to be aware of the boundary case.

Yes. It's a continuum, going from one extreme to the other. As Ian has
pointed out several times, any theory should be able to transition from
one to the other. The example Cecil posted on his web page was one for
which the L could be modeled completely adequately as a lumped L, at
least so far as its current input and output properties were concerned.
Being a significant fraction of the antenna's total length, it of course
does a substantial amount of radiating which a lumped model does not.

Because the LC section's properties are identical to a transmission
line's at one frequency, we have our choice in analyzing the circuit.
We can pretend it's a transmission line, or we can view it as a lumped
LC network. If we go back to the fundamental equations of each circuit
element, we'll find that the equations end up exactly the same in
either case. And the results from analyzing using each method are
identical -- if not, we've made an error.

But a continuous coil is not a series of discrete lumped inductances
with discrete capacitances between them to ground, but a continuous
thing. In that regard, it bears a lot of similarity to a transmission
line. But it has flux coupling between nearby turns, so it also has
inductive properties different from a simple transmission line. Which
effect dominates depends on frequency.

Yes, that's correct. But if it's short in terms of wavelength, a more
elaborate model than a single lumped inductance won't provide any
different results.


The coil in the EZNEC model on Cecil's web page acts just like we'd
expect an inductor to act.

A perfect point sized inductor? I don't think so.

Except for the radiation, yes. In what ways do you see it differing?

With ground present constituting a C, the circuit acts like an L
network made of lumped L and C which behaves similarly to a
transmission line. With ground, hence external C, absent, it acts like
a lumped L. (There are actually some minor differences, due to
imperfect coupling between turns and to coupling to the finite sized
external circuit.) The combination of L and C "act like" a
transmission line, just like any lumped L and C. And it doesn't care
whether the load is a whip or just lumped components.

I agree with the last sentence. The ones before that seem self
contradictory. First you say it acts just like an inductor, then you
say it acts like a transmission line. These things (in the ideal case)
act very differently.

Let me try again. The combination of L and the C to ground act like a
transmission line, just like a lumped LC acts like a transmission line.
With the ground removed, there's nearly no C, so there's very little
transmission-line like qualities. Of course you could correctly argue
that there's still a tiny amount of C to somewhere and so you could
still model the circuit as a transmission line. The equivalent
transmission line would have very high impedance and a velocity factor
very near one. Such a transmission line is difficult to distinguish from
a plain inductor.

. . .
Important for what? No matter how long the coil or how many turns of
the wire, a small (in terms of wavelength) inductor won't act like a
slow wave structure or an axial mode helical antenna.

But its propagation speed will be slower than it would be if the wire
were straight. don't know if that qualifies it for a "slow wave" line
or not.

That's the third time for this. Sure. A theoretical lumped inductor and
a theoretical lumped shunt capacitor can have a very slow propagation
velocity, and with no physical length at all. I'm failing to see why
this has some special relevance.

This is for the same reason that a two inch diameter pipe won't
perform as a waveguide at 80 meters -- there's not enough room inside
to fit the field distribution required for that mode of signal
propagation. There will of course be some point at which it'll no
longer act as a lumped inductor but would have to be modeled as a
transmission line. But this is when it becomes a significant fraction
of a wavelength long.

Why can't it be modeled as a transmission line before it is that long?
will you get an incorrect result, or is it just a convenience to model
it as a lumped inductor, instead?

Hm, I tried to explain that, but obviously failed. You can model it
either way. If you've done your math right, you'll get exactly the same
answer, because you'll find that you're actually solving the same equations.

. . .

Roy Lewallen, W7EL