QCW Tesla coil tuning as the frequency slides down the ramp

On a QCW Tesla coil the operating frequency falls through the bang as the arc grows. On our machine it runs from 519.1 kHz down to 463.3 over a 1.5 m arc. Every setting timed against that frequency is exactly right at only one point on the ramp.

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.

If one of them changes while the circuit runs, the resonance follows it. On its own that is harmless. The circuit is still resonant, just at a different frequency from a moment ago.

The trouble 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 is faulty. They were designed at one frequency and are now working at another, and they do not all drift 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 animation shows three tracks, because "the frequency" means four different numbers on this machine, and only one of them stays put. The primary is 349.9 kHz and does not move, because nothing in it is exposed to the arc. That is 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. It falls 10.7 per cent, 0.64 of the secondary's travel, because of that anchor. The lower pole is what you get if nothing forces the upper one, and it starts below where the other two finish. So every setting timed against the switching sees the smaller movement, and every setting matched to the arc sees the larger one. The rest of the article follows that split.

Every table here is one coil, not a reference

Every table here rests on the arc's capacitance, and that will be different on your machine. This is not measurement error. How much capacitance a metre of streamer adds depends on the topload it grows from, on how the arc branches, and on where the walls are.

Two published measurements hold up, and both sit above our calibration. Neither builder gives a figure per metre. Each measured 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. Our 4.14 is a calibration on one coil, not another measurement and not a reference constant. It sits below both, which fits a smaller topload and a shorter arc:

Anders' figure has no independent check. The 5.03 pF/m in the row above comes from dividing his measured 16 pF by a 3.18 m arc, so multiplying it back by that length just returns the 16 pF. That can look like the number and the machine agreeing without being made to, but the division made them agree. It is one figure written twice. The row rests on the arc length, and that is the one number here we have not found stated in 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. For Weston the conversion shows a real disagreement, and its size depends on whose coil you run it on. Weston's 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 3.49 pF/m, the figure we have been quoting [derived, Cp = Cs/(1 + (ω·Rs·Cs)²)]. Run on his own coil instead, three feet of arc across the 390 to 330 kHz his ramp covered, the same two constants give 1.0 to 1.3 pF/m [derived, the same expression]. So on his own coil, his model and his capture are six or seven times apart. The factor of two you see on ours is a result of reducing it to our frequency and our arc length.

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 a lot more. Across the measured range, the point where the lower pole leaves the straight-sword band runs from 1.20 m down to 0.65 m.

That is more than half a metre of spread on a figure that looks like a specification. Read it as somewhere between two thirds of a metre and a metre and a fifth, and work it out from your own capacitance once you have one. Do not read it as 1.20 m.

And what the spread does not touch

These carry over 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 direction of every conclusion here. Only the kilohertz move, not which pole is where or which way anything goes.

The decision that matters is which end of the ramp to set each thing at, because the two ends give different answers.

Whether the slide is a nuisance or a favour

So far the slide has been treated as a problem. Someone who runs these machines asked the opposite question on HVF: "I'm wondering if there is an advantage in frequency dropping some during arc growth" (HVF 3140). The answer has two sides, and both are davekni's.

Early in the arc you want the frequency high, and that part 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: "Higher frequency mitigates this during initial arc growth." That mechanism is covered with the arc, and it is why a low frequency QCW bends before it branches.

Late in the arc he suspects you want it lower, and he says it is 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.

A QCW already does that sweep by itself, high at the start and falling as the arc loads the secondary. If his guess is right, the slide is roughly the trajectory you would have chosen, and the question becomes how far to let it run rather than how to stop it. None of our sources has tested it, and davekni says himself that it is speculation. Treat it as an open question, not as a reason to change anything.

The phase lead gives you least time where you need most

The lead network holds an angle, but 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, are on its own page. Which way round the error goes is less often written down. Here it is on the trajectory above, with L/R chosen so 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 flattens 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. That is where the period is shortest and each fixed nanosecond of hardware delay matters most.

The lead should be set at the start. Set it 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, so 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

The setting is the same. The four tenths of a point come back only because the period grew. It moves the same way as the phase lead but much less: at 37 ns the dead time barely changes across the ramp. (The dead time is a fraction article has a 377 ns figure, but that is a 150 kHz cautionary case, not this coil.)

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 with no arc. The evidence is the current envelope, which only tells you anything once the coil is loaded. Turns and tap work the same way. The tank current is different again. It is not a point on the ramp at all, because an MMC integrates the whole envelope.

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.

And no measurement transfers across the ramp

More generally, a capture is taken at an instant, so it tells you about one frequency, not about the whole 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.

More captures will not fix that. What helps 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 moving frequency also decides which of the two coupled modes a ramped coil can use. That argument is in full with the poles: where the driver lands if nothing 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.

Only the ramp part belongs here. The detuning rule and the gain criterion contradict each other by design, 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 the secondary everywhere short of the design arc, which covers the useful part of the ramp. davekni says the same from the other side: the ideal is the upper pole with the primary tuned below the secondary, and that ideal requires either a PLL or self-oscillation. So if you detune, you have to modify the driver.

