Brainteaser

[W5DXP]

Someone's mathematics is a bit off.

The math is off by the losses (I^2*R and radiation) in the coil which are unknown.

[W8JI]

Here's a graphic of a black box containing one real-world component along with lab measurements made on the current in and current out of the black box. What's in the black box?

http://www.w5dxp.com/branteas.GIF

It's not a two terminal network because it is a physically large coil placed where it has considerable shunting capacitance to ground.

It is, in that condition, a distributed network.

You can see the very same effect in RF chokes on amplifiers as the approach self-resonance. As a matter of fact, at some frequency they have an exteremly high voltage in the center. All because of the stray capacitance to the outside world resonating with the series inductance.

[W5DXP]

It is, in that condition, a distributed network.

Tom, then so were your bench coil delay measurements made on a distributed network because you certainly had a ground return. The Louisiana Tech team probably duplicated your bench measurements using a 50 ohm load because the results were virtually the same as yours at:

http://www.w8ji.com/inductor_current_time_delay.htm

Since, under those conditions, the current out of the coil is 60% higher than the current into the coil, the circuit is obviously a distributed network. Hint: it is impossible for a lumped inductor to increase the current through the coil by 60%. Did you even notice that fact during your measurements? The calculated delay based on the measured phase shift is the same as yours at 3 ns for a 50 ohm load, but since the calculated delay changes radically with load resistance, seems we can say that calculation must necessarily be in error. It doesn't make sense that the constant frequency delay through the coil could vary by more than a magnitude depending on the load resistance. Here is a graph of the phase shift vs load resistance:

http://www.w5dxp.com/coilmes2.GIF

So between the 50 ohm load phase shift and the 1930 ohm phase shift does the 4 MHz traveling wave current phase shift through the coil really change from 4 deg to 41 deg? For your bench measurements, did you try other resistive loads besides 50 ohms to see what delay you would measure?

The coil appears to have a Z0 around 2000 ohms. In a distributed network environment, a load of 50 ohms would result in an SWR of about 40:1. When the SWR is high, i.e. when reflected energy is an appreciable percentage of forward energy, phase measurements are virtually meaningless for calculating delays since for pure standing waves, the phase shift is zero over any 180 degree length. Does a standing wave phase shift of zero between two points mean that signals travel through the standing wave faster than the speed of light? Of course not.

More than 5 years ago, I mathematically explained to you and Roy why standing wave current phase measurement on a standing wave antenna could not be used to calculate the delay through the loading coil. What I said then is still true. The only way to make valid coil delay measurements is to eliminate the reflected energy flowing back through the coil. That means loading the coil with its characteristic impedance, not with 50 ohms (nor with a six foot whip).

[N3OX]

It's not a two terminal network because it is a physically large coil placed where it has considerable shunting capacitance to ground.

External objects are not necessarily required for displacement current to become significant.

[W8JI]

It's not a two terminal network because it is a physically large coil placed where it has considerable shunting capacitance to ground.

External objects are not necessarily required for displacement current to become significant.

There must and will always be something for the field to terminate into. Always. :-)

[W5DXP]

[There must and will always be something for the field to terminate into. Always. :-)

Tom, you need to bring your concepts up to date.

"The Displacement/Photon Current"

"Maxwell, in his endeavor to prove that light was indeed electromagnetic waves of changing electric and magnetic fields, used classical concepts in electromagnetism already known at the time to prove his argument. His greatest accomplishment was his modification to Ampere’s law, where he introduced a quantity called the displacement current."

"However, as was stated earlier Maxwell did not introduce the quantum concept into his theory. If Maxwell’s equations are to be a complete theory, then the quantum concept must be unified with the time varying fields. Maxwell’s displacement current must be quantized like energy, frequency, wavelength, and as will be shown, the changing electric and magnetic fields. Thus the displacement current will be called the photon current, because it too is quantized in nature."

Electrons are blocked by a capacitor dielectric. Guess what energy carrying particle is not blocked by a capacitor dielectric - the same one that, unlike an electron, propagates EM energy through free space at the speed of light.

[G8HQP]

It's not a two terminal network

He never said it was a two-terminal network. He said it was a real component. Real components have stray capacitance to the box etc.

Last time I studied EM, fields were allowed to go off to infinity. It is true that a diverging electric field must come from a charge, but it can go either to another charge at a finite distance or off to infinity. Otherwise you could not calculate the Coulomb field from a single charge in an otherwise empty universe. A time-varying field will have curling components too and they just go round in circles, never landing anywhere. Bringing in photons to explain low frequency phenomena is generally a bad idea, as most of the photons around components are virtual; only in the radiation field do you get real photons.

