Roy Lewallen wrote:
John Popelish wrote:
(snip)

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.

I don't disagree with anything you've said. The point I was trying to
make was that the resemblance of a coil to a transmission line depends
not only on the coil but also its capacitance to other objects -- and
not to its relationship to traveling current waves. One thing I've seen
done on this thread is to use the C across the inductor in transmission
line formulas, appearing to give the coil a transmission line property
all by itself and without any external C. This is incorrect.

Yep. It is capacitance between each part of the coil and somewhere
other than the coil that makes it act like a transmission line.

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?


Actually, you can reduce it to a negligible value by a number of means.
One I've done is to wind it as a physically small toroid.

Yes, smaller means less shunt capacitance. But less is not zero.
There is always some.

In the example
discussed in the next paragraph, removing ground from the model reduces
the external C to a small enough value that the current at the coil ends
become nearly equal.

Nearly equal, but not equal, yes. In some cases nearly is close
enough to equal that you can neglect it and get a reasonable
approximation. In other cases the approximation is not so reasonable.
It is a matter of degree.

That of course isn't an option in a real mobile
coil environment, but it illustrates that the current drop from one end
to the other, which in some ways mimics a transmission line, is due to
external C rather than reaction with traveling waves as Cecil claims.

I don't see it as a "rather", but as an effect that becomes non
negligible under some circumstances.

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.

This isn't, however, to discount the possibility of the coil
interacting with the antenna's field. It just wasn't significant in that
case.

Okay.

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.


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?

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.

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?

And let's talk for a minute about the coil "acting like" a transmission
line. A transmission line is of course a distributed circuit. But you
can make a single pi or tee section with lumped series L and shunt C
which has all the characteristics of a transmission line at one
frequency(*), including time delay, phase shift, characteristic
impedance, impedance transformation, and everything else. If put into a
black box, you wouldn't be able to tell the difference among the pi,
tee, or transmission line -- at one frequency. You could even sample the
voltage and current with a Bird wattmeter and conclude that there are
traveling voltage and current waves in both cases, and calculate the
values of the standing waves on either "transmission line". And this is
with a pure inductance and capacitance, smaller than the tiniest
components you can really make. With a single section, you can mimic any
transmission line Z0 and any length from 0 to a half wavelength. (The
limiting cases, however, require some components to be zero or
infinite.) So you can say if you wish that the inductor in this network
"acts like" a transmission line -- or you can equally correctly say that
the capacitor does, because it's actually the combination which mimics a
transmission line. But only over a narrow range of frequencies, beyond
which it begins deviating more and more from true transmission line
behavior. To mimic longer lines or mimic lines over a wider frequency
range requires more sections.

Hence a description that includes both lumped and distributed attributes.

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.

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.

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.

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.

(*) It actually acts like a transmission line at many frequencies, but a
different length and Z0 of line at each frequency. To mimic a single
line over a wide frequency range requires additional sections.

I think I agree with this. Either a simple transmission line or a
simple inductance description is incomplete. It does some of both.

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.


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.

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?

If the turns are very loosely
coupled to each other, the wire length becomes more of a determining
factor. As I mentioned in earlier postings, there's a continuum between
a straight wire and that same wire wound into an inductor. As the
straight wire is wound more and more tightly, the behavior transitions
from that of a wire to that of an inductance. There's no abrupt point
where a sudden change occurs.

Yes.

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

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.

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

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.

John Popelish wrote:

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.

Cecil's point is rather obscure, but as I read it Cecil thinks the ONLY
way to model a loaded antenna is through reflected wave theory.

As I understand what Cecil writes, he seems to be saying if we use a
current meter we cannot measure current. If we look at an inductor's
properties he seems to say they change in the presence of standing
waves. He also seems to be saying a loading inductor replaces a certain
number of electrical degrees through some reflection property.

What most others seem to be saying is an inductor is an inductor. It
behaves the same way and has the same characteristics no matter how it
is used, so long as we don't change the displacement currents by
varying capacitive coupling to surroundings.

That is where the difference is.

I can easily build a loading coil that has no appreciable change in
current from end-to-end. My measurements of typical loading coils shows
it is the ratio of load (termination) impedance to capacitance to the
outside world that controls any difference in current, and not the
"electrical degrees" the coil replaces. It is also not the reflected
waves that cause the unequal currents, but rather the fact the inductor
has distributed capacitance to earth or other objects besides the coil.

Capacitance from the coil to itself won't cause these problems. The
change in phase of current at each end of a coil would depend heavily
on stray C of the coil to the outside world as compared to reactance of
the coil, and it would also depend on less than perfect flux linkage
across the inductor.

I measured a typical inductor and found it did have more phase delay in
current at each terminal than the actual spatial length of the coil
form would indicate. I measured a delay about equal to double the
length of the 10 inch coil form length. If the inductor was perfect,
the delay would be about equal to light speed across the length of the
inductor form.

