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#31
04-05-2014, 03:02 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
Current = movement of charge.
1 A = 1 C / s (by definition, see also Maxwell's work)
Every movement has a velocity and a direction. So does movement of charge and so the same goes for current.
You say
Quote:
 The current doesn't necessarily have to "go" anywhere
that implies you can have a movement without direction...

On another thread on this forum I also encounter "exotic (re-) definitions"....
Yeah well, let me leave it there.

Good luck with your experiments!

Ernst.
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#32
04-05-2014, 03:34 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Ernst Current = movement of charge. 1 A = 1 C / s (by definition, see also Maxwell's work) Every movement has a velocity and a direction. So does movement of charge and so the same goes for current. You say that implies you can have a movement without direction... On another thread on this forum I also encounter "exotic (re-) definitions".... Yeah well, let me leave it there. Good luck with your experiments! Ernst.
The energy is (mostly) circulating in the coil, there is no load to absorb the energy, also there is no measuring of "current flow", only the current distribution in the coil in the same way as measuring the potential distribution. The term "magnetic component" might be more useful than "current".
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#33
04-05-2014, 10:29 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
I am trying to understand this (but failing...) can someone tell me what I am doing wrong?

Quote:
 7) EXTRA COIL DIMENSIONS AND CONSTANTS Diameter: 8.4 feet Height: 8.0 feet Number of Turns: 100 numeric Mean Length of Turn: 8 meters Total Length of Turns: 800 meters Luminal Wavelength: 3200 meters Self Capacitance: 112 picoFarad Self Inductance: 25 milliHenry Luminal Frequency: 94 Kc/sec Free Space Frequency: 176 Kc/sec Actual Frequency: 116 Kc/sec Free Space Propagation: 187% Actual Propagation: 123% Transmission Impedance: 15 Kilo-Ohm Dielectric Burden: 26 picoFarads
Using equation #1 to compute the inductance:
Diameter: 8.4 feet = 100.8 inch --> radius 50.4 inch
Height: 8 feet = 96 inch
Turns: 100
9 r + 10 l = 453.6 + 960 = 1413.6
(rN)^2 = 5040^2 = 25401600
Static inductance: 25401600 / 1413.6 = 17969 uH = 17.969 mH

Using equation #2 to compute the capacitance:
Diameter: 8.4 feet = 100.8 inch = 256.0 cm
factor p = 0.46
Static Capacitance = 117.8 pF

When oscillating at resonance the effective values become:
Inductance: 8.98 mH
Capacitance: 95.5 pF

Propagation velocity: 1079841 being 0.36% of c
Resonance frequency using equation (7): 337.45 Hz

Impedance using equation (9): 9725 Ohm

It is especially these values marked in red that I find hard to believe.
Now someone already told me that according to EPD the extra coil is not resonating at its natural frequency so the effective values may not apply, but even then would this coil resonate at 337.45 Hz???

Using these same equations for the CS secondary, which is in resonance, I get equally strange values.
So... what am I doing wrong?

Ernst.
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#34
04-05-2014, 10:08 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
I had trouble with that. In basic terms equation (7) is simply the speed of light divided by 4 times the conductor length. This gives the luminal frequency, as the conductor length is 1/4 the wavelength.

 Taking the free space self capacitance and then applying the effective capacitance (and inductance) given by Miller, for the given extra coil

L = 8.84mH
C = 93.7 pF
Z = 9711 Ohms
Angular Frequency ω = 1/Sqrt LC = 1098258.497 Radians/sec
Natural Frequency = ω/2*Pi = 174.793 kc

Taking the burdened coil self capacitance given the measured frequency

C = 211.17 pF
Z = 6470 Ohms
ω = 731806.1566 Radians/sec
Natural Frequency = 116.47 kc

It would appear that the number "1079841" you posted as "propagation velocity" is the angular frequency in radians per second, dividing it by 2*Pi gives 171.862 kc
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Last edited by dR-Green; 04-06-2014 at 03:06 AM.
#35
04-06-2014, 03:26 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
Ok, thank you.
That clears things up.
So we have to look at EPD's source material to find the good stuff.
Reading EPD's work only produces confusion.

