[ §1 · winding ]

How to wind and measure a Tesla coil secondary for an SSTC

Not a transformer winding that happens to be long. Almost everything that goes wrong with one goes wrong because it was wound as though turns were the point.

CommonGnd4 August 202625 min read

A Tesla coil's secondary is not a transformer winding that happens to be long. It is one half of a resonator, and almost everything that goes wrong with one goes wrong because it was wound as though turns were the point.

What a secondary actually is

A long coil of thin wire on a plastic tube. Not a transformer. A resonator. The second winding does not receive energy in proportion to its turns; it is rung, and the high voltage appears because a resonance builds it up, not because of a turns ratio. Everything else on this page follows from that one fact.

The wire picks the frequency

Close-wound, single layer, on a former of a fixed length. This page used to make the turn count length ÷ wire diameter, and nothing else, and two things hide in that. The first is which diameter: what goes on the former is the insulated wire, and on fine wire the enamel is worth about a tenth. Mads Barnkob works the example, 0.25 mm of copper measuring 0.275 mm over the varnish, a ratio of 1.1 on a coil he calls close wound. The second is that close wound is itself a choice: he describes deliberate spacing as a method of its own, the wire laid beside a nylon line that is drawn out afterwards, and Finn Hammer's Energimuseet secondary, 1680 turns of 0.224 mm wire, is space wound by its builder's own description. So the count carries a packing factor, and the factor is the part nobody states.

At 0.909, which is the enamel on its own, the turn count falls 9.1 per cent, the inductance falls 17.4 because it goes as N², and the frequency rises 10.0 [derived]. That moves every absolute turn count and every absolute frequency below it. It does not move the shape, because a constant packing factor is a constant multiplier, which is why the rule in the next line survives unchanged.

Work that through: inductance goes as N², the capacitance barely moves because the toroid owns most of it, and something unexpectedly simple falls out:

The resonant frequency is directly proportional to the wire diameter. Double the wire, double the frequency.

On one real coil, 150 mm of winding, 90 mm former, Ces 14.03 pF:

wire       turns        L   frequency         Z
0.15 mm     1000   39.7 mH    213 kHz   53.2 kΩ
0.20 mm      750   22.3       284       39.9
0.238 mm     630   15.8       338       33.5     the copper rule
0.30 mm      500    9.9       426       26.6     this coil
0.40 mm      375    5.6       569       19.9
0.50 mm      300    3.6       711       16.0

One knob, four numbers, two of them going the other way. And the coil is exactly as tall in every row: 500 × 0.30 mm is 150 mm, which is the winding.

That last line is also how you read someone else's build page. Turns, winding length and wire gauge over-determine one another, and the wire on the former is N × π × D after that, so a published secondary can be closed on itself before any of its numbers are used. Thaumati's QCW closes: 750 turns over a 6″ winding is 125 turns to the inch, and 1/125″ is 0.008″, the bare diameter of the 32 AWG it states; 750 × π × 3.5″ is about 209 m of wire against the 200 m it states. Neither check is published. Both are arithmetic on what is. Run the other way, the same identity fills gaps: an 8 kW continuous DRSSTC never gave a turn count, and its stated inductance and frequency put the winding near 1440 turns, which is also where close-winding its stated gauge lands. A page whose pitch works out finer than its own wire is thick was written from memory, and the rest of it deserves the same suspicion.

Wire diameter, the only thing you actually choose

0.15 mm0.30 mm, this coil0.50 mm

Drag the wire. The winding length is fixed, so the turns, the inductance, the frequency and the impedance all move together, and the coil stays exactly as tall.

Assumptions. Winding 150 mm on a 90 mm former, Ces 14.03 pF and Les 9.925 mH at 500 turns of 0.30 mm, from JavaTC; skin depth calibrated to the same tool as δ = 70.2/√f mm. The capacitance is held constant as the turns change. The toroid provides 78 per cent of it, so the winding's own share moves the answer by a few per cent at the extremes, not more. The reference mark is a built coil's published wire; its turns were fitted to its published frequency.

