[ §1 · tuning ]

How to tune a QCW DRSSTC as the frequency slides down the ramp

A DRSSTC has a frequency. A QCW has a different one at every instant of the bang, and the four things timed against it do not move in the same direction.

CommonGnd5 August 202636 min read

A DRSSTC has a frequency. A QCW Tesla coil has a different one at every instant of the bang, and every setting that is timed against it is only exactly right at the moment you set it.

Why a QCW has no single frequency

A resonant circuit's frequency comes from its inductance and its capacitance, and in most electronics both of those are components. They are soldered down, they do not move, and the frequency is a property of the board.

Now let one of them change while the circuit is running. The resonance follows it, continuously, and nothing about that is dramatic on its own, the circuit is still resonant, just at a different frequency than it was a moment ago.

What is dramatic is everything else in the system that was set relative to the old frequency. A delay chosen as a fraction of a period is now a different fraction. A network that produces a fixed phase angle now produces that angle at a different number of nanoseconds. A filter's corner has moved relative to the signal going through it.

None of those parts broke. They are doing exactly what they were built to do. They were simply designed at one frequency and are now being asked to work at another, and they do not all fail in the same direction or at the same rate.

What you decide: dead time, phase lead, detuning and turns

On a coil the moving capacitance is the arc a QCW grows. It grows off the topload, and while it grows it adds capacitance to the secondary, which pulls the resonance down. On a DRSSTC that happens inside a few hundred microseconds and the feedback loop absorbs it. On a QCW the bang lasts twenty five milliseconds, the arc reaches a metre or more, and the frequency spends the whole time sliding.

The arc is capacitance hanging off the topload, so the secondary's own resonance falls 16.7 per cent as it grows. The pole the bridge actually switches falls 10.7, because the primary sits at 349.9 kHz and does not move, which is within 1.5 per cent of where the secondary ends a 1.5 m ramp and exactly where it would end a 1.65 m one. That is the detuning rule satisfied. The third track is the coil you get if nobody forces the upper pole: it starts below where the others finish and sinks under 300 kHz, which is where straight swords stop forming, and the marker warms for that reason rather than a thermal one, since a lower frequency is actually easier on the copper and on the gate supply. Derived from JavaTC's figures rather than measured, and only for the arc length the capacitance was calibrated on.

Three tracks there and not one, because "the frequency" is four numbers on this machine and only one of them is a single number. The primary is 349.9 kHz and never moves at all: nothing in it is exposed to the arc, which is exactly why it anchors the poles. The secondary's own resonance is what the arc loads, and it falls 16.7 per cent. The upper pole is what the bridge is switching, 519.1 kHz down to 463.3, and it falls 10.7, which is 0.64 of the secondary's travel because of that anchor. The lower pole is the coil you get if nobody forces the upper one, and it starts below where the other two finish. So every setting timed against the switching is timed against the smaller movement, and every setting matched to the arc is matched against the larger one. That split is the rest of this page.

One arc length, and only one. Everything above is calibrated on a 1.5 m arc, which works out at 4.14 pF per metre of streamer. This page used to carry a 1.8 m column as well and it has been withdrawn, because the figure it rested on does not derive. Reproducing the published 289 kHz needs two wrong inputs at once: a 430 kHz base, which was retracted in favour of JavaTC's 426.49, and the toroid's 10.7 pF where the resonance actually runs on Ces of 14.031. Both err the same way, so they compounded into a number about 56 kHz low. The check that settles it: L from 426.49 kHz and 14.031 pF comes out at 9.9251 mH, and JavaTC prints Les = 9.925. The resonance is on Ces. On our own calibration a 1.8 m arc lands at 344.7 kHz, not 289. And the calibration should not be stretched anyway. The capacitance of a long thin conductor does not grow linearly with its length: it goes roughly as L/ln(L/r), so pF per metre is a local approximation, good near the point it was fitted at and worse away from it.

Every table here is one coil, not a reference

The number under all of them is the arc's capacitance, and it is not the same on your machine. That is not measurement error, it is a property: how much capacitance a metre of streamer adds depends on the topload it grows from, on how the arc branches, on where the walls are.

