Tesla's Magnifying Transmitter "Replications"

[Farmhand]

Here is a drawing showing the tuning/adjustment I have in my LV setup.

Transmitter


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Receiver


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The circuits are almost identical except for the switch and the primary cap at
the transmitter, however I've found that the tuning cap value can be used for
the charging cap and the tuning cap dispensed with which seems to work
much the same ( the receiver tuning cap must remain ).

Although when using the lower frequencies the above arrangement works well.

..
Now to the transformer coupling in my little HV setup.

This is how I am coupling the LV transformer to the HV transformer without
coupling them correctly I don't get enough to run the gap . I chose 40 Khz
because it seems the HV secondary with the HV primary caps is about that.
Close to NST frequency too.



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.

On a side note, Everybody, if we could keep in mind that some people have
slow internet connections and if we stick to using thumbnails for pictures it
will help the pages load faster for them. I think the main thing is the file size
even a big picture if it has a small file size will load ok. A page full of high
quality large photos takes forever to load on a slow connection. I am guilty of
this myself and will try to limit the large pictures I embed, linked photos can
be High quality and big if we want so maybe an alternative link for big pics
where detail is wanted to be kept.

Thanks
Cheers

[Farmhand]

For instance I counted the turns in my coils and calculated the wire length of
the secondaries, it turns out to be approximately 273 meters and it's
inductance is roughly 8.6 mH from memory and with the three different terminal
arrangements (capacities) I get three different resonant frequencies with the
smallest terminal capacitance I get about 485 Khz add another ring to the
terminal and it's 470 Khz another one which causes a big increase and its 430 Khz
to keep the primary resonant I adjust its charging inductance and capacitance.

To keep the receiver resonant it gets the same terminal and the same primary tuning.

The 275 meters is a lot more wire than the regular calculator would say for
that frequency range. Working it out on the highest frequency I get with the
smallest capacitance it is say 480 Khz this calculator says the 1/4 wavelength is 156 meters but I need at least
273 with 5.6 pf or so added by the terminal. If I used only 156 meters the
frequency would be higher and could be worked out roughly by this calculator
using the method i described above.

So for a given frequency say 480 Khz I need to use more
than the wire length indicated by the regular calculator and it is dependent on
the way the coil is wound as well as the added capacitance of the terminal
and/or surroundings.

Going back to the 20400 Hz frequency I said above 20400, is a multiple of 60
and 12, and much more of course, 6800 is 1/3 of that and 4080 is 1/5, so
there are a lot of options. We shouldn't limit ourselves except to what we
want. Those two frequencies 6800 and 4080 are favorite roundabout
frequencies for me they seem to work well with my other stuff which is a
coincidence I hadn't thought of till just now.

As the input frequency is lowered the Overtones or harmonics or whatever
show up and can be easily tuned to. By scope and output at the receiver.

Cheers

[Farmhand]

But is he talking here about the primary or the secondary? Sounds like the secondary, because he is talking about the size and construction (capacity) of the antenna? If so, then it sounds like the primary circuit should be tuned to 50Hz (for example), and a secondary ("circuit") of a large inductance, tuned to 30KHz? But 1/4 of what wavelength? 120KHz discharge?

Back to this



So if you increase the inductance of your primary (like spaced turns), the current would be magnified greater than the same amount of wire that isn't spaced?

That's the secondary yes, Tesla had chosen his frequency and I presume the
Large Metal Toroid terminal he had planned originally did not fit in the budget.
So he had to design a different terminal out of necessity not choice, this
meant if the new cheaper terminal had a lower capacitance he would then
need to increase the inductance to keep the frequency at the pre-chosen
one.

He had alternators that could work at 20 Khz, not that I'm saying that is the
frequency he used. He did things a lot of different ways he had no real set
rule as to how everything should be always, it depends on what you want to
do.

It complex. The coil can be wound in an infinite number of ways. It's the L/C
ratio of the coil and the terminal which will actually determine the frequency.

Which I think is what this means below. Without doing complex calculations
some feel is required or experience, exactly like you say, we can get our feel
different ways. Or a java calculator can be used but they are only so useful.

It's not the physical length of the wire but rather the velocity inhibited electrical length of the helical coil which must be quarter-wave resonant

If the If the chosen frequency was say 20 400 Hz the full wavelength is
14706 meters the 1/4 WL is 3676 meters. So to work at 20 Khz the secondary
should be approximately 3676 meters.

By using that length of wire in the online calculator I use,

I can see very close to what close wound coils will end up. But it can't do the
"A" and "B" coils combined, so I wing it by finding the inductance of each and
adding them together, so then I just design a coil in there with about the
same inductance and wire length as my two coils added and it gives me the
resonant frequency, but, at least 1 pF must be entered in the toroid
capacitance box.

Here's an example take the above 1/4 WL wire length from the regular calculator above 3676 meters.

Go to this calculator OLTC Calculator
And enter the following list of numbers in the boxes with white text next to them top to bottom.

Secondary
880
0.5
700

Primary
20
10
750
200
2

Toroid capacitance
1

Click in one of the boxes in the results section and you should see 25.886 Khz.
Which is higher than the 20.4 Khz used to get the 1/4 WL wire length and
the inductance is higher, then there is also distributed capacitance and
resistance, it's very complex to work out but very simple by "feel".

Then change the toroid capacitance to 21.4 the frequency becomes 20.398 Khz.

Note the primary capacitance. It changes. Change the primary turns and such to alter the
primary capacitance required if desired anytime later is ok.

Now enter in the Bangs per second box
20398 and the voltage you desire to use in the next one, click in a red box
and the results are displayed. (I used 1000v)

This just gives an idea of how everything interacts it's a very useful tool even
if just to play with and see the different results. Try changing some things to
see the resultant changes. It tells a lot of what does what.

Back to the primary capacitance if the primary is made with more inductance
it requires less capacitance but the input and output will be less.

Change the primary to 40 high and 4 turns and it goes from 2 joules per bang
to 0.5 joules per bang. The average current in the tank goes from 186 amps
to 48 and the terminal voltage goes from 278 Kv to 141 Kv double the primary
turns and have 1/4 the input 1/3 the amperes in the tank and half the
terminal voltage. Going by this calculator, I won't say that part is 100 %
correct but close. (EDIT; I fixed a mistake with amps above)
(EDIT: As primary capacitance is made less the input and output is lessened)
And
(The amount of current that can be displaced/caused by the terminal is
relative to the Potential and the capacity of the Terminal.)
As I see it anyway. Just like a regular capacitor kinda.

I can do the same thing with the wire length in my coils the unknown is the
value of my various forms of Terminal I use to alter the resonant frequency of
the secondary, I can change it by almost 50 Khz from 480 to 430 Khz.

That calculator , what I see on my scope and the way the coils check out
with the function generator and experimenting and some calculation give me
my "feel".

Cheers


.

[dR-Green]

My thinking is ( and I need to test this ) with the secondary, that when the
coil turns are spaced the self capacitance of the coil is increased and the
frequency lowered but to use the same amount of wire the coil must be much
bigger because of the spaces and then the terminal will lower the frequency
again. I need to do some experiments with some spaced turns.

Ah, well I posted the above before reading this. But I think that is something good

[dR-Green]

Now I see what the odd resonant overtones means. The fundamental quarter
wave frequency is odd but there are no Voltage nodes on the coil only a
V-max loop at the top. At the odd resonant overtones there is V-min "Nodes"
on the coil.

Yes that makes sense "Overtones" being frequencies above the fundamental frequency, and "undertones" being below. So the higher ones would be shorter wavelength so there will be these V-min nodes.

To actually make it resonant at 208 Khz. I would need a few meters less than
1.5 x 360 meters = 540 meters of wire in the secondaries.

I'll go with the 300 Khz, darn it no wonder it is difficult to get the frequency down.

Well I'm not really sure what's going on here Until I get my head around it all I think I'll just have to build different things and experiment and see what happens. If everything is measured and weighed and all that, and by seeing the actual effect, then I think it will all make a lot more sense. I suppose making things small scale is ok just to see what happens, but bigger is apparently more powerful. But the small scale version first might be good for deciding what to make bigger.

For instance, if I use an alternator, I shunt its terminals with a condenser in order to magnify the current in the primary. I then tune this circuit to the alternator, and magnify the current in the primary in the ratio of the inductance to the resistance. Therefore, this condenser here stands for either method, and simply means that in this system, as is obvious from the description in the patent, the waves are undamped because high rises of potential would not be obtained otherwise. Whenever I wanted to obtain a high potential, I had to observe these rules in order to force the potential up to that value.

So the primary and cap is tuned to the power supply? In that case if you were using an NST off 50Hz mains, the primary circuit should be tuned for 50Hz.

As you see, you are limited by cost as to the size of the antenna; that is, you are limited as to the capacity and, furthermore, you have selected the frequency. In order to lower the frequency so that there would be no wasteful radiation of energy, you have to employ a large inductance. You have to employ a capacity as large as permissible, and you must use a large inductance in order that you may reach the low frequency which is economical.

But is he talking here about the primary or the secondary? Sounds like the secondary, because he is talking about the size and construction (capacity) of the antenna? If so, then it sounds like the primary circuit should be tuned to 50Hz (for example), and a secondary ("circuit") of a large inductance, tuned to 30KHz? But 1/4 of what wavelength? 120KHz discharge?

Back to this

I then tune this circuit to the alternator, and magnify the current in the primary in the ratio of the inductance to the resistance.

So if you increase the inductance of your primary (like spaced turns), the current would be magnified greater than the same amount of wire that isn't spaced?

[Farmhand]

Hi Mate,

No I haven't read that book. I'll have to get a copy.

I don't have anymore info about the setup apart from the witness descriptions contained in Margaret Cheney's book "Tesla - Man out of time". The guests to his laboratory describe the light as "strange and beautiful", so I suppose that would fit the description of aurora type lighting. He also had at his disposal in that lab a 2 million volt + power supply. I'm sure that helped some what.

It's the possibility of generating these high frequencies that interests me. Much of Keeley's work required combinations of ultra high frequencies. I imagine the coil Tesla used for this setup was reasonably large due to the windings required.

Cheers,

Steve

P.S In case you were interested, Keeley charted visible light beginning not in the low THz like I said, but at approximately 140.7 THz (140,737,488,355,328 cycles per second) and ending at approximately 1.1 PHz (1,125,899,906,842,624 cycles per second). Just to put those into real numbers.

Hi dambit, I found a reference to the effect you were interested in. in this
book Here Page 218 He is talking of a similarity to the aurora's.

When the necessary
adjustments in the length and distance of the wires above
the oil and in the arc of discharge are made, a luminous sheet is
produced between the wires which is perfectly smooth and textureless,
like the ordinary discharge through a moderately exhausted
tube.
I have purposely dwelt upon this apparently insignificant experiment.
In trials of this kind the experimenter arrives at the
startling conclusion that, to pass ordinary luminous discharges
through gases, no particular degree of exhaustion is needed, but
that the gas may be at ordinary or even greater pressure. To
accomplish this, a very high frequency is essential ; a high potential
is likewise required, but this is merely an incidental necessity.
These experiments teach us that, in endeavoring to discover novel
methods of producing light by the agitation of atoms,
or molecules, of a gas, we need not limit our research to the
vacuum tube, but may look forward quite seriously to the possibility
of obtaining the light effects without the use of any vessel
whatever, with air at ordinary pressure.

Such discharges of very high frequency, which render luminous
the air at ordinary pressures, we have probably occasion often to
witness in Nature. I have no doubt that if, as many believe, the
aurora borealis is produced by sudden cosmic disturbances, such
as eruptions at the sun's surface, which set the electrostatic charge
of the earth in an extremely rapid vibration, the red glow observed
is not confined to the upper rarefied strata of the air, but
the discharge traverses, by reason of its very high frequency,
also the dense atmosphere in the form of a glow, such as we ordinarily
produce in a slightly exhausted tube. If the frequency
were very low, or even more so, if the charge were not at all
vibrating, the dense air would break down as in a lightning discharge.
Indications of such breaking down of the lower dense
strata of the air have been repeatedly observed at the occurence
of this marvelous phenomenon ; but if it does occur, it can only
be attributed to the fundamental disturbances, which are few in
number, for the vibration produced by them would be far too
rapid to allow a disruptive break. It is the original and irregular
impulses which affect the instruments ; the superimposed vibrations
probably pass unnoticed.

[Farmhand]

Another thing I considered dR is that the connecting wire if an odd multiple of
the 1/4 wavelength could work better as Tesla says the Earth should be a 1/4
wavelength and the receiver should be far enough from the transmitter so that
the transmitter does not directly impose it's vibrations on the receiver
capacitively or otherwise.

So I would need a wire at least 170 meters long to be 1 x 1/4 wavelength.

Your's would be a lot shorter I think but you'll need to determine the resonant frequency of your coil to be able to do that.

Cheers

[Farmhand]

Hi dR, I think you are onto something with the ruler. It sure did cause me to
think a bit more about it. And do some more study, so it helped me a lot already.

It's not the physical length of the wire but rather the velocity inhibited electrical length of the helical coil which must be quarter-wave resonant

I think that means it depends on how the wire is wound into a coil as to the
inductance it will have and with distributed capacitance and so forth.

My thinking is ( and I need to test this ) with the secondary, that when the
coil turns are spaced the self capacitance of the coil is increased and the
frequency lowered but to use the same amount of wire the coil must be much
bigger because of the spaces and then the terminal will lower the frequency
again. I need to do some experiments with some spaced turns.

I'll make three test coils, One with no turn spaces. (control) One with the
same wire but spaced turns. And One the same height and diameter as the
control but with spaced turns, shorter wire. That should tell me something to
go by. And imprint the result on my noggin mush. Experiments have a
way of doing that.

Like Tesla Said, If we base our designs/machines from experimental data they
will work, that's engineering.

Cheers

[dR-Green]

OK Some of this is what I see on my scope this is the same with my signal
generator pulsing the primary or my circuit. Pleas forgive the waves I drew
them freehand.



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The whole top wave is the transmitter.

The first half is pulsed at full frequency both primary and secondary have the
same period and each wave is exactly the same.

The second half of the top line shows what happens when pulsed at half
frequency,, when the input pulse is missed the wave form starts to get
smaller, but the period still remains the same for both, the frequency of both
does not change. The wave starts to look like a funny kind of M with one
short arch then is put back normal to repeat but the reduction is small for the
input saving.

Well I'm going to have to take a closer look again at the new stuff you posted, I know the "ruler effect" won't apply physically to the coil, but I will be thinking about it more to see how it all might fit together, just in case The "extra wave" when pulsed at 1/2 frequency could be a sort of "ringing" effect. As for the ruler, that at least tells me something about how a wave "wants" to express itself naturally over a free object. The end needs to be tied down in order to force the wave to fit or reflect. But I at least find it interesting that it's not how I thought it was, that a 1m object would have a 1m wave length.

My new "extra coils" will be (about) the same height as they are wide. At least the frame will be, the wire "should" end up somewhere around the right place. I hope

It's not the physical length of the wire but rather the velocity inhibited electrical length of the helical coil which must be quarter-wave resonant

"the velocity inhibited electrical length of the helical coil"... What does this mean? "velocity inhibited electrical length"?

I don't know but I might play around with the geometry as well, basically designing the frame like a drum or acoustic instrument, so the shape will resonate at a certain frequency. That's why my "extra coils" will be as wide as they are high. They will also have 2 closely wound turns then a bigger gap, same amount of wire as the spiral secondary. I can then also replace the 1.5mm primary with 3mm to match the primary weight, but I don't have any wire for that so it won't be immediately.

[Farmhand]

In this patent.NIKOLA TESLA - Google Patents He talks of a speed of
471,240 Kilometers per second which is unless I'm mistaken about 1.57 times
the speed of light which is about 299,792 kilometers per second according to wiki.



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And also mentions the Earths diameter should be an odd multiple of the 1/4
wavelength. And the frequencies again, along with talking of the nodes.



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I should be able to post a scope shot showing the nodes, they show up on
the scope, but I'll have to put my coils back together, I've had them apart
counting turns. There is actually 273 meters of wire in my LV secondaries.

Cheers

[Farmhand]

Hi all I would recommend anyone interested in this stuff to read this document linked below.

Nikola Tesla On His Work With Alternating Currents -- Chapter IV

After reading it more I can see I have made some assumptions that are not correct. So I advise people read it for themselves.

Here is one thing i assumed when skimming through the document, I quoted above where Tesla used 44 000 volts to his primary but now I read at the bottom this quote below.

Counsel

Was the method you used there [in Colorado], a spark? -- an arc? -- or what was the method where you got continuous generation?

Tesla

The method was this: I had a 550-volt current with which I charged the condensers. These condensers I discharged through a primary in the form of an arc, sometimes I also introduced in this arc a mechanical break of several thousand per second. And I obtained a perfectly continuous train of waves as has been described in my patents. The reason why I show the condenser here [Fig. 83] is that that is synonymous with undamped waves. If I had shown the whole apparatus as arranged there, then I might still have damped waves; but whether I use an alternator or some other way of getting energy to that condenser, the condenser is usually there. For instance, if I use an alternator, I shunt its terminals with a condenser in order to magnify the current in the primary. I then tune this circuit to the alternator, and magnify the current in the primary in the ratio of the inductance to the resistance. Therefore, this condenser here stands for either method, and simply means that in this system, as is obvious from the description in the patent, the waves are undamped because high rises of potential would not be obtained otherwise. Whenever I wanted to obtain a high potential, I had to observe these rules in order to force the potential up to that value.

Counsel

He would have to get very much more inductance in the system than he has today, relatively?

Tesla

It is just like this: In an enterprise of this kind, you have to start with certain fundamental propositions. If you are to build a commercial plant, the question comes up how much money is it to cost. Now, you go to specify before your capitalists the various parts of the plant, and you will find that your machinery and the aerial structure will cost so much. If your capitalists are willing to go deep into their pockets, you can put up a tremendous antenna because, as you know, as I pointed out in 1893, that the effects will be proportionate to the capital invested in that part; but you will find great limits there.

I designed a plant [Wardenclyffe, referring to Fig. 83] years ago with a large capacity and put it before certain architects. They figured that the antenna would cost $450,000 and I had to modify my plans. As you see, you are limited by cost as to the size of the antenna; that is, you are limited as to the capacity and, furthermore, you have selected the frequency. In order to lower the frequency so that there would be no wasteful radiation of energy, you have to employ a large inductance. You have to employ a capacity as large as permissible, and you must use a large inductance in order that you may reach the low frequency which is economical.

Counsel

What low frequency is it that is economical?

Tesla

In a patent which appeared in April 1905, the application of which was filed on May 15, 1900, I have enunciated the law of propagation, which I have explained, and have stated that the frequencies should not be more than 30,000 or 35,000 cycles at most, in order to operate economically.

He dispels a lot of myths in the document linked above.

[Farmhand]

Thinking of my new coils.

Using the 1.5 times the wire the online calculator says I need for 208 Khz gives
me 540 meters of wire required for 208 Khz rather than 360 meters the
calculator says.

So if it works out that way the new setup will be resonant at 300 Khz or so
with the terminal capacitance added, and using 360 meters of wire for the
secondaries. The calculation says 312 Khz but it'll be less with the terminal.

To actually make it resonant at 208 Khz. I would need a few meters less than
1.5 x 360 meters = 540 meters of wire in the secondaries.

I'll go with the 300 Khz, darn it no wonder it is difficult to get the frequency down.
I knew there was something funny going on because things didn't add up, but
I just wound bigger resonators to get the frequency down to what I could
pulse with my circuit.

Cheers

P.S. It should kinda work out in a strange numbers way, I'll have a 300mm
diameter Coil "A" a 300mm tall Coil "B" and I will pulse the primary at 300 Khz
about, that's 3 - 300's. I'm not overly numberstitious though.


EDIT:
This calculator works out the wire length for the frequency quite well.
It tells me for 246 meters of wire I get 438 Khz with 6.5 pF toroid capacitance
which is almost spot on. Obviously it is factored into this one.
OLTC Calculator


This one seems wrong it tells me for 246 meters of wire I get 304 Khz
which is much lower frequency with no added capacitance.
Frequency Wavelength Calculator

..

[Farmhand]

Unless I'm mistaken or making wrong calculations it appears the wire length
should be estimated based on a velocity of propagation of the disturbance
through the circuit of about 1.5 times the speed of light.

For me this would give me a wire length of 255 meters for 440 Khz not (170 meters)
a bit less when the toroid capacitance is taken into account.
And so it's about 246 meters of wire is what I have. EDIT; This is for my
Low voltage setup, Coils "A" and "B" combined.

(The HV setup only has 107 meters of wire in each secondary Coil "A" and "B" combined.)

This seems easy to calculate by just multiplying the 170 meters for a 1/4
wavelength of 680 meters (440 Khz) by 1.5. So 170 x 1.5 = 255 meters
however to get 440 Khz a bit less wire is actually needed because of the
toroid terminal capacitance I need 246 meters or so, so the terminal
capacitance shortens the length of wire needed by 9 meters.

I think this all checks out as me having accomplished one goal already.

I would seem to have broken the speed of light. Is there no comment ?

One does not need to know they have broken the speed of light to have done
it. It already happened before I worked it out, if it did happen.

So do I give myself the speeding ticket for working out I did it, or for doing it.

Not to worry back to the experiments. I've broken plenty of speed limits and
laws before so it's no big deal to me.

It doesn't make any sense for nothing to be faster than the speed of light.
Not to me anyway, the speed of dark is faster

I don't think the MIB's will be visiting the house of everyone with a resonant
Air Cored Tesla Transmitter/Transformer. I think everyone is safe.

Cheers

P.S. going by the 1.5 times the speed of light propagation velocity my small
HV coils should be resonant at about 1 Mhz for 107 meters of wire. Not the
700 Khz the online calculator tells me, I think.

Frequency Wavelength Calculator

Still this will only determine the frequency for a given length of wire or the
length of wire for a given frequency, all the tuning still needs to be done.

..

[Farmhand]

Hi all, I did a quick test with my small HV coils using a neon, I held it with the
glass touching the coil and moved it up the coil to the top, as I get to the top
the coil arcs around the glass of the neon to the leg of the neon I am holding
showing a fairly steady increase in voltage up the coil to maximum at the top.
I had the input just so the sparks won't jump to the metal leg of the neon
until near the top. The test wont really work unless I either hold the leg of
the neon or presumably connect the leg of the neon to ground.

I filmed it so here is the short clip. Voltage test on coils.wmv - YouTube

Even though the gap only seems to be running slow the voltage is still at the top
and significant as compared to the input. This was with the two primaries in
series, though I don't think that will make much difference, I think because my
HV source is spongy and the coupling fairly close the oscillations of the
secondary are determining when the gap fires most of the time, when i put my
hand near the coils it affects the frequency of the secondary and so too the
spark gap. It's not ideal but it'll tick over just fine till I get some more wire on
the HV supply transformer secondaries, and speed up the gap and build some
better gaps than spark plugs..

These coils have about 100 meters of .5 mm wire in the secondaries by
calculation. I'll redo the calculations when I count the turns properly. For both
sets the LV one's too just be sure of the amount of wire.

This pic shows the sparks "if you click on the thumbnail", the neon is glowing
yellow and orange, cool. And it looks like the sparks leave the neon and go the the coil.


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Cheers

[Farmhand]

Now I read some more from that document I linked above.

I think this says it all.

From the document.