I have read Miller and find it very useful indeed. From his work I can derive the equations that I was looking for.

Thanks again!

Ernst.
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#36
04-06-2014, 08:23 AM
 Natusake Junior Member Join Date: Mar 2014 Posts: 13
Quote:
Originally Posted by Ernst
Current = movement of charge.
1 A = 1 C / s (by definition, see also Maxwell's work)
Every movement has a velocity and a direction. So does movement of charge and so the same goes for current.
You say
Quote:
 The current doesn't necessarily have to "go" anywhere
that implies you can have a movement without direction...
Since we're working with alternating currents here, the charge simply vibrates across a certain axis. There doesn't need to be any net movement, nor does the charge need to 'go' anywhere.

You're thinking about it wrong. Take a magnet for instance, it always has current, where does the charge go? Nowhere! There is no charge!
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#37
04-06-2014, 10:04 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Ernst Ok, thank you. That clears things up. So we have to look at EPD's source material to find the good stuff. Reading EPD's work only produces confusion. I have read Miller and find it very useful indeed. From his work I can derive the equations that I was looking for. Thanks again! Ernst.
It just means that you have to think and research in order to figure it out
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#38
04-09-2014, 03:40 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
That is what I am doing, dR-Green!

Have you already thought of this one:

(referring to Millers book, the last few chapters and Fig 8)

Quote:
 Using the same notation as before, an expression for the reactance of the coil, regarded from the terminals AB (x=0) will be determined considering the line as closed at the far end D (x=l). Equations (3) and (4) will again be applied, taking account of the new terminal condition: that is for x=l; v=0.
Now if you look at Fig 8. D (x=l) is not the end of the coil, it is half-way the coil. Thus l equals half the wire length and thus SQRT(C1 L1) times l equals SQRT(C0 L0) divided by 2.
So equation 23 should read:

X' = SQRT(L0/C0) TAN(w SQRT(C0 L0) / 2)

and not as Miller states:

X' = SQRT(L0/C0) TAN(w SQRT(C0 L0) )

What are your ideas on this?

Ernst.
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#39
04-10-2014, 05:01 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
I just got the pdf and looked quickly so I don't know what x=l etc means, but it says "regarded from the terminals AB (x=0) will be determined considering the line as closed at the far end D (x=l)" so it's one length anyway, from terminals AB.

If they all derive the same answers and there is nothing really to "solve" as such because you already know the frequency and everything else, then the reactance is given by

Inductive Reactance XL = ω*L
Capacitive Reactance XC = 1/ω*C

Where ω = 2*Pi*F = 1/Sqrt LC as derived before.

Steinmetz says effective inductance for a cosine quarter wavelength current distribution is two over Pi the total inductance, and effective capacitance for sine quarter wave distribution is two over Pi times the (burdened) self capacitance.
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#40
04-10-2014, 05:31 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
If there is nothing to solve, you don't need any equations.
If you can measure the frequency response of a coil, then you must have built it already.
My point is I am looking for design equations.
I want to have some ready to use math that you can put in a spreadsheet, for example, so you can play with various designs before you actually build it.

If you would read through the whole pdf (it is only a few pages) you will find that his last equation is wrong. Either that, or it is derived in a wrong manner.
No big deal, there is still quite a bit of valuable info there.

So now you are directing me to Steinmetz, correct?
I'll have a look.
Any suggestions on where to start?

Ernst.
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#41
04-10-2014, 07:18 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Not directing you to Steinmetz as such but pointing out an alternative approach if you haven't already seen it. Although the effective values are different everything must ultimately end up at the same frequency, so who knows which one of them is actually right if any. Eric recommended Electric Discharges, Waves And Impulses.