Two measurements survive checking, and both sit above our own calibration. Neither builder publishes a figure per metre, though. What each measured is a total, 16 pF on Anders' arc and about 7 on Weston's, and the per-metre column below is ours: their capacitance divided by their arc length. The 4.14 used here is our own calibration on one coil, not a fourth measurement and not a reference constant. It sits below both, which fits a smaller topload and a shorter arc:

coil	pF/m	source
here	4.14	calibrated, one coil
Anders	5.03	16 pF measured, over 3.18 m here · HVF 3097
Weston, 3 ft	7.66	about 7 pF measured, over 3 ft here · HVF 1024

Anders' figure carries no independent check. The 5.03 pF/m in the row above was obtained by dividing his measured 16 pF by a 3.18 m arc, so multiplying it back by that same length returns the 16 pF it started from. This page used to read that as agreement and said the number and the machine agree without being made to. They were made to, by the division that produced the rate. It is one figure written twice. The arc length is the input the whole row rests on, and it is the one number here that has not been read back out of the thread.

The parallel-form conversion in the note below applies to sources that state the arc as a series RC. A capacitance read off a frequency shift is already the loading capacitance and needs no conversion. This surfaces a real disagreement rather than a bookkeeping one, and how big it is depends on whose coil the conversion is run on. His series model is 210 kΩ a foot with 2.3 pF a foot (HVF 1024). Reduced to our 1.5 m arc at our loaded 355.1 kHz that gives the 3.49 pF/m this corpus has been quoting [derived, Cp = Cs/(1 + (ω·Rs·Cs)²)]. Run instead on his coil, three feet of arc across the 390 to 330 kHz his own ramp covered, the same two constants give 1.0 to 1.3 pF/m [derived, the same expression]. So on the coil both figures describe, his model and his capture are six or seven times apart, and the factor of two is what the reduction to our frequency and our arc length makes it look like.

Two rows that used to sit in this list have been taken out of it, and the reason is worth more than the figures. A "Weston, two-foot 3.28" was a phantom: the source (HVF 1024) carries one capture, about 7 pF at three feet, and no two-foot measurement, and the 3.28 does not reproduce from his data at any capacitance a resonator could have. Worse, this page had used that phantom to retract his real 7.66, on the grounds that a two- and three-foot pair implied C ∝ L³·¹, which no conductor does. With the two-foot figure gone that argument goes with it, and 7.66 stands as his measurement. A "QCW 1.5, 3.31" was a different error. Its 413 to 377 kHz shift starts above that coil's own secondary resonance near 343 kHz, so it is a pole shift, not a secondary shift; a running coil shows the pole, which this corpus says on the poles page, and reading it with the secondary formula overstates the capacitance nearly threefold. Its honest value is about 1.3 pF/m. This page also carried, for a day, a reading in which 4.14 was the middle of a measured range. That rested on those two rows. With them gone, 4.14 is simply our own calibration on one coil, below the two measurements that survive.

What the spread actually moves

Not much, in kilohertz. The frequencies shift by single-figure percentages across the whole range:

pF/m   secondary   lower   upper   lower pole
       at 1.5 m    pole    pole    leaves < 300 at
4.14   355         296     463     1.20 m
5.03   344         291     456     0.99 m
7.66   316         277     440     0.65 m
8.00   313         276     438     0.62 m

The marks move by metres, and that is the part to carry away. Across the surviving range the point where the lower pole leaves the straight-sword band runs from 1.20 m down to 0.65 m.

More than half a metre of spread on a mark that reads like a specification. So read it as somewhere between two thirds of a metre and a metre and a fifth, and compute it against your own capacitance when you have one, never as 1.20 m.

And what the spread does not touch

More useful than the caveat, because this is what transfers to your coil whatever its arc turns out to be:

The lower pole is out of the straight-sword band before 1.5 m. At every capacitance in the measured range.
The upper pole never leaves it, at any arc length this coil can reach, at any capacitance in the range.
The poles with no arc out, 519.1 and 317.0, have no arc capacitance in them at all. There is no arc. Those two are as firm as k and the two resonances that produced them.
The order and the sign of every conclusion on this page. What moves is the kilohertz, not which pole is where or which way anything goes.

So the real decision is not what to set anything to. It is which end of the ramp you set each thing at, and the reason that is a decision at all is that the ends disagree.

Whether the slide is a nuisance or a favour

Everything above treats the slide as something to be survived. It gets asked the other way round on HVF, by somebody who runs the machines: "I'm wondering if there is an advantage in frequency dropping some during arc growth" (HVF 3140). The answer that comes back is two sided, and both sides are davekni's own.

