Current through coils
 

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

Current through coils
 

John Popelish wrote:

You two are so close to agreement. Standing waves have a current that
varies with position. The fact that the EZNEC simulation of a loading
coil shows differing current in a situation that is a fairly pure
standing wave situation (more energy bouncing up and down the antenna
than is radiating from it) means that the RMS current will vary along
the standing wave. And, since the simulation shows a different current
magnitude at the two ends of the coil, a significant part of a standing
wave cycle must reside inside the coil (more than the physical length
between the two ends of the coil would account for).

No, you're misinterpreting what you're seeing. Imagine an LC L network
with theoretically lumped series L and shunt C. If you look at the
currents at the input and output of the perfect inductor, you'll find
that they're exactly the same. If, however, you look at the currents in
and out of the *network* you'll see that they're different, because of
current going to ground through the C. And, as I said before, you can
even pretend it's a transmission line and measure forward and reverse
traveling waves and a standing wave ratio. But with zero length, there
can be no standing waves inside the inductor. Yet the terminal
characteristics of the network are the same as a transmission line. You
don't need to imagine standing waves residing inside the inductor in the
LC circuit, and you don't need to imagine them inside the inductor in
Cecil's model, either.

When you look at the currents reported by EZNEC for the model on Cecil's
web page, the current at the top of the coil is the equivalent to the
*network* current described above. It's the current flowing through the
inductance minus the current being shunted to ground via the C between
the coil and ground. You can tell just how much this is by looking at my
modified model and subtracting the current going into the coil from
ground from the current going into ground from the added wire. They're
not the same -- the difference is the displacement current through the C
from the inductor to ground. When I removed the ground, you could then
see the current flowing through the inductor, by itself, without the
current being shunted off. And lo and behold, it's nearly the same at
both ends of the inductor, showing that the inductor is behaving very
much like a lumped L. Only in conjunction with the C to ground does the
combination mimic a transmission line -- just like any other lumped LC
circuit.

Of course, at some length and/or poorness of interturn coupling, a coil
will start behaving in a way we can't adequately model as a lumped L.
But that's not the case here.

. . .

Roy Lewallen, W7EL

Current through coils
 

Cecil Moore wrote:
That's exactly the difference. But if you measure a single point,
you can't tell whether you are measuring a point on a traveling wave
or a standing wave. Agree?

I agree but who would be stupid enough to measure just a single
point?

Electronic components are exactly that stupid. They have no conception
of traveling or standing waves. They react simply to the voltages and
currents they experience at their terminals.

As far as current is concerned, that means the simple movement of charge
past a single point.

You see a larger picture of the whole antenna, so you can choose many
different ways to theorize about it. But your theory cannot be correct
if it requires that components behave in different, special ways
according to the way you happen to be thinking about it at the time.



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

Current through coils
 

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

Current through coils
 

John Popelish wrote:
Oh poo. At current nodes charge piles up and spreads out, on
alternating half cycles. For one half cycle, the pile is positive, and
for the next it is negative. This is a basic transmission line
concept. If transmission lines had no shunt capacitance, there would be
no place to put this charge. But there is, so it is no problem. Whether
the transmission line is coax, twin line or a slow wave helix makes
little difference. The process is similar. Isn't this what you have
been arguing?

If the forward traveling wave is equal in magnitude at both ends of the
coil, there is no net storage of energy due to the forward traveling wave.

If the reflected traveling wave is equal in magnitude at both ends of the
coil, there is no net storage of energy due to the reflected traveling
wave.

Superposing those two waves still results in no net storage of energy.
Sorry, got to hit the road.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

John Popelish wrote:
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.

Dr. Corum says the boundary is 15 degrees, or 0.04 wavelength.
Another place in his class notes he says that if 1/6 of a wavelength
of wire is used to make the coil, the lumped-circuit model will NOT
work. My 75m bugcatcher coil is more than 1/6 of a wavelength of
wire.

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.

Dr. Corum has a test equation to see if his velocity factor equation
applies. The test is: 5*N*D^2/lamda(0) = 1 where N is number of turns,
D is the diameter of the coil, and lamda(0) is the self-resonant
frequency. If this equation is satisfied, then equation (32) applies
for velocity factor. For my 75m bugcatcher coil, the test number is
0.4 = 1 and the velocity factor equation yields 0.0175. That's certainly
a slow wave device.

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.

A velocity factor of 0.0175 for a 75m bugcatcher seems to qualify.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

John Popelish wrote:
If there is a standing wave on a wire, and you have a
tiny current transformer sensor you can slide along the wire, you can
measure the instantaneous current (or the RMS) at any point along the
wire. If the sensor sits at a single point and sees an AC current, you
have no way, from this one measurement, if this current is the result of
a standing wave (two oppositely traveling equal waves adding), or a
single traveling wave, or any combination of traveling waves of
different amplitudes. You know only the net current at that point.

But if one it smart enough to slide the sensor up and down the wire
and note the phase is fixed and unchanging, one knows he is dealing
with a standing wave.

If you add the traveling current waves at each point along the line
and plot the amplitude of the sum (that is, of the total current)
versus position, you see a periodic relationship between the amplitude
and position. It's this relationship which is called a "standing
wave". It's so called because its position relative to the line stays
fixed. It's simply a graph of the total current (the sum of the
traveling waves) vs. position.

And that's all it is - the sum of two traveling waves. A standing wave
has no separate existence of its own. It is an artifact of superposition.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

John Popelish wrote:
Standing waves have a current that
varies with position. The fact that the EZNEC simulation of a loading
coil shows differing current in a situation that is a fairly pure
standing wave situation (more energy bouncing up and down the antenna
than is radiating from it) means that the RMS current will vary along
the standing wave. And, since the simulation shows a different current
magnitude at the two ends of the coil, a significant part of a standing
wave cycle must reside inside the coil (more than the physical length
between the two ends of the coil would account for).

And since a significant part of a standing wave cycle resides inside
the coil, it occupies a non-negligible percentage of a wavelength.
By every valid method, measured or calculated, a 75m bugcatcher
coil occupies tens of degrees of a wavelength (out of 360 degrees).
My best estimate is 60 degrees in a 75m mobile antenna.

In one case (the highest frequency one) the phase of the current even
reverses from one end of the coil to the other, as well as an amplitude
variation, indicating that a standing wave node occurs some where inside
the coil, and the two ends are on opposite ends of that node. If the
two currents had been equal, but 180 degrees out of phase, the node
would have been in the center of the coil.

Yes, if a current node exists inside a coil, the standing wave currents
are flowing into the coil at the same time from both ends and 1/2 cycle
later they are both flowing out of the coil at the same time. Wonder
how a lumped-circuit inductance handles that? :-)
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

K7ITM wrote:

Cecil wrote,
"The forward current is equal at both ends of the coil. The reflected
current is equal at both ends of the coil."

If that's really true, then the net current is precisely equal at both
ends of the coil.

I was speaking above about the magnitudes only, not the phases.
It was clear from the rest of my posting that was the assumption.
The fact that you attempted to change the meaning by trimming is
noted.

So to be perfectly clear, here is my statement re-worded using
a 45 degree phase shift through the coil.

The forward current magnitude is equal at both ends of the coil.
The reflected current magnitude is equal at both ends of the coil.

At the bottom of the coil, the forward current is 1 amp at zero deg.
At the bottom of the coil, the reflected current is 1 amp at zero deg.
At the bottom of the coil, the standing wave current is 2 amps at
zero deg.

At the top of the coil, the forward current is 1 amp at -45 deg.
At the top of the coil, the reflected current is 1 amp at +45 deg.
At the bottom of the coil, the standing wave current is 1.4 amp at
zero deg.

I asked if you knew how to do phasor math but you trimmed out that
phasor math part of my posting.
--
73, Cecil http://www.qsl.net/w5dxp

Current through coils
 

K7ITM wrote:

Cecil wrote, among other things,
"One amp of forward current is flowing into the coil and one
amp of forward current is flowing out of the coil. Charge is
balanced."

Absolutely NOT! You said the phase difference between the two ends is
45 degrees. Therefore, charge "input" and "output" is balanced ONLY
twice during a cycle, when the instantaneous currents are the same. No
phase need apply he we're talking INSTANTANEOUS currents.

Give us a break, Tom. Of course, we are *NOT* and never have been
talking instantaneous currents. All currents ever discussed concerning
this subject have been RMS currents. That's just your instantaneous
strawman. Long term charge accumulation is averaged over many cycles.
There is simply none of that because the traveling waves are not storing
any net charge inside the coil. How can you get so desperate as to play
such silly games?

My statement obviously meant: One amp of RMS forward current is flowing
into the coil and one amp of RMS forward current is flowing out of the
coil. Average charge is balanced.

Even though the standing wave current is different at each end of the
coil, the average charge into and out of the coil is still balanced.
--
73, Cecil http://www.qsl.net/w5dxp