[W5DXP]

... most of the photons around components are virtual; only in the radiation field do you get real photons.

I'm no physics expert but wouldn't any field, that can be detected by a device capable of detecting the field, i.e. capable of collecting photons, necessarily consist of real photons capable of being collected? Since photons cannot flow inside a conductor, seems to me, all of the photons surrounding a conductor would necessarily have to be real? A few escape as radiation and most are re-absorbed by the free electrons in the conductor?

I think the point was that a component in free space can transfer energy from one terminal to the other even though there is nothing around for the displacement current to flow through. Photonic energy simply has different characteristics from electronic energy. If Maxwell, who died in 1879, had known about photons, he would not have had to invent the concept of displacement current. Any transfer of electrical energy that is not steady-state DC, involves photons, i.e. any transfer of energy through a capacitor is photonic energy. Although not entirely technically correct, that transfer has been called "photon current".

[N3OX]

A time-varying field will have curling components too and they just go round in circles, never landing anywhere.

Yep.  You can also have charge bunching and rarefaction on a coil in isolation which results in field lines that go from one part of the coil to another, no external metal required.

Bringing in photons to explain low frequency phenomena is generally a bad idea, as most of the photons around components are virtual; only in the radiation field do you get real photons.

And at any detectable amount of energy floating around at HF and you have so many photons that there are no observable quantum-specific phenomena.    There are RF photons.  If you set up a massive experiment in an incredibly cold quiet place maybe you could observe some HF-frequency single-photon weirdness.  But the quantum description is not necessary in ham radio because it reduces to the classical field description when there are these huge numbers of photons.  If you want to calculate mathematically what happens to a few photons in quantum mechanics, you actually use Maxwell's equations as the quantum operator that evolves those photons forward in time.   But we're launching so many photons that individual photons' quantum nature is not recognizable.    That doesn't mean RF isn't made of photons.  It just means that there are no physically observable phenomena about HF components that require quantum mechanical calculations.

Maxwell's equations are the correct description.  The question HERE is what are the relevant solutions to Maxwell's equations for a helix of wire?  Many classical solutions to Maxwell's equations can be counter-intuitive, like the metamaterial "invisibility cloaking" stuff.   It's too weird to solve a problem by imagining what waves would do in that situation.  You have to set out with a goal in mind and actually work directly with Maxwell's equations.

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A big coil will of course have a high inductance and a relatively low capacitance (when compared to coax) so at some frequencies can behave like a section of transmission line.

Solutions of Maxwell's equations for waves propagating on a simplified coil geometry (a tube of metal that conducts only in a helical direction) are suggested here:

Corum K. L. and Corum J. F., "RF coils, helical resonators and voltage magnification by coherent spatial modes," Microwave Review, IEEE, Vol. 7, No. 2, Sep. 2001, pp. 36-45

and the predictions of that paper are included in ON4AA's inductance calculator here:

http://hamwaves.com/antennas/inductance.html

It is well known generally that coils support slowly propagating electromagnetic modes... the coil in a traveling wave tube is an example, slowing down electromagnetic waves to match the velocity of an electron beam shooting down the middle of the coil.  The energy transferred from that beam to the waves is useful in microwave amplifiers.  The Corums' paper is by far not the first or only on this subject but it is one that particularly addressed low frequencies, in particular in in the context of Tesla coils, and maybe more important for amateur experimenters, the predictions of that paper have been coded into an online calculator!

===============

There is a long ham debate that hinges partially on whether or not a "typical" (terrible, terrible word) loading inductor at 4MHz can  show slow wave effects .. whether or not it supports slowly traveling electromagnetic modes when it is considered as an isolated system.  The Corums'  paper presents a mathematical model for slow wave propagation on helices that is purportedly valid for densely wound coils of small diameter with respect to a wavelength (different modes possible than, say, a traveling wave tube or a helix antenna which may have electrons bunching up in different spots on a single turn)

It should be valid for a coil like the one Cecil is talking about and the one Tom measured here:  

http://www.w8ji.com/inductor_current_time_delay.htm

That particular one is 100 turns 10 turns per inch (10 inches long) and two inches diameter, 18AWG wire.  

