Roy Lewallen wrote:
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.

And a transmission line mimics a lumped LC network, over a limited range.

We are still talking about an antenna loading coil, aren't we? This
is a coil made with a length of conductor that is a significant
fraction of a wavelength at the frequency of interest, and with low
coupling between the most separated turns. And with non zero
capacitance of every inch of that length to the rest of the universe
and to neighboring inches of the coil. To say it is acting in a
lumped way I can only assume that you mean a lumped model of it can be
produced that predicts its behavior with an acceptable approximation
at a given frequency. Sure, at a single frequency, lots of different
models can be useful. I am trying to get inside the black box and
understand how the device acts as it acts, not discover what
simplified models might approximate it under specific conditions.

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.

What can be calculated and what is going on are two different
subjects. Perhaps this difference in our interests is the basis of
our contention.

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.

Then we agree on this. Perhaps the words "slow wave transmission
line" have been copyrighted to mean a specific mechanism of slow wave
propagation, not all mechanisms that propagate significantly slower
than straight wire transmission lines do. If so, I missed that.

....
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.

I'll do a bit of looking. Thanks.

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.

You keep going back to how lumped components can mimic actual
distributed ones (over a narrow frequency range). I get it. I have
no argument with it. But why do you keep bringing it up? We are
talking about a case that is at least a border line distributed device
case. I am not interested in how it can be modeled approximately by
lumped, ideal components. I am interested in understanding what is
actually going on inside the distributed device.

. . .

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.

Or start with a less simplified theory that covers all cases, so you
don't have to decide when to switch tools.

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.

(if you add to that model, the appropriate lumped capacitors at the
appropriate places)

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.
Another reason to avoid that model, unless you are just looking for
the least amount of math to get an approximation. But computation has
gotten very cheap.

....
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?

A lumped inductor has no stray capacitance. Those also have to be
added to the model, before the effect would mimic the real coil
(neglecting radiation).

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.

But in the real world, the capacitance is always there. It varies,
depending on the location of the coil, but it never approaches zero.