Quote:
 My point is I am looking for design equations. I want to have some ready to use math that you can put in a spreadsheet, for example, so you can play with various designs before you actually build it.
Basic LC calculations based on the coil dimensions come quite close. If you start with

λ = c/F

λ = wavelength in metres
c = speed of light in metres per second
F = frequency in cycles per second

Then λ/4 = conductor length, divide conductor length by the desired number of turns = coil circumference. Given a coil height you can then easily calculate L and C from the equations on page 1 of this thread and therefore the approximate frequency you'll end up with. If it's in a spreadsheet then you can easily adjust the conductor length/coil size to correct the variation in frequency caused by the coil geometry. But I doubt it's possible to get it 100% accurate on the bench because it's sensitive to such things as the frame it's wound on.

Alternatively there is Eric's design on page 1, and another alternative is to scale down the Colorado Springs coil and tune the whole thing according to the scale ratio constant in order to match the coil characteristics of the original. Z = Sqrt L/C for example so L/C ratio must match original.
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#42
04-10-2014, 09:40 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
That is very close to how I did it the first time:
1/4 wavelength for the secondary and 1/2 wavelength for the extra wound in opposite directions.
Then build the prim/sec using JavaTC, measure its frequency (at low voltage), use JavaTC again to design the extra, keeping the frequency just a little bit too high so you can lower it (once built) by adding the right top-load.
But I still had to rebuild the extra 4 times...
Also JavaTC gives me very long and thin coils for 1/2 wavelength.
And for the extra coil JavaTC is not very accurate as I mentioned earlier.
The error margin seems to increase with lower frequencies and has to do with the different mode of resonance.

This procedure gives me a coil that no longer fits in my house for frequencies around 200KHz. I have reason to believe (incl. experimental evidence) that a shorter and fatter coil can be used, but no math to support the design procedure.
Also I want to see if it would be possible to split the extra into two 1/4 wave coils.

If there are no math-models and (too) little info to make one by myself, then I guess I will just have to try...

Any news from your coils?

Ernst.
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#43
04-11-2014, 02:48 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
The only real guideline is Tesla's CS data, otherwise it's all speculation and totally open to experiment, unless you assume that the proportions etc in the patent diagram represent real and practical values. Because there's no other known "ideal" to aim for, even if you get the right conductor length and apparent frequency then who's to say that you then choose the right number of turns and coil diameter and impedance in relation to the secondary etc, there's all kinds of unknown variables that make it practically impossible unless you actually build something and start gathering the data.

I don't think it will be possible to "virtually" split an extra coil into two. Like the AT&T/Bell Labs video shows, the wave must reflect at the end of the transmission line in order to produce standing waves, if it's one continuous line then it's exactly that, so it will just reflect at the actual end of the line. Although the info "indio" posted regarding the nodes on the other thread might be relevant. This is also the basis of the concatenated resonance that Eric mentioned, which involves setting up separate/independent 1/4 wave resonant conditions in each coil. In theory the top end of the secondary (transmission line) must have a certain impedance to allow for reflection and a 1/4 wave distribution over the coil as if the extra coil wasn't there, but a certain amount of energy must also be transferred to engage the extra coil to allow for the same but independent 1/4 wave condition. So it's all about the impedance mismatch between the secondary and extra coil, otherwise it's likely to behave as one continuous line, or the opposite being not enough energy transferred to the extra coil etc. I assume it's possible to calculate the amount of reflection in a transmission line with a given termination impedance from info in books, but then what "should" it be anyway?

There's no news on my coils other than they are operating like the big CS coil in that they are similarly tuned with the same impedances and L/C ratios etc and the end operating frequency is near the design frequency (they are prototypes to determine and correct the margin of error in the scaling spreadsheet), designed for 1860 kc but so far seemingly best at 1800 kc, so CS Notes provides enough information to make a working system, but apparently not 1/4 wave concatenated resonance. But more extra coils can easily be built and experimented with the secondary to develop that as a work in progress.
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Last edited by dR-Green; 04-11-2014 at 03:12 AM.
#44
04-11-2014, 08:30 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
Trying to avoid "wrong and right" discussions but let me just tell you how I see it.