Early in the arc you want the frequency high, and that half is not speculation. His 100 kHz QCW went from a straight arc to a zigzagged one, the discussion put it down to the channel repelling itself, and his conclusion was flat: "Higher frequency mitigates this during initial arc growth." That mechanism is with the arc, and it is the reason a low frequency QCW bends before it branches.

Late in the arc he suspects you want it lower, and he marks it as a guess:

My speculation is that somewhat lower frequency (not down to 100kHz) later in arc growth might have an advantage in feeding power to end of arc. Lower total capacitive current through an already ionized air path might reduce voltage drop along arc, increasing voltage at tip. This is just speculation.

Which is worth carrying for one reason. A QCW does that sweep by itself, high at the wick and falling as the arc loads the secondary, and this page has spent its length treating that as the problem. If the guess is right the slide is roughly the trajectory you would have chosen, and the design question stops being how to stop it and becomes how far to let it run. Nobody in this corpus has tested it, and the man who proposed it says so in the same breath, so read it as the most interesting open question on this page rather than as a reason to change anything.

The phase lead gives you least time where you need most

The lead network holds an angle. The hardware (the comparator, the logic, the gate transformer) needs nanoseconds. That mismatch is well known and it is the limit of the technique; what the lead is made of, how much of it is the ZVS floor rather than the delay chain, and which inductor delivers it, is on its own page. What is not usually written down is which way round it goes, so here it is worked on the trajectory above, taking L/R such that the network gives 45 degrees at the bottom of the ramp:

phi = arctan(w·L/R)
t   = phi / w

  f kHz    phi       t
    519  48.3 deg  258 ns   start
    490  46.6 deg  264 ns
    463  45.0 deg  270 ns   end

The angle grows with frequency and the time falls. The arctangent compresses faster than ω rises, so the network delivers 11.7 ns less at the top of the ramp than at the bottom, 4.3 per cent down, exactly where the period is shortest and every fixed nanosecond of hardware delay is worth the most.

Which settles the direction. Set the lead at the end of the ramp and there is not enough of it at the beginning. Set it at the beginning and there is a small surplus at the end, meaning the bridge switches slightly early. A surplus is the gentler failure: early switching costs a little efficiency, late switching commutates into a conducting diode.

And the dead time points the same way

2·t_dead·f is directly proportional to frequency, so a fixed dead time takes its largest share of the period at the top of the sweep. On this machine's 37 ns, across this trajectory:

3.8 % of the period at 519 kHz
3.4 %              at 463 kHz

Same setting, and four tenths of a point given back purely because the period grew. The direction is the phase lead's, but not the weight: at 37 ns the dead time barely moves across the ramp. (The dead time is a fraction page carries a 377 ns figure, but that is a 150 kHz cautionary case, not this coil.)

Net advance delivered

68 ns

lead 258 − driver 190

Advance required here

145 ns

to move 297 nC

Margin

−77 ns

short, hard

Turn-off loss ▲ right

n/a µJ

t_fall 30 ns, assumed, not measured

The inductor L1, the phase-lead. It lifts the delivered line; it cannot lift it past the start

1.15 µHplan · 1.342 µH1.60 µH

Where you are on the ramp. The arc grows, current rises, the period stretches

start of bang · 519 kHz · ~20 Afull arc · 463 kHz · ~160 A

Two boundaries, not one. Soft switching lives in a corridor. The lower edge is a hard requirement: to swing the bridge node across, the current has to deliver a fixed charge, C_o·V = 675 pF × 440 V = 297 nC, and near the current zero there is barely any current to do it, so the advance you need blows up. The upper edge is not a wall, it is a price: push the edge further out and the outgoing switch tears a bigger current, so the turn-off loss climbs: 244 µJ at 80 ns, 332 at 110, against a hard turn-on that only ever costs ½C·V² = 65 µJ. So the aim is the smallest advance that clears the lower edge, not the largest.

Why the start is the hard part. The current is smallest at the start of the bang, so the lower edge is highest there, and the lead network delivers its fewest nanoseconds there too, because the period is shortest. Both move against you at the same end. Raising L1 lifts the whole delivered line, but even at 1.60 µH it tops out near 95 ns while the start needs ~145, and no inductor in this range makes the start soft. That is why the plan's 1.342 µH is right for a reason the plan never wrote down: it clears as much of the ramp as a bigger one would in practice, without paying ~90 µJ of extra turn-off loss on every transition for the whole bang.

