John Popelish wrote:
. . .
I think I agree with just about every conclusion you are making about
treating coils as slow wave transmission lines. . .

A coil itself isn't a slow wave transmission line. In conjunction with
shunt C, it can be analyzed as a transmission line, but only in
conjunction with shunt C. Remove the shunt C and it ceases looking like
a transmission line. The earlier example of the modification to Cecil's
EZNEC model illustrated this -- when the ground (the other side of the
shunt capacitor) was removed, the current drop across the coil disappeared.

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.

Roy Lewallen, W7EL

Roy Lewallen wrote:
A coil itself isn't a slow wave transmission line. In conjunction with
shunt C, it can be analyzed as a transmission line, but only in
conjunction with shunt C.

A 75m bugcatcher has its own shunt C called "distributed capacitance".
It's what causes the self-resonant frequency of my 75m bugcatcher coil
to be only 60% higher than the 4 MHz operating frequency.

Remove the shunt C and it ceases looking like a transmission line.

That's true *only* for a lumped-circuit inductance. It is NOT true
for a 75m bugcatcher which has it very own distributed capacitance
built in. It is *IMPOSSIBLE* to remove the distributed shunt
capacitance from a 75m bugcatcher coil.

The earlier example of the modification to Cecil's
EZNEC model illustrated this -- when the ground (the other side of the
shunt capacitor) was removed, the current drop across the coil disappeared.

That may be true but please tell us how to remove the ground from a
75m mobile bugcatcher mobile antenna installation.

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.

Sorry Roy, Dr. Corum disagrees with your statement. You really should
read the details of the Dr. Corum web page references that I posted.

His test for the validity of his helix equations is:

5*N*D^2/lamda(0) = 1 where N is number of turns, D is diameter,
and lamda(0) is the self-resonant frequency.

That value for my 75m bugcatcher coil is 0.4 so his equation for
velocity factor is valid. The velocity factor for my 75m bugcatcher
coil calculates out to be 0.0175. Now that's what I call a "slow
wave" coil.

But I have offered all these references weeks ago. Are you too
arrogant to even have read them? (Another rhetorical question)
--
73, Cecil http://www.qsl.net/w5dxp

Roy Lewallen wrote:
John Popelish wrote:

. . .
I think I agree with just about every conclusion you are making about
treating coils as slow wave transmission lines. . .


A coil itself isn't a slow wave transmission line.

Not at all? It seems to me that any real, physical inductor must have
some lumped properties and some transmission line properties, and it
is the balance of these that must be considered in any particular case
to decide which analysis is the more accurate way to deal with it in a
circuit. Solenoidal air core inductors have a lot of transmission
line properties if the frequency is high enough. If this were not so,
they would look exactly like fixed capacitors above self resonance,
instead of having multiple impedance peaks and valleys.

In conjunction with
shunt C, it can be analyzed as a transmission line, but only in
conjunction with shunt C.

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.

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?

The earlier example of the modification to Cecil's
EZNEC model illustrated this -- when the ground (the other side of the
shunt capacitor) was removed, the current drop across the coil disappeared.

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.

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.

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

. . .
I think I agree with just about every conclusion you are making about
treating coils as slow wave transmission lines. . .


A coil itself isn't a slow wave transmission line.

Not at all? It seems to me that any real, physical inductor must have
some lumped properties and some transmission line properties, and it is
the balance of these that must be considered in any particular case to
decide which analysis is the more accurate way to deal with it in a
circuit. Solenoidal air core inductors have a lot of transmission line
properties if the frequency is high enough. If this were not so, they
would look exactly like fixed capacitors above self resonance, instead
of having multiple impedance peaks and valleys.

In conjunction with shunt C, it can be analyzed as a transmission
line, but only in conjunction with shunt C.

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.


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. 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. 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. 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. 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.

The earlier example of the modification to Cecil's EZNEC model
illustrated this -- when the ground (the other side of the shunt
capacitor) was removed, the current drop across the coil disappeared.

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

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.

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.

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.

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

(*) 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.

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. 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. 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.

Roy Lewallen, W7EL

Roy Lewallen wrote:
Well, not a "slow wave" transmission line. We shouldn't confuse an
ordinary lumped LC transmission line approximation with a true slow wave
structure such as a helical waveguide (next item). 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.

Dr. Corum gives a formula for calculating the velocity factor of coils
which meet a certain criteria. My 75m bugcatcher coil meets that
criteria. It's velocity factor calculates out to be 0.0175. It's
measured velocity factor is 0.015. That sounds like a "slow wave"
device to me.

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

The subject is 75m bugcatcher loading coils mounted on GMC pickups.
How the heck does the ground get removed?

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 ...

A 75m bugcatcher coil is not small.
--
73, Cecil http://www.qsl.net/w5dxp

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

But the point is that the delay through the coil is somewhere
between 40 degrees and 60 degrees. When you tried to measure
the phase shift through a coil, you used standing wave current
phase to make the measurement. Standing wave current phase is
unchanging so you made a measurement blunder.
--
73, Cecil http://www.qsl.net/w5dxp

Correction:

Roy Lewallen wrote:

(Last paragraph)

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. . .

The word "diameter" should be added:

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

Roy Lewallen, W7EL

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

So many words trying to avoid the real issue which is: What is
the percentage of a wavelength occupied by a loading coil. It
doesn't matter what the size of the coil is. In the real world,
a loading coil occupies a certain percentage of a wavelength.

For a small coil, that percentage will be small. For a large
coil that percentage will be large.

We have had to throw out your phase measurements using the phase
of standing wave currents because that phase you used is unchanging
whether in a wire or in a coil. Your phase measurements tell us
zero information about the delay through a coil.

That leaves us only with indirect measurements based on the self-
resonant frequency of the coil in the mobile environment or the
phase information left in the standing wave current amplitude over
the 90 degree antenna.

My self-resonant frequency measurements indicate that a 75m loading-
coil occupies 40-60 degrees of a 360 degree wavelength. That's
11%-17% of a wavelength. Dr. Corum's papers agree with that
estimate.

Another way of estimating the percentage of the antenna occupied
by the loading coil would be to plot the current segments from
feedpoint to tip. Then draw a cosine wave on the same graph with
0 degrees at the feedpoint and 90 degrees at the tip. A rough
estimate of the percentage occupied by the coil would be the
slice of the cosine wave from the bottom of the coil to the
top of the coil.

Mere words are not going to change the percentage of a wavelength
occupied by a real-world loading coil.
--
73, Cecil http://www.qsl.net/w5dxp

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