11 ft streamers
Much research and simulated waveforms, not so many actual measurements
There is much serious research done on Tesla coils in the last decades, and many simulations of waveforms based on mathematical models have been published. There are however not as much actual waveform measurements published.
Therefore I will try to make the measurments that I can, and I will publish them.
I do not have access to expensive measuring equipment, so I will have to make the best of what I have available.
Comments and critique is welcome to my e-mail adress, my knowledge of measurements is perhaps somewhat outdated, and I must admit that my mathematical understanding is very limited.
What is difficult about making waveform measurements on a Tesla coil?
One major problem is that a mains powered oscilloscope is referred to mains ground, while the Tesla coil is referred to it´s own ground. The tesla ground connection carries a lot of RF-current, and it´s potential is often at several hundred volts from the mains ground connection. This is because of the inevitable inductance of the tesla ground lead and of the ground itself. Therefore it is not possible to connect the oscilloscope ground to the tesla ground. This makes it neccessary to use differential current or voltage probes, that do not connect the different grounds, and that are immune to different ground potentials.
Radio frequency interference could also sneak in by every cable connection. A WiFi connected scope module eliminates some cabling, and battery powering of scope and active probes eliminates yet more cables. A WiFi connected scope module could be screened for the lower frequency range of the Tesla coil, but still allow the WiFi signal in the GHz range through.
And the other problem, of course, are the vast currents and voltages that are present in the tesla primary or secondary circuits. Most differential input high voltage probes are not able to handle the voltages in the tesla primary circuit. Current transformers are differential by nature, but have bandwidth limitations, as well as a limited amplitude range.
This is my primary cap voltage at 12 kV / div. A little more than six periods of the 50 Hz mains voltage can be seen on the horisontal axis. There are 43 discharges visible, that corresponds to 331 bps of the asynchronous spark gap. The voltage at discharge varies from 0 volts to 29 kV. The average energy at discharge is 35 Joule, based on the data in the graph and the 200 nF cap. That corresponds to 11,5 kW at 331 bps.
Would I benefit from a synchronous spark gap?
I doubt that, but I must admit that the energy per half period varies by about 20 percent, depending on where the discharges happens in the half period. But one must remember that the best half periods, energywise, are a consequence of less successful half periods before and after.
A synchronous gap would allow me to place the discharges at the most favorable moments, but for the reasons mentioned above, that would not supply as much energy as my best half periods. So my conclusion is that I would probably not gain so much over my present average energy per half period. And I would have lost the opportunity to vary the bps continously, which is a great asset when trying to optimize the charging.
But I would get a more constant energy level with a synchronous gap, of course.
The high voltage capability of the primary circuit
This measurement makes it clear that the primary circuit clearancies could not be designed based just on the HV transformer peak voltage, in this case 17 kV. The capacitor voltage is much higher at times, 29 kV in this measurement.
That puts strict demands on insulation and distances in the circuit, otherwise there will inevitably be destructive flash over or arcing. I have seen many examples of too tight layout of MMC capacitor arrays on the internet and my initial MMC layout was bad, before I realized the voltages that was actually present.
Richard Burnett´s resonant charging concept
My HV transformer puts out 11,8 kV rms unloaded, or about 17 kV peak. I have tried to design the charging circuit according to mr Burnett´s suggestions.
That must have been successful to some extent, as I would hardly have been able to charge my tank capacitor over the rms value of the transformer, on average, without some inductive kick effect. The average charging voltage in the graph is 18 kV.
But if my charging circuit is fully optimized, I don´t know. Actually I doubt it, I think I should be able to put more than 11,5 kW into the coil, based on the current into the HV transformer. Perhaps my power factor could be better.
How this measurement was made
I have used an active differential high voltage probe, Cal Test CT4079. The probe has a max of 15 kV, which is too low for my measurement, so I have doubled up on the input series stage of the voltage dividing network for 30 kV. That was no trivial task, as the voltage dividing network of a HV probe is resistive at low frequency but capacitive at high frequencies.
I did this by taking the input stage from another destroyed and similar probe, and adding that. I will not tell you the story of how that probe was destroyed, that would be too embarrassing, but the good side of the story is that I had another input stage available.
After some fiddling of the capacitor values, I was able to get a flat frequency response and good common mode rejection with the added input stage, and a 30 kV capability.
The yellow graph is input voltage, the blue is input current
The asynchronous rotating sparkgap was set to 340 bps, the ballast tap for max current and the contactor was connected at the instant visible on the left side of the time line. That moment was somewhat after the voltage sinus peak, but not by much.
