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Re: Tesla Coil RF Transmitter

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 01:17 PM 9/25/2005, Tesla list wrote: 
Original poster: "Dan" <DUllfig@xxxxxxxxxxxxx>

Jim:

Two issues to bring up. First, earth as a resonator:

Standing waves are THE definition of resonance in a sphere. There is no known mechanism by which a sphere can show increased response to certain frequencies, and not have standing waves.

I can think of at least one. Cover the sphere with a material that is frequency selective (in terms of its absorption vs frequency). Such a material exists: the ionosphere.


When you look at a Schumann resonance spectral chart, you see peeks in frequency response that correspond very nicely with what would be expected if you divide the speed of light by the circumference of the earth. But you are saying that these peaks are due to some not-yet-explained phenomena.

Not at all.. All I a am saying is that the peaks do not imply a resonance. A implies B, but B does not imply A. (Not B would imply Not A)


Your implication fails Occam's razor too! ( they don't call it "Schumann Resonance" for nothing :)

The only reason you don't want to accept that the earth resonates, is that you are not comfortable with the implication: global power distribution.

hardly.. I see so many practical problems with global power distribution on so many levels that I'm not willing to give it a whole lot of thought (rodent fuzzy behind comes to mind).

HOWEVER, I am willing to entertain analysis and/or measurement that shows it's possible, within the confines of physics as currently understood (i.e. no resorting to "special things")


You say the attenuation is too great, that the earth has a low Q. But if waves don't make it all the way around the earth, there are no standing waves.

Waves CAN make it all the way around the earth. I've personally made and observed them (as have many others) However, the loss in the path was phenomenal.

Consider a classic microwave circuit used for high power breakdown testing: the resonant ring. You build a loop of waveguide that is an integral number of wavelengths long (typically, there's a trombone section in there somewhere, so you can "dial it in"). You start injecting power and the circulating power increases until the power lost in one transit equals the power inserted. Say, for instance, that the loss is 10% (about 0.5 dB). If I put one watt into the system, eventually, the circulating power will be 10 watts. This system has a Q of 10.

If the system is a bit lossier.. say it loses 50% of the power. Then I'll only get 2 watts circulating when I've put in 1 watt. Thats a Q of 2.

Now, however, look at long path HF (for an example). You might transmit 1000 W (+60dBm), and receive -150dBm, for a path loss of a mere 210 dB. (Hey, it's a lower path loss than a earth/moon/earth reflection) The loss is 99.999 99999 99999 99999 9% (I might be off by a 9). By any normal measure, this would not be considered a resonant system. It would be considered a "dummy load" and a very good one at that.

However, if I were to sweep my transmitter over frequency, even with that phenomenal loss, I'd notice that there was a definite frequency dependent effect, and a fairly narrow band one, at that. I don't have the data in front of me, but I'd hazard a guess that the bandwidth of the peak is less than a MHz (with a peak frequency of 10-20 MHz). By the usual Center Frequency/Bandwidth measurement of Q, this would imply a Q of 10. But it's not.


And without standing waves, there is no resonance. Without resonance, the earth would have equal frequency response to all frequencies, BUT IT DOESN'T!

Again.. frequency selective absorption exists in all kinds of materials, with no resonance (at least at frequencies near the frequencies being absorbed) needed. Selectivity does NOT imply resonance. Conversely, it doesn't imply that there isn't resonance.

Second, LC tank circuits as lumped circuits:

There is a tendency to think that just because a formula accurately predicts the outcome of an event, that the formula "explains" what is going on. This is not so.

True. However, if the formula is based on the underlying physics, there's a reasonable presumption that it explains the phenomenon.


Just because lumped circuit calculations can predict the resonant frequency of an LC tank circuit, does not mean that an LC tank is a lumped circuit.

The LC formulas work for infinitely small lumped components (where the size is a tiny fraction of the wavelength).

At resonance, the electrical charge is bouncing back and forth between the two sides of the capacitor, passing through the inductor on its way back and forth. By definition, the voltage HAS to be higher at the capacitor plates than it is at the center turn of the inductor coil. You admitted as much without even realizing: you said that there was uneven current distribution. Lumped circuit calculations assume up front even current distribution!

There's an uneven distribution in the typical tesla coil, because of distributed capacitance. There isn't an uneven distribution in the run of the mill lumped LC. If I build an audio frequency LC resonant circuit using a iron core inductor and a small ceramic capacitor, the fields are uniform, at least to the measurable limit.


These kind of approximations are done in physics all the time, because the difference between an approximation, and an accurate description, is so small that the extra effort is a waste of time. The formula for the period of a pendulum only holds true for small arcs of swing.

Funny thing, that,... In high school I spent some amount of time deriving an exact formula for the pendulum (i.e. not using the small angle approximation) in order to determine the change in period due to the gravitational pull of the moon and/or sun.

However, the LC model for a lumped circuit is not an approximation of a transmission line system. One can account for all the parasitics, also as lumped components, and get an exact solution.

When we push a car, we figure out acceleration by assuming it is going in a straight line, but in fact it is moving in a 17500 km circle! An LC tank circuit at resonance is not really a lumped circuit,

it isn't? How far different is it? What model would you propose instead? Sure, one can model it using FDTD methods and break it up into tiny cells using Yee's model (which is transmission line based), but it's hardly a single transmission line. And, I venture to say that a FDTD model isn't any better, nor does it provide any additional intuitive insight, over the lumped model.

but the lumped circuit calculations give numbers that are so close, why bother with more accurate formulas? But never forget that lumped circuit calculations are approximations that give reasonable numbers, not a description of what is going on.


Look.. Tesla's writings imply that this resonance phenomenon is not a parts per billion kind of effect, or else it wouldn't be practical for worldwide power distribution. Tesla certainly implied (if not explicitly said) that his scheme was practical, and he had a very, very good knowledge of what "practical" means.

Your claims of the non-fidelity of lumped models for LC are at the ppm or ppb level. If you start bringing in all sorts of deviations at any level, then should we not start worrying about including relativistic effects? What about controlling for thermal effects (the temperature coefficient of resistance is in the 1 part in 1E5 range for most metals). What about magnetostriction? The magnetic and electrostatic fields in TC will cause dimensional variations substantially larger than that. Folks who design busbars in power substations worry about such things.

If Tesla's ideas have any possibility of being practical, then they should be readily detectable, and should be predictable using simple analysis.



Dan

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