The only thing in all of this I can't find agreement with is what Cecil
is saying. I'm not disputing currebnt can be different, and phase can
be different. What I am disputing are Cecil's claims that an inductor
behaves differently in an antenna than in a lumped system that
represents the antenna, and that the cause of inequality in currents or
phase delay is caused by reflected waves and cannot be understood
without applying reflected wave theory.

In my experience, either lumped circuits or reflected waves will work
IF applied correctly.

This is my take of the disagreement.

73 Tom

Tom, the W8JI one, wrote, among other things,
"Capacitance from the coil to itself won't cause these problems. The
change in phase of current at each end of a coil would depend heavily
on stray C of the coil to the outside world as compared to reactance of
the coil, and it would also depend on less than perfect flux linkage
across the inductor."

I've lost track of exactly what "these problems" are, but I was
wondering about the "and it would also depend on less than perfect flux
linkage across the inductor" part. To help resolve that, I did a Spice
simulation; I modelled a transmission line with ten "L" sections
cascaded. Each was 1uH series, followed by 100pF shunt to ground. I
put a 100 ohm load on one end and fed the other end with a 2.5MHz sine
wave with 100 ohms source resistance. Sqrt(LC) is 10 nanoseconds per
section, so I expect 100 nanoseconds total delay, or 90 degrees at
2.5MHz. That's what I saw. Then I added unity coupling among all the
coils, and to keep the same net inductance, I decreased each inductor
to 100nH. The result was STILL very close to a 90 degree phase shift,
with a small loss in amplitude. In each case, the current in each
successive inductor shifts phase by about 1/10 the total. Although the
simulation is less than a perfect match to a completely distributed
system with perfect flux linkage (and just how you do that I'm not
quite sure anyway...), but it's close enough to convince me that
perfect flux linkage would not prevent behaviour like a transmission
line, given the requisite distributed capacitance.

(That was from a "transient" simulation, 10usec after startup so it
should be essentially steady-state; but I'll probably play with an AC
sweep of both cases as I find time.)

Cheers,
Tom

On Fri, 24 Mar 2006 20:13:26 -0500, John Popelish
wrote:

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.

Hi John,

One of the problems is the thread discussion is freely mixed with
practical observations and theoretical arguments - these can clash,
especially when mixed indiscriminately to prove one point.

First, several years ago, came the shocking observation that the
current into a coil is not the same as the current out of it.
Somewhere along the debate, this practical measurement was then
expressed to be in conflict with Kirchhoff's theories. However,
Kirchhoff's current law is for currents into and out of the same point
intersection, not component. The association with a point is found in
that the "lumped" inductance is a dimensionless load. The association
with Kirchhoff was strained to fit the load to then condemn the load
instead of simply rejecting that failed model and using the correct
one.

The problem came from incorrectly specifying the coil in EZNEC which
offers a coil generator (inductor) in the wires table as well as a
coil specification (inductance) in the loads table. This shocking
difference between model and observation would have been easily
resolved by simply using the coil generator (inductor) in place of the
lumped equivalent (inductance).

How do you know when you've made a mistake in application? You do two
designs and compare each to what nature provides. You discard the
model that does not conform to nature.

Want to know what the difference is between the two (the good and the
bad design) at the far receiver? ±.32dB Hence the name of my thread
"Current through coils - BFD."

....snip

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.

Roy's point is that the proposed "theory," as Ian has also pointed
out, has to correctly answer all scenarios, not just one. We don't
have enough shelf space in libraries that prove the resistance of each
resistor constructed - one formula does quite well for 99.999% of
them, and a couple more formulas for those that don't (and those new
formulas will give the same answer for the first 99.999% as well).

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.

You are mixing an observational fact with a theoretical statement. The
lumped model contains ONLY inductance, to make it conform to nature,
as Roy is doing here, you have to add in all the nasty bits.

OR

Build a helix (inductor) in the wires table.

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.

These are all properties that reside in a helix (inductor) constructed
in the wires table. Some of these properties (like inductance) also
reside in the load table, but not the capacitance to earth. If it
matters, it is up to you to make the correct choice.

....snip

Well, the rest was more conflict between theory and practice that is
and has been resolvable for a long time. Even the conflict is
separable. For those who persist in making poor choices, they will
always have either a problem with a model, or the genesis of a new
theory, or rattle on beyond 500 posts - sometimes all three.

73's
Richard Clark, KB7QHC

Thanks, Tom and Richard. I've said what I want to say in just about
every way I can possibly think of, and without a great deal of success
in communicating to John what I mean. I hope you'll have better luck --
I've run out of different ways to say it. I hope some of the readers, at
least, have understood what I've been saying.