It's not the physical length of the wire but rather the velocity inhibited electrical length of the helical coil which must be quarter-wave resonant (i.e., have forward and reflected wave-interference producing a standing quarter-wave resonance)

I think this means I done good with my coils because I have more wire than I
should by theoretical calculations should need for the frequency I have. I
have 240 meters of wire in my secondaries, but the terminal capacitance is
about 25 to 30 pF which would lower the frequency a fair bit but not that
much I don't think.

Therefore the forward and reflected wave interference
must be faster than light to be able to go through more wire in the same time.
I think. Anyone have any thoughts on that ? Who knows and
it really doesn't matter as long as they work. The only difference it will make
is the frequency I get from my coils will be higher than it should be in
conventional terms. EDIT; Or is it lower, it's a bit confusing. I need a sleep too.

Now I know why the online calculators are not quite right.

It's not the physical length of the wire but rather the velocity inhibited electrical length of the helical coil which must be quarter-wave resonant (i.e., have forward and reflected wave-interference producing a standing quarter-wave resonance)

Class Notes: Tesla Coils and the Failure of Lumped-Element Circuit Theory

It makes no difference whether the coil is a cylindrical helix, a conical frustum, or a flat spiral. Tesla clearly understood the velocity-inhibited nature of spiral and helical resonators and taught that, "The length of the wire coil in each transformer should be approximately one-quarter of the wave length of the electric disturbance in the circuit, this estimate being based on the velocity of propagation of the disturbance through the coil itself." [US Patent 645,576; Applied for Sept. 2, 1897] It's not the physical length of the wire but rather the velocity inhibited electrical length of the helical coil which must be quarter-wave resonant (i.e., have forward and reflected wave-interference producing a standing quarter-wave resonance). This was recognized by Tesla, and this is the meaning of the phrase "...this estimate being based on the velocity of propagation of the disturbance through the coil itself." (The consideration could not exist for a lumped element, obviously.) Berkeley physicist David Sloan, ("An RF High Voltage Generator," Phys. Rev., Vol. 47, 1935, pp. 62-70), did not know how to mathematically handle the inhibited velocity of propagation on the helical resonator, and a suitable engineering analysis was provided only a decade ago.

Is there any question that Tesla is speaking of a distributed transmission-line resonator? Well, if so, listen to his correspondence to the US Patent Examiner on November 15, 1897. He is explaining what happens if the resonator excitation-frequency is raised (i.e., the wavelength shortened). As every electrical engineer knows, a grounded quarter-wave transmission-line resonator possesses a Vmin at the base and a Vmax at the top. If the frequency is lowered, the structure is too short for quarter-wave resonance, and if the frequency is raised, then Vmax positions form down in the resonator. The same is true for both helical coils and spiral coils. Concerning the latter, Tesla wrote,

"If the transmitting and receiving coil were made longer than the quarter of the wave-length of the electrical disturbance in the wire, then the points of highest potential would not fall at the inner ends of the coils ... as required, but nodal points would form, as the case may be, somewhere in the middle of the coils ..." [Dr. Nikola Tesla - Selected Patent Wrappers, compiled by J.T. Ratzlaff, Tesla Book Company, 1980, Vol. 1, p. 150.]

This phenomenon is decisive. It occurs only on distributed resonators: it is impossible with any lumped circuit element! (The current has the same value at every point along a lumped-element.) To understand what is happening, consider a cylindrical helical coil of height H. The base is always forced to be a voltage node (it's grounded). The top is always a relative voltage loop at the odd quarter-wave resonances and a voltage node at the even (half-wave) resonances. These boundary conditions constrain the mode patterns on the structure (called spatial harmonics). We assert that velocity inhibited partially coherent forward and reflected RF traveling waves form interference patterns on the coil.

Now I see what the odd resonant overtones means. The fundamental quarter
wave frequency is odd but there are no Voltage nodes on the coil only a
V-max loop at the top. At the odd resonant overtones there is V-min "Nodes"
on the coil.

At the fundamental (quarter-wave) resonant frequency there is a Vmin at the base and the Vmax appears at H (the top)

At all the odd resonant overtones, there is always a Vmax at the top and a Vmin at the base

Cheers