A 1/4 wave resonant system (organ-pipe, string, spring, anything...) has a node on one (closed/fixed) end and an anti-node on the other (open/free) end.
In an electrical transmission line, I would say that a ground connection will force a (voltage) node, so the other end should be open. In the free end you will then have maximum voltage swings with no current, while in the ground connection you will have maximum current (swings) at a 0 voltage.

The same goes for a 3/4 wave resonant system. But this one will have a HV region at 1/4 wavelength from the ground at which point you will also see a current reversal. This is easy to visualize if you imagine charge accumulating at this point, it goes upward from the ground and comes down from the open end. Then half a period later the charge will flow out of this point both downward to the ground and upward to the open end., and exactly in the middle of this point the current will not go up or down; there will be no current. So again, we see the voltage anti-node being a current node.

If you can have a 3/4 wave transmission line and coil it up into 1 coil, or coil it up in 2 coils, then 3 coils should also be possible. If you have 2 coils and move them so close together that their mutual induction becomes (close to) 100%, then it has become 1 coil.
So the opposite should also be possible, just remove the mutual induction between the upper and lower half and you get 2 coils.
That would help me a lot in the design, because:
1 - the overall induction goes down a lot and in my designs (1/2 wave coil) the induction usually gets too high
2 - most coil design software is based on 1/4 wave coils

What I described here is what Eric would call "tandem-mode", if I am correct?
Can you visualize what you would call "concatenated-mode", or better, do you know of any mechanical analogue?

How do you see the road ahead for your experiments?

Ernst.
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#45
04-11-2014, 10:25 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
I suppose the question is what are you trying to do? The tandem mode resonance is the "easy" one to achieve as Eric says, because it requires no particular special design as the whole thing acts as one coil, so you could pretty much throw anything together and it will "work". But the resonant frequency tends to relate to the overall wire length as 1/4 wave, or slightly less because the extra coil propagation is "faster than light" so the effective wire length is shorter than the total physical length. 3/4 wave seems tricky. According to this image, if we use it to represent the extra coil, then it would seem possible through coupling the secondary to the extra coil through a condenser. The size of the "receiving" plate or ring on the bottom end relative to the free end capacitance should move the node along the extra coil. Although it remains to be seen.

I would say that an analogue of concatenated resonance might be two (organ) pipes, which may be of different geometries but having the same resonant frequency. One pipe is made to resonate through direct excitation, the output of which is input to the other pipe in such a way that the second pipe doesn't impede the efficiency or quality of the first. But while the first pipe must be free to resonate naturally, the physical gap must be so that energy is also efficiently transferred from one pipe to the other in order that the second pipe produces an appreciable output at exactly the same frequency.

My experiments will mostly be communication based because that seems the most practical application to develop the whole thing, and the same power is transmitted anyway whether there's a signal or not. Eric proposed the 160 metre ham radio band for experimentation, because among other things that normally requires a big antenna, 1/4 wavelength would be 40 metres high. So it's intended to show that it's possible to communicate on the same frequency without such a monstrosity. Also to discover the amount of power required in order to make a signal reach <somewhere>. So far the famous "inverse square law from a radiating source" doesn't seem to apply at all. So that's why I scaled down the CS coil, the end frequency was (closely enough) calculable to start on those things without getting caught up in making a thousand coils. It would also be fun to improve on Konstantin Meyl's demonstrations a bit...
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#46
04-12-2014, 03:25 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
I have attached 4 images to show the different resonant modes.

mode 0: 1/4 wave spread over two coils. This seems possible, I think we all agree.

mode 2: two 1/4 wave coils in concatenated mode. This is what Eric believes to be in Tesla's dream. The problem that I am having visualizing this mode is in the forces acting between the coils. The secondary is exiting the extra by a force F-sec. The extra has some inertia (inductance) which will counteract this force with an equal and opposite force F-ine. So in order to make the swing go the other way, it would seem to me that an extra (outside?) force F-? is needed to overcome F-ine.

mode 1: this seems to me the logical outcome of two 1/4 concatenated coils.

mode 3: the solution that I am using and which is working.

The reason I asked you if you could visualize your mode of resonance (#2) is twofold:
1 - because I can not, and I want to see if I am missing something
2 - if you can, you must also be able to define the conditions for obtaining this mode of resonance, and then it would seem to me only a small step to implement it.