The one thing here we have not measured. The hard stretch at the start is set by how fast the current builds, and that current curve is the assumption in this widget. Linear 20 → 160 A is a stand-in; the real curve bends. The ramp impedance rises then falls, so the current is sub-linear early and super-linear later. What does not depend on it: the start is the hard part, and no inductor in this range removes it. Ours, derived, and not measured. T_d 190 ns is a sum over the datasheets of this bridge, an IPW65R080CFD, and not a measurement of anything; its links are ranges, so the sum is really 167 to 202 ns, and it has never been checked on a bench. The 20 A handover current is a calculation too, though an independently reworked one. C_o(tr) 675 pF at 440 V, dead time 37 ns; trajectory 519.1 → 463.3 kHz on a 1.5 m arc. The burden here is 3.9 Ω, well under the 51 Ω a stock board carries, and that is deliberate: the current transformer's own phase error goes as one over frequency squared, so a large burden hands the lower pole more lead than the upper and invites the driver to settle there. Burden sets the henries and nothing else, so the slider reads in the small-burden currency; the same network against 51 Ω would be thirteen times the inductance. The turn-off loss uses a 30 ns fall time that is a typical value, not a measurement of this bridge. This machine has not been switched on: none of it is a measurement.

So the fixed nanoseconds weigh most at the top of the ramp, which is why both settings are set there. The half-period is shortest at the start, so a fixed window takes its largest share there. But at 37 ns the dead time's share only moves from 3.4 to 3.8 per cent across the ramp: it points the right way and weighs almost nothing. What carries the setting is the phase lead, which gives 11.7 ns fewer at the top than the bottom, 4.3 per cent, exactly where the network can least afford it. Set both for that case and they hold all the way down, the one conclusion the four pages cannot reach separately, each honest about its own parameter and none seeing that the fixed window bites hardest exactly where the period is shortest. This page used to soften that with two further margins said to run the other way at the top, a spare past the crossing of 119 ns against 107 and a turn-off current of 75 per cent of peak against 71, and neither survives checking. The 119 and the 107 do not come out of the widget above, or out of anything else here, so that quantity is not established and it is withdrawn rather than quietly kept. The percentages are real and they are percentages of two different peaks: the same widget carries about 20 A at 519 kHz and about 160 A at 463 kHz, so in amperes the switch lets go of 14.9 A at the top against 113 at the bottom [derived, I_pk·sin(phi) on the two angles printed above]. Less current is what makes the top the hard end and not the easy one, because the charge that has to swing the bridge node is fixed whatever the current is. Every margin here that can be checked points the same way. Both calculations here are ours, off phi = arctan(w·L/R) and 2·t_dead·f on a published 519-to-463 trajectory. Neither is a measurement, and the 11.7 ns depends on where L/R is anchored: 45 degrees at the bottom of the ramp, here. Move the anchor and the window slides; the geometry does not.

But the things you can see are at the other end

Detuning is the opposite case. Anders' rule is to detune by as much as the arc detunes you, and you cannot check that against no arc: the evidence is the current envelope, and the envelope only says anything once the coil is loaded. Turns and tap follow the same logic. So does the tank current, which is not a point on the ramp at all: an MMC integrates the whole envelope.

Which is the actual subject of this page. There is no single operating point to tune a QCW at. "Tuned" means tuned along a trajectory, and the settings do not all read out at the same place on it.

Where on the ramp to set each thing

set at the START
  dead time     2·t_dead·f worst
  phase lead    least time up top

set at the END
  detune, turns  match the arc

set over the WHOLE
  MMC current    envelope total

The top two are arithmetic and the bottom two are evidence. That is why they land at opposite ends: you compute what you cannot see, and you look at what you cannot compute.
Do the start-of-ramp pair first. They are the ones that end bangs, and neither of them needs an arc to be set, so they can be settled before the coil is making anything worth watching.
Then tune against a full arc without going back and touching the first two, because nothing you see down there is evidence about the top.
The tank current is checked last and over the whole bang, because it is the only one that is not a point at all.

And no measurement transfers across the ramp

Which generalises. A capture is taken at an instant, so it is a statement about one frequency and not about the bang. A gate waveform photographed at the start of the ramp is not evidence about the end. A dead time judged at full arc says nothing about the first millisecond. An overcurrent threshold set where the current happens to be visible is being applied across the whole sweep.

The cure is not more captures. It is knowing, for each number, whether it gets better or worse as the frequency falls.

Two more that move, and are owned elsewhere

The envelope and the bank under it: read the envelope for the tuning instrument, and sized by RMS current for what the shape costs the capacitors.

And one of them is which pole you are on

The frequency moving is also what decides which of the two coupled modes a ramped coil can use, and that argument got long enough to leave. It is with the poles now, in full: where the driver lands if nobody stops it, why forcing the upper pole is required rather than preferred, the three strategies, and the point past which there is no pole to choose at all.

What belongs here is only the part that is about the ramp. The detuning rule and the gain criterion contradict each other by construction, so following the first commits you to modifying the driver:

detuning rule
  primary ~= loaded secondary
  at the arc you designed for

Anders' gain criterion
  primary ABOVE loaded secondary
  for the upper pole to win

Put the primary at the loaded secondary and it sits below it everywhere short of the design arc, which is the whole useful part of a ramp. davekni says the same thing from the other end: the ideal is the upper pole with the primary tuned below the secondary, and that ideal requires either a PLL or self-oscillation. Detuning and the driver modification are not two decisions. The first makes the second compulsory.

And chasing it with primary capacitance has been tried

There is a third way out of that, and it does not work. If the arc adds capacitance to the secondary through the bang, add capacitance to the primary through the bang and let the two frequencies track. davekni built that and published it as an unsuccessful attempt at within-pulse MMC tuning: 432 TRIACs on six boards, 72 gate drive transformers, one for each set of six paralleled devices, running near 80 kHz at about twice the devices' rated dI/dt.

It destroyed itself, and the way it went is the part to carry. A TRIAC breaks down from its main terminal to its gate. That breakdown drives a spike backwards through its own gate transformer and into the others, so the whole array fires at the wrong moment, and the devices that survive the first round are stressed into failing in the next. One part that cannot take the duty takes most of its board with it. That is a systemic failure and not a rating failure: the shared gate drive is the path it travels, and more margin per device does not close a path.

Read the frequency before deciding what it means here. That machine was switching near 80 kHz, and the bridge on this page commutates between 519 and 463 kHz, about six times higher, so the same current gives several times the dI/dt before anything else is asked of the devices. Which is why the static answer stands. Aiming the primary at the loaded secondary you expect is not what anyone settled for out of habit. It is what is left after the better answer was attempted and lost.

The numbers

The trajectory used throughout: 519.1 kHz to 463.3, a fall of 10.7 per cent, on a 1.5 m arc. That is the upper pole. See the section below on why that is the one that belongs here, and why it is not the number you will find quoted for the same coil elsewhere.
Phase lead across it: 258 ns at the top against 270 at the bottom. 11.7 ns of spread, 4.3 per cent, with the network anchored at 45 degrees at the bottom.
Dead time across it: 3.8 per cent of the period against 3.4, on this coil's 37 ns. It points the right way but barely moves.
Set both at the top: that is where the fixed costs bind, the phase lead delivers its fewest nanoseconds there, and the dead-time share, though tiny, is largest there too. The turn-off current points there as well once it is read in amperes instead of as a fraction of a peak that grows eightfold across the ramp: 14.9 A at the top against 113 at the bottom. The spare past the crossing is not a quantity this page can establish.

Which frequency, though, and it is not the secondary's

There are two different numbers in circulation for how far a QCW's frequency moves and they differ by a factor of nearly two, and neither of them says which quantity it is measuring.

Arc length, drag to run the ramp

Primary, tapped and fixed

349.9 kHz

0.0 %, nothing in it sees the arc

Secondary's own

426.5 kHz

0.0 %

Upper pole, what the bridge switches

519.1 kHz

0.0 %

Lower pole, where it lands unforced

317.0 kHz

0.0 %

What to watch. One thing moves, the arc's capacitance, and four numbers respond to it differently. The primary never moves at all, because nothing in it is exposed to the arc, and that is exactly why it anchors both poles. The secondary is what the arc loads and it travels furthest. The poles are made out of both resonators, so they travel somewhere in between: the upper one covers about 0.64 of the secondary's fall on this coil.