ON4AA's calculator at http://hamwaves.com/antennas/inductance.html has an entry for the axial propagation constant beta in radians/meter at a given frequency for modes that are specific to propagation on a helical structure.  It incorporates the formulas from the Corums' paper in an easy-to-use way.  

The prediction is that wave propagation of a particular form on pretty "typical" (ugh) inductors at a few MHz is actually quite slow and the coils are dispersive.  The wave speed changes with frequency, so the propagation constant beta (related to the physical wavelength of the slow wave modes) changes with frequency... so you specify the physical dimensions of the coil and the frequency and it calculates beta *at that frequency*

From beta you can calculate the physical wavelength of the waves traveling on the coil... I must stress that this is wavelengths of traveling electromagnetic waves specific to the coil as a transmission line and it simply has nothing to do with free space modes.

If you plug in a 50.4mm diameter coil with 100 turns 254mm long with 1.02mm wire (18AWG) it gives a propagation constant beta of 2.12 radians per meter for 4MHz.  Two pi radians is just about three meter wavelength. If you do it at 8MHz you get 4.94 radians per meter.  That's a 1.27 meter wavelength (it is not 1.5m wavelength... there's the dispersion showing up)  If you do it for 16MHz you get 12.93 radians per meter, or just about 0.5m/ 20 inches wavelength.  Around 26MHz the wavelength is about 10 inches.

That means a 10 inch coil should have a half wavelength resonance around 16MHz and another full wavelength around 26MHz, a non-trivial prediction because of the dispersion.. 26/16 is a weird frequency ratio for a "half wavelength" and a "full wavelength" resonance...  it's also pretty much the frequencies of the two big peaks in Tom W8JI's delay plot... group delay should go through a maximum at self-resonance.  The little delay "twiddle" around 9.6MHz is about a quarter-wavelength  but the "0.75wl" prediction has no signature at all which is maybe a little troublesome.  


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There are lots of predictable phenomena that come out of this.  More or less current out of one end of a coil than you put in the other end is one of them.  Self-resonances of coils should be predictable, and I think that may be a non-trivial and fairly easily measured prediction.

I think that the prediction of coil self-resonances is actually one of the easiest things to test.

Of course, you can never have an isolated coil if you want to do measurements on it (though G3YNH took a damn good stab at it in a technique worth serious consideration: http://www.g3ynh.info/zdocs/magnetics/appendix/self_res/scat_18T_2.jpg)

But I'm not worried about "coil in isolation" in a basic way.  The transmission-line behavior of the coils that we're considering seem to have fields that are relatively tightly confined to the coil.  Termination impedances matter though I still need to plot the actual mode fields and figure out how the termination should really go... Cecil has shown me some EZNEC models that suggest that feeding the coil over a ground plane and terminating it to that ground plane in  its characteristic impedance is just fine.  But as I understand it the 1930 ohm characteristic impedance of the coil and the electrical length of the coil as measured recently don't really match the predictions (Cecil, please correct me if I am wrong... I guess you hypothesize that the paint is the problem).  The data is interesting... no doubt.. but I am interested in whether or not we can use the model to closely predict things or not.

I feel that it is important to quantitatively test possible models.  Certainly, a coil over a ground plane will have other modes of wave propagation than a coil in isolation... the sort of delay line formed by an inductor with capacitance to the ground plane should have very different characteristics.  

If we just list every possible different explanations and argue over them we get nowhere.  If we make specific predictions using different models (slow waves like the Corums' paper, delay line formed by inductor over a ground plane) and predict several different things (different terminating impedances, locations of self resonances)  then work together to test what happens, we can understand something.  If we make specific predictions about the behavior of  a particular piece of coil stock using any model and those predictions do not closely match the model to within reasonable measurement errors, we need to work to figure out why.  To make progress in a scientific endeavor, it is important to try to be the biggest skeptic about one's favored model.  I have seen several decent pieces of evidence that the Corums' coil model is a quantitative predictive model for how electromagnetic energy gets from one end to the other on a "typical" (aaah!) ham antenna inductor.  But what I'd really like to see is a wide-band verification of the propagation constant beta (Lecher line style), and I'd like to see close quantitative agreement for termination impedance and phase shifts or a quantitative explanation for why it doesn't agree.

I hope this doesn't make anyone mad.  This topic has always suffered from the fact that the discussion is going on in public.  It has been confrontational  (very badly so at some times) and prone to tangents and that makes it hard to have a skeptical critical discussion.  I just know there is a specific mathematical model for slow-wave propagation on coils of ordinary inductor stock form at HF frequencies and I'd like to know how closely that model predicts the behavior of the coils.