Roy Lewallen, W7EL

Richard Clark wrote:

First, several years ago, came the shocking observation that the
current into a coil is not the same as the current out of it. Somewhere
along the debate, this practical measurement was then expressed to be
in conflict with Kirchhoff's theories. However, Kirchhoff's current
law is for currents into and out of the same point intersection, not
component. The association with a point is found in that the "lumped"
inductance is a dimensionless load. The association with Kirchhoff was
strained to fit the load to then condemn the load instead of simply
rejecting that failed model and using the correct one.


So much has been said in this debate - and this is at least the third or
fourth re-make of the whole show - that I honestly cannot remember if
the exact words that Richard reports were ever used.

If they were, then they were excessively condensed, skipping some
essential steps in the explanation. Both sides of the debate have often
been guilty of skipping details that seemed "obvious" (at least to their
way of thinking) in order to get to their main point.

So please let me try to respond to Richard's criticism above. Since I
don't want to skip anything this time, this is going to take a little
longer.

If there's anything that someone doesn't agree with, please comment...
but please read the whole thing first. Many of the problems with this
debate are because people start to throw in comments before finding out
where the original poster is heading. This destroys any kind of
connected thinking, and reduces the "debate" into a series of
disconnected nit-picks.


The main electrical property of the thing we call a "coil" or "inductor"
is - obviously - inductance. But a real-life coil has many other
properties as well, and these complicate the picture.

If we're going to understand loading coils at all, we first need to
strip away all the complications, and understand what loading by pure
inductance would do. Then we can put back the complications and see what
difference they make.

If we want to understand real-life loading coils, it's absolutely vital
to understand which parts of the coil's behaviour are due to its
inductance, and which parts are due to other things.

Please have patience about this. If we cannot even agree what pure
inductance does, then this debate will run forever...

From the beginning, then:

"Lumped" inductance is another name for the pure electrical property of
inductance, applied at a single point in a circuit. It has none of the
complications of a real-life coil: no physical size, no distributed
self-capacitance, and no external electric or magnetic fields. Its only
connections with the antenna are through its two terminals. Lumped
inductance is just inductance and nothing else.

Unlike capacitance, inductance has NO ability to store charge. If you
push an electron into one terminal of a pure inductance, one electron
must instantaneously pop out from the other terminal. If there was any
delay in this process, it would mean that charge is being stored
somewhere... and then we'd no longer be talking about pure inductance
[1].

The inability to store charge means there can be no difference between
the instantaneous currents at the two terminals of a lumped/pure
inductance. Any difference in amplitude or phase at a given instant
would mean that charge is being stored or borrowed from some other time
in the RF cycle... which inductance cannot do. There is some kind of
difference in phase and amplitude in the voltage between its two
terminals, but not in the current.

Therefore any difference in currents between the two ends of a real-life
coil are NOT due to its inductance. They come from those OTHER
properties that make a real-life coil more complicated.

But let's stay with loading by pure lumped inductance for a little
longer, and look at a centre-loaded whip. The loading inductance is
responsible for almost all the features of the voltage and current
profiles along the antenna.

Starting at the bottom (the feedpoint), voltages are low and currents
are high, so the feedpoint impedance is low. Going up the lower part of
the whip, the magnitudes of the voltage and current remain almost
constant until we meet the loading inductance.

As we have seen, if the whip is loaded by pure inductance only, there is
no change in current between the two terminals of the inductance - but
there's a big step increase in voltage. At the upper terminal, the
current is the same but the voltage is very high, so we're into a much
higher-impedance environment.

As we go further up towards the top of the whip, current magnitude has
to taper off to zero at the very top. This also means that the voltage
magnitude has to increase even more as we approach the top of the whip.

Single-point loading by pure inductance has thus created almost all the
major features that we see in a practical centre-loaded whip -
particularly the big step change in voltage across the loading coil.

What we don't see in a practical antenna are exactly equal current
magnitudes and zero phase shift between the terminals of a real-life
loading coil - but that is ONLY because a real-life coil is not a pure
inductance. The harder we try to reach that ideal (by winding the coil
on a high-permeability toroidal core which confines the external fields
and allows the whole thing to become very small), the closer the
currents at the bottom of the coil come to being equal. Solid theory and
accurate measurements come together to support each other. The only gap
between theory and practice is due to our inability to construct a pure
inductance that has no other complicating properties.

If we can agree about pure inductive loading, we all have a firm place
to stand. Then we can then put back those "other" complicating
properties of a real-life loading coil, and see what difference they
make.





[1] This principle of "conservation of charge" is also the underlying
principle of Kirchhoff's current law. If you connect three ordinary
wires together, the current flowing into the junction from one wire must
be exactly and instantaneously balanced by the currents flowing in or
out on the other two wires. If this was not so, there would have to be
some means of adding, storing or losing electrons at the junction...
which contradicts our initial assumption of three simple wires with no
special properties.

It is not strictly accurate to say that Kirchhoff's current law applies
to pure inductance, but the underlying principle of "conservation of
charge" does apply.





--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek