Finding Resonant Modes of a Tesla Transformer

[G.G. Brock]

The following is in reference to a previous conversation on the matter of series and parallel modes of resonance, as applied to Tesla's Colorado Springs Transmitter.

The coil illustrated on page 349 is describing the extra coil at the central shack/station, which has a wire length of 2660 feet, equating to a calculated quarter wavelength frequency of 92,504 cycles. Granted this extra coil is of 1:1 geometric proportion, the assumption would be that the series mode exists at around 115,000 cycles while the parallel mode is found at roughly 123,000 cycles.


Starting from page 350 to the first half of page 355, tesla describes multiple instances whereby a separate receiving coil is used at different distances for “pickup”. Figures XXV, and XXVI are supposedly the same coil design as Tesla describes them to be, in which they possess a total length of wire 2198 feet, allowing for a calculated quarter wave frequency of 111,000 cycles per second.





By due of the photographic plates, the measured height of the coils is 68 inches, given that the coil’s diameter is 25.25 inches, allowing for a 2.7% height to diameter ratio. This means that a frequency compensation factor of 150% will entail a series mode of the coil to be 167,000 cycles per second. Likewise, the parallel mode will be 162% than of the quarter wavelength frequency, giving 179,000 cycles.


Summing up, the main station would have operated on a series mode frequency of roughly 115,000 cycles per second, with an accompanying parallel mode of 123,000 cycles.


The receiving coils which Tesla speaks of would have likely operated on a series mode of 167,000 cycles, whereas its natural parallel mode would be around 179,000 cycles per second, granted its calculated wavelength frequency is 111,000 cycles.


On a side note, I have just deduced that for a 1:1 end fed extra coil, its series mode will be roughly 120% higher than its quarter wave calculated frequency, as its parallel mode will be 130% higher, as previously stated. Yet, what is interesting is that if we take the ratio of series to parallel, 1.20/1.30, we obtain 0.92. Likewise, 1.30/1.20 yields 1.08. Now if we compare that to elongated coils and flattened coils with different aspect height to width ratios, this proportionality still seems to apply. In the example where an elongated coil possesses a 1.87% height to diameter ratio, its calculated quarter wavelength frequency is 325 kilocycles. According to VNA measurements conducted, its series mode is 476 kilocycles and parallel at 521 kilocycles. According to frequency compensation, the series mode should be 147% higher than of the “fundamental”, which it turns out to be. What is most interesting is how this coil’s parallel mode is 160% higher than of the fundamental frequency of 325 kc meaning that this coil’s series to parallel percentage ratio: 1.46/1.60 is equal to 0.91. Likewise, the opposite, 1.60/1.46 giving 1.08. Now take a look, this is awfully close to the same ratios obtained with every other 1:1 coil. I’ve tested this ratio on other coils, and surprisingly, it holds up!


I suppose in the end, this means a possibility that to determine the series mode of a coil, this depends on the coil’s geometry (frequency compensation factor), granting the parallel mode being 108% to 108.5% higher than of the series mode frequency. Therefore, the general ratio of series to parallel is derived as being,


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[Hakasays]

What we're finding so far is that the longitudinal/parallel mode for a single Tesla extra coil tends to be about 7-15% above the normal series/quarter-wave mode (average 10%).
Unfortunately this doesn't directly correlate with any resonant peaks in the electrostatic field, or SWR on the transmitter, which forces us to find more complex/creative means.

We want to find a more simple means of tuning Tesla Coils because not everyone's going to have a vector network analyzer handy, and even fewer will know how to 'read the tea leaves' to understand what the various traces mean.


The best indicator thus-far appears to be found by measuring the electrostatic field in-air with one probe and measuring the current to ground with a second probe (single-turn current transformer).

At the series(normal) peak the potential and current gradients both peak and are in-phase.
At the parallel peak, the potential and current modes appear shifted either 90 or 180deg to the potential trace. With both traces on the scope you can see a phase-shift clearly when scanning 5-20% above the series peak.

It's still a bit fuzzy at the moment because there seems to be some variation based on the transmitter used and the specific coil being tested. After this problem is solved, the next will be finding out how to balance 2+3 coil systems using a similar technique. And once that's done, anyone should be able to participate in these experiments at a very high-level without using a VNA

[G.G. Brock]

This section will confine itself to research into the measurement of various resonant modes and optimization of a Tesla Resonant Transformer, with respect to its configuration.