[W8JI]

It's not a two terminal network

He never said it was a two-terminal network. He said it was a real component. Real components have stray capacitance to the box etc.

My point exactly. What is around it affects it greatly.

Last time I studied EM, fields were allowed to go off to infinity. It is true that a diverging electric field must come from a charge, but it can go either to another charge at a finite distance or off to infinity. Otherwise you could not calculate the Coulomb field from a single charge in an otherwise empty universe. A time-varying field will have curling components too and they just go round in circles, never landing anywhere.

That's true, but if you look at the drawing it is a test setup. The test setup, by definition, has things well in the nearfield of the coil. It isn't, as I pointed out, a two-terminal system.

If this was a common sense non-personal debate where everyone talked about the theory and practice, and no one reworded what other people said, it would easily get resolved. Unfortunately, that is probably not going to be the case.

73 Tom

 

 

[N3OX]

That's true, but if you look at the drawing it is a test setup. The test setup, by definition, has things well in the nearfield of the coil. It isn't, as I pointed out, a two-terminal system.

Perfectly non-perturbing measurements are always impossible.  The question is what can be done to check these ideas out in a way that checks, for example, whether the Corums' model is describing what's going on or whether it's more like you say, like the presence of the ground plane is most important.

One way to try to sort this out is to try to eliminate the perturbing influence as much as possible or at least change the perturbing influence systematically.  I think G3YNH's coil scattering setup was intended to eliminate the external influence as much as possible.  But if you want to actually try to terminate a coil and measure its transmission line properties when it's only acting as a  20 or 30 degree long transmission line section you can't do the inductive coupling thing.  There just won't be any signal.  I also tried the loose inductive coupling setup on a trap recently and it makes it really hard to do quantitative measurements.  You get a hell of a nice signal where the trap is resonant, and this would be good for checking the sequence of resonant frequencies of a coil (which are then subsequently predicted by the Corums' model).  But I know that there's been some contention on whether or not this is something that's only valid near self resonances, etc.  


Another way to work things out is to start by not assuming that the perturbation will ruin your results and don't even bother to try to minimize it, and then compare the particular mathematical theory with the results in a quantitative way.   If I put some current probes on either end of the coil and use ON4AA's calculator to calculate the characteristic impedance according to the Corums' model and I find that at dozens and dozens of frequencies the coil currents in and out are equal at that predicted termination, that's a good indication that the coil is

1) acting according to the model
2) not particularly perturbed

If that experiment does NOT agree, that's another matter.  It could indeed mean that the model is simply totally wrong or invalid at those frequencies.  It could mean that the perturbations are simply too great.  Then you just need to move on theoretically or experimentally and try to figure out what's going on.  Theoretically you can modify the model to include the perturbing influences like ground planes.  Experimentally you can try to figure out a way to excite and measure a coil that is less perturbing.  The experiment itself will probably suggest how to modify the theory if necessary.

I think sometimes we miss out on learning things because we decide that the "perfect" experiment is impossible.  I see it happen  even to talented professionals in science and I've (thankfully) pretty much had a goal for PERFECTION beat out of me.   Experiments only have to be good enough to clearly and unambiguously sort out one phenomenon from another and if the experiment is designed well that might work even if everything is pretty sloppy.   In this case, I think an experiment that is clearly and obviously un-perturbed is simply impossible.  The coil is always close to some stuff and connected to some stuff and electric fields are important.  In that case I think that quantitatively comparing the measured results to the various possible theoretical models is really the way to go.  

The quantitative prediction of the Corums' model suggests that it is possible for the coils in question, small chunks of ordinary miniductor stock, to significantly act as delay lines by themselves at a few megahertz if they were just floating in free space.  I think it's worth testing whether or not the predictions hold even when the coil is close to stuff because I think the fields responsible are really more kind of "inter-turn" not "coil to environment" and so maybe aren't as affected by external influence as we might expect.  Or maybe external influences are a disaster.  Who knows?

But there's no way to tell besides testing the quantitative predictions in the real messy world... and figuring out the results after.

[W5DXP]

That's true, but if you look at the drawing it is a test setup. The test setup, by definition, has things well in the nearfield of the coil. It isn't, as I pointed out, a two-terminal system.