The two marks on the axis. At 1.20 m the lower pole drops under 300 kHz, which is the edge of the straight-sword band. From there on that mode is out of the band the machine was built for. At 1.65 m the secondary passes the primary on the way down. That is a crossing of the two uncoupled frequencies, and it is worth marking, but it is not where the modes trade roles. Differentiating the pole equations gives the lower pole a flat rate of about 14 kHz per metre for the entire ramp, peaking at 1.65 m and slowing after it; the upper pole is the one that changes, decelerating from 54 to 12 kHz/m. The two rates only cross at about 2.7 m, and so does the exchange of modal character. At k 0.421 the coupling is strong enough to smear that exchange over metres rather than snapping it at the crossing.

Why the upper one moves faster, which the rates alone do not say. The second panel is the same fact turned round: it plots how the secondary's movement is divided between the two poles. The division is a fixed budget. Differentiate the pole equations with respect to the secondary's frequency squared and the two sensitivities always add to 1/(1−k²), which is 1.2154 here, at every arc length without exception. However far the secondary travels, that total never changes. Only the split does.

At no arc the upper pole is taking about 80 per cent of the movement in kilohertz and the lower one 20. That is because the secondary sits above the primary, so the upper mode is substantially the secondary and follows it, while the lower mode is substantially the primary and the primary does not move. As the arc pulls the secondary down through the primary the two trade character, and the shares slide towards each other. They are even at 2.73 m, which is exactly where the rates cross, and that is a metre past 1.65 where the two uncoupled frequencies met. The gap between those two marks is what k 0.421 buys: strong coupling smears the exchange over metres instead of snapping it at the crossing.

And 2.7 m is probably not reachable. Pole collapse sets in at 2.81 m by the undamped condition, Lenz adds that a large split brings it earlier, and this coil's two uncoupled resonances are 21.9 per cent apart measured against the primary. Not the gap between the poles, which on the same coil is 39 per cent of the upper one. So the rate crossing is a property of the arithmetic more than of any bang you will fire.

Which number belongs where. Dead time and phase lead are timed against the frequency the bridge is commutating, which is the pole, 10.7 per cent. Detuning and turns are set against the loaded secondary, 16.7. They are not roundings of each other, and quoting either without saying which one it is, and at what arc length, is the mistake this whole page exists to prevent.

Derived, not measured. Secondary 426.49 kHz on Ces 14.031 pF and Les 9.925 mH, primary 349.9 kHz, k 0.421, all from JavaTC. Arc capacitance 4.14 pF per metre, calibrated at 1.5 m. Past about 2 m that calibration is being stretched: the capacitance of a long thin conductor goes roughly as L/ln(L/r), not linearly, so the trend is right and the kilohertz are not. One measurement of the frequency at the end of a real ramp replaces this entire chart.

The pole moves less than the secondary because the primary does not move at all. It sits where it was tapped, at 349.9 kHz, whatever the arc does, and a pole is made out of both resonators, so the primary anchors it and the secondary's 16.7 per cent arrives at the pole as 10.7. A factor of about 0.64 on this coil.

Which decides which number belongs on this page. Dead time and phase lead live at the frequency the bridge is commutating, and the bridge commutates the pole. The 10.7 per cent is the right one here, and it is not a rounding of the other.

The secondary's own movement is the right number somewhere else: detuning and turns are set against the loaded secondary, which is what the primary's page is choosing turns for, what a QCW adds capacitance is working in, and what winding and measuring a secondary is choosing wire for.

