SSTC racing sparks and flashover mid-winding: the second mode

A secondary that flashes over across the middle of its winding is usually blamed on coupling, and sometimes that is the cause. The same failure also comes from the secondary's second resonant mode, with the coupling unchanged. That mode is also a likely reason a small secondary can work in one topology and burn in another.

What it is

A resonator has more than one mode. The lowest is the one everybody tunes, and its voltage peak sits on the topload. Anders Mikkelsen went after a flashover on his own coil, measured the base impedance of the winding with no topload fitted, and found the higher modes where a resonator's modes are expected to be, with the second at roughly twice the fundamental (HVF 3097). That is twice on that coil, bare. The ratio that causes trouble is three.

The topload closes the gap. Capacitance at the top pulls the fundamental down harder than it pulls the higher modes. When he added enough of it to stand for the detuning his own sparks produced, the fundamental and the second mode came to sit three to one apart.

A square wave drive carries a strong third harmonic. At that spacing the third harmonic lands on the second mode and pumps energy into it. In his words, the result is "a voltage peak in the middle of the secondary coil".

So the usual chain has one more step at the front:

topload and arc pull the fundamental down
        ->  the second mode ends up near 3x the fundamental
square wave drive
        ->  strong third harmonic
        ->  the third harmonic drives the SECOND mode
        ->  voltage peak in the MIDDLE of the winding
        ->  flashover

He measured it rather than inferring it. At the operating point where the flashovers happened, the base current was mostly the third harmonic of the drive. Spark loading makes it worse in two ways. It is part of what pulls the fundamental into the three to one spacing in the first place, and it damps the fundamental harder than the second mode. The arc both sets up the problem and then keeps the energy in the second mode.

The top of the coil looks fine, so the damage is in a place people don't check.

Both accounts of this failure put the peak level with the top of the primary, and on both coils that is a fair description. Anders' primary covers half the length of his secondary, which he also suspects is why the primary sees that mode at all. But the height is set by the mode, not by the primary. On a coil whose primary covers only a short stretch at the base of the winding, the middle of the secondary and the top of the primary are different places, and the middle is where to look.

On his coil, the bare second mode sat at roughly twice the fundamental, and the trouble arrived at three times. If the second mode barely moves, which is his stated premise rather than something he measured, the fundamental has to fall to two thirds of its bare value before the third harmonic lands on the second mode [derived: 2/3, from his two ratios, 2:1 bare and 3:1 loaded]. Capacitance goes as the inverse square of frequency, so by then the coil carries about 2.25 times the capacitance the bare winding had [derived: (3/2)^2]. That is a lot of detuning, far more than a bench measurement of the bare coil will show you.

What goes wrong, and how to tell it from coupling

• A flashover across the middle of the winding. This mechanism. Racing sparks from coupling strike the winding low down instead, which is how the secondary is a resonator sorts the two by height. Where the ceiling on coupling actually sits is a different page's question, and this failure does not move it.
• A small secondary that works in a DRSSTC or a QCW and burns in a bare SSTC. ZakW could not get his old potted 2 in secondary to run without flashovers on a single resonant machine, nowhere near full input voltage, while the same coil gives him no real trouble in his ramped dual resonant one (HVF 3425). That is one builder, one small coil, in both machines. Why small is worse is not established, and two guesses are given further down.
• The arc squeals. This is not a mechanical noise. ZakW hears a squeaking or screeching arc when his primary is not high enough on the secondary. davekni, offering what he calls a loosely described guess, puts it down to a beat: the second mode sitting near the third harmonic, with the difference between them landing on the primary's own resonance. There is some evidence for it: ZakW's scope capture of the squeal shows the third harmonic appearing periodically in the secondary current, which is what pointed davekni at it. Take the squeal as a sign that the second mode is being fed, not as proof of which of the two frequencies is at fault.
• The bridge locks onto the second mode itself. This is a different failure and a worse one. davekni's account is that standard SSTCs with long secondaries and short antennas, or with secondary current feedback, sometimes oscillate at the second mode outright. The bridge then runs at that frequency rather than at the third harmonic of a lower one, and the overly high frequency often kills IGBTs. On a coil with a short secondary and a comparatively large topload he expects antenna feedback to avoid the instability, because the antenna hears the topload far more than it hears the middle of the winding.

In QCW, the shape of the ramp puts a squealing arc down to the shape of the ramp, or to the buck skipping cycles. That needs a buck to be true. ZakW's coil is mains ramped off a doubler and has no modulator to skip anything, so on a single resonant machine the second-mode reading applies. Both causes are real. If your coil has no buck in it, don't take the QCW explanation at face value.

What you do about it

Anders lists three cures on HVF 3097. His order is a good one, because the first is the only one that gets better as the arc grows.

• Put the second resonance above three times the fundamental at design time, by giving a secondary of a given inductance a larger toroid. Once the mode sits above three times, further spark loading only pulls the two further apart, so the coil moves away from the trouble instead of into it.
• Move the primary against the secondary to couple less into that mode and more into the fundamental.
• Resonate the primary. He calls this the easiest and most robust. It works without moving any mode: a resonant primary cuts the reflected impedance of the fundamental until the fundamental draws far more power than the higher modes do. He fitted one and performance improved greatly. This is also why the same small coil behaves in a DRSSTC or a QCW. It has a cost, because a primary at resonance is a DRSSTC, with a DRSSTC's currents and its need for overcurrent protection.