And chasing it with primary capacitance has been tried

A third way out has been tried, and it failed. 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 how it failed is the useful part. 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, not a rating failure. The fault travels through the shared gate drive, and more margin per device does not close that path.

Note the frequency. That machine was switching near 80 kHz, and our bridge 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. So the static approach stays: aim the primary at the loaded secondary you expect. That is not habit. It is what is left after the better approach was tried and failed.

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. The section below explains why that is the right one here, and why other articles quote a different number for the same coil.
• 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, 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 you read it 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 established.

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

Two different numbers circulate for how far a QCW's frequency moves. They differ by a factor of nearly two, and neither says which quantity it measures.

Every figure in that table is derived, from JavaTC capacitances, a coupling factor and the pole equations, and the first trajectory measured on a running coil will replace all of it. Other articles link here for these numbers instead of repeating them, so they can be replaced in one place. Anders' 409 to 335, below, is the only measured line, and it is not part of this set. The table covers one arc length, the one the capacitance was fitted at. There is no 1.8 m row, for the reason given near the top.

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. A pole is made from 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.

Dead time and phase lead depend on the frequency the bridge is commutating, and the bridge commutates the pole. So 10.7 per cent is the right figure here. It is a different quantity from the 16.7, not a rounding of it.

The secondary's own movement is the right number for detuning and turns, which are set against the loaded secondary. That 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.

None of these percentages means anything without the arc length beside it. That is what went wrong with the 1.8 m column. A detuning figure taken from somebody else's machine brings their arc with it, the same defect as quoting millimetres per watt without the ramp length.

One figure here 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 here is computed.

Compare it with the right row. On a running coil you measure the frequency the bridge is switching, which is the pole. The secondary's own resonance cannot be observed while the machine runs. So his 18.1 goes against our 10.7, pole against pole, and they are a factor of 1.7 apart. That is not agreement, and calling it agreement would be the same substitution the section above warns against.

The gap can be explained. 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. But an explained gap is still a gap.

We previously gave his secondary's own frequency as 332.65 kHz, 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 we could not find a source for it. 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 332.65 figure only existed to produce that 0.7.

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 needs 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 that 332.65 supported is gone too, and Anders himself 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. Go with 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 can look as if it contradicts the 409 to 335. It does not, because it is the secondary's own frequency, not a pole. 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. Even without that, the 180 shows a real arc taking a secondary to a third below a primary tapped at 270. His own gain criterion holds on his own coil, not just on paper.

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

A driver that loses the upper pole part way up gives no sign of it. It keeps running on the lower one, and you get a bang that starts correctly and turns into something else. It looks like a tuning fault, but it is a tracking fault. Check at the very beginning of the arc, at minimum loading, where the two poles are furthest apart and the frequency tells you at a glance which one you are on. Later in the ramp both have come down and the reading is ambiguous.

Both come from the same mistake: treating the frequency as a setting when the machine is sweeping it 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 will stay that way until this coil is switched on. Other builders have published the frequency at both ends of a real ramp, though, and their fall can be read off directly.

The computed fall, 10.7 per cent, lands in the middle of that spread. That does not verify it. The four measured falls differ from each other by a factor of nearly four, so the range would accept almost anything. It does mean the figure no longer stands on nothing.

The pole equation itself has been checked properly, against a built coil. On davekni's machine it predicts 485.8 kHz from the component values where they measured 485, 0.17 per cent off. That checks the equation, not our coil (the working is on the poles page), but every row of the table rests on that equation.

The two davekni rows are the same coil on the same day, and the second is an arc that reached earth. It fell 27 kHz further than his ordinary arc did. Allow for that in any detuning budget: what a strike does is not limited by what the arc you designed for does.

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. None of it is measured.

One capture on the first real bang will answer most of it: the frequency at each end of one ramp.

What each result would mean: if the start reads near 317, the pole argument is not wrong but this coil is not following it. If the fall is much larger than 10.7 per cent, the capacitance calibration is wrong and every derived figure here moves with it. If it is close, the arithmetic held, and these figures become a record instead of a derivation.

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.

Gao's QCW 1.5 publishes the pair: it reads 339.3 kHz alone and 285.6 kHz with a metre of wire to the table, a fall of 15.8 per cent. That is one coil and one length of wire, so take it as the method working, not as a figure to expect from yours.

Compare it with the 16.7 per cent, not the 10.7. The wire moves the secondary's own resonance, the quantity you cannot see on a running machine. So the bench test and the capture each give a number the other cannot, and neither replaces the other.

The limitation is the wire itself. 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 wire test as a lower bound on your own coil's movement. It is useful before the first bang, but it does not replace the calibration, because 4.14 pF per metre describes an arc, not a wire.

Where next

Each consequence of the moving frequency has its own article.

What moves, and why there are poles at all

• There is no secondary frequency, where the two poles come from, which one holds up under 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 worked across the ramp above.

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 decides where in the bang to set each one, is ours. Each consequence is covered in the article linked beside it, and the measurements behind them are other people's.