And one of these is a measurement rather than arithmetic. Anders Mikkelsen's machine ran 409 kHz down to 335 across a ramp, 18.1 per cent, measured (HVF 3097, where he gives the poles as 238 and 409 and the ramp ending "around 335 kHz"). Everything else on this page is computed. Compare it with the right row. What you measure on a running coil is the frequency the bridge is switching, which is the pole: the secondary's own resonance is not observable while the machine is running. So his 18.1 goes against our 10.7, pole against pole, and that is a factor of 1.7 apart. It is not agreement, and calling it agreement means doing the exact substitution the section above exists to stop. The gap is explainable: his k is 0.473 against our 0.421 [derived, below], his primary and secondary sit at a different spacing, and his arc length at the end of that ramp is not recorded. Explainable is not the same as agreeing, and only the first one is honest. And 332.65 has come out of this page. It stood here as his secondary's own frequency, with his ramp's end landing within 0.7 per cent of it. He publishes no such figure, in that thread or in the other one, and looking for it failed. What he does publish about that resonator is the pair of poles, 238 and 409, and a primary "tuned to 270 kHz". Solve the coupled pair on those three, using f₊² + f₋² = (f_p² + f_s²)/(1 − k²) and f₊²·f₋² = f_p²·f_s²/(1 − k²), and his unloaded secondary comes out at 317.6 kHz with k = 0.473 [derived, on 238, 409 and 270]. His ramp ends at 335, which is 5.5 per cent above that, not 0.7 [derived]. The 0.7 was the only work 332.65 was doing. That solution assumes he had not retuned the primary between the sweep and the sentence about the tap, which are two months apart and in two threads. It is the only route to his k and his secondary that uses no guess about the two resonators being tuned alike; assuming they are gives 0.494 and 290.9 kHz instead [derived, from the pole ratio alone], and his own 270 says they are not. The reading 332.65 was serving has gone as well, and he is the one who replaced it. In December 2024 he writes that the arc load is heavy enough that there is "only one ZVS frequency near the secondary unloaded frequency" (HVF 3097). In February 2025, on the same machine, he puts the floor on the primary instead: under heavy loading the system reaches zero phase at a frequency set by the primary capacitance and the uncoupled part of the primary inductance, so the operating frequency "doesn't drop below 330 kHz" while the arc has the secondary down at 180 (HVF 3140). His own F_pri/√(1 − k²) puts that floor at 306.5 kHz [derived, 270 and k = 0.473], below where he actually runs. Take the later account: what holds his working frequency up is the primary he tapped high, not the secondary's own resonance arriving underneath it. That 180 looks at first as though it contradicts the 409 to 335, and it does not. It is the secondary's own frequency and not a pole, so it does not belong beside them at all: one is the quantity you can read off a running machine and the other is the quantity you cannot. He gives no unloaded figure in that thread, so the percentage between them is only as good as the 317.6 derived above and the assumption under it; on that pairing the arc takes his secondary down 43 per cent [derived, 317.6 to 180], against the 16.7 this coil's table gives at a metre and a half of arc. What the 180 shows without any of that is a real arc taking a secondary to a third below a primary tapped at 270, which is his own gain criterion holding on his own coil rather than on paper.

What will get you: dead time set at the wrong end, and a pole lost mid-ramp

Both of those are the same mistake in different clothes: treating the frequency as a setting rather than as a variable that the machine is sweeping on purpose.

What goes wrong, and what each symptom means

It behaves at low power and misbehaves as the arc grows. Something is timed as an angle and needed as a time, or the tracking is losing the pole. Both get worse with arc length because both are driven by the frequency, and the arc is what moves it.
The bang starts clean and degrades identically every time. Look for something that scales with frequency rather than with power. A supply drooping does this too, and the gate rail is the usual one.
The current envelope curls up at the end, or is flat from the start. That is the detuning against the frequency movement, and it is read off the envelope.
Everything measures correctly and the coil still misbehaves. Check where in the bang each measurement was taken. On this machine that is part of the measurement.

Where our number sits among measured ones

Everything in the trajectory above is computed, and it stays computed until this coil is switched on. What has changed is that it is no longer alone: four other builders have published the frequency at both ends of a real ramp, and the fall can be read off directly.

coil	start → end (kHz)	fall	source
corn can	462 → 440	4.8 %	measured · HVF 3522
davekni	485 → 440	9.3 %	measured · HVF 2397
davekni, ground strike	485 → 413	14.8 %	measured · HVF 2397
Anders Mikkelsen	409 → 335	18.1 %	measured · HVF 3097

The computed fall, 10.7 per cent, lands in the middle of that spread. This is not verification. A number sitting inside a range of other people's numbers has not been checked, only found unremarkable: the four measured coils differ from each other by a factor of nearly four, so the range is wide enough to accept almost anything. But the figure previously had nothing at all behind it, and it is not in that position any more.

The equation those poles come from has since been checked properly, against a built coil rather than against a range: on davekni's machine it predicts 485.8 kHz from the component values where they measured 485, which is 0.17 per cent. That is the equation rather than our coil (the working is on the poles page) but it is the equation this whole table rests on.

The capture that replaces most of this page

Everything above is derived. The trajectory comes out of JavaTC's capacitances, a coupling factor and one constant, 4.14 pF per metre, fitted at a single arc length. It is arranged carefully and it is not measured, and those are different things.

One capture on the first real bang settles most of it. Not a campaign: a frequency at each end of one ramp.

What to catch on the first bang

probe   primary current, CT
capture whole bang, single shot

read  f at the start of the arc
read  f at the end of the ramp
watch for a step change between

The frequency at the start, at minimum loading, says which pole you are on. That is where the two are furthest apart, so the answer is unambiguous: near 519 kHz and the forcing worked, near 317 and it did not and the machine is in the mode it was not built for. Nothing else on this page matters until that reads right.
The two ends together replace the whole trajectory. Start and end give the fall directly; the 4.14 pF/m calibration is then either confirmed or gone, and with it every derived row here, on the poles' page, and on the primary's.
A step of about 1.6 in the middle is the failure mode, not a tuning fault. That is the ratio between the poles, and it is worth being exact because the ratio narrows through the ramp: 519.1/317.0 is 1.64 with no arc and 463.3/295.7 is 1.57 at 1.5 m, since both poles are falling. So the test is sharper than "about 1.6": take where in the bang the step happened, read the expected ratio for that point, and compare. A jump well outside 1.55 to 1.65 is not a lost pole at all and wants looking at as something else. A smooth slide from one end to the other is the healthy case.
And the frequency at the start is the one to set dead time and lead from, which is the argument at the top of this page arriving as a measurement rather than as arithmetic.

And there is a cheaper one before the first bang

The capture needs a coil that runs. The loading does not. Hang a wire of known length off the topload, run it out to the table, and read the secondary's resonance with it and without. The wire is a conductor of about the right length in about the right place, which is a fair part of what a streamer is to the resonance, and nothing has to be switched on to do it.

Two builders publish the pair. Gao's QCW 1.5 reads 339.3 kHz alone and 285.6 kHz with a metre of wire to the table, a fall of 15.8 per cent. Mads Barnkob, on HVF 24, reads 101 kHz down to 91 kHz with 80 cm, 9.9 per cent. The two coils are more than three to one apart in their own frequencies and the shorter wire moves less, so what the reading responds to is the wire and not the coil. That is the method working, and it is two builders rather than one habit.

It reads against the 16.7 per cent, not the 10.7. What the wire moves is the secondary's own resonance, which is the quantity this page keeps saying you cannot see on a running machine. So the bench gives you the number the capture cannot, and the capture gives you the number the bench cannot, and neither one stands in for the other.

Then the limit, which is the wire. It does not branch, it does not move, it is not hot, and it hangs there from the first microsecond instead of growing through the bang. A real arc does more: Anders Mikkelsen reports one pulling a secondary's uncoupled resonance down to 180 kHz against a primary at 270, which is a long way past anything a metre of wire produced on a bench. So take the surrogate as a floor on your own coil's movement. It is worth having before the first bang, and it is not the calibration, because 4.14 pF per metre is a statement about an arc and not about a wire.

Where next

Everything on this page is a consequence of one thing moving, so the rest of it is spread across the pages that own each consequence.

What moves, and why there are poles at all

There is no secondary frequency, where the two poles come from, which one survives heavy loading, and the condition that decides it.
A QCW adds capacitance, the arc as a capacitor, and what a bigger topload does to the same arithmetic.
The second mode, the other thing a coupled pair can do that gets mistaken for detuning.

The driver, which has to follow it

The QCW driver: what changes on it, and how to convert one, the four jobs each changed by the frequency running away underneath them, and the starting oscillator or PLL that holds the upper pole, as an actual list of changes.
Inside a driver, the comparator, the lead network and the protection, on any coil.
DRSSTC phase lead: what it is made of, which inductor to fit, the angle-against-time problem this page works across the ramp.

Set at the start of the ramp

Dead time is a fraction, the arithmetic, and the same fraction moving inside one bang.

Read at the end of it

Read the envelope, the cheapest instrument there is for the loaded end.
The primary is an impedance, turns and detuning, set against the loaded secondary.
The MMC is sized by current, what the envelope's shape costs the tank.
The gate supply is a power supply, the other thing that degrades steadily through a bang and looks like this one.

The connecting argument here (that the four consequences move in different directions, and that this is what decides where in the bang to set each one) is ours. Each individual consequence belongs to the page linked beside it, and the measurements behind them are other people's.

tuningpolesQCW