Two marks on that axis, and they are not in conflict

0.211 mm   →  300 kHz, the edge of the straight-sword band
0.238 mm   →  where a rule of thumb says the copper is best used
0.232 mm   →  a built QCW
0.300 mm   →  this coil

The copper rule is wire diameter about twice the skin depth, so the current reaches the middle of the wire instead of hugging the surface. Below that you are wasting copper cross-section; above it, the middle carries almost nothing.

And the copper rule matters far less than it looks

This is the part worth getting right, because the skin-effect calculation is quoted everywhere and almost never followed through to a consequence.

this coil    0.300 mm = 2.79δ    R_ac/R_dc 3.92    unloaded Q 199
a built QCW  0.232 mm = 1.94δ    R_ac/R_dc 2.58    unloaded Q 231

That coil is on the rule and we are 1.4× over it in skin depths, 1.3× in diameter, and its copper is genuinely better. Now put an arc on both. The arc sits in parallel with the copper, so it decides the loaded Q, and it takes an arc resistance to say by how much. This site publishes 210 kΩ for that, which Uspring worked out of Hydron's measured toroid currents in his own words, "a strong resistive load of about 210kOhm" at the point of maximum current 180 µs into the burst. The Terry Fritz SPICE fitting of about twenty years earlier, at around 220, is quoted beside it here and carries no link on that thread or anywhere else, so read the agreement as this corpus's claim rather than as a second source you can go and read:

                                       Q under arc   to the copper
this coil, unloaded Q 199                     7.59          3.82 %
the built QCW's wire, unloaded Q 231          7.63          3.31 %

Both lines are computed at this coil's 26.6 kΩ, because the other coil's impedance is not published and inventing one would decide the answer [derived from 210 kΩ, that impedance and the two unloaded Q]. What the two lines compare is the wire, which is what the section is about.

Half a percentage point of the power. Arc length goes as the cube root of energy, so that is under a fifth of a per cent of arc: under three millimetres on a metre and a half [derived, 0.177 per cent of 1500 mm].

And the loaded figure is a function of impedance, which the top of this page can show without leaving it. Uspring computes a Q of about 4 under that same 210 kΩ, on Hydron's coil rather than his own (HVF 117), and a coil at 53.2 kΩ, the first line of the wire block above, computes to 3.9. Twice the impedance, half the loaded Q, because under an arc the number is R_arc over Z and very little else.

Q is the impedance divided by the resistance

No mystery, and both numbers are already in front of you:

Z = sqrt(L/C)      = 26 596 Ω     JavaTC prints "Reactance at Resonance" 26596
Q = Z / R_ac       = 199          JavaTC prints "Secondary Q" 199

And the same Z works under the arc, the other way up

no arc      Q = Z / R_ac          = 199   the copper, in SERIES
under arc   1/Q = 1/199 + Z/R_arc = 7.6   the arc, in PARALLEL, on 210 kilohms

The same Z, once on top and once underneath. Lower impedance means a worse unloaded Q and a better tolerance of arc loading. Which is why there is no single right answer to "what should the secondary impedance be", it depends on which of those two you are being judged on.

And it is why the unloaded Q above, the one every calculator prints, is close to irrelevant once there is an arc. 199 and 231 become 7.59 and 7.63, half a per cent apart on a sixteen per cent difference in the unloaded figure, because under the arc the number is set by the impedance and the arc and the copper has almost dropped out of it.

A QCW secondary is not a DRSSTC secondary

Two numbers get quoted everywhere, and both are DRSSTC numbers:

"Target secondary impedance is 50 kΩ for a classic low-impedance DRSSTC", and the familiar 4:1 to 5:1 height-to-diameter alongside it.

