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Comments and critique is welcome to my e-mail adress, my knowledge of measurements is perhaps somewhat outdated, and I must admit that my mathematical understanding is very limited.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 24 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.
More current, more resonance
The ballast winding taps were rearranged for 6,6 mH minimum ballast inductance. The blue graph shows the input current to the HV transformer at 24 A / div, the yellow graph is the input voltage to the transformer, after the ballast.
The peak current value in the graph is about 90 A and the calculated rms current is 67 A. The vertical scale of the graph is the same as the graph above, so they can be compared. The difference, aside from the higher current, is the much larger resonance swings in the graph to the right.
The resonance swings comes from the ballast inductance and the primary cap. This resonance can be calculated to 149 Hz, based on the ballast inductance and the value of the primary cap, when the latter is refered to the primary side of the transformer (200 nF - 174 uF).
The mechanism of resonant charging
At the moment when he cap is discharged after each bang, there is no voltage over the cap, all the available voltage is over the ballast. This results in a rising current in the inductor, which builds stored energy in it´s magnetic field. This is the rising part of the resonance swings in the blue graph, and at the same time the voltage over the cap builds up.
When the voltage over the cap equals the voltage over the inductor, the current build up in the inductor stops. This is at the local peaks of the blue graph.
After the local current peak the process reverses, the ballast will be inducing voltage into the cap. That is the falling part of the blue graph, the energy stored in the magnetic field of the inductor is transferred to the cap. This results in a higher charging voltage, the theoretical limit is twice the available peak voltage of the transformer.
This effect is more prominent at the 50 Hz voltage peaks, which can be seen in the graph. There is one period of the mains 50 Hz in the graph.
Richard Burnett´s simulations versus my measurements
Richard Burnett, who pioneered the resonant charging concept, suggests in one diagram 85 Hz charging resonance for my bps, and in another he states that max power factor would be achieved at about 120 Hz.
In my first measurement, the first graph with the not so prominent resonance swings, the resonance would be about 106 Hz. This would be closer to Richard´s suggested values, but results in less resonance in my setup.
I am not sure how to explain this discrepance. Richard´s data was based on simulations, mine are based on measurement. In both cases there are possibilities for error. Simulations implies some simplification, perhaps factors not accounted for could be significant, for example the HV transformer characteristics. And there are some uncertain input values in my calculations, for example the ballast inductance value.
Short circuit current limitation, knife fuses
The lowered ballast inductance calls for other forms of current limitation. Otherwise a firing safety gap would blow my fuses, or worse, blow the fuses att the other side of the incoming power lines, that I don´t have access to.
Knife fuses are very tolerant of slight overcurrent, but very fast at high overcurrents. I installed a set of 40 A knife fuses in my control cabinet, after the main switch but before everything else. They will stand 80 A for several minutes, but will always blow before the 63 A incoming power line fuses at high current.
I have added a home made current transformer (CT) over the outgoing connection to the HV transformer. The CT is a powdered iron toroid core, wound with about 30 turns enameled copper wire and connected to a 0,1 ohm resistor. A voltage is generated over the resistor from the magnetic field of the power line through the toroid.
This voltage is connected to the overvoltage sensing relay (Broyce
LMCVR-20V 24-230VAC/DC). The normally conected relay output disconnects the holding current for the main contactor, in case of an overcurrent condition.
This protects the knife fuses for reasonable overcurrent conditions, such as a firing safety gap, while the really heavy short circuit currents are handled by the knife fuses, if they should ever occur.
And a few after thoughts...
When I installed these items, I took the opportunity to clean up my control cabinet. From the beginning I had installed inrush current limiting resistors, heavy NTC-resistors, for the purpose of handling the transformer startup current. I even installed three of them with a switch, so that a new cool and therefore ready resistor could be used for the next start.
I found out that these were totally unnecessary, as there was no inrush current at all. The ballast took care of this, so I removed the resistors. But I kept the switch, as an extra series switch for safety, when working on the coil. It is a bit scary to use just one switch to disconnect power, the contacts could be welded together by arcs.
For safety, I use two swiches in series, and the main contactor, for making sure that everything is disconnected before touching anything. And then I short the HV transformer secondary with a long stick, as well as directly over the primary cap bus bars.
How to optimize resonant charging
The resonant charging requires one half period of resonance between each bang, to work at max efficiency. This half period is from max voltage over the ballast to max induced voltage of the opposite polarity into the cap.
There is 2,7 ms between bangs in the graph, while my calculated resonance of the charging circuit would correspond to 2,3 ms for a half period. This would be quite close to optimum.
It is not so easy to measure the ballast inductance with precision. This is because of the unlinear behaviour of the iron core. The inductance should preferably be measured close to the current it is actually used for, which is not so easy to achieve. If I put the full 400 V over the ballast, that would result in a scary 200 A current draw at 6,4 mH. So I have measured it at a much lower current, but that results in an inductance value that has to be viewed as approximate. Therefore I don´t know the exact charging resonance frequency, the 149 Hz is an estimation.
The ballast and the short circuit current
Richard Burnett suggests that the ballast could initially be dimensioned for the wanted input current to the HV transformer, calculated as a short circuit current at 50 Hz. That would in my case be 19 mH for 67 A. A correction factor of 0,64 should then be applied for my bps, this would suggest 12 mH for the same 67 A when the coil is running.
This is quite far from my 6,4 mH ballast inductance for 67 A. And the possible short circuit current, for example if the safety gap fires, would be quite scary, about 200 A at 6,4 mH. Richard´s suggestions would result in a not quite so scary 105 A short circuit current.
In both cases there would also be some resistive limiting of the short circuit current, because of copper losses at the ballast and HV transformer windings. There is probably some leakage inductance at the transformer as well, that would also be limiting the current. But it is frightening, even with these limitations.
I would also build the ballast differently, if I did it again. I vastly overestimated the need for a high inductance value in the beginning, before I had a clear understanding of the resonant charging concept. I also overestimated the reluctance of my very large core, such a large core is very efficient.
For this UI 240 core, 200 mm deep, I would use about 45 turns for 6,4 mH if I did it again. And the additional three windings for lower current would be an additional 7 turns each. This would supply about the right inductance with an air gap of perhaps 4-6 mm. And an opportunity for diminishing the current in three steps to about half the max value, by adding the extra windings.
My main winding now is 66 turns, and the additional windings are 11 turns each. This is way too much, I can´t use any core I part at all, only the U-part. So the air gap is maxed out. And therefore I can not use the air gap for fine adjustments, which is very much desireable.