John Popelish wrote:
Roy Lewallen wrote:
John Popelish wrote:
Roy Lewallen 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. 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.

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.

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. 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. 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).


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.

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?

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)

No. The inductor itself can be adequately modeled as a lumped inductor
without any capacitors at all. 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. 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.
Removing the ground lets us see the inductor current by itself.


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.

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.

. . .

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).

By removing the ground in the model on my web site, I found that a
lumped inductor mimics the real inductor very well without any C. Of
course, to model an inductor close to ground requires adding a shunt C.
Modeling an inductor connected to a resistor would require adding a
resistor to the model. But we shouldn't confuse what the inductor is
contributing to the performance of the circuit with what the other
components are. And that confusion has been common here.

. . .

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

It can get insignificantly small, as in the modified model. But that's
really beside the point. The point is that the shunt C isn't an inherent
property of the inductor, and the current difference between the top and
bottom of an electrically short coil is due to the current flowing
through the external shunt C, however big or small it is. It's not due
to waves bouncing around inside the coil or painstakingly winding their
way turn by turn from one end to the other, or by any inherent and fixed
property of the inductor or the antenna it's connected to.

Roy Lewallen, W7EL