They are correct, and they are for a different machine. Built QCW coils sit elsewhere:

Arc length, the ramp runs left to right

no arc1.5 m3.0 m

Coupling, everything else held, so this is the pole spacing on its own

0.3000.421, this coil0.750

Why three and not one. Couple two resonators and neither of their own frequencies survives. The system runs at a pair of poles, one above and one below, and the coil's own 426.5 kHz is a number that appears on no oscilloscope. This coil's primary sits at 349.9 kHz and its secondary at 426.5, deliberately apart, so the poles are not the textbook f₀/√(1±k). They come out of the coupled pair:

f² = [(f₁²+f₂²) ± √((f₁²+f₂²)² − 4f₁²f₂²(1−k²))] / 2(1−k²)

That returns 317.0 and 519.1 kHz with no arc, and it tracks the whole ramp to a tenth of a kilohertz.

What the arc does. It hangs off the topload as capacitance, about 4.14 pF per metre on this coil, so the secondary's own frequency falls, and both poles follow it down. Nothing here is a fitted curve; it is that one capacitance and the formula above.

Why the lower pole is not a choice. Arcs grow as straight swords above roughly 300 kHz and start branching below it. The lower pole crosses that line at 1.20 m of arc, inside a working flash. The upper pole does not cross it at eight metres. That is the whole argument, and it is arithmetic rather than preference.

Where they give way. The arc is also a resistance, and past a point it damps the pair into a single hill. The threshold is R_arc < Z/k, and with a published arc model of about 75 kΩ·m that becomes a length: 75000·k/Z. Low impedance and high coupling both push it further out, which is why the table below runs the way it does, and why the builds at the top of it are the ones chasing metres.

The measured bars, and where they come from. Four published ramps, read off coils that exist: a corn-can build on HVF 3522, and two runs of the same oversized QCW on HVF 2397, one an ordinary arc, one a ground strike, which is why that build appears twice and falls further the second time. The steepest, at 18.1 per cent, is a high-coupling QCW build whose thread we have not recorded.

The bars are measurements. The curves are not. The curves on the left are computed for a coil that has not been built, from its geometry and one arc-capacitance figure. They are here because the shape is the lesson; the absolute frequencies are pending until something is switched on. Nothing of ours appears among the measured bars, and it should not.

Past the merge the coil still runs. What is left is a single hill near the primary's own frequency, about 350 kHz here, above the 300 kHz threshold, so the arc is still in the band where it grows straight. What is lost is the pole structure a phase-lead driver was tracking, and what is gained is that there is no longer a second pole for the drive to be captured by. The published inversion is worth holding on to: the ground strike that does NOT collapse the structure is the more dangerous one, because there the upper pole's ring lasts about a cycle and a half, recapture happens out of noise, and the lower pole has the advantage there.

And the primary is doing more than being detuned. Three things follow from where it sits and how big its capacitor is, and all three are somebody's published rule rather than ours. Its frequency sets a floor: under heavy arc loading the system cannot fall below f_pri/√(1−k²), which is 385.8 kHz here, comfortably above the sword threshold, so the machine stays in the straight-arc band however long the arc gets. Its capacitance sets the smoothness: a lower primary capacitance flattens the current envelope. And there is a ceiling on that capacitance for a given coupling, past which the coil will not transition cleanly between operating modes; the ceiling rises as coupling rises, which is one more reason the two levers point the same way.

The collapse column is the near edge. It uses the harshest arc-resistance model in circulation; the models spread by more than a factor of two, and the whole column moves with them. Read the order, not the absolute metres. Two of the impedances are computed from published geometry rather than published by their builders.

