Tesla Magnifying Transmitter/Eric Dollard Type Coils Compendium

[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

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.

[dR-Green]

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".

[Ernst]

I am trying to understand this (but failing...) can someone tell me what I am doing wrong?

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.

[dR-Green]

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.

[edit] 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

[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.

[Natusake]

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

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!

[dR-Green]

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

[Ernst]

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)

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.

[dR-Green]

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.

[Ernst]

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.

[dR-Green]

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.

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.

[Ernst]

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.

[dR-Green]

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.

[Ernst]

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.

[dR-Green]

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...