For example in mode 3 the conditions are:
The secondary is freely resonating, that is without capacative or inductive load, meaning at its self-resonance frequency.
The extra and the top-load form a second resonating system so it only acts as a resistive load on the secondary.
Knowing the frequency, you know the wirelength in each coil, and from this you can design both coils.
The ideal secondary will be what I have called a phi-coil since its length to diameter ratio is the golden ratio (phi). The matching extra will become a long thin coil, especially at high frequencies. (but as you know I am still working on that)

But if my interpretation of your answer is correct, you are no longer pursuing mode 2?

Ernst.
Attached Images
 Mode 0.png (6.2 KB, 18 views) Mode 1.png (9.9 KB, 14 views) Mode 2.jpg (9.4 KB, 13 views) Mode 3.png (13.3 KB, 11 views)
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#47
04-14-2014, 04:27 AM
 Sputins Silver Member Join Date: Aug 2009 Posts: 531
Analogue

Quote:
 Originally Posted by dR-Green I would say that an analogue of concatenated resonance might be two (organ) pipes, which may be of different geometries but having the same resonant frequency. One pipe is made to resonate through direct excitation, the output of which is input to the other pipe in such a way that the second pipe doesn't impede the efficiency or quality of the first. But while the first pipe must be free to resonate naturally, the physical gap must be so that energy is also efficiently transferred from one pipe to the other in order that the second pipe produces an appreciable output at exactly the same frequency.
Pretty good analogy of concatenated resonance regarding the organ pipes.

I was looking for an analogue, or even just a parable concerning this!
- An added complication to the pipe analogy might be that the ‘secondary pipe’ is housed in one particular medium and the ‘extra pipe’ in housed in another type of medium where the speed of the sound propagation is somewhat different for each pipe. (?)
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#48
04-20-2014, 04:17 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Ernst mode 1: this seems to me the logical outcome of two 1/4 concatenated coils. But if my interpretation of your answer is correct, you are no longer pursuing mode 2?
Yes I see what you're saying. But then that would either be 1/2 wave, or it would have to take the time/phase factor into account. With no time then you could fit half the wave over both coils with the same distribution, but if the extra coil is considered to be lagging by 90 degrees (in time) and alternating if you will with the secondary, then both coils have a 1/4 wave distribution but at different moments in time. But this is just thinking out loud as you will soon see...

I'm not "no longer pursuing mode 2", just that it could take a while assuming it's even possible, so I built the CS coil as a "working benchmark" to bring the more application orientated experiments sooner in the timeline, and like I mentioned I can easily experiment with different extra coils on the same secondary, there's no particular optimised design so the CS secondary will do just as well as any other (that I would have to build!).

Anyway I've been thinking of making an animation of the waves and coils for months so these discussions urged me to finally do it, it's based on the info in the Bell Labs video. It assumes the secondary to be "low" impedance and the extra coil "high" impedance relative to each other, and so the reflection between the coils is inverted and returns 180 degrees out of phase, and the free end of the extra coil is an "open circuit" so that reflection is also inverted. There's then a "2nd generation" reflection of the extra coil reflection which is non-inverted since it's journey from extra coil to secondary is high to low impedance, although some things seem to cancel each other out so these reflections are questionable. A non-inverted reflection at the top of the secondary wasn't included because apparently whether it's an extra coil or an open circuit, the wave is inverted in both instances, based on the assumption that the extra coil is a higher impedance. There's also a possibility, or perhaps impossibility, for the concatenated mode where both coils are in phase (or perhaps the extra coil lagging by 360 degrees), which is represented by the wave propagating along both coils simultaneously in what could be called parallel, but I guess in order for that to happen there would have to be some induction involved, thus the extra coil is "grounded" to the secondary but working "independently" from an alternating ground potential. In which case the centre horizontal line doesn't necessarily represent 0 volts.

Resonant Modes And Reflections-01 (TMT) - YouTube
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#49
04-20-2014, 06:19 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Sputins Pretty good analogy of concatenated resonance regarding the organ pipes. I was looking for an analogue, or even just a parable concerning this! - An added complication to the pipe analogy might be that the ‘secondary pipe’ is housed in one particular medium and the ‘extra pipe’ in housed in another type of medium where the speed of the sound propagation is somewhat different for each pipe. (?)
As long as each one is designed to end up at a certain frequency within its intended environment then I should think that it wouldn't make any difference beyond that. A short and wide pipe can have the same resonant frequency as a long and thin one.
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#50
04-20-2014, 10:29 AM
 Ernst Silver Member Join Date: Jul 2012 Posts: 895
Nice animation! What program did you make that with?

Ernst
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#51
04-20-2014, 08:44 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Ernst Nice animation! What program did you make that with? Ernst
Thanks, I used Macromedia Flash MX 2004

Macromedia - Studio : Studio MX 2004 Documentation

But as the name suggests it's old and might not be easy to get hold of these days.

This is the latest incarnation

Animation software, multimedia programs | Download Adobe Flash Professional CC
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#52
04-27-2014, 07:05 PM
 Kokomoj0 Senior Member Join Date: Jul 2011 Posts: 426
Quote:
 Originally Posted by dR-Green Resonant Modes And Reflections-01 (TMT) - YouTube

I think you would find that in order to add another 1/4 wavelength you can add as many coils as you wish and they will operate as one coil.

take a close look and see what you can gleen from this

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#53
04-27-2014, 09:00 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

"Once men died for Truth, but now Truth dies at the hands of men." - Manly P. Hall
#54
04-29-2014, 12:45 AM
 Kokomoj0 Senior Member Join Date: Jul 2011 Posts: 426
Quote:
 Originally Posted by dR-Green
the att one is kool.
never seen this done so well mechanically before, though that is not really what a wave in space would look like, its still a great representation. always visualized it electrically or acoustically or water. 1:1 match always gives optimal power transfer. I am glad he showed the importance of SWR. I dont remember where but when I first came on this board I posted a really el cheapo DIY near lossless inline for Tcoil builders to take the pains out of tuning.
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#55
06-20-2014, 04:17 PM
 GeorgeKn Member Join Date: Jun 2014 Location: Kuwait Posts: 8
リモワ ポルシェ

#56
05-22-2015, 03:13 PM
 orgonaut314 Senior Member Join Date: Jul 2013 Posts: 222
One very basic question on the extra coil.

Might be useful to add this picture in this thread.

My question is when tuning is the capacitor to earth also there? I would think that this capacity would have a resonant frequency with the extra coil. Is it so that first the extra coil is tuned and than the capacitor is added and tuned to get the same resonance?
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#57
06-06-2015, 12:25 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Which capacity to earth do you mean? The coil exists in space so whatever resonant frequency it has includes it's self-capacitance to ground. The only way that would not be present is perhaps if you put it in a vacuum, or make the coil cease to exist. Also there's a certain amount of capacitance between one end of the coil and the other which you can't get rid of without getting rid of the coil itself.
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#58
06-07-2015, 07:41 AM
 upgradd Junior Member Join Date: Dec 2013 Posts: 23
Passing Thoughts

While likely redundant, I thought I would add my 2cents to the discussion on resonance.

First, I think it's important to realize that many inductance calculators calculate the DC inductance, that is, the total magnetic field energy present if a current of equal intensity is present at ALL points along the coil. At frequencies well below resonance the DC calculation is adequate. However, at resonance the magnitude of the current (and its distribution inside the wire) varies significantly along the coil. I think everyone here understands this point, but its good to rehash none the less.

The most problematic issue for resonant frequency calculations is that a similar situation exists for capacitance, its value is dependent upon the electric field distribution along the coil winding. As a consequence, the effective value of capacitance is dependent upon excitation frequency. When well below resonance it appears to be stable, however, reach resonance and its value becomes highly dependent on the mode of excitation.

Something like an elephant in the room is that wire length of a coil isn't very indicative of what a coil will do or SHOULD do. Winding pitch, wire diameter, number of turns, coil diameter and height have a much more pronounced effect on frequency than total length of conductor. Ultimately the wire length shenanigans is referencing a quarter-wave distribution along a STRAIGHT wire. As such it can only be used as a baseline REFERENCE and really is not indicative of what YOUR coil should do. Of course any coil that favors propagation across the coil, rather than along it, will APPEAR faster than c! But that doesn't mean that the actual signal velocity is faster than c! The comparison is flawed from the beginning by assuming that the two geometries (helix and straight wire) can be compared quantitatively as an "apples to apples" situation. The confusion can be eliminated by realizing that the signal is propagating at an angle greater than the pitch angle of the winding but less than pi/2 radians: pi/2 >> pitch angle of incident wave > pitch angle of wire. Ultimately propagation velocity is slower than c, regardless of what coil geometry you use.

Some thoughts on the concatenation/tandem modes: has anyone tried tying the extra coil to ground at the same point as the secondary? This would force separate 1/4 wave resonance in both coils, though the electric field distribution across the two coils would no longer be in series. In reflection this seems what a possible "tandem" mode would actually look like. It might be possible to force concatenation by using two primary windings one at the base of both the secondary and the extra coil. You may need to space the the extra coil a little bit further away to lower mutual coupling and the two primary loops should be in series to share excitation current equally. As a variation you could place the second primary loop at the top of the extra coil but reverse its current sense. This last idea would produce two 1/4 waves that are additive but the gradient would look like (0V___+V)-(-V___0V), while the alternate possibility is (0V___+V)+(0V___+V), where + and - denote the relative phase of standing waves and 0 refers to virtual ground. Couldn't hurt to try.

I really don't see the concatenation mode working without forced excitation by a second primary loop, but it might be possible. The major issue for its existence is how the extra is excited by the secondary. If there is a large amount of mutual inductance it would seem unlikely, as transmission line action won't be very dominant. Capacitive coupling seems to be the better bet and the extra coil may need to be turned sideways for this to work with a tuning capacitor plate near the end terminal to force 1/4 wave resonance. Though it's likely that a 1/2 wave mode will appear at the extra coil. Though that may not be bad if the ends are anti nodes as you could still get an additive field gradient. Would certainly be a weird 3/4 wave mode if it could be done.
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Last edited by upgradd; 06-07-2015 at 07:52 AM.
#59
06-11-2015, 07:51 AM
 orgonaut314 Senior Member Join Date: Jul 2013 Posts: 222
Quote:
 2) Next is the extra coil. This coil here operates with a propagation constant less than an eighth of a wavelength. Therefore the coil is operating as a simple inductance coil, not as a distributed network. The distributed network capacity of this mode can be expressed as a definite terminal capacitance. Hence the inductance of this coil is adequately represented by its static inductance.
This post from Eric got me confused. Does the extra in tandem mode not act as a distributed network?

In that same post (beginning of this thread) Eric says that together with its elevated capacity the coil acts as a simple LC resonance network.

Perhaps the secondary is in resonance in this mode and the extra coil is not operated on its resonance frequency?

Anyway it seems that the understanding might have changed?

BTW thansk for the explanations also last poster. Self capacitance is much clearer now.
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#60
06-11-2015, 01:19 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Be careful that you're not mixing descriptions of one thing and applying it to another.

Quote:
 2) Next is the extra coil. This coil here operates with a propagation constant less than an eighth of a wavelength. Therefore the coil is operating as a simple inductance coil, not as a distributed network. The distributed network capacity of this mode can be expressed as a definite terminal capacitance. Hence the inductance of this coil is adequately represented by its static inductance.
That is about the Colorado Springs coil, NOT the theoretical operation of the DMT style coils with experimental extra coil and intended concatenated resonance. It was established that the CS coil is not operating in concatenated mode, and the TOTAL wire length across both secondary and extra coil approx = 1/4 wave, so each coil is in effect approx 1/8 wave. Hence it's "adequately represented" by the lumped/static L and C - Close enough for meaningful calculation.
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