The Z and L of that built QCW, below, are ours, not a formula: its published geometry entered into JavaTC, with the turn count fitted until it reproduced the published 340 kHz, it lands at 342.95, within 0.9 %. The wire pitch that makes 603 turns fit the winding is the second constraint. Neither number was published. Fitting the turns is the general case, not a dodge for this one coil. In a build report the turn count is the least reliable figure, and it is the figure a builder tends to write with a tilde. dr. kilovolt's SiC coil gives a 125 mm former, a 150 mm winding, about 400 turns and 19 mH. Wheeler's formula over that geometry returns 11.9 mH, and 19 mH would want nearer 505 turns. Nothing else in the report moves: 19 mH at its measured 251 kHz asks for 21.2 pF across the coil, its 6 × 25 cm toroid is about 10.8 pF of that, and what is left is an ordinary self-capacitance for a coil that size. The inductance, the frequency and the coupling all stand. Only the turn count should not be quoted. Those figures are ours, from its published geometry.

Three QCW aspect ratios on the plot, 1.49:1 and 1.58:1 built and 1.28:1 on a machine that is not built yet, against a DRSSTC norm three times that. Read that norm as the rule quoted above and not as what DRSSTCs measure: the two built machines whose ratios we have sit at 2.06 and 3.43, so against those the gap is one and a third to two and a half times, not three. Neither of them is inside the 4:1 to 5:1 the rule asks for either. That is not scatter. A low aspect ratio buys coupling, and coupling is the whole point of a QCW: a long arc from a small resonator.

A builder running 1.5:1 (HVF 3140): "A low aspect ratio secondary is definitely a good way [to raise coupling]… but even going below 1:1 could be practical for larger coils."

What pays that price is the ramp. An arc allowed to form early holds the secondary voltage down for the rest of the ramp, and the rest follows from that clamp: a short resonator throws a long arc without flashing over, and the coupling can go where it would have arced over on a coil driven the ordinary way. Ramp rate, high coupling and a short secondary are not three decisions (HVF 3140). They are one decision described three ways, which is why the aspect ratio here cannot be read off a DRSSTC's.

The field is moving down

Not a right value, a direction of travel. The lever is coupling. Raising it moves the primary-impedance turnover out past the end of the ramp, so a growing arc stops crossing the peak. That is what "flatter" means here, and it is not a smaller spread: the spread is not even monotonic in coupling at a fixed primary tap. It is the turnover leaving the ramp, which is what leaves the load rising monotonically instead of turning over halfway up. A low aspect ratio buys that coupling and lowers the impedance at the same time, which may be why the two get conflated.

The topload owns the coil

Ces total       14.031 pF
of which the toroid   10.879 pF   =  78 %
the winding itself     3.152 pF   =  22 %

So the toroid sets the frequency, the impedance and the tolerance of arc loading, and the winding sets the remaining 22 per cent. In practice, "tuning the secondary" means "choosing the toroid".

Bare, this winding would ring at about 900 kHz. The toroid it carries brings it to 426, more than halved by one part.

What a toroid costs is its own page.

One built coil does isolate the toroid, and it takes two of its builder's pages to see it. Gao Guangyan wound one 32 AWG secondary, 5.55 inches of winding, and measured it standing alone under two toroids a year apart:

the same 32 AWG, 5.55 in winding, measured standing alone
   8 in toroid,           2014     408 kHz
   11.25 x 3.4 in toroid, 2015     339.3 kHz
                                   16.8 per cent lower   [derived]

The first reading is on QCW 1.0, the second on QCW 1.5, where he writes that he went back to that original 32 AWG coil for the experiment. Both are his own readings on the bare resonator, so the new primary that arrived with the fat toroid is in neither of them. What is in them is a year, two rooms and two supports, the second a floating wooden plank. Take 16.8 per cent as the size of the effect and not as a repeat measurement.

The two rows that used to sit here read 406 kHz against 343, with impedances of 48.1 and 40.7 kΩ beside them. Those were JavaTC fits doing a measurement's work, which is why they tracked each other exactly: both came out of the same fitted model. The nearest published figure to 406 is the 406 to 409 kHz he quotes in 2013 for the earlier toroid on this same winding, and 343 is the fit that lands at 342.95 in the note above, against his measured 339.3. What a topload costs withdrew the same two rows and went one step too far, reading them as two different machines. That holds only if the small-toroid row is the 34 AWG coil of the QCW 1.5 log, which measures 302.7 kHz and is indeed a different winding. It is not: it is QCW 1.0's, the winding he came back to. Both pages now carry the pair above.