Tom, neither was your test setup at:

http://www.w8ji.com/inductor_current_time_delay.htm

You say you measured a 3 ns delay through the coil. But what you actually measured was a 4.3 degree phase shift between the two currents at the ends of the coil. A conversion from 4.3 degrees to 3 ns assumes that a traveling wave is being measured. But the SWR in your test circuit was probably at least 40:1, maybe higher so you were not measuring a traveling wave. What you measured was standing wave current phase which defeats any attempt to measure the delay through the coil. For pure standing waves, the current doesn't change phase at all over each 1/2 wavelength.

Take a look at the data measured by the Louisiana Tech graduate students. With a 50 ohm load on the Texas Bugcatcher coil, the results are identical to yours. But the other three measurement points indicate something radically wrong with assuming that the 4.3 degree phase shift measured with a 50 ohm load has anything to do with the delay through the coil which is definitely exhibiting transmission line effects.

If the Z0 and electrical length of a short piece of transmission line were unknown, how could we determine those two parameters? Assuming negligible I^2*R losses and negligible radiation from the short piece of transmission line:

1. Adjust the resistive load until the current in equals the current out.

2. Measure the phase shift between current in and current out.

3. Convert the phase shift to nanoseconds to obtain the delay.

This is what the Louisiana Tech grad students did. Assuming the I^2*R losses in the coil plus the radiation resistance of the coil is small compared to the 1930 ohm load, we see the phase shift through the coil is 41 degrees and the delay through the coil is 41/1.44 = ~28.5 ns.

Back to transmission lines: Let's say we have a piece of VF=1.0 450 ohm line that is 0.1 wavelength long and we attach a 50 ohm load to it. 0.1 WL is 36 degrees which would cause an end-to-end delay of 25 ns at 4 MHz. With a forward current of 1.0 amp at the source end, what would be the current in and current out magnitude and phase?

Here's what I get: Current In = 1.46a at 4.63 deg, Current Out = 1.8a at 0 deg (reference).

Using the same logic as you used on your loading coil "measurements", we would calculate the 4 MHz delay through the piece of 450 ohm at 4.63deg/1.44 = 3.2 ns. But we already calculated the delay at 25 ns and we know that a 3.2 ns delay at 4 MHz through a 36 degree long piece of 450 ohm ladder line is impossible and would violate the speed of light limit. Yet exactly the same logic is rationalized as valid for your 100 turn loading coil at 4 MHz. Why is exactly the same measurement technique valid for your loading coil and invalid for a piece of transmission line?

[W5DXP]

But there's no way to tell besides testing the quantitative predictions in the real messy world... and figuring out the results after.

Here's a formula that might help. It's the formula for the characteristic impedance of a single wire transmission line located horizontally over a ground plane.

Z0 = 138*log(4D/d)

where d is the diameter of the wire and D is the distance above ground. As D decreases, Z0 decreases. That same principle should apply to loading coils and there's no mention of a ground plane for the Hamwaves inductance calculator.

[W5DXP]

If this was a common sense non-personal debate where everyone talked about the theory and practice, ...

Tom, sometimes common sense is wrong. It is common sense to assume that antenna current delays are proportional to antenna current phase shifts but that common sense is just plain wrong when we are talking about standing wave antenna currents. Here is another example from EZNEC that shows how it is wrong.

http://www.w5dxp.com/80mdip4.GIF

The current phase shift from the 1/3 point to the 2/3 point is 0.93 degrees. Dividing by 1.44 deg/ns (at 4 MHz) we get a "delay" of ~0.65 ns. Can EM energy travel 20 feet in 0.65 ns? The speed of light in free space is 0.984 ft/ns so the answer is NO. There is something wrong with the common sense assumption that one can divide the phase shift by 1.44 deg/ns (at 4 MHz) to obtain the delay through a wire or through a loading coil on standing wave antennas or in a bench setup with standing waves present.

[G8HQP]

I don't wish to take part in the debate about loading coils. If I had realised that the 'brainteaser' was related to that issue I would have kept well away.

Going back briefly to virtual photons, it is a long time since I seriously studied EM and QM but I seem to remember that static and quasi-static fields, when quantised, give rise to virtual photons (i.e. off mass-shell). Only radiation fields have real photons. Note that a virtual photon is just as real as a real photon, but it can temporarily misbehave (as far as it is allowed to by the Heisenberg uncertainty principle). In any case, invoking photons to explain low frequency phenomena (anything much below infra-red) is daft, and can be a sign that someone is either confused or desperate.