No inrush current
The blue current graph corresponds to 25 A /div. It is interestng that there is no inrush current at all. On the contarary, the first current peak is at less than half the following peak values.
Coilers generally use an expensive and heavy variac for bringing up the voltage and current gradually to the coil. This measurement shows that this is unnecessary, as long as the ballast core is non saturating at start up. Just throw the switch, and the coil starts softly all by itself.
The current lags
One period is 4 divisions, and the blue current graph lags sligtly more than 0,2 division, or about 20 angular degrees at 50 Hz. This could not be converted straight off to a power factor, as there are severe overtones and therefore several frequencies present at once. But it is obvious that the ballast reactance dominates over the capacitor reactance, as the current lags.
I had expected more current
My moving iron current panel meter shows over 50 A, but the scope calculates the rms current to 41 A. The panel meter is designed for 50 Hz only, and can not measure the overtone rich current correctly.
I want to supply more current to the coil, so I will have to reduce the ballast inductance. That will also make the current less lagging, which will put more real power into the coil.
My resonant charging is not yet optimized
I think there are two signs that my ballast inductance is too high for optimal charging. One is that the current is lagging, the other is that there is no tendency for the rate of change of the charging voltage ramp (in the graph at the top of this page) to diminish at the top of the ramp.
The first sign shows that the reactance of the inductor dominates over the reactance of the capacitor, they are not in the balance that they should be. The other sign shows that there is still unused stored energy in the ballast, by the time of the firing.
A lower ballast inductance will hopefully make the charging more resonant, and at the same time supply more current.
In case of a firing safety gap, there will be severe overcurrent
The ballast value that is optimal for the charging, will let very high resistive overload currents pass through. In case of a short over the primary cap, or in case of the safety gap firing, the current will almost only be limited by the ballast inductance.
At the moment my ballast inductance is 15 mH, which has a reactance of 4,7 ohm at 50 Hz. That corresponds to a short circuit current of 85 A at 400 V. If I lower the inductance to 10 mH as planned, this will be 130 A. That is way too much for my local fuses, and also for the fuses at the other end of my incoming cable. And I really want to avoid the latter scenario, as I have no access to those.
So I will probably have to use a combination of very fast acting local knife fuses for the really high short circuit currents, combined with an over current sensing relay for the lower over current range. More on that later.
Resonant charging - no magic
There are 3, or at the most 4 firings of the spark gap, each half period at 50 Hz. These can be seen on the current graph, more clearly when they are at the top of the voltage sinus graph. There is also a visible extra swing after each firing. That is the resonant charging process, as predicted by Richard Burnett. Each time the capacitor is drained of energy, the ballast initially stores energy in it´s magnetic field, and then releases this energy as voltage into the cap.
A mechanic analogy to this is when a weight is suspended hanging from a spring. If the weight is pulled down and then released, it does not only swing back to it´s resting position, but it overshoots this to a bit less than double the distance it was initially pulled down.
This is what happens to the capacitor, it could be charged to a bit less than double the peak output voltage of the HV-transformer. This can be seen in the capacitor voltage graph at the top of this page. The peak voltage of my HV-transformer is about 17 kV, but the cap gets charged to at most 29 kV.
There is no magic about this, the time integrated value of the cap voltage is no higher than the same for the unloaded transformer output voltage. But the peak charging voltage is, and that is what determines the energy content of each bang. Another way of putting this is that a charging circuit without resonance supplies a very bad power factor, and therefore is very inefficient.
The horrible overtones
From the power company´s point of view, a load current that has so prominent overtones as this, constitutes a horrible load. In my case, I am in an industrial environment with very high loads and a stiff grid, therefore I expect my overtones will drown in the much higher general load, so I don´t care too much about these. In a more sensitive environment, where the tesla load would be the dominant one, there could be flicker of fluorescent tubes and all kinds of other nasty problems.
The overtones comes from my bps rate, 340 bps, and also from the charging system resonance. This is determined by the cap and ballast values, and in my case should resonate at about 100 Hz. This will tend towards 120 Hz if I lower the ballast value as planned.
It could be argued that a resonance corresponding to half the bps, that is 170 Hz in my case, would be optimal as that should enable the maximum voltage swing. But i think a somewhat lower frequency might be better, as the rate of change of a full half period sinus ramp is very low at the very top and bottom.
Richard Burnett´s work suggests about 120 Hz for my setup. His recommendations are based on simulations. But I am a bit old school, and prefer to experiment and measure, as I am not familiar with simulations or advanced mathematics.