→ what a topload costs

What the arc does to it

The arc hangs off the topload as a capacitance and a resistance at once.

The capacitance adds to the coil's own, so the resonance moves down, badly, in a QCW.
The resistance drops the Q from 199 to about 7.6. The sharp peak becomes a low hill.

→ the frequency slides down the ramp

Why the upper pole, seen from the winding

Three arguments, and none of them is about the driver:

The secondary's field is lower inside the winding on the upper pole, so bringing the coils closer is less dangerous there.
The lower pole changes the voltage distribution along the winding in a way that makes a primary-to-secondary flashover more likely.
The upper pole follows the detuning downward; the lower one runs into the primary and stops.

loneoceans' first-light report on his first QCW, and the second half of it is the whole point: "primary set at turn 7.5 (392kHz) but coil oscillates itself to the upper pole" A plain UD2.7, no modification, the primary tuned below the secondary, which he measured alone at 408 kHz, and the driver goes to the upper pole on its own. Measured, not argued, and it is the one of these that settles the reader's worry that the upper pole needs a special driver.

→ there is no secondary frequency

How to wind it

Tight turns, one layer. Winding with a space between turns raises the frequency, which is usually the opposite of what you wanted.
No bubbles in the varnish. Every bubble is a corona site and a future puncture.
Ring out topload to ground before power. Continuity, with a meter, every time.

How to ground it

The ground is the other plate

The toroid's capacitance is capacitance to ground, and at 426 kHz its reactance is about 34 kΩ. Every bit of displacement current that leaves the topload has to arrive somewhere and get back to the bottom of the winding, and what it gets back through is the counterpoise. The ground connection is not a safety accessory bolted on at the end. It is one plate of the capacitor that sets your frequency.

Without a counterpoise the room is that other plate, which still resonates and is simply not a capacitance you can repeat. The evidence for it, in the calculator everyone already uses, is on what RF ground is.

Which is also the mechanism behind something two sections down: the lead running to the counterpoise shifts the measured frequency, and now it is obvious why.

Not to mains earth. Not ever.
A counterpoise: a large metal sheet under the coil. Roofing aluminium beats foil, and round the corners off.
A short lead, not run alongside anything else.
The bottom of the secondary goes to both the counterpoise and the strike ring.

How big it should be is a calculator on the page that owns it.

What will get you: two layers, unchecked varnish, and ferrite you did not design around

A gap that is nearly closed is worse than one that is open. If you sleeve the secondary, the space between the winding and the sleeve is the thing to get right, and davekni names what goes on in a tight one: "A tight space between secondary and insulation sleeve often creates corona discharge between secondary windings and adjacent insulation, at least in normal (non-QCW) SSTCs and DRSSTCs" (HVF 3522). He puts two costs on it and they are on different timescales:

One is slow degradation of secondary wire enamel insulation. Other is ionized air provides a conductive path that may initiate arcs along secondary surface

The first eats the coil over months and the second ends a run, and both come from the same millimetre. Note also which machines he says it on: ordinary SSTCs and DRSSTCs, and he is explicit that he does not know how much of it applies to a QCW at its lower secondary voltage. So this is a live question rather than a settled rule, and the safe reading is that a sleeve either stands well clear of the winding or is wound against it with nothing in between.

And the cheap fix, from somebody who lost a secondary to find it. After a winding was destroyed by a primary-to-secondary flashover on first power up, "原来那个次级因为耦合太大，在170几v上电时初次火导致次级被玩坏掉了", because the coupling was too large and it flashed over at a bus of about 170 V, the replacement was wrapped in a layer of mica insulation paper, bought at 30 yuan for a one by five metre sheet. His report on it afterwards: "这个次级玩坏2个管子也没打火", this secondary has destroyed two transistors and still has not flashed over (hvdiy 33610).

