Roy Lewallen wrote:
John Popelish wrote:

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.


I'm sorry I haven't explained this better. If we start with the inductor
in, say, the example antenna on Cecil's web page, we see that the
magnitude of current at the top of the inductor is less than at the
bottom of the inductor. Cecil has promoted various theories about why
this happens, mostly involving traveling wave currents and "replacement"
of "electrical degrees" of the antenna. He and others have given this as
proof that the current at the two ends of an inductor are inherently
different, regardless of its physical size.

I agree up till you add, "regardless of physical size". I have seen
him talk only about large air core space wound coils. I came to the
discussion late, but this is what I have seen.

My counter argument goes
something like this:

1. If we substitute a lumped component network for the antenna, there
are no longer traveling waves -- along the antenna at least -- and no
number of "missing electrical length" for the inductor to replace. Or if
there is, it's "replacing" the whole antenna of 90 degrees. Yet the
currents in and out of the inductor are the same as they were before. I
feel this is adequate proof of the invalidity of the "replacement" and
traveling wave arguments, since I can reproduce the same results with
the same inductor without either an antenna or traveling waves. This is
shown in the modified EZNEC file I posted.

But what is the need for such an argument? Just to prove that lumped
component networks can model real, distributed things? I get that.
As I see Cecil's point (and I hate to say this with him absent), it is
that real, large coils with all their poor turns coupling and stray
capacitance both turn to turn and more important, to ground, take a
lot of those lumped components to model, accurately, but only their
own self, described by distributed network concepts to model, accurately.

2. The argument that currents are inherently different at the ends of an
inductor is shown to be false by removing the ground in the model I
posted and replacing it with a wire. Doing so makes the currents nearly
equal.

But the ground is there, in the application under discussion. All
components act differently if you connect them to something else.
This coil is connected to ground by its capacitance.

3. Arguments have then been raised about the significance of the wire
and inductor length, and various theories traveling waves and standing
waves within the length of the coil. Let's start with the inductor and
no ground, with currents nearly equal at both ends. Now shrink the coil
physically by shortening it, changing its diameter, introducing a
permeable core, or whatever you want, until you get an inductance that
has the same value but is infinitesimal in physical size. For the whole
transition from the original to the lumped coil, you won't see any
significant(*) change in terminal characteristics, in its behavior in
the circuit, or the behavior of the whole circuit.

Sounds reasonable to me. But it is not the application in question.

So I conclude there's
no significant electrical difference in any respect between the physical
inductor we started with and the infinitesimally small lumped inductor
we end up with. And from that I conclude that any explanation for how
the original inductor worked must also apply to the lumped one.

But only if you reduce the capacitance to ground to a low enough value.

That's
why I keep bringing up the lumped equivalents. We can easily analyze the
lumped circuit with elementary techniques; the same techniques are
completely adequate to fully analyze the circuit with real inductor and
capacitance to ground.

(*) I'm qualifying with "significant" because the real inductor doesn't
act *exactly* like a lumped one. For example, the currents at the ends
are slightly different due to several effects, and the current at a
point along the coil is greater than at either end due to imperfect
coupling among turns. But the agreement is close -- very much closer
than the alternative theories predict (to the extent that they predict
any quantitative result).

I have no argument with any of that.

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


That's fine, too. Will Cecil's theory explain the behavior of a lumped
constant circuit? Or everywhere along the transition between the
physical inductor and lumped circuit I described above?

Distributed network theory includes the possibility of lumped
components, it is just not limited to them.

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


No. The inductor itself can be adequately modeled as a lumped inductor
without any capacitors at all.

Not if it is located in close proximity to ground, as this coil in
question is located. It does not act like any kind of pure
inductance, but as a network that contains some inductance and also
some other effects.

When you add ground to the model, you
have to add the equivalent shunt C to the lumped model. The C isn't a
property of the inductor itself; it's the capacitance between the
inductor and ground.

That is a very strange statement to my mind. Stray capacitance is an
unavoidable effect that any real inductor in any real application will
have as a result of it having non zero size. A thing made of wire
that takes up space has inductive character and capacitive character,
and transmission line character, and loss, all rolled into one. You
can set the situation up that it finds itself in, is that some of
those properties not very significant, but that are all part of the
effect of a real, physical inductor. I don't understand why you keep
pretending that these non ideal effects are the fault of something
else. They are a result of the device taking up space and being made
of metal.

This difference is the source of confusion and
misunderstanding about the current -- the current we see at the top of
the inductor is the current exiting the inductor minus the current going
via the shunt C to ground. It's not due to a property of the inductor
itself. We're seeing the *network* current, not the inductor current.

I agree. But a large, air core, spaced turn coil is a network, not a
pure inductance. This is just reality.

Removing the ground lets us see the inductor current by itself.

Or, emphasizes that particular aspect of its nature.

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.


The problem is that it obscures what's happening -- we can no longer
easily tell which effects are due to the radiation, which are due to the
capacitance, and which are inherent properties of inductance unless we
separately analyze separate simplified circuits (as I did with EZNEC).
And that's really what the whole disagreement has been about. Effects
due to shunt capacitance have been claimed to be inherent properties of
all inductors, and elaborately crafted theories developed to attempt to
explain it. If all you want is numbers, they're plenty easy to get
without the programmer needing to have the slightest understanding of
what's happening. And he will have learned nothing he can apply to other
situations.

Distributed analysis is just fine, but it should predict the same coil
currents with the antenna replaced by lumped components. And it should
predict nearly equal currents in the inductor ends when ground is
removed. And it should predict the same results when the coil and the
shunt C to ground are replaced by lumped components. Because that's what
really happens. My simplified lumped component analysis does all this. A
rigorous solution of the fundamental equations for distributed networks
does this also -- EZNEC does its calculations with just such equations
and reaches the correct conclusions. But I don't believe that Cecil's
theories and methods provide the correct results in all these cases.
(snip)

Sorry, here is where I have to withdraw. I can't say what Cecil is
thinking.