On a coil that is already built, the thing to adjust is the height of the primary. You search for it, and each end has its own symptom:

• Too low and the arc squeals and the switching goes strange. Raise it and the switching goes back to normal.
• Too high and you get a flashover anyway.

That is ZakW's own procedure, and he reports the same behaviour on his older ramped hardware, so it is not a property of one driver. Anders arrives at the top end of it independently on a later resonator of his own (HVF 3097, later in the thread). He put occasional flashovers down to an optimistically high primary and cured them by moving it down and spacing the turns out, which took coupling from 0.45 to 0.50. A new primary later reduced the flashover risk again while taking coupling to about 0.55. He does not say those flashovers were the second mode, and that resonator is not the one he diagnosed it on. What it does show is the same builder finding primary height to be the flashover control, on a coil where coupling went up while flashovers went down.

The other adjustment is the series capacitor, which ZakW calls the DC blocking cap and davekni the coupling cap. It is the same part either way. It sets the primary's own resonance, and in davekni's guess that resonance is what the beat has to match, so moving it moves the trouble. He suggests making the capacitor much larger. That drops the primary resonance low enough that little of it gets through the gate transformer, and it lowers the primary's resonant Q as well. The same page of the thread also says that a larger capacitor does not remove the mechanism, it only moves it. With the primary resonance lower, the beat can only match it if the second mode sits closer to three times the drive, and once those two are close enough you get the flashover instead of the squeal.

What the evidence does not support

That the beat is established. davekni offers it as a guess and says so. What is measured is the third harmonic in ZakW's secondary current during the squeal, and the link between the squeal and the primary's height. The rest is a plausible mechanism that has not been tested.

That thin secondaries are simply worse. There are two explanations for ZakW's small coil and neither was tested. davekni's is that the smaller coil may have had its second mode closer to three times the operating frequency; he writes it with a "perhaps". ZakW's own is geometric and has nothing to do with modes: on a coil that short the primary is simply too close to the middle of the winding, and the bus voltage sets how small you can go. Anders' fix list suggests a third reading, since his design cure is the ratio of toroid to secondary inductance rather than the size of the secondary. None of this rules out a small secondary.

That there is a number for how close is too close. The arithmetic below turns davekni's guess into a prediction, and it is still only a prediction.

The numbers

• Where it strikes: the middle of the winding. Racing sparks strike low down, and that height belongs to the coupling pages.
• What excites it: the third harmonic of a square wave drive, once the fundamental and the second mode have come to sit three to one apart.
• Anders' bare coil: second mode at roughly twice the fundamental, measured at the base with no topload. His coil, his measurement, and not a property of resonators in general.
• The detuning it takes on that coil: fundamental down to two thirds of its bare value, which is about 2.25 times the bare winding's capacitance in place [derived: 2/3 and (3/2)^2 from his 2:1 and 3:1].
• ZakW's primary resonance at 1.0 µF: about a third of the working frequency, davekni's figure. Put through the criterion on the blocking capacitor page, X_C / X_L = (f_res / f)^2, that is a frequency margin of 3, which cancels a ninth of the primary's reactance, 11.1 per cent [derived: (1/3)^2]. It sits between the two published SSTCs that page records, at 17 per cent and 1.1 per cent, so davekni's figure describes an ordinarily tuned single resonant coil rather than a strange one.
• The cross-check on that figure: ten times less capacitance raises a resonance by the square root of ten, so a third of the working frequency at 1.0 µF becomes 1.05 times it at 0.1 µF [derived: 3.162 / 3]. That matches what ZakW calls close to resonance, and the two men made their statements independently.
• What the beat predicts, if it is right: the difference between the second mode and three times the drive equals the primary resonance, so on that coil the second mode would sit at 2.67 or 3.33 times the drive [derived: 3 ± 1/3]. It could be measured and has not been.
• ZakW's coil, for scale: 31 in of arc from a 4 in secondary at 40 A, off a 340 V half wave doubler into a half bridge, his figures. He does not say whether the four inches is the diameter or the winding length.
• Not established: whether a smaller secondary is worse, and if so why.

Where next

• Winding and measuring a secondary, the rest of what goes wrong with one, sorted by the height of the damage.
• DRSSTC coupling: how far above critical, and what raising it buys, the other flashover mechanism and its ceiling.
• An SSTC primary is a different part, since the fix here is where that winding sits and how much it covers.
• The capacitor that decides what you built, which is where the series capacitor's value is actually decided.

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The mechanism, the measurement and the three cures are Anders Mikkelsen's, on HVF 3097. The squeal, the primary height procedure and the small-coil comparison are ZakW's, on HVF 3425, where davekni proposed the beat and the second mode lock. The arithmetic tying their figures to the capacitor criterion is ours and is marked where it appears.