Read the second sentence as the measurement it is. He is not saying the coil got better; he is saying the failure moved. The bridge now dies before the winding does, which is the right order for a part you can replace in an evening against one you cannot.

Which joins up with the varnish below, because a corona site is a corona site whatever made it. Barnkob's version is the same failure arriving through the finish rather than through a gap: corona glows at "spots with imperfections in the varnish", air bubbles, brush hairs, insects, and UV from the sparks helps turn that spot into a burning one.

Ferrite inside the secondary is a trade, not free coupling. Ferrite conductivity rises with temperature, so a warm core starts loading the resonator it sits inside, and a coil that was not designed around that gets worse the longer it runs. It is not a wall, though. davekni's oversized QCW is built on ferrite deliberately: a floor and a centre post, the top of the post NiZn "for low conductivity", no potting, k = 0.71 on an 11.8 mH secondary over a 300 mm core (HVF 2397). The material and the cooling are chosen with the rest of the machine, or the core stays out.

And metal closer than half the secondary's diameter kills the Q. A chassis, a case, a rack, a radiator: they load the resonator and steal energy into induction heating, and nothing on a scope tells you it is happening.

Measuring it

Whatever the calculator said, the coil you wound has a different resonant frequency. The topload moves it, the bench moves it, the wall behind it moves it, and the lead down to the counterpoise moves it. Three ways to find out what you actually have:

A signal generator through a resistor. Start at 1k and go to 10k when you want the dip sharp enough to read.
Ring it down. A nanofarad into the scope, and watch it decay.
An antenna near the topload, looking for the peak in the field.

Measure it assembled, with the topload on. A bare winding is a different resonator and its number is no use to you.

What goes wrong, and what each symptom means

Where the winding is damaged is most of the diagnosis, because the mechanisms that damage a secondary sit at different heights and want different cures.

The measured frequency is well above the calculated one. Instruments floating, or the coil measured bare without its topload.
Flashover across the winding, low down. Racing sparks: a strike rail too close to the primary, defects on the toroid, humidity, or coupling simply too high. The usual advice that tight coupling is survivable holds on the upper pole, where the secondary's field is lower inside the winding; on the lower pole, bringing the windings together is noticeably more dangerous.
Inter-turn arcing in the bottom fifth, with nothing jumping to the primary. Not racing sparks. That is the whiplash failure, and it wants the opposite treatment: the ground is too low an impedance, the coupling is not too high.
Flashover across the middle, level with the top of the primary. A different mechanism entirely: the second mode.
Damage at the top of the winding, and no arc leaving the topload. Nothing broke out, so the voltage up there climbed until something else gave. Give the arc somewhere to leave from: what a DRSSTC breakout point is for.
Damage spread the length of the winding rather than gathered at one height. Running on the lower pole.
The coil performs worse than an identical one with no visible difference. Something metal is inside half a diameter of it.
The frequency walks down as the arc grows. Working as designed. The arc's capacitance adds to the coil's, and on a QCW it does so catastrophically.
The topload voltage stops responding to more power. It clamped. Current, not voltage, is the better indicator of arc length from there on.

Where the edge of this is

The largest QCW being designed at the time of writing does three things to the secondary that no hobby coil does yet: litz instead of solid wire, a secondary MMC of C0G ceramics to add capacitance without adding winding, and an aspect ratio of 1.28:1. All three point the same way: lower impedance, higher coupling.

Where next

What a topload costs, the trade at the top of it.
What RF ground is, the connection at the bottom.
There is no secondary frequency, which pole the winding wants and why.
The second mode, the flashover that is not about coupling.

Figures here are collected from published measurements rather than taken on this bench. The one coil measured throughout is not switched on yet: its numbers are JavaTC's, and a cold-coil sweep will replace them with its own.